ReERfin = {{1/10000, 0.7955727545023072}, {11/100000, 0.7956509752436762}, 
     {3/25000, 0.7955792476988761}, {13/100000, 0.7955720225096292}, 
     {7/50000, 0.7956471064612156}, {3/20000, 0.795585211523238}, 
     {1/6250, 0.7955799203847764}, {17/100000, 0.7955891171102052}, 
     {9/50000, 0.7956397362519674}, {19/100000, 0.7955891861679754}, 
     {1/5000, 0.7955933698533966}, {21/100000, 0.7955923396570759}, 
     {11/50000, 0.7955938888242167}, {23/100000, 0.7956338190739256}, 
     {3/12500, 0.7955948197583989}, {1/4000, 0.7955850005925034}, 
     {13/50000, 0.7956308347883936}, {27/100000, 0.7955880032650882}, 
     {7/25000, 0.7955991768831407}, {29/100000, 0.7955962880882828}, 
     {3/10000, 0.795596987100569}, {31/100000, 0.7955986050323016}, 
     {1/3125, 0.7955987918902179}, {33/100000, 0.7955976108650176}, 
     {17/50000, 0.7955968884697402}, {7/20000, 0.7955999396326954}, 
     {9/25000, 0.7955901605293612}, {37/100000, 0.7955991693965352}, 
     {19/50000, 0.7955908345817453}, {39/100000, 0.7955998594204048}, 
     {1/2500, 0.795590875960734}, {41/100000, 0.7956245101744415}, 
     {21/50000, 0.7956005647347708}, {43/100000, 0.7956226721060058}, 
     {11/25000, 0.7956241863701101}, {9/20000, 0.795601032295929}, 
     {23/50000, 0.7956026978325044}, {47/100000, 0.7956022815192383}, 
     {3/6250, 0.795602026250954}, {49/100000, 0.7956025678370264}, 
     {1/2000, 0.7955942373204232}, {51/100000, 0.7955952072982626}, 
     {13/25000, 0.7956010077834401}, {53/100000, 0.7956202594537043}, 
     {27/50000, 0.7956009323036914}, {11/20000, 0.7956045950918891}, 
     {7/12500, 0.7956033083397487}, {57/100000, 0.7955944100831629}, 
     {29/50000, 0.7955943008324069}, {59/100000, 0.7956196992317697}, 
     {3/5000, 0.7955945161640052}, {61/100000, 0.7956190002990207}, 
     {31/50000, 0.7955947016733624}, {63/100000, 0.7956197220523009}, 
     {2/3125, 0.7955824570775771}, {13/20000, 0.7955962107535894}, 
     {33/50000, 0.7955956653390865}, {67/100000, 0.795618969142827}, 
     {17/25000, 0.7956043808364641}, {69/100000, 0.79560497430881}, 
     {7/10000, 0.7955960967016287}, {71/100000, 0.7955968804508249}, 
     {9/12500, 0.7956189086211638}, {73/100000, 0.7955965599577999}, 
     {37/50000, 0.7956071486988376}, {3/4000, 0.7956039250536602}, 
     {19/25000, 0.7955975234405344}, {77/100000, 0.7955971272415843}, 
     {39/50000, 0.7956180592569808}, {79/100000, 0.7955974047244023}, 
     {1/1250, 0.7956053767160083}, {81/100000, 0.7956170825677238}, 
     {41/50000, 0.7955983271567999}, {83/100000, 0.7956074129761044}, 
     {21/25000, 0.7955978692919254}, {17/20000, 0.7955975860100684}, 
     {43/50000, 0.7955972361333661}, {87/100000, 0.7956052478283615}, 
     {11/12500, 0.7956051806398197}, {89/100000, 0.7956072331355175}, 
     {9/10000, 0.7956074877967545}, {91/100000, 0.795605731828684}, 
     {23/25000, 0.795598281028703}, {93/100000, 0.7956068343607203}, 
     {47/50000, 0.7956060423527114}, {19/20000, 0.7956069667824712}, 
     {3/3125, 0.7955984175040962}, {97/100000, 0.7955993861005428}, 
     {49/50000, 0.7956160308649682}, {99/100000, 0.7956073288649366}, 
     {1/1000, 0.7955990581241639}, {101/100000, 0.795598339824648}, 
     {51/50000, 0.7956077252195355}, {103/100000, 0.7955988113585448}, 
     {13/12500, 0.7955997521078015}, {21/20000, 0.795614842880247}, 
     {53/50000, 0.7955989761225837}, {107/100000, 0.7956077384481475}, 
     {27/25000, 0.7956075665004638}, {109/100000, 0.7956058567834456}, 
     {11/10000, 0.7956074192602971}, {111/100000, 0.7956076462513226}, 
     {7/6250, 0.795608720534799}, {113/100000, 0.7956077986175591}, 
     {57/50000, 0.7956088249970952}, {23/20000, 0.7956152812268815}, 
     {29/25000, 0.7955992805614471}, {117/100000, 0.7955993677123452}, 
     {59/50000, 0.7955994521986822}, {119/100000, 0.7955994661805104}, 
     {3/2500, 0.795608051681592}, {121/100000, 0.795607481418247}, 
     {61/50000, 0.7956151729362677}, {123/100000, 0.7956095007301798}, 
     {31/25000, 0.7956153234906331}, {1/800, 0.7956091407497854}, 
     {63/50000, 0.7956089203834185}, {127/100000, 0.7956090690014261}, 
     {4/3125, 0.7955999496385497}, {129/100000, 0.7956147628792847}, 
     {13/10000, 0.7956149959966918}, {131/100000, 0.7955999486972245}, 
     {33/25000, 0.7956004197952464}, {133/100000, 0.7955998035534284}, 
     {67/50000, 0.7956069431587287}, {27/20000, 0.7956150942780225}, 
     {17/12500, 0.7956073188555397}, {137/100000, 0.7956131311948491}, 
     {69/50000, 0.7956005578247152}, {139/100000, 0.7956085165736999}, 
     {7/5000, 0.7956146286563164}, {141/100000, 0.7956088549057614}, 
     {71/50000, 0.7956145251082645}, {143/100000, 0.7956001440376297}, 
     {9/6250, 0.7956010627001784}, {29/20000, 0.795607938062671}, 
     {73/50000, 0.7956087212966292}, {147/100000, 0.7956003689457374}, 
     {37/25000, 0.7956002513212406}, {149/100000, 0.7956090092442807}, 
     {3/2000, 0.795608582034963}, {151/100000, 0.7956001993784585}, 
     {19/12500, 0.795608572635901}, {153/100000, 0.7956086582946065}, 
     {77/50000, 0.7956003736968129}, {31/20000, 0.7956134361409166}, 
     {39/25000, 0.7956081136976003}, {157/100000, 0.7956007501062636}, 
     {79/50000, 0.7956080259501923}, {159/100000, 0.7956073078594685}, 
     {1/625, 0.7956093959822828}, {161/100000, 0.7956079611653148}, 
     {81/50000, 0.7956071231496895}, {163/100000, 0.7956007850153379}, 
     {41/25000, 0.7956009967436684}, {33/20000, 0.7956013665885164}, 
     {83/50000, 0.7956146061107461}, {167/100000, 0.7956071983723203}, 
     {21/12500, 0.7956094087302206}, {169/100000, 0.7956089551181869}, 
     {17/10000, 0.7956013730413694}, {171/100000, 0.7956132394541053}, 
     {43/25000, 0.795601580279754}, {173/100000, 0.795612929286281}, 
     {87/50000, 0.7956071724739204}, {7/4000, 0.7956074652871363}, 
     {11/6250, 0.7956088728803876}, {177/100000, 0.7956016853219863}, 
     {89/50000, 0.7956009890916}, {179/100000, 0.7956013997367473}, 
     {9/5000, 0.7956146918971561}, {181/100000, 0.7956019648325641}, 
     {91/50000, 0.7956013038690419}, {183/100000, 0.795608820942038}, 
     {23/12500, 0.7956079537272789}, {37/20000, 0.7956027432560124}, 
     {93/50000, 0.7956095763793649}, {187/100000, 0.7956091954524096}, 
     {47/25000, 0.7956093110149607}, {189/100000, 0.79560212897987}, 
     {19/10000, 0.7956021139941805}, {191/100000, 0.7956078109595568}, 
     {6/3125, 0.7956086876675648}, {193/100000, 0.7956142537005717}, 
     {97/50000, 0.7956069119004239}, {39/20000, 0.7956089055853446}, 
     {49/25000, 0.7956132590000773}, {197/100000, 0.7956027263746996}, 
     {99/50000, 0.7956083747343867}, {199/100000, 0.7956090134881171}, 
     {1/500, 0.7956093712431067}, {201/100000, 0.7956028466552016}, 
     {101/50000, 0.7956078992360927}, {203/100000, 0.7956135228543206}, 
     {51/25000, 0.7956089912414646}, {41/20000, 0.7956098317700206}, 
     {103/50000, 0.7956021102703361}, {207/100000, 0.7956014666026228}, 
     {13/6250, 0.7956028240926907}, {209/100000, 0.7956079660857371}, 
     {21/10000, 0.7956127346161095}, {211/100000, 0.795602059204723}, 
     {53/25000, 0.7956023987176257}, {213/100000, 0.7956032678069929}, 
     {107/50000, 0.7956089190277287}, {43/20000, 0.7956028807498781}, 
     {27/12500, 0.7956131433294762}, {217/100000, 0.7956128486667708}, 
     {109/50000, 0.7956024206550243}, {219/100000, 0.7956037863011503}, 
     {11/5000, 0.7956130660713394}, {221/100000, 0.7956091001232215}, 
     {111/50000, 0.7956022020516036}, {223/100000, 0.7956136192910503}, 
     {7/3125, 0.7956124440376011}, {9/4000, 0.7956091370571987}, 
     {113/50000, 0.7956093967226572}, {227/100000, 0.7956081678184281}, 
     {57/25000, 0.7956029930961388}, {229/100000, 0.7956127861071987}, 
     {23/10000, 0.7956088880694843}, {231/100000, 0.7956093794741808}, 
     {29/12500, 0.7956083534528244}, {233/100000, 0.7956087506763492}, 
     {117/50000, 0.7956030873177404}, {47/20000, 0.7956034489152541}, 
     {59/25000, 0.7956090233251127}, {237/100000, 0.7956073767487171}, 
     {119/50000, 0.795607514891238}, {239/100000, 0.7956076625184121}, 
     {3/1250, 0.7956081703368723}, {241/100000, 0.7956030442209987}, 
     {121/50000, 0.7956040099335189}, {243/100000, 0.7956075830538429}, 
     {61/25000, 0.7956085970864888}, {49/20000, 0.7956029473837654}, 
     {123/50000, 0.7956077842407336}, {247/100000, 0.7956039321559154}, 
     {31/12500, 0.7956135363404679}, {249/100000, 0.7956044149594974}, 
     {1/400, 0.7956084688472371}, {251/100000, 0.7956097645803921}, 
     {63/25000, 0.7956043233650285}, {253/100000, 0.795609546367186}, 
     {127/50000, 0.795609990198388}, {51/20000, 0.7955984200580217}, 
     {8/3125, 0.7956097844784225}, {257/100000, 0.7956036427604349}, 
     {129/50000, 0.7956097853295936}, {259/100000, 0.7956084154022722}, 
     {13/5000, 0.7956124137574929}, {261/100000, 0.7956133009948654}, 
     {131/50000, 0.7956033092836812}, {263/100000, 0.7956038433858779}, 
     {33/12500, 0.7956035640051855}, {53/20000, 0.795608947340801}, 
     {133/50000, 0.7956043380881548}, {267/100000, 0.7956041292083}, 
     {67/25000, 0.7956099195609658}, {269/100000, 0.795604224627124}, 
     {27/10000, 0.7956037825429232}, {271/100000, 0.7956080286994971}, 
     {17/6250, 0.7956043415648217}, {273/100000, 0.7956132024352831}, 
     {137/50000, 0.7956040787402725}, {11/4000, 0.7956092031181488}, 
     {69/25000, 0.7956089812256408}, {277/100000, 0.7956139064781653}, 
     {139/50000, 0.7956036281282084}, {279/100000, 0.7955986972233364}, 
     {7/2500, 0.7956136488430845}, {281/100000, 0.7956077112827704}, 
     {141/50000, 0.7956129440624689}, {283/100000, 0.7956033014483923}, 
     {71/25000, 0.7956044367234667}, {57/20000, 0.7956050172244913}, 
     {143/50000, 0.7956124783373624}, {287/100000, 0.7956088651218338}, 
     {9/3125, 0.7955993082887813}, {289/100000, 0.7956076216082333}, 
     {29/10000, 0.7956035275140061}, {291/100000, 0.7956049168516834}, 
     {73/25000, 0.7956042095913807}, {293/100000, 0.7956140614051312}, 
     {147/50000, 0.7956043406123676}, {59/20000, 0.7956039931482053}, 
     {37/12500, 0.7956101096948096}, {297/100000, 0.7956100311666789}, 
     {149/50000, 0.7956095356701454}, {299/100000, 0.7956047766120151}, 
     {3/1000, 0.7956102482511982}, {301/100000, 0.7956090722863038}, 
     {151/50000, 0.795605183638278}, {303/100000, 0.7956100549757252}, 
     {19/6250, 0.795609657019722}, {61/20000, 0.7956084055721333}, 
     {153/50000, 0.7956086254668508}, {307/100000, 0.7956131453117932}, 
     {77/25000, 0.795613411224172}, {309/100000, 0.7956098633184943}, 
     {31/10000, 0.7956101905990827}, {311/100000, 0.7956092690461434}, 
     {39/12500, 0.7956130994441017}, {313/100000, 0.7956104800456334}, 
     {157/50000, 0.7956097931374995}, {63/20000, 0.7956098360283419}, 
     {79/25000, 0.7956045315579612}, {317/100000, 0.795604671943833}, 
     {159/50000, 0.7956056323618288}, {319/100000, 0.7956085573246412}, 
     {2/625, 0.7956095480996472}, {321/100000, 0.7956051439741514}, 
     {161/50000, 0.7956128706085859}, {323/100000, 0.7956140954788529}, 
     {81/25000, 0.7956135129895743}, {13/4000, 0.7956054255615288}, 
     {163/50000, 0.7956102076844411}, {327/100000, 0.7956110420850853}, 
     {41/12500, 0.7956107263787255}, {329/100000, 0.7956106085739694}, 
     {33/10000, 0.7956089192841516}, {331/100000, 0.795605593914162}, 
     {83/25000, 0.795610386854428}, {333/100000, 0.7956046540468091}, 
     {167/50000, 0.7956090449279163}, {67/20000, 0.7956093004034908}, 
     {21/6250, 0.7956141455434627}, {337/100000, 0.7956103013060858}, 
     {169/50000, 0.7956060220094789}, {339/100000, 0.7956050053419266}, 
     {17/5000, 0.7956101389438768}, {341/100000, 0.7956054933434173}, 
     {171/50000, 0.7956140441880502}, {343/100000, 0.7956067400897702}, 
     {43/12500, 0.7956112771219601}, {69/20000, 0.7956143222167067}, 
     {173/50000, 0.7956100738518539}, {347/100000, 0.795609705523292}, 
     {87/25000, 0.7956103737554345}, {349/100000, 0.7956136444621129}, 
     {7/2000, 0.7956110323822232}, {351/100000, 0.7956087811761581}, 
     {11/3125, 0.7956057910561243}, {353/100000, 0.7956066122804253}, 
     {177/50000, 0.7956095689156237}, {71/20000, 0.7956060093699451}, 
     {89/25000, 0.795609842034223}, {357/100000, 0.7956141593612558}, 
     {179/50000, 0.7956106911552787}, {359/100000, 0.795609711134305}, 
     {9/2500, 0.7956135407896294}, {361/100000, 0.7956142115232674}, 
     {181/50000, 0.7956134500272807}, {363/100000, 0.7956097542421117}, 
     {91/25000, 0.7956101824575881}, {73/20000, 0.7956059899117145}, 
     {183/50000, 0.795609559438565}, {367/100000, 0.7956110035641619}, 
     {23/6250, 0.7956139984458592}, {369/100000, 0.7956139796994446}, 
     {37/10000, 0.7956114289998291}, {371/100000, 0.7956118132380241}, 
     {93/25000, 0.7956066753627029}, {373/100000, 0.7956063624321676}, 
     {187/50000, 0.795606634031099}, {3/800, 0.7956109878500519}, 
     {47/12500, 0.7956143475081965}, {377/100000, 0.7956147166508503}, 
     {189/50000, 0.795611439116934}, {379/100000, 0.79560606163998}, 
     {19/5000, 0.7956141755311537}, {381/100000, 0.7956099627125734}, 
     {191/50000, 0.7956142185187169}, {383/100000, 0.7956140853561986}, 
     {12/3125, 0.7956142960556498}, {77/20000, 0.7956104432267952}, 
     {193/50000, 0.7956149244362565}, {387/100000, 0.7956116123066876}, 
     {97/25000, 0.795606940454507}, {389/100000, 0.795609951617986}, 
     {39/10000, 0.7956095797544838}, {391/100000, 0.7956141297871859}, 
     {49/12500, 0.7956151021253826}, {393/100000, 0.7956112834060489}, 
     {197/50000, 0.7956071263359101}, {79/20000, 0.7956067579828767}, 
     {99/25000, 0.7956114634574152}, {397/100000, 0.7956114645958161}, 
     {199/50000, 0.7956070058964935}, {399/100000, 0.7956063750545312}, 
     {1/250, 0.795611786755611}, {401/100000, 0.7956100674673774}, 
     {201/50000, 0.7956139495509476}, {403/100000, 0.795615353387062}, 
     {101/25000, 0.7956079224041055}, {81/20000, 0.7956114457130505}, 
     {203/50000, 0.7956109781733258}, {407/100000, 0.7956112901811028}, 
     {51/12500, 0.7956151857046811}, {409/100000, 0.7956073028441137}, 
     {41/10000, 0.7956110500131786}, {411/100000, 0.7956121786261181}, 
     {103/25000, 0.7956108292256947}, {413/100000, 0.7956126931022851}, 
     {207/50000, 0.7956154180650086}, {83/20000, 0.7956078273180234}, 
     {13/3125, 0.7956107958987717}, {417/100000, 0.7956076908173646}, 
     {209/50000, 0.7956087283899227}, {419/100000, 0.7956069159277117}, 
     {21/5000, 0.7956080790389519}, {421/100000, 0.7956129703285413}, 
     {211/50000, 0.7956079580703737}, {423/100000, 0.7956120786921934}, 
     {53/12500, 0.7956108972873475}, {17/4000, 0.7956079188324905}, 
     {213/50000, 0.7956127473160999}, {427/100000, 0.795610701211372}, 
     {107/25000, 0.7956121256006305}, {429/100000, 0.7956107908848993}, 
     {43/10000, 0.7956157612760055}, {431/100000, 0.7956129539878058}, 
     {27/6250, 0.7956083720934455}, {433/100000, 0.7956082714099049}, 
     {217/50000, 0.7956087484336671}, {87/20000, 0.7956083589885479}, 
     {109/25000, 0.795616260587666}, {437/100000, 0.7956154744557189}, 
     {219/50000, 0.7956128392255728}, {439/100000, 0.7956083944724379}, 
     {11/2500, 0.7956081768953891}, {441/100000, 0.7956083393258657}, 
     {221/50000, 0.7956122415795321}, {443/100000, 0.7956087736139112}, 
     {111/25000, 0.7956162570127874}, {89/20000, 0.795615650886297}, 
     {223/50000, 0.7956113975942363}, {447/100000, 0.7956159828567637}, 
     {14/3125, 0.7956132560392142}, {449/100000, 0.7956121059925834}, 
     {9/2000, 0.795615736919411}, {451/100000, 0.7956054185193429}, 
     {113/25000, 0.7956122618318355}, {453/100000, 0.7956129492774631}, 
     {227/50000, 0.7956161188465973}, {91/20000, 0.7956128381649461}, 
     {57/12500, 0.7956153990976138}, {457/100000, 0.7956165451598762}, 
     {229/50000, 0.7956124740014037}, {459/100000, 0.7956170006432473}, 
     {23/5000, 0.7956166597820302}, {461/100000, 0.7956125000533838}, 
     {231/50000, 0.7956094833112246}, {463/100000, 0.7956135470030103}, 
     {29/6250, 0.7956084556134426}, {93/20000, 0.7956120098397643}, 
     {233/50000, 0.7956089433948401}, {467/100000, 0.79560964882269}, 
     {117/25000, 0.7956165763431313}, {469/100000, 0.7956135697967013}, 
     {47/10000, 0.7956087845133202}, {471/100000, 0.7956136660468007}, 
     {59/12500, 0.795609070671011}, {473/100000, 0.7956120069475157}, 
     {237/50000, 0.7956145715123664}, {19/4000, 0.7956127880523973}, 
     {119/25000, 0.7956129358043791}, {477/100000, 0.795610217755145}, 
     {239/50000, 0.7956089420998214}, {479/100000, 0.7956165900591459}, 
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     {19/2000, 0.7956311716046152}, {951/100000, 0.7956357513536494}, 
     {119/12500, 0.7956311950381556}, {953/100000, 0.7956366114346052}, 
     {477/50000, 0.7956309116217155}, {191/20000, 0.7956328353818098}, 
     {239/25000, 0.7956332159717814}, {957/100000, 0.7956330058000933}, 
     {479/50000, 0.7956307580363498}, {959/100000, 0.7956318705293355}, 
     {6/625, 0.7956315991689231}, {961/100000, 0.7956309870255938}, 
     {481/50000, 0.7956337737588428}, {963/100000, 0.7956314386385057}, 
     {241/25000, 0.7956305711678162}, {193/20000, 0.7956325169166258}, 
     {483/50000, 0.7956318164350185}, {967/100000, 0.7956370495324592}, 
     {121/12500, 0.7956354368193432}, {969/100000, 0.795636607215596}, 
     {97/10000, 0.7956316275901472}, {971/100000, 0.7956346123689468}, 
     {243/25000, 0.7956369421585294}, {973/100000, 0.7956326771600075}, 
     {487/50000, 0.7956348562910387}, {39/4000, 0.795634077303196}, 
     {61/6250, 0.7956317771479178}, {977/100000, 0.7956380322134082}, 
     {489/50000, 0.7956349701196554}, {979/100000, 0.7956359942388991}, 
     {49/5000, 0.7956323537399363}, {981/100000, 0.795632085157151}, 
     {491/50000, 0.7956325207604666}, {983/100000, 0.7956355012484284}, 
     {123/12500, 0.7956354276212387}, {197/20000, 0.7956381261008345}, 
     {493/50000, 0.7956358431153623}, {987/100000, 0.7956386248189071}, 
     {247/25000, 0.7956343069592613}, {989/100000, 0.7956352391950858}, 
     {99/10000, 0.7956387412472865}, {991/100000, 0.7956322593481824}, 
     {31/3125, 0.7956349807837735}, {993/100000, 0.7956328211980495}, 
     {497/50000, 0.7956364579569319}, {199/20000, 0.7956352921544125}, 
     {249/25000, 0.7956360345845717}, {997/100000, 0.7956361262845593}, 
     {499/50000, 0.795633147768827}, {999/100000, 0.7956341797072426}, 
     {1/100, 0.79563574503553}}
 
ReERfinb = {{1/100, 0.79563574503553}, {11/1000, 0.7956414461383887}, 
     {3/250, 0.7956512661651209}, {13/1000, 0.7956599069040626}, 
     {7/500, 0.7956679073444768}, {3/200, 0.7956719519250424}, 
     {2/125, 0.7956858717443227}, {17/1000, 0.7956926639385413}, 
     {9/500, 0.7957019166633268}, {19/1000, 0.7957129442458721}, 
     {1/50, 0.7957246830112212}, {21/1000, 0.7957374371809802}, 
     {11/500, 0.7957520771230375}, {23/1000, 0.7957663909682311}, 
     {3/125, 0.7957807402047661}, {1/40, 0.7957937460710931}, 
     {13/500, 0.7958123524176246}, {27/1000, 0.7958248542833202}, 
     {7/250, 0.7958456807611665}, {29/1000, 0.7958592445897703}, 
     {3/100, 0.7958781946232221}, {31/1000, 0.7958965755115148}, 
     {4/125, 0.7959161207794772}, {33/1000, 0.7959358384368018}, 
     {17/500, 0.7959568955732905}, {7/200, 0.795976100950416}, 
     {9/250, 0.7959942582739199}, {37/1000, 0.7960204598328735}, 
     {19/500, 0.7960436755224078}, {39/1000, 0.7960637671466211}, 
     {1/25, 0.7960876626137465}, {41/1000, 0.7961121506688449}, 
     {21/500, 0.7961391017445467}, {43/1000, 0.7961647169815187}, 
     {11/250, 0.7961900461175024}, {9/200, 0.796216844757891}, 
     {23/500, 0.7962440408902816}, {47/1000, 0.7962749694684761}, 
     {6/125, 0.796300619510093}, {49/1000, 0.7963293282363466}, 
     {1/20, 0.7963594787613473}, {51/1000, 0.7963901212964224}, 
     {13/250, 0.7964207583009069}, {53/1000, 0.7964546591038393}, 
     {27/500, 0.7964856962098632}, {11/200, 0.7965206491229475}, 
     {7/125, 0.7965525094724324}, {57/1000, 0.7965859248712395}, 
     {29/500, 0.7966221176175066}, {59/1000, 0.796656162976952}, 
     {3/50, 0.7966912711943235}, {61/1000, 0.7967272973152375}, 
     {31/500, 0.796763591094181}, {63/1000, 0.7968021550152073}, 
     {8/125, 0.796838998734335}, {13/200, 0.796877812299523}, 
     {33/500, 0.7969168383698664}, {67/1000, 0.7969587182750146}, 
     {17/250, 0.7969968122910727}, {69/1000, 0.7970408735043493}, 
     {7/100, 0.7970794622542288}, {71/1000, 0.7971219954303224}, 
     {9/125, 0.7971663005808969}, {73/1000, 0.7972083730818289}, 
     {37/500, 0.7972518369646164}, {3/40, 0.7972967838190943}, 
     {19/250, 0.7973420534692623}, {77/1000, 0.7973888464479333}, 
     {39/500, 0.7974341669917471}, {79/1000, 0.7974804900942027}, 
     {2/25, 0.7975282040143412}, {81/1000, 0.7975760741857796}, 
     {41/500, 0.7976246931564699}, {83/1000, 0.7976731002853015}, 
     {21/250, 0.797723790479401}, {17/200, 0.7977747060474805}, 
     {43/500, 0.797825398341014}, {87/1000, 0.797878407958776}, 
     {11/125, 0.7979282506057963}, {89/1000, 0.7979812439453431}, 
     {9/100, 0.7980336069411376}, {91/1000, 0.7980885993542541}, 
     {23/250, 0.7981417014096341}, {93/1000, 0.798198414816683}, 
     {47/500, 0.7982519480480046}, {19/200, 0.7983080122051778}, 
     {12/125, 0.7983640419393883}, {97/1000, 0.7984222540003141}, 
     {49/500, 0.7984801567981652}, {99/1000, 0.7985372204463701}, 
     {1/10, 0.7985970440875505}, {101/1000, 0.7986559585512034}, 
     {51/500, 0.7987152854122934}, {103/1000, 0.7987754406143313}, 
     {13/125, 0.7988363302960195}, {21/200, 0.7988979506786245}, 
     {53/500, 0.7989602712658099}, {107/1000, 0.7990250746532599}, 
     {27/250, 0.7990864412514691}, {109/1000, 0.7991503050449413}, 
     {11/100, 0.7992143807507239}, {111/1000, 0.7992792737573744}, 
     {14/125, 0.799345607889129}, {113/1000, 0.799411556270484}, 
     {57/500, 0.7994774432607761}, {23/200, 0.7995439788218262}, 
     {29/250, 0.7996127568472104}, {117/1000, 0.7996796999103579}, 
     {59/500, 0.7997488014812633}, {119/1000, 0.7998187856595966}, 
     {3/25, 0.7998877772470268}, {121/1000, 0.7999578524900763}, 
     {61/500, 0.800029524685864}, {123/1000, 0.8001010139604752}, 
     {31/250, 0.8001722846162393}, {1/8, 0.8002447861940123}, 
     {63/500, 0.8003175025238352}, {127/1000, 0.8003920764154389}, 
     {16/125, 0.8004658947654777}, {129/1000, 0.8005412857907181}, 
     {13/100, 0.8006157493042565}, {131/1000, 0.8006922475720955}, 
     {33/250, 0.8007667637866627}, {133/1000, 0.8008433586306616}, 
     {67/500, 0.800921618084077}, {27/200, 0.8009992720412824}, 
     {17/125, 0.8010775484433323}, {137/1000, 0.8011558717532625}, 
     {69/500, 0.8012349619357133}, {139/1000, 0.8013150069989301}, 
     {7/50, 0.8013959099363812}, {141/1000, 0.8014759370504154}, 
     {71/500, 0.8015575138826434}, {143/1000, 0.8016394405315732}, 
     {18/125, 0.8017217780861303}, {29/200, 0.801804873930954}, 
     {73/500, 0.8018885218367973}, {147/1000, 0.8019729268186122}, 
     {37/250, 0.8020567875992892}, {149/1000, 0.8021417792810497}, 
     {3/20, 0.8022285835313769}, {151/1000, 0.8023134714925271}, 
     {19/125, 0.8024011181303674}, {153/1000, 0.8024869483631862}, 
     {77/500, 0.802574952650096}, {31/200, 0.8026624878172464}, 
     {39/250, 0.8027508022112153}, {157/1000, 0.8028400229084394}, 
     {79/500, 0.8029295706290016}, {159/1000, 0.8030195656837895}, 
     {4/25, 0.8031104485675806}, {161/1000, 0.803201465510317}, 
     {81/500, 0.8032929069415777}, {163/1000, 0.8033849066502681}, 
     {41/250, 0.8034774496290185}, {33/200, 0.8035699114566186}, 
     {83/500, 0.803663420924345}, {167/1000, 0.8037576889034068}, 
     {21/125, 0.8038521909725849}, {169/1000, 0.8039463316865834}, 
     {17/100, 0.8040418739716126}, {171/1000, 0.8041380812999663}, 
     {43/250, 0.8042339117683528}, {173/1000, 0.8043308072667612}, 
     {87/500, 0.8044281963192614}, {7/40, 0.804525797341658}, 
     {22/125, 0.8046245288427594}, {177/1000, 0.8047228528238888}, 
     {89/500, 0.8048224159804884}, {179/1000, 0.8049215310094642}, 
     {9/50, 0.8050218151679909}, {181/1000, 0.8051223839248509}, 
     {91/500, 0.8052233586263471}, {183/1000, 0.8053248909000827}, 
     {23/125, 0.8054267243452884}, {37/200, 0.8055292843079798}, 
     {93/500, 0.8056321534495927}, {187/1000, 0.805735741034141}, 
     {47/250, 0.8058393053791248}, {189/1000, 0.8059437179691482}, 
     {19/100, 0.8060481319711719}, {191/1000, 0.8061534609677286}, 
     {24/125, 0.8062588142400693}, {193/1000, 0.8063648688743834}, 
     {97/500, 0.8064713580786886}, {39/200, 0.8065783680452205}, 
     {49/250, 0.8066856711605852}, {197/1000, 0.8067936201847026}, 
     {99/500, 0.8069015742776595}, {199/1000, 0.8070105594765469}, 
     {1/5, 0.8071196035290762}, {201/1000, 0.8072296010260942}, 
     {101/500, 0.8073394864757071}, {203/1000, 0.807449621794821}, 
     {51/250, 0.8075607193412089}, {41/200, 0.8076718397722567}, 
     {103/500, 0.8077836767884703}, {207/1000, 0.8078955446383649}, 
     {26/125, 0.8080085167643243}, {209/1000, 0.8081212228779573}, 
     {21/100, 0.8082346754656564}, {211/1000, 0.8083485886981632}, 
     {53/250, 0.808462943377735}, {213/1000, 0.8085779283545742}, 
     {107/500, 0.8086927191888469}, {43/200, 0.8088084789605356}, 
     {27/125, 0.8089241614999398}, {217/1000, 0.8090405127022402}, 
     {109/500, 0.8091575058236224}, {219/1000, 0.8092747967878475}, 
     {11/50, 0.8093921918470581}, {221/1000, 0.8095100192532398}, 
     {111/500, 0.8096285765522899}, {223/1000, 0.8097472156019814}, 
     {28/125, 0.8098663402432829}, {9/40, 0.809986211536621}, 
     {113/500, 0.8101062097363729}, {227/1000, 0.8102266824538811}, 
     {57/250, 0.8103475207056756}, {229/1000, 0.8104685118931503}, 
     {23/100, 0.8105899916102488}, {231/1000, 0.8107120286385263}, 
     {29/125, 0.8108344585961911}, {233/1000, 0.8109570335516736}, 
     {117/500, 0.8110802742540546}, {47/200, 0.8112035990290871}, 
     {59/250, 0.8113275141619289}, {237/1000, 0.8114518693899431}, 
     {119/500, 0.8115766448250996}, {239/1000, 0.8117014930906663}, 
     {6/25, 0.8118269745921465}, {241/1000, 0.8119528163685179}, 
     {121/500, 0.8120790819856216}, {243/1000, 0.8122054148301228}, 
     {61/250, 0.8123322860782536}, {49/200, 0.812459354903571}, 
     {123/500, 0.8125872355015522}, {247/1000, 0.8127152489457363}, 
     {31/125, 0.8128435357157797}, {249/1000, 0.8129722254808485}, 
     {1/4, 0.8131012877958446}, {251/1000, 0.8132307241447041}, 
     {63/250, 0.8133605348176753}, {253/1000, 0.8134906319339348}, 
     {127/500, 0.8136210861334048}, {51/200, 0.8137519941583}, 
     {32/125, 0.8138831704271468}, {257/1000, 0.8140147636762394}, 
     {129/500, 0.8141467075720366}, {259/1000, 0.814278859294431}, 
     {13/50, 0.8144115229217963}, {261/1000, 0.8145444251559089}, 
     {131/500, 0.8146775916254505}, {263/1000, 0.8148112455901995}, 
     {33/125, 0.8149451960685856}, {53/200, 0.8150794720560182}, 
     {133/500, 0.815214029782434}, {267/1000, 0.8153490441266045}, 
     {67/250, 0.8154842644339961}, {269/1000, 0.8156199580108185}, 
     {27/100, 0.8157558576853976}, {271/1000, 0.8158920460831394}, 
     {34/125, 0.8160286779141037}, {273/1000, 0.8161655351598593}, 
     {137/500, 0.8163027443626758}, {11/40, 0.8164403626293977}, 
     {69/250, 0.8165781434965966}, {277/1000, 0.8167164106286946}, 
     {139/500, 0.8168547667633472}, {279/1000, 0.816993672659696}, 
     {7/25, 0.8171327234656829}, {281/1000, 0.8172721301969701}, 
     {141/500, 0.8174118500226109}, {283/1000, 0.817551948126257}, 
     {71/250, 0.8176921753309694}, {57/200, 0.8178328356206581}, 
     {143/500, 0.8179738600226001}, {287/1000, 0.8181150398588883}, 
     {36/125, 0.8182565516874329}, {289/1000, 0.8183983955738654}, 
     {29/100, 0.8185405590421824}, {291/1000, 0.8186830254870459}, 
     {73/250, 0.818825688096041}, {293/1000, 0.8189686342575611}, 
     {147/500, 0.8191119826325086}, {59/200, 0.8192554888826793}, 
     {37/125, 0.8193993618411719}, {297/1000, 0.8195435374517492}, 
     {149/500, 0.8196879588125872}, {299/1000, 0.8198325898340619}, 
     {3/10, 0.8199775673894139}, {301/1000, 0.820122881961892}, 
     {151/500, 0.8202683349111277}, {303/1000, 0.8204142128949599}, 
     {38/125, 0.8205602120683486}, {61/200, 0.8207066265991982}, 
     {153/500, 0.8208531767113905}, {307/1000, 0.821000037413441}, 
     {77/250, 0.821147129659815}, {309/1000, 0.8212945335224568}, 
     {31/100, 0.8214422480599406}, {311/1000, 0.8215901501691196}, 
     {39/125, 0.8217383931859581}, {313/1000, 0.8218867853955247}, 
     {157/500, 0.8220354396473906}, {63/200, 0.8221843638576014}, 
     {79/250, 0.8223335171013317}, {317/1000, 0.8224830958409171}, 
     {159/500, 0.8226327486769875}, {319/1000, 0.8227826395249687}, 
     {8/25, 0.8229328663256221}, {321/1000, 0.8230832891428319}, 
     {161/500, 0.8232339114729936}, {323/1000, 0.823384847300273}, 
     {81/250, 0.8235359818537296}, {13/40, 0.8236873731254808}, 
     {163/500, 0.8238390047725579}, {327/1000, 0.8239908430915936}, 
     {41/125, 0.8241429306794616}, {329/1000, 0.8242951291466998}, 
     {33/100, 0.8244477588649057}, {331/1000, 0.824600521823823}, 
     {83/250, 0.8247535872423695}, {333/1000, 0.824906716421276}, 
     {167/500, 0.8250601740213694}, {67/200, 0.8252139253428032}, 
     {42/125, 0.8253677687732068}, {337/1000, 0.8255219185172042}, 
     {169/500, 0.8256760685116564}, {339/1000, 0.8258306926756969}, 
     {17/50, 0.8259853305676108}, {341/1000, 0.8261403467050688}, 
     {171/500, 0.8262954503439401}, {343/1000, 0.8264508452322374}, 
     {43/125, 0.8266065275681074}, {69/200, 0.8267622348454291}, 
     {173/500, 0.8269181656843587}, {347/1000, 0.8270743059642522}, 
     {87/250, 0.8272307052172798}, {349/1000, 0.8273873331637103}, 
     {7/20, 0.8275440760627444}, {351/1000, 0.827701070294351}, 
     {44/125, 0.8278582027310177}, {353/1000, 0.8280156279511677}, 
     {177/500, 0.8281731436815738}, {71/200, 0.8283308823879842}, 
     {89/250, 0.828488668909336}, {357/1000, 0.8286468698654306}, 
     {179/500, 0.8288051707604271}, {359/1000, 0.8289636299259622}, 
     {9/25, 0.8291222939372593}, {361/1000, 0.8292810543087978}, 
     {181/500, 0.8294400907140282}, {363/1000, 0.8295993149865648}, 
     {91/250, 0.8297586310729819}, {73/200, 0.8299183053767487}, 
     {183/500, 0.8300779868676438}, {367/1000, 0.8302377957026452}, 
     {46/125, 0.8303978063104012}, {369/1000, 0.8305580417454357}, 
     {37/100, 0.8307183860097571}, {371/1000, 0.8308790310732976}, 
     {93/250, 0.8310396120384449}, {373/1000, 0.8312005233487938}, 
     {187/500, 0.8313616373620625}, {3/8, 0.8315227728705852}, 
     {47/125, 0.8316841064083857}, {377/1000, 0.8318455480034939}, 
     {189/500, 0.8320072542932957}, {379/1000, 0.8321690471326153}, 
     {19/50, 0.8323310433721087}, {381/1000, 0.8324930950284091}, 
     {191/500, 0.8326552768753217}, {383/1000, 0.8328176529075355}, 
     {48/125, 0.8329801907709711}, {77/200, 0.8331428884315071}, 
     {193/500, 0.8333057109439181}, {387/1000, 0.8334685998453466}, 
     {97/250, 0.8336317656016088}, {389/1000, 0.8337950185396159}, 
     {39/100, 0.8339583079567461}, {391/1000, 0.8341218035457452}, 
     {49/125, 0.8342854373755708}, {393/1000, 0.8344492475804719}, 
     {197/500, 0.8346131048887817}, {79/200, 0.8347771563646735}, 
     {99/250, 0.8349412955024267}, {397/1000, 0.8351056149491574}, 
     {199/500, 0.835269991661324}, {399/1000, 0.8354344479272378}, 
     {2/5, 0.8355990695168687}, {401/1000, 0.8357638420341573}, 
     {201/500, 0.8359287899870762}, {403/1000, 0.8360937070350203}, 
     {101/250, 0.8362588122461494}, {81/200, 0.8364240289560367}, 
     {203/500, 0.8365893566237126}, {407/1000, 0.8367548241880991}, 
     {51/125, 0.836920316414087}, {409/1000, 0.8370860042203474}, 
     {41/100, 0.8372518203201254}, {411/1000, 0.837417623390714}, 
     {103/250, 0.8375835676842978}, {413/1000, 0.8377496635041404}, 
     {207/500, 0.8379158372932245}, {83/200, 0.8380820795534227}, 
     {52/125, 0.8382484723349313}, {417/1000, 0.8384149439655224}, 
     {209/500, 0.8385815508188426}, {419/1000, 0.8387481972568027}, 
     {21/50, 0.8389149372648661}, {421/1000, 0.8390817648182445}, 
     {211/500, 0.8392486907712522}, {423/1000, 0.839415710451008}, 
     {53/125, 0.839582798658588}, {17/40, 0.8397500631678638}, 
     {213/500, 0.8399172634444421}, {427/1000, 0.8400846436036962}, 
     {107/250, 0.840252055100744}, {429/1000, 0.8404195751887302}, 
     {43/100, 0.8405871805669662}, {431/1000, 0.8407547574422574}, 
     {54/125, 0.8409225981682629}, {433/1000, 0.841090422296833}, 
     {217/500, 0.8412583136277152}, {87/200, 0.8414262298205304}, 
     {109/250, 0.8415942597255492}, {437/1000, 0.841762418628857}, 
     {219/500, 0.841930621415647}, {439/1000, 0.8420987992290307}, 
     {11/25, 0.8422671591322075}, {441/1000, 0.8424354659798847}, 
     {221/500, 0.8426039751584069}, {443/1000, 0.8427724042185183}, 
     {111/250, 0.8429409658458931}, {89/200, 0.8431096227619042}, 
     {223/500, 0.8432782167754005}, {447/1000, 0.8434469988893678}, 
     {56/125, 0.8436157952104941}, {449/1000, 0.8437846430913929}, 
     {9/20, 0.8439535064994041}, {451/1000, 0.8441224485010239}, 
     {113/250, 0.8442914585772989}, {453/1000, 0.8444604622979557}, 
     {227/500, 0.8446295815637233}, {91/200, 0.8447986564046306}, 
     {57/125, 0.8449679297402435}, {457/1000, 0.8451371042846292}, 
     {229/500, 0.8453064346161068}, {459/1000, 0.8454756378268664}, 
     {23/50, 0.8456450348370523}, {461/1000, 0.8458144107468528}, 
     {231/500, 0.8459838418319614}, {463/1000, 0.8461532078802212}, 
     {58/125, 0.8463227480611637}, {93/200, 0.8464922445794745}, 
     {233/500, 0.8466618667729215}, {467/1000, 0.8468314633187155}, 
     {117/250, 0.8470010425117263}, {469/1000, 0.8471707392498848}, 
     {47/100, 0.8473403837000864}, {471/1000, 0.8475101666290641}, 
     {59/125, 0.8476798823537117}, {473/1000, 0.8478496119793484}, 
     {237/500, 0.8480194463484376}, {19/40, 0.8481890937905194}, 
     {119/250, 0.8483589891267866}, {477/1000, 0.8485288407760849}, 
     {239/500, 0.8486987361690224}, {479/1000, 0.8488685939568321}, 
     {12/25, 0.8490384934371882}, {481/1000, 0.8492083277578544}, 
     {241/500, 0.8493783248478155}, {483/1000, 0.8495482683154312}, 
     {121/250, 0.8497182288758349}, {97/200, 0.8498881704321108}, 
     {243/500, 0.8500581364018169}, {487/1000, 0.8502280132612183}, 
     {61/125, 0.8503980167077803}, {489/1000, 0.8505679738330065}, 
     {49/100, 0.8507380243428238}, {491/1000, 0.8509079692419939}, 
     {123/250, 0.8510780010397905}, {493/1000, 0.8512479156510215}, 
     {247/500, 0.8514179870733973}, {99/200, 0.8515880201632813}, 
     {62/125, 0.8517580277563859}, {497/1000, 0.8519279702741618}, 
     {249/500, 0.8520980708586705}, {499/1000, 0.8522680250907975}, 
     {1/2, 0.8524380397797362}, {501/1000, 0.8526079994214608}, 
     {251/500, 0.852777977573115}, {503/1000, 0.8529478622329045}, 
     {63/125, 0.8531178633525358}, {101/200, 0.8532877397446459}, 
     {253/500, 0.8534575780869105}, {507/1000, 0.8536275320379783}, 
     {127/250, 0.8537974036036302}, {509/1000, 0.8539673768678053}, 
     {51/100, 0.85413717955762}, {511/1000, 0.8543070421720118}, 
     {64/125, 0.8544768725697884}, {513/1000, 0.8546467606195591}, 
     {257/500, 0.8548164908680393}, {103/200, 0.8549862656539688}, 
     {129/250, 0.8551559485273761}, {517/1000, 0.8553257688287497}, 
     {259/500, 0.8554954273311828}, {519/1000, 0.8556649906781768}, 
     {13/25, 0.85583468239067}, {521/1000, 0.8560044075031465}, 
     {261/500, 0.8561738235081107}, {523/1000, 0.8563435560610855}, 
     {131/250, 0.8565130630397306}, {21/40, 0.8566824160523017}, 
     {263/500, 0.8568519186586958}, {527/1000, 0.8570213230293486}, 
     {66/125, 0.8571907430922745}, {529/1000, 0.8573601932625623}, 
     {53/100, 0.8575293806209019}, {531/1000, 0.8576986796317825}, 
     {133/250, 0.8578680321550358}, {533/1000, 0.858037209750556}, 
     {267/500, 0.8582064593972818}, {107/200, 0.8583755785238996}, 
     {67/125, 0.8585445128017342}, {537/1000, 0.858713672829688}, 
     {269/500, 0.8588826514092074}, {539/1000, 0.859051498753928}, 
     {27/50, 0.8592204823952485}, {541/1000, 0.8593894313835018}, 
     {271/500, 0.8595581838847759}, {543/1000, 0.8597269978534232}, 
     {68/125, 0.8598956503025479}, {109/200, 0.8600642444768383}, 
     {273/500, 0.8602329048976465}, {547/1000, 0.8604016012985616}, 
     {137/250, 0.8605700123314914}, {549/1000, 0.8607385520965398}, 
     {11/20, 0.8609068698838791}, {551/1000, 0.8610753118345531}, 
     {69/125, 0.8612435012841322}, {553/1000, 0.8614119845819359}, 
     {277/500, 0.8615800730142111}, {111/200, 0.86174808401785}, 
     {139/250, 0.8619160800774321}, {557/1000, 0.8620840766458091}, 
     {279/500, 0.8622520481342593}, {559/1000, 0.8624200403002293}, 
     {14/25, 0.8625878474432906}, {561/1000, 0.8627556211544625}, 
     {281/500, 0.8629232163709761}, {563/1000, 0.8630908070069812}, 
     {141/250, 0.8632584217282706}, {113/200, 0.863425914715247}, 
     {283/500, 0.8635932512976869}, {567/1000, 0.8637606133475342}, 
     {71/125, 0.8639281521357334}, {569/1000, 0.864095293110656}, 
     {57/100, 0.8642624537027774}, {571/1000, 0.864429443701775}, 
     {143/250, 0.8645964493850604}, {573/1000, 0.8647632790336415}, 
     {287/500, 0.8649303466159113}, {23/40, 0.8650971207455567}, 
     {72/125, 0.8652636570139314}, {577/1000, 0.8654304370827153}, 
     {289/500, 0.8655970002470661}, {579/1000, 0.8657632966153541}, 
     {29/50, 0.8659297924195171}, {581/1000, 0.8660962247073254}, 
     {291/500, 0.8662623375213472}, {583/1000, 0.8664286123382245}, 
     {73/125, 0.8665947623670118}, {117/200, 0.8667606476931211}, 
     {293/500, 0.8669265609436616}, {587/1000, 0.8670924115483443}, 
     {147/250, 0.8672581538240014}, {589/1000, 0.8674238855824556}, 
     {59/100, 0.867589377548871}, {591/1000, 0.8677548964187913}, 
     {74/125, 0.8679202914752016}, {593/1000, 0.8680855005008328}, 
     {297/500, 0.8682507239941548}, {119/200, 0.8684159834136298}, 
     {149/250, 0.868580836793684}, {597/1000, 0.8687459755812112}, 
     {299/500, 0.8689106427176962}, {599/1000, 0.8690756067082939}, 
     {3/5, 0.86924031920029}, {601/1000, 0.8694049209365324}, 
     {301/500, 0.8695694051379081}, {603/1000, 0.8697336739694239}, 
     {151/250, 0.8698979005679994}, {121/200, 0.8700622702269702}, 
     {303/500, 0.8702262193326971}, {607/1000, 0.8703905674207719}, 
     {76/125, 0.8705542633605188}, {609/1000, 0.8707180092318865}, 
     {61/100, 0.8708816966400816}, {611/1000, 0.87104554463171}, 
     {153/250, 0.8712091784599787}, {613/1000, 0.8713724462939973}, 
     {307/500, 0.8715356963346694}, {123/200, 0.871699037069785}, 
     {77/125, 0.8718621272151175}, {617/1000, 0.872025064015657}, 
     {309/500, 0.8721881060680485}, {619/1000, 0.8723507828068724}, 
     {31/50, 0.8725135477874952}, {621/1000, 0.8726762756952722}, 
     {311/500, 0.872838473348786}, {623/1000, 0.873000837743392}, 
     {78/125, 0.8731631253205223}, {5/8, 0.8733255055620752}, 
     {313/500, 0.8734873398135818}, {627/1000, 0.8736492949490906}, 
     {157/250, 0.8738111624791154}, {629/1000, 0.8739729843653821}, 
     {63/100, 0.8741346083464867}, {631/1000, 0.874296217409803}, 
     {79/125, 0.8744576810016764}, {633/1000, 0.8746186959205928}, 
     {317/500, 0.8747801646466451}, {127/200, 0.8749411627279098}, 
     {159/250, 0.875102057567386}, {637/1000, 0.8752628133723555}, 
     {319/500, 0.8754235099337293}, {639/1000, 0.8755842195398913}, 
     {16/25, 0.875744584009819}, {641/1000, 0.8759049602410465}, 
     {321/500, 0.8760654033028867}, {643/1000, 0.876225434672107}, 
     {161/250, 0.8763855882731852}, {129/200, 0.8765452568985417}, 
     {323/500, 0.8767052395066333}, {647/1000, 0.8768647029686598}, 
     {81/125, 0.8770242226555833}, {649/1000, 0.8771836419983758}, 
     {13/20, 0.8773429580921237}, {651/1000, 0.8775022425202816}, 
     {163/250, 0.8776610406023553}, {653/1000, 0.8778201068146392}, 
     {327/500, 0.877979119668554}, {131/200, 0.8781375862688063}, 
     {82/125, 0.8782961687039359}, {657/1000, 0.8784545647208899}, 
     {329/500, 0.8786128797244921}, {659/1000, 0.8787711768224498}, 
     {33/50, 0.878929348921935}, {661/1000, 0.8790870559663131}, 
     {331/500, 0.8792448812757581}, {663/1000, 0.8794026692051159}, 
     {83/125, 0.8795599922710192}, {133/200, 0.8797176410449077}, 
     {333/500, 0.8798749340037546}, {667/1000, 0.8800319597960842}, 
     {167/250, 0.8801891528361689}, {669/1000, 0.8803459369030682}, 
     {67/100, 0.8805025830400294}, {671/1000, 0.8806594915942367}, 
     {84/125, 0.8808160008301462}, {673/1000, 0.8809722567422066}, 
     {337/500, 0.8811284034250038}, {27/40, 0.8812848418159798}, 
     {169/250, 0.8814405859316017}, {677/1000, 0.8815963497919308}, 
     {339/500, 0.8817523089053225}, {679/1000, 0.8819077379225921}, 
     {17/25, 0.8820633153222963}, {681/1000, 0.8822185188904543}, 
     {341/500, 0.882373727290307}, {683/1000, 0.882528628059104}, 
     {171/250, 0.8826835552749168}, {137/200, 0.8828385506779457}, 
     {343/500, 0.8829929803538756}, {687/1000, 0.8831475750987512}, 
     {86/125, 0.8833021046091499}, {689/1000, 0.8834563084778726}, 
     {69/100, 0.8836104179445522}, {691/1000, 0.8837640788917014}, 
     {173/250, 0.8839178969193642}, {693/1000, 0.8840717052680752}, 
     {347/500, 0.8842252454620557}, {139/200, 0.8843786175045454}, 
     {87/125, 0.8845318802458471}, {697/1000, 0.8846852176649778}, 
     {349/500, 0.8848381170737265}, {699/1000, 0.8849907741859249}, 
     {7/10, 0.8851434635427293}, {701/1000, 0.8852961678562377}, 
     {351/500, 0.8854484365779526}, {703/1000, 0.8856008403089848}, 
     {88/125, 0.8857528316065281}, {141/200, 0.8859048222186225}, 
     {353/500, 0.8860566186124144}, {707/1000, 0.8862082261901775}, 
     {177/250, 0.8863598594680893}, {709/1000, 0.886511244368545}, 
     {71/100, 0.8866626598291747}, {711/1000, 0.8868138860035808}, 
     {89/125, 0.8869646193863361}, {713/1000, 0.8871154086292294}, 
     {357/500, 0.8872662314984687}, {143/200, 0.8874168673044851}, 
     {179/250, 0.887566926615568}, {717/1000, 0.8877172396126694}, 
     {359/500, 0.887867358855545}, {719/1000, 0.8880172910550432}, 
     {18/25, 0.8881670477417217}, {721/1000, 0.8883169957091022}, 
     {361/500, 0.8884663998095403}, {723/1000, 0.8886154584797368}, 
     {181/250, 0.8887647533877023}, {29/40, 0.8889137903697596}, 
     {363/500, 0.8890627329579106}, {727/1000, 0.8892113522165273}, 
     {91/125, 0.8893600813067515}, {729/1000, 0.8895085217152889}, 
     {73/100, 0.8896568226875632}, {731/1000, 0.8898049653530673}, 
     {183/250, 0.8899529898602998}, {733/1000, 0.8901008227051974}, 
     {367/500, 0.8902485238383429}, {147/200, 0.8903963560233248}, 
     {92/125, 0.8905434696352705}, {737/1000, 0.8906907304110017}, 
     {369/500, 0.8908378138965218}, {739/1000, 0.8909850757688484}, 
     {37/50, 0.8911315727590501}, {741/1000, 0.8912781987147358}, 
     {371/500, 0.8914249788315838}, {743/1000, 0.8915709140945719}, 
     {93/125, 0.8917172069985297}, {149/200, 0.8918631985026493}, 
     {373/500, 0.8920093258474013}, {747/1000, 0.8921547852929644}, 
     {187/250, 0.892300623223317}, {749/1000, 0.8924457709875027}, 
     {3/4, 0.8925912722901265}, {751/1000, 0.8927360929966138}, 
     {94/125, 0.8928810476929089}, {753/1000, 0.8930258188127311}, 
     {377/500, 0.8931705647953588}, {151/200, 0.8933149252238838}, 
     {189/250, 0.8934592251859986}, {757/1000, 0.8936033988965604}, 
     {379/500, 0.8937477203827492}, {759/1000, 0.8938913030481893}, 
     {19/25, 0.8940352142582242}, {761/1000, 0.8941785062266415}, 
     {381/500, 0.894321930509121}, {763/1000, 0.8944654212195431}, 
     {191/250, 0.8946084664128426}, {153/200, 0.8947509454828146}, 
     {383/500, 0.8948940494485806}, {767/1000, 0.8950362930732995}, 
     {96/125, 0.895178775922588}, {769/1000, 0.8953211330954246}, 
     {77/100, 0.8954632091677996}, {771/1000, 0.8956054613294322}, 
     {193/250, 0.8957469961561031}, {773/1000, 0.8958886381677258}, 
     {387/500, 0.8960300890083376}, {31/40, 0.8961715632306695}, 
     {97/125, 0.8963128767093665}, {777/1000, 0.8964539111161209}, 
     {389/500, 0.8965947696442131}, {779/1000, 0.8967351204236851}, 
     {39/50, 0.8968756346806832}, {781/1000, 0.8970163025701157}, 
     {391/500, 0.8971562416971777}, {783/1000, 0.8972965515340534}, 
     {98/125, 0.8974361810915126}, {157/200, 0.8975759054968941}, 
     {393/500, 0.8977157578119868}, {787/1000, 0.8978551384346929}, 
     {197/250, 0.8979944359318919}, {789/1000, 0.8981332007205779}, 
     {79/100, 0.8982721098536802}, {791/1000, 0.8984108784422264}, 
     {99/125, 0.8985497264756157}, {793/1000, 0.8986879068760618}, 
     {397/500, 0.8988262334153375}, {159/200, 0.898964161354015}, 
     {199/250, 0.8991025421608954}, {797/1000, 0.8992400234267777}, 
     {399/500, 0.8993779653940281}, {799/1000, 0.8995151324682551}, 
     {4/5, 0.8996524813199694}, {801/1000, 0.899789919070751}, 
     {401/500, 0.8999268964477855}, {803/1000, 0.9000633799154538}, 
     {201/250, 0.9002003183888807}, {161/200, 0.9003365482792134}, 
     {403/500, 0.9004728774579016}, {807/1000, 0.9006089212542687}, 
     {101/125, 0.9007453340646188}, {809/1000, 0.9008811849612344}, 
     {81/100, 0.9010168551497345}, {811/1000, 0.9011523953669104}, 
     {203/250, 0.9012874026649722}, {813/1000, 0.9014225839491776}, 
     {407/500, 0.9015579946507759}, {163/200, 0.901692361517108}, 
     {102/125, 0.9018272467387412}, {817/1000, 0.9019617374967617}, 
     {409/500, 0.9020964080327505}, {819/1000, 0.9022301912226449}, 
     {41/50, 0.9023643627505844}, {821/1000, 0.9024982717479504}, 
     {411/500, 0.9026319599415626}, {823/1000, 0.9027655282351754}, 
     {103/125, 0.9028992184306612}, {33/40, 0.9030324497317546}, 
     {413/500, 0.9031652186233103}, {827/1000, 0.9032979543475491}, 
     {207/250, 0.9034311368594323}, {829/1000, 0.9035637425614234}, 
     {83/100, 0.9036958043579575}, {831/1000, 0.9038280387726341}, 
     {104/125, 0.9039604599453381}, {833/1000, 0.9040923835439648}, 
     {417/500, 0.9042236566443156}, {167/200, 0.9043552310673635}, 
     {209/250, 0.9044868052257671}, {837/1000, 0.9046179071875868}, 
     {419/500, 0.9047494807264316}, {839/1000, 0.9048801124565016}, 
     {21/25, 0.9050108829419938}, {841/1000, 0.905141473700535}, 
     {421/500, 0.9052718774696531}, {843/1000, 0.9054024471993793}, 
     {211/250, 0.9055322434945199}, {169/200, 0.9056621993918437}, 
     {423/500, 0.9057920119505458}, {847/1000, 0.9059219145855066}, 
     {106/125, 0.9060509994977155}, {849/1000, 0.9061803285313156}, 
     {17/20, 0.9063094465638903}, {851/1000, 0.9064381992898131}, 
     {213/250, 0.9065674785097968}, {853/1000, 0.9066957873799262}, 
     {427/500, 0.9068240772712558}, {171/200, 0.906952862440698}, 
     {107/125, 0.9070804962676243}, {857/1000, 0.9072084431848269}, 
     {429/500, 0.9073367383681366}, {859/1000, 0.9074644090310345}, 
     {43/50, 0.9075918567920203}, {861/1000, 0.9077191864143092}, 
     {431/500, 0.9078463193494029}, {863/1000, 0.9079727594555544}, 
     {108/125, 0.9080997570223137}, {173/200, 0.9082264278725249}, 
     {433/500, 0.9083532145934068}, {867/1000, 0.9084795248559745}, 
     {217/250, 0.9086051818513088}, {869/1000, 0.9087316485940589}, 
     {87/100, 0.9088575172250963}, {871/1000, 0.9089828200759674}, 
     {109/125, 0.9091083011268082}, {873/1000, 0.9092339945818436}, 
     {437/500, 0.9093587793849283}, {7/8, 0.9094838071519016}, 
     {219/250, 0.9096089639917525}, {877/1000, 0.9097333132016343}, 
     {439/500, 0.909857796206449}, {879/1000, 0.9099821400278532}, 
     {22/25, 0.9101061238660343}, {881/1000, 0.9102303472950065}, 
     {441/500, 0.9103542022999649}, {883/1000, 0.9104778509291802}, 
     {221/250, 0.9106013933061268}, {177/200, 0.9107250156765712}, 
     {443/500, 0.9108482266660761}, {887/1000, 0.9109707670872923}, 
     {111/125, 0.9110937842238209}, {889/1000, 0.9112165160245542}, 
     {89/100, 0.911339365188053}, {891/1000, 0.9114617502065796}, 
     {223/250, 0.9115836069445006}, {893/1000, 0.911705451650973}, 
     {447/500, 0.9118278220609832}, {179/200, 0.9119492263084008}, 
     {112/125, 0.9120707913613234}, {897/1000, 0.9121919821300194}, 
     {449/500, 0.9123131764135584}, {899/1000, 0.9124344506888106}, 
     {9/10, 0.9125553471519771}, {901/1000, 0.912676068766578}, 
     {451/500, 0.912796452343716}, {903/1000, 0.9129170439025018}, 
     {113/125, 0.9130370844213426}, {181/200, 0.9131571640876022}, 
     {453/500, 0.9132770671340322}, {907/1000, 0.913396820940424}, 
     {227/250, 0.9135169210162721}, {909/1000, 0.9136363565290873}, 
     {91/100, 0.9137551109133086}, {911/1000, 0.9138743835131165}, 
     {114/125, 0.9139931107144224}, {913/1000, 0.9141118936834073}, 
     {457/500, 0.9142309613024718}, {183/200, 0.9143489366576741}, 
     {229/250, 0.9144674189640487}, {917/1000, 0.9145858626714763}, 
     {459/500, 0.9147037992415786}, {919/1000, 0.9148216266553345}, 
     {23/25, 0.9149389420978682}, {921/1000, 0.915056190534351}, 
     {461/500, 0.9151737021628867}, {923/1000, 0.9152906406094488}, 
     {231/250, 0.9154081772321524}, {37/40, 0.9155249808160466}, 
     {463/500, 0.9156411023008599}, {927/1000, 0.9157578253975545}, 
     {116/125, 0.9158739322289751}, {929/1000, 0.9159906406654748}, 
     {93/100, 0.9161063524431601}, {931/1000, 0.9162221653579834}, 
     {233/250, 0.9163378624726647}, {933/1000, 0.9164533784139408}, 
     {467/500, 0.916568551106764}, {187/200, 0.9166842317761845}, 
     {117/125, 0.9167993336927682}, {937/1000, 0.9169138563668666}, 
     {469/500, 0.9170288873393247}, {939/1000, 0.9171431610893326}, 
     {47/50, 0.9172575272867467}, {941/1000, 0.9173721295918666}, 
     {471/500, 0.9174858721283912}, {943/1000, 0.9175998055515209}, 
     {118/125, 0.9177133485743948}, {189/200, 0.9178271148626711}, 
     {473/500, 0.9179408856172173}, {947/1000, 0.9180538632386436}, 
     {237/250, 0.9181667684012402}, {949/1000, 0.9182799103913502}, 
     {19/20, 0.9183930111456823}, {951/1000, 0.9185056376836729}, 
     {119/125, 0.9186178239053858}, {953/1000, 0.9187301617226746}, 
     {477/500, 0.918842322882109}, {191/200, 0.9189546248067624}, 
     {239/250, 0.9190664633533654}, {957/1000, 0.9191778019576688}, 
     {479/500, 0.9192893492552355}, {959/1000, 0.9194004879367814}, 
     {24/25, 0.919512193597732}, {961/1000, 0.9196229296631149}, 
     {481/500, 0.9197338473210324}, {963/1000, 0.9198445460616582}, 
     {241/250, 0.9199551104446606}, {193/200, 0.9200655217835966}, 
     {483/500, 0.9201757770781562}, {967/1000, 0.9202856445610808}, 
     {121/125, 0.9203961308677426}, {969/1000, 0.9205055903325408}, 
     {97/100, 0.9206155344606224}, {971/1000, 0.9207250243078792}, 
     {243/250, 0.9208337494677747}, {973/1000, 0.9209428860653365}, 
     {487/500, 0.9210524243800872}, {39/40, 0.9211607140203845}, 
     {122/125, 0.9212694039096843}, {977/1000, 0.921378130336141}, 
     {489/500, 0.9214864919040242}, {979/1000, 0.9215950065555798}, 
     {49/50, 0.9217025408211109}, {981/1000, 0.9218106211722273}, 
     {491/500, 0.9219183617115652}, {983/1000, 0.9220257339488473}, 
     {123/125, 0.9221336967961249}, {197/200, 0.9222406075032366}, 
     {493/500, 0.9223477373472548}, {987/1000, 0.9224550352469707}, 
     {247/250, 0.922561494567914}, {989/1000, 0.9226679148408904}, 
     {99/100, 0.922774939781096}, {991/1000, 0.9228809348264607}, 
     {124/125, 0.9229871435073778}, {993/1000, 0.9230931596177026}, 
     {497/500, 0.9231990363385743}, {199/200, 0.923304713884402}, 
     {249/250, 0.9234100821870164}, {997/1000, 0.923516022945212}, 
     {499/500, 0.9236212557853359}, {999/1000, 0.923726074704956}, 
     {1, 0.9238309855127701}}
 
ReERfinc = {{1, 0.9238561075656262}, {201/200, 0.9243777859624978}, 
     {101/100, 0.9248956464711466}, {203/200, 0.925409706867305}, 
     {51/50, 0.925919985675224}, {41/40, 0.9264264398484887}, 
     {103/100, 0.926929198366007}, {207/200, 0.9274282250907028}, 
     {26/25, 0.9279235426807995}, {209/200, 0.9284151807078899}, 
     {21/20, 0.9289031469867092}, {211/200, 0.9293874568005009}, 
     {53/50, 0.9298681286065203}, {213/200, 0.9303451951171604}, 
     {107/100, 0.9308186405208162}, {43/40, 0.9312885320473342}, 
     {27/25, 0.9317548687604369}, {217/200, 0.9322176610321755}, 
     {109/100, 0.9326769740103296}, {219/200, 0.9331327726278048}, 
     {11/10, 0.9335851196080136}, {221/200, 0.9340340180133939}, 
     {111/100, 0.9344794818423008}, {223/200, 0.9349215306097709}, 
     {28/25, 0.935360184178241}, {9/8, 0.9357954735962135}, 
     {113/100, 0.9362274357082523}, {227/200, 0.9366560454347631}, 
     {57/50, 0.9370813471828304}, {229/200, 0.9375033672648474}, 
     {23/20, 0.937922128439941}, {231/200, 0.9383376521644679}, 
     {29/25, 0.9387499585321954}, {233/200, 0.9391590674680714}, 
     {117/100, 0.9395649982952526}, {47/40, 0.9399677376234828}, 
     {59/50, 0.9403673630949365}, {237/200, 0.9407638571874022}, 
     {119/100, 0.9411572511011925}, {239/200, 0.9415475673169965}, 
     {6/5, 0.9419348345020226}, {241/200, 0.9423190737446129}, 
     {121/100, 0.942700305501081}, {243/200, 0.9430785486636517}, 
     {61/50, 0.9434538222763882}, {49/40, 0.9438261044334608}, 
     {123/100, 0.9441954694797597}, {247/200, 0.9445619268628004}, 
     {31/25, 0.9449255020913944}, {249/200, 0.9452862155186499}, 
     {5/4, 0.9456440859485135}, {251/200, 0.9459991326591739}, 
     {63/50, 0.946351375402237}, {253/200, 0.946700784668431}, 
     {127/100, 0.9470474619730805}, {51/40, 0.9473913751453056}, 
     {32/25, 0.947732558930416}, {257/200, 0.948071040091214}, 
     {129/100, 0.9484068498468229}, {259/200, 0.948739998321095}, 
     {13/10, 0.9490705009823038}, {261/200, 0.9493983645221086}, 
     {131/100, 0.9497236345676142}, {263/200, 0.9500463221476588}, 
     {33/25, 0.9503664417344246}, {53/40, 0.950684017366748}, 
     {133/100, 0.9509990679581131}, {267/200, 0.9513116030634357}, 
     {67/50, 0.9516216426288348}, {269/200, 0.9519292015925702}, 
     {27/20, 0.9522343282843255}, {271/200, 0.9525370438581948}, 
     {34/25, 0.9528373479615302}, {273/200, 0.9531352494878799}, 
     {137/100, 0.9534307868925128}, {11/8, 0.9537239761611257}, 
     {69/50, 0.9540148316354455}, {277/200, 0.9543033547953943}, 
     {139/100, 0.9545895644831573}, {279/200, 0.9548735222482558}, 
     {7/5, 0.955155240600159}, {281/200, 0.9554347101952637}, 
     {141/100, 0.9557119628211918}, {283/200, 0.9559870089256178}, 
     {71/50, 0.9562598603018033}, {57/40, 0.9565305575210244}, 
     {143/100, 0.9567990648625609}, {287/200, 0.9570654643373395}, 
     {36/25, 0.9573297545021767}, {289/200, 0.9575919666497021}, 
     {29/20, 0.9578521087360969}, {291/200, 0.958110187647858}, 
     {73/50, 0.958366199029133}, {293/200, 0.9586201855848657}, 
     {147/100, 0.9588722120659356}, {59/40, 0.959122200947915}, 
     {37/25, 0.9593702363413759}, {297/200, 0.95961631679992}, 
     {149/100, 0.9598604519802431}, {299/200, 0.960102657649009}, 
     {3/2, 0.9603429516387055}, {301/200, 0.960581349518717}, 
     {151/100, 0.9608178777308902}, {303/200, 0.9610525552113565}, 
     {38/25, 0.9612853918262433}, {61/40, 0.9615164065347469}, 
     {153/100, 0.961745614729226}, {307/200, 0.9619730309882885}, 
     {77/50, 0.9621986646302375}, {309/200, 0.9624225476819884}, 
     {31/20, 0.9626446707070715}, {311/200, 0.9628650685222276}, 
     {39/25, 0.9630837135995692}, {313/200, 0.963300681102354}, 
     {157/100, 0.9635159581717201}, {63/40, 0.9637295596158042}, 
     {79/50, 0.9639415017588673}, {317/200, 0.9641518004661461}, 
     {159/100, 0.9643604704847599}, {319/200, 0.9645675257412196}, 
     {8/5, 0.9647729827561594}, {321/200, 0.9649768992449356}, 
     {161/100, 0.9651792051812998}, {323/200, 0.9653799468278333}, 
     {81/50, 0.9655791370934078}, {13/8, 0.9657767971351894}, 
     {163/100, 0.9659729549429826}, {327/200, 0.9661675963948788}, 
     {41/25, 0.9663607400481317}, {329/200, 0.9665524015932352}, 
     {33/20, 0.9667425971280741}, {331/200, 0.9669313417154535}, 
     {83/50, 0.9671186493822507}, {333/200, 0.9673045898576718}, 
     {167/100, 0.9674890351747031}, {67/40, 0.9676721004390756}, 
     {42/25, 0.9678537688890656}, {337/200, 0.9680340905893328}, 
     {169/100, 0.9682130148711172}, {339/200, 0.9683905821766621}, 
     {17/10, 0.9685667721767953}, {341/200, 0.9687416784905056}, 
     {171/100, 0.9689152656891837}, {343/200, 0.9690875553516347}, 
     {43/25, 0.9692585438291733}, {69/40, 0.9694282254751991}, 
     {173/100, 0.9695966497718636}, {347/200, 0.9697637883580414}, 
     {87/50, 0.9699296769739945}, {349/200, 0.9700943258134531}, 
     {7/4, 0.9702577485070176}, {351/200, 0.9704199563427278}, 
     {44/25, 0.9705809644790708}, {353/200, 0.9707407571622614}, 
     {177/100, 0.9708993755653154}, {71/40, 0.9710568174849561}, 
     {89/50, 0.9712130950330101}, {357/200, 0.971368209481193}, 
     {179/100, 0.9715221693811327}, {359/200, 0.9716749287043219}, 
     {9/5, 0.9718266328191263}, {361/200, 0.9719772125025691}, 
     {181/100, 0.9721266579723608}, {363/200, 0.972275010835695}, 
     {91/50, 0.9724222769854357}, {73/40, 0.9725684765552126}, 
     {183/100, 0.9727136300172913}, {367/200, 0.9728576534677335}, 
     {46/25, 0.9730006674270087}, {369/200, 0.9731426136738786}, 
     {37/20, 0.9732835148048276}, {371/200, 0.9734233898456727}, 
     {93/50, 0.9735622489949061}, {373/200, 0.9737001303718499}, 
     {187/100, 0.9738369715812868}, {15/8, 0.9739728302752906}, 
     {47/25, 0.9741077395356275}, {377/200, 0.9742416557074386}, 
     {189/100, 0.9743745922659088}, {379/200, 0.9745065849910384}, 
     {19/10, 0.974637620533572}, {381/200, 0.9747677047793082}, 
     {191/100, 0.9748968443039807}, {383/200, 0.9750250541032606}, 
     {48/25, 0.975152366608897}, {77/40, 0.9752787437818798}, 
     {193/100, 0.9754042694096867}, {387/200, 0.9755288768301555}, 
     {97/50, 0.9756525963043647}, {389/200, 0.9757754272561547}, 
     {39/20, 0.9758973713732272}, {391/200, 0.9760184507388497}, 
     {49/25, 0.9761386807962451}, {393/200, 0.9762580768149769}, 
     {197/100, 0.9763766175462308}, {79/40, 0.9764943157400384}, 
     {99/50, 0.9766111870991934}, {397/200, 0.9767272473013917}, 
     {199/100, 0.9768424888771103}, {399/200, 0.976956936654897}, 
     {2, 0.9770705737407667}, {401/200, 0.9771834168139193}, 
     {201/100, 0.9772954640020873}, {403/200, 0.9774067267919709}, 
     {101/50, 0.9775172096856767}, {81/40, 0.9776269268436372}, 
     {203/100, 0.9777358864331679}, {407/200, 0.9778440951661573}, 
     {51/25, 0.9779515555167705}, {409/200, 0.9780582800719587}, 
     {41/20, 0.9781642706366006}, {411/200, 0.9782695379686921}, 
     {103/50, 0.9783740582436112}, {413/200, 0.9784778779154251}, 
     {207/100, 0.9785809776616974}, {83/40, 0.9786833700763125}, 
     {52/25, 0.9787850604153099}, {417/200, 0.9788860568647874}, 
     {209/100, 0.9789863699574372}, {419/200, 0.9790860058199954}, 
     {21/10, 0.9791849698245737}, {421/200, 0.9792832670493257}, 
     {211/100, 0.9793809014012005}, {423/200, 0.9794778776020635}, 
     {53/25, 0.97957418162595}, {17/8, 0.9796698488656808}, 
     {213/100, 0.9797648700337837}, {427/200, 0.9798592457422041}, 
     {107/50, 0.9799529907879103}, {429/200, 0.980046110843201}, 
     {43/20, 0.9801386206400603}, {431/200, 0.9802305120623682}, 
     {54/25, 0.9803217753194626}, {433/200, 0.9804124658722678}, 
     {217/100, 0.98050255348153}, {87/40, 0.9805920370246177}, 
     {109/50, 0.9806809257217362}, {437/200, 0.9807692180765527}, 
     {219/100, 0.9808569268677028}, {439/200, 0.9809440634715425}, 
     {11/5, 0.981030609914192}, {441/200, 0.9811166164681188}, 
     {221/100, 0.981202076601122}, {443/200, 0.9812869619442618}, 
     {111/50, 0.9813713077744842}, {89/40, 0.9814551058578356}, 
     {223/100, 0.981538344957887}, {447/200, 0.9816210178747096}, 
     {56/25, 0.9817031705676609}, {449/200, 0.9817847956304383}, 
     {9/4, 0.9818659204461325}, {451/200, 0.981946498167852}, 
     {113/50, 0.982026571099524}, {453/200, 0.982106137044228}, 
     {227/100, 0.9821852049869673}, {91/40, 0.9822637204117969}, 
     {57/25, 0.9823417480537608}, {457/200, 0.9824193031388337}, 
     {229/100, 0.9824963401253305}, {459/200, 0.9825728770026141}, 
     {23/10, 0.9826489445414346}, {461/200, 0.9827245570763177}, 
     {231/100, 0.9827996801463288}, {463/200, 0.9828743316361492}, 
     {58/25, 0.9829484711354305}, {93/40, 0.9830221803088073}, 
     {233/100, 0.9830954051229822}, {467/200, 0.9831681662498407}, 
     {117/50, 0.9832404865522594}, {469/200, 0.9833123645550448}, 
     {47/20, 0.9833837784480459}, {471/200, 0.983454758550837}, 
     {59/25, 0.9835252949255123}, {473/200, 0.98359540976995}, 
     {237/100, 0.9836650540938627}, {19/8, 0.983734298274201}, 
     {119/50, 0.9838031135427641}, {477/200, 0.9838714607081168}, 
     {239/100, 0.9839394220160951}, {479/200, 0.9840069495307108}, 
     {12/5, 0.984074084721069}, {481/200, 0.9841407853453431}, 
     {241/100, 0.9842070917781472}, {483/200, 0.9842730254479622}, 
     {121/50, 0.9843384905104159}, {97/40, 0.9844035817537317}, 
     {243/100, 0.9844682751294636}, {487/200, 0.9845325785798276}, 
     {61/25, 0.9845964922441534}, {489/200, 0.9846600245554593}, 
     {49/20, 0.9847231750639307}, {491/200, 0.9847859499604049}, 
     {123/50, 0.9848483443647963}, {493/200, 0.9849106638216226}, 
     {247/100, 0.9849723080253264}, {99/40, 0.9850335736350123}, 
     {62/25, 0.985094463543414}, {497/200, 0.9851549834428888}, 
     {249/100, 0.9852151404992648}, {499/200, 0.9852749543827997}, 
     {5/2, 0.9853344382519691}, {501/200, 0.985393586964174}, 
     {251/100, 0.9854523857995867}, {503/200, 0.9855108206517181}, 
     {63/25, 0.9855688720315757}, {101/40, 0.9856262403143761}, 
     {253/100, 0.9856836452585513}, {507/200, 0.9857406882397621}, 
     {127/50, 0.9857974236937761}, {509/200, 0.9858538040354057}, 
     {51/20, 0.9859100844467616}, {511/200, 0.9859655525007136}, 
     {64/25, 0.9860209407294634}, {513/200, 0.9860760227578261}, 
     {257/100, 0.9861307933862701}, {103/40, 0.9861855388186576}, 
     {129/50, 0.9862393885649635}, {517/200, 0.98629318870278}, 
     {259/100, 0.9863466942764015}, {519/200, 0.9863998856135695}, 
     {13/5, 0.9864531004084033}, {521/200, 0.9865053437566046}, 
     {261/100, 0.9865576332972741}, {523/200, 0.9866096172729341}, 
     {131/50, 0.9866613033108463}, {21/8, 0.9867126947140856}, 
     {263/100, 0.9867640893201591}, {527/200, 0.9868146156331763}, 
     {66/25, 0.9868651397589516}, {529/200, 0.9869153578940896}, 
     {53/20, 0.9869653062012038}, {531/200, 0.9870149850039729}, 
     {133/50, 0.9870643640603862}, {533/200, 0.9871134668081326}, 
     {267/100, 0.9871623330221005}, {107/40, 0.9872108644808524}, 
     {67/25, 0.9872591528311571}, {537/200, 0.98730718061735}, 
     {269/100, 0.9873549683926597}, {539/200, 0.9874024140123367}, 
     {27/10, 0.9874496287286311}, {541/200, 0.9874966026697624}, 
     {271/100, 0.9875433153050727}, {543/200, 0.9875897456126078}, 
     {68/25, 0.987635924579753}, {109/40, 0.9876818947908785}, 
     {273/100, 0.9877275704264449}, {547/200, 0.9877729733147755}, 
     {137/50, 0.987818200426374}, {549/200, 0.9878631062202298}, 
     {11/4, 0.987907783240289}, {551/200, 0.9879522072968407}, 
     {69/25, 0.9879964243289054}, {553/200, 0.9880403961273719}, 
     {277/100, 0.988084109486107}, {111/40, 0.988127597121467}, 
     {139/50, 0.9881708385178026}, {557/200, 0.988213866210798}, 
     {279/100, 0.9882566110203579}, {559/200, 0.9882991721835045}, 
     {14/5, 0.9883415153929758}, {561/200, 0.9883836278488942}, 
     {281/100, 0.9884255181799164}, {563/200, 0.9884671478114616}, 
     {141/50, 0.9885085724912779}, {113/40, 0.9885500786162051}, 
     {283/100, 0.9885910638207142}, {567/200, 0.9886318170278233}, 
     {71/25, 0.9886723510898202}, {569/200, 0.9887126743334111}, 
     {57/20, 0.9887527994114456}, {571/200, 0.9887927276524459}, 
     {143/50, 0.9888324380907021}, {573/200, 0.988871653798555}, 
     {287/100, 0.9889109404862403}, {23/8, 0.9889500236420802}, 
     {72/25, 0.988988895853733}, {577/200, 0.9890275720587135}, 
     {289/100, 0.9890660436442997}, {579/200, 0.989104288346632}, 
     {29/10, 0.9891423544843914}, {581/200, 0.9891802226657214}, 
     {291/100, 0.9892179088858851}, {583/200, 0.9892553873305128}, 
     {73/25, 0.9892926914606576}, {117/40, 0.9893300116212246}, 
     {293/100, 0.989366942137421}, {587/200, 0.9894034105533452}, 
     {147/50, 0.9894399379452923}, {589/200, 0.989476252911493}, 
     {59/20, 0.9895126900143187}, {591/200, 0.9895483514009856}, 
     {74/25, 0.9895841387919486}, {593/200, 0.9896197651709006}, 
     {297/100, 0.9896555013238144}, {119/40, 0.989690431574277}, 
     {149/50, 0.9897254951388701}, {597/200, 0.989760366247168}, 
     {299/100, 0.9897950156091897}, {599/200, 0.9898298619892195}, 
     {3, 0.9898639598550305}, {601/200, 0.9898981485851249}, 
     {301/100, 0.989932159144645}, {603/200, 0.9899659704897087}, 
     {151/50, 0.9899999513593994}, {121/40, 0.9900331826496679}, 
     {303/100, 0.9900665235774424}, {607/200, 0.9900996810648074}, 
     {76/25, 0.9901325746390545}, {609/200, 0.9901655289605054}, 
     {61/20, 0.9901982148665348}, {611/200, 0.9902307390708294}, 
     {153/50, 0.9902630677496315}, {613/200, 0.9902952797655517}, 
     {307/100, 0.9903273280479801}, {123/40, 0.9903591982179245}, 
     {77/25, 0.9903908976636232}, {617/200, 0.9904224623177513}, 
     {309/100, 0.9904538855093629}, {619/200, 0.9904851168875036}, 
     {31/10, 0.9905162275474784}, {621/200, 0.990547196204724}, 
     {311/100, 0.9905780152357101}, {623/200, 0.9906086541313476}, 
     {78/25, 0.9906391435321713}, {25/8, 0.9906694929376176}, 
     {313/100, 0.9906996938789673}, {627/200, 0.990729747548607}, 
     {157/50, 0.9907596713530501}, {629/200, 0.9907894739446294}, 
     {63/20, 0.9908191071341536}, {631/200, 0.990848581972725}, 
     {79/25, 0.9908779255895245}, {633/200, 0.9909071140811607}, 
     {317/100, 0.9909361660396389}, {127/40, 0.9909650963029646}, 
     {159/50, 0.9909939018704729}, {637/200, 0.9910225647541063}, 
     {319/100, 0.99105109685221}, {639/200, 0.9910794514824938}, 
     {16/5, 0.9911076845131441}, {641/200, 0.9911358085845925}, 
     {321/100, 0.9911637707830737}, {643/200, 0.9911916086216425}, 
     {161/50, 0.9912193217679954}, {129/40, 0.9912469072250545}, 
     {323/100, 0.9912743698804621}, {647/200, 0.9913017110117176}, 
     {81/25, 0.9913289166520213}, {649/200, 0.9913559735089434}, 
     {13/4, 0.9913829275704464}, {651/200, 0.9914097430421248}, 
     {163/50, 0.9914364258851168}, {653/200, 0.9914629807121434}, 
     {327/100, 0.9914894239265677}, {131/40, 0.9915157292221491}, 
     {82/25, 0.9915419403083409}, {657/200, 0.9915680486056089}, 
     {329/100, 0.9915942728952186}, {659/200, 0.9916200576526633}, 
     {33/10, 0.9916455678267054}, {661/200, 0.9916711557614092}, 
     {331/100, 0.991696667177977}, {663/200, 0.9917220215144602}, 
     {83/25, 0.9917471779623073}, {133/40, 0.9917724151645383}, 
     {333/100, 0.9917977193199038}, {667/200, 0.9918223865622839}, 
     {167/50, 0.9918471473889631}, {669/200, 0.9918718567892869}, 
     {67/20, 0.9918963190206715}, {671/200, 0.9919207835129522}, 
     {84/25, 0.991945457944646}, {673/200, 0.9919694559833997}, 
     {337/100, 0.991993586097498}, {27/8, 0.9920176111979466}, 
     {169/50, 0.9920415388178672}, {677/200, 0.9920653558644641}, 
     {339/100, 0.9920890698914568}, {679/200, 0.9921126581481038}, 
     {17/5, 0.9921361338295759}, {681/200, 0.9921595393860559}, 
     {341/100, 0.9921828097959892}, {683/200, 0.992205978679968}, 
     {171/50, 0.992229053794691}, {137/40, 0.99225205235126}, 
     {343/100, 0.9922749335732327}, {687/200, 0.9922977045313355}, 
     {86/25, 0.9923203698043849}, {689/200, 0.9923429433075778}, 
     {69/20, 0.9923654035001529}, {691/200, 0.9923877629668343}, 
     {173/50, 0.9924100466696625}, {693/200, 0.9924322358588568}, 
     {347/100, 0.9924543249368509}, {139/40, 0.9924762909825391}, 
     {87/25, 0.9924981936041287}, {697/200, 0.9925199885975371}, 
     {349/100, 0.9925416862466562}, {699/200, 0.9925632816794471}, 
     {7/2, 0.9925847785453786}, {701/200, 0.9926061805547699}, 
     {351/100, 0.9926275144829537}, {703/200, 0.9926487643853636}, 
     {88/25, 0.9926699306033391}, {141/40, 0.992690965063944}, 
     {353/100, 0.9927119237455345}, {707/200, 0.9927328010122323}, 
     {177/50, 0.9927535723820379}, {709/200, 0.992774229689742}, 
     {71/20, 0.9927948521062897}, {711/200, 0.9928153833239959}, 
     {89/25, 0.9928357816041524}, {713/200, 0.9928561387209415}, 
     {357/100, 0.9928764055447982}, {143/40, 0.9928965502764}, 
     {179/50, 0.992916631512524}, {717/200, 0.9929366146541785}, 
     {359/100, 0.9929565216782802}, {719/200, 0.9929763541279617}, 
     {18/5, 0.9929961077995574}, {721/200, 0.9930157778368958}, 
     {361/100, 0.993035363198548}, {723/200, 0.9930548616741111}, 
     {181/50, 0.993074270024772}, {29/8, 0.993093568463564}, 
     {363/100, 0.9931128162879025}, {727/200, 0.993131991872652}, 
     {91/25, 0.9931510962621793}, {729/200, 0.9931701172902473}, 
     {73/20, 0.9931890566322522}, {731/200, 0.9932079149039011}, 
     {183/50, 0.9932266846482523}, {733/200, 0.9932453871470128}, 
     {367/100, 0.9932640049481413}, {147/40, 0.9932825355917613}, 
     {92/25, 0.9933009848698037}, {737/200, 0.9933193716720778}, 
     {369/100, 0.9933376964415201}, {739/200, 0.9933559481238018}, 
     {37/10, 0.9933741220831754}, {741/200, 0.9933922110706682}, 
     {371/100, 0.993410225824199}, {743/200, 0.9934281705884779}, 
     {93/25, 0.9934460320062761}, {149/40, 0.9934637958687477}, 
     {373/100, 0.99348152231394}, {747/200, 0.9934991881255585}, 
     {187/50, 0.9935167785046666}, {749/200, 0.9935342773092396}, 
     {15/4, 0.9935517269781378}, {751/200, 0.9935691021407282}, 
     {94/25, 0.9935863918591075}, {753/200, 0.993603592135984}, 
     {377/100, 0.9936207446510876}, {151/40, 0.9936378404019268}, 
     {189/50, 0.9936548616193726}, {757/200, 0.9936718204989496}, 
     {379/100, 0.9936887166057845}, {759/200, 0.9937055215943646}, 
     {19/5, 0.9937222839627747}, {761/200, 0.9937389735236484}, 
     {381/100, 0.9937555812096326}, {763/200, 0.9937721111759746}, 
     {191/50, 0.9937885942799982}, {153/40, 0.9938050048792813}, 
     {383/100, 0.9938213600306793}, {767/200, 0.9938376622849753}, 
     {96/25, 0.9938538931856684}, {769/200, 0.9938700710196389}, 
     {77/20, 0.9938861573013414}, {771/200, 0.9939021751737002}, 
     {193/50, 0.9939181323911761}, {773/200, 0.9939340516602713}, 
     {387/100, 0.9939498892219865}, {31/8, 0.9939656769281177}, 
     {97/25, 0.9939814126497011}, {777/200, 0.9939970740927708}, 
     {389/100, 0.9940126649904137}, {779/200, 0.9940282108416274}, 
     {39/10, 0.9940436749288436}, {781/200, 0.9940590803224787}, 
     {391/100, 0.9940744653090424}, {783/200, 0.994089755096211}, 
     {98/25, 0.9941049958001662}, {157/40, 0.9941201669442952}, 
     {393/100, 0.9941352970150094}, {787/200, 0.9941503536436582}, 
     {197/50, 0.9941653493858342}, {789/200, 0.9941802888309254}, 
     {79/20, 0.994195175275537}, {791/200, 0.9942100280897992}, 
     {99/25, 0.9942248052180904}, {793/200, 0.9942395194500636}, 
     {397/100, 0.9942541714005393}, {159/40, 0.9942687719195077}, 
     {199/50, 0.994283318200372}, {797/200, 0.9942978176018661}, 
     {399/100, 0.9943122463925831}, {799/200, 0.9943266260826861}, 
     {4, 0.9943409613257077}, {801/200, 0.9943552465673857}, 
     {401/100, 0.9943694797178948}, {803/200, 0.9943836563891749}, 
     {201/50, 0.9943977641602415}, {161/40, 0.9944118182497134}, 
     {403/100, 0.9944258200522706}, {807/200, 0.9944397799103437}, 
     {101/25, 0.9944536923681182}, {809/200, 0.9944675220674365}, 
     {81/20, 0.9944813292182254}, {811/200, 0.994495087863789}, 
     {203/50, 0.9945087894871183}, {813/200, 0.9945224458189361}, 
     {407/100, 0.9945360272947869}, {163/40, 0.9945495635706574}, 
     {102/25, 0.9945630629011063}, {817/200, 0.9945764939267174}, 
     {409/100, 0.9945898870957476}, {819/200, 0.9946032403650725}, 
     {41/10, 0.9946165420960298}, {821/200, 0.9946297979452906}, 
     {411/100, 0.9946429740010129}, {823/200, 0.9946561344730871}, 
     {103/25, 0.994669230501862}, {33/8, 0.9946822863618624}, 
     {413/100, 0.9946952839054419}, {827/200, 0.9947082410174384}, 
     {207/50, 0.9947211388757876}, {829/200, 0.9947339971099706}, 
     {83/20, 0.9947468367108436}, {831/200, 0.9947596088808439}, 
     {104/25, 0.9947723249300102}, {833/200, 0.994785000373993}, 
     {417/100, 0.994797622698179}, {167/40, 0.9948101913444178}, 
     {209/50, 0.9948227274961983}, {837/200, 0.9948352320702988}, 
     {419/100, 0.9948476853266697}, {839/200, 0.9948600826259737}, 
     {21/5, 0.994872427398793}, {841/200, 0.9948847322546595}, 
     {421/100, 0.9948969922093841}, {843/200, 0.9949092198022822}, 
     {211/50, 0.994921408739642}, {169/40, 0.9949335533817413}, 
     {423/100, 0.9949456466548986}, {847/200, 0.9949576930071753}, 
     {106/25, 0.9949696851383392}, {849/200, 0.994981643992291}, 
     {17/4, 0.9949935745887}, {851/200, 0.995005449539315}, 
     {213/50, 0.9950172903722944}, {853/200, 0.9950290877837397}, 
     {427/100, 0.9950408361509981}, {171/40, 0.9950525420501586}, 
     {107/25, 0.9950642049007772}, {857/200, 0.995075823373378}, 
     {429/100, 0.9950874149309288}, {859/200, 0.995098951628028}, 
     {43/10, 0.9951104501608646}, {861/200, 0.9951219098152151}, 
     {431/100, 0.9951333456739845}, {863/200, 0.9951447316762876}, 
     {108/25, 0.9951560710833867}, {173/40, 0.9951673682027121}, 
     {433/100, 0.9951786264948175}, {867/200, 0.9951898461565294}, 
     {217/50, 0.99520102395552}, {869/200, 0.9952121669305259}, 
     {87/20, 0.9952232699135706}, {871/200, 0.9952343421980965}, 
     {109/25, 0.9952453917989069}, {873/200, 0.9952563802253956}, 
     {437/100, 0.9952673256155627}, {35/8, 0.9952782323788231}, 
     {219/50, 0.9952891154228591}, {877/200, 0.995299958883689}, 
     {439/100, 0.9953107520063783}, {879/200, 0.9953215105004553}, 
     {22/5, 0.9953322392566457}, {881/200, 0.9953429380400367}, 
     {441/100, 0.9953535988627301}, {883/200, 0.9953642146386145}, 
     {221/50, 0.9953748067303595}, {177/40, 0.9953853433455703}, 
     {443/100, 0.9953958410371051}, {887/200, 0.9954063178589894}, 
     {111/25, 0.99541674775323}, {889/200, 0.9954271594272521}, 
     {89/20, 0.9954375341100808}, {891/200, 0.9954478692258258}, 
     {223/50, 0.9954581529506973}, {893/200, 0.9954684185309998}, 
     {447/100, 0.9954786308916517}, {179/40, 0.9954888218128475}, 
     {112/25, 0.9954989829866684}, {897/200, 0.9955091046752726}, 
     {449/100, 0.9955192010851158}, {899/200, 0.9955292547526868}, 
     {9/2, 0.9955392727848287}, {901/200, 0.9955492531289496}, 
     {451/100, 0.9955591935399145}, {903/200, 0.9955691172299955}, 
     {113/25, 0.9955790143726214}, {181/40, 0.995588873049834}, 
     {453/100, 0.9955986981337106}, {907/200, 0.9956084828426787}, 
     {227/50, 0.995618225228252}, {909/200, 0.9956279401375092}, 
     {91/20, 0.9956376314760362}, {911/200, 0.9956472966841645}, 
     {114/25, 0.9956569314846264}, {913/200, 0.9956665259632304}, 
     {457/100, 0.9956760872109763}, {183/40, 0.9956856070886144}, 
     {229/50, 0.9956951018955128}, {917/200, 0.9957045673584426}, 
     {459/100, 0.9957140074754088}, {919/200, 0.9957234219001141}, 
     {23/5, 0.995732800680084}, {921/200, 0.9957421446670113}, 
     {461/100, 0.9957514481227611}, {923/200, 0.9957607237220557}, 
     {231/50, 0.9957699695869}, {37/8, 0.9957791891454325}, 
     {463/100, 0.9957883798703187}, {927/200, 0.9957975415682055}, 
     {116/25, 0.9958066721613055}, {929/200, 0.9958157850287015}, 
     {93/20, 0.9958248548483662}, {931/200, 0.9958338940032931}, 
     {233/50, 0.9958429037991686}, {933/200, 0.9958518852622228}, 
     {467/100, 0.9958608326302953}, {187/40, 0.995869756830688}, 
     {117/25, 0.9958786524886357}, {937/200, 0.9958875372920565}, 
     {469/100, 0.9958963760225814}, {939/200, 0.9959051771499503}, 
     {47/10, 0.9959139518357105}, {941/200, 0.9959227111887844}, 
     {471/100, 0.9959314312968356}, {943/200, 0.9959401304601923}, 
     {118/25, 0.9959488017808313}, {189/40, 0.9959574361117554}, 
     {473/100, 0.9959660512176581}, {947/200, 0.9959746327858434}, 
     {237/50, 0.9959831976175381}, {949/200, 0.9959917353853652}, 
     {19/4, 0.9960002433588789}, {951/200, 0.9960087170863159}, 
     {119/25, 0.9960171621722342}, {953/200, 0.9960255823981742}, 
     {477/100, 0.9960339771046114}, {191/40, 0.9960423523540585}, 
     {239/50, 0.9960507035958864}, {957/200, 0.9960590240949345}, 
     {479/100, 0.9960673146102587}, {959/200, 0.9960755753802397}, 
     {24/5, 0.996083801110887}, {961/200, 0.9960920161452264}, 
     {481/100, 0.9961002059619652}, {963/200, 0.996108373179523}, 
     {241/50, 0.9961165040786717}, {193/40, 0.9961246164642988}, 
     {483/100, 0.9961326961183592}, {967/200, 0.9961407527055477}, 
     {121/25, 0.996148786300684}, {969/200, 0.9961567890451426}, 
     {97/20, 0.9961647798848594}, {971/200, 0.9961727446455367}, 
     {243/50, 0.9961806802175474}, {973/200, 0.9961885873018202}, 
     {487/100, 0.9961964666100598}, {39/8, 0.9962043307301521}, 
     {122/25, 0.9962121577904133}, {977/200, 0.9962199729920712}, 
     {489/100, 0.99622776627997}, {979/200, 0.9962355323706785}, 
     {49/10, 0.996243267367993}, {981/200, 0.9962509822403283}, 
     {491/100, 0.9962586745701993}, {983/200, 0.9962663328149407}, 
     {123/25, 0.9962739828263827}, {197/40, 0.9962815996150896}, 
     {493/100, 0.9962892030063055}, {987/200, 0.9962967773080708}, 
     {247/50, 0.9963043239642143}, {989/200, 0.9963118449342051}, 
     {99/20, 0.9963193476356627}, {991/200, 0.99632682911312}, 
     {124/25, 0.996334289563329}, {993/200, 0.9963417272204629}, 
     {497/100, 0.9963491427872491}, {199/40, 0.996356535124814}, 
     {249/50, 0.9963639035268763}, {997/200, 0.9963712477666504}, 
     {499/100, 0.996378567566463}, {999/200, 0.9963858643127953}, 
     {5, 0.9963931391718367}, {1001/200, 0.9964003946664419}, 
     {501/100, 0.9964076294284483}, {1003/200, 0.9964148450040642}, 
     {251/50, 0.9964220395275}, {201/40, 0.9964292128579402}, 
     {503/100, 0.9964363626972403}, {1007/200, 0.9964434915721594}, 
     {126/25, 0.9964505964175864}, {1009/200, 0.9964576813290555}, 
     {101/20, 0.9964647320138154}, {1011/200, 0.9964717750204832}, 
     {253/50, 0.9964787989009932}, {1013/200, 0.996485802660464}, 
     {507/100, 0.996492785291813}, {203/40, 0.996499744047407}, 
     {127/25, 0.9965066800672275}, {1017/200, 0.9965135929150614}, 
     {509/100, 0.9965205626802879}, {1019/200, 0.9965273736907556}, 
     {51/10, 0.9965342218699507}, {1021/200, 0.996541060557356}, 
     {511/100, 0.9965478799478074}, {1023/200, 0.9965546779256823}, 
     {128/25, 0.9965614577547304}, {41/8, 0.9965682188956083}, 
     {513/100, 0.9965749669423963}, {1027/200, 0.9965816455034949}, 
     {257/50, 0.9965883452914563}, {1029/200, 0.9965950152335324}, 
     {103/20, 0.9966016746872489}, {1031/200, 0.9966083153805451}, 
     {129/25, 0.9966149468065078}, {1033/200, 0.9966215433993586}, 
     {517/100, 0.9966281575537201}, {207/40, 0.9966346606853367}, 
     {259/50, 0.9966412035131428}, {1037/200, 0.9966477300978597}, 
     {519/100, 0.9966542244724597}, {1039/200, 0.9966607304203107}, 
     {26/5, 0.9966671931354708}, {1041/200, 0.9966736773475053}, 
     {521/100, 0.9966800459951474}, {1043/200, 0.9966864507820166}, 
     {261/50, 0.9966928418067247}, {209/40, 0.9966992194532055}, 
     {523/100, 0.9967055834113668}, {1047/200, 0.996711918977685}, 
     {131/25, 0.9967182136381747}, {1049/200, 0.9967245022119943}, 
     {21/4, 0.9967307869952452}, {1051/200, 0.9967370523978126}, 
     {263/50, 0.996743309998091}, {1053/200, 0.9967495364549895}, 
     {527/100, 0.9967557876791582}, {211/40, 0.9967619171118496}, 
     {132/25, 0.9967680818979854}, {1057/200, 0.9967742385226371}, 
     {529/100, 0.996780398516653}, {1059/200, 0.9967865142472248}, 
     {53/10, 0.9967925865720603}, {1061/200, 0.9967986756131477}, 
     {531/100, 0.9968047571165359}, {1063/200, 0.996810808597805}, 
     {133/25, 0.9968168477823066}, {213/40, 0.9968228367197294}, 
     {533/100, 0.9968288259635559}, {1067/200, 0.9968348123507638}, 
     {267/50, 0.9968407815090969}, {1069/200, 0.9968467433413318}, 
     {107/20, 0.9968526752387259}, {1071/200, 0.9968585671953224}, 
     {134/25, 0.9968644571602384}, {1073/200, 0.9968703401220497}, 
     {537/100, 0.9968762094072309}, {43/8, 0.9968820756238861}, 
     {269/50, 0.9968879062612058}, {1077/200, 0.9968937491661172}, 
     {539/100, 0.9968994977168707}, {1079/200, 0.9969052780503356}, 
     {27/5, 0.9969110438554327}, {1081/200, 0.9969168207723302}, 
     {541/100, 0.9969225524916455}, {1083/200, 0.9969282491515159}, 
     {271/50, 0.996933950458223}, {217/40, 0.9969396361859244}, 
     {543/100, 0.996945304163339}, {1087/200, 0.9969509820153949}, 
     {136/25, 0.9969566235879795}, {1089/200, 0.996962218520649}, 
     {109/20, 0.9969678260992482}, {1091/200, 0.9969734224186754}, 
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     {137/25, 0.9970011264796557}, {1097/200, 0.997006629458826}, 
     {549/100, 0.9970121386979186}, {1099/200, 0.9970175925134719}, 
     {11/2, 0.997023045778393}, {1101/200, 0.9970284782510135}, 
     {551/100, 0.9970339013577465}, {1103/200, 0.9970393573948754}, 
     {138/25, 0.9970447113332357}, {221/40, 0.9970501078153842}, 
     {553/100, 0.997055454794636}, {1107/200, 0.9970608036303336}, 
     {277/50, 0.9970661406415171}, {1109/200, 0.9970714548514095}, 
     {111/20, 0.9970767616509307}, {1111/200, 0.9970820539387756}, 
     {139/25, 0.9970873264145369}, {1113/200, 0.9970925904029242}, 
     {557/100, 0.9970978400366597}, {223/40, 0.9971030756414735}, 
     {279/50, 0.9971082974780644}, {1117/200, 0.9971135038810076}, 
     {559/100, 0.9971186950834695}, {1119/200, 0.997123872351999}, 
     {28/5, 0.9971290430274676}, {1121/200, 0.9971342005897961}, 
     {561/100, 0.9971393242755554}, {1123/200, 0.9971444456600718}, 
     {281/50, 0.9971495587937304}, {45/8, 0.9971546468630493}, 
     {563/100, 0.9971597284817962}, {1127/200, 0.9971647964908933}, 
     {141/25, 0.9971698523997703}, {1129/200, 0.9971748941375855}, 
     {113/20, 0.9971799148829656}, {1131/200, 0.9971849293198539}, 
     {283/50, 0.9971899306633224}, {1133/200, 0.9971949184529704}, 
     {567/100, 0.9971998920500273}, {227/40, 0.9972048520168555}, 
     {142/25, 0.9972097991798018}, {1137/200, 0.9972147336702429}, 
     {569/100, 0.9972196551041386}, {1139/200, 0.9972245601955232}, 
     {57/10, 0.9972294601159113}, {1141/200, 0.9972343426516219}, 
     {571/100, 0.9972392051818137}, {1143/200, 0.9972440618136021}, 
     {143/25, 0.9972489061624954}, {229/40, 0.9972537378734743}, 
     {573/100, 0.9972585569940235}, {1147/200, 0.9972633619129458}, 
     {287/50, 0.9972681540511303}, {1149/200, 0.9972729289979847}, 
     {23/4, 0.9972776967648397}, {1151/200, 0.9972824511540747}, 
     {144/25, 0.9972871931714432}, {1153/200, 0.9972919397367758}, 
     {577/100, 0.9972966435871982}, {231/40, 0.9973013514453452}, 
     {289/50, 0.9973060406791001}, {1157/200, 0.9973107231108281}, 
     {579/100, 0.9973154175897755}, {1159/200, 0.9973200780287308}, 
     {29/5, 0.9973246859937601}, {1161/200, 0.9973293189992155}, 
     {581/100, 0.9973339405350375}, {1163/200, 0.9973385485427032}, 
     {291/50, 0.9973431586058537}, {233/40, 0.9973477534025782}, 
     {583/100, 0.9973522976152374}, {1167/200, 0.9973568525506631}, 
     {146/25, 0.9973614011698905}, {1169/200, 0.9973659817262436}, 
     {117/20, 0.9973704679478683}, {1171/200, 0.9973750066082165}, 
     {293/50, 0.9973794812551278}, {1173/200, 0.9973839621571507}, 
     {587/100, 0.9973884649639555}, {47/8, 0.9973929115195699}, 
     {147/25, 0.997397364520806}, {1177/200, 0.9974018014502176}, 
     {589/100, 0.9974062373503869}, {1179/200, 0.9974106656110256}, 
     {59/10, 0.9974150893607218}, {1181/200, 0.9974194615089209}, 
     {591/100, 0.9974238465822427}, {1183/200, 0.9974282259902582}, 
     {148/25, 0.9974326256396948}, {237/40, 0.9974369667981158}, 
     {593/100, 0.9974412713803463}, {1187/200, 0.9974456078445814}, 
     {297/50, 0.9974499306712307}, {1189/200, 0.9974542726295863}, 
     {119/20, 0.9974585727444395}, {1191/200, 0.9974628103582375}, 
     {149/25, 0.9974670915335465}, {1193/200, 0.997471392188582}, 
     {597/100, 0.9974756464932323}, {239/40, 0.9974798496092188}, 
     {299/50, 0.9974840814394271}, {1197/200, 0.9974883150521355}, 
     {599/100, 0.9974925159874964}, {1199/200, 0.9974967247739507}, 
     {6, 0.9975009251946542}}
 
ReERfind = {{6, 0.9975009251946542}, {151/25, 0.9975339565673959}, 
     {152/25, 0.9975664621801158}, {153/25, 0.9975983132988057}, 
     {154/25, 0.9976295493835979}, {31/5, 0.9976600276700027}, 
     {156/25, 0.997690061688577}, {157/25, 0.9977195527008179}, 
     {158/25, 0.9977484213394265}, {159/25, 0.997776776330495}, 
     {32/5, 0.997804604608733}, {161/25, 0.9978319157940413}, 
     {162/25, 0.9978587272975654}, {163/25, 0.9978850252145236}, 
     {164/25, 0.9979108575930556}, {33/5, 0.9979361869195271}, 
     {166/25, 0.9979610774988638}, {167/25, 0.9979855281443717}, 
     {168/25, 0.9980095320002526}, {169/25, 0.9980331078321036}, 
     {34/5, 0.9980562658773002}, {171/25, 0.99807900683686}, 
     {172/25, 0.998101381409685}, {173/25, 0.9981233483719388}, 
     {174/25, 0.9981449555682881}, {7, 0.9981661706337094}, 
     {176/25, 0.9981870300039669}, {177/25, 0.9982075291622016}, 
     {178/25, 0.9982276812380373}, {179/25, 0.9982475070540316}, 
     {36/5, 0.9982669954696499}, {181/25, 0.9982861515228308}, 
     {182/25, 0.9983049983520398}, {183/25, 0.9983235217129497}, 
     {184/25, 0.9983417595891783}, {37/5, 0.998359769137564}, 
     {186/25, 0.9983773575390966}, {187/25, 0.9983947334398644}, 
     {188/25, 0.998411812072874}, {189/25, 0.9984286257944224}, 
     {38/5, 0.9984451760297399}, {191/25, 0.9984614491427112}, 
     {192/25, 0.9984774954947557}, {193/25, 0.9984932744427477}, 
     {194/25, 0.9985087969673925}, {39/5, 0.9985240923492499}, 
     {196/25, 0.9985391870836747}, {197/25, 0.9985540245369943}, 
     {198/25, 0.9985686352585857}, {199/25, 0.9985830248362366}, 
     {8, 0.9985971992173179}, {201/25, 0.998611162734933}, 
     {202/25, 0.9986249195957361}, {203/25, 0.9986384749229954}, 
     {204/25, 0.9986518370253953}, {41/5, 0.9986649945093486}, 
     {206/25, 0.99867795917203}, {207/25, 0.9986907366010002}, 
     {208/25, 0.9987034169078504}, {209/25, 0.9987157339429961}, 
     {42/5, 0.9987279666735143}, {211/25, 0.998740027514773}, 
     {212/25, 0.9987519155159742}, {213/25, 0.9987636379859072}, 
     {214/25, 0.9987752864690936}, {43/5, 0.9987865911071536}, 
     {216/25, 0.9987979227566776}, {217/25, 0.998808921464152}, 
     {218/25, 0.9988198520545895}, {219/25, 0.998830629052839}, 
     {44/5, 0.9988412644448866}, {221/25, 0.9988517381689516}, 
     {222/25, 0.9988620784720271}, {223/25, 0.9988723243146518}, 
     {224/25, 0.9988823808735172}, {9, 0.9988923132898069}, 
     {226/25, 0.9989022065645897}, {227/25, 0.9989117784813167}, 
     {228/25, 0.9989214301407932}, {229/25, 0.998930748178837}, 
     {46/5, 0.9989400502398329}, {231/25, 0.9989491585883744}, 
     {232/25, 0.9989582882649267}, {233/25, 0.9989672299082129}, 
     {234/25, 0.998975985371481}, {47/5, 0.9989847654340599}, 
     {236/25, 0.9989933597319728}, {237/25, 0.9990018654709957}, 
     {238/25, 0.9990102553281534}, {239/25, 0.9990185393222685}, 
     {48/5, 0.9990266361375085}, {241/25, 0.9990346903630029}, 
     {242/25, 0.9990427755099006}, {243/25, 0.9990505560652162}, 
     {244/25, 0.9990584454832826}, {49/5, 0.9990661322924135}, 
     {246/25, 0.9990737708636084}, {247/25, 0.9990812111113947}, 
     {248/25, 0.9990886168609647}, {249/25, 0.9990959411130353}, 
     {10, 0.9991031894873227}, {251/25, 0.9991103189063172}, 
     {252/25, 0.9991173855777429}, {253/25, 0.9991244170087548}, 
     {254/25, 0.999131263709473}, {51/5, 0.9991380845426835}, 
     {256/25, 0.9991448241218828}, {257/25, 0.9991514817087467}, 
     {258/25, 0.9991580570386792}, {259/25, 0.9991645450977095}, 
     {52/5, 0.9991709544854124}, {261/25, 0.9991773072574244}, 
     {262/25, 0.9991836041621145}, {263/25, 0.9991897926210488}, 
     {264/25, 0.9991959416364711}, {53/5, 0.9992020293877428}, 
     {266/25, 0.9992080265572735}, {267/25, 0.9992139594662774}, 
     {268/25, 0.999219830184173}, {269/25, 0.9992256203123189}, 
     {54/5, 0.9992313449275215}, {271/25, 0.9992370302817462}, 
     {272/25, 0.9992426224330911}, {273/25, 0.9992481731963903}, 
     {274/25, 0.9992536516132232}, {11, 0.9992590915947778}, 
     {276/25, 0.9992644672798942}, {277/25, 0.9992697685341977}, 
     {278/25, 0.9992750456681196}, {279/25, 0.9992802426934769}, 
     {56/5, 0.9992853725177561}, {281/25, 0.9992904622823464}, 
     {282/25, 0.9992954797011465}, {283/25, 0.9993004579587379}, 
     {284/25, 0.9993053827212507}, {57/5, 0.9993102615457443}, 
     {286/25, 0.9993150673059704}, {287/25, 0.9993198646694332}, 
     {288/25, 0.9993246017192912}, {289/25, 0.9993292265139414}, 
     {58/5, 0.9993338859679081}, {291/25, 0.9993384415528122}, 
     {292/25, 0.9993429955508057}, {293/25, 0.9993474693574195}, 
     {294/25, 0.9993519090696865}, {59/5, 0.9993562781638915}, 
     {296/25, 0.9993606448220679}, {297/25, 0.999364966172947}, 
     {298/25, 0.9993692160772895}, {299/25, 0.999373412748831}, 
     {12, 0.9993776216858562}, {301/25, 0.9993817636387144}, 
     {302/25, 0.9993858268248528}, {303/25, 0.9993898759717771}, 
     {304/25, 0.9993939020814157}, {61/5, 0.9993978741882112}, 
     {306/25, 0.9994018180021235}, {307/25, 0.9994056908843273}, 
     {308/25, 0.9994095589083762}, {309/25, 0.9994133813795536}, 
     {62/5, 0.9994171837076739}, {311/25, 0.9994209244809902}, 
     {312/25, 0.9994245977868863}, {313/25, 0.9994282976547919}, 
     {314/25, 0.9994319496446334}, {63/5, 0.9994355832330709}, 
     {316/25, 0.99943911130504}, {317/25, 0.9994426603492796}, 
     {318/25, 0.999446158350906}, {319/25, 0.9994496318636866}, 
     {64/5, 0.9994530606234551}, {321/25, 0.9994564673654154}, 
     {322/25, 0.9994598424018832}, {323/25, 0.999463196745954}, 
     {324/25, 0.9994665067912961}, {13, 0.999469808224693}, 
     {326/25, 0.9994730356795536}, {327/25, 0.9994762228795353}, 
     {328/25, 0.999479418373183}, {329/25, 0.9994825869693474}, 
     {66/5, 0.999485701531577}, {331/25, 0.9994888697751859}, 
     {332/25, 0.9994919076289956}, {333/25, 0.99949496064861}, 
     {334/25, 0.9994980298876088}, {67/5, 0.999501014297411}, 
     {336/25, 0.9995039928508185}, {337/25, 0.9995068955061776}, 
     {338/25, 0.999509801309555}, {339/25, 0.999512736045698}, 
     {68/5, 0.999515597102018}, {341/25, 0.9995184378728323}, 
     {342/25, 0.9995212448237687}, {343/25, 0.9995240231595454}, 
     {344/25, 0.9995268015165323}, {69/5, 0.999529548085476}, 
     {346/25, 0.9995322638183965}, {347/25, 0.9995349543320137}, 
     {348/25, 0.9995376021409754}, {349/25, 0.9995402674872174}, 
     {14, 0.9995429001561325}, {351/25, 0.9995455021060551}, 
     {352/25, 0.9995480255438758}, {353/25, 0.9995506362415232}, 
     {354/25, 0.9995531758029569}, {71/5, 0.9995556536078398}, 
     {356/25, 0.9995581561062858}, {357/25, 0.9995606535733513}, 
     {358/25, 0.9995631055126575}, {359/25, 0.9995655099888671}, 
     {72/5, 0.9995679282867257}, {361/25, 0.9995703072602087}, 
     {362/25, 0.9995726664929024}, {363/25, 0.9995750226293322}, 
     {364/25, 0.9995773789901713}, {73/5, 0.9995797163165598}, 
     {366/25, 0.9995819949918481}, {367/25, 0.9995842990868998}, 
     {368/25, 0.9995865206596679}, {369/25, 0.9995887563790328}, 
     {74/5, 0.9995909669123185}, {371/25, 0.9995931929793292}, 
     {372/25, 0.9995953810847503}, {373/25, 0.9995975239514374}, 
     {374/25, 0.9995997247167586}, {15, 0.9996018417727591}, 
     {376/25, 0.9996039239244394}, {377/25, 0.9996059891946395}, 
     {378/25, 0.9996080801039857}, {379/25, 0.999610200850264}, 
     {76/5, 0.9996122482343172}, {381/25, 0.9996142775548456}, 
     {382/25, 0.9996163227569104}, {383/25, 0.9996183111549276}, 
     {384/25, 0.9996202843490638}, {77/5, 0.9996222166896358}, 
     {386/25, 0.9996241702512891}, {387/25, 0.9996261093219194}, 
     {388/25, 0.9996280420061519}, {389/25, 0.9996299422211214}, 
     {78/5, 0.9996318963040022}, {391/25, 0.9996337633067557}, 
     {392/25, 0.9996355873181909}, {393/25, 0.9996374364635006}, 
     {394/25, 0.9996393117679607}, {79/5, 0.999641132522515}, 
     {396/25, 0.9996429396082168}, {397/25, 0.9996447325523272}, 
     {398/25, 0.999646517792747}, {399/25, 0.9996482760078489}, 
     {16, 0.9996500597381752}, {401/25, 0.9996517748609993}, 
     {402/25, 0.99965348421286}, {403/25, 0.9996552185325474}, 
     {404/25, 0.9996568942837378}, {81/5, 0.9996585697290572}, 
     {406/25, 0.9996602902355588}, {407/25, 0.9996619599635462}, 
     {408/25, 0.9996636241820629}, {409/25, 0.9996652531395572}, 
     {82/5, 0.9996668811058815}, {411/25, 0.9996685199087327}, 
     {412/25, 0.9996700950527978}, {413/25, 0.9996716901427102}, 
     {414/25, 0.9996732725904302}, {83/5, 0.999674852596616}, 
     {416/25, 0.999676403861288}, {417/25, 0.9996779448500338}, 
     {418/25, 0.9996795053078568}, {419/25, 0.999681017506488}, 
     {84/5, 0.999682523741736}, {421/25, 0.9996840526751617}, 
     {422/25, 0.9996855285002718}, {423/25, 0.9996870172438137}, 
     {424/25, 0.9996884555200197}, {17, 0.9996899362555115}, 
     {426/25, 0.9996913692122964}, {427/25, 0.9996928286793573}, 
     {428/25, 0.9996942603881618}, {429/25, 0.9996957093493858}, 
     {86/5, 0.9996971137789328}, {431/25, 0.9996985560471806}, 
     {432/25, 0.9996999171261637}, {433/25, 0.9997013140718585}, 
     {434/25, 0.9997026720631484}, {87/5, 0.9997040438928113}, 
     {436/25, 0.9997054126314945}, {437/25, 0.9997067339669528}, 
     {438/25, 0.999708091386649}, {439/25, 0.999709422581018}, 
     {88/5, 0.9997107194344897}, {441/25, 0.9997120520190675}, 
     {442/25, 0.9997133757978436}, {443/25, 0.9997146316017556}, 
     {444/25, 0.9997158962204328}, {89/5, 0.9997172218724414}, 
     {446/25, 0.9997184465328113}, {447/25, 0.9997197632907453}, 
     {448/25, 0.9997209474858023}, {449/25, 0.9997222512409047}, 
     {18, 0.9997234145922829}, {451/25, 0.9997246553062804}, 
     {452/25, 0.9997258511545911}, {453/25, 0.9997270825161191}, 
     {454/25, 0.9997282556710785}, {91/5, 0.999729518586834}, 
     {456/25, 0.9997306371984864}, {457/25, 0.9997318732292823}, 
     {458/25, 0.9997330297602469}, {459/25, 0.9997341919745321}, 
     {92/5, 0.9997353398350921}, {461/25, 0.9997364662862418}, 
     {462/25, 0.9997376450284162}, {463/25, 0.9997387325683639}, 
     {464/25, 0.9997398973802013}, {93/5, 0.9997409718158786}, 
     {466/25, 0.9997420535251349}, {467/25, 0.9997431891334976}, 
     {468/25, 0.9997442638773711}, {469/25, 0.9997453632942167}, 
     {94/5, 0.9997464237400913}, {471/25, 0.9997475130348117}, 
     {472/25, 0.9997486202901005}, {473/25, 0.9997496688723309}, 
     {474/25, 0.9997507469119633}, {19, 0.9997517587547502}, 
     {476/25, 0.9997527802134418}, {477/25, 0.9997538138437997}, 
     {478/25, 0.9997548382291009}, {479/25, 0.9997559042148427}, 
     {96/5, 0.9997569021494918}, {481/25, 0.9997579370226746}, 
     {482/25, 0.99975894324988}, {483/25, 0.9997598844083816}, 
     {484/25, 0.9997609243178753}, {97/5, 0.9997618937313693}, 
     {486/25, 0.999762858382881}, {487/25, 0.9997636947472687}, 
     {488/25, 0.9997647932600744}, {489/25, 0.9997657382726272}, 
     {98/5, 0.9997665924941382}, {491/25, 0.9997675126756176}, 
     {492/25, 0.9997684710201441}, {493/25, 0.9997695400352805}, 
     {494/25, 0.999770310635819}, {99/5, 0.9997712814773524}, 
     {496/25, 0.9997722028263669}, {497/25, 0.9997731186356758}, 
     {498/25, 0.9997741560885455}, {499/25, 0.9997749075817363}, 
     {20, 0.9997758062474135}, {501/25, 0.9997767146783063}, 
     {502/25, 0.9997777151552584}, {503/25, 0.9997784793317488}, 
     {504/25, 0.9997793892608243}, {101/5, 0.9997803449718627}, 
     {506/25, 0.9997811317560458}, {507/25, 0.9997820610690621}, 
     {508/25, 0.9997829110383877}, {509/25, 0.9997837731137147}, 
     {102/5, 0.9997846356503542}, {511/25, 0.9997854688118528}, 
     {512/25, 0.9997863142482243}, {513/25, 0.9997871328547167}, 
     {514/25, 0.9997879540985015}, {103/5, 0.9997887670300006}, 
     {516/25, 0.9997896074171904}, {517/25, 0.9997904237833001}, 
     {518/25, 0.9997912150723834}, {519/25, 0.9997920321916346}, 
     {104/5, 0.9997928182681874}, {521/25, 0.9997936065441684}, 
     {522/25, 0.9997943869865326}, {523/25, 0.9997951716504527}, 
     {524/25, 0.9997959731277902}, {21, 0.9997967299701437}, 
     {526/25, 0.9997975093717077}, {527/25, 0.9997982921387113}, 
     {528/25, 0.9997990481415167}, {529/25, 0.9997997922910489}, 
     {106/5, 0.9998005526720815}, {531/25, 0.9998013146592586}, 
     {532/25, 0.9998020590514152}, {533/25, 0.9998027970456559}, 
     {534/25, 0.9998035566137575}, {107/5, 0.9998042716482097}, 
     {536/25, 0.9998049770492946}, {537/25, 0.9998057474962815}, 
     {538/25, 0.9998064561550182}, {539/25, 0.9998072085456973}, 
     {108/5, 0.9998078853771106}, {541/25, 0.9998085736092925}, 
     {542/25, 0.9998092791095177}, {543/25, 0.9998099987939835}, 
     {544/25, 0.9998106738621227}, {109/5, 0.9998114065006212}, 
     {546/25, 0.9998120789840085}, {547/25, 0.9998127775896198}, 
     {548/25, 0.9998134513367827}, {549/25, 0.9998141325018021}, 
     {22, 0.9998148060096321}, {551/25, 0.9998154827723276}, 
     {552/25, 0.9998161414511293}, {553/25, 0.9998168102968717}, 
     {554/25, 0.9998175005543714}, {111/5, 0.999818141790237}, 
     {556/25, 0.9998188255483238}, {557/25, 0.9998194593416115}, 
     {558/25, 0.9998201281927344}, {559/25, 0.9998207122176399}, 
     {112/5, 0.9998213762546383}, {561/25, 0.9998220106904581}, 
     {562/25, 0.9998226433420738}, {563/25, 0.9998232798174138}, 
     {564/25, 0.9998239152398479}, {113/5, 0.9998244869455971}, 
     {566/25, 0.9998251261725195}, {567/25, 0.9998257544453687}, 
     {568/25, 0.9998263815870083}, {569/25, 0.9998269996772607}, 
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     {1076/25, 0.9999516548469563}, {1077/25, 0.9999516967162599}, 
     {1078/25, 0.9999518577144659}, {1079/25, 0.9999518987121659}, 
     {216/5, 0.9999519802790358}, {1081/25, 0.9999521117073998}, 
     {1082/25, 0.9999519308132715}, {1083/25, 0.9999522268687295}, 
     {1084/25, 0.9999523242612695}, {217/5, 0.999952416758051}, 
     {1086/25, 0.9999525044483554}, {1087/25, 0.9999523216514973}, 
     {1088/25, 0.9999526767858865}, {1089/25, 0.9999527773414263}, 
     {218/5, 0.9999528790207762}, {1091/25, 0.9999530013112373}, 
     {1092/25, 0.9999527707888825}, {1093/25, 0.9999528844971122}, 
     {1094/25, 0.9999532451060023}, {219/5, 0.9999533100779548}, 
     {1096/25, 0.9999533798390232}, {1097/25, 0.9999533845826528}, 
     {1098/25, 0.999953309348673}, {1099/25, 0.9999535650151266}, 
     {44, 0.9999536892220415}, {1101/25, 0.9999535180988283}, 
     {1102/25, 0.9999535631304626}, {1103/25, 0.9999539033040228}, 
     {1104/25, 0.9999537915012002}, {221/5, 0.9999541101883764}, 
     {1106/25, 0.9999541351084031}, {1107/25, 0.9999539861904871}, 
     {1108/25, 0.9999543197155548}, {1109/25, 0.9999544175661217}, 
     {222/5, 0.9999544931086335}, {1111/25, 0.9999545757323038}, 
     {1112/25, 0.9999546579545345}, {1113/25, 0.9999545007139323}, 
     {1114/25, 0.9999547784355293}, {223/5, 0.9999549062108556}, 
     {1116/25, 0.9999549279528345}, {1117/25, 0.9999550254216067}, 
     {1118/25, 0.9999551249927723}, {1119/25, 0.9999551871466843}, 
     {224/5, 0.9999553284238752}, {1121/25, 0.9999553287356188}, 
     {1122/25, 0.999955491320608}, {1123/25, 0.9999552608720637}, 
     {1124/25, 0.9999555707965376}, {45, 0.99995542755088}, 
     {1126/25, 0.9999557710329253}, {1127/25, 0.9999555811958358}, 
     {1128/25, 0.9999556534378106}, {1129/25, 0.9999559478260823}, 
     {226/5, 0.9999560238015808}, {1131/25, 0.9999561440720289}, 
     {1132/25, 0.9999561900813926}, {1133/25, 0.9999562787446955}, 
     {1134/25, 0.9999563711152727}, {227/5, 0.9999561074345874}, 
     {1136/25, 0.999956521434632}, {1137/25, 0.999956577183948}, 
     {1138/25, 0.9999566639711432}, {1139/25, 0.9999567485920268}, 
     {228/5, 0.9999567497046191}, {1141/25, 0.9999569012976481}, 
     {1142/25, 0.9999569153353574}, {1143/25, 0.9999570191581839}, 
     {1144/25, 0.9999571239988435}, {229/5, 0.9999572039208697}, 
     {1146/25, 0.9999570004735784}, {1147/25, 0.9999573484937762}, 
     {1148/25, 0.9999573650863183}, {1149/25, 0.999957162430703}, 
     {46, 0.9999575757944408}, {1151/25, 0.9999575831167362}, 
     {1152/25, 0.9999576453116269}, {1153/25, 0.9999577658427324}, 
     {1154/25, 0.9999575679307456}, {231/5, 0.9999579110235153}, 
     {1156/25, 0.9999579306257506}, {1157/25, 0.9999580189853592}, 
     {1158/25, 0.9999581748230325}, {1159/25, 0.999958126776544}, 
     {232/5, 0.999958323985565}, {1161/25, 0.999958278390977}, 
     {1162/25, 0.9999583805745125}, {1163/25, 0.9999584397218946}, 
     {1164/25, 0.9999585317066783}, {233/5, 0.9999585910503815}, 
     {1166/25, 0.9999586652671612}, {1167/25, 0.9999587317507898}, 
     {1168/25, 0.9999588251761847}, {1169/25, 0.9999588381825957}, 
     {234/5, 0.9999589433312865}, {1171/25, 0.9999589878373116}, 
     {1172/25, 0.9999590680565177}, {1173/25, 0.999959134597146}, 
     {1174/25, 0.9999592108665137}, {47, 0.9999593362084557}, 
     {1176/25, 0.9999593728056246}, {1177/25, 0.99995938837463}, 
     {1178/25, 0.9999594721027595}, {1179/25, 0.9999595557829991}, 
     {236/5, 0.9999596142041944}, {1181/25, 0.9999596482768757}, 
     {1182/25, 0.9999596842966672}, {1183/25, 0.9999598306687775}, 
     {1184/25, 0.9999599053586024}, {237/5, 0.9999599327063915}, 
     {1186/25, 0.999960059688734}, {1187/25, 0.9999601173234194}, 
     {1188/25, 0.9999601770955646}, {1189/25, 0.9999602294436846}, 
     {238/5, 0.999960318790449}, {1191/25, 0.9999603521067044}, 
     {1192/25, 0.9999603666987795}, {1193/25, 0.9999604994895183}, 
     {1194/25, 0.9999605510881365}, {239/5, 0.9999606157968876}, 
     {1196/25, 0.9999606773179396}, {1197/25, 0.999960738847091}, 
     {1198/25, 0.9999607991370564}, {1199/25, 0.9999608404755138}, 
     {48, 0.9999609174641461}, {1201/25, 0.9999609126910055}, 
     {1202/25, 0.9999610215871211}, {1203/25, 0.9999611184445976}, 
     {1204/25, 0.9999611862518984}, {241/5, 0.9999612388010182}, 
     {1206/25, 0.9999613259113523}, {1207/25, 0.9999613801262025}, 
     {1208/25, 0.9999614111878895}, {1209/25, 0.9999615275109172}, 
     {242/5, 0.999961555820576}, {1211/25, 0.9999616080285778}, 
     {1212/25, 0.9999616921563477}, {1213/25, 0.9999614219798869}, 
     {1214/25, 0.9999618248090657}, {243/5, 0.9999618801940422}, 
     {1216/25, 0.9999619200653007}, {1217/25, 0.9999619598207321}, 
     {1218/25, 0.9999620591513029}, {1219/25, 0.9999621130018318}, 
     {244/5, 0.9999621277508925}, {1221/25, 0.9999622432323674}, 
     {1222/25, 0.9999622760978604}, {1223/25, 0.9999623296505273}, 
     {1224/25, 0.9999623754520869}, {49, 0.9999624324227889}, 
     {1226/25, 0.9999625052204781}, {1227/25, 0.9999625867665438}, 
     {1228/25, 0.999962602979823}, {1229/25, 0.9999627150981653}, 
     {246/5, 0.9999627755068496}, {1231/25, 0.9999625497764992}, 
     {1232/25, 0.9999628329525216}, {1233/25, 0.9999629190108429}, 
     {1234/25, 0.9999630131090913}, {247/5, 0.9999630844222877}, 
     {1236/25, 0.9999631149916194}, {1237/25, 0.9999632371678228}, 
     {1238/25, 0.9999632348660594}, {1239/25, 0.9999633276224498}, 
     {248/5, 0.9999633506320558}, {1241/25, 0.9999634116187244}, 
     {1242/25, 0.9999634961004815}, {1243/25, 0.9999635226581552}, 
     {1244/25, 0.9999635552344063}, {249/5, 0.9999636792822436}, 
     {1246/25, 0.9999637365946722}, {1247/25, 0.999963732243136}, 
     {1248/25, 0.999963829223027}, {1249/25, 0.9999638945121573}, 
     {50, 0.9999639053390172}}
 
ReERfine = {{50, 0.9999639053390172}, {1001/20, 0.9999640190042306}, 
     {501/10, 0.9999640529692273}, {1003/20, 0.9999641458582277}, 
     {251/5, 0.9999642023425771}, {201/4, 0.9999642309361897}, 
     {503/10, 0.9999643613715519}, {1007/20, 0.9999644125057044}, 
     {252/5, 0.9999645103231783}, {1009/20, 0.9999645471831894}, 
     {101/2, 0.9999646263301555}, {1011/20, 0.9999646842335417}, 
     {253/5, 0.9999647302687034}, {1013/20, 0.9999647993362011}, 
     {507/10, 0.9999648867475981}, {203/4, 0.9999649156943801}, 
     {254/5, 0.999964995720825}, {1017/20, 0.9999650710069834}, 
     {509/10, 0.9999651126732771}, {1019/20, 0.9999652054220407}, 
     {51, 0.9999652309552758}, {1021/20, 0.999965371724319}, 
     {511/10, 0.9999653787168234}, {1023/20, 0.9999654942562707}, 
     {256/5, 0.9999654990611202}, {205/4, 0.999965562354221}, 
     {513/10, 0.9999656188397757}, {1027/20, 0.9999656808303321}, 
     {257/5, 0.9999657524011116}, {1029/20, 0.9999658718933587}, 
     {103/2, 0.9999658727567099}, {1031/20, 0.9999659041411701}, 
     {258/5, 0.9999659855625691}, {1033/20, 0.9999660766187224}, 
     {517/10, 0.9999660688130217}, {207/4, 0.9999661618731864}, 
     {259/5, 0.9999663007647411}, {1037/20, 0.999966306052798}, 
     {519/10, 0.9999663299236391}, {1039/20, 0.9999663740029254}, 
     {52, 0.9999665369019735}, {1041/20, 0.9999666014701861}, 
     {521/10, 0.9999666282650497}, {1043/20, 0.999966719791825}, 
     {261/5, 0.9999667359612131}, {209/4, 0.999966822118798}, 
     {523/10, 0.9999668912875727}, {1047/20, 0.9999669070826838}, 
     {262/5, 0.9999669744568197}, {1049/20, 0.9999670687159998}, 
     {105/2, 0.9999671054512392}, {1051/20, 0.9999671798917867}, 
     {263/5, 0.9999672542814764}, {1053/20, 0.9999672794583118}, 
     {527/10, 0.9999673493942857}, {211/4, 0.9999674210237085}, 
     {264/5, 0.9999674517671358}, {1057/20, 0.9999675415013083}, 
     {529/10, 0.9999675651292717}, {1059/20, 0.9999676555983856}, 
     {53, 0.9999677132131174}, {1061/20, 0.9999677447597606}, 
     {531/10, 0.9999678504103563}, {1063/20, 0.9999678464234287}, 
     {266/5, 0.9999679097099138}, {213/4, 0.9999679854722945}, 
     {533/10, 0.9999680128069587}, {1067/20, 0.9999680781249223}, 
     {267/5, 0.9999681604066352}, {1069/20, 0.999968219777113}, 
     {107/2, 0.9999682097647512}, {1071/20, 0.9999682570440139}, 
     {268/5, 0.9999683684552871}, {1073/20, 0.9999684471953506}, 
     {537/10, 0.9999684876751601}, {215/4, 0.9999684714254015}, 
     {269/5, 0.9999685154595074}, {1077/20, 0.9999686624511602}, 
     {539/10, 0.9999687099654468}, {1079/20, 0.9999687746699603}, 
     {54, 0.9999687201365535}, {1081/20, 0.9999688507836808}, 
     {541/10, 0.999968851096851}, {1083/20, 0.9999689743671916}, 
     {271/5, 0.9999690416720471}, {217/4, 0.9999690236690707}, 
     {543/10, 0.9999691216336407}, {1087/20, 0.9999691635826822}, 
     {272/5, 0.99996922600759}, {1089/20, 0.9999692797319324}, 
     {109/2, 0.9999693592801181}, {1091/20, 0.9999693573998789}, 
     {273/5, 0.9999694647086599}, {1093/20, 0.9999694296541389}, 
     {547/10, 0.9999695156516695}, {219/4, 0.9999696013711639}, 
     {274/5, 0.999969711552062}, {1097/20, 0.99996966851941}, 
     {549/10, 0.9999696673402438}, {1099/20, 0.999969739063028}, 
     {55, 0.9999699151328973}, {1101/20, 0.9999699356222592}, 
     {551/10, 0.9999699480021014}, {1103/20, 0.9999699560614426}, 
     {276/5, 0.9999700268436107}, {221/4, 0.9999701413856676}, 
     {553/10, 0.9999701430296305}, {1107/20, 0.9999702372383631}, 
     {277/5, 0.9999702449614548}, {1109/20, 0.9999703163518464}, 
     {111/2, 0.9999702501194171}, {1111/20, 0.999970380020219}, 
     {278/5, 0.99997035850207}, {1113/20, 0.9999705269642171}, 
     {557/10, 0.9999705694210256}, {223/4, 0.9999705356397699}, 
     {279/5, 0.9999706166220427}, {1117/20, 0.9999706314713435}, 
     {559/10, 0.9999707589488954}, {1119/20, 0.9999707871865362}, 
     {56, 0.9999707456102949}, {1121/20, 0.9999708497412635}, 
     {561/10, 0.9999709364842722}, {1123/20, 0.9999709876916644}, 
     {281/5, 0.9999710203447083}, {225/4, 0.9999710061058534}, 
     {563/10, 0.9999711132522066}, {1127/20, 0.999971218005265}, 
     {282/5, 0.9999712113600973}, {1129/20, 0.9999713006962426}, 
     {113/2, 0.9999711888112348}, {1131/20, 0.9999713550065517}, 
     {283/5, 0.9999714035309081}, {1133/20, 0.9999711470579137}, 
     {567/10, 0.9999714776739084}, {227/4, 0.9999714027260262}, 
     {284/5, 0.9999715893982715}, {1137/20, 0.999971633673618}, 
     {569/10, 0.9999716594551972}, {1139/20, 0.9999716921439097}, 
     {57, 0.999971797367738}, {1141/20, 0.9999717970332381}, 
     {571/10, 0.999971894871199}, {1143/20, 0.9999719441359267}, 
     {286/5, 0.9999719055498171}, {229/4, 0.9999720264846438}, 
     {573/10, 0.9999719710842621}, {1147/20, 0.9999721259713963}, 
     {287/5, 0.9999721201383215}, {1149/20, 0.9999721437607572}, 
     {115/2, 0.9999722376797172}, {1151/20, 0.9999723066313136}, 
     {288/5, 0.9999722444119351}, {1153/20, 0.999972322625186}, 
     {577/10, 0.9999724002666756}, {231/4, 0.9999724303402202}, 
     {289/5, 0.9999724998771834}, {1157/20, 0.9999724987303569}, 
     {579/10, 0.9999725819124079}, {1159/20, 0.9999726053086414}, 
     {58, 0.9999726456196513}, {1161/20, 0.9999726506793409}, 
     {581/10, 0.9999727460318395}, {1163/20, 0.9999727889176309}, 
     {291/5, 0.9999727936624739}, {233/4, 0.9999728984617623}, 
     {583/10, 0.9999728922652673}, {1167/20, 0.999972990959141}, 
     {292/5, 0.9999729930207221}, {1169/20, 0.999973012264705}, 
     {117/2, 0.9999730903306482}, {1171/20, 0.9999730914282268}, 
     {293/5, 0.9999731817288909}, {1173/20, 0.9999732257789875}, 
     {587/10, 0.9999732570649903}, {235/4, 0.9999732756176677}, 
     {294/5, 0.9999733744663316}, {1177/20, 0.9999733342125532}, 
     {589/10, 0.9999735095833735}, {1179/20, 0.9999735436309323}, 
     {59, 0.9999734442298026}, {1181/20, 0.9999736022040444}, 
     {591/10, 0.9999735390208736}, {1183/20, 0.99997361335873}, 
     {296/5, 0.9999736464557685}, {237/4, 0.999973774483793}, 
     {593/10, 0.9999737592388473}, {1187/20, 0.9999738654942943}, 
     {297/5, 0.999973834114316}, {1189/20, 0.9999738661230111}, 
     {119/2, 0.9999739288841378}, {1191/20, 0.9999739727054272}, 
     {298/5, 0.9999739882968417}, {1193/20, 0.9999739997139423}, 
     {597/10, 0.9999740916115535}, {239/4, 0.9999741307943412}, 
     {299/5, 0.9999741767283908}, {1197/20, 0.9999742103442175}, 
     {599/10, 0.9999742593468229}, {1199/20, 0.9999742892717532}, 
     {60, 0.9999743217889283}, {1201/20, 0.9999743517001901}, 
     {601/10, 0.999974413455305}, {1203/20, 0.9999744811048974}, 
     {301/5, 0.9999743804498019}, {241/4, 0.9999744744225736}, 
     {603/10, 0.9999746305569378}, {1207/20, 0.9999744139663833}, 
     {302/5, 0.9999746268991618}, {1209/20, 0.9999745788199607}, 
     {121/2, 0.9999747321642385}, {1211/20, 0.9999745259428483}, 
     {303/5, 0.999974818902586}, {1213/20, 0.9999748161591048}, 
     {607/10, 0.9999747959099272}, {243/4, 0.9999748941954617}, 
     {304/5, 0.999974763391794}, {1217/20, 0.9999747750476701}, 
     {609/10, 0.9999750009454438}, {1219/20, 0.999975048115194}, 
     {61, 0.9999750884368548}, {1221/20, 0.9999751269059408}, 
     {611/10, 0.9999751789475659}, {1223/20, 0.999975193802796}, 
     {306/5, 0.9999752331788293}, {245/4, 0.9999752048577454}, 
     {613/10, 0.9999753113671109}, {1227/20, 0.9999753486026657}, 
     {307/5, 0.9999753798287964}, {1229/20, 0.999975461963161}, 
     {123/2, 0.9999754505700199}, {1231/20, 0.9999754873375629}, 
     {308/5, 0.9999754677006014}, {1233/20, 0.9999755306177184}, 
     {617/10, 0.9999755757061682}, {247/4, 0.99997558545274}, 
     {309/5, 0.9999756417978168}, {1237/20, 0.9999757068676981}, 
     {619/10, 0.9999757158037869}, {1239/20, 0.9999757504577694}, 
     {62, 0.9999757440753526}, {1241/20, 0.9999758473149266}, 
     {621/10, 0.999975881432884}, {1243/20, 0.9999758812491466}, 
     {311/5, 0.9999759303446021}, {249/4, 0.9999759546788535}, 
     {623/10, 0.999975994010453}, {1247/20, 0.9999759611258832}, 
     {312/5, 0.9999760623694782}, {1249/20, 0.9999760946757609}, 
     {125/2, 0.9999761260522891}, {1251/20, 0.9999761757912088}, 
     {313/5, 0.9999761963462556}, {1253/20, 0.9999762458007716}, 
     {627/10, 0.9999762916731233}, {251/4, 0.9999763260640403}, 
     {314/5, 0.9999763423317843}, {1257/20, 0.99997637108258}, 
     {629/10, 0.9999764477366914}, {1259/20, 0.9999764198493533}, 
     {63, 0.9999764656024219}, {1261/20, 0.9999765055460971}, 
     {631/10, 0.9999765327628924}, {1263/20, 0.9999765745745001}, 
     {316/5, 0.9999766344685558}, {253/4, 0.999976673119724}, 
     {633/10, 0.9999766750222342}, {1267/20, 0.9999767412313803}, 
     {317/5, 0.999976758143367}, {1269/20, 0.9999768155099975}, 
     {127/2, 0.9999769167643968}, {1271/20, 0.999976842999722}, 
     {318/5, 0.9999768980391847}, {1273/20, 0.9999769186635844}, 
     {637/10, 0.9999769713143616}, {255/4, 0.9999769816506692}, 
     {319/5, 0.9999770350120126}, {1277/20, 0.9999770502087371}, 
     {639/10, 0.9999771145709612}, {1279/20, 0.9999771201546407}, 
     {64, 0.9999771252981782}, {1281/20, 0.999977148975451}, 
     {641/10, 0.9999772142003729}, {1283/20, 0.9999772586973107}, 
     {321/5, 0.9999772892016223}, {257/4, 0.999977346791249}, 
     {643/10, 0.9999773591114606}, {1287/20, 0.9999773818217732}, 
     {322/5, 0.9999774128789054}, {1289/20, 0.9999774433812018}, 
     {129/2, 0.9999775102006839}, {1291/20, 0.9999774994891149}, 
     {323/5, 0.9999775463071341}, {1293/20, 0.9999775797795831}, 
     {647/10, 0.9999775917514528}, {259/4, 0.9999776246409076}, 
     {324/5, 0.9999776710837597}, {1297/20, 0.9999776020466573}, 
     {649/10, 0.9999777051720344}, {1299/20, 0.9999777668588327}, 
     {65, 0.9999777949585984}, {1301/20, 0.9999777470132418}, 
     {651/10, 0.9999779541961024}, {1303/20, 0.9999778966599296}, 
     {326/5, 0.9999779134519592}, {261/4, 0.9999779433760649}, 
     {653/10, 0.9999778959421686}, {1307/20, 0.999978044559593}, 
     {327/5, 0.9999780162592791}, {1309/20, 0.9999780745321497}, 
     {131/2, 0.999978037363566}, {1311/20, 0.9999781357764168}, 
     {328/5, 0.9999782044229969}, {1313/20, 0.9999781877915029}, 
     {657/10, 0.9999782051226033}, {263/4, 0.9999782317759563}, 
     {329/5, 0.9999783051300628}, {1317/20, 0.9999783098609009}, 
     {659/10, 0.9999783627558492}, {1319/20, 0.9999783552815604}, 
     {66, 0.9999784279321422}, {1321/20, 0.9999784588564612}, 
     {661/10, 0.9999784640812672}, {1323/20, 0.9999784977615052}, 
     {331/5, 0.999978561364076}, {265/4, 0.9999786199715314}, 
     {663/10, 0.9999785810822436}, {1327/20, 0.9999786202028985}, 
     {332/5, 0.999978619580387}, {1329/20, 0.9999785056476617}, 
     {133/2, 0.9999787095728215}, {1331/20, 0.9999786792250234}, 
     {333/5, 0.9999787479937773}, {1333/20, 0.9999788277040762}, 
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     {917/10, 0.9999885155907191}, {367/4, 0.9999885558018043}, 
     {459/5, 0.9999877592937356}, {1837/20, 0.9999877526621189}, 
     {919/10, 0.9999886217643946}, {1839/20, 0.9999885700537378}, 
     {92, 0.9999878250421846}, {1841/20, 0.999987802434485}, 
     {921/10, 0.9999877776544989}, {1843/20, 0.9999886393346045}, 
     {461/5, 0.9999887103962992}, {369/4, 0.9999878763788526}, 
     {923/10, 0.9999878978110361}, {1847/20, 0.9999886890246082}, 
     {462/5, 0.9999882477852567}, {1849/20, 0.9999879469291152}, 
     {185/2, 0.9999879327591362}, {1851/20, 0.9999879526916132}, 
     {463/5, 0.9999879840726484}, {1853/20, 0.9999887376852818}, 
     {927/10, 0.9999887968967971}, {371/4, 0.9999880215112065}, 
     {464/5, 0.9999879991987078}, {1857/20, 0.9999888411593315}, 
     {929/10, 0.9999888140182628}, {1859/20, 0.9999880827223753}, 
     {93, 0.9999880638813635}, {1861/20, 0.9999880479715452}, 
     {931/10, 0.9999887871807084}, {1863/20, 0.9999884952935908}, 
     {466/5, 0.9999881086006188}, {373/4, 0.9999880860398483}, 
     {933/10, 0.9999888771368217}, {1867/20, 0.9999882501409502}, 
     {467/5, 0.9999881615120543}, {1869/20, 0.9999881536850949}, 
     {187/2, 0.999988141954117}, {1871/20, 0.9999889365331106}, 
     {468/5, 0.9999889485493137}, {1873/20, 0.9999882239467321}, 
     {937/10, 0.9999889869313872}, {375/4, 0.9999889333452384}, 
     {469/5, 0.9999891261471405}, {1877/20, 0.9999882663779611}, 
     {939/10, 0.999988257754922}, {1879/20, 0.9999882214403775}, 
     {94, 0.9999890271670844}, {1881/20, 0.999989097766849}, 
     {941/10, 0.9999883252205032}, {1883/20, 0.9999883157332368}, 
     {471/5, 0.9999889860530448}, {377/4, 0.9999891111477797}, 
     {943/10, 0.9999883630391155}, {1887/20, 0.9999883717998134}, 
     {472/5, 0.9999890887266215}, {1889/20, 0.9999891805670387}, 
     {189/2, 0.9999892345456252}, {1891/20, 0.9999884166024143}, 
     {473/5, 0.999988405374591}, {1893/20, 0.9999891802310491}, 
     {947/10, 0.999989204188119}, {379/4, 0.9999884634347292}, 
     {474/5, 0.9999884523485721}, {1897/20, 0.9999892649800626}, 
     {949/10, 0.9999892353341103}, {1899/20, 0.9999888075743479}, 
     {95, 0.9999885070362629}, {1901/20, 0.9999884945294402}, 
     {951/10, 0.9999892723410471}, {1903/20, 0.9999889526400677}, 
     {476/5, 0.9999885727284201}, {381/4, 0.9999893043845001}, 
     {953/10, 0.999988775216202}, {1907/20, 0.9999893298961146}, 
     {477/5, 0.9999894309643366}, {1909/20, 0.9999885851671915}, 
     {191/2, 0.9999885855705587}, {1911/20, 0.9999893270689626}, 
     {478/5, 0.9999895001245656}, {1913/20, 0.9999886414270245}, 
     {957/10, 0.9999886424699729}, {383/4, 0.999988890040613}, 
     {479/5, 0.9999889901181915}, {1917/20, 0.9999886728610706}, 
     {959/10, 0.9999886722607524}, {1919/20, 0.9999895831920789}, 
     {96, 0.9999894542438126}, {1921/20, 0.9999896252869426}, 
     {961/10, 0.9999887127338842}, {1923/20, 0.9999887226819769}, 
     {481/5, 0.9999896436106253}, {385/4, 0.9999895950806416}, 
     {963/10, 0.999988763144206}, {1927/20, 0.9999896205824074}, 
     {482/5, 0.9999895187944116}, {1929/20, 0.9999890040558376}, 
     {193/2, 0.9999896797149542}, {1931/20, 0.9999887840456149}, 
     {483/5, 0.9999888105524732}, {1933/20, 0.9999897756669762}, 
     {967/10, 0.999988918344769}, {387/4, 0.9999888506270995}, 
     {484/5, 0.9999888749906223}, {1937/20, 0.9999896364292462}, 
     {969/10, 0.999989609966841}, {1939/20, 0.9999898055540263}, 
     {97, 0.999988890623179}, {1941/20, 0.9999897146227544}, 
     {971/10, 0.9999897751762636}, {1943/20, 0.999989791627778}, 
     {486/5, 0.9999889266648446}, {389/4, 0.9999889280545708}, 
     {973/10, 0.9999897146617489}, {1947/20, 0.9999898743282876}, 
     {487/5, 0.9999889783988513}, {1949/20, 0.9999898126415957}, 
     {195/2, 0.9999891619093548}, {1951/20, 0.9999897435594715}, 
     {488/5, 0.9999899302297641}, {1953/20, 0.9999890285528499}, 
     {977/10, 0.9999889765109051}, {391/4, 0.999989826854075}, 
     {489/5, 0.999989860907866}, {1957/20, 0.9999890604321052}, 
     {979/10, 0.9999890771968875}, {1959/20, 0.9999892504365536}, 
     {98, 0.9999898923391953}, {1961/20, 0.9999900374684791}, 
     {981/10, 0.9999891012763341}, {1963/20, 0.9999890810060137}, 
     {491/5, 0.9999899617963368}, {393/4, 0.9999899285812093}, 
     {983/10, 0.9999891400939687}, {1967/20, 0.999989130063347}, 
     {492/5, 0.9999893051723456}, {1969/20, 0.9999899942458569}, 
     {197/2, 0.9999901668645991}, {1971/20, 0.9999900715558077}, 
     {493/5, 0.9999893345412124}, {1973/20, 0.9999893370181578}, 
     {987/10, 0.9999901324547402}, {395/4, 0.999989564005704}, 
     {494/5, 0.9999892422627562}, {1977/20, 0.9999892616982766}, 
     {989/10, 0.9999894068553813}, {1979/20, 0.9999894013854793}, 
     {99, 0.9999902457646311}, {1981/20, 0.9999901798837424}, 
     {991/10, 0.99998946870865}, {1983/20, 0.9999894520086166}, 
     {496/5, 0.9999902432999069}, {397/4, 0.9999893445165654}, 
     {993/10, 0.9999893478280155}, {1987/20, 0.9999895004811704}, 
     {497/5, 0.9999896999793135}, {1989/20, 0.9999903191592194}, 
     {199/2, 0.9999893896249197}, {1991/20, 0.9999895679022491}, 
     {498/5, 0.9999895490602058}, {1993/20, 0.9999902671276427}, 
     {997/10, 0.9999903372808283}, {399/4, 0.999989404656626}, 
     {499/5, 0.9999895807349823}, {1997/20, 0.9999902692015188}, 
     {999/10, 0.999989478858893}, {1999/20, 0.9999894744573751}, 
     {100, 0.9999896456540717}}
 
ImERfin = {{1/10000, 5722.89586495466}, {11/100000, 5202.628540109963}, 
     {3/25000, 4769.075732990486}, {13/100000, 4402.223994990231}, 
     {7/50000, 4087.779343337441}, {3/20000, 3815.26072944953}, 
     {1/6250, 3576.8068994205423}, {17/100000, 3366.4064667484554}, 
     {9/50000, 3179.3840299916064}, {19/100000, 3012.047913569513}, 
     {1/5000, 2861.4455386880263}, {21/100000, 2725.1886396343853}, 
     {11/50000, 2601.314059123988}, {23/100000, 2488.213471554782}, 
     {3/12500, 2384.5379586366616}, {1/4000, 2289.1563784325267}, 
     {13/50000, 2201.111909435635}, {27/100000, 2119.589268048231}, 
     {7/25000, 2043.8913024909443}, {29/100000, 1973.4106225397381}, 
     {3/10000, 1907.6302653730463}, {31/100000, 1846.0938567163507}, 
     {1/3125, 1788.4047148019554}, {33/100000, 1734.2093741703206}, 
     {17/50000, 1683.2032259868588}, {7/20000, 1635.111585524112}, 
     {9/25000, 1589.691810806793}, {37/100000, 1546.7272607772857}, 
     {19/50000, 1506.0249733350738}, {39/100000, 1467.408950336037}, 
     {1/2500, 1430.7226201776448}, {41/100000, 1395.8270029647692}, 
     {21/50000, 1362.5929099686305}, {43/100000, 1330.9047879216077}, 
     {11/25000, 1300.6569747648955}, {9/20000, 1271.7545463391812}, 
     {23/50000, 1244.106574945908}, {47/100000, 1217.6362257647907}, 
     {3/6250, 1192.2687757273775}, {49/100000, 1167.9367989810944}, 
     {1/2000, 1144.5781265900528}, {51/100000, 1122.1353921164693}, 
     {13/25000, 1100.5558789073943}, {53/100000, 1079.790652964321}, 
     {27/50000, 1059.7945304924274}, {11/20000, 1040.5255066791829}, 
     {7/12500, 1021.944670831667}, {57/100000, 1004.016729264602}, 
     {29/50000, 986.7060512160454}, {59/100000, 969.9814238257773}, 
     {3/5000, 953.8150194664581}, {61/100000, 938.1787484994572}, 
     {31/50000, 923.0467670894598}, {63/100000, 908.3952716027609}, 
     {2/3125, 894.2019906934056}, {13/20000, 880.4453477806369}, 
     {33/50000, 867.1045664999383}, {67/100000, 854.1626885456419}, 
     {17/25000, 841.6021666015972}, {69/100000, 829.4050142265123}, 
     {7/10000, 817.5556637007949}, {71/100000, 806.0415225583274}, 
     {9/12500, 794.8457899227076}, {73/100000, 783.9575248595684}, 
     {37/50000, 773.363462681423}, {3/4000, 763.0518828811014}, 
     {19/25000, 753.0118026697876}, {77/100000, 743.2324273355441}, 
     {39/50000, 733.7037882765621}, {79/100000, 724.4163741252423}, 
     {1/1250, 715.3617030116882}, {81/100000, 706.5295818291245}, 
     {41/50000, 697.9133303358983}, {83/100000, 689.505314679669}, 
     {21/25000, 681.2963420549065}, {17/20000, 673.2810711154311}, 
     {43/50000, 665.4522470708778}, {87/100000, 657.8033327192368}, 
     {11/12500, 650.3287625925102}, {89/100000, 643.0212261662414}, 
     {9/10000, 635.8765118922033}, {91/100000, 628.8893645473911}, 
     {23/25000, 622.0531332255491}, {93/100000, 615.3644072470743}, 
     {47/50000, 608.8179725005841}, {19/20000, 602.4098675543139}, 
     {3/3125, 596.1342299193188}, {97/100000, 589.9890541697745}, 
     {49/50000, 583.9682511271993}, {99/100000, 578.0695431066399}, 
     {1/1000, 572.2888194189891}, {101/100000, 566.6226032377435}, 
     {51/50000, 561.0675094183807}, {103/100000, 555.6202337979754}, 
     {13/12500, 550.277691578237}, {21/20000, 545.0369641383336}, 
     {53/50000, 539.8951268465596}, {107/100000, 534.8493582103945}, 
     {27/25000, 529.8970602295435}, {109/100000, 525.0360633098096}, 
     {11/10000, 520.2625187306257}, {111/100000, 515.5758735329649}, 
     {7/6250, 510.9721234374797}, {113/100000, 506.4506580056167}, 
     {57/50000, 502.0077149713709}, {23/20000, 497.6424093546466}, 
     {29/25000, 493.35238322764394}, {117/100000, 489.13603755196766}, 
     {59/50000, 484.99047753920036}, {119/100000, 480.9148971615749}, 
     {3/2500, 476.90723923394273}, {121/100000, 472.9662979167641}, 
     {61/50000, 469.0891439143212}, {123/100000, 465.2757622302827}, 
     {31/25000, 461.5231617014489}, {1/800, 457.8312991258099}, 
     {63/50000, 454.1977469358213}, {127/100000, 450.62140812385405}, 
     {4/3125, 447.10054975358696}, {129/100000, 443.6346544823557}, 
     {13/10000, 440.2220722220658}, {131/100000, 436.86158875555793}, 
     {33/25000, 433.55235501402876}, {133/100000, 430.29258556467096}, 
     {67/50000, 427.08142728274504}, {27/20000, 423.9175242832532}, 
     {17/12500, 420.80077060354006}, {137/100000, 417.72893607452784}, 
     {69/50000, 414.70191036569724}, {139/100000, 411.7184106164078}, 
     {7/5000, 408.77757743402583}, {141/100000, 405.8787865276646}, 
     {71/50000, 403.0201504332766}, {143/100000, 400.20177827655573}, 
     {9/6250, 397.4226307284039}, {29/20000, 394.6820693288431}, 
     {73/50000, 391.97876620142847}, {147/100000, 389.3122491202098}, 
     {37/25000, 386.6814335063548}, {149/100000, 384.0866130441325}, 
     {3/2000, 381.5260171472851}, {151/100000, 378.99899272849007}, 
     {19/12500, 376.50555644571386}, {153/100000, 374.0451079803894}, 
     {77/50000, 371.61591343284067}, {31/20000, 369.2183858643235}, 
     {39/25000, 366.8518684072736}, {157/100000, 364.5149507195896}, 
     {79/50000, 362.2078583152611}, {159/100000, 359.9301100581142}, 
     {1/625, 357.680554230712}, {161/100000, 355.45891864520183}, 
     {81/50000, 353.26474284800395}, {163/100000, 351.097455824545}, 
     {41/25000, 348.9563220591158}, {33/20000, 346.8414729314918}, 
     {83/50000, 344.7520598554838}, {167/100000, 342.68790437105895}, 
     {21/12500, 340.6481172604815}, {169/100000, 338.6324453432562}, 
     {17/10000, 336.64021455760565}, {171/100000, 334.6715604602333}, 
     {43/25000, 332.7257724897762}, {173/100000, 330.8025085767447}, 
     {87/50000, 328.90161955711756}, {7/4000, 327.0218790024653}, 
     {11/6250, 325.16403056247134}, {177/100000, 323.32696508048866}, 
     {89/50000, 321.5102736074123}, {179/100000, 319.71413723737646}, 
     {9/5000, 317.9379363805027}, {181/100000, 316.18137360019136}, 
     {91/50000, 314.44435826861366}, {183/100000, 312.7260444546074}, 
     {23/12500, 311.0264661575411}, {37/20000, 309.3449749651302}, 
     {93/50000, 307.68206395289985}, {187/100000, 306.0367075299461}, 
     {47/25000, 304.40887391688005}, {189/100000, 302.79797833277956}, 
     {19/10000, 301.2042912322744}, {191/100000, 299.62756612316787}, 
     {6/3125, 298.0670235390494}, {193/100000, 296.5223657489165}, 
     {97/50000, 294.9941359085094}, {39/20000, 293.48131417103826}, 
     {49/25000, 291.9837405514726}, {197/100000, 290.5018465242048}, 
     {99/50000, 289.03462567746396}, {199/100000, 287.5821887730042}, 
     {1/500, 286.1442723676457}, {201/100000, 284.7204230806733}, 
     {101/50000, 283.3111700057393}, {203/100000, 281.9153087996137}, 
     {51/25000, 280.5335893862923}, {41/20000, 279.16510386676873}, 
     {103/50000, 277.80970665881375}, {207/100000, 276.4676341547748}, 
     {13/6250, 275.1384610210687}, {209/100000, 273.822249108425}, 
     {21/10000, 272.5181033421302}, {211/100000, 271.2265071213574}, 
     {53/25000, 269.94714787146256}, {213/100000, 268.67978373941764}, 
     {107/50000, 267.42423695148864}, {43/20000, 266.1804151564371}, 
     {27/12500, 264.9481185466319}, {217/100000, 263.7271520293818}, 
     {109/50000, 262.51737540903434}, {219/100000, 261.31866750766653}, 
     {11/5000, 260.13084856920045}, {221/100000, 258.9539920766322}, 
     {111/50000, 257.7873283313394}, {223/100000, 256.6313186201693}, 
     {7/3125, 255.48563717166974}, {9/4000, 254.3503674006638}, 
     {113/50000, 253.22487442538937}, {227/100000, 252.10937863515488}, 
     {57/25000, 251.00362145240263}, {229/100000, 249.9073357120089}, 
     {23/10000, 248.8209748282651}, {231/100000, 247.74380812192476}, 
     {29/12500, 246.67595354661734}, {233/100000, 245.61723005886324}, 
     {117/50000, 244.56757301711224}, {47/20000, 243.52666984495545}, 
     {59/25000, 242.4949687500274}, {237/100000, 241.47179702354407}, 
     {119/50000, 240.45720052999684}, {239/100000, 239.45109075886967}, 
     {3/1250, 238.45335269937482}, {241/100000, 237.46375236167847}, 
     {121/50000, 236.48248922821938}, {243/100000, 235.5094993999918}, 
     {61/25000, 234.54428573082242}, {49/20000, 233.58676949978593}, 
     {123/50000, 232.63740938435137}, {247/100000, 231.69534945774632}, 
     {31/12500, 230.7611120081031}, {249/100000, 229.834339310181}, 
     {1/400, 228.91518121956182}, {251/100000, 228.00297383685933}, 
     {63/25000, 227.09819929203707}, {253/100000, 226.20073832032614}, 
     {127/50000, 225.3102048805917}, {51/20000, 224.42654332856074}, 
     {8/3125, 223.5499749943695}, {257/100000, 222.67993244480425}, 
     {129/50000, 221.81702821018098}, {259/100000, 220.96056429706067}, 
     {13/5000, 220.1105332789249}, {261/100000, 219.2671901798189}, 
     {131/50000, 218.43028866267417}, {263/100000, 217.59975321652774}, 
     {33/12500, 216.77549411096646}, {53/20000, 215.95765242313945}, 
     {133/50000, 215.14559691784507}, {267/100000, 214.33980294154532}, 
     {67/25000, 213.54000725645886}, {269/100000, 212.74618060203852}, 
     {27/10000, 211.95824021743306}, {271/100000, 211.1762554014765}, 
     {17/6250, 210.39969229217576}, {273/100000, 209.62901271572707}, 
     {137/50000, 208.86393114484707}, {11/4000, 208.10460880121724}, 
     {69/25000, 207.3505834778868}, {277/100000, 206.60185864069643}, 
     {139/50000, 205.85867493279994}, {279/100000, 205.12091588676952}, 
     {7/2500, 204.3882634737596}, {281/100000, 203.6608693967667}, 
     {141/50000, 202.93868361130933}, {283/100000, 202.22175093760046}, 
     {71/25000, 201.50951369176823}, {57/20000, 200.8024620355353}, 
     {143/50000, 200.1003597632831}, {287/100000, 199.40327673702393}, 
     {9/3125, 198.71084033357567}, {289/100000, 198.02332352708538}, 
     {29/10000, 197.34048451349884}, {291/100000, 196.66217076435623}, 
     {73/25000, 195.98868326369217}, {293/100000, 195.31977481418534}, 
     {147/50000, 194.65556451267952}, {59/20000, 193.995552756108}, 
     {37/12500, 193.34014851817562}, {297/100000, 192.6893235187096}, 
     {149/50000, 192.0427171611002}, {299/100000, 191.40026386112032}, 
     {3/1000, 190.76243655314943}, {301/100000, 190.12864263505503}, 
     {151/50000, 189.49907220468464}, {303/100000, 188.873682073434}, 
     {19/6250, 188.25237148685494}, {61/20000, 187.6351370752268}, 
     {153/50000, 187.02178576542417}, {307/100000, 186.41261701309134}, 
     {77/25000, 185.8073675205344}, {309/100000, 185.20602136559182}, 
     {31/10000, 184.60875060771383}, {311/100000, 184.015122054328}, 
     {39/12500, 183.42520860825402}, {313/100000, 182.83929964362466}, 
     {157/50000, 182.25686776681067}, {63/20000, 181.67844242457528}, 
     {79/25000, 181.10349157258565}, {317/100000, 180.53202187270068}, 
     {159/50000, 179.96431392369652}, {319/100000, 179.40028458434853}, 
     {2/625, 178.83964772224232}, {321/100000, 178.28238209274696}, 
     {161/50000, 177.72871158610383}, {323/100000, 177.17847676114786}, 
     {81/25000, 176.63161655172183}, {13/4000, 176.08812197841297}, 
     {163/50000, 175.5481119313468}, {327/100000, 175.0112684665566}, 
     {41/12500, 174.47754041874094}, {329/100000, 173.9472064608687}, 
     {33/10000, 173.42022338559718}, {331/100000, 172.89616013947227}, 
     {83/25000, 172.3755099367799}, {333/100000, 171.8577450635524}, 
     {167/50000, 171.34333768620183}, {67/20000, 170.8318575668825}, 
     {21/6250, 170.32328877204475}, {337/100000, 169.8180019695123}, 
     {169/50000, 169.31544167185905}, {339/100000, 168.8161100604667}, 
     {17/5000, 168.31957573903463}, {341/100000, 167.82598294119106}, 
     {171/50000, 167.33513297872088}, {343/100000, 166.84725130644608}, 
     {43/12500, 166.36235083600502}, {69/20000, 165.8800285220803}, 
     {173/50000, 165.40071722747325}, {347/100000, 164.9239190940387}, 
     {87/25000, 164.44999248536794}, {349/100000, 163.97880502542665}, 
     {7/2000, 163.5104166270687}, {351/100000, 163.04456725520748}, 
     {11/3125, 162.58123485662645}, {353/100000, 162.1207691300558}, 
     {177/50000, 161.66280320220892}, {71/20000, 161.2074158555888}, 
     {89/25000, 160.75456558396507}, {357/100000, 160.30416121799743}, 
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     {181/50000, 158.08999881626124}, {363/100000, 157.65459273267663}, 
     {91/25000, 157.2214844001836}, {73/20000, 156.79059822651135}, 
     {183/50000, 156.36234533577863}, {367/100000, 155.93614112849622}, 
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     {37/10000, 154.67177686678775}, {371/100000, 154.25499346488925}, 
     {93/25000, 153.84020041625627}, {373/100000, 153.42776270319888}, 
     {187/50000, 153.01763984721998}, {3/800, 152.6095855731971}, 
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     {189/50000, 151.39836617236568}, {379/100000, 150.99879502122062}, 
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     {193/50000, 148.26044978877536}, {387/100000, 147.87746417128938}, 
     {97/25000, 147.49620178280477}, {389/100000, 147.11715455033965}, 
     {39/10000, 146.73990364297723}, {391/100000, 146.36450588526992}, 
     {49/12500, 145.991120153934}, {393/100000, 145.61976486290928}, 
     {197/50000, 145.25003633006475}, {79/20000, 144.8823069274341}, 
     {99/25000, 144.5164244328199}, {397/100000, 144.15252029401054}, 
     {199/50000, 143.79032908820224}, {399/100000, 143.42983723892058}, 
     {1/250, 143.07138330595126}, {401/100000, 142.7145852167822}, 
     {201/50000, 142.35945324378645}, {403/100000, 142.00619677754472}, 
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     {51/12500, 140.2659059999006}, {409/100000, 139.92294232441577}, 
     {41/10000, 139.58176157886908}, {411/100000, 139.24213958981576}, 
     {103/25000, 138.9041650123268}, {413/100000, 138.5678396766732}, 
     {207/50000, 138.2330329115182}, {83/20000, 137.8999301050868}, 
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     {209/50000, 136.91019750065533}, {419/100000, 136.58344773957376}, 
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     {211/50000, 135.61245505329634}, {423/100000, 135.29195950879097}, 
     {53/12500, 134.9728576372159}, {17/4000, 134.65517728911954}, 
     {213/50000, 134.33918187260514}, {427/100000, 134.02456752630275}, 
     {107/25000, 133.71142316481075}, {429/100000, 133.39973056804553}, 
     {43/10000, 133.08940004812507}, {431/100000, 132.78070580716383}, 
     {27/6250, 132.47321723913566}, {433/100000, 132.16728183688116}, 
     {217/50000, 131.86274186551634}, {87/20000, 131.55959875897793}, 
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     {11/2500, 130.06458318889312}, {441/100000, 129.76964691915921}, 
     {221/50000, 129.4761493958795}, {443/100000, 129.18377184605643}, 
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     {223/50000, 128.3149012288186}, {447/100000, 128.0277488866431}, 
     {14/3125, 127.74195233773844}, {449/100000, 127.45744318035037}, 
     {9/2000, 127.17421626954945}, {451/100000, 126.89227162989602}, 
     {113/25000, 126.61156877595971}, {453/100000, 126.33206878945998}, 
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     {229/50000, 124.95276891148501}, {459/100000, 124.680559465465}, 
     {23/5000, 124.4094988529445}, {461/100000, 124.13961950768717}, 
     {231/50000, 123.87092347032055}, {463/100000, 123.60336575696496}, 
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     {233/50000, 122.8076344477671}, {467/100000, 122.54465651506274}, 
     {117/25000, 122.28280572078893}, {469/100000, 122.02217592702749}, 
     {47/10000, 121.76244496994349}, {471/100000, 121.50401729868884}, 
     {59/12500, 121.24648874225528}, {473/100000, 120.99024559530739}, 
     {237/50000, 120.73498433616606}, {19/4000, 120.48069392379193}, 
     {119/25000, 120.22769491995166}, {477/100000, 119.9755287016921}, 
     {239/50000, 119.72453444638734}, {479/100000, 119.47458566393107}, 
     {3/625, 119.2256777254592}, {481/100000, 118.97779457878488}, 
     {241/50000, 118.73094321226833}, {483/100000, 118.48512956295525}, 
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     {243/50000, 117.75379683886251}, {487/100000, 117.51191919959632}, 
     {61/12500, 117.27110979466877}, {489/100000, 117.03137928657293}, 
     {49/10000, 116.79244241835698}, {491/100000, 116.5546677022335}, 
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     {247/50000, 115.84683384062234}, {99/20000, 115.6127016543775}, 
     {31/6250, 115.37960221220848}, {497/100000, 115.14744818225643}, 
     {249/50000, 114.91621294865138}, {499/100000, 114.68600285417665}, 
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     {251/50000, 114.00054066064004}, {503/100000, 113.77388169124208}, 
     {63/12500, 113.54822559782784}, {101/20000, 113.32337963738965}, 
     {253/50000, 113.09932266971268}, {507/100000, 112.87623569375009}, 
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     {51/10000, 112.2123268355322}, {511/100000, 111.99265256145475}, 
     {16/3125, 111.77389744379508}, {513/100000, 111.55610295485019}, 
     {257/50000, 111.33906089738514}, {103/20000, 111.12287024811891}, 
     {129/25000, 110.9075110838159}, {517/100000, 110.69289269501218}, 
     {259/50000, 110.47928916453466}, {519/100000, 110.26640805741172}, 
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     {261/50000, 109.63259335350747}, {523/100000, 109.42296566225801}, 
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     {263/50000, 108.79885849181852}, {527/100000, 108.59249962799294}, 
     {33/6250, 108.38683654844613}, {529/100000, 108.18192903691016}, 
     {53/10000, 107.97781083387798}, {531/100000, 107.77446622903713}, 
     {133/25000, 107.5717895430302}, {533/100000, 107.37002642546341}, 
     {267/50000, 107.168870446667}, {107/20000, 106.96855479076495}, 
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     {269/50000, 106.3720726561784}, {539/100000, 106.1747992224727}, 
     {27/5000, 105.97816940594032}, {541/100000, 105.78226278648171}, 
     {271/50000, 105.58700828427419}, {543/100000, 105.39263900804377}, 
     {17/3125, 105.19888638190241}, {109/20000, 105.00578646851957}, 
     {273/50000, 104.81353765221337}, {547/100000, 104.62183128122632}, 
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     {11/2000, 104.0512478484136}, {551/100000, 103.86232232388122}, 
     {69/12500, 103.67423072592169}, {553/100000, 103.4866646037986}, 
     {277/50000, 103.29995968632875}, {111/20000, 103.11374094868597}, 
     {139/25000, 102.92835474561281}, {557/100000, 102.74357053119954}, 
     {279/50000, 102.55938913442893}, {559/100000, 102.37586553595546}, 
     {7/1250, 102.19305849132556}, {561/100000, 102.01097761349132}, 
     {281/50000, 101.82936807321997}, {563/100000, 101.64857090907427}, 
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     {283/50000, 101.10978914699905}, {567/100000, 100.93137990455108}, 
     {71/12500, 100.75367244068664}, {569/100000, 100.57659797313391}, 
     {57/10000, 100.40022477431086}, {571/100000, 100.22437856587024}, 
     {143/25000, 100.04915967009129}, {573/100000, 99.87454030219862}, 
     {287/50000, 99.70046213203722}, {23/4000, 99.52716361127543}, 
     {18/3125, 99.35435138869684}, {577/100000, 99.18216269014954}, 
     {289/50000, 99.01047900031594}, {579/100000, 98.83953883581128}, 
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     {291/50000, 98.33004941506758}, {583/100000, 98.1613910187045}, 
     {73/12500, 97.9932960806677}, {117/20000, 97.82570304936309}, 
     {293/50000, 97.65882943183189}, {587/100000, 97.49238452389483}, 
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     {59/10000, 96.99671021477442}, {591/100000, 96.83252138354504}, 
     {37/6250, 96.66902357923513}, {593/100000, 96.50599991880986}, 
     {297/50000, 96.34352529500885}, {119/20000, 96.18151997569692}, 
     {149/25000, 96.0201417271638}, {597/100000, 95.85938116983132}, 
     {299/50000, 95.69907352200241}, {599/100000, 95.53922595614696}, 
     {3/500, 95.3799813632792}, {601/100000, 95.22127790512855}, 
     {301/50000, 95.06317015398861}, {603/100000, 94.90551879078672}, 
     {151/25000, 94.74830716504098}, {121/20000, 94.5916988123839}, 
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     {61/10000, 93.81633171836609}, {611/100000, 93.66277375305776}, 
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     {307/50000, 93.20512966865564}, {123/20000, 93.05356623304883}, 
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     {309/50000, 92.6019042607549}, {619/100000, 92.45230017980771}, 
     {31/5000, 92.30311290037397}, {621/100000, 92.15455520965554}, 
     {311/50000, 92.00630897419168}, {623/100000, 91.85868294667134}, 
     {39/6250, 91.71140377378717}, {1/160, 91.56473008692615}, 
     {313/50000, 91.41845375605112}, {627/100000, 91.27265143459695}, 
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     {63/10000, 90.83792875042363}, {631/100000, 90.69396700009932}, 
     {79/12500, 90.5505385883038}, {633/100000, 90.40740115050457}, 
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     {319/50000, 89.69885684516919}, {639/100000, 89.55854602103585}, 
     {4/625, 89.41853682940746}, {641/100000, 89.27904263744577}, 
     {321/50000, 89.14002992178175}, {643/100000, 89.00139938488329}, 
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     {329/50000, 86.97241116459497}, {659/100000, 86.84036767711908}, 
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     {331/50000, 86.44687832027745}, {663/100000, 86.31650096465566}, 
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     {343/50000, 83.4223852346594}, {687/100000, 83.30088776028086}, 
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     {347/50000, 82.46062632430457}, {139/20000, 82.34204614660914}, 
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     {351/50000, 81.52094630940215}, {703/100000, 81.40496344541862}, 
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     {71/10000, 80.60228332622106}, {711/100000, 80.4889179039771}, 
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     {367/50000, 77.96666703804289}, {147/20000, 77.86065604444099}, 
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     {37/5000, 77.33448123024988}, {741/100000, 77.23016326031603}, 
     {371/50000, 77.12601711215873}, {743/100000, 77.0222639179562}, 
     {93/12500, 76.91868052444443}, {149/20000, 76.81548703669506}, 
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     {187/25000, 76.50732961734306}, {749/100000, 76.40524550888827}, 
     {3/400, 76.30330219764447}, {751/100000, 76.20169364268189}, 
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     {377/50000, 75.89848739315124}, {151/20000, 75.7979519430566}, 
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     {379/50000, 75.49800738838263}, {759/100000, 75.39853497057103}, 
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     {383/50000, 74.70947209275042}, {767/100000, 74.61207213611905}, 
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     {77/10000, 74.32134830483096}, {771/100000, 74.22495256518226}, 
     {193/25000, 74.12879958995961}, {773/100000, 74.03283914988762}, 
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     {39/5000, 73.36840794314074}, {781/100000, 73.27451665602058}, 
     {391/50000, 73.18075652508566}, {783/100000, 73.08734742605529}, 
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     {79/10000, 72.43969960005806}, {791/100000, 72.34812284074869}, 
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     {417/50000, 68.61772247920234}, {167/20000, 68.53548072548773}, 
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     {421/50000, 67.96573437727051}, {843/100000, 67.8850453455453}, 
     {211/25000, 67.80460523599953}, {169/20000, 67.72436939030821}, 
     {423/50000, 67.644304419852}, {847/100000, 67.56443616705275}, 
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     {17/2000, 67.32600872644579}, {851/100000, 67.24684320682441}, 
     {213/25000, 67.16796411968704}, {853/100000, 67.0892213755036}, 
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     {429/50000, 66.69817417626217}, {859/100000, 66.62056978670768}, 
     {43/5000, 66.5430484924478}, {861/100000, 66.46575659935013}, 
     {431/50000, 66.38864882352905}, {863/100000, 66.31176980500902}, 
     {27/3125, 66.23500979998715}, {173/20000, 66.15838900878285}, 
     {433/50000, 66.08204325321827}, {867/100000, 66.00576316217109}, 
     {217/25000, 65.92971049620022}, {869/100000, 65.85389129047749}, 
     {87/10000, 65.7781919147809}, {871/100000, 65.70266138750739}, 
     {109/12500, 65.62730258972341}, {873/100000, 65.55208162036257}, 
     {437/50000, 65.47706926797508}, {7/800, 65.40229285647314}, 
     {219/25000, 65.32762379416812}, {877/100000, 65.25313159271143}, 
     {439/50000, 65.17875091009662}, {879/100000, 65.10464833341241}, 
     {11/1250, 65.03060431851898}, {881/100000, 64.95678255160621}, 
     {441/50000, 64.88313366721906}, {883/100000, 64.80969388315103}, 
     {221/25000, 64.73632809301058}, {177/20000, 64.66323524260359}, 
     {443/50000, 64.59018941878324}, {887/100000, 64.51736145911394}, 
     {111/12500, 64.44470329134523}, {889/100000, 64.37226143893739}, 
     {89/10000, 64.29992317734599}, {891/100000, 64.22775345975494}, 
     {223/25000, 64.15569165529675}, {893/100000, 64.08388905329598}, 
     {447/50000, 64.01216001067735}, {179/20000, 63.94068590988505}, 
     {28/3125, 63.86926867207487}, {897/100000, 63.7981046919389}, 
     {449/50000, 63.72701279108284}, {899/100000, 63.65611595532188}, 
     {9/1000, 63.58542658288614}, {901/100000, 63.51480550310379}, 
     {451/50000, 63.44443181105059}, {903/100000, 63.37411606023025}, 
     {113/12500, 63.30400681785676}, {181/20000, 63.23404936867725}, 
     {453/50000, 63.164306374142384}, {907/100000, 63.09460735485604}, 
     {227/25000, 63.02516592744148}, {909/100000, 62.955834911703946}, 
     {91/10000, 62.886635333253224}, {911/100000, 62.817552452456795}, 
     {57/6250, 62.748671944605206}, {913/100000, 62.679942905920115}, 
     {457/50000, 62.6114055777463}, {183/20000, 62.54292294393278}, 
     {229/25000, 62.474644060802405}, {917/100000, 62.406548307190974}, 
     {459/50000, 62.338523491384876}, {919/100000, 62.27067477046657}, 
     {23/2500, 62.203040592521674}, {921/100000, 62.13544926168444}, 
     {461/50000, 62.068048978331774}, {923/100000, 62.0007966348993}, 
     {231/25000, 61.93374300492049}, {37/4000, 61.8667810035913}, 
     {463/50000, 61.79995934785825}, {927/100000, 61.73324273427335}, 
     {29/3125, 61.66671714869531}, {929/100000, 61.6003296402354}, 
     {93/10000, 61.534140681882306}, {931/100000, 61.46803985154807}, 
     {233/25000, 61.402087974960864}, {933/100000, 61.33626183178967}, 
     {467/50000, 61.27059497831476}, {187/20000, 61.20505260759566}, 
     {117/12500, 61.13966609782608}, {937/100000, 61.07435903656375}, 
     {469/50000, 61.00928210496535}, {939/100000, 60.944311646243875}, 
     {47/5000, 60.879469151624164}, {941/100000, 60.81476803921748}, 
     {471/50000, 60.75020332337735}, {943/100000, 60.685774997906975}, 
     {59/6250, 60.62148711973974}, {189/20000, 60.55732579859931}, 
     {473/50000, 60.49326296566008}, {947/100000, 60.42942526638204}, 
     {237/25000, 60.36567476954343}, {949/100000, 60.30206258129246}, 
     {19/2000, 60.238536101959}, {951/100000, 60.17518813481769}, 
     {119/12500, 60.1119706805884}, {953/100000, 60.04889544319104}, 
     {477/50000, 59.98598681787061}, {191/20000, 59.92317322395698}, 
     {239/25000, 59.86048643198396}, {957/100000, 59.79793416713292}, 
     {479/50000, 59.735457701937975}, {959/100000, 59.67316515604601}, 
     {6/625, 59.61099678134805}, {961/100000, 59.54896316588936}, 
     {481/50000, 59.48705385966649}, {963/100000, 59.42528168275999}, 
     {241/25000, 59.363631223896775}, {193/20000, 59.302155844837614}, 
     {483/50000, 59.24071399672029}, {967/100000, 59.179450454708956}, 
     {121/12500, 59.1183018218093}, {969/100000, 59.05729460560784}, 
     {97/10000, 58.99639779251213}, {971/100000, 58.935634410795984}, 
     {243/25000, 58.875003229077464}, {973/100000, 58.8144882857879}, 
     {487/50000, 58.75414291500955}, {39/4000, 58.69382449727213}, 
     {61/6250, 58.6336871331239}, {977/100000, 58.57367116162544}, 
     {489/50000, 58.51381632433379}, {979/100000, 58.45404192096245}, 
     {49/5000, 58.39434633223772}, {981/100000, 58.33481407162718}, 
     {491/50000, 58.27540450124802}, {983/100000, 58.21616517419483}, 
     {123/12500, 58.156999967154036}, {197/20000, 58.09790426099316}, 
     {493/50000, 58.03902318322619}, {987/100000, 57.980170856244214}, 
     {247/25000, 57.92151972787124}, {989/100000, 57.86295162358164}, 
     {99/10000, 57.804456862002425}, {991/100000, 57.74612114100211}, 
     {31/3125, 57.68789713249481}, {993/100000, 57.62980345351251}, 
     {497/50000, 57.57187001739241}, {199/20000, 57.514001824254066}, 
     {249/25000, 57.456244397757175}, {997/100000, 57.398618644463426}, 
     {499/50000, 57.34105418119786}, {999/100000, 57.2836465085328}, 
     {1/100, 57.2264039454212}}
 
ImERfinb = {{1/100, 57.2264039454212}, {11/1000, 52.02351793442526}, 
     {3/250, 47.68769872219946}, {13/1000, 44.01892258092791}, 
     {7/500, 40.87422299327032}, {3/200, 38.14878104108838}, 
     {2/125, 35.76398905373679}, {17/1000, 33.65975450877812}, 
     {9/500, 31.7892484852826}, {19/1000, 30.11565766234542}, 
     {1/50, 28.60937511025164}, {21/1000, 27.246525895881753}, 
     {11/500, 26.007555980625106}, {23/1000, 24.87629210467614}, 
     {3/125, 23.83928125057323}, {1/40, 22.885192398519713}, 
     {13/500, 22.004493123928626}, {27/1000, 21.18902948640268}, 
     {7/250, 20.43176307260869}, {29/1000, 19.726731751705664}, 
     {3/100, 19.068674112920434}, {31/1000, 18.45305548835553}, 
     {4/125, 17.87588218725481}, {33/1000, 17.333702006613734}, 
     {17/500, 16.823374047622195}, {7/200, 16.342216540100893}, 
     {9/250, 15.88775706280856}, {37/1000, 15.45786360927789}, 
     {19/500, 15.050565980379421}, {39/1000, 14.664151234973861}, 
     {1/25, 14.29704572166023}, {41/1000, 13.947834817959915}, 
     {21/500, 13.615253226116238}, {43/1000, 13.298117178391056}, 
     {11/250, 12.995386726830297}, {9/200, 12.70609884989387}, 
     {23/500, 12.429375338382055}, {47/1000, 12.164412045623674}, 
     {6/125, 11.91048384592419}, {49/1000, 11.666909957266558}, 
     {1/20, 11.433070623413297}, {51/1000, 11.208399520888793}, 
     {13/250, 10.992342648479429}, {53/1000, 10.784440431284917}, 
     {27/500, 10.584233958327637}, {11/200, 10.391285704616024}, 
     {7/125, 10.205231357283555}, {57/1000, 10.025692689451898}, 
     {29/500, 9.852326744764092}, {59/1000, 9.684843795047586}, 
     {3/50, 9.522928668174714}, {61/1000, 9.366313696360574}, 
     {31/500, 9.21473706499263}, {63/1000, 9.06797712857756}, 
     {8/125, 8.925782512981852}, {13/200, 8.787961696978677}, 
     {33/500, 8.654317384010827}, {67/1000, 8.524649467274788}, 
     {17/250, 8.398778096442069}, {69/1000, 8.276559083863823}, 
     {7/100, 8.157820526453332}, {71/1000, 8.042422731921675}, 
     {9/125, 7.930229853915}, {73/1000, 7.821090422432878}, 
     {37/500, 7.714905978897907}, {3/40, 7.611541812084065}, 
     {19/250, 7.510885191787802}, {77/1000, 7.412849224297981}, 
     {39/500, 7.3173139746578375}, {79/1000, 7.22418424032643}, 
     {2/25, 7.133390070080111}, {81/1000, 7.044819894474571}, 
     {41/500, 6.958413674857651}, {83/1000, 6.8740797351520495}, 
     {21/250, 6.791748846390176}, {17/200, 6.71134859344888}, 
     {43/500, 6.632813239744346}, {87/1000, 6.5560730773899145}, 
     {11/125, 6.4810786547341515}, {89/1000, 6.407761434409116}, 
     {9/100, 6.336066724107813}, {91/1000, 6.265939602127293}, 
     {23/250, 6.197339871800306}, {93/1000, 6.130202568789192}, 
     {47/500, 6.064496119254592}, {19/200, 6.000163541929917}, 
     {12/125, 5.937166428657749}, {97/1000, 5.875465267011528}, 
     {49/500, 5.815016946354394}, {99/1000, 5.755779630720085}, 
     {1/10, 5.697728086986407}, {101/1000, 5.640825705244117}, 
     {51/500, 5.585029609119877}, {103/1000, 5.530308002101597}, 
     {13/125, 5.476642735159439}, {21/200, 5.423991708637022}, 
     {53/500, 5.372325643005945}, {107/1000, 5.3216266024370285}, 
     {27/250, 5.2718620012071895}, {109/1000, 5.223005627543092}, 
     {11/100, 5.17503091607403}, {111/1000, 5.127918339261258}, 
     {14/125, 5.081643726622854}, {113/1000, 5.036177837618155}, 
     {57/500, 4.99151402916978}, {23/200, 4.947615231848207}, 
     {29/250, 4.904474289945581}, {117/1000, 4.862064940732408}, 
     {59/500, 4.820376283859471}, {119/1000, 4.779380553639578}, 
     {3/25, 4.739063051193574}, {121/1000, 4.699405150238667}, 
     {61/500, 4.660401841780551}, {123/1000, 4.622024236413784}, 
     {31/250, 4.584262288065011}, {1/8, 4.5471014861782155}, 
     {63/500, 4.510522225401571}, {127/1000, 4.4745205871942995}, 
     {16/125, 4.439080499235475}, {129/1000, 4.404180085244939}, 
     {13/100, 4.369819312700617}, {131/1000, 4.33597504463166}, 
     {33/250, 4.302639410470312}, {133/1000, 4.269807261347131}, 
     {67/500, 4.237456460939012}, {27/200, 4.205587658083856}, 
     {17/125, 4.17418079606721}, {137/1000, 4.143227818194211}, 
     {69/500, 4.112718830091265}, {139/1000, 4.082651523206696}, 
     {7/50, 4.0530084807715765}, {141/1000, 4.02378099657738}, 
     {71/500, 3.994959724216292}, {143/1000, 3.9665423829137687}, 
     {18/125, 3.9385187995582527}, {29/200, 3.910872938556021}, 
     {73/500, 3.8836096434523473}, {147/1000, 3.8567118020781894}, 
     {37/250, 3.8301691892230574}, {149/1000, 3.803984530153034}, 
     {3/20, 3.7781487835294314}, {151/1000, 3.7526504607858344}, 
     {19/125, 3.727483174738188}, {153/1000, 3.7026444771628464}, 
     {77/500, 3.678124707462474}, {31/200, 3.6539179684499885}, 
     {39/250, 3.630016049724044}, {157/1000, 3.606422123616068}, 
     {79/500, 3.5831209921041998}, {159/1000, 3.5601103336580415}, 
     {4/25, 3.5373854695531426}, {161/1000, 3.514940045051155}, 
     {81/500, 3.4927695291675533}, {163/1000, 3.470867357466373}, 
     {41/250, 3.4492277123156487}, {33/200, 3.4278527452520917}, 
     {83/500, 3.4067305277517788}, {167/1000, 3.38585964491741}, 
     {21/125, 3.365231901551308}, {169/1000, 3.3448477229118847}, 
     {17/100, 3.3247007348655337}, {171/1000, 3.304791822090878}, 
     {43/250, 3.2851047398231774}, {173/1000, 3.2656493418573174}, 
     {87/500, 3.246408612697704}, {7/40, 3.2273895857903643}, 
     {22/125, 3.208587158946086}, {177/1000, 3.1899886609485577}, 
     {89/500, 3.171601236970205}, {179/1000, 3.1534152128040622}, 
     {9/50, 3.135429160182599}, {181/1000, 3.1176433046183485}, 
     {91/500, 3.100045334002437}, {183/1000, 3.0826430435785097}, 
     {23/125, 3.06542516121638}, {37/200, 3.0483879981792548}, 
     {93/500, 3.031537827184036}, {187/1000, 3.014861581770284}, 
     {47/250, 2.9983649831020003}, {189/1000, 2.982037937785953}, 
     {19/100, 2.9658777705405663}, {191/1000, 2.949891596202513}, 
     {24/125, 2.9340633712944344}, {193/1000, 2.918402869428231}, 
     {97/500, 2.9028994876503305}, {39/200, 2.887550718473549}, 
     {49/250, 2.872359230622566}, {197/1000, 2.8573200354879287}, 
     {99/500, 2.8424313245746697}, {199/1000, 2.8276922137416465}, 
     {1/5, 2.8130941505958713}, {201/1000, 2.798642527462601}, 
     {101/500, 2.784333799143121}, {203/1000, 2.770161322962609}, 
     {51/250, 2.756127771418673}, {41/200, 2.742227152041339}, 
     {103/500, 2.7284623099978993}, {207/1000, 2.714826902757533}, 
     {26/125, 2.701322065044887}, {209/1000, 2.6879432522090574}, 
     {21/100, 2.6746908709325687}, {211/1000, 2.6615606653365917}, 
     {53/250, 2.6485547115763115}, {213/1000, 2.6356711303902562}, 
     {107/500, 2.6229045499018255}, {43/200, 2.61025402906367}, 
     {27/125, 2.5977212329188593}, {217/1000, 2.585299091523584}, 
     {109/500, 2.572994367566791}, {219/1000, 2.560796672849767}, 
     {11/50, 2.5487103055023628}, {221/1000, 2.536727829721279}, 
     {111/500, 2.524854817428891}, {223/1000, 2.513088884975794}, 
     {28/125, 2.501424538588862}, {9/40, 2.489862597677697}, 
     {113/500, 2.4783982679543204}, {227/1000, 2.4670384081016796}, 
     {57/250, 2.4557748406931115}, {229/1000, 2.4446062388956094}, 
     {23/100, 2.4335372138910536}, {231/1000, 2.422561641089132}, 
     {29/125, 2.411678370514701}, {233/1000, 2.4008861884198227}, 
     {117/500, 2.390187356941538}, {47/200, 2.379573455010645}, 
     {59/250, 2.369051576818215}, {237/1000, 2.358618966686751}, 
     {119/500, 2.3482712037192557}, {239/1000, 2.338005907146139}, 
     {6/25, 2.3278272006477208}, {241/1000, 2.3177316578192793}, 
     {121/500, 2.307719907901267}, {243/1000, 2.297787947679982}, 
     {61/250, 2.287934251562617}, {49/200, 2.2781637271954183}, 
     {123/500, 2.268470029788243}, {247/1000, 2.2588505867434456}, 
     {31/125, 2.249308994387907}, {249/1000, 2.2398453030977707}, 
     {1/4, 2.2304540839074214}, {251/1000, 2.221135387132482}, 
     {63/250, 2.2118934781981707}, {253/1000, 2.202720377568837}, 
     {127/500, 2.1936170792750653}, {51/200, 2.1845881995988568}, 
     {32/125, 2.1756264755219408}, {257/1000, 2.166733555456298}, 
     {129/500, 2.1579057625684865}, {259/1000, 2.149149511087889}, 
     {13/50, 2.1404580817012318}, {261/1000, 2.1318292698442}, 
     {131/500, 2.123269745348229}, {263/1000, 2.114771739356792}, 
     {33/125, 2.1063383244103346}, {53/200, 2.097964514017086}, 
     {133/500, 2.089656595602558}, {267/1000, 2.0814063184589564}, 
     {67/250, 2.0732206014501666}, {269/1000, 2.0650919641141936}, 
     {27/100, 2.0570217296693984}, {271/1000, 2.049013873310319}, 
     {34/125, 2.0410592627841453}, {273/1000, 2.0331663106082187}, 
     {137/500, 2.0253280730298178}, {11/40, 2.0175452847387665}, 
     {69/250, 2.009819518665024}, {277/1000, 2.002145249132607}, 
     {139/500, 1.9945293406357156}, {279/1000, 1.9869636089599791}, 
     {7/25, 1.9794549979408167}, {281/1000, 1.971996586088535}, 
     {141/500, 1.9645902062830687}, {283/1000, 1.9572350624444743}, 
     {71/250, 1.9499316645426266}, {57/200, 1.942678499241524}, 
     {143/500, 1.9354742915812846}, {287/1000, 1.9283208110534904}, 
     {36/125, 1.9212150185124388}, {289/1000, 1.9141585002390582}, 
     {29/100, 1.9071478291903223}, {291/1000, 1.9001855211532828}, 
     {73/250, 1.8932722949087517}, {293/1000, 1.886404092549562}, 
     {147/500, 1.879580063625327}, {59/200, 1.8728045751296216}, 
     {37/125, 1.8660725768396427}, {297/1000, 1.8593829211370076}, 
     {149/500, 1.8527394358626554}, {299/1000, 1.8461414883175213}, 
     {3/10, 1.839585230709408}, {301/1000, 1.8330709488647057}, 
     {151/500, 1.826599962688063}, {303/1000, 1.8201704932427765}, 
     {38/125, 1.8137833088092745}, {61/200, 1.8074353622444117}, 
     {153/500, 1.8011311415278706}, {307/1000, 1.7948658275405478}, 
     {77/250, 1.78864094875444}, {309/1000, 1.782455297943963}, 
     {31/100, 1.7763088548154804}, {311/1000, 1.7702008324250533}, 
     {39/125, 1.764131400390216}, {313/1000, 1.758099339619341}, 
     {157/500, 1.7521077246915522}, {63/200, 1.7461521909815625}, 
     {79/250, 1.7402326185290709}, {317/1000, 1.7343496959254288}, 
     {159/500, 1.7285053304165048}, {319/1000, 1.7226961102321072}, 
     {8/25, 1.7169216314573221}, {321/1000, 1.7111818300661787}, 
     {161/500, 1.70547977248828}, {323/1000, 1.6998097362151823}, 
     {81/250, 1.6941769736626189}, {13/40, 1.688576802268874}, 
     {163/500, 1.683009112487177}, {327/1000, 1.677475744081935}, 
     {41/125, 1.6719769322288145}, {329/1000, 1.6665105504495006}, 
     {33/100, 1.661075848084733}, {331/1000, 1.6556743915021248}, 
     {83/250, 1.65030257630063}, {333/1000, 1.6449641243567155}, 
     {167/500, 1.6396586161822415}, {67/200, 1.6343826455834576}, 
     {42/125, 1.6291369249111851}, {337/1000, 1.6239236862100386}, 
     {169/500, 1.6187401559776726}, {339/1000, 1.6135850663197222}, 
     {17/50, 1.6084623190324705}, {341/1000, 1.6033676878325291}, 
     {171/500, 1.5983029549215289}, {343/1000, 1.593265716414706}, 
     {43/125, 1.5882595772962627}, {69/200, 1.583281085936866}, 
     {173/500, 1.5783301623336163}, {347/1000, 1.5734073369796098}, 
     {87/250, 1.5685147055825457}, {349/1000, 1.563647904876474}, 
     {7/20, 1.558807012368419}, {351/1000, 1.553994698092472}, 
     {44/125, 1.5492102794195746}, {353/1000, 1.5444523855407493}, 
     {177/500, 1.539719626821535}, {71/200, 1.5350126883122692}, 
     {89/250, 1.5303340611590963}, {357/1000, 1.525679683856334}, 
     {179/500, 1.521051372829532}, {359/1000, 1.5164471175212118}, 
     {9/25, 1.5118706870589174}, {361/1000, 1.5073177167279361}, 
     {181/500, 1.5027891979397308}, {363/1000, 1.4982854972602655}, 
     {91/250, 1.4938069316794582}, {73/200, 1.4893515049394992}, 
     {183/500, 1.4849206739429603}, {367/1000, 1.4805131376022502}, 
     {46/125, 1.4761297207417514}, {369/1000, 1.4717698607628982}, 
     {37/100, 1.4674324839915158}, {371/1000, 1.4631187260715208}, 
     {93/250, 1.4588280173666104}, {373/1000, 1.4545596628045545}, 
     {187/500, 1.4503132855591327}, {3/8, 1.4460900868814477}, 
     {47/125, 1.4418875564342206}, {377/1000, 1.4377095511039997}, 
     {189/500, 1.4335512156169994}, {379/1000, 1.429415697959877}, 
     {19/50, 1.4253009474965888}, {381/1000, 1.4212076072133635}, 
     {191/500, 1.4171361310778448}, {383/1000, 1.4130848912255127}, 
     {48/125, 1.409053448214593}, {77/200, 1.405044952993602}, 
     {193/500, 1.4010558830499842}, {387/1000, 1.3970870735404708}, 
     {97/250, 1.3931389050592677}, {389/1000, 1.389210315205863}, 
     {39/100, 1.3853004617937992}, {391/1000, 1.3814127133432286}, 
     {49/125, 1.3775422588974608}, {393/1000, 1.3736937998165606}, 
     {197/500, 1.3698630765586894}, {79/200, 1.3660517421634581}, 
     {99/250, 1.3622594490452982}, {397/1000, 1.3584864229449338}, 
     {199/500, 1.3547311791224157}, {399/1000, 1.3509951108600113}, 
     {2/5, 1.3472775715912464}, {401/1000, 1.3435779451551806}, 
     {201/500, 1.3398967563267634}, {403/1000, 1.3362337100892845}, 
     {101/250, 1.3325886285160102}, {81/200, 1.328960305582332}, 
     {203/500, 1.3253517519932927}, {407/1000, 1.3217597409701873}, 
     {51/125, 1.318183758576602}, {409/1000, 1.3146275795886646}, 
     {41/100, 1.3110870607317038}, {411/1000, 1.3075639706945272}, 
     {103/250, 1.304056605517081}, {413/1000, 1.3005680124870287}, 
     {207/500, 1.297095544143508}, {83/200, 1.2936382056344486}, 
     {52/125, 1.290199571743616}, {417/1000, 1.286776161841889}, 
     {209/500, 1.283368919050411}, {419/1000, 1.2799778947229798}, 
     {21/50, 1.27660260628795}, {421/1000, 1.2732436726946146}, 
     {211/500, 1.26989989585255}, {423/1000, 1.2665720415612558}, 
     {53/125, 1.263260327776496}, {17/40, 1.2599639760375063}, 
     {213/500, 1.256682127188526}, {427/1000, 1.253416024068193}, 
     {107/250, 1.250164565244031}, {429/1000, 1.2469289203167495}, 
     {43/100, 1.243707880270082}, {431/1000, 1.2405011496958072}, 
     {54/125, 1.2373102554636428}, {433/1000, 1.2341337002623611}, 
     {217/500, 1.2309708377292168}, {87/200, 1.227822469369318}, 
     {109/250, 1.2246887650264373}, {437/1000, 1.2215701306710267}, 
     {219/500, 1.2184653244471053}, {439/1000, 1.215373023387302}, 
     {11/25, 1.2122969744815948}, {441/1000, 1.209232845585631}, 
     {221/500, 1.2061843981847915}, {443/1000, 1.2031479644680638}, 
     {111/250, 1.200125257047738}, {89/200, 1.1971178722285911}, 
     {223/500, 1.1941218677740835}, {447/1000, 1.1911406948700516}, 
     {56/125, 1.1881716232402886}, {449/1000, 1.1852161828059586}, 
     {9/20, 1.1822736587754745}, {451/1000, 1.179344108794396}, 
     {113/250, 1.176427435809336}, {453/1000, 1.1735229430777445}, 
     {227/500, 1.1706331709965303}, {91/200, 1.1677536374743536}, 
     {57/125, 1.1648883888701722}, {457/1000, 1.1620354258650223}, 
     {229/500, 1.1591947996497147}, {459/1000, 1.1563650178987213}, 
     {23/50, 1.1535499594690837}, {461/1000, 1.150745844207886}, 
     {231/500, 1.14795391627076}, {463/1000, 1.1451727970839216}, 
     {58/125, 1.142404707423594}, {93/200, 1.1396490797953729}, 
     {233/500, 1.1369050443630453}, {467/1000, 1.1341728328641572}, 
     {117/250, 1.1314512907261252}, {469/1000, 1.1287422038709372}, 
     {47/100, 1.126044406563095}, {471/1000, 1.1233579834410032}, 
     {59/125, 1.1206833055195276}, {473/1000, 1.1180195118459453}, 
     {237/500, 1.115367023324969}, {19/40, 1.1127247932738993}, 
     {119/250, 1.1100953339190784}, {477/1000, 1.1074760191236763}, 
     {239/500, 1.1048677527384934}, {479/1000, 1.1022707615521834}, 
     {12/25, 1.0996842454438545}, {481/1000, 1.0971077088562684}, 
     {241/500, 1.094543423510016}, {483/1000, 1.0919890554543985}, 
     {121/250, 1.0894450707398415}, {97/200, 1.0869118095312433}, 
     {243/500, 1.0843885023866684}, {487/1000, 1.0818752680493375}, 
     {61/125, 1.0793730665591723}, {489/1000, 1.076881124585328}, 
     {49/100, 1.074399320538094}, {491/1000, 1.0719276900347754}, 
     {123/250, 1.0694661354644421}, {493/1000, 1.0670150419611335}, 
     {247/500, 1.0645738883799865}, {99/200, 1.0621413663286026}, 
     {62/125, 1.0597202358438815}, {497/1000, 1.0573075233718439}, 
     {249/500, 1.0549061940224793}, {499/1000, 1.0525136014182053}, 
     {1/2, 1.050130484831036}, {501/1000, 1.047757069017739}, 
     {251/500, 1.0453928296282573}, {503/1000, 1.0430386155307712}, 
     {63/125, 1.040693255528882}, {101/200, 1.0383579288237936}, 
     {253/500, 1.036030448706786}, {507/1000, 1.033713587611868}, 
     {127/250, 1.0314046766334342}, {509/1000, 1.029106696111736}, 
     {51/100, 1.0268158036180863}, {511/1000, 1.0245356872847229}, 
     {64/125, 1.0222629912511059}, {513/1000, 1.0200009665912244}, 
     {257/500, 1.0177468855601888}, {103/200, 1.0155016908003427}, 
     {129/250, 1.013264117022184}, {517/1000, 1.0110373268308677}, 
     {259/500, 1.0088171126773873}, {519/1000, 1.0066075043011733}, 
     {13/25, 1.004404749435622}, {521/1000, 1.002212399909819}, 
     {261/500, 1.000026831656759}, {523/1000, 0.997850528664453}, 
     {131/250, 0.9956828186131684}, {21/40, 0.9935225983894911}, 
     {263/500, 0.9913706663806152}, {527/1000, 0.9892283137994163}, 
     {66/125, 0.9870932897539679}, {529/1000, 0.9849662057753039}, 
     {53/100, 0.9828472882575803}, {531/1000, 0.9807366324952338}, 
     {133/250, 0.9786342047466772}, {533/1000, 0.9765400159924779}, 
     {267/500, 0.9744532559449417}, {107/200, 0.9723744887458982}, 
     {67/125, 0.9703028858223011}, {537/1000, 0.968240309168273}, 
     {269/500, 0.966184938629594}, {539/1000, 0.9641371385461939}, 
     {27/50, 0.9620963471932613}, {541/1000, 0.9600650866912388}, 
     {271/500, 0.9580402608443748}, {543/1000, 0.9560230811441817}, 
     {68/125, 0.9540125166070728}, {109/200, 0.952011175249577}, 
     {273/500, 0.9500160915071173}, {547/1000, 0.9480293521501146}, 
     {137/250, 0.9460483897397858}, {549/1000, 0.9440766924691495}, 
     {11/20, 0.9421104594030582}, {551/1000, 0.9401533249500421}, 
     {69/125, 0.9382015453018929}, {553/1000, 0.9362584326289057}, 
     {277/500, 0.9343221850229564}, {111/200, 0.9323917964964445}, 
     {139/250, 0.9304700852866346}, {557/1000, 0.9285543651588307}, 
     {279/500, 0.9266459756717571}, {559/1000, 0.9247450319302278}, 
     {14/25, 0.9228504570092281}, {561/1000, 0.9209628156039343}, 
     {281/500, 0.919081115877723}, {563/1000, 0.9172075015134507}, 
     {141/250, 0.9153398694985162}, {113/200, 0.913479357772695}, 
     {283/500, 0.9116263107070508}, {567/1000, 0.9097788243168881}, 
     {71/125, 0.907938469527445}, {569/1000, 0.9061049687780788}, 
     {57/100, 0.9042777274766662}, {571/1000, 0.9024560590935808}, 
     {143/250, 0.9006417210158497}, {573/1000, 0.8988346265573176}, 
     {287/500, 0.8970334706503952}, {23/40, 0.8952384595860948}, 
     {72/125, 0.8934492903857822}, {577/1000, 0.8916675985521404}, 
     {289/500, 0.8898915712540976}, {579/1000, 0.8881217877992116}, 
     {29/50, 0.8863576541700982}, {581/1000, 0.8846008655012396}, 
     {291/500, 0.8828493753834492}, {583/1000, 0.8811052951682238}, 
     {73/125, 0.879366214729699}, {117/200, 0.8776338017133396}, 
     {293/500, 0.8759071907111611}, {587/1000, 0.8741866598699348}, 
     {147/250, 0.8724720835832394}, {589/1000, 0.8707631278929896}, 
     {59/100, 0.8690607035254186}, {591/1000, 0.8673639750078552}, 
     {74/125, 0.8656731581170716}, {593/1000, 0.86398725183458}, 
     {297/500, 0.8623080442165756}, {119/200, 0.8606355171626137}, 
     {149/250, 0.8589677387404929}, {597/1000, 0.8573059966225081}, 
     {299/500, 0.8556496304945689}, {599/1000, 0.8539992696481391}, 
     {3/5, 0.8523544489277096}, {601/1000, 0.8507152514806668}, 
     {301/500, 0.8490816622826836}, {603/1000, 0.8474527936971045}, 
     {151/250, 0.8458306953226611}, {121/200, 0.844214446558768}, 
     {303/500, 0.8426022697175973}, {607/1000, 0.8409964635507471}, 
     {76/125, 0.8393954173555551}, {609/1000, 0.8378006546595272}, 
     {61/100, 0.8362111961756578}, {611/1000, 0.8346270016075585}, 
     {153/250, 0.8330476689964967}, {613/1000, 0.8314742126483183}, 
     {307/500, 0.8299050688255705}, {123/200, 0.8283426911099938}, 
     {77/125, 0.8267847991869844}, {617/1000, 0.8252313703394701}, 
     {309/500, 0.8236846952684937}, {619/1000, 0.8221415478408673}, 
     {31/50, 0.8206050293972654}, {621/1000, 0.8190726977569478}, 
     {311/500, 0.8175456604211511}, {623/1000, 0.8160240282163809}, 
     {78/125, 0.8145069197637805}, {5/8, 0.8129955101739069}, 
     {313/500, 0.8114885431022115}, {627/1000, 0.8099864003653711}, 
     {157/250, 0.8084898918194847}, {629/1000, 0.8069972537190749}, 
     {63/100, 0.805510203091282}, {631/1000, 0.8040287690217482}, 
     {79/125, 0.8025510490828411}, {633/1000, 0.801078899193479}, 
     {317/500, 0.7996109982115395}, {127/200, 0.7981485554012558}, 
     {159/250, 0.7966907246758848}, {637/1000, 0.7952364671690725}, 
     {319/500, 0.7937878503847071}, {639/1000, 0.7923446581097543}, 
     {16/25, 0.7909047759473723}, {641/1000, 0.7894702902666346}, 
     {321/500, 0.7880407589928499}, {643/1000, 0.7866158081539442}, 
     {161/250, 0.7851949474711776}, {129/200, 0.7837784901749476}, 
     {323/500, 0.7823673311154365}, {647/1000, 0.780960083499385}, 
     {81/125, 0.7795576190390126}, {649/1000, 0.7781597278636346}, 
     {13/20, 0.7767663021326221}, {651/1000, 0.7753779949069299}, 
     {163/250, 0.773993006751743}, {653/1000, 0.7726126612312124}, 
     {327/500, 0.7712372562176106}, {131/200, 0.7698655932787994}, 
     {82/125, 0.7684987578429454}, {657/1000, 0.7671360165004876}, 
     {329/500, 0.7657776814180034}, {659/1000, 0.7644243279734656}, 
     {33/50, 0.7630743836134717}, {661/1000, 0.7617285838771639}, 
     {331/500, 0.7603874140489548}, {663/1000, 0.7590511291574265}, 
     {83/125, 0.757718351121182}, {133/200, 0.7563897555356912}, 
     {333/500, 0.7550654283347383}, {667/1000, 0.7537445002753443}, 
     {167/250, 0.7524291400612177}, {669/1000, 0.7511165531764539}, 
     {67/100, 0.7498089003393704}, {671/1000, 0.7485054808954915}, 
     {84/125, 0.7472057856653863}, {673/1000, 0.7459094314045922}, 
     {337/500, 0.7446184569167303}, {27/40, 0.7433305447541156}, 
     {169/250, 0.7420466031418369}, {677/1000, 0.7407674598758569}, 
     {339/500, 0.7394919934757406}, {679/1000, 0.7382195565428933}, 
     {17/25, 0.7369522989134594}, {681/1000, 0.7356878704040499}, 
     {341/500, 0.7344279424694258}, {683/1000, 0.7331720128073094}, 
     {171/250, 0.7319200425738375}, {137/200, 0.7306716562804543}, 
     {343/500, 0.7294267961603877}, {687/1000, 0.7281855595262047}, 
     {86/125, 0.7269493858314529}, {689/1000, 0.7257161154099911}, 
     {69/100, 0.7244865752294347}, {691/1000, 0.723260707850912}, 
     {173/250, 0.7220387570562009}, {693/1000, 0.7208202807465096}, 
     {347/500, 0.7196057591121237}, {139/200, 0.7183948727346476}, 
     {87/125, 0.7171876037802055}, {697/1000, 0.7159844006943419}, 
     {349/500, 0.7147848384733002}, {699/1000, 0.713588007257657}, 
     {7/10, 0.712395310963211}, {701/1000, 0.7112068725599259}, 
     {351/500, 0.7100207655726211}, {703/1000, 0.7088394375899905}, 
     {88/125, 0.7076604247866952}, {141/200, 0.706485519239332}, 
     {353/500, 0.7053143348375746}, {707/1000, 0.7041471426759667}, 
     {177/250, 0.7029821845582329}, {709/1000, 0.7018213254416884}, 
     {71/100, 0.7006644671320739}, {711/1000, 0.699510226501933}, 
     {89/125, 0.6983594710627541}, {713/1000, 0.6972124436377267}, 
     {357/500, 0.6960695899298591}, {143/200, 0.6949286998681642}, 
     {179/250, 0.6937921102862783}, {717/1000, 0.6926578844566935}, 
     {359/500, 0.6915277136852166}, {719/1000, 0.6904008396870998}, 
     {18/25, 0.689277355871772}, {721/1000, 0.6881573095150961}, 
     {361/500, 0.6870406909004882}, {723/1000, 0.6859270360971906}, 
     {181/250, 0.6848160764700257}, {29/40, 0.6837089080439049}, 
     {363/500, 0.6826049670326297}, {727/1000, 0.6815049284832844}, 
     {91/125, 0.680406945853951}, {729/1000, 0.6793126296069587}, 
     {73/100, 0.6782216080145047}, {731/1000, 0.6771337018032293}, 
     {183/250, 0.676048992173159}, {733/1000, 0.674967381279116}, 
     {367/500, 0.6738889508518248}, {147/200, 0.6728138976156575}, 
     {92/125, 0.6717414862134623}, {737/1000, 0.6706723721629055}, 
     {369/500, 0.6696063902025704}, {739/1000, 0.6685436171673262}, 
     {37/50, 0.6674835319427953}, {741/1000, 0.6664267125453531}, 
     {371/500, 0.6653732048691988}, {743/1000, 0.6643228173695305}, 
     {93/125, 0.6632745160876683}, {149/200, 0.6622298491290813}, 
     {373/500, 0.6611883951540394}, {747/1000, 0.6601493229593981}, 
     {187/250, 0.6591137610293912}, {749/1000, 0.6580807069973276}, 
     {3/4, 0.6570510936282088}, {751/1000, 0.6560238651465079}, 
     {94/125, 0.6549999084840927}, {753/1000, 0.653978708269888}, 
     {377/500, 0.6529613034679667}, {151/200, 0.651945255527282}, 
     {189/250, 0.6509327828656601}, {757/1000, 0.6499231509948005}, 
     {379/500, 0.6489166557964364}, {759/1000, 0.6479124571684483}, 
     {19/25, 0.6469116848563587}, {761/1000, 0.6459132842708795}, 
     {381/500, 0.644917771591701}, {763/1000, 0.6439253345037983}, 
     {191/250, 0.6429355439482854}, {153/200, 0.6419488263900024}, 
     {383/500, 0.6409642512693259}, {767/1000, 0.6399830767786014}, 
     {96/125, 0.6390041749565348}, {769/1000, 0.6380275822732617}, 
     {77/100, 0.6370543113674858}, {771/1000, 0.6360838624526325}, 
     {193/250, 0.6351157018339453}, {773/1000, 0.6341504880168845}, 
     {387/500, 0.6331879786970163}, {31/40, 0.6322288537712671}, 
     {97/125, 0.6312710277250282}, {777/1000, 0.6303165548004089}, 
     {389/500, 0.6293646260586849}, {779/1000, 0.6284151594875436}, 
     {39/50, 0.6274685034550547}, {781/1000, 0.626524634741509}, 
     {391/500, 0.6255830182357952}, {783/1000, 0.6246443141066336}, 
     {98/125, 0.6237078493359591}, {157/200, 0.6227741606264923}, 
     {393/500, 0.6218432174772741}, {787/1000, 0.620914644531923}, 
     {197/250, 0.6199885819265188}, {789/1000, 0.6190648579229449}, 
     {79/100, 0.6181439393073294}, {791/1000, 0.6172254388663113}, 
     {99/125, 0.616309654419087}, {793/1000, 0.6153960080505907}, 
     {397/500, 0.6144850357318622}, {159/200, 0.6135771328913695}, 
     {199/250, 0.6126706510549992}, {797/1000, 0.6117669484018944}, 
     {399/500, 0.6108659678288227}, {799/1000, 0.609967130472437}, 
     {4/5, 0.6090708648668213}, {801/1000, 0.6081772064921533}, 
     {401/500, 0.6072858129069939}, {803/1000, 0.6063966380106167}, 
     {201/250, 0.6055101696995305}, {161/200, 0.6046257350971972}, 
     {403/500, 0.603743946579361}, {807/1000, 0.6028650122497643}, 
     {101/125, 0.6019875391702695}, {809/1000, 0.6011126778522499}, 
     {81/100, 0.6002402899031782}, {811/1000, 0.599370171675959}, 
     {203/250, 0.5985022945447849}, {813/1000, 0.5976368374146177}, 
     {407/500, 0.5967737883100849}, {163/200, 0.5959134387608758}, 
     {102/125, 0.5950542641649519}, {817/1000, 0.594198032074827}, 
     {409/500, 0.5933441520525152}, {819/1000, 0.5924928764474007}, 
     {41/50, 0.5916428506280148}, {821/1000, 0.590795613439332}, 
     {411/500, 0.5899506204423146}, {823/1000, 0.5891079266872952}, 
     {103/125, 0.588267557828994}, {33/40, 0.5874292801688612}, 
     {413/500, 0.5865930253495215}, {827/1000, 0.5857597008919854}, 
     {207/250, 0.5849275513675852}, {829/1000, 0.5840980536984473}, 
     {83/100, 0.5832706305257007}, {831/1000, 0.5824454799671133}, 
     {104/125, 0.5816225565875099}, {833/1000, 0.5808017260594234}, 
     {417/500, 0.579983495154395}, {167/200, 0.5791668982069127}, 
     {209/250, 0.5783519121040287}, {837/1000, 0.5775401805620812}, 
     {419/500, 0.5767295770743339}, {839/1000, 0.5759213357048847}, 
     {21/25, 0.5751153897574692}, {841/1000, 0.5743114737209063}, 
     {421/500, 0.5735097048464066}, {843/1000, 0.5727101224774397}, 
     {211/250, 0.5719123240998718}, {169/200, 0.5711167416743133}, 
     {423/500, 0.5703232524573647}, {847/1000, 0.5695318436913992}, 
     {106/125, 0.5687423533215181}, {849/1000, 0.5679548744056382}, 
     {17/20, 0.5671695398353791}, {851/1000, 0.5663867518854724}, 
     {213/250, 0.5656049587443495}, {853/1000, 0.5648254890701372}, 
     {427/500, 0.5640487135685492}, {171/200, 0.563272905591859}, 
     {107/125, 0.5625000003419133}, {857/1000, 0.5617286080594492}, 
     {429/500, 0.5609587391443591}, {859/1000, 0.5601912887525652}, 
     {43/50, 0.55942581267359}, {861/1000, 0.5586623140546103}, 
     {431/500, 0.5579006771744794}, {863/1000, 0.557141457633779}, 
     {108/125, 0.5563831984196361}, {173/200, 0.55562733282707}, 
     {433/500, 0.5548735874055137}, {867/1000, 0.5541216053390909}, 
     {217/250, 0.5533719693388182}, {869/1000, 0.552623299576261}, 
     {87/100, 0.5518770091486788}, {871/1000, 0.5511325391657425}, 
     {109/125, 0.5503899951479495}, {873/1000, 0.5496494330994883}, 
     {437/500, 0.5489105138065142}, {7/8, 0.5481735521183313}, 
     {219/250, 0.5474386477269866}, {877/1000, 0.5467052360577926}, 
     {439/500, 0.5459738355782299}, {879/1000, 0.5452442593117411}, 
     {22/25, 0.5445170404898183}, {881/1000, 0.5437905256241213}, 
     {441/500, 0.5430664409778451}, {883/1000, 0.5423441231747772}, 
     {221/250, 0.541623610759397}, {177/200, 0.5409049986897738}, 
     {443/500, 0.5401880508144699}, {887/1000, 0.5394732985177488}, 
     {111/125, 0.5387594193763868}, {889/1000, 0.5380477910601615}, 
     {89/100, 0.537338111421181}, {891/1000, 0.5366299959981922}, 
     {223/250, 0.5359235507846136}, {893/1000, 0.5352194552698906}, 
     {447/500, 0.5345162047648558}, {179/200, 0.5338150295090458}, 
     {112/125, 0.5331156436850856}, {897/1000, 0.532418502493789}, 
     {449/500, 0.5317225680365898}, {899/1000, 0.5310277864105002}, 
     {9/10, 0.5303352880293398}, {901/1000, 0.5296444150738855}, 
     {451/500, 0.5289558445399911}, {903/1000, 0.5282678599621361}, 
     {113/125, 0.5275825881456364}, {181/200, 0.5268985334833007}, 
     {453/500, 0.5262160759817874}, {907/1000, 0.5255353274368609}, 
     {227/250, 0.5248557981171436}, {909/1000, 0.524178391281201}, 
     {91/100, 0.5235030167876075}, {911/1000, 0.522828308014345}, 
     {114/125, 0.5221563300649102}, {913/1000, 0.5214854137357061}, 
     {457/500, 0.5208157163237173}, {183/200, 0.5201485617794818}, 
     {229/250, 0.5194819876423014}, {917/1000, 0.5188176675504841}, 
     {459/500, 0.5181548794235468}, {919/1000, 0.5174936956275374}, 
     {23/25, 0.5168339488291904}, {921/1000, 0.5161764643986201}, 
     {461/500, 0.5155194962410364}, {923/1000, 0.514865175101123}, 
     {231/250, 0.5142114203384809}, {37/40, 0.5135596914666866}, 
     {463/500, 0.512909966992726}, {927/1000, 0.5122608850227254}, 
     {116/125, 0.5116143101748507}, {929/1000, 0.5109684279600661}, 
     {93/100, 0.5103243462145904}, {931/1000, 0.5096819133956942}, 
     {233/250, 0.5090410397324742}, {933/1000, 0.5084016710050845}, 
     {467/500, 0.5077643646986888}, {187/200, 0.5071275421404393}, 
     {117/125, 0.5064927518631851}, {937/1000, 0.5058594275883113}, 
     {469/500, 0.5052277132275731}, {939/1000, 0.5045972874917777}, 
     {47/50, 0.5039685085018147}, {941/1000, 0.5033412005393139}, 
     {471/500, 0.5027152581389431}, {943/1000, 0.5020909259307902}, 
     {118/125, 0.5014685089948501}, {189/200, 0.5008466085822352}, 
     {473/500, 0.5002266754941957}, {947/1000, 0.49960817561689713}, 
     {237/250, 0.4989915490683477}, {949/1000, 0.4983755267398663}, 
     {19/20, 0.4977614134261857}, {951/1000, 0.49714865256959806}, 
     {119/125, 0.49653730589300804}, {953/1000, 0.4959275103416144}, 
     {477/500, 0.49531902176624454}, {191/200, 0.4947121145319735}, 
     {239/250, 0.49410649534409146}, {957/1000, 0.49350231070280826}, 
     {479/500, 0.49289947675566115}, {959/1000, 0.49229865848762355}, 
     {24/25, 0.4916982878192742}, {961/1000, 0.4910996409174911}, 
     {481/500, 0.49050237137434005}, {963/1000, 0.4899066472703289}, 
     {241/250, 0.4893121615838233}, {193/200, 0.4887191716655789}, 
     {483/500, 0.48812751956602984}, {967/1000, 0.48753768977340817}, 
     {121/125, 0.486948309271475}, {969/1000, 0.4863606873149761}, 
     {97/100, 0.48577453394708503}, {971/1000, 0.48518958565008874}, 
     {243/250, 0.48460654323533264}, {973/1000, 0.4840243486917365}, 
     {487/500, 0.4834430550825251}, {39/40, 0.4828639872075573}, 
     {122/125, 0.4822857726718972}, {977/1000, 0.4817083950843992}, 
     {489/500, 0.48113285977036946}, {979/1000, 0.48055869261122974}, 
     {49/50, 0.4799861694076257}, {981/1000, 0.4794141181316369}, 
     {491/500, 0.47884384693070303}, {983/1000, 0.4782752808700314}, 
     {123/125, 0.4777071318578036}, {197/200, 0.47714071221652826}, 
     {493/500, 0.47657556978391813}, {987/1000, 0.47601172866044744}, 
     {247/250, 0.47544910691282166}, {989/1000, 0.4748882927160427}, 
     {99/100, 0.4743277937449547}, {991/1000, 0.47376905564175004}, 
     {124/125, 0.4732115295088331}, {993/1000, 0.4726553278681766}, 
     {497/500, 0.4721002833369996}, {199/200, 0.47154663351992676}, 
     {249/250, 0.47099457287605057}, {997/1000, 0.47044292015050937}, 
     {499/500, 0.4698929499065999}, {999/1000, 0.46934405746999486}, 
     {1, 0.4687965901518582}}
 
ImERfinc = {{1, 0.4687611149491187}, {201/200, 0.46604201109691973}, 
     {101/100, 0.46335311160501574}, {203/200, 0.4606939528456454}, 
     {51/50, 0.458064080024001}, {41/40, 0.4554630481565217}, 
     {103/100, 0.45289041829414156}, {207/200, 0.45034576331167525}, 
     {26/25, 0.44782866093876184}, {209/200, 0.4453386972563127}, 
     {21/20, 0.44287546745970685}, {211/200, 0.44043857394631103}, 
     {53/50, 0.4380276268132808}, {213/200, 0.4356422414605786}, 
     {107/100, 0.43328204369582335}, {43/40, 0.430946662030251}, 
     {27/25, 0.4286357351678289}, {217/200, 0.42634891447919987}, 
     {109/100, 0.4240858348036556}, {219/200, 0.4218461621793143}, 
     {11/10, 0.41962955785906136}, {221/200, 0.4174356915204947}, 
     {111/100, 0.4152642384020733}, {223/200, 0.413114880265573}, 
     {28/25, 0.4109873016943456}, {9/8, 0.4088811940128999}, 
     {113/100, 0.4067962556114896}, {227/200, 0.40473219075925604}, 
     {57/50, 0.40268870593539163}, {229/200, 0.4006655136631331}, 
     {23/20, 0.39866233155560427}, {231/200, 0.39667888204613605}, 
     {29/25, 0.3947148925514224}, {233/200, 0.3927700951274334}, 
     {117/100, 0.39084422642441413}, {47/40, 0.38893703111319644}, 
     {59/50, 0.3870482478117027}, {237/200, 0.3851776324143705}, 
     {119/100, 0.3833249366326009}, {239/200, 0.3814899186416114}, 
     {6/5, 0.3796723397095218}, {241/200, 0.37787196580158366}, 
     {121/100, 0.37608856674732893}, {243/200, 0.37432191632400436}, 
     {61/50, 0.37257179205762125}, {49/40, 0.3708379786419975}, 
     {123/100, 0.3691202573548641}, {247/200, 0.3674184164393447}, 
     {31/25, 0.3657322469246006}, {249/200, 0.36406154354626274}, 
     {5/4, 0.3624061047894336}, {251/200, 0.3607657322268268}, 
     {63/50, 0.35914023056695826}, {253/200, 0.35752941397487004}, 
     {127/100, 0.3559330820179667}, {51/40, 0.3543510575648505}, 
     {32/25, 0.3527831544814536}, {257/200, 0.3512291917050533}, 
     {129/100, 0.34968899016741833}, {259/200, 0.3481623766712716}, 
     {13/10, 0.3466491798125029}, {261/200, 0.3451492314473058}, 
     {131/100, 0.343662361339344}, {263/200, 0.3421884092433115}, 
     {33/25, 0.34072721291247066}, {53/40, 0.3392786123886573}, 
     {133/100, 0.3378424514622087}, {267/200, 0.33641857753755644}, 
     {67/50, 0.33500683878028514}, {269/200, 0.3336070859576849}, 
     {27/20, 0.332219168959606}, {271/200, 0.3308429427020461}, 
     {34/25, 0.3294782665949755}, {273/200, 0.3281250013066435}, 
     {137/100, 0.3267830068287356}, {11/8, 0.3254521465227733}, 
     {69/50, 0.32413228684977075}, {277/200, 0.3228232978200817}, 
     {139/100, 0.32152505033345313}, {279/200, 0.32023740982466253}, 
     {7/5, 0.31896024994855704}, {281/200, 0.31769345107423763}, 
     {141/100, 0.31643688802057557}, {283/200, 0.31519044141372216}, 
     {71/50, 0.31395399213339925}, {57/40, 0.3127274222220056}, 
     {143/100, 0.31151062251090056}, {287/200, 0.31030347064553454}, 
     {36/25, 0.30910585689732273}, {289/200, 0.307917668002368}, 
     {29/20, 0.3067387971705322}, {291/200, 0.3055691391199031}, 
     {73/50, 0.3044085902092918}, {293/200, 0.30325704335602055}, 
     {147/100, 0.3021143890374085}, {59/40, 0.3009805401725948}, 
     {37/25, 0.29985538750373286}, {297/200, 0.29873883481594077}, 
     {149/100, 0.2976307867697444}, {299/200, 0.29653114815628023}, 
     {3/2, 0.2954398246952678}, {301/200, 0.29435672392851164}, 
     {151/100, 0.2932817524795107}, {303/200, 0.2922148197299787}, 
     {38/25, 0.2911558381311799}, {61/40, 0.29010471952652117}, 
     {153/100, 0.289061377676714}, {307/200, 0.28802572770153645}, 
     {77/50, 0.28699768706045664}, {309/200, 0.28597716944921125}, 
     {31/20, 0.2849640987347494}, {311/200, 0.28395839021574426}, 
     {39/25, 0.2829599730125898}, {313/200, 0.2819687573985059}, 
     {157/100, 0.2809846716084735}, {63/40, 0.2800076395989642}, 
     {79/50, 0.2790375860258026}, {317/200, 0.27807443663578246}, 
     {159/100, 0.2771181184324278}, {319/200, 0.2761685596129831}, 
     {8/5, 0.275225688548988}, {321/200, 0.2742894270627596}, 
     {161/100, 0.2733597217799204}, {323/200, 0.27243649876563625}, 
     {81/50, 0.2715196909897005}, {13/8, 0.27060923178143337}, 
     {163/100, 0.2697050448747546}, {327/200, 0.2688070837526389}, 
     {41/25, 0.2679152778171218}, {329/200, 0.26702956358513563}, 
     {33/20, 0.26614987836152737}, {331/200, 0.2652761604044828}, 
     {83/50, 0.26440834899497156}, {333/200, 0.26354636975638723}, 
     {167/100, 0.2626902001902778}, {67/40, 0.26183975632973616}, 
     {42/25, 0.2609949874738386}, {337/200, 0.26015582758968203}, 
     {169/100, 0.2593222365460609}, {339/200, 0.25849415210198445}, 
     {17/10, 0.2576715255889036}, {341/200, 0.2568542884341369}, 
     {171/100, 0.2560423963033143}, {343/200, 0.2552357939205536}, 
     {43/25, 0.25443443341263694}, {69/40, 0.25363826732497724}, 
     {173/100, 0.25284723615502636}, {347/200, 0.25206129981795894}, 
     {87/50, 0.251280405262022}, {349/200, 0.25050450230390187}, 
     {7/4, 0.24973354213275795}, {351/200, 0.2489674774674436}, 
     {44/25, 0.24820626017844943}, {353/200, 0.2474498490845081}, 
     {177/100, 0.24669819176718416}, {71/40, 0.24595124950913666}, 
     {89/50, 0.24520897499668073}, {357/200, 0.24447132669781285}, 
     {179/100, 0.2437382609964579}, {359/200, 0.2430097516267248}, 
     {9/5, 0.24228571560298942}, {361/200, 0.2415661344405512}, 
     {181/100, 0.24085097524537563}, {363/200, 0.24014018582492658}, 
     {91/50, 0.23943372692082587}, {73/40, 0.23873155527732234}, 
     {183/100, 0.23803362857859106}, {367/200, 0.23733993428548358}, 
     {46/25, 0.23665040013218458}, {369/200, 0.23596501160131375}, 
     {37/20, 0.2352837247473109}, {371/200, 0.23460649940052636}, 
     {93/50, 0.2339332986517765}, {373/200, 0.23326407709591154}, 
     {187/100, 0.2325988297496446}, {15/8, 0.23193748802716993}, 
     {47/25, 0.23128001835438838}, {377/200, 0.23062640254283345}, 
     {189/100, 0.22997660162696554}, {379/200, 0.22933057867867623}, 
     {19/10, 0.2286883041381107}, {381/200, 0.22804974545700374}, 
     {191/100, 0.2274148705117527}, {383/200, 0.22678364456671962}, 
     {48/25, 0.22615602901060822}, {77/40, 0.22553200215877403}, 
     {193/100, 0.22491151804010262}, {387/200, 0.2242945627759543}, 
     {97/50, 0.22368109972948524}, {389/200, 0.22307110090251187}, 
     {39/20, 0.22246453969642446}, {391/200, 0.2218613809964166}, 
     {49/25, 0.2212615891420914}, {393/200, 0.22066514260025638}, 
     {197/100, 0.22007201449049885}, {79/40, 0.21948217112320273}, 
     {99/50, 0.2188955923895382}, {397/200, 0.21831224270293265}, 
     {199/100, 0.2177321000978113}, {399/200, 0.2171551311176226}, 
     {2, 0.21658131780398113}, {401/200, 0.2160106298356378}, 
     {201/100, 0.21544304418162463}, {403/200, 0.21487853352588868}, 
     {101/50, 0.2143170731526754}, {81/40, 0.21375863522968463}, 
     {203/100, 0.21320319429841625}, {407/200, 0.21265072565786963}, 
     {51/25, 0.21210120637085794}, {409/200, 0.2115546100747658}, 
     {41/20, 0.21101091450047207}, {411/200, 0.21047009431497715}, 
     {103/50, 0.20993213764248533}, {413/200, 0.2093970062247219}, 
     {207/100, 0.2088646864161137}, {83/40, 0.20833514957972465}, 
     {52/25, 0.20780838143086539}, {417/200, 0.2072843550164594}, 
     {209/100, 0.20676304679124297}, {419/200, 0.20624443505021706}, 
     {21/10, 0.20572849855647557}, {421/200, 0.20521521637192597}, 
     {211/100, 0.20470456816807747}, {423/200, 0.20419653356075956}, 
     {53/25, 0.20369110030899312}, {17/8, 0.20318823558192423}, 
     {213/100, 0.20268792151856696}, {427/200, 0.20219014789196343}, 
     {107/50, 0.20169488735349914}, {429/200, 0.2012021203940057}, 
     {43/20, 0.20071182406587657}, {431/200, 0.20022398467168995}, 
     {54/25, 0.19973858881353773}, {433/200, 0.1992555994655653}, 
     {217/100, 0.19877501087298657}, {87/40, 0.19829680331087718}, 
     {109/50, 0.19782096504786192}, {437/200, 0.1973474766967136}, 
     {219/100, 0.19687631735732353}, {439/200, 0.19640746687564992}, 
     {11/5, 0.19594091644832007}, {441/200, 0.19547663251526234}, 
     {221/100, 0.19501459656252723}, {443/200, 0.19455481625365356}, 
     {111/50, 0.1940972548055781}, {89/40, 0.19364190227322658}, 
     {223/100, 0.19318874868629035}, {447/200, 0.19273778166676847}, 
     {56/25, 0.19228897081362029}, {449/200, 0.19184230338007924}, 
     {9/4, 0.19139774980666915}, {451/200, 0.19095532612616284}, 
     {113/50, 0.19051499390446247}, {453/200, 0.19007674196839952}, 
     {227/100, 0.18964055271170283}, {91/40, 0.18920643727312847}, 
     {57/25, 0.18877435467153142}, {457/200, 0.18834428090137625}, 
     {229/100, 0.18791623079340525}, {459/200, 0.18749018160716355}, 
     {23/10, 0.18706610460455964}, {461/200, 0.18664398182034914}, 
     {231/100, 0.18622381770012292}, {463/200, 0.18580559128505925}, 
     {58/25, 0.18538930486912414}, {93/40, 0.18497491758732723}, 
     {233/100, 0.18456243924153232}, {467/200, 0.18415184645505614}, 
     {117/50, 0.1837431177020833}, {469/200, 0.18333623916717579}, 
     {47/20, 0.18293121825351832}, {471/200, 0.1825280243137603}, 
     {59/25, 0.1821266523947797}, {473/200, 0.18172708474075638}, 
     {237/100, 0.1813293238821005}, {19/8, 0.18093332411540547}, 
     {119/50, 0.1805391034049463}, {477/200, 0.18014666281700908}, 
     {239/100, 0.1797559515703567}, {479/200, 0.1793669814190074}, 
     {12/5, 0.1789797272205514}, {481/200, 0.17859418288799137}, 
     {241/100, 0.17821033969992162}, {483/200, 0.17782816931750853}, 
     {121/50, 0.17744772359950067}, {97/40, 0.17706891346889048}, 
     {243/100, 0.17669175837061363}, {487/200, 0.17631624480803232}, 
     {61/25, 0.1759423633104943}, {489/200, 0.17557010020901312}, 
     {49/20, 0.1751994464446073}, {491/200, 0.17483038956613664}, 
     {123/50, 0.1744629230361213}, {493/200, 0.17409685197043176}, 
     {247/100, 0.17373253334338423}, {99/40, 0.17336977671036788}, 
     {62/25, 0.17300857165785155}, {497/200, 0.17264890677385913}, 
     {249/100, 0.1722907704628694}, {499/200, 0.17193414478549712}, 
     {5/2, 0.17157901550687912}, {501/200, 0.17122537655347508}, 
     {251/100, 0.17087322609039157}, {503/200, 0.17052256238534774}, 
     {63/25, 0.1701733851466998}, {101/40, 0.1698258815835745}, 
     {253/100, 0.1694795987303197}, {507/200, 0.16913476661297266}, 
     {127/50, 0.16879135497269987}, {509/200, 0.1684493848470653}, 
     {51/20, 0.16810864367984182}, {511/200, 0.16776966209029362}, 
     {64/25, 0.16743190556348034}, {513/200, 0.1670955244257593}, 
     {257/100, 0.16676052727492074}, {103/40, 0.16642668015390555}, 
     {129/50, 0.1660945992339589}, {517/200, 0.16576369102082114}, 
     {259/100, 0.16543411520402274}, {519/200, 0.16510589025626143}, 
     {13/5, 0.1647787502547012}, {521/200, 0.16445338298438925}, 
     {261/100, 0.16412910153000393}, {523/200, 0.16380612348488566}, 
     {131/50, 0.16348446268108596}, {21/8, 0.16316405704490453}, 
     {263/100, 0.16284472435796885}, {527/200, 0.16252707648671874}, 
     {66/25, 0.1622104920963471}, {529/200, 0.16189517669340686}, 
     {53/20, 0.16158106702398772}, {531/200, 0.1612682220113349}, 
     {133/50, 0.16095662309368308}, {533/200, 0.16064624894343318}, 
     {267/100, 0.160337075012923}, {107/40, 0.1600291321811521}, 
     {67/25, 0.15972238696248303}, {537/200, 0.15941683317908628}, 
     {269/100, 0.15911245363354312}, {539/200, 0.15880930041715213}, 
     {27/10, 0.1585073019768071}, {541/200, 0.1582064615192505}, 
     {271/100, 0.15790677067425662}, {543/200, 0.15760825885299892}, 
     {68/25, 0.15731089162148976}, {109/40, 0.15701464078255187}, 
     {273/100, 0.15671954621723067}, {547/200, 0.1564255927555319}, 
     {137/50, 0.1561327076650437}, {549/200, 0.15584099066931806}, 
     {11/4, 0.15555037127080965}, {551/200, 0.15526086148745333}, 
     {69/25, 0.15497242324365043}, {553/200, 0.15468507661630304}, 
     {277/100, 0.15439882467343402}, {111/40, 0.15411363684746132}, 
     {139/50, 0.1538295319010587}, {557/200, 0.15354647646673403}, 
     {279/100, 0.15326451514103792}, {559/200, 0.15298357495104348}, 
     {14/5, 0.15270367353621045}, {561/200, 0.15242480905327443}, 
     {281/100, 0.1521469818151423}, {563/200, 0.15187022334412517}, 
     {141/50, 0.15159445770016333}, {113/40, 0.15131947692458994}, 
     {283/100, 0.15104573779151728}, {567/200, 0.1507730119960417}, 
     {71/25, 0.15050128695124135}, {569/200, 0.15023055381793765}, 
     {57/20, 0.14996080052807564}, {571/200, 0.14969202134047466}, 
     {143/50, 0.1494242245225832}, {573/200, 0.14915764831595726}, 
     {287/100, 0.14889179638665606}, {23/8, 0.14862690376060825}, 
     {72/25, 0.14836296837232782}, {577/200, 0.1480999826645019}, 
     {289/100, 0.14783794457758956}, {579/200, 0.147576868034185}, 
     {29/10, 0.14731671089084622}, {581/200, 0.14705748531406418}, 
     {291/100, 0.1467991729667605}, {583/200, 0.14654179681221066}, 
     {73/25, 0.14628532079605452}, {117/40, 0.14602954440576596}, 
     {293/100, 0.14577488103647954}, {587/200, 0.14552135375060146}, 
     {147/50, 0.14526849665857114}, {589/200, 0.1450165585325201}, 
     {59/20, 0.14476521682771584}, {591/200, 0.1445152855085657}, 
     {74/25, 0.14426596131029723}, {593/200, 0.14401750713319772}, 
     {297/100, 0.14376964202669065}, {119/40, 0.14352318725157534}, 
     {149/50, 0.14327732428913414}, {597/200, 0.14303232783413602}, 
     {299/100, 0.14278823534686041}, {599/200, 0.14254461841066146}, 
     {3, 0.1423023810993711}, {601/200, 0.1420607390115807}, 
     {301/100, 0.14181993173072624}, {603/200, 0.1415800018361363}, 
     {151/50, 0.14134054486813097}, {121/40, 0.14110245087267675}, 
     {303/100, 0.1408649216600291}, {607/200, 0.1406282141752463}, 
     {76/25, 0.14039242305978805}, {609/200, 0.1401571626478237}, 
     {61/20, 0.13992284542843675}, {611/200, 0.1396893206394222}, 
     {153/50, 0.13945660525947443}, {613/200, 0.1392246486759703}, 
     {307/100, 0.13899347617374397}, {123/40, 0.13876309329583206}, 
     {77/25, 0.13853349823785188}, {617/200, 0.13830465406721223}, 
     {309/100, 0.13807656422485037}, {619/200, 0.13784925939590836}, 
     {31/10, 0.13762269404835575}, {621/200, 0.13739687418410573}, 
     {311/100, 0.13717180257612716}, {623/200, 0.1369474997133376}, 
     {78/25, 0.13672393918542775}, {25/8, 0.13650111073150656}, 
     {313/100, 0.13627901248855367}, {627/200, 0.13605765248241847}, 
     {157/50, 0.1358370076014648}, {629/200, 0.13561706873524115}, 
     {63/20, 0.13539786906314275}, {631/200, 0.13517939824413971}, 
     {79/25, 0.13496162627591954}, {633/200, 0.13474458165160047}, 
     {317/100, 0.13452824019501414}, {127/40, 0.1343125883728167}, 
     {159/50, 0.13409762378677192}, {637/200, 0.1338833585454748}, 
     {319/100, 0.1336697738555855}, {639/200, 0.1334569196559465}, 
     {16/5, 0.13324473957997945}, {641/200, 0.13303321768175863}, 
     {321/100, 0.13282242133056796}, {643/200, 0.13261227253074984}, 
     {161/50, 0.13240279030468197}, {129/40, 0.13219397475511493}, 
     {323/100, 0.13198581870290518}, {647/200, 0.1317783181426628}, 
     {81/25, 0.1315714838235233}, {649/200, 0.13136532275447985}, 
     {13/4, 0.13115979166717587}, {651/200, 0.13095492417342322}, 
     {163/50, 0.13075070980878623}, {653/200, 0.13054714249399857}, 
     {327/100, 0.13034420532745933}, {131/40, 0.13014195100497308}, 
     {82/25, 0.12994027471594072}, {657/200, 0.12973919676040488}, 
     {329/100, 0.12953848692571276}, {659/200, 0.12933874496474743}, 
     {33/10, 0.1291398290397136}, {661/200, 0.12894130233266338}, 
     {331/100, 0.12874334971170223}, {663/200, 0.12854605200484742}, 
     {83/25, 0.12834947831207083}, {133/40, 0.12815327083861003}, 
     {333/100, 0.12795746414826525}, {667/200, 0.12776284492257795}, 
     {167/50, 0.1275685846006954}, {669/200, 0.12737487311652998}, 
     {67/20, 0.1271819189829085}, {671/200, 0.12698940886298704}, 
     {84/25, 0.12679709473428843}, {673/200, 0.1266060403378176}, 
     {337/100, 0.12641528648314693}, {27/8, 0.12622508497405313}, 
     {169/50, 0.1260354807139624}, {677/200, 0.12584645478608478}, 
     {339/100, 0.12565799734199287}, {679/200, 0.1254701265589409}, 
     {17/5, 0.1252828294545072}, {681/200, 0.12509605955067027}, 
     {341/100, 0.12490988558322846}, {683/200, 0.12472426898921486}, 
     {171/50, 0.12453920089909966}, {137/40, 0.12435466337087243}, 
     {343/100, 0.12417069059738296}, {687/200, 0.1239872753844322}, 
     {86/25, 0.12380440666554675}, {689/200, 0.12362207990604827}, 
     {69/20, 0.12344030783330172}, {691/200, 0.12325907707010927}, 
     {173/50, 0.12307836236183944}, {693/200, 0.12289817830191187}, 
     {347/100, 0.12271852888005427}, {139/40, 0.12253942916393064}, 
     {87/25, 0.12236083157048105}, {697/200, 0.12218276996837735}, 
     {349/100, 0.12200522861622828}, {699/200, 0.1218282197509824}, 
     {7/2, 0.12165173352493021}, {701/200, 0.12147576323876261}, 
     {351/100, 0.12130028559657363}, {703/200, 0.12112531007726614}, 
     {88/25, 0.12095082929121068}, {141/40, 0.1207769008867827}, 
     {353/100, 0.12060346132762002}, {707/200, 0.12043051036341988}, 
     {177/50, 0.12025808102723522}, {709/200, 0.12008617969766364}, 
     {71/20, 0.11991471103357061}, {711/200, 0.11974374256890484}, 
     {89/25, 0.11957330415951314}, {713/200, 0.11940331745811364}, 
     {357/100, 0.11923381982004012}, {143/40, 0.11906484357289845}, 
     {179/50, 0.11889632067228564}, {717/200, 0.11872829732811237}, 
     {359/100, 0.11856074390178231}, {719/200, 0.11839365724921186}, 
     {18/5, 0.11822703998879946}, {721/200, 0.11806089532645582}, 
     {361/100, 0.11789522279776458}, {723/200, 0.11773002326857097}, 
     {181/50, 0.11756529869700441}, {29/8, 0.11740106897754485}, 
     {363/100, 0.11723726972272035}, {727/200, 0.11707392221375622}, 
     {91/25, 0.11691102383118361}, {729/200, 0.11674858705504097}, 
     {73/20, 0.11658660645400332}, {731/200, 0.11642508037017052}, 
     {183/50, 0.11626401002375364}, {733/200, 0.11610338367743568}, 
     {367/100, 0.11594321199103606}, {147/40, 0.1157834962305354}, 
     {92/25, 0.1156242294056403}, {737/200, 0.11546538970157065}, 
     {369/100, 0.1153069748382799}, {739/200, 0.11514899460477235}, 
     {37/10, 0.11499145233427309}, {741/200, 0.11483435543591608}, 
     {371/100, 0.11467768485469483}, {743/200, 0.11452144703808487}, 
     {93/25, 0.11436564845438121}, {149/40, 0.11421030529676483}, 
     {373/100, 0.11405534764573917}, {747/200, 0.11390080034921099}, 
     {187/50, 0.11374667979945437}, {749/200, 0.11359299350043664}, 
     {15/4, 0.1134397084113151}, {751/200, 0.11328684349007068}, 
     {94/25, 0.11313440742590887}, {753/200, 0.1129824128210781}, 
     {377/100, 0.11283080155706106}, {151/40, 0.11267958569018079}, 
     {189/50, 0.11252877830257622}, {757/200, 0.11237837801000004}, 
     {379/100, 0.11222837526182596}, {759/200, 0.11207879824194869}, 
     {19/5, 0.11192959833108326}, {761/200, 0.1117808040441152}, 
     {381/100, 0.11163241795780031}, {763/200, 0.11148445524467361}, 
     {191/50, 0.1113368602241518}, {153/40, 0.11118966153554657}, 
     {383/100, 0.11104284950355728}, {767/200, 0.1108964125186893}, 
     {96/25, 0.11075036348170154}, {769/200, 0.11060469774190534}, 
     {77/20, 0.11045944867995584}, {771/200, 0.11031459028145016}, 
     {193/50, 0.11017011076738055}, {773/200, 0.11002597506082375}, 
     {387/100, 0.1098822504457046}, {31/8, 0.10973888919742994}, 
     {97/25, 0.10959589171636117}, {777/200, 0.10945328337196464}, 
     {389/100, 0.10931105966654818}, {779/200, 0.10916918178123255}, 
     {39/10, 0.10902770772866424}, {781/200, 0.10888660168440224}, 
     {391/100, 0.10874581451878228}, {783/200, 0.10860543700596685}, 
     {98/25, 0.10846540575137498}, {157/40, 0.10832575576657799}, 
     {393/100, 0.10818644031605708}, {787/200, 0.1080475068723734}, 
     {197/50, 0.10790893601278415}, {789/200, 0.10777072116098603}, 
     {79/20, 0.10763285701639545}, {791/200, 0.10749532473475978}, 
     {99/25, 0.10735816235401129}, {793/200, 0.10722135989327013}, 
     {397/100, 0.10708491616978305}, {159/40, 0.10694881572656487}, 
     {199/50, 0.10681306188005561}, {797/200, 0.10667763459121431}, 
     {399/100, 0.1065425813505046}, {799/200, 0.10640786485094882}, 
     {4, 0.10627347797565283}, {801/200, 0.10613942823992409}, 
     {401/100, 0.10600571473312936}, {803/200, 0.10587234299662508}, 
     {201/50, 0.10573933004891965}, {161/40, 0.10560665276082318}, 
     {403/100, 0.10547431017869531}, {807/200, 0.10534228607922379}, 
     {101/25, 0.10521058775905238}, {809/200, 0.10507925111513203}, 
     {81/20, 0.10494821590331198}, {811/200, 0.10481750647049266}, 
     {203/50, 0.10468712701200435}, {813/200, 0.10455706833251442}, 
     {407/100, 0.10442737125187182}, {163/40, 0.10429798642567627}, 
     {102/25, 0.1041688957915902}, {817/200, 0.1040401608442001}, 
     {409/100, 0.10391172957204622}, {819/200, 0.1037836013510795}, 
     {41/10, 0.10365579607311629}, {821/200, 0.10352830190655639}, 
     {411/100, 0.10340115647586534}, {823/200, 0.10327429000116868}, 
     {103/25, 0.1031477609292721}, {33/8, 0.1030215250935055}, 
     {413/100, 0.10289561698536084}, {827/200, 0.10277000803170373}, 
     {207/50, 0.1026447147337428}, {829/200, 0.10251972938870842}, 
     {83/20, 0.10239501136861393}, {831/200, 0.1022706230646237}, 
     {104/25, 0.10214655109463582}, {833/200, 0.10202276496657814}, 
     {417/100, 0.10189929993078106}, {167/40, 0.10177614587149725}, 
     {209/50, 0.10165327710045699}, {837/200, 0.10153068249015568}, 
     {419/100, 0.101408392617107}, {839/200, 0.10128640843262247}, 
     {21/5, 0.1011647364157087}, {841/200, 0.10104334921399567}, 
     {421/100, 0.10092225861456634}, {843/200, 0.10080144253219178}, 
     {211/50, 0.10068090381718008}, {169/40, 0.10056065996149213}, 
     {423/100, 0.10044071556194871}, {847/200, 0.10032106112073058}, 
     {106/25, 0.10020171244228405}, {849/200, 0.10008262974021863}, 
     {17/4, 0.09996381647625614}, {851/200, 0.09984530647054513}, 
     {213/50, 0.09972706151130215}, {853/200, 0.09960910218400817}, 
     {427/100, 0.09949143362322266}, {171/40, 0.09937403506608199}, 
     {107/25, 0.09925692486997403}, {857/200, 0.09914009697947193}, 
     {429/100, 0.09902352110225587}, {859/200, 0.0989072441631203}, 
     {43/10, 0.0987912378504965}, {861/200, 0.09867550357751431}, 
     {431/100, 0.098560023038137}, {863/200, 0.09844482016858144}, 
     {108/25, 0.09832989838132976}, {173/40, 0.09821524987156416}, 
     {433/100, 0.09810086862227177}, {867/200, 0.09798675831502875}, 
     {217/50, 0.09787291519607791}, {869/200, 0.09775933190763679}, 
     {87/20, 0.09764600888891851}, {871/200, 0.09753294386443175}, 
     {109/25, 0.09742012378150211}, {873/200, 0.09730759379399855}, 
     {437/100, 0.09719533188833547}, {35/8, 0.09708333163447794}, 
     {219/50, 0.09697158187720119}, {877/200, 0.09686008093031592}, 
     {439/100, 0.09674883691364865}, {879/200, 0.09663786339405768}, 
     {22/5, 0.09652713885027309}, {881/200, 0.09641665634611905}, 
     {441/100, 0.09630644695805034}, {883/200, 0.09619646071933761}, 
     {221/50, 0.09608673508284768}, {177/40, 0.09597728895440837}, 
     {443/100, 0.09586809708202144}, {887/200, 0.09575912100546936}, 
     {111/25, 0.09565042300371741}, {889/200, 0.09554194862088493}, 
     {89/20, 0.09543371789205207}, {891/200, 0.09532573922968013}, 
     {223/50, 0.09521802904302522}, {893/200, 0.09511053657044438}, 
     {447/100, 0.095003324097051}, {179/40, 0.0948963324780626}, 
     {112/25, 0.0947895732831725}, {897/200, 0.0946830586184019}, 
     {449/100, 0.09457677455029191}, {899/200, 0.09447074346212057}, 
     {9/2, 0.09436495188763451}, {901/200, 0.09425940709487368}, 
     {451/100, 0.09415410580946065}, {903/200, 0.09404901990023606}, 
     {113/25, 0.09394415668237927}, {181/40, 0.09383953325609391}, 
     {453/100, 0.09373514668048734}, {907/200, 0.09363100538238134}, 
     {227/50, 0.09352710821482962}, {909/200, 0.09342344278407778}, 
     {91/20, 0.09331998826611594}, {911/200, 0.09321675625786072}, 
     {114/25, 0.09311374910347896}, {913/200, 0.09301097831657512}, 
     {457/100, 0.09290844396560595}, {183/40, 0.0928061536099441}, 
     {229/50, 0.09270407687819611}, {917/200, 0.09260222485885544}, 
     {459/100, 0.09250058075133459}, {919/200, 0.0923991560322169}, 
     {23/5, 0.09229796162884896}, {921/200, 0.09219699379620407}, 
     {461/100, 0.09209625889539498}, {923/200, 0.09199574656483843}, 
     {231/50, 0.09189545342139802}, {37/8, 0.09179537282014662}, 
     {463/100, 0.0916955088236773}, {927/200, 0.09159586079682033}, 
     {116/25, 0.09149643441884422}, {929/200, 0.09139720086094043}, 
     {93/20, 0.09129821062002802}, {931/200, 0.0911994387466969}, 
     {233/50, 0.09110087764313156}, {933/200, 0.09100252505759605}, 
     {467/100, 0.09090439490174543}, {187/40, 0.09080646532466083}, 
     {117/25, 0.09070875631748866}, {937/200, 0.09061122486804521}, 
     {469/100, 0.09051393278735413}, {939/200, 0.09041686191259647}, 
     {47/10, 0.09032000098380151}, {941/200, 0.09022332360183177}, 
     {471/100, 0.09012686728272429}, {943/200, 0.0900306077204191}, 
     {118/25, 0.08993455599286097}, {189/40, 0.08983874202379043}, 
     {473/100, 0.08974310567118093}, {947/200, 0.08964767229971712}, 
     {237/50, 0.08955243533879612}, {949/200, 0.08945739905394431}, 
     {19/4, 0.08936256889136021}, {951/200, 0.08926795275240983}, 
     {119/25, 0.08917354567726923}, {953/200, 0.08907933239917298}, 
     {477/100, 0.08898532040392403}, {191/40, 0.08889148873929419}, 
     {239/50, 0.08879785247869532}, {957/200, 0.08870442101082508}, 
     {479/100, 0.08861119558615703}, {959/200, 0.08851817184925607}, 
     {24/5, 0.08842536292914563}, {961/200, 0.08833272200528253}, 
     {481/100, 0.0882402711115913}, {963/200, 0.08814800884982692}, 
     {241/50, 0.0880559559477726}, {193/40, 0.08796408752909984}, 
     {483/100, 0.08787242636840911}, {967/200, 0.08778095122309348}, 
     {121/25, 0.08768966507951913}, {969/200, 0.08759857325285214}, 
     {97/20, 0.08750765307539732}, {971/200, 0.08741692254936895}, 
     {243/50, 0.0873263860406037}, {973/200, 0.08723604791745196}, 
     {487/100, 0.08714589377695474}, {39/8, 0.08705591106428047}, 
     {122/25, 0.08696616439067215}, {977/200, 0.08687655873633139}, 
     {489/100, 0.0867871360222938}, {979/200, 0.08669790299802438}, 
     {49/10, 0.08660885892590733}, {981/200, 0.08651999560647326}, 
     {491/100, 0.08643131774994395}, {983/200, 0.08634285733423333}, 
     {123/25, 0.08625453417393233}, {197/40, 0.08616640168925674}, 
     {493/100, 0.08607843886797055}, {987/200, 0.08599066889768318}, 
     {247/50, 0.08590308824878612}, {989/200, 0.08581567976047323}, 
     {99/20, 0.08572844862040523}, {991/200, 0.08564139161770158}, 
     {124/25, 0.08555450774764965}, {993/200, 0.08546780034137838}, 
     {497/100, 0.08538126722068332}, {199/40, 0.08529491075265896}, 
     {249/50, 0.08520873254238266}, {997/200, 0.08512273316623986}, 
     {499/100, 0.0850369130305998}, {999/200, 0.08495126867250717}, 
     {5, 0.08486580011778959}, {1001/200, 0.08478049671878977}, 
     {501/100, 0.08469536291797587}, {1003/200, 0.08461039606208157}, 
     {251/50, 0.0845255967824382}, {201/40, 0.08444096624422003}, 
     {503/100, 0.08435651046283217}, {1007/200, 0.08427222125107031}, 
     {126/25, 0.08418810806963398}, {1009/200, 0.08410416013770985}, 
     {101/20, 0.08402041118314925}, {1011/200, 0.08393679983256155}, 
     {253/50, 0.08385335061946511}, {1013/200, 0.08377006441665671}, 
     {507/100, 0.08368694326983211}, {203/40, 0.08360399089304986}, 
     {127/25, 0.08352121305220081}, {1017/200, 0.0834386096716852}, 
     {509/100, 0.08335573000560029}, {1019/200, 0.08327385219272815}, 
     {51/10, 0.08319172262048247}, {1021/200, 0.08310975390715969}, 
     {511/100, 0.08302794267217828}, {1023/200, 0.08294629298397993}, 
     {128/25, 0.08286495652226386}, {41/8, 0.08278356241283924}, 
     {513/100, 0.08270199006691609}, {1027/200, 0.08262136035513391}, 
     {257/50, 0.08254051482139599}, {1029/200, 0.08245982693042458}, 
     {103/20, 0.08237929906222277}, {1031/200, 0.0822989242710766}, 
     {129/25, 0.08221877553768903}, {1033/200, 0.08213872432257502}, 
     {517/100, 0.08205836838404632}, {207/40, 0.08197904070963034}, 
     {259/50, 0.08189942695876949}, {1037/200, 0.0818199862635584}, 
     {519/100, 0.08174073910166146}, {1039/200, 0.08166165620679249}, 
     {26/5, 0.08158268882358707}, {1041/200, 0.08150340679145461}, 
     {521/100, 0.08142516425698679}, {1043/200, 0.08134664370809194}, 
     {261/50, 0.0812682858660611}, {209/40, 0.08119006113265265}, 
     {523/100, 0.08111208087320733}, {1047/200, 0.0810341685385154}, 
     {131/25, 0.08095636821596937}, {1049/200, 0.08087876866747051}, 
     {21/4, 0.0808013029188617}, {1051/200, 0.08072398665144169}, 
     {263/50, 0.0806468927583451}, {1053/200, 0.08056987712769693}, 
     {527/100, 0.08049252834463376}, {211/40, 0.08041624259994136}, 
     {132/25, 0.08033967217245912}, {1057/200, 0.0802632462292474}, 
     {529/100, 0.08018700557984247}, {1059/200, 0.08011088088468558}, 
     {53/10, 0.0800348076056933}, {1061/200, 0.07995895680414221}, 
     {531/100, 0.07988332961717547}, {1063/200, 0.0798077642988988}, 
     {133/25, 0.07973191823891414}, {213/40, 0.07965702717824082}, 
     {533/100, 0.0795819078591929}, {1067/200, 0.07950691182725664}, 
     {267/50, 0.07943205359739314}, {1069/200, 0.07935742411445235}, 
     {107/20, 0.07928285617875828}, {1071/200, 0.07920838770406446}, 
     {134/25, 0.07913410761796631}, {1073/200, 0.07905996561360315}, 
     {537/100, 0.07898594936099425}, {43/8, 0.07891214208868952}, 
     {269/50, 0.0788384167914432}, {1077/200, 0.07876434074578087}, 
     {539/100, 0.07869130897484103}, {1079/200, 0.07861801070773539}, 
     {27/5, 0.07854484136542982}, {1081/200, 0.07847183124168218}, 
     {541/100, 0.07839893231745741}, {1083/200, 0.0783261121179086}, 
     {271/50, 0.07825346377008777}, {217/40, 0.0781809745270605}, 
     {543/100, 0.07810862487377283}, {1087/200, 0.07803643908939263}, 
     {136/25, 0.07796412713692583}, {1089/200, 0.07789234214605693}, 
     {109/20, 0.07782049904833291}, {1091/200, 0.07774879215127506}, 
     {273/50, 0.07767723601028863}, {1093/200, 0.07760582432371647}, 
     {547/100, 0.07753449155980285}, {219/40, 0.07746333842534943}, 
     {137/25, 0.07739231447422115}, {1097/200, 0.07732140021606129}, 
     {549/100, 0.07725066211349896}, {1099/200, 0.07717959673996783}, 
     {11/2, 0.07710943165234527}, {1101/200, 0.07703904822061383}, 
     {551/100, 0.07696880139340548}, {1103/200, 0.07689853057101173}, 
     {138/25, 0.0768288319421796}, {221/40, 0.07675838212036845}, 
     {553/100, 0.07668903595347151}, {1107/200, 0.07661940426231628}, 
     {277/50, 0.07654991327184596}, {1109/200, 0.07648056377833196}, 
     {111/20, 0.07641132200566586}, {1111/200, 0.07634220649097333}, 
     {139/25, 0.07627320087120996}, {1113/200, 0.07620433430208581}, 
     {557/100, 0.07613559139487239}, {223/40, 0.07606697178918859}, 
     {279/50, 0.07599847305720585}, {1117/200, 0.0759301034720574}, 
     {559/100, 0.0758618619464857}, {1119/200, 0.07579374392109532}, 
     {28/5, 0.07572590526468269}, {1121/200, 0.07565769349098979}, 
     {561/100, 0.07559009589079006}, {1123/200, 0.07552245275070235}, 
     {281/50, 0.07545492717672263}, {45/8, 0.0753875599419403}, 
     {563/100, 0.07532028886622634}, {1127/200, 0.07525313860901525}, 
     {141/25, 0.07518609974010625}, {1129/200, 0.07511918498187302}, 
     {113/20, 0.07505238360699942}, {1131/200, 0.07498570673002437}, 
     {283/50, 0.0749191496874208}, {1133/200, 0.07485271017922952}, 
     {567/100, 0.07478639238296093}, {227/40, 0.07472019484065434}, 
     {142/25, 0.07465411339278583}, {1137/200, 0.07458814713800181}, 
     {569/100, 0.07452229851650734}, {1139/200, 0.07445654469065244}, 
     {57/10, 0.07439091701991701}, {1141/200, 0.0743254288138287}, 
     {571/100, 0.07426005582555781}, {1143/200, 0.07419478532181695}, 
     {143/25, 0.07412962681695112}, {229/40, 0.0740645833934316}, 
     {573/100, 0.07399965199838632}, {1147/200, 0.07393484168346334}, 
     {287/50, 0.07387014700181652}, {1149/200, 0.0738055431794415}, 
     {23/4, 0.07374106943704564}, {1151/200, 0.07367671339852816}, 
     {144/25, 0.07361246985661665}, {1153/200, 0.07354849569034866}, 
     {577/100, 0.07348416298940713}, {231/40, 0.07342038284591401}, 
     {289/50, 0.07335657567151951}, {1157/200, 0.07329289755102597}, 
     {579/100, 0.07322918728015393}, {1159/200, 0.07316570220643442}, 
     {29/5, 0.07310250802087519}, {1161/200, 0.07303925919399125}, 
     {581/100, 0.07297611501085388}, {1163/200, 0.07291308784376926}, 
     {291/50, 0.07285030492414266}, {233/40, 0.07278719750529522}, 
     {583/100, 0.07272464890401645}, {1167/200, 0.07266205316480479}, 
     {146/25, 0.07259958159166091}, {1169/200, 0.07253702448950487}, 
     {117/20, 0.07247476697246497}, {1171/200, 0.07241262575066833}, 
     {293/50, 0.0723506821045095}, {1173/200, 0.07228873228380131}, 
     {587/100, 0.07222703446719438}, {47/8, 0.07216496473816254}, 
     {147/25, 0.07210352414763757}, {1177/200, 0.07204200597590252}, 
     {589/100, 0.07198058862041722}, {1179/200, 0.07191924314993704}, 
     {59/10, 0.07185787752244444}, {1181/200, 0.07179693553328649}, 
     {591/100, 0.07173591545854978}, {1183/200, 0.07167501670215194}, 
     {148/25, 0.0716140615938566}, {237/40, 0.07155371400539506}, 
     {593/100, 0.07149293742221494}, {1187/200, 0.07143244100801295}, 
     {297/50, 0.07137205652294402}, {1189/200, 0.07131182436192443}, 
     {119/20, 0.07125163813217884}, {1191/200, 0.07119151987864465}, 
     {149/25, 0.07113153127292934}, {1193/200, 0.0710717016404071}, 
     {597/100, 0.071011935289639}, {239/40, 0.07095222410045941}, 
     {299/50, 0.0708926484977664}, {1197/200, 0.0708331549257239}, 
     {599/100, 0.0707736286807346}, {1199/200, 0.07071450690399876}, 
     {6, 0.07065533658933325}}
 
ImERfind = {{6, 0.07065533658933325}, {151/25, 0.07018558298578534}, 
     {152/25, 0.06972180023181372}, {153/25, 0.06926440712703133}, 
     {154/25, 0.06881284860519084}, {31/5, 0.06836680928077293}, 
     {156/25, 0.06792699999764985}, {157/25, 0.06749270465134623}, 
     {158/25, 0.06706392418304437}, {159/25, 0.06664053826476353}, 
     {32/5, 0.06622250837711727}, {161/25, 0.06580969290064706}, 
     {162/25, 0.06540201370104969}, {163/25, 0.0649993446882271}, 
     {164/25, 0.06460161497439726}, {33/5, 0.06420874783912649}, 
     {166/25, 0.06382062179370734}, {167/25, 0.06343717822070818}, 
     {168/25, 0.06305831064162996}, {169/25, 0.0626839612758173}, 
     {34/5, 0.062314060256292506}, {171/25, 0.0619482965873813}, 
     {172/25, 0.06158718271387692}, {173/25, 0.06123008137412348}, 
     {174/25, 0.06087710615172331}, {7, 0.06052816605090126}, 
     {176/25, 0.06018321664800341}, {177/25, 0.05984207715317307}, 
     {178/25, 0.05950501267168035}, {179/25, 0.05917162757836637}, 
     {36/5, 0.05884193327189685}, {181/25, 0.05851590696554265}, 
     {182/25, 0.05819349877117291}, {183/25, 0.05787446897155343}, 
     {184/25, 0.05755923500361533}, {37/5, 0.05724736346049406}, 
     {186/25, 0.05693865830846147}, {187/25, 0.056633356174685706}, 
     {188/25, 0.05633134941685903}, {189/25, 0.05603252893693678}, 
     {38/5, 0.05573686179694949}, {191/25, 0.05544419018779618}, 
     {192/25, 0.0551547882267895}, {193/25, 0.054868307284893586}, 
     {194/25, 0.054584654116164255}, {39/5, 0.054304027035358006}, 
     {196/25, 0.054026468207136844}, {197/25, 0.05375156745802619}, 
     {198/25, 0.05347945740757529}, {199/25, 0.05321009220557276}, 
     {8, 0.05294343066167798}, {201/25, 0.05267943106816932}, 
     {202/25, 0.05241805459298526}, {203/25, 0.052159264210157916}, 
     {204/25, 0.05190302859937684}, {41/5, 0.051649290472291144}, 
     {206/25, 0.05139802275223824}, {207/25, 0.05114919148318611}, 
     {208/25, 0.050902898321386704}, {209/25, 0.050658692768069176}, 
     {42/5, 0.050416961667837386}, {211/25, 0.05017753283615762}, 
     {212/25, 0.049940363934996075}, {213/25, 0.04970542991448665}, 
     {214/25, 0.04947280425801642}, {43/5, 0.04924213888035235}, 
     {216/25, 0.04901386546040258}, {217/25, 0.04878745082921451}, 
     {218/25, 0.04856322249985182}, {219/25, 0.04834105849197458}, 
     {44/5, 0.04812089669141463}, {221/25, 0.04790276205687079}, 
     {222/25, 0.04768656937939476}, {223/25, 0.04747233398985253}, 
     {224/25, 0.04726005042757855}, {9, 0.04704963444641558}, 
     {226/25, 0.0468411378957909}, {227/25, 0.04663435062649935}, 
     {228/25, 0.046429532508203426}, {229/25, 0.0462263866970716}, 
     {46/5, 0.046025051477057995}, {231/25, 0.045825339025773244}, 
     {232/25, 0.0456276158966069}, {233/25, 0.045431467077884584}, 
     {234/25, 0.04523686693896358}, {47/5, 0.04504419409731662}, 
     {236/25, 0.04485302684346796}, {237/25, 0.044663486779329534}, 
     {238/25, 0.0444755315273776}, {239/25, 0.044289148294995064}, 
     {48/5, 0.04410415800496151}, {241/25, 0.043920872157021236}, 
     {242/25, 0.04373927129023118}, {243/25, 0.04355882558024996}, 
     {244/25, 0.04338020875617006}, {49/5, 0.04320288310771363}, 
     {246/25, 0.04302698133174914}, {247/25, 0.042852548671376826}, 
     {248/25, 0.04267950739364932}, {249/25, 0.042507859982400954}, 
     {10, 0.0423376036868942}, {251/25, 0.042168678042456914}, 
     {252/25, 0.042001112556764496}, {253/25, 0.04183484485274024}, 
     {254/25, 0.041669951542749384}, {51/5, 0.04150632406596561}, 
     {256/25, 0.04134398380909148}, {257/25, 0.04118289804666943}, 
     {258/25, 0.04102306262632729}, {259/25, 0.04086443840993892}, 
     {52/5, 0.04070705461654792}, {261/25, 0.040550890802447434}, 
     {262/25, 0.04039592825634914}, {263/25, 0.040242105605822344}, 
     {264/25, 0.040089515014582716}, {53/5, 0.039938054900824575}, 
     {266/25, 0.039787719691787106}, {267/25, 0.03963853697971384}, 
     {268/25, 0.03949044973599423}, {269/25, 0.03934346326506128}, 
     {54/5, 0.03919756553924457}, {271/25, 0.03905276166322031}, 
     {272/25, 0.03890900650257666}, {273/25, 0.03876632176425912}, 
     {274/25, 0.03862465479478464}, {11, 0.038484068667006106}, 
     {276/25, 0.03834448127975456}, {277/25, 0.03820589360374618}, 
     {278/25, 0.03806832504558919}, {279/25, 0.03793172676365457}, 
     {56/5, 0.03779610272970351}, {281/25, 0.03766145441382935}, 
     {282/25, 0.03752775004053492}, {283/25, 0.03739500213361082}, 
     {284/25, 0.03726319375669055}, {57/5, 0.03713231019092022}, 
     {286/25, 0.037002334499371646}, {287/25, 0.03687328894306706}, 
     {288/25, 0.03674513171487909}, {289/25, 0.036617833070672234}, 
     {58/5, 0.03649145273637363}, {291/25, 0.036365916495173324}, 
     {292/25, 0.03624127109307113}, {293/25, 0.03611744732383834}, 
     {294/25, 0.035994484928803576}, {59/5, 0.03587233545295968}, 
     {296/25, 0.03575104156766966}, {297/25, 0.03563056497919916}, 
     {298/25, 0.03551087882955392}, {299/25, 0.03539199106271777}, 
     {12, 0.03527392366751983}, {301/25, 0.03515663405517047}, 
     {302/25, 0.035040102692736684}, {303/25, 0.03492435311120767}, 
     {304/25, 0.03480936943522133}, {61/5, 0.0346951438105602}, 
     {306/25, 0.03458167097304339}, {307/25, 0.03446890756594038}, 
     {308/25, 0.03435690165726157}, {309/25, 0.03424562491263245}, 
     {62/5, 0.03413506847376617}, {311/25, 0.034025216429779744}, 
     {312/25, 0.0339160575707131}, {313/25, 0.033807611163864854}, 
     {314/25, 0.03369985836194413}, {63/5, 0.03359279576852612}, 
     {316/25, 0.033486393812823805}, {317/25, 0.033380673086040986}, 
     {318/25, 0.0332756127123714}, {319/25, 0.033171214845813125}, 
     {64/5, 0.03306747426820982}, {321/25, 0.03296438875179592}, 
     {322/25, 0.03286193348677572}, {323/25, 0.03276011004880002}, 
     {324/25, 0.03265891782663957}, {13, 0.0325583749593629}, 
     {326/25, 0.0324584125342256}, {327/25, 0.032359063418364795}, 
     {328/25, 0.03226033319123181}, {329/25, 0.03216220486471775}, 
     {66/5, 0.03206468035892118}, {331/25, 0.03196775749314044}, 
     {332/25, 0.03187138416756672}, {333/25, 0.03177560543569973}, 
     {334/25, 0.031680424686167365}, {67/5, 0.03158578517920121}, 
     {336/25, 0.031491710201110024}, {337/25, 0.031398183699253394}, 
     {338/25, 0.03130522091549202}, {339/25, 0.03121283318930892}, 
     {68/5, 0.031120975100706032}, {341/25, 0.031029646268892895}, 
     {342/25, 0.030938851664393613}, {343/25, 0.03084859682061503}, 
     {344/25, 0.030758861904062903}, {69/5, 0.030669647472485656}, 
     {346/25, 0.030580946185491065}, {347/25, 0.030492756971284188}, 
     {348/25, 0.030405079291781722}, {349/25, 0.030317902571726077}, 
     {14, 0.030231232041206323}, {351/25, 0.03014504697170168}, 
     {352/25, 0.030059348099270113}, {353/25, 0.029974150963662842}, 
     {354/25, 0.029889425195229885}, {71/5, 0.029805173684252912}, 
     {356/25, 0.029721400870499248}, {357/25, 0.029638103704832542}, 
     {358/25, 0.029555263068583214}, {359/25, 0.029472891746491762}, 
     {72/5, 0.029390975560223728}, {361/25, 0.02930951519110213}, 
     {362/25, 0.029228497310117636}, {363/25, 0.0291479307247736}, 
     {364/25, 0.029067809114023898}, {73/5, 0.028988132553394944}, 
     {366/25, 0.0289088897680775}, {367/25, 0.028830067818468454}, 
     {368/25, 0.028751685087503285}, {369/25, 0.028673728817031993}, 
     {74/5, 0.028596192763989503}, {371/25, 0.02851907265744429}, 
     {372/25, 0.02844236545041928}, {373/25, 0.02836606930753704}, 
     {374/25, 0.02829019029123854}, {15, 0.02821470873350417}, 
     {376/25, 0.028139624041314943}, {377/25, 0.02806494612907786}, 
     {378/25, 0.027990666875727453}, {379/25, 0.027916780385115293}, 
     {76/5, 0.027843286403168063}, {381/25, 0.027770164521660656}, 
     {382/25, 0.027697429823474704}, {383/25, 0.02762507695330973}, 
     {384/25, 0.027553106553054055}, {77/5, 0.027481501830771728}, 
     {386/25, 0.027410273096865584}, {387/25, 0.027339411124915957}, 
     {388/25, 0.027268922044309404}, {389/25, 0.02719878647993941}, 
     {78/5, 0.02712900769286278}, {391/25, 0.02705959438103364}, 
     {392/25, 0.026990542739058335}, {393/25, 0.026921831262890876}, 
     {394/25, 0.02685346857433478}, {79/5, 0.026785453792440468}, 
     {396/25, 0.02671777483104525}, {397/25, 0.026650457470458477}, 
     {398/25, 0.026583469293129734}, {399/25, 0.026516814755468906}, 
     {16, 0.026450485074785188}, {401/25, 0.02638450825114388}, 
     {402/25, 0.02631885177717264}, {403/25, 0.026253505926384632}, 
     {404/25, 0.026188493035841785}, {81/5, 0.02612380949558018}, 
     {406/25, 0.026059436984996655}, {407/25, 0.025995382558248438}, 
     {408/25, 0.025931639258609147}, {409/25, 0.025868215342827527}, 
     {82/5, 0.02580509350210301}, {411/25, 0.025742276495934795}, 
     {412/25, 0.025679778328681235}, {413/25, 0.02561757304944197}, 
     {414/25, 0.02555566981920108}, {83/5, 0.025494065483549995}, 
     {416/25, 0.02543275929092287}, {417/25, 0.02537174767321152}, 
     {418/25, 0.025311020201510485}, {419/25, 0.025250597505849192}, 
     {84/5, 0.025190449723960163}, {421/25, 0.02513058299092128}, 
     {422/25, 0.025071017391933882}, {423/25, 0.025011718277048157}, 
     {424/25, 0.024952726479120634}, {17, 0.02489398519429354}, 
     {426/25, 0.024835532323999373}, {427/25, 0.024777344155134377}, 
     {428/25, 0.024719433730671612}, {429/25, 0.024661783007186584}, 
     {86/5, 0.0246044064936332}, {431/25, 0.024547284952329145}, 
     {432/25, 0.024490454442990434}, {433/25, 0.024433866748200476}, 
     {434/25, 0.024377550550512724}, {87/5, 0.024321491985344133}, 
     {436/25, 0.02426568086101318}, {437/25, 0.02421015307918953}, 
     {438/25, 0.024154843251987537}, {439/25, 0.024099800684872937}, 
     {88/5, 0.024045016816445042}, {441/25, 0.023990469415111737}, 
     {442/25, 0.023936163046751596}, {443/25, 0.02388212376596168}, 
     {444/25, 0.02382833524676498}, {89/5, 0.023774741191477777}, 
     {446/25, 0.023721436198465787}, {447/25, 0.02366832202256796}, 
     {448/25, 0.023615504541632654}, {449/25, 0.023562859709064195}, 
     {18, 0.023510512398219746}, {451/25, 0.023458358759202578}, 
     {452/25, 0.023406461084543542}, {453/25, 0.023354747106880507}, 
     {454/25, 0.023303314387236387}, {91/5, 0.023252044004103082}, 
     {456/25, 0.023201060339399365}, {457/25, 0.02315025285746826}, 
     {458/25, 0.023099692560761175}, {459/25, 0.023049351181924308}, 
     {92/5, 0.022999225469391947}, {461/25, 0.02294933614319898}, 
     {462/25, 0.022899621062500305}, {463/25, 0.02285017496437493}, 
     {464/25, 0.022800883982007372}, {93/5, 0.022751847440510016}, 
     {466/25, 0.022703049375187103}, {467/25, 0.022654394430918625}, 
     {468/25, 0.022605992241959912}, {469/25, 0.022557763149898026}, 
     {94/5, 0.022509765125470458}, {471/25, 0.022461946791494537}, 
     {472/25, 0.0224143252370289}, {473/25, 0.02236691946459832}, 
     {474/25, 0.022319708315282183}, {19, 0.022272715669936168}, 
     {476/25, 0.02222593890737463}, {477/25, 0.02217932748512961}, 
     {478/25, 0.022132915905363246}, {479/25, 0.02208666347330468}, 
     {96/5, 0.02204064723869814}, {481/25, 0.021994789145855176}, 
     {482/25, 0.021949141451702812}, {483/25, 0.02190370986788421}, 
     {484/25, 0.021858282486114825}, {97/5, 0.02181334717938645}, 
     {486/25, 0.02176846559426012}, {487/25, 0.02172383207354997}, 
     {488/25, 0.021679213375160215}, {489/25, 0.02163488502527811}, 
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     {494/25, 0.02141592197846227}, {99/5, 0.02137263866651552}, 
     {496/25, 0.02132952471743491}, {497/25, 0.021286595632726214}, 
     {498/25, 0.021243754678269677}, {499/25, 0.021201272785185372}, 
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     {502/25, 0.02107444761373056}, {503/25, 0.021032614592308662}, 
     {504/25, 0.02099086076184179}, {101/5, 0.020949204874461565}, 
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     {516/25, 0.02050247682707425}, {517/25, 0.020462799496552376}, 
     {518/25, 0.020423304026473597}, {519/25, 0.02038392278773584}, 
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     {522/25, 0.020266752401822758}, {523/25, 0.020228003096582903}, 
     {524/25, 0.02018936394784283}, {21, 0.020150911425769507}, 
     {526/25, 0.02011258836311392}, {527/25, 0.020074387161833178}, 
     {528/25, 0.02003636999697437}, {529/25, 0.019998471774816243}, 
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     {532/25, 0.019885673180657173}, {533/25, 0.019848341558689506}, 
     {534/25, 0.01981114580262038}, {107/5, 0.019774106547575793}, 
     {536/25, 0.01973722112728642}, {537/25, 0.019700421800927657}, 
     {538/25, 0.019663793565709055}, {539/25, 0.019627276273876556}, 
     {108/5, 0.01959095034012503}, {541/25, 0.01955474795837355}, 
     {542/25, 0.01951865214078575}, {543/25, 0.019482694563696223}, 
     {544/25, 0.01944688517114305}, {109/5, 0.01941115555180182}, 
     {546/25, 0.019375610703700755}, {547/25, 0.019340120226448664}, 
     {548/25, 0.019304842257353256}, {549/25, 0.019269673871444265}, 
     {22, 0.01923462285282815}, {551/25, 0.01919969690830048}, 
     {552/25, 0.01916492854149971}, {553/25, 0.019130225343216394}, 
     {554/25, 0.019095678212732333}, {111/5, 0.019061269427493137}, 
     {556/25, 0.01902694993346407}, {557/25, 0.018992788892204696}, 
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     {112/5, 0.018891040856352806}, {561/25, 0.018857345988495554}, 
     {562/25, 0.01882380389953259}, {563/25, 0.01879033283653489}, 
     {564/25, 0.01875698351284425}, {113/5, 0.018723824657868628}, 
     {566/25, 0.018690707877903966}, {567/25, 0.018657737177435827}, 
     {568/25, 0.018624865759347447}, {569/25, 0.018592109353987536}, 
     {114/5, 0.01855950389165162}, {571/25, 0.018526971042212206}, 
     {572/25, 0.01849454153447685}, {573/25, 0.018462288742924826}, 
     {574/25, 0.018430101064476883}, {23, 0.018398055847800788}, 
     {576/25, 0.01836610051298142}, {577/25, 0.018334244035019917}, 
     {578/25, 0.018302520387320345}, {579/25, 0.01827090246945795}, 
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     {582/25, 0.018176669024426016}, {583/25, 0.018145464752489304}, 
     {584/25, 0.018114434217632473}, {117/5, 0.01808342063624903}, 
     {586/25, 0.01805259012053185}, {587/25, 0.01802178448283158}, 
     {588/25, 0.017991161480630506}, {589/25, 0.017960585924666296}, 
     {118/5, 0.0179301160605911}, {591/25, 0.01789976124134399}, 
     {592/25, 0.01786951256399182}, {593/25, 0.017839371598887443}, 
     {594/25, 0.017809326787834156}, {119/5, 0.01777938605677619}, 
     {596/25, 0.01774958575508528}, {597/25, 0.017719860222183834}, 
     {598/25, 0.017690228311711027}, {599/25, 0.017660687951143998}, 
     {24, 0.017631256428426993}, {601/25, 0.01760186712697694}, 
     {602/25, 0.017572643247398906}, {603/25, 0.017543490634616646}, 
     {604/25, 0.017514441090171518}, {121/5, 0.017485464125870025}, 
     {606/25, 0.0174566189057871}, {607/25, 0.017427815499733153}, 
     {608/25, 0.01739915776327338}, {609/25, 0.017370570564901235}, 
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     {612/25, 0.017285379978643663}, {613/25, 0.017257156743469393}, 
     {614/25, 0.01722907894895509}, {123/5, 0.01720106287494415}, 
     {616/25, 0.017173152106565493}, {617/25, 0.017145334480417055}, 
     {618/25, 0.017117516623875718}, {619/25, 0.01708983062763576}, 
     {124/5, 0.017062311720238883}, {621/25, 0.017034809391300625}, 
     {622/25, 0.01700740086400243}, {623/25, 0.016980110900536912}, 
     {624/25, 0.016952871068355007}, {25, 0.016925724260127954}, 
     {626/25, 0.016898656518096616}, {627/25, 0.016871679368689784}, 
     {628/25, 0.016844809836648662}, {629/25, 0.01681809605253823}, 
     {126/5, 0.016791390913150187}, {631/25, 0.016764742461088205}, 
     {632/25, 0.01673822626272224}, {633/25, 0.01671179056495164}, 
     {634/25, 0.01668540163692955}, {127/5, 0.016659077361332857}, 
     {636/25, 0.016632919367103982}, {637/25, 0.01660675893642867}, 
     {638/25, 0.016580746396060612}, {639/25, 0.01655476056607591}, 
     {128/5, 0.01652893784795911}, {641/25, 0.016503128493303466}, 
     {642/25, 0.01647738480829683}, {643/25, 0.016451729046702016}, 
     {644/25, 0.01642617423971144}, {129/5, 0.01640071841667287}, 
     {646/25, 0.016375354080684124}, {647/25, 0.01635000687443589}, 
     {648/25, 0.016324755968560117}, {649/25, 0.01629955945431678}, 
     {26, 0.016274499968624134}, {651/25, 0.01624952962763646}, 
     {652/25, 0.016224581694198575}, {653/25, 0.016199731546765482}, 
     {654/25, 0.016174959394482744}, {131/5, 0.016150171747387986}, 
     {656/25, 0.016125582741859525}, {657/25, 0.016101084696236962}, 
     {658/25, 0.016076638887416207}, {659/25, 0.016052209511696693}, 
     {132/5, 0.016027899153217763}, {661/25, 0.0160035696938819}, 
     {662/25, 0.015979341878259733}, {663/25, 0.015955367230273902}, 
     {664/25, 0.015931289708518034}, {133/5, 0.015907352169511793}, 
     {666/25, 0.015883480403529996}, {667/25, 0.01585957131937801}, 
     {668/25, 0.01583584302347475}, {669/25, 0.01581223868308507}, 
     {134/5, 0.01578864686740652}, {671/25, 0.015765069221180626}, 
     {672/25, 0.015741531603916364}, {673/25, 0.015718147668110746}, 
     {674/25, 0.01569486967623483}, {27, 0.01567161959471936}, 
     {676/25, 0.01564842217891397}, {677/25, 0.015625329452363886}, 
     {678/25, 0.015602174857823527}, {679/25, 0.015579174079546594}, 
     {136/5, 0.015556321271276265}, {681/25, 0.01553350228369241}, 
     {682/25, 0.015510670559568868}, {683/25, 0.01548795420064546}, 
     {684/25, 0.015465273142254082}, {137/5, 0.015442690546484714}, 
     {686/25, 0.01542024832162034}, {687/25, 0.01539779308099003}, 
     {688/25, 0.015375403833885064}, {689/25, 0.015353081676630262}, 
     {138/5, 0.015330744876413949}, {691/25, 0.015308546411819862}, 
     {692/25, 0.015286482259819772}, {693/25, 0.015264379897888411}, 
     {694/25, 0.015242422898936193}, {139/5, 0.015220497222617028}, 
     {696/25, 0.015198548973536148}, {697/25, 0.015176721764974272}, 
     {698/25, 0.015154977027099753}, {699/25, 0.01513330777613643}, 
     {28, 0.015111713307474971}, {701/25, 0.015090159264112443}, 
     {702/25, 0.015068570082706317}, {703/25, 0.015047115915712601}, 
     {704/25, 0.015025744957335406}, {141/5, 0.015004410968699143}, 
     {706/25, 0.014983240159928848}, {707/25, 0.014962013931411713}, 
     {708/25, 0.014940823244845733}, {709/25, 0.014919738937981673}, 
     {142/5, 0.014898692682313508}, {711/25, 0.014877746857186108}, 
     {712/25, 0.01485685168327553}, {713/25, 0.014836050856393028}, 
     {714/25, 0.01481521485280379}, {143/5, 0.01479448435022193}, 
     {716/25, 0.014773812696548396}, {717/25, 0.01475320102413991}, 
     {718/25, 0.01473265478805874}, {719/25, 0.01471217113810009}, 
     {144/5, 0.014691732923049846}, {721/25, 0.014671349998845652}, 
     {722/25, 0.014651007135863665}, {723/25, 0.014630695936119055}, 
     {724/25, 0.014610465848786454}, {29, 0.014590311521964794}, 
     {726/25, 0.01457020855198052}, {727/25, 0.01455015410558958}, 
     {728/25, 0.014530145526264006}, {729/25, 0.014510275997199167}, 
     {146/5, 0.014490409899003957}, {731/25, 0.014470552127249629}, 
     {732/25, 0.01445075548809807}, {733/25, 0.014431067267456054}, 
     {734/25, 0.014411414157409881}, {147/5, 0.014391769437448547}, 
     {736/25, 0.01437219717993644}, {737/25, 0.014352691577221823}, 
     {738/25, 0.014333227738550702}, {739/25, 0.014313833598157726}, 
     {148/5, 0.01429448615690684}, {741/25, 0.014275210439064472}, 
     {742/25, 0.014255962834652641}, {743/25, 0.014236749258564602}, 
     {744/25, 0.014217606054999384}, {149/5, 0.014198528962002181}, 
     {746/25, 0.014179479555377366}, {747/25, 0.014160468011832461}, 
     {748/25, 0.014141555650895834}, {749/25, 0.014122661236195284}, 
     {30, 0.01410383509930702}, {751/25, 0.014085032437355923}, 
     {752/25, 0.014066286594176308}, {753/25, 0.014047610879084375}, 
     {754/25, 0.014028972918501907}, {151/5, 0.014010367252188297}, 
     {756/25, 0.013991823108962199}, {757/25, 0.013973348785881015}, 
     {758/25, 0.013954922452011484}, {759/25, 0.013936522329531138}, 
     {152/5, 0.01391817395599845}, {761/25, 0.01389988269656573}, 
     {762/25, 0.013881609486654335}, {763/25, 0.01386343630251901}, 
     {764/25, 0.013845258803932878}, {153/5, 0.013827131529008031}, 
     {766/25, 0.013809089629625241}, {767/25, 0.01379108676562823}, 
     {768/25, 0.013773105788348517}, {769/25, 0.013755218551335798}, 
     {154/5, 0.01373733681584943}, {771/25, 0.013719529051955379}, 
     {772/25, 0.013701741273998628}, {773/25, 0.013683991495352703}, 
     {774/25, 0.013666322795822024}, {31, 0.01364869671318177}, 
     {776/25, 0.013631101075513926}, {777/25, 0.013613487129119762}, 
     {778/25, 0.01359598412945644}, {779/25, 0.013578591655518137}, 
     {156/5, 0.013561174153369524}, {781/25, 0.013543779980384918}, 
     {782/25, 0.013526402799311686}, {783/25, 0.01350913155843884}, 
     {784/25, 0.013491907754976332}, {157/5, 0.013474738336133867}, 
     {786/25, 0.013457618027494261}, {787/25, 0.013440449546099667}, 
     {788/25, 0.013423493995987737}, {789/25, 0.01340641135221097}, 
     {158/5, 0.013389518742020929}, {791/25, 0.013372509605605728}, 
     {792/25, 0.013355625472382875}, {793/25, 0.013338808898710156}, 
     {794/25, 0.013321960170037455}, {159/5, 0.01330522952286931}, 
     {796/25, 0.013288526667958572}, {797/25, 0.013271868937111414}, 
     {798/25, 0.013255125097176308}, {799/25, 0.013238630346276467}, 
     {32, 0.013221969473650922}, {801/25, 0.01320549484743375}, 
     {802/25, 0.013189056144214041}, {803/25, 0.013172609593218667}, 
     {804/25, 0.013156212733585302}, {161/5, 0.013139883592863716}, 
     {806/25, 0.01312360239314671}, {807/25, 0.013107293246278596}, 
     {808/25, 0.013090947863491187}, {809/25, 0.013074882128970722}, 
     {162/5, 0.013058627775903423}, {811/25, 0.013042573958090437}, 
     {812/25, 0.013026615287220385}, {813/25, 0.013010588844531141}, 
     {814/25, 0.012994552131283487}, {163/5, 0.012978585827542435}, 
     {816/25, 0.012962674275035536}, {817/25, 0.012946842831249705}, 
     {818/25, 0.012930921547607142}, {819/25, 0.01291517626408797}, 
     {164/5, 0.012899457441570414}, {821/25, 0.012883750425943457}, 
     {822/25, 0.012867914234420219}, {823/25, 0.01285240010185773}, 
     {824/25, 0.012836716989634126}, {33, 0.012821242439275696}, 
     {826/25, 0.012805732870851148}, {827/25, 0.012790091665466942}, 
     {828/25, 0.012774654340618329}, {829/25, 0.01275935125590409}, 
     {166/5, 0.012743890289771548}, {831/25, 0.012728667948392067}, 
     {832/25, 0.01271330717176285}, {833/25, 0.01269809562684488}, 
     {834/25, 0.012682702530296013}, {167/5, 0.012667522839939532}, 
     {836/25, 0.012652361417340217}, {837/25, 0.012637237809494566}, 
     {838/25, 0.012622176795861657}, {839/25, 0.012607237971269801}, 
     {168/5, 0.012592210053378995}, {841/25, 0.012577205085354927}, 
     {842/25, 0.01256230123816266}, {843/25, 0.012547405888885078}, 
     {844/25, 0.012532497091915576}, {169/5, 0.012517530442171586}, 
     {846/25, 0.012502900004818601}, {847/25, 0.01248793662181271}, 
     {848/25, 0.01247336156786213}, {849/25, 0.01245860595303295}, 
     {34, 0.012444021856097713}, {851/25, 0.01242920317080061}, 
     {852/25, 0.01241471205991361}, {853/25, 0.012400124559268953}, 
     {854/25, 0.012385711740221642}, {171/5, 0.012371074233916656}, 
     {856/25, 0.012356681554844182}, {857/25, 0.01234222636609653}, 
     {858/25, 0.012327935871491663}, {859/25, 0.012313435914183291}, 
     {172/5, 0.012299231865619733}, {861/25, 0.01228487826275296}, 
     {862/25, 0.01227062079883061}, {863/25, 0.012256419690926388}, 
     {864/25, 0.01224210144384954}, {173/5, 0.012228059233010055}, 
     {866/25, 0.012213899566233394}, {867/25, 0.012199821688748752}, 
     {868/25, 0.012185663976829667}, {869/25, 0.012171755137542147}, 
     {174/5, 0.012157750501111965}, {871/25, 0.012143822543356992}, 
     {872/25, 0.012129762298441052}, {873/25, 0.012115859799486045}, 
     {874/25, 0.012102092069551327}, {35, 0.01208825141242686}, 
     {876/25, 0.012074426813584269}, {877/25, 0.012060662945385752}, 
     {878/25, 0.01204692883862118}, {879/25, 0.012033215011925908}, 
     {176/5, 0.01201938286602704}, {881/25, 0.012005922331081323}, 
     {882/25, 0.011992137221109546}, {883/25, 0.011978712330143419}, 
     {884/25, 0.011964988213829336}, {177/5, 0.011951458954344078}, 
     {886/25, 0.011938088767605728}, {887/25, 0.011924501370943164}, 
     {888/25, 0.011911211771032526}, {889/25, 0.011897654441245058}, 
     {178/5, 0.011884408516280684}, {891/25, 0.011870945765323533}, 
     {892/25, 0.011857683240173443}, {893/25, 0.011844524525825462}, 
     {894/25, 0.011831145583505292}, {179/5, 0.011817987710917363}, 
     {896/25, 0.01180471194104867}, {897/25, 0.011791657970246536}, 
     {898/25, 0.011778524917439437}, {899/25, 0.01176527296228002}, 
     {36, 0.011752208923804488}, {901/25, 0.011739166612202942}, 
     {902/25, 0.011726161120681946}, {903/25, 0.011713133846675779}, 
     {904/25, 0.011700185693972747}, {181/5, 0.011687262243950147}, 
     {906/25, 0.011674364742416253}, {907/25, 0.011661604401075533}, 
     {908/25, 0.011648625837809073}, {909/25, 0.011635803276985818}, 
     {182/5, 0.011623021047084275}, {911/25, 0.011610253799106037}, 
     {912/25, 0.011597535430051178}, {913/25, 0.011584796943917338}, 
     {914/25, 0.011572114953207844}, {183/5, 0.011559484558574964}, 
     {916/25, 0.011546860728800215}, {917/25, 0.011534266982259421}, 
     {918/25, 0.011521674103521014}, {919/25, 0.01150914837949693}, 
     {184/5, 0.01149663260310337}, {921/25, 0.01148412912378247}, 
     {922/25, 0.011471673783741454}, {923/25, 0.011459219964774852}, 
     {924/25, 0.011446839845027708}, {37, 0.011434467137993228}, 
     {926/25, 0.011422083651252357}, {927/25, 0.011409749331676084}, 
     {928/25, 0.011397613043266024}, {929/25, 0.011385178431967591}, 
     {186/5, 0.011373086852885574}, {931/25, 0.011360725411480966}, 
     {932/25, 0.01134850896176069}, {933/25, 0.011336420028902434}, 
     {934/25, 0.011324236829328965}, {187/5, 0.011312097838577145}, 
     {936/25, 0.011300019574459464}, {937/25, 0.011287947659222185}, 
     {938/25, 0.011275917638097157}, {939/25, 0.01126389915305266}, 
     {188/5, 0.011251914102641265}, {941/25, 0.011239938872270308}, 
     {942/25, 0.01122801230501472}, {943/25, 0.01121610473903146}, 
     {944/25, 0.011204200378860463}, {189/5, 0.01119235974193222}, 
     {946/25, 0.011180503559973012}, {947/25, 0.011168707516492488}, 
     {948/25, 0.011156927286480607}, {949/25, 0.011145153276731113}, 
     {38, 0.011133475925771847}, {951/25, 0.01112172128325075}, 
     {952/25, 0.011110119166144813}, {953/25, 0.011098388064120177}, 
     {954/25, 0.011086755499521438}, {191/5, 0.011075087601672577}, 
     {956/25, 0.011063544437081288}, {957/25, 0.011051956865865341}, 
     {958/25, 0.011040444187128705}, {959/25, 0.011028892702715435}, 
     {192/5, 0.01101747072040673}, {961/25, 0.011005933399140003}, 
     {962/25, 0.010994516060115587}, {963/25, 0.010983072133203237}, 
     {964/25, 0.010971693809155761}, {193/5, 0.01096030992885036}, 
     {966/25, 0.01094896992579024}, {967/25, 0.010937613759776227}, 
     {968/25, 0.010926337257565134}, {969/25, 0.01091501906979696}, 
     {194/5, 0.010903773738905078}, {971/25, 0.010892519125364777}, 
     {972/25, 0.010881330678801615}, {973/25, 0.01087016262097623}, 
     {974/25, 0.010859007690706779}, {39, 0.010847859180892231}, 
     {976/25, 0.010836746735503961}, {977/25, 0.010825642590782015}, 
     {978/25, 0.010814559710535151}, {979/25, 0.010803500785883104}, 
     {196/5, 0.010792439782252692}, {981/25, 0.010781485301776887}, 
     {982/25, 0.01077044680956895}, {983/25, 0.010759590191222955}, 
     {984/25, 0.010748556005468504}, {197/5, 0.010737704690998892}, 
     {986/25, 0.01072678944167873}, {987/25, 0.010715944947583139}, 
     {988/25, 0.010705071377348954}, {989/25, 0.010694269036040647}, 
     {198/5, 0.01068342732526505}, {991/25, 0.010672656013267742}, 
     {992/25, 0.01066187248743697}, {993/25, 0.010651148933584322}, 
     {994/25, 0.010640411818410515}, {199/5, 0.010629722415282162}, 
     {996/25, 0.010619050443617774}, {997/25, 0.010608385634954708}, 
     {998/25, 0.010597737345188192}, {999/25, 0.010587144834393268}, 
     {40, 0.010576526363737336}, {1001/25, 0.010565985490331917}, 
     {1002/25, 0.01055542602154023}, {1003/25, 0.01054486207745426}, 
     {1004/25, 0.010534387915350104}, {201/5, 0.010523880733963872}, 
     {1006/25, 0.01051343816227826}, {1007/25, 0.010503009426243689}, 
     {1008/25, 0.01049255788785477}, {1009/25, 0.010482147003167058}, 
     {202/5, 0.01047177857874047}, {1011/25, 0.010461395312925972}, 
     {1012/25, 0.010451075190470149}, {1013/25, 0.01044073198157876}, 
     {1014/25, 0.010430431310282743}, {203/5, 0.010420184589023239}, 
     {1016/25, 0.01040988771225604}, {1017/25, 0.010399685176026916}, 
     {1018/25, 0.010389430263146704}, {1019/25, 0.01037926181487695}, 
     {204/5, 0.010369072178001152}, {1021/25, 0.010358922561910122}, 
     {1022/25, 0.010348766266900592}, {1023/25, 0.010338656207891678}, 
     {1024/25, 0.01032854232250896}, {41, 0.010318456423047849}, 
     {1026/25, 0.01030843088559437}, {1027/25, 0.010298363957936962}, 
     {1028/25, 0.010288337254248565}, {1029/25, 0.010278350797303843}, 
     {206/5, 0.010268368657344845}, {1031/25, 0.010258406127250902}, 
     {1032/25, 0.010248477105931152}, {1033/25, 0.010238512116400748}, 
     {1034/25, 0.010228639459398076}, {207/5, 0.010218712870964597}, 
     {1036/25, 0.010208889284495802}, {1037/25, 0.010199019630558541}, 
     {1038/25, 0.010189210660652686}, {1039/25, 0.010179387006319814}, 
     {208/5, 0.010169612628491182}, {1041/25, 0.010159827937780416}, 
     {1042/25, 0.01015008687141328}, {1043/25, 0.010140301842695286}, 
     {1044/25, 0.010130584446632725}, {209/5, 0.010120869695636562}, 
     {1046/25, 0.010111208298987012}, {1047/25, 0.010101536029355773}, 
     {1048/25, 0.01009196754918898}, {1049/25, 0.010082316274473509}, 
     {42, 0.010072756660352955}, {1051/25, 0.010063124703589088}, 
     {1052/25, 0.010053561904388768}, {1053/25, 0.010043998024525998}, 
     {1054/25, 0.010034510924585634}, {211/5, 0.010024949375876113}, 
     {1056/25, 0.010015482080980874}, {1057/25, 0.010005978018405517}, 
     {1058/25, 0.00999653222162697}, {1059/25, 0.009987071415345968}, 
     {212/5, 0.009977678805653197}, {1061/25, 0.009968255264858498}, 
     {1062/25, 0.009958872102066429}, {1063/25, 0.009949457173857708}, 
     {1064/25, 0.009940149005354535}, {213/5, 0.00993077014822234}, 
     {1066/25, 0.009921485572500959}, {1067/25, 0.009912170645200674}, 
     {1068/25, 0.00990290670649397}, {1069/25, 0.009893627934494473}, 
     {214/5, 0.009884391419290105}, {1071/25, 0.00987513728850637}, 
     {1072/25, 0.009865931786591358}, {1073/25, 0.009856719364091484}, 
     {1074/25, 0.009847586380549413}, {43, 0.00983837768985802}, 
     {1076/25, 0.009829247454723508}, {1077/25, 0.009820113816299159}, 
     {1078/25, 0.009811006870907055}, {1079/25, 0.00980191075044203}, 
     {216/5, 0.009792816758164003}, {1081/25, 0.009783753464899207}, 
     {1082/25, 0.009774687761552554}, {1083/25, 0.009765678165191638}, 
     {1084/25, 0.00975665253048107}, {217/5, 0.009747664397121412}, 
     {1086/25, 0.009738678037836202}, {1087/25, 0.009729793940359346}, 
     {1088/25, 0.009720758106208342}, {1089/25, 0.00971185544981523}, 
     {218/5, 0.009702920994169487}, {1091/25, 0.009694037786060298}, 
     {1092/25, 0.009685162019439428}, {1093/25, 0.009676319525222497}, 
     {1094/25, 0.00966744394146894}, {219/5, 0.009658628606722522}, 
     {1096/25, 0.009649786545222054}, {1097/25, 0.00964104676973482}, 
     {1098/25, 0.009632295227346755}, {1099/25, 0.009623455041939637}, 
     {44, 0.009614676462716692}, {1101/25, 0.009605995163150405}, 
     {1102/25, 0.009597260464181063}, {1103/25, 0.009588527003674423}, 
     {1104/25, 0.009579957431638659}, {221/5, 0.009571166900233305}, 
     {1106/25, 0.009562489336293625}, {1107/25, 0.00955390187888975}, 
     {1108/25, 0.009545226021815095}, {1109/25, 0.009536653446657594}, 
     {222/5, 0.009528027184385699}, {1111/25, 0.009519442294670678}, 
     {1112/25, 0.009510878901428363}, {1113/25, 0.00950242316810923}, 
     {1114/25, 0.009493796152845213}, {223/5, 0.009485339704363565}, 
     {1116/25, 0.009476778649468751}, {1117/25, 0.009468294840557013}, 
     {1118/25, 0.009459815502661006}, {1119/25, 0.009451358994603355}, 
     {224/5, 0.009442920618181843}, {1121/25, 0.009434484997086457}, 
     {1122/25, 0.009426084944512568}, {1123/25, 0.00941774817284484}, 
     {1124/25, 0.009409279133455135}, {45, 0.009400978496906704}, 
     {1126/25, 0.009392583216192494}, {1127/25, 0.009384295737238348}, 
     {1128/25, 0.009376028570841525}, {1129/25, 0.009367616348825455}, 
     {226/5, 0.009359301162009302}, {1131/25, 0.009351048643901034}, 
     {1132/25, 0.009342756680457913}, {1133/25, 0.009334550487256475}, 
     {1134/25, 0.009326335102249991}, {227/5, 0.00931813407022083}, 
     {1136/25, 0.009309847529070037}, {1137/25, 0.00930167364708413}, 
     {1138/25, 0.009293488508299865}, {1139/25, 0.009285357466100487}, 
     {228/5, 0.009277175923414928}, {1141/25, 0.009269060113963837}, 
     {1142/25, 0.009260969549243525}, {1143/25, 0.009252800051013397}, 
     {1144/25, 0.009244709872030188}, {229/5, 0.00923662490734024}, 
     {1146/25, 0.0092286971310156}, {1147/25, 0.009220518503580128}, 
     {1148/25, 0.009212508784679564}, {1149/25, 0.00920451373622053}, 
     {46, 0.009196443286878084}, {1151/25, 0.00918846335883882}, 
     {1152/25, 0.009180621560422927}, {1153/25, 0.009172514852784037}, 
     {1154/25, 0.009164682958507003}, {231/5, 0.0091566240308941}, 
     {1156/25, 0.009148705344302599}, {1157/25, 0.009140801088412368}, 
     {1158/25, 0.009132920135517192}, {1159/25, 0.009125014112835622}, 
     {232/5, 0.00911722436999065}, {1161/25, 0.009109295210932884}, 
     {1162/25, 0.009101466430217642}, {1163/25, 0.009093615525020776}, 
     {1164/25, 0.009085809788333708}, {233/5, 0.009077991785865897}, 
     {1166/25, 0.009070253382931779}, {1167/25, 0.009062428912354646}, 
     {1168/25, 0.009054672022702442}, {1169/25, 0.00904691392881679}, 
     {234/5, 0.009039206804414663}, {1171/25, 0.009031458167480057}, 
     {1172/25, 0.00902379215618877}, {1173/25, 0.009016045865872792}, 
     {1174/25, 0.009008367891629187}, {47, 0.00900068665615712}, 
     {1176/25, 0.008993038573947313}, {1177/25, 0.008985379080430003}, 
     {1178/25, 0.00897777426759953}, {1179/25, 0.008970129350982042}, 
     {236/5, 0.008962576644691259}, {1181/25, 0.00895497396534984}, 
     {1182/25, 0.008947377604742448}, {1183/25, 0.008939772967854052}, 
     {1184/25, 0.008932246276502742}, {237/5, 0.008924686459719944}, 
     {1186/25, 0.008917218691668283}, {1187/25, 0.008909660142156049}, 
     {1188/25, 0.008902156411234274}, {1189/25, 0.008894652070367475}, 
     {238/5, 0.008887188142671594}, {1191/25, 0.008879723925098355}, 
     {1192/25, 0.008872247781570367}, {1193/25, 0.008864933273174256}, 
     {1194/25, 0.008857377720207357}, {239/5, 0.008849947018554325}, 
     {1196/25, 0.008842699181937192}, {1197/25, 0.008835171084071407}, 
     {1198/25, 0.00882778606156719}, {1199/25, 0.008820433804351139}, 
     {48, 0.008813096352421007}, {1201/25, 0.008805824703715414}, 
     {1202/25, 0.008798406108757754}, {1203/25, 0.008791085009532455}, 
     {1204/25, 0.008783773777153524}, {241/5, 0.00877651330036469}, 
     {1206/25, 0.008769227219926118}, {1207/25, 0.008761916281121157}, 
     {1208/25, 0.0087546791104224}, {1209/25, 0.008747476609440405}, 
     {242/5, 0.008740195829726937}, {1211/25, 0.008732929327112638}, 
     {1212/25, 0.008725820024715485}, {1213/25, 0.008718756458908804}, 
     {1214/25, 0.008711320876275293}, {243/5, 0.008704206454753779}, 
     {1216/25, 0.008697034426561862}, {1217/25, 0.00868996455346518}, 
     {1218/25, 0.008682764506024615}, {1219/25, 0.008675712879772202}, 
     {244/5, 0.008668635922516727}, {1221/25, 0.008661400708489815}, 
     {1222/25, 0.008654338704522988}, {1223/25, 0.008647290585895927}, 
     {1224/25, 0.008640167911796566}, {49, 0.008633185542998204}, 
     {1226/25, 0.008626062531976963}, {1227/25, 0.008618968820899563}, 
     {1228/25, 0.008612003601912614}, {1229/25, 0.008605063432611918}, 
     {246/5, 0.008597922758079024}, {1231/25, 0.008591228133410312}, 
     {1232/25, 0.008584026278873736}, {1233/25, 0.008577120611725738}, 
     {1234/25, 0.00857010654552449}, {247/5, 0.008563213748144163}, 
     {1236/25, 0.008556258821307103}, {1237/25, 0.008549254461050218}, 
     {1238/25, 0.008542400089607086}, {1239/25, 0.00853554000917218}, 
     {248/5, 0.008528637198250321}, {1241/25, 0.008521780130107065}, 
     {1242/25, 0.008514901961118078}, {1243/25, 0.008507918211460165}, 
     {1244/25, 0.008501174407833122}, {249/5, 0.008494378632031667}, 
     {1246/25, 0.008487416147372766}, {1247/25, 0.008480771091811423}, 
     {1248/25, 0.00847392403572237}, {1249/25, 0.008467046883761674}, 
     {50, 0.00846032729686426}}
 
ImERfine = {{50, 0.00846032729686426}, {1001/20, 0.008451905394343668}, 
     {501/10, 0.008443334872912408}, {1003/20, 0.008435039807236368}, 
     {251/5, 0.008426635741513462}, {201/4, 0.008418211640666095}, 
     {503/10, 0.008409875783107404}, {1007/20, 0.008401422320437717}, 
     {252/5, 0.00839308578130354}, {1009/20, 0.008384855878269344}, 
     {101/2, 0.008376458945608702}, {1011/20, 0.008368266643038406}, 
     {253/5, 0.008359892861406143}, {1013/20, 0.008351744141591302}, 
     {507/10, 0.008343487713061721}, {203/4, 0.008335287734814938}, 
     {254/5, 0.008327070758157328}, {1017/20, 0.008318752738517394}, 
     {509/10, 0.008310705175916415}, {1019/20, 0.008302521558717005}, 
     {51, 0.008294401251805705}, {1021/20, 0.008286268955577478}, 
     {511/10, 0.008278028929707913}, {1023/20, 0.008270068969162974}, 
     {256/5, 0.008261973085564547}, {205/4, 0.008253911388431092}, 
     {513/10, 0.008245882026249016}, {1027/20, 0.008237821832986898}, 
     {257/5, 0.008229822071430182}, {1029/20, 0.008221801372800876}, 
     {103/2, 0.008213844117860641}, {1031/20, 0.008205877056597914}, 
     {258/5, 0.008197899021896082}, {1033/20, 0.008189821903366314}, 
     {517/10, 0.008182051179460942}, {207/4, 0.008173986147526315}, 
     {259/5, 0.00816623082605997}, {1037/20, 0.008158251423926522}, 
     {519/10, 0.0081505202946392}, {1039/20, 0.00814265506958791}, 
     {52, 0.008134820158369428}, {1041/20, 0.008126986354037326}, 
     {521/10, 0.008119076958255981}, {1043/20, 0.008111401575941174}, 
     {261/5, 0.008103657814223739}, {209/4, 0.008095874132372997}, 
     {523/10, 0.008088119941541664}, {1047/20, 0.00808028551478269}, 
     {262/5, 0.008072698315876335}, {1049/20, 0.008064988476292164}, 
     {105/2, 0.008057322001853393}, {1051/20, 0.008049630621616132}, 
     {263/5, 0.008041973165701299}, {1053/20, 0.008034371672050518}, 
     {527/10, 0.008026574674168153}, {211/4, 0.008019102363063158}, 
     {264/5, 0.008011370869699445}, {1057/20, 0.008003917843530727}, 
     {529/10, 0.00799635205380135}, {1059/20, 0.007988801738707366}, 
     {53, 0.007981255726721617}, {1061/20, 0.007973575546816089}, 
     {531/10, 0.007966222604281942}, {1063/20, 0.007958719207022772}, 
     {266/5, 0.007951243346440878}, {213/4, 0.007943782534773538}, 
     {533/10, 0.007936165526765251}, {1067/20, 0.007928882681942554}, 
     {267/5, 0.007921444097102418}, {1069/20, 0.007914035547051293}, 
     {107/2, 0.007906475793485723}, {1071/20, 0.00789911076604102}, 
     {268/5, 0.007891884870164555}, {1073/20, 0.007884508254824058}, 
     {537/10, 0.007877173066961484}, {215/4, 0.007869683381283838}, 
     {269/5, 0.007862392558939522}, {1077/20, 0.007855215422110345}, 
     {539/10, 0.007847928535636161}, {1079/20, 0.007840695340828353}, 
     {54, 0.007833236929862838}, {1081/20, 0.007826175812494307}, 
     {541/10, 0.007818759959131852}, {1083/20, 0.00781167398867417}, 
     {271/5, 0.007804516704440461}, {217/4, 0.007797298604101208}, 
     {543/10, 0.007790080445530726}, {1087/20, 0.007782744385219509}, 
     {272/5, 0.007775595856022154}, {1089/20, 0.007768634173865426}, 
     {109/2, 0.007761489439365714}, {1091/20, 0.007754393832185495}, 
     {273/5, 0.0077472598459453375}, {1093/20, 0.007740043133190501}, 
     {547/10, 0.007733118220707138}, {219/4, 0.0077260392450389705}, 
     {274/5, 0.0077190025370384874}, {1097/20, 0.007711965173970034}, 
     {549/10, 0.007704779353697865}, {1099/20, 0.0076977643815922476}, 
     {55, 0.007690875004541009}, {1101/20, 0.0076839194518009005}, 
     {551/10, 0.007676977471004991}, {1103/20, 0.007669798878395331}, 
     {276/5, 0.007662853698925278}, {221/4, 0.007656078678746683}, 
     {553/10, 0.007649164339039817}, {1107/20, 0.007642286014361437}, 
     {277/5, 0.007635349852917467}, {1109/20, 0.007628485311033245}, 
     {111/2, 0.007621435125086721}, {1111/20, 0.00761475438676313}, 
     {278/5, 0.0076077287535400735}, {1113/20, 0.0076010343981235216}, 
     {557/10, 0.007594221334930034}, {223/4, 0.007587231594900121}, 
     {279/5, 0.00758065368848502}, {1117/20, 0.007573656547363292}, 
     {559/10, 0.0075670244202724}, {1119/20, 0.0075602940240551844}, 
     {56, 0.007553347054961804}, {1121/20, 0.007546779937237666}, 
     {561/10, 0.00754005592903174}, {1123/20, 0.0075333291950286495}, 
     {281/5, 0.007526639500093082}, {225/4, 0.007519746649120609}, 
     {563/10, 0.007513217669335727}, {1127/20, 0.007506579682343938}, 
     {282/5, 0.007499928717433596}, {1129/20, 0.007493276181192462}, 
     {113/2, 0.00748649795143478}, {1131/20, 0.007480031899938825}, 
     {283/5, 0.007473435546436329}, {1133/20, 0.007467189181155532}, 
     {567/10, 0.007460266669267978}, {227/4, 0.007453502714123613}, 
     {284/5, 0.00744708378599696}, {1137/20, 0.007440549156104367}, 
     {569/10, 0.007433984198604002}, {1139/20, 0.007427517502332921}, 
     {57, 0.007421021367121435}, {1141/20, 0.0074144431477067025}, 
     {571/10, 0.007407938425131949}, {1143/20, 0.007401476957114586}, 
     {286/5, 0.007395006690561146}, {229/4, 0.007388519748720967}, 
     {573/10, 0.007382103123315358}, {1147/20, 0.0073756197968596}, 
     {287/5, 0.00736925817807192}, {1149/20, 0.007362815302861626}, 
     {115/2, 0.007356369462248621}, {1151/20, 0.00734999716581314}, 
     {288/5, 0.007343676226626511}, {1153/20, 0.007337229040155272}, 
     {577/10, 0.007330923767884974}, {231/4, 0.007324520230025696}, 
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     {609/10, 0.006945427875162634}, {1219/20, 0.00693987078776253}, 
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     {639/10, 0.006619447615833137}, {1279/20, 0.006614255747068391}, 
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     {322/5, 0.006568051086642178}, {1289/20, 0.006562962016799737}, 
     {129/2, 0.006557883203730838}, {1291/20, 0.0065526035392370644}, 
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     {649/10, 0.006517461606161306}, {1299/20, 0.0065124375132358725}, 
     {65, 0.006507221670318045}, {1301/20, 0.0065023733799145726}, 
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     {653/10, 0.006477475952699147}, {1307/20, 0.006472522366977776}, 
     {327/5, 0.006467600636298227}, {1309/20, 0.0064624804796819}, 
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     {329/5, 0.006428304745704898}, {1317/20, 0.006423401394500897}, 
     {659/10, 0.006418309264832092}, {1319/20, 0.006413461183218994}, 
     {66, 0.00640894478703235}, {1321/20, 0.006403926376601797}, 
     {661/10, 0.0063988929278516685}, {1323/20, 0.0063940868040861494}, 
     {331/5, 0.0063894991131521976}, {265/4, 0.006384646877352736}, 
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     {332/5, 0.006369988391527614}, {1329/20, 0.006365792776104622}, 
     {133/2, 0.00636070179250173}, {1331/20, 0.0063559219287360885}, 
     {333/5, 0.0063508777988717366}, {1333/20, 0.0063463470972570804}, 
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     {669/10, 0.006322617848755289}, {1339/20, 0.006317897500388777}, 
     {67, 0.006313203312243249}, {1341/20, 0.006308249299941672}, 
     {671/10, 0.006303470759250304}, {1343/20, 0.006299020470450063}, 
     {336/5, 0.006294414963383073}, {269/4, 0.0062894592965464236}, 
     {673/10, 0.0062848034691952645}, {1347/20, 0.006280280945415883}, 
     {337/5, 0.0062757861619042255}, {1349/20, 0.006270990591022764}, 
     {135/2, 0.006266177851360481}, {1351/20, 0.006261490607386428}, 
     {338/5, 0.006257163831423325}, {1353/20, 0.00625270625737818}, 
     {677/10, 0.0062476489572557605}, {271/4, 0.006243067911900745}, 
     {339/5, 0.006238608107625122}, {1357/20, 0.006234032754901967}, 
     {679/10, 0.00622943804695897}, {1359/20, 0.006224680067932061}, 
     {68, 0.006220107715892901}, {1361/20, 0.006216169653286107}, 
     {681/10, 0.006211478335322109}, {1363/20, 0.006206830659052993}, 
     {341/5, 0.006201783740531977}, {273/4, 0.006197278755178171}, 
     {683/10, 0.006193070976139525}, {1367/20, 0.006188918076399392}, 
     {342/5, 0.006183694721978327}, {1369/20, 0.006179133646346686}, 
     {137/2, 0.006174994360836205}, {1371/20, 0.006170544500988296}, 
     {343/5, 0.006166027539229697}, {1373/20, 0.0061618638909091}, 
     {687/10, 0.006156689037483002}, {275/4, 0.006152180970080663}, 
     {344/5, 0.006148059269268913}, {1377/20, 0.006143714966395816}, 
     {689/10, 0.006139468662942246}, {1379/20, 0.006134329285078154}, 
     {69, 0.006129880584991384}, {1381/20, 0.0061258081187256334}, 
     {691/10, 0.006121548862567534}, {1383/20, 0.006116600627157074}, 
     {346/5, 0.006112149241874339}, {277/4, 0.006108108429784963}, 
     {693/10, 0.006103800452111563}, {1387/20, 0.0060991683210006725}, 
     {347/5, 0.006094501956647968}, {1389/20, 0.006090148975598823}, 
     {139/2, 0.006086171982155612}, {1391/20, 0.00608203974677968}, 
     {348/5, 0.0060770618433375525}, {1393/20, 0.006072648932679708}, 
     {697/10, 0.006068230592496131}, {279/4, 0.006064602866089423}, 
     {349/5, 0.006060033622067012}, {1397/20, 0.006055306543819649}, 
     {699/10, 0.006050938026164639}, {1399/20, 0.006046981884191848}, 
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     {701/10, 0.006033702107680297}, {1403/20, 0.006029328799281848}, 
     {351/5, 0.006025726343341795}, {281/4, 0.006021357914498657}, 
     {703/10, 0.006016529575217864}, {1407/20, 0.006012195461071707}, 
     {352/5, 0.006008539997212939}, {1409/20, 0.006004122748649381}, 
     {141/2, 0.006000103340888454}, {1411/20, 0.005995187286293801}, 
     {353/5, 0.005990877810441917}, {1413/20, 0.005987327161984503}, 
     {707/10, 0.005983076067922326}, {283/4, 0.005978172557158168}, 
     {354/5, 0.005973944389180334}, {1417/20, 0.005970430665775639}, 
     {709/10, 0.0059656992295612325}, {1419/20, 0.005962023263000958}, 
     {71, 0.005957116434480214}, {1421/20, 0.005952924584260304}, 
     {711/10, 0.005949150971394924}, {1423/20, 0.005944889545191859}, 
     {356/5, 0.005940395562629521}, {285/4, 0.0059362266208335766}, 
     {713/10, 0.005932056565662569}, {1427/20, 0.0059286506750368334}, 
     {357/5, 0.005924142286190641}, {1429/20, 0.005919617618418798}, 
     {143/2, 0.005915451178861893}, {1431/20, 0.005911746891050806}, 
     {358/5, 0.00590752992696976}, {1433/20, 0.005903057983483374}, 
     {717/10, 0.0058989572108620394}, {287/4, 0.005894844598409136}, 
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     {719/10, 0.005882577947115155}, {1439/20, 0.005878450372722216}, 
     {72, 0.0058751171301304065}, {1441/20, 0.005871015981479938}, 
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     {361/5, 0.005858083115529146}, {289/4, 0.005854486882620578}, 
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     {362/5, 0.005841909027035751}, {1449/20, 0.005837884479985}, 
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     {363/5, 0.005825822740763658}, {1453/20, 0.0058217793085344974}, 
     {727/10, 0.005818536586006597}, {291/4, 0.0058144238608378845}, 
     {364/5, 0.005809825933433859}, {1457/20, 0.005805805842244582}, 
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     {366/5, 0.00577834774425315}, {293/4, 0.005774117444531692}, 
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     {371/5, 0.0057001949461948686}, {297/4, 0.005696368275227366}, 
     {743/10, 0.0056932278900205064}, {1487/20, 0.005688718838471735}, 
     {372/5, 0.005684865411662063}, {1489/20, 0.0056810687059140035}, 
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     {75, 0.005639405886826557}, {1501/20, 0.00563636451647484}, 
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     {377/5, 0.0056095021523591155}, {1509/20, 0.005605772580518347}, 
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     {759/10, 0.005572534273809677}, {1519/20, 0.00556940033583284}, 
     {76, 0.005565447852758747}, {1521/20, 0.00556146871219684}, 
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     {807/10, 0.005240985365539864}, {323/4, 0.005237748948498771}, 
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     {809/10, 0.005228054516735327}, {1619/20, 0.005224839241703593}, 
     {81, 0.0052215749667137695}, {1621/20, 0.0052184918431919195}, 
     {811/10, 0.005215864052465825}, {1623/20, 0.005211920553054486}, 
     {406/5, 0.0052087520119806175}, {325/4, 0.0052056670719869596}, 
     {813/10, 0.005203110065195443}, {1627/20, 0.005199171901283703}, 
     {407/5, 0.005195951980271283}, {1629/20, 0.005192745252796334}, 
     {163/2, 0.005189685705610401}, {1631/20, 0.005187112790668629}, 
     {408/5, 0.005183173682080549}, {1633/20, 0.005179998978943851}, 
     {817/10, 0.005176974574550383}, {327/4, 0.005174417624190972}, 
     {409/5, 0.005171240034163827}, {1637/20, 0.005167346484497402}, 
     {819/10, 0.005164212089003562}, {1639/20, 0.005161182080048079}, 
     {82, 0.00515792739850683}, {1641/20, 0.005154780517191256}, 
     {821/10, 0.005151613618723961}, {1643/20, 0.0051486474242201895}, 
     {411/5, 0.00514546553356251}, {329/4, 0.005142543939496991}, 
     {823/10, 0.005139098475356198}, {1647/20, 0.005136722194176252}, 
     {412/5, 0.0051329655669476604}, {1649/20, 0.005129838714224914}, 
     {165/2, 0.005126678850683026}, {1651/20, 0.005123543245399233}, 
     {413/5, 0.005120590713095758}, {1653/20, 0.005117437028384799}, 
     {827/10, 0.005114598391713149}, {331/4, 0.005111184638609835}, 
     {414/5, 0.005108077259441477}, {1657/20, 0.005105121241171785}, 
     {829/10, 0.005102640641166388}, {1659/20, 0.005098828920938787}, 
     {83, 0.0050957854241577925}, {1661/20, 0.005092786877347554}, 
     {831/10, 0.005089745542850867}, {1663/20, 0.005086878158393417}, 
     {416/5, 0.005083524971573274}, {333/4, 0.005080439717690772}, 
     {833/10, 0.005077534084165428}, {1667/20, 0.005075095557298891}, 
     {417/5, 0.005071334407073842}, {1669/20, 0.0050682856236117565}, 
     {167/2, 0.005065256784802496}, {1671/20, 0.005062331824684292}, 
     {418/5, 0.005059957228280527}, {1673/20, 0.005056171349463996}, 
     {837/10, 0.005053150588951115}, {335/4, 0.005050233783457474}, 
     {419/5, 0.005047118923019063}, {1677/20, 0.005044115782627712}, 
     {839/10, 0.005041122322675782}, {1679/20, 0.0050381146794949705}, 
     {84, 0.0050352270765871175}, {1681/20, 0.0050328713757473295}, 
     {841/10, 0.005029143970393921}, {1683/20, 0.005026123675990172}, 
     {421/5, 0.005023229596424178}, {337/4, 0.00502091236911425}, 
     {843/10, 0.0050171673039151165}, {1687/20, 0.005014232473085662}, 
     {422/5, 0.005011255619073111}, {1689/20, 0.005008358371751193}, 
     {169/2, 0.005006064524433606}, {1691/20, 0.00500234817391884}, 
     {423/5, 0.004999373922195936}, {1693/20, 0.004996563292219096}, 
     {847/10, 0.004993998106794244}, {339/4, 0.00499058985761508}, 
     {424/5, 0.004987602884062451}, {1697/20, 0.004984649778549075}, 
     {849/10, 0.0049818405599383565}, {1699/20, 0.004979578808218357}, 
     {85, 0.0049758913606373426}, {1701/20, 0.004972971195353774}, 
     {851/10, 0.004970754436753674}, {1703/20, 0.004967615011290274}, 
     {426/5, 0.004964199877849921}, {341/4, 0.004961302424995505}, 
     {853/10, 0.004958348899645904}, {1707/20, 0.0049562283007861824}, 
     {427/5, 0.004953338636952765}, {1709/20, 0.0049496837545211}, 
     {171/2, 0.004946771301576515}, {1711/20, 0.004944171123205271}, 
     {428/5, 0.004941512915821112}, {1713/20, 0.004938112617079076}, 
     {857/10, 0.0049352242850725925}, {343/4, 0.004932380156411897}, 
     {429/5, 0.004929762442056826}, {1717/20, 0.004927368257747303}, 
     {859/10, 0.0049237740599945715}, {1719/20, 0.004920889300039433}, 
     {86, 0.004918750078796366}, {1721/20, 0.004915687806060853}, 
     {861/10, 0.004912328483598057}, {1723/20, 0.0049094549636654935}, 
     {431/5, 0.004906650656071405}, {345/4, 0.004904221544980844}, 
     {863/10, 0.004901653526276773}, {1727/20, 0.0048980737400635245}, 
     {432/5, 0.0048952590085617025}, {1729/20, 0.004892447326658248}, 
     {173/2, 0.004889565845011991}, {1731/20, 0.004887200209856863}, 
     {433/5, 0.004884656524473568}, {1733/20, 0.004881120673110313}, 
     {867/10, 0.004878313735163339}, {347/4, 0.004875940392543137}, 
     {434/5, 0.0048732957699952825}, {1737/20, 0.004869916923194748}, 
     {869/10, 0.004867059191157454}, {1739/20, 0.004864255510835696}, 
     {87, 0.004861990370007662}, {1741/20, 0.004859395541007137}, 
     {871/10, 0.004855907326332744}, {1743/20, 0.004853150751790906}, 
     {436/5, 0.00485083641616841}, {349/4, 0.004848094412735307}, 
     {873/10, 0.004844791210658048}, {1747/20, 0.004842005012138109}, 
     {437/5, 0.0048392575824013455}, {1749/20, 0.0048369427600956204}, 
     {175/2, 0.004834099568402294}, {1751/20, 0.004830930495231917}, 
     {438/5, 0.004828230367818843}, {1753/20, 0.00482617803184266}, 
     {877/10, 0.004823329715909933}, {351/4, 0.004819979265079616}, 
     {439/5, 0.004817193072134278}, {1757/20, 0.004814488608972594}, 
     {879/10, 0.004812391059201256}, {1759/20, 0.0048096813161549274}, 
     {88, 0.0048062613943557295}, {1761/20, 0.004803550364239203}, 
     {881/10, 0.00480150544276985}, {1763/20, 0.004798702716147339}, 
     {441/5, 0.004795355830199365}, {353/4, 0.004792652598710067}, 
     {883/10, 0.004789950087224529}, {1767/20, 0.0047879283518040645}, 
     {442/5, 0.004785185453015619}, {1769/20, 0.004781791242232511}, 
     {177/2, 0.004779107860851213}, {1771/20, 0.004777092985412515}, 
     {443/5, 0.004774337958131346}, {1773/20, 0.004771004110423511}, 
     {887/10, 0.004768293675200761}, {355/4, 0.004765636506553074}, 
     {444/5, 0.004763187494517061}, {1777/20, 0.004760926145713303}, 
     {889/10, 0.004757562643275004}, {1779/20, 0.0047555488190353535}, 
     {89, 0.004752932339379664}, {1781/20, 0.0047502575253511896}, 
     {891/10, 0.004746830232519315}, {1783/20, 0.004744206661767416}, 
     {446/5, 0.004742302408624844}, {357/4, 0.00473961826726801}, 
     {893/10, 0.004736965040268664}, {1787/20, 0.004733556809261411}, 
     {447/5, 0.004730995903750576}, {1789/20, 0.004729038439990824}, 
     {179/2, 0.004726299913117644}, {1791/20, 0.004723017351189851}, 
     {448/5, 0.004720404187815403}, {1793/20, 0.004718507723824972}, 
     {897/10, 0.0047158272187542375}, {359/4, 0.004712683859593991}, 
     {449/5, 0.004709898711817585}, {1797/20, 0.004707272478947857}, 
     {899/10, 0.004705382760853966}, {1799/20, 0.004702682270725229}, 
     {90, 0.004699416812037135}, {1801/20, 0.004696784982577364}, 
     {901/10, 0.004694922102304521}, {1803/20, 0.004692289179361041}, 
     {451/5, 0.0046897009952867955}, {361/4, 0.004686366453027562}, 
     {903/10, 0.004683798232402229}, {1807/20, 0.004681925141631878}, 
     {452/5, 0.004679312234352679}, {1809/20, 0.004676020753135944}, 
     {181/2, 0.004673457392474345}, {1811/20, 0.004671579719245476}, 
     {453/5, 0.004668997436941194}, {1813/20, 0.0046657249153644114}, 
     {907/10, 0.004663154638845712}, {363/4, 0.004660565659965625}, 
     {454/5, 0.0046587037028698736}, {1817/20, 0.004656111137658334}, 
     {909/10, 0.004652897874083366}, {1819/20, 0.00465030299770597}, 
     {91, 0.004648448591536723}, {1821/20, 0.00464592596551829}, 
     {911/10, 0.0046426586972407435}, {1823/20, 0.004640139126071431}, 
     {456/5, 0.004637602530760225}, {365/4, 0.004635726949749074}, 
     {913/10, 0.0046331845786699724}, {1827/20, 0.004629975290437247}, 
     {457/5, 0.004627423019214127}, {1829/20, 0.004625571759886872}, 
     {183/2, 0.0046230438207370585}, {1831/20, 0.004619865657254746}, 
     {458/5, 0.0046173588807962955}, {1833/20, 0.004614869800500301}, 
     {917/10, 0.004612944103040393}, {367/4, 0.004610456148553848}, 
     {459/5, 0.004607288520459004}, {1837/20, 0.0046047332039756686}, 
     {919/10, 0.004602931355527437}, {1839/20, 0.0046004365160715035}, 
     {92, 0.004597263065618995}, {1841/20, 0.0045947408778499385}, 
     {921/10, 0.004592245439857862}, {1843/20, 0.004590447202145601}, 
     {461/5, 0.0045879735237565325}, {369/4, 0.004584802779278174}, 
     {923/10, 0.0045823542402384605}, {1847/20, 0.00458050979893687}, 
     {462/5, 0.004577500679423974}, {1849/20, 0.004574945753727255}, 
     {185/2, 0.004572457452589191}, {1851/20, 0.004569937968829318}, 
     {463/5, 0.004567508772069454}, {1853/20, 0.00456568941197275}, 
     {927/10, 0.004563170359891164}, {371/4, 0.004560137759263712}, 
     {464/5, 0.0045576764675590966}, {1857/20, 0.004555837392591003}, 
     {929/10, 0.004553362655801571}, {1859/20, 0.004550316115007868}, 
     {93, 0.004547893300875644}, {1861/20, 0.004545386908508612}, 
     {931/10, 0.004543655484846706}, {1863/20, 0.004540725778533803}, 
     {466/5, 0.004538095790459228}, {373/4, 0.004535644291405629}, 
     {933/10, 0.004533872179937859}, {1867/20, 0.004530921261115794}, 
     {467/5, 0.00452839816219062}, {1869/20, 0.004525966179800531}, 
     {187/2, 0.00452354518555885}, {1871/20, 0.00452170690873441}, 
     {468/5, 0.004519317914081504}, {1873/20, 0.004516286138814099}, 
     {937/10, 0.004514480614626311}, {375/4, 0.0045121311229266705}, 
     {469/5, 0.0045096550039703176}, {1877/20, 0.004506683479898844}, 
     {939/10, 0.0045042700425666545}, {1879/20, 0.004501861392166149}, 
     {94, 0.004500093279161365}, {1881/20, 0.004497712080957044}, 
     {941/10, 0.004494694392103953}, {1883/20, 0.0044922867660758675}, 
     {471/5, 0.004490627966496646}, {377/4, 0.004488142519315514}, 
     {943/10, 0.00448518150711812}, {1887/20, 0.004482828694292117}, 
     {472/5, 0.004481007206769152}, {1889/20, 0.004478668374796836}, 
     {189/2, 0.004476284921267966}, {1891/20, 0.0044733341266960346}, 
     {473/5, 0.004470965978951451}, {1893/20, 0.004469222441283246}, 
     {947/10, 0.004466817851636501}, {379/4, 0.0044638773721747335}, 
     {474/5, 0.004461537968733824}, {1897/20, 0.004459821085378063}, 
     {949/10, 0.0044574983290090265}, {1899/20, 0.004454585823193919}, 
     {95, 0.004452149865993723}, {1901/20, 0.004449789489751682}, 
     {951/10, 0.0044480647344055995}, {1903/20, 0.004445242407942203}, 
     {476/5, 0.004442804559403961}, {381/4, 0.004440957412822105}, 
     {953/10, 0.004438205994425018}, {1907/20, 0.0044364120559663}, 
     {477/5, 0.00443403070613177}, {1909/20, 0.004431172984108276}, 
     {191/2, 0.004428872271644929}, {1911/20, 0.004427070720575545}, 
     {478/5, 0.004424739616129513}, {1913/20, 0.004421929205206252}, 
     {957/10, 0.004419610950771566}, {383/4, 0.004417357220663824}, 
     {479/5, 0.004415046911780986}, {1917/20, 0.004412644473254577}, 
     {959/10, 0.00441034739680499}, {1919/20, 0.004408565045823301}, 
     {96, 0.004406424547493509}, {1921/20, 0.0044039765050605875}, 
     {961/10, 0.004401148668725253}, {1923/20, 0.004398856694992738}, 
     {481/5, 0.0043971558949405}, {385/4, 0.004394870463710114}, 
     {963/10, 0.004392015080638259}, {1927/20, 0.004390397600327551}, 
     {482/5, 0.004388072174624602}, {1929/20, 0.004385271146621241}, 
     {193/2, 0.0043834712648837745}, {1931/20, 0.004380586150065356}, 
     {483/5, 0.004378427673454561}, {1933/20, 0.004376630103945695}, 
     {967/10, 0.004373902728410108}, {387/4, 0.004371606050192179}, 
     {484/5, 0.004369355341976067}, {1937/20, 0.004367675665184714}, 
     {969/10, 0.004365481145267271}, {1939/20, 0.0043631398050509255}, 
     {97, 0.004360302937647203}, {1941/20, 0.004358663346708952}, 
     {971/10, 0.004356394208902421}, {1943/20, 0.00435413559484016}, 
     {486/5, 0.004351361697332708}, {389/4, 0.0043491106386783825}, 
     {973/10, 0.0043474766419272955}, {1947/20, 0.004345182612230199}, 
     {487/5, 0.004342431829712484}, {1949/20, 0.004340728111742742}, 
     {195/2, 0.004338058470132708}, {1951/20, 0.004336372421175229}, 
     {488/5, 0.004334029872452722}, {1953/20, 0.004331358095674911}, 
     {977/10, 0.004329071562002636}, {391/4, 0.004327464033877194}, 
     {489/5, 0.004325163730716654}, {1957/20, 0.004322499184444703}, 
     {979/10, 0.004320283327999209}, {1959/20, 0.004318096758316996}, 
     {98, 0.004316422451942268}, {1961/20, 0.004314140509350089}, 
     {981/10, 0.004311462403178194}, {1963/20, 0.004309295805424029}, 
     {491/5, 0.0043076022221033685}, {393/4, 0.004305446720092638}, 
     {983/10, 0.0043026927225698584}, {1967/20, 0.004300476837682572}, 
     {492/5, 0.0042983359378212915}, {1969/20, 0.004296692392656972}, 
     {197/2, 0.004294429462132611}, {1971/20, 0.004292301627646447}, 
     {493/5, 0.004289648101024296}, {1973/20, 0.004287481771795257}, 
     {987/10, 0.004285752660462416}, {395/4, 0.004283209003068328}, 
     {494/5, 0.004280914541685578}, {1977/20, 0.004278758795787232}, 
     {989/10, 0.004276620301670646}, {1979/20, 0.004274457834559875}, 
     {99, 0.00427274838948043}, {1981/20, 0.004270635874987554}, 
     {991/10, 0.004267987202885768}, {1983/20, 0.00426582469888292}, 
     {496/5, 0.004264130685117336}, {397/4, 0.0042615067079696}, 
     {993/10, 0.004259388430191976}, {1987/20, 0.004257250988775731}, 
     {497/5, 0.004255168164968551}, {1989/20, 0.004253399132037776}, 
     {199/2, 0.0042508094652834475}, {1991/20, 0.004248693980429034}, 
     {498/5, 0.004246597765359305}, {1993/20, 0.004244924359543922}, 
     {997/10, 0.0042427982769659275}, {399/4, 0.004240137106355377}, 
     {499/5, 0.004238064628412345}, {1997/20, 0.004236340795098747}, 
     {999/10, 0.004233792823548559}, {1999/20, 0.00423167086406778}, 
     {100, 0.004229586668117907}}
 
ReFRfin = {{1/10000, 0.5869362818701296}, {11/100000, 0.5868585166135558}, 
     {3/25000, 0.5869302709745372}, {13/100000, 0.5869374408309449}, 
     {7/50000, 0.5868624160725906}, {3/20000, 0.5869242583754573}, 
     {1/6250, 0.5869295429753247}, {17/100000, 0.5869203666670408}, 
     {9/50000, 0.5868697528708027}, {19/100000, 0.5869202954300419}, 
     {1/5000, 0.5869160713331745}, {21/100000, 0.5869165892473869}, 
     {11/50000, 0.5869155633782808}, {23/100000, 0.5868756733183469}, 
     {3/12500, 0.5869146106046275}, {1/4000, 0.5869244524061288}, 
     {13/50000, 0.5868786544749707}, {27/100000, 0.5869214164606431}, 
     {7/25000, 0.5869098070486616}, {29/100000, 0.5869131452604122}, 
     {3/10000, 0.5869124523820264}, {31/100000, 0.586910814565313}, 
     {1/3125, 0.5869102406063704}, {33/100000, 0.5869117983901346}, 
     {17/50000, 0.5869125054303237}, {7/20000, 0.586909506391029}, 
     {9/25000, 0.586919288579586}, {37/100000, 0.5869102189881907}, 
     {19/50000, 0.5869181285760474}, {39/100000, 0.5869090994824937}, 
     {1/2500, 0.5869184888966608}, {41/100000, 0.5868849005556083}, 
     {21/50000, 0.5869088413760317}, {43/100000, 0.5868867314093333}, 
     {11/25000, 0.5868851972943654}, {9/20000, 0.5869078020832563}, 
     {23/50000, 0.5869066801030862}, {47/100000, 0.5869070477661782}, 
     {3/6250, 0.5869073364190016}, {49/100000, 0.5869067765856344}, 
     {1/2000, 0.586915053542381}, {51/100000, 0.5869140828916324}, 
     {13/25000, 0.5869082846825187}, {53/100000, 0.5868890542579441}, 
     {27/50000, 0.5869083210179973}, {11/20000, 0.5869046704375376}, 
     {7/12500, 0.5869059657730991}, {57/100000, 0.5869143252834412}, 
     {29/50000, 0.5869144861001567}, {59/100000, 0.5868895531065741}, 
     {3/5000, 0.5869147310777332}, {61/100000, 0.5868902342309665}, 
     {31/50000, 0.5869145385898307}, {63/100000, 0.5868895057840318}, 
     {2/3125, 0.5869265439901756}, {13/20000, 0.5869125266189332}, 
     {33/50000, 0.5869134908779401}, {67/100000, 0.5868902363332582}, 
     {17/25000, 0.5869042653344412}, {69/100000, 0.5869036858046655}, 
     {7/10000, 0.5869130664474111}, {71/100000, 0.5869117096593297}, 
     {9/12500, 0.586890261589601}, {73/100000, 0.5869125123087615}, 
     {37/50000, 0.586901951925483}, {3/4000, 0.5869051946290123}, 
     {19/25000, 0.5869115299188983}, {77/100000, 0.5869119215083041}, 
     {39/50000, 0.5868910399351428}, {79/100000, 0.5869116209589595}, 
     {1/1250, 0.5869032647943238}, {81/100000, 0.5868919340514607}, 
     {41/50000, 0.586910677919124}, {83/100000, 0.5869010740611644}, 
     {21/25000, 0.5869111032876599}, {17/20000, 0.5869114037178131}, 
     {43/50000, 0.5869117025402368}, {87/100000, 0.586903698029805}, 
     {11/12500, 0.586903397879615}, {89/100000, 0.5869016874845543}, 
     {9/10000, 0.5869014614984454}, {91/100000, 0.5869027301411696}, 
     {23/25000, 0.5869105935502175}, {93/100000, 0.5869020254202262}, 
     {47/50000, 0.5869027964191256}, {19/20000, 0.5869013394237816}, 
     {3/3125, 0.5869104064530815}, {97/100000, 0.586908901057337}, 
     {49/50000, 0.5868927732503657}, {99/100000, 0.5869014530578225}, 
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     {289/50000, 0.5868660293928905}, {579/100000, 0.5868679531343632}, 
     {29/5000, 0.5868694386571454}, {581/100000, 0.5868673580483144}, 
     {291/50000, 0.5868695153493726}, {583/100000, 0.5868716044506535}, 
     {73/12500, 0.5868674253637263}, {117/20000, 0.5868663055212364}, 
     {293/50000, 0.5868685569109671}, {587/100000, 0.5868707695721147}, 
     {147/25000, 0.586867890091407}, {589/100000, 0.5868705668102328}, 
     {59/10000, 0.586868289368546}, {591/100000, 0.5868707640555444}, 
     {37/6250, 0.5868701992710803}, {593/100000, 0.5868666872180479}, 
     {297/50000, 0.5868661238827073}, {119/20000, 0.5868663497901014}, 
     {149/25000, 0.5868702561892389}, {597/100000, 0.5868699680454492}, 
     {299/50000, 0.5868662170276933}, {599/100000, 0.5868640014326054}, 
     {3/500, 0.5868689776485843}, {601/100000, 0.5868698590612818}, 
     {301/50000, 0.5868660130766905}, {603/100000, 0.5868650450570803}, 
     {151/25000, 0.5868685031530765}, {121/20000, 0.5868690437056912}, 
     {303/50000, 0.5868645679659918}, {607/100000, 0.5868686692377976}, 
     {19/3125, 0.5868678647701633}, {609/100000, 0.5868643913044034}, 
     {61/10000, 0.5868619766557708}, {611/100000, 0.5868684729083888}, 
     {153/25000, 0.586862046070534}, {613/100000, 0.5868679049812933}, 
     {307/50000, 0.586867460065772}, {123/20000, 0.5868680109502522}, 
     {77/12500, 0.586860784885781}, {617/100000, 0.5868607003673847}, 
     {309/50000, 0.5868646173543026}, {619/100000, 0.5868642475216039}, 
     {31/5000, 0.5868672584220915}, {621/100000, 0.5868623826990054}, 
     {311/50000, 0.586860487910918}, {623/100000, 0.5868627139607745}, 
     {39/6250, 0.5868667153381559}, {1/160, 0.5868623041976742}, 
     {313/50000, 0.5868625032116608}, {627/100000, 0.5868618314397294}, 
     {157/25000, 0.5868617767882625}, {629/100000, 0.586865101707561}, 
     {63/10000, 0.5868614238814525}, {631/100000, 0.586865214137863}, 
     {79/12500, 0.5868623592301239}, {633/100000, 0.5868660487707231}, 
     {317/50000, 0.586865293586551}, {127/20000, 0.5868592719199013}, 
     {159/25000, 0.5868643190921103}, {637/100000, 0.586860594608293}, 
     {319/50000, 0.5868649830772226}, {639/100000, 0.5868639402619351}, 
     {4/625, 0.5868645493052043}, {641/100000, 0.5868585184115602}, 
     {321/50000, 0.5868604860282205}, {643/100000, 0.5868604136048763}, 
     {161/25000, 0.5868600376612636}, {129/20000, 0.58686160456051}, 
     {323/50000, 0.5868611089768949}, {647/100000, 0.5868593240606161}, 
     {81/12500, 0.5868577800428598}, {649/100000, 0.5868574994363409}, 
     {13/2000, 0.5868633382980155}, {651/100000, 0.5868591202779361}, 
     {163/25000, 0.5868587956529341}, {653/100000, 0.5868591361881181}, 
     {327/50000, 0.5868604001815392}, {131/20000, 0.5868621559545026}, 
     {41/6250, 0.5868580988606564}, {657/100000, 0.5868618889380244}, 
     {329/50000, 0.5868595108673258}, {659/100000, 0.5868615336458287}, 
     {33/5000, 0.586856042857645}, {661/100000, 0.5868580241725545}, 
     {331/50000, 0.5868577234154273}, {663/100000, 0.5868609679629446}, 
     {83/12500, 0.5868617548981083}, {133/20000, 0.5868548186911573}, 
     {333/50000, 0.5868569388361435}, {667/100000, 0.586857651352815}, 
     {167/25000, 0.5868571105049956}, {669/100000, 0.5868563339155668}, 
     {67/10000, 0.5868560879050047}, {671/100000, 0.5868596374902095}, 
     {21/3125, 0.586859497289506}, {673/100000, 0.5868592624387174}, 
     {337/50000, 0.5868571478335527}, {27/4000, 0.5868603555355159}, 
     {169/25000, 0.5868572045911318}, {677/100000, 0.5868571474970432}, 
     {339/50000, 0.5868591002494772}, {679/100000, 0.5868592743963337}, 
     {17/2500, 0.5868586795308692}, {681/100000, 0.5868559240922169}, 
     {341/50000, 0.5868550914093458}, {683/100000, 0.5868560738341815}, 
     {171/25000, 0.5868522623488777}, {137/20000, 0.586858210233828}, 
     {343/50000, 0.5868553443498401}, {687/100000, 0.5868518321971026}, 
     {43/6250, 0.5868576266493091}, {689/100000, 0.5868551706870724}, 
     {69/10000, 0.5868577339139298}, {691/100000, 0.586857208949283}, 
     {173/25000, 0.586851898322462}, {693/100000, 0.5868570212074062}, 
     {347/50000, 0.5868550766040479}, {139/20000, 0.5868530084401797}, 
     {87/12500, 0.5868515297221908}, {697/100000, 0.5868536102307527}, 
     {349/50000, 0.5868560730353662}, {699/100000, 0.5868506247131666}, 
     {7/1000, 0.5868536578248067}, {701/100000, 0.586853367452743}, 
     {351/50000, 0.5868514168529022}, {703/100000, 0.5868515391085789}, 
     {22/3125, 0.586854850870107}, {141/20000, 0.5868511941296757}, 
     {353/50000, 0.5868533239213294}, {707/100000, 0.5868527346209902}, 
     {177/25000, 0.5868482733867362}, {709/100000, 0.5868548706894878}, 
     {71/10000, 0.5868521007777452}, {711/100000, 0.5868540011366585}, 
     {89/12500, 0.5868507793246027}, {713/100000, 0.5868532240926445}, 
     {357/50000, 0.5868536613560669}, {143/20000, 0.5868480772474856}, 
     {179/25000, 0.5868495588738494}, {717/100000, 0.5868534942870829}, 
     {359/50000, 0.5868496082689321}, {719/100000, 0.5868526129549498}, 
     {9/1250, 0.5868532927829708}, {721/100000, 0.5868472004737897}, 
     {361/50000, 0.5868482483651256}, {723/100000, 0.5868494321135014}, 
     {181/25000, 0.5868482508171087}, {29/4000, 0.5868469670582099}, 
     {363/50000, 0.5868489539239059}, {727/100000, 0.5868462562130747}, 
     {91/12500, 0.5868487760766894}, {729/100000, 0.5868518409097945}, 
     {73/10000, 0.5868479755073679}, {731/100000, 0.5868490418255674}, 
     {183/25000, 0.586848652529866}, {733/100000, 0.5868515619627162}, 
     {367/50000, 0.5868492728178016}, {147/20000, 0.5868466901977607}, 
     {23/3125, 0.5868480475800051}, {737/100000, 0.586845075436158}, 
     {369/50000, 0.5868464041057311}, {739/100000, 0.5868479253340899}, 
     {37/5000, 0.5868438471252375}, {741/100000, 0.5868476656915238}, 
     {371/50000, 0.5868499841134711}, {743/100000, 0.5868461889618244}, 
     {93/12500, 0.5868496156290046}, {149/20000, 0.5868466816484776}, 
     {373/50000, 0.5868452977554703}, {747/100000, 0.5868452076825386}, 
     {187/25000, 0.586848761090669}, {749/100000, 0.5868444035350593}, 
     {3/400, 0.5868432017392871}, {751/100000, 0.5868481038821178}, 
     {47/6250, 0.586843894471579}, {753/100000, 0.5868484784541934}, 
     {377/50000, 0.5868419336291208}, {151/20000, 0.5868480597194647}, 
     {189/25000, 0.5868441865560055}, {757/100000, 0.586845137510601}, 
     {379/50000, 0.5868439974244719}, {759/100000, 0.5868442659991064}, 
     {19/2500, 0.5868434326732155}, {761/100000, 0.5868448388144465}, 
     {381/50000, 0.5868469671280265}, {763/100000, 0.5868470530149783}, 
     {191/25000, 0.5868465998953463}, {153/20000, 0.5868432918079103}, 
     {383/50000, 0.5868422678134508}, {767/100000, 0.5868438311653228}, 
     {24/3125, 0.5868401274535282}, {769/100000, 0.58684466385803}, 
     {77/10000, 0.5868418268548545}, {771/100000, 0.5868435454055154}, 
     {193/25000, 0.5868427292472669}, {773/100000, 0.5868449281718369}, 
     {387/50000, 0.5868446225678268}, {31/4000, 0.5868446000723804}, 
     {97/12500, 0.5868416663682186}, {777/100000, 0.5868445965297062}, 
     {389/50000, 0.5868438323402647}, {779/100000, 0.5868425103977915}, 
     {39/5000, 0.5868381203576347}, {781/100000, 0.5868408829022869}, 
     {391/50000, 0.5868375550255833}, {783/100000, 0.5868425316434687}, 
     {49/6250, 0.5868396667495905}, {157/20000, 0.5868429932312225}, 
     {393/50000, 0.586842315023266}, {787/100000, 0.5868401128998944}, 
     {197/25000, 0.5868386049339986}, {789/100000, 0.5868386359140407}, 
     {79/10000, 0.5868385606071329}, {791/100000, 0.5868394768760989}, 
     {99/12500, 0.5868382893050068}, {793/100000, 0.5868395209849666}, 
     {397/50000, 0.5868387934013812}, {159/20000, 0.5868368280970993}, 
     {199/25000, 0.586840508602843}, {797/100000, 0.5868374503161609}, 
     {399/50000, 0.586837358488542}, {799/100000, 0.5868409320379215}, 
     {1/125, 0.5868394589455073}, {801/100000, 0.5868381572727519}, 
     {401/50000, 0.5868372800308297}, {803/100000, 0.5868407665742712}, 
     {201/25000, 0.5868374995185279}, {161/20000, 0.5868389960012679}, 
     {403/50000, 0.586836235751437}, {807/100000, 0.5868383421310504}, 
     {101/12500, 0.586833229392612}, {809/100000, 0.5868335779272318}, 
     {81/10000, 0.5868351251847326}, {811/100000, 0.5868375451821248}, 
     {203/25000, 0.5868390538483159}, {813/100000, 0.5868333443501474}, 
     {407/50000, 0.5868377593980143}, {163/20000, 0.5868326464560378}, 
     {51/6250, 0.586837386867153}, {817/100000, 0.5868351751542544}, 
     {409/50000, 0.5868370339182487}, {819/100000, 0.5868367316125589}, 
     {41/5000, 0.5868334931053578}, {821/100000, 0.5868334319849962}, 
     {411/50000, 0.5868343974983485}, {823/100000, 0.5868374399016325}, 
     {103/12500, 0.5868336834377295}, {33/4000, 0.5868355890752799}, 
     {413/50000, 0.5868327283034134}, {827/100000, 0.5868330370938963}, 
     {207/25000, 0.5868308572846672}, {829/100000, 0.5868357729621261}, 
     {83/10000, 0.5868315474196031}, {831/100000, 0.5868320838246168}, 
     {26/3125, 0.586832766999684}, {833/100000, 0.5868330294947715}, 
     {417/50000, 0.5868313016694717}, {167/20000, 0.5868309493530175}, 
     {209/25000, 0.5868308202587813}, {837/100000, 0.5868348059958377}, 
     {419/50000, 0.5868344129296785}, {839/100000, 0.5868306074006053}, 
     {21/2500, 0.5868334138691744}, {841/100000, 0.5868306741755509}, 
     {421/50000, 0.5868313916432397}, {843/100000, 0.5868306289885505}, 
     {211/25000, 0.5868314985577436}, {169/20000, 0.5868272294750119}, 
     {423/50000, 0.5868303867098663}, {847/100000, 0.586831793427177}, 
     {53/6250, 0.586828706400746}, {849/100000, 0.5868319211780615}, 
     {17/2000, 0.5868301240053606}, {851/100000, 0.5868312440518748}, 
     {213/25000, 0.5868279494230393}, {853/100000, 0.5868270336402688}, 
     {427/50000, 0.5868312457801013}, {171/20000, 0.5868289206647757}, 
     {107/12500, 0.5868262512423725}, {857/100000, 0.5868271083407355}, 
     {429/50000, 0.5868296581889982}, {859/100000, 0.5868300407892741}, 
     {43/5000, 0.5868269461076632}, {861/100000, 0.5868303460602959}, 
     {431/50000, 0.5868300553590542}, {863/100000, 0.5868274623479453}, 
     {27/3125, 0.5868293475257618}, {173/20000, 0.5868241792226696}, 
     {433/50000, 0.586826705104988}, {867/100000, 0.5868236165273562}, 
     {217/25000, 0.586829439772468}, {869/100000, 0.586827991678474}, 
     {87/10000, 0.5868249346972911}, {871/100000, 0.5868287066102491}, 
     {109/12500, 0.5868247994511351}, {873/100000, 0.5868277458412918}, 
     {437/50000, 0.586824925426527}, {7/800, 0.586823614276895}, 
     {219/25000, 0.5868246158985904}, {877/100000, 0.5868239331338563}, 
     {439/50000, 0.5868273526594958}, {879/100000, 0.5868232426855906}, 
     {11/1250, 0.5868247294278199}, {881/100000, 0.5868249740329716}, 
     {441/50000, 0.5868261740403646}, {883/100000, 0.5868239767401873}, 
     {221/25000, 0.5868226651334822}, {177/20000, 0.5868253738727622}, 
     {443/50000, 0.5868252880829319}, {887/100000, 0.5868246996008262}, 
     {111/12500, 0.5868254040266252}, {889/100000, 0.5868229584826024}, 
     {89/10000, 0.5868212566755631}, {891/100000, 0.5868199428852634}, 
     {223/25000, 0.5868248170771566}, {893/100000, 0.5868234081001265}, 
     {447/50000, 0.5868239482522162}, {179/20000, 0.5868219790152742}, 
     {28/3125, 0.5868179995295666}, {897/100000, 0.5868213999847374}, 
     {449/50000, 0.5868182144543637}, {899/100000, 0.5868227477830659}, 
     {9/1000, 0.5868199453022962}, {901/100000, 0.5868177619542108}, 
     {451/50000, 0.5868198599688577}, {903/100000, 0.5868223390162779}, 
     {113/12500, 0.586820307917673}, {181/20000, 0.5868205186736151}, 
     {453/50000, 0.5868216508565753}, {907/100000, 0.5868200818443796}, 
     {227/25000, 0.5868192750124779}, {909/100000, 0.5868180205673847}, 
     {91/10000, 0.5868188245654973}, {911/100000, 0.5868208111475832}, 
     {57/6250, 0.5868151993766899}, {913/100000, 0.5868150140062678}, 
     {457/50000, 0.586818141705792}, {183/20000, 0.5868207631640159}, 
     {229/25000, 0.5868138208899247}, {917/100000, 0.5868163110452773}, 
     {459/50000, 0.5868146268266217}, {919/100000, 0.5868164003397709}, 
     {23/2500, 0.5868154740318454}, {921/100000, 0.5868140683634637}, 
     {461/50000, 0.5868189516972055}, {923/100000, 0.5868183299128193}, 
     {231/25000, 0.5868152674729323}, {37/4000, 0.5868167186126989}, 
     {463/50000, 0.5868149783684515}, {927/100000, 0.5868150326766175}, 
     {29/3125, 0.5868124157117593}, {929/100000, 0.5868175934098376}, 
     {93/10000, 0.58681398787111}, {931/100000, 0.586813871641747}, 
     {233/25000, 0.5868162864180473}, {933/100000, 0.586816024510695}, 
     {467/50000, 0.5868160699765146}, {187/20000, 0.5868143659896976}, 
     {117/12500, 0.5868123594888495}, {937/100000, 0.5868107892001242}, 
     {469/50000, 0.5868120879441303}, {939/100000, 0.5868120408377702}, 
     {47/5000, 0.586811986860055}, {941/100000, 0.5868134648416929}, 
     {471/50000, 0.586812921968384}, {943/100000, 0.5868123847997002}, 
     {59/6250, 0.5868117919225497}, {189/20000, 0.5868113814901479}, 
     {473/50000, 0.5868144197929697}, {947/100000, 0.5868109287267518}, 
     {237/25000, 0.586810387077648}, {949/100000, 0.586810780985517}, 
     {19/2000, 0.5868129794222954}, {951/100000, 0.5868082927802818}, 
     {119/12500, 0.5868127079360921}, {953/100000, 0.586807125212458}, 
     {477/50000, 0.5868122816797401}, {191/20000, 0.5868101001296782}, 
     {239/25000, 0.5868096545889303}, {957/100000, 0.5868096938819889}, 
     {479/50000, 0.5868122882200528}, {959/100000, 0.5868110393115415}, 
     {6/625, 0.5868112134621626}, {961/100000, 0.5868116461729018}, 
     {481/50000, 0.5868087321948425}, {963/100000, 0.5868108901335392}, 
     {241/25000, 0.5868116312363592}, {193/20000, 0.5868090955745351}, 
     {483/50000, 0.5868101038221258}, {967/100000, 0.5868047402673602}, 
     {121/12500, 0.5868062373317482}, {969/100000, 0.5868049106320523}, 
     {97/10000, 0.5868097840788407}, {971/100000, 0.5868066147610396}, 
     {243/25000, 0.5868041533757093}, {973/100000, 0.5868082523840843}, 
     {487/50000, 0.5868055069545872}, {39/4000, 0.5868066374596492}, 
     {61/6250, 0.5868087755103266}, {977/100000, 0.5868024006795367}, 
     {489/50000, 0.5868048720077663}, {979/100000, 0.5868037145029898}, 
     {49/5000, 0.5868076126503405}, {981/100000, 0.586807786370374}, 
     {491/50000, 0.5868072012957759}, {983/100000, 0.586803566909019}, 
     {123/12500, 0.586803478867358}, {197/20000, 0.5868011748624191}, 
     {493/50000, 0.5868027786686021}, {987/100000, 0.5868003517423763}, 
     {247/25000, 0.586804081487986}, {989/100000, 0.5868029458688269}, 
     {99/10000, 0.5867998051094547}, {991/100000, 0.5868061207372017}, 
     {31/3125, 0.5868033256557901}, {993/100000, 0.5868052874635588}, 
     {497/50000, 0.5868010298841506}, {199/20000, 0.5868020420001567}, 
     {249/25000, 0.5868012545807719}, {997/100000, 0.586800936805902}, 
     {499/50000, 0.5868042117523196}, {999/100000, 0.5868031066278059}, 
     {1/100, 0.5868009114624879}}
 
ReFRfinb = {{1/100, 0.5868009114624879}, {11/1000, 0.5867799463992345}, 
     {3/250, 0.5867540285704864}, {13/1000, 0.5867273115158231}, 
     {7/500, 0.5866997777346774}, {3/200, 0.5866746925538626}, 
     {2/125, 0.5866383869158946}, {17/1000, 0.5866072474080033}, 
     {9/500, 0.5865731064984123}, {19/1000, 0.5865348402389645}, 
     {1/50, 0.5864949808266782}, {21/1000, 0.5864526015636318}, 
     {11/500, 0.5864067255222571}, {23/1000, 0.5863599481916024}, 
     {3/125, 0.5863115765101559}, {1/40, 0.5862636431035373}, 
     {13/500, 0.5862082686679422}, {27/1000, 0.5861568653425406}, 
     {7/250, 0.5860968712863093}, {29/1000, 0.5860416240505288}, 
     {3/100, 0.5859801314187894}, {31/1000, 0.5859176738334018}, 
     {4/125, 0.5858530939548152}, {33/1000, 0.5857860381134326}, 
     {17/500, 0.5857170280127653}, {7/200, 0.5856475158745176}, 
     {9/250, 0.5855784886359485}, {37/1000, 0.5854994240300977}, 
     {19/500, 0.5854225008158904}, {39/1000, 0.5853468249125409}, 
     {1/25, 0.5852659774857054}, {41/1000, 0.5851831618993018}, 
     {21/500, 0.5850959544561398}, {43/1000, 0.5850091306252994}, 
     {11/250, 0.5849210559777269}, {9/200, 0.5848301424962004}, 
     {23/500, 0.5847375307888547}, {47/1000, 0.5846401876670262}, 
     {6/125, 0.5845460756048042}, {49/1000, 0.5844476007265134}, 
     {1/20, 0.584346241948273}, {51/1000, 0.5842425589374378}, 
     {13/250, 0.5841383385474601}, {53/1000, 0.584028995194652}, 
     {27/500, 0.5839206343830936}, {11/200, 0.5838079990376381}, 
     {7/125, 0.5836960146312098}, {57/1000, 0.5835813095145888}, 
     {29/500, 0.583463238643692}, {59/1000, 0.5833447929093349}, 
     {3/50, 0.5832242268560539}, {61/1000, 0.5831015625420921}, 
     {31/500, 0.5829774557209362}, {63/1000, 0.5828490079840378}, 
     {8/125, 0.5827215659753096}, {13/200, 0.5825904763010636}, 
     {33/500, 0.5824572210398467}, {67/1000, 0.5823203242857935}, 
     {17/250, 0.5821859829766045}, {69/1000, 0.582044217358975}, 
     {7/100, 0.5819060803815703}, {71/1000, 0.5817628435142375}, 
     {9/125, 0.5816161166797267}, {73/1000, 0.5814709247384808}, 
     {37/500, 0.5813221088019267}, {3/40, 0.58117089055074}, 
     {19/250, 0.5810185343142531}, {77/1000, 0.5808623135984421}, 
     {39/500, 0.580706506897616}, {79/1000, 0.5805488687715714}, 
     {2/25, 0.5803875109248811}, {81/1000, 0.5802255983894336}, 
     {41/500, 0.580060662167563}, {83/1000, 0.5798948833817725}, 
     {21/250, 0.5797257266649245}, {17/200, 0.5795548677451228}, 
     {43/500, 0.5793826386406726}, {87/1000, 0.5792076949477591}, 
     {11/125, 0.5790329868868742}, {89/1000, 0.5788545489043928}, 
     {9/100, 0.5786753099843045}, {91/1000, 0.578492851169274}, 
     {23/250, 0.5783096262690077}, {93/1000, 0.5781227516839822}, 
     {47/500, 0.5779362588223913}, {19/200, 0.5777467638710676}, 
     {12/125, 0.5775555852340526}, {97/1000, 0.5773613223413783}, 
     {49/500, 0.5771660163931758}, {99/1000, 0.5769703139625628}, 
     {1/10, 0.5767703269258728}, {101/1000, 0.5765691642904374}, 
     {51/500, 0.5763668674557993}, {103/1000, 0.5761629249251325}, 
     {13/125, 0.5759559904192231}, {21/200, 0.5757475191341435}, 
     {53/500, 0.5755374516191849}, {107/1000, 0.5753236121361147}, 
     {27/250, 0.5751105670464534}, {109/1000, 0.5748944941257017}, 
     {11/100, 0.5746768156195476}, {111/1000, 0.5744570960388398}, 
     {14/125, 0.5742349592593996}, {113/1000, 0.5740119841862521}, 
     {57/500, 0.5737869918746545}, {23/200, 0.5735605305272617}, 
     {29/250, 0.5733307851324692}, {117/1000, 0.5731008528090817}, 
     {59/500, 0.5728676196934943}, {119/1000, 0.572632715280748}, 
     {3/25, 0.5723968970114024}, {121/1000, 0.5721594317187737}, 
     {61/500, 0.5719183901805649}, {123/1000, 0.5716767001851175}, 
     {31/250, 0.5714336145488024}, {1/8, 0.5711882843020604}, 
     {63/500, 0.5709417147290226}, {127/1000, 0.5706920666146926}, 
     {16/125, 0.5704409121050955}, {129/1000, 0.5701881885299827}, 
     {13/100, 0.5699340937034805}, {131/1000, 0.5696778626770707}, 
     {33/250, 0.5694210233532173}, {133/1000, 0.5691609653836989}, 
     {67/500, 0.5688991299738295}, {27/200, 0.5686355106045538}, 
     {17/125, 0.5683706414290759}, {137/1000, 0.5681040621478539}, 
     {69/500, 0.5678362657236535}, {139/1000, 0.5675653504140596}, 
     {7/50, 0.5672929676278233}, {141/1000, 0.5670196539365246}, 
     {71/500, 0.5667444481974702}, {143/1000, 0.5664673069599839}, 
     {18/125, 0.5661879174803639}, {29/200, 0.5659073658871376}, 
     {73/500, 0.5656244939073316}, {147/1000, 0.5653400042907473}, 
     {37/250, 0.5650547532706671}, {149/1000, 0.5647671617368726}, 
     {3/20, 0.5644773151410414}, {151/1000, 0.5641863843736656}, 
     {19/125, 0.5638934267762163}, {153/1000, 0.5635991167232755}, 
     {77/500, 0.5633027003580136}, {31/200, 0.5630053569914173}, 
     {39/250, 0.5627062405928274}, {157/1000, 0.5624046078505822}, 
     {79/500, 0.5621014112788338}, {159/1000, 0.5617971340601478}, 
     {4/25, 0.5614908926628859}, {161/1000, 0.5611828524171814}, 
     {81/500, 0.5608734136221476}, {163/1000, 0.5605621862392853}, 
     {41/250, 0.5602498244941723}, {33/200, 0.5599349107167386}, 
     {83/500, 0.5596188848206416}, {167/1000, 0.5593010085692742}, 
     {21/125, 0.558981978553382}, {169/1000, 0.5586614524553943}, 
     {17/100, 0.5583384982338337}, {171/1000, 0.5580140673798613}, 
     {43/250, 0.5576887215140793}, {173/1000, 0.5573609538228252}, 
     {87/500, 0.5570318793343207}, {7/40, 0.5567015112189249}, 
     {22/125, 0.5563687506174673}, {177/1000, 0.5560351593049275}, 
     {89/500, 0.5557000086020731}, {179/1000, 0.5553630094252697}, 
     {9/50, 0.5550242162696533}, {181/1000, 0.5546838917368442}, 
     {91/500, 0.5543425117951335}, {183/1000, 0.5539988829012179}, 
     {23/125, 0.5536543765342641}, {37/200, 0.5533080427784149}, 
     {93/500, 0.552959938372279}, {187/1000, 0.5526110613113548}, 
     {47/250, 0.5522599543554545}, {189/1000, 0.551907257556393}, 
     {19/100, 0.5515534342295298}, {191/1000, 0.5511977953574307}, 
     {24/125, 0.5508409742828762}, {193/1000, 0.5504822001086569}, 
     {97/500, 0.5501221613424723}, {39/200, 0.5497607247227085}, 
     {49/250, 0.5493978000675486}, {197/1000, 0.5490330619582684}, 
     {99/500, 0.5486675940490633}, {199/1000, 0.5482994389900204}, 
     {1/5, 0.5479308217582952}, {201/1000, 0.5475604259946847}, 
     {101/500, 0.5471883527286634}, {203/1000, 0.5468150546241222}, 
     {51/250, 0.54644023624234}, {41/200, 0.5460636721439265}, 
     {103/500, 0.5456865205510089}, {207/1000, 0.5453074631537582}, 
     {26/125, 0.5449266716634522}, {209/1000, 0.5445449037608139}, 
     {21/100, 0.5441611247909091}, {211/1000, 0.543776782733262}, 
     {53/250, 0.5433904138446062}, {213/1000, 0.5430034566400623}, 
     {107/500, 0.5426133608062957}, {43/200, 0.5422237420320863}, 
     {27/125, 0.5418315127875402}, {217/1000, 0.5414385511883197}, 
     {109/500, 0.5410437881535426}, {219/1000, 0.5406485847749289}, 
     {11/50, 0.5402507403516603}, {221/1000, 0.5398521626007513}, 
     {111/500, 0.5394518892385638}, {223/1000, 0.5390505500105687}, 
     {28/125, 0.5386479519611616}, {9/40, 0.5382438378852883}, 
     {113/500, 0.5378383922996219}, {227/1000, 0.5374324704836337}, 
     {57/250, 0.5370243304948592}, {229/1000, 0.5366143778649923}, 
     {23/100, 0.5362033316487205}, {231/1000, 0.5357918053776132}, 
     {29/125, 0.5353784015658385}, {233/1000, 0.5349638461862867}, 
     {117/500, 0.534548441180613}, {47/200, 0.5341311448498809}, 
     {59/250, 0.5337126143076665}, {237/1000, 0.5332926306613812}, 
     {119/500, 0.5328717934918936}, {239/1000, 0.5324496808217036}, 
     {6/25, 0.5320261233040009}, {241/1000, 0.5316013570721827}, 
     {121/500, 0.5311760873500719}, {243/1000, 0.5307480263116418}, 
     {61/250, 0.5303198512302489}, {49/200, 0.5298900657573973}, 
     {123/500, 0.5294595478395645}, {247/1000, 0.5290274205088945}, 
     {31/125, 0.5285936917163889}, {249/1000, 0.528159004229757}, 
     {1/4, 0.5277230763949556}, {251/1000, 0.527286508288487}, 
     {63/250, 0.5268483512663624}, {253/1000, 0.5264088106400018}, 
     {127/500, 0.5259686182261145}, {51/200, 0.5255269549594912}, 
     {32/125, 0.5250840887638786}, {257/1000, 0.5246399850214685}, 
     {129/500, 0.5241948141781538}, {259/1000, 0.5237483403264207}, 
     {13/50, 0.5233010424160671}, {261/1000, 0.5228524987604679}, 
     {131/500, 0.5224025749623582}, {263/1000, 0.5219515314436691}, 
     {33/125, 0.5214999946224386}, {53/200, 0.5210468507394896}, 
     {133/500, 0.5205924697694737}, {267/1000, 0.5201373590077756}, 
     {67/250, 0.5196810002297152}, {269/1000, 0.5192240556692891}, 
     {27/100, 0.5187648345363156}, {271/1000, 0.5183051761583997}, 
     {34/125, 0.5178444023077478}, {273/1000, 0.5173823034500185}, 
     {137/500, 0.5169197883405747}, {11/40, 0.5164563409862972}, 
     {69/250, 0.5159906952497098}, {277/1000, 0.5155246217570753}, 
     {139/500, 0.5150573949686081}, {279/1000, 0.5145894127134722}, 
     {7/25, 0.514120273923953}, {281/1000, 0.51364980977019}, 
     {141/500, 0.5131786308574613}, {283/1000, 0.5127072392815757}, 
     {71/250, 0.5122332065009112}, {57/200, 0.5117592387706345}, 
     {143/500, 0.511284508504632}, {287/1000, 0.510807702342857}, 
     {36/125, 0.5103303202017027}, {289/1000, 0.5098522969378423}, 
     {29/100, 0.5093735167584694}, {291/1000, 0.5088929347682463}, 
     {73/250, 0.5084116152419575}, {293/1000, 0.5079298092916686}, 
     {147/500, 0.5074471858031195}, {59/200, 0.5069628267862454}, 
     {37/125, 0.5064779070399554}, {297/1000, 0.5059921150414048}, 
     {149/500, 0.505505378695168}, {299/1000, 0.505017440626566}, 
     {3/10, 0.5045291262999858}, {301/1000, 0.5040401393036333}, 
     {151/500, 0.5035489686835635}, {303/1000, 0.5030584004851253}, 
     {38/125, 0.5025653921064634}, {61/200, 0.5020724719665788}, 
     {153/500, 0.5015782732215373}, {307/1000, 0.5010834433607352}, 
     {77/250, 0.5005879014259706}, {309/1000, 0.500091311493807}, 
     {31/100, 0.4995938188081359}, {311/1000, 0.4990953239524041}, 
     {39/125, 0.49859688513081757}, {313/1000, 0.498096352652015}, 
     {157/500, 0.497595232322666}, {63/200, 0.4970938076362872}, 
     {79/250, 0.49659104473184534}, {317/1000, 0.4960879217623364}, 
     {159/500, 0.49558359155490583}, {319/1000, 0.49507887169424425}, 
     {8/25, 0.49457277406982136}, {321/1000, 0.4940665751302671}, 
     {161/500, 0.49355881857756767}, {323/1000, 0.49305106191953296}, 
     {81/250, 0.4925421664344296}, {13/40, 0.49203244190283035}, 
     {163/500, 0.49152232958341147}, {327/1000, 0.4910107082057138}, 
     {41/125, 0.4904984099813543}, {329/1000, 0.48998601366478534}, 
     {33/100, 0.4894723291399461}, {331/1000, 0.4889582177869518}, 
     {83/250, 0.48844327384700303}, {333/1000, 0.48792762550004776}, 
     {167/500, 0.4874109543606422}, {67/200, 0.48689450304614734}, 
     {42/125, 0.48637610801946174}, {337/1000, 0.48585805341712174}, 
     {169/500, 0.4853380459229415}, {339/1000, 0.484818327215474}, 
     {17/50, 0.4842972659974243}, {341/1000, 0.48377677072773384}, 
     {171/500, 0.4832540227876083}, {343/1000, 0.482731575971731}, 
     {43/125, 0.4822086219126618}, {69/200, 0.481683756783605}, 
     {173/500, 0.4811596877367159}, {347/1000, 0.48063405498125267}, 
     {87/250, 0.4801079671348809}, {349/1000, 0.4795813080297737}, 
     {7/20, 0.4790540370949756}, {351/1000, 0.4785261509179124}, 
     {44/125, 0.4779972997362867}, {353/1000, 0.4774683553035337}, 
     {177/500, 0.47693832117824986}, {71/200, 0.47640826423508464}, 
     {89/250, 0.4758772122498067}, {357/1000, 0.4753453061403894}, 
     {179/500, 0.4748131948912815}, {359/1000, 0.4742806337114418}, 
     {9/25, 0.4737472323099321}, {361/1000, 0.4732132761159997}, 
     {181/500, 0.47267845331547065}, {363/1000, 0.4721440997783377}, 
     {91/250, 0.471607953805695}, {73/200, 0.47107226939844526}, 
     {183/500, 0.47053473180668925}, {367/1000, 0.46999818579417774}, 
     {46/125, 0.46945956318177684}, {369/1000, 0.46892150275724465}, 
     {37/100, 0.4683822817933039}, {371/1000, 0.4678428813509332}, 
     {93/250, 0.4673030982568456}, {373/1000, 0.4667626834250802}, 
     {187/500, 0.46622218687740613}, {3/8, 0.4656800119463407}, 
     {47/125, 0.4651383563860412}, {377/1000, 0.4645956996242946}, 
     {189/500, 0.4640532842856393}, {379/1000, 0.4635091890658285}, 
     {19/50, 0.46296594325253215}, {381/1000, 0.46242153159351895}, 
     {191/500, 0.4618761731079313}, {383/1000, 0.4613308766221338}, 
     {48/125, 0.4607851791644535}, {77/200, 0.4602386513107217}, 
     {193/500, 0.4596918889386421}, {387/1000, 0.4591447698324118}, 
     {97/250, 0.4585972994152936}, {389/1000, 0.45804934667373054}, 
     {39/100, 0.45750113756451594}, {391/1000, 0.4569522106911217}, 
     {49/125, 0.45640304130641685}, {393/1000, 0.4558533715393671}, 
     {197/500, 0.45530296674237825}, {79/200, 0.4547526138560136}, 
     {99/250, 0.4542018611895431}, {397/1000, 0.4536507982053548}, 
     {199/500, 0.45309891140670544}, {399/1000, 0.45254693061285156}, 
     {2/5, 0.4519944911050091}, {401/1000, 0.4514416716833729}, 
     {201/500, 0.45088915003497254}, {403/1000, 0.4503350116442446}, 
     {101/250, 0.4497811136407197}, {81/200, 0.44922720912566483}, 
     {203/500, 0.44867256792529675}, {407/1000, 0.4481176843049104}, 
     {51/125, 0.44756262039259065}, {409/1000, 0.44700687478160717}, 
     {41/100, 0.4464515350961955}, {411/1000, 0.4458946105516932}, 
     {103/250, 0.44533835231895313}, {413/1000, 0.4447811511415507}, 
     {207/500, 0.4442243027320383}, {83/200, 0.443666938083747}, 
     {52/125, 0.44310898717504443}, {417/1000, 0.44255108106784347}, 
     {209/500, 0.4419926657126929}, {419/1000, 0.44143415511678485}, 
     {21/50, 0.44087580991087183}, {421/1000, 0.4403159406212689}, 
     {211/500, 0.4397563262482094}, {423/1000, 0.4391965062283236}, 
     {53/125, 0.43863696554809994}, {17/40, 0.4380768459875988}, 
     {213/500, 0.43751621275364183}, {427/1000, 0.4369555651402486}, 
     {107/250, 0.43639438913594386}, {429/1000, 0.43583332929424135}, 
     {43/100, 0.43527271209450014}, {431/1000, 0.4347109033171197}, 
     {54/125, 0.43414841686254313}, {433/1000, 0.4335864829928102}, 
     {217/500, 0.43302396330375537}, {87/200, 0.43246199766728566}, 
     {109/250, 0.4318991595174464}, {437/1000, 0.4313358513288925}, 
     {219/500, 0.43077292386661314}, {439/1000, 0.43020969851991575}, 
     {11/25, 0.4296461439618309}, {441/1000, 0.4290827243063253}, 
     {221/500, 0.4285186016022209}, {443/1000, 0.4279551636460974}, 
     {111/250, 0.42739067238370954}, {89/200, 0.4268263109399384}, 
     {223/500, 0.4262621813228469}, {447/1000, 0.42569713623219974}, 
     {56/125, 0.4251329142263578}, {449/1000, 0.42456720550692806}, 
     {9/20, 0.42400291411653424}, {451/1000, 0.4234368779585309}, 
     {113/250, 0.4228714646951861}, {453/1000, 0.42230626523058534}, 
     {227/500, 0.42174064228581853}, {91/200, 0.42117497175887353}, 
     {57/125, 0.4206094261834461}, {457/1000, 0.4200429829188099}, 
     {229/500, 0.4194769530635174}, {459/1000, 0.4189108975515299}, 
     {23/50, 0.41834459241557154}, {461/1000, 0.4177782243546142}, 
     {231/500, 0.41721175179400305}, {463/1000, 0.4166454213642026}, 
     {58/125, 0.4160786818859199}, {93/200, 0.41551231859164517}, 
     {233/500, 0.4149449305616706}, {467/1000, 0.4143783483841421}, 
     {117/250, 0.4138117823416265}, {469/1000, 0.413244198083353}, 
     {47/100, 0.41267724855627286}, {471/1000, 0.4121101445490165}, 
     {59/125, 0.41154324673398435}, {473/1000, 0.41097604028820944}, 
     {237/500, 0.4104087566400554}, {19/40, 0.4098417627311908}, 
     {119/250, 0.4092748631292258}, {477/1000, 0.40870691632667544}, 
     {239/500, 0.4081395354481989}, {479/1000, 0.4075723282918342}, 
     {12/25, 0.4070049424604445}, {481/1000, 0.4064379016000217}, 
     {241/500, 0.4058701785411296}, {483/1000, 0.40530275845216535}, 
     {121/250, 0.40473534592931726}, {97/200, 0.40416799488863564}, 
     {243/500, 0.4036010723059782}, {487/1000, 0.4030332875793583}, 
     {61/125, 0.40246591650618146}, {489/1000, 0.4018986026079139}, 
     {49/100, 0.4013311826520871}, {491/1000, 0.4007639800552827}, 
     {123/250, 0.4001966176758791}, {493/1000, 0.39962974277009256}, 
     {247/500, 0.39906272077989113}, {99/200, 0.3984950158026721}, 
     {62/125, 0.39792763520306274}, {497/1000, 0.39736086273985505}, 
     {249/500, 0.3967937050050083}, {499/1000, 0.39622678054212335}, 
     {1/2, 0.3956598369141475}, {501/1000, 0.39509305977331755}, 
     {251/500, 0.3945260995572908}, {503/1000, 0.3939596183630196}, 
     {63/125, 0.3933929149083184}, {101/200, 0.39282666410652656}, 
     {253/500, 0.3922603193505223}, {507/1000, 0.39169410694425455}, 
     {127/250, 0.39112734136889005}, {509/1000, 0.3905610178577401}, 
     {51/100, 0.38999494759733144}, {511/1000, 0.3894294195801984}, 
     {64/125, 0.3888630109755469}, {513/1000, 0.3882971211599413}, 
     {257/500, 0.3877314789442452}, {103/200, 0.38716586942747666}, 
     {129/250, 0.3866004873648139}, {517/1000, 0.3860349892873849}, 
     {259/500, 0.38546982094538285}, {519/1000, 0.38490527317671797}, 
     {13/25, 0.38433978687611825}, {521/1000, 0.3837748459287993}, 
     {261/500, 0.38321057656445356}, {523/1000, 0.3826453028962895}, 
     {131/250, 0.3820811616176183}, {21/40, 0.3815172379931546}, 
     {263/500, 0.38095282518120177}, {527/1000, 0.3803893156912084}, 
     {66/125, 0.37982545087720077}, {529/1000, 0.37926101029370285}, 
     {53/100, 0.3786981821463149}, {531/1000, 0.37813480778088815}, 
     {133/250, 0.3775710212847132}, {533/1000, 0.37700826664911125}, 
     {267/500, 0.37644539866648596}, {107/200, 0.3758827504166069}, 
     {67/125, 0.375320710401029}, {537/1000, 0.37475809075097155}, 
     {269/500, 0.37419599702232453}, {539/1000, 0.3736346321790496}, 
     {27/50, 0.3730724574710904}, {541/1000, 0.3725108135422275}, 
     {271/500, 0.3719496157013631}, {543/1000, 0.3713884548148614}, 
     {68/125, 0.37082762205437847}, {109/200, 0.37026739707768286}, 
     {273/500, 0.36970671157852397}, {547/1000, 0.3691460320650868}, 
     {137/250, 0.3685861751147206}, {549/1000, 0.36802622694692166}, 
     {11/20, 0.36746675236158755}, {551/1000, 0.3669072581800856}, 
     {69/125, 0.36634820504058174}, {553/1000, 0.3657888471119368}, 
     {277/500, 0.3652305021274427}, {111/200, 0.36467216173355377}, 
     {139/250, 0.36411443796731513}, {557/1000, 0.36355631090657914}, 
     {279/500, 0.36299859583632976}, {559/1000, 0.36244077126309593}, 
     {14/25, 0.3618836017442324}, {561/1000, 0.36132663366082873}, 
     {281/500, 0.36077003140165287}, {563/1000, 0.3602138366071381}, 
     {141/250, 0.35965741007780405}, {113/200, 0.35910152849923227}, 
     {283/500, 0.3585463315244848}, {567/1000, 0.357990814486016}, 
     {71/125, 0.3574350454325468}, {569/1000, 0.35688052381370206}, 
     {57/100, 0.3563259475057663}, {571/1000, 0.35577182622829184}, 
     {143/250, 0.3552178941592148}, {573/1000, 0.3546646443157391}, 
     {287/500, 0.35411065748550064}, {23/40, 0.35355761511266914}, 
     {72/125, 0.3530052132012731}, {577/1000, 0.3524523139582434}, 
     {289/500, 0.35190014338792475}, {579/1000, 0.3513487643965889}, 
     {29/50, 0.3507967578991851}, {581/1000, 0.3502451456303861}, 
     {291/500, 0.3496945142199577}, {583/1000, 0.34914373121775855}, 
     {73/125, 0.34859311191373266}, {117/200, 0.3480434621329067}, 
     {293/500, 0.34749373063708955}, {587/1000, 0.3469443160552159}, 
     {147/250, 0.3463952465496094}, {589/1000, 0.34584625555990334}, 
     {59/100, 0.3452981762698588}, {591/1000, 0.3447501004997564}, 
     {74/125, 0.34420230909054217}, {593/1000, 0.34365507997814637}, 
     {297/500, 0.3431080346501414}, {119/200, 0.34256117466483227}, 
     {149/250, 0.3420153224711364}, {597/1000, 0.34146879151898313}, 
     {299/500, 0.3409236595464513}, {599/1000, 0.34037785534928844}, 
     {3/5, 0.33983284766932886}, {601/1000, 0.33928823023738897}, 
     {301/500, 0.33874399312639536}, {603/1000, 0.3382002350532116}, 
     {151/250, 0.3376569674840546}, {121/200, 0.33711353038664926}, 
     {303/500, 0.3365709977419111}, {607/1000, 0.33602792147955185}, 
     {76/125, 0.33548625387645603}, {609/1000, 0.3349448373543509}, 
     {61/100, 0.33440361401379803}, {611/1000, 0.3338621801499362}, 
     {153/250, 0.33332138966980107}, {613/1000, 0.33278149390469225}, 
     {307/500, 0.3322417950349019}, {123/200, 0.33170225991378466}, 
     {77/125, 0.3311632794162205}, {617/1000, 0.3306247706073875}, 
     {309/500, 0.33008638406681845}, {619/1000, 0.3295487128519017}, 
     {31/50, 0.3290111150779489}, {621/1000, 0.3284737927053172}, 
     {311/500, 0.32793780244487736}, {623/1000, 0.32740163671815914}, 
     {78/125, 0.326865742758806}, {5/8, 0.32632994095635937}, 
     {313/500, 0.3257953459352332}, {627/1000, 0.3252606493426766}, 
     {157/250, 0.32472656051441495}, {629/1000, 0.324192387427769}, 
     {63/100, 0.32365899856279556}, {631/1000, 0.3231260111335259}, 
     {79/125, 0.32259318715246676}, {633/1000, 0.3220617089208866}, 
     {317/500, 0.32152933126931016}, {127/200, 0.3209982844112722}, 
     {159/250, 0.32046760062049495}, {637/1000, 0.3199372139866594}, 
     {319/500, 0.3194072050416157}, {639/1000, 0.31887748139681804}, 
     {16/25, 0.3183485217358888}, {641/1000, 0.317819847464174}, 
     {321/500, 0.31729125211799625}, {643/1000, 0.3167635670691009}, 
     {161/250, 0.3162360475330317}, {129/200, 0.31570943809430685}, 
     {323/500, 0.31518260337767057}, {647/1000, 0.3146569317328898}, 
     {81/125, 0.31413132763450924}, {649/1000, 0.313606191007582}, 
     {13/20, 0.3130814632955279}, {651/1000, 0.31255710289104366}, 
     {163/250, 0.31203365007692874}, {653/1000, 0.311510089038445}, 
     {327/500, 0.3109868223503718}, {131/200, 0.3104647701350729}, 
     {82/125, 0.3099429128707065}, {657/1000, 0.3094213726794641}, 
     {329/500, 0.3089002831879304}, {659/1000, 0.30837957723495224}, 
     {33/50, 0.30785928448476674}, {661/1000, 0.30734000336562284}, 
     {331/500, 0.3068208127768206}, {663/1000, 0.3063020355075228}, 
     {83/125, 0.3057842422827801}, {133/200, 0.30526594495883863}, 
     {333/500, 0.30474875559320447}, {667/1000, 0.3042320776540772}, 
     {167/250, 0.3037156014928435}, {669/1000, 0.30319991524098633}, 
     {67/100, 0.30268473026190046}, {671/1000, 0.30216944590260963}, 
     {84/125, 0.3016550638291311}, {673/1000, 0.3011412567957259}, 
     {337/500, 0.3006281785796743}, {27/40, 0.3001146184672361}, 
     {169/250, 0.29960252133896725}, {677/1000, 0.2990907356142789}, 
     {339/500, 0.29857897996908056}, {679/1000, 0.2980681445165083}, 
     {17/25, 0.2975574375819765}, {681/1000, 0.297047649113797}, 
     {341/500, 0.29653817563147955}, {683/1000, 0.2960293498256048}, 
     {171/250, 0.2955209248190678}, {137/200, 0.2950125289921264}, 
     {343/500, 0.2945053681261225}, {687/1000, 0.29399806473936163}, 
     {86/125, 0.2934915255618715}, {689/1000, 0.2929855325796207}, 
     {69/100, 0.2924799348631488}, {691/1000, 0.29197550579224796}, 
     {173/250, 0.2914710304812842}, {693/1000, 0.29096689482283966}, 
     {347/500, 0.2904634772114729}, {139/200, 0.2899605677262391}, 
     {87/125, 0.28945807919508004}, {697/1000, 0.28895588187916266}, 
     {349/500, 0.28845465277534443}, {699/1000, 0.28795404026123084}, 
     {7/10, 0.2874536632899103}, {701/1000, 0.286953694632164}, 
     {351/500, 0.286454524192038}, {703/1000, 0.28595555465862854}, 
     {88/125, 0.2854574371435339}, {141/200, 0.28495962305412914}, 
     {353/500, 0.2844625735499189}, {707/1000, 0.28396613938848114}, 
     {177/250, 0.28346968574295617}, {709/1000, 0.282974099638831}, 
     {71/100, 0.2824787677627236}, {711/1000, 0.2819840206610362}, 
     {89/125, 0.28149032788048123}, {713/1000, 0.28099690107735986}, 
     {357/500, 0.2805038308393841}, {143/200, 0.2800111241999734}, 
     {179/250, 0.27951975145492125}, {717/1000, 0.27902810466585337}, 
     {359/500, 0.27853725046024813}, {719/1000, 0.27804695574586846}, 
     {18/25, 0.2775572906216133}, {721/1000, 0.2770676267105143}, 
     {361/500, 0.2765791071729833}, {723/1000, 0.2760914532637906}, 
     {181/250, 0.2756036127108987}, {29/40, 0.27511652448408697}, 
     {363/500, 0.2746299733384008}, {727/1000, 0.2741443209578498}, 
     {91/125, 0.27365863514062316}, {729/1000, 0.2731737345115146}, 
     {73/100, 0.2726894122839636}, {731/1000, 0.27220561636389706}, 
     {183/250, 0.2717223627633929}, {733/1000, 0.2712396729935769}, 
     {367/500, 0.27075756245255933}, {147/200, 0.27027561282135837}, 
     {92/125, 0.2697949462460685}, {737/1000, 0.2693144313118365}, 
     {369/500, 0.2688345132505794}, {739/1000, 0.2683547075225696}, 
     {37/50, 0.26787625778538304}, {741/1000, 0.2673979994216824}, 
     {371/500, 0.26691992835019596}, {743/1000, 0.26644338469396334}, 
     {93/125, 0.2659665117106127}, {149/200, 0.2654905316849949}, 
     {373/500, 0.2650147512615417}, {747/1000, 0.26454011903380215}, 
     {187/250, 0.26406538737813445}, {749/1000, 0.2635919301649572}, 
     {3/4, 0.26311840002789255}, {751/1000, 0.2626460076867756}, 
     {94/125, 0.2621739121179738}, {753/1000, 0.26170234077696897}, 
     {377/500, 0.26123135047357326}, {151/200, 0.26076097720321467}, 
     {189/250, 0.2602910710622899}, {757/1000, 0.25982178738973527}, 
     {379/500, 0.259352680436322}, {759/1000, 0.25888483603972445}, 
     {19/25, 0.25841698176566097}, {761/1000, 0.2579502996358114}, 
     {381/500, 0.25748372888381055}, {763/1000, 0.2570175431425965}, 
     {191/250, 0.25655225519884395}, {153/200, 0.2560881041359495}, 
     {383/500, 0.25562338222332315}, {767/1000, 0.25516029525864714}, 
     {96/125, 0.2546972226844515}, {769/1000, 0.2542345507159649}, 
     {77/100, 0.2537726747330131}, {771/1000, 0.25331102017796026}, 
     {193/250, 0.2528505576819893}, {773/1000, 0.2523903697285865}, 
     {387/500, 0.2519308378343805}, {31/40, 0.25147177816945177}, 
     {97/125, 0.2510130563046067}, {777/1000, 0.25055514404874923}, 
     {389/500, 0.25009780875016396}, {779/1000, 0.24964149899451793}, 
     {39/50, 0.24918532499564594}, {781/1000, 0.24872943295149796}, 
     {391/500, 0.24827475530920395}, {783/1000, 0.24782005048795552}, 
     {98/125, 0.24736651613653726}, {157/200, 0.24691323744131966}, 
     {393/500, 0.2464602673936045}, {787/1000, 0.24600817966687627}, 
     {197/250, 0.2455566280003625}, {789/1000, 0.24510604597431795}, 
     {79/100, 0.24465566307417586}, {791/1000, 0.24420589700190543}, 
     {99/125, 0.24375644805159458}, {793/1000, 0.24330813181609523}, 
     {397/500, 0.24286008380195878}, {159/200, 0.24241294488785448}, 
     {199/250, 0.24196551126575638}, {797/1000, 0.24151952339649507}, 
     {399/500, 0.24107355880199766}, {799/1000, 0.24062872144644998}, 
     {4/5, 0.24018418774558126}, {801/1000, 0.23973994173852842}, 
     {401/500, 0.23929657991295716}, {803/1000, 0.2388541553147392}, 
     {201/250, 0.23841167639360616}, {161/200, 0.2379703724561646}, 
     {403/500, 0.23752933690189715}, {807/1000, 0.23708916182317852}, 
     {101/125, 0.23664879089018243}, {809/1000, 0.23620953896480046}, 
     {81/100, 0.2357709046338301}, {811/1000, 0.23533278411885883}, 
     {203/250, 0.23489557828365504}, {813/1000, 0.23445865537273392}, 
     {407/500, 0.2340220308853771}, {163/200, 0.23358680970240275}, 
     {102/125, 0.23315142679004186}, {817/1000, 0.23271687606232683}, 
     {409/500, 0.23228263593681064}, {819/1000, 0.23184976581177974}, 
     {41/50, 0.23141678609171112}, {821/1000, 0.23098451888170213}, 
     {411/500, 0.23055294165417073}, {823/1000, 0.23012187965514297}, 
     {103/125, 0.22969113811228836}, {33/40, 0.22926126556899207}, 
     {413/500, 0.22883231306565}, {827/1000, 0.2284038715189245}, 
     {207/250, 0.22797529781177994}, {829/1000, 0.22754776118062203}, 
     {83/100, 0.22712114378402126}, {831/1000, 0.2266948339010062}, 
     {104/125, 0.22626882907203472}, {833/1000, 0.22584368774924957}, 
     {417/500, 0.22541963739105397}, {167/200, 0.22499571087844594}, 
     {209/250, 0.22457210752351742}, {837/1000, 0.2241495461151488}, 
     {419/500, 0.22372685003777404}, {839/1000, 0.2233055537601738}, 
     {21/25, 0.2228845158240682}, {841/1000, 0.22246411398489885}, 
     {421/500, 0.22204428136445764}, {843/1000, 0.22162476884884086}, 
     {211/250, 0.22120641335594393}, {169/200, 0.22078835983839307}, 
     {423/500, 0.22037086485577406}, {847/1000, 0.21995376266397404}, 
     {106/125, 0.21953772578799158}, {849/1000, 0.21912203086562276}, 
     {17/20, 0.21870688969552132}, {851/1000, 0.21829261871425998}, 
     {213/250, 0.21787820549236492}, {853/1000, 0.21746514949618434}, 
     {427/500, 0.21705262628941968}, {171/200, 0.21663999934709333}, 
     {107/125, 0.21622891089268115}, {857/1000, 0.21581793156777374}, 
     {429/500, 0.21540707490233246}, {859/1000, 0.21499730343641543}, 
     {43/50, 0.21458809624975306}, {861/1000, 0.21417943694057184}, 
     {431/500, 0.21377143205523108}, {863/1000, 0.21336448553376863}, 
     {108/125, 0.21295740734593305}, {173/200, 0.2125511637775308}, 
     {433/500, 0.2121452312240122}, {867/1000, 0.21174017490066555}, 
     {217/250, 0.21133615360643265}, {869/1000, 0.21093181794389126}, 
     {87/100, 0.21052849865929968}, {871/1000, 0.21012601178246992}, 
     {109/125, 0.20972389100812516}, {873/1000, 0.20932209367326715}, 
     {437/500, 0.20892141431933609}, {7/8, 0.20852103548702527}, 
     {219/250, 0.20812101444764086}, {877/1000, 0.20772207976911838}, 
     {439/500, 0.2073234920946947}, {879/1000, 0.20692548337200756}, 
     {22/25, 0.20652825922990425}, {881/1000, 0.206131208422196}, 
     {441/500, 0.20573497550732078}, {883/1000, 0.20533935581635343}, 
     {221/250, 0.20494425206234013}, {177/200, 0.20454951177368774}, 
     {443/500, 0.20415559614012446}, {887/1000, 0.2037627004526168}, 
     {111/125, 0.2033698452297965}, {889/1000, 0.20297767900642105}, 
     {89/100, 0.20258586835796266}, {891/1000, 0.20219489288254566}, 
     {223/250, 0.20180480480789287}, {893/1000, 0.2014151478964119}, 
     {447/500, 0.20102556986116915}, {179/200, 0.2006371521696626}, 
     {112/125, 0.20024913949773104}, {897/1000, 0.19986182239441996}, 
     {449/500, 0.19947497738449438}, {899/1000, 0.19908851478432554}, 
     {9/10, 0.19870279332924357}, {901/1000, 0.19831769277623357}, 
     {451/500, 0.19793332411018172}, {903/1000, 0.19754920421549604}, 
     {113/125, 0.19716599529711876}, {181/200, 0.19678322185052788}, 
     {453/500, 0.19640098875888445}, {907/1000, 0.1960193650103761}, 
     {227/250, 0.19563797692749363}, {909/1000, 0.19525752558544718}, 
     {91/100, 0.19487801316530118}, {911/1000, 0.19449853982600795}, 
     {114/125, 0.19412000862080303}, {913/1000, 0.19374186067898513}, 
     {457/500, 0.19336397977808994}, {183/200, 0.19298735441884762}, 
     {229/250, 0.19261079175593765}, {917/1000, 0.19223473956765047}, 
     {459/500, 0.19185955718157843}, {919/1000, 0.19148489968174864}, 
     {23/25, 0.19111102051822226}, {921/1000, 0.1907376688971305}, 
     {461/500, 0.19036458570246362}, {923/1000, 0.18999243527689447}, 
     {231/250, 0.18962029106409384}, {37/40, 0.18924904693620492}, 
     {463/500, 0.18887883438912456}, {927/1000, 0.18850866038898095}, 
     {116/125, 0.1881393408568921}, {929/1000, 0.18777015803842523}, 
     {93/100, 0.18740200873644852}, {931/1000, 0.18703432059123482}, 
     {233/250, 0.18666717651130504}, {933/1000, 0.18630058510636727}, 
     {467/500, 0.1859347285334001}, {187/200, 0.18556891923793284}, 
     {117/125, 0.18520408155033508}, {937/1000, 0.18484006201176195}, 
     {469/500, 0.1844761076317627}, {939/1000, 0.18411316973413516}, 
     {47/50, 0.18375063404546899}, {941/1000, 0.18338838021909687}, 
     {471/500, 0.18302712640680652}, {943/1000, 0.18266630389253824}, 
     {118/125, 0.18230612131080004}, {189/200, 0.1819463422418246}, 
     {473/500, 0.18158695992994334}, {947/1000, 0.18122863286389268}, 
     {237/250, 0.18087067906850895}, {949/1000, 0.18051321732377723}, 
     {19/20, 0.1801561202105757}, {951/1000, 0.17979981561769542}, 
     {119/125, 0.1794442721346221}, {953/1000, 0.1790891277301765}, 
     {477/500, 0.17873447379635166}, {191/200, 0.1783802865230899}, 
     {239/250, 0.1780267824173818}, {957/1000, 0.17767414163673267}, 
     {479/500, 0.1773217605592371}, {959/1000, 0.17697013729261957}, 
     {24/25, 0.17661864441520492}, {961/1000, 0.17626819074771694}, 
     {481/500, 0.17591804397298882}, {963/1000, 0.17556860238198368}, 
     {241/250, 0.17521957534991528}, {193/200, 0.17487124749898852}, 
     {483/500, 0.17452340485762607}, {967/1000, 0.17417626392869456}, 
     {121/125, 0.17382924865216043}, {969/1000, 0.17348330558050495}, 
     {97/100, 0.17313751934798538}, {971/1000, 0.17279246498063694}, 
     {243/250, 0.17244833183311226}, {973/1000, 0.17210443345754867}, 
     {487/500, 0.17176075442824312}, {39/40, 0.1714182921523033}, 
     {122/125, 0.17107604584788683}, {977/1000, 0.1707342359160151}, 
     {489/500, 0.17039313003810952}, {979/1000, 0.1700523770887199}, 
     {49/50, 0.1697126571815043}, {981/1000, 0.16937314315463536}, 
     {491/500, 0.1690342386640984}, {983/1000, 0.168695945984511}, 
     {123/125, 0.16835788079523972}, {197/200, 0.16802088790997027}, 
     {493/500, 0.16768415100512013}, {987/1000, 0.1673478443546923}, 
     {247/250, 0.16701242051066045}, {989/1000, 0.16667751083656668}, 
     {99/100, 0.16634272453162624}, {991/1000, 0.16600901477635477}, 
     {124/125, 0.16567562175670514}, {993/1000, 0.1653428053007815}, 
     {497/500, 0.1650104991266348}, {199/200, 0.16467880990660655}, 
     {249/250, 0.16434769616802458}, {997/1000, 0.16401677286842076}, 
     {499/500, 0.1636866870995799}, {999/1000, 0.16335728303166086}, 
     {1, 0.16302831028146658}}
 
ReFRfinc = {{1, 0.16305016862734167}, {201/200, 0.16141354353420811}, 
     {101/100, 0.15979038296366244}, {203/200, 0.15818062522047138}, 
     {51/50, 0.1565842075881242}, {41/40, 0.1550010703496203}, 
     {103/100, 0.1534311299731903}, {207/200, 0.15187433896312386}, 
     {26/25, 0.15033062793481877}, {209/200, 0.14879993354506582}, 
     {21/20, 0.14728218738826582}, {211/200, 0.14577732144979738}, 
     {53/50, 0.14428525692333072}, {213/200, 0.14280594673322888}, 
     {107/100, 0.1413393060636562}, {43/40, 0.1398852761490863}, 
     {27/25, 0.13844378119421785}, {217/200, 0.13701474896807364}, 
     {109/100, 0.13559811523241266}, {219/200, 0.1341937954489062}, 
     {11/10, 0.1328017383045304}, {221/200, 0.1314218630957223}, 
     {111/100, 0.1300540969642412}, {223/200, 0.12869837079047486}, 
     {28/25, 0.12735460599275295}, {9/8, 0.1260227198487292}, 
     {113/100, 0.12470266264029306}, {227/200, 0.12339435134714893}, 
     {57/50, 0.12209770920711072}, {229/200, 0.12081266243688604}, 
     {23/20, 0.11953913769722208}, {231/200, 0.11827706145890204}, 
     {29/25, 0.11702635945222414}, {233/200, 0.11578695713092363}, 
     {117/100, 0.11455877944955506}, {47/40, 0.11334173573594816}, 
     {59/50, 0.11213577592955717}, {237/200, 0.1109408093103322}, 
     {119/100, 0.10975676202476248}, {239/200, 0.10858355612407494}, 
     {6/5, 0.10742111813881544}, {241/200, 0.10626937291234281}, 
     {121/100, 0.10512824487572928}, {243/200, 0.1039976578102968}, 
     {61/50, 0.10287753517810214}, {49/40, 0.10176778758888269}, 
     {123/100, 0.1006683523551548}, {247/200, 0.09957914741129198}, 
     {31/25, 0.09850009903034583}, {249/200, 0.0974311315065341}, 
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     {289/50, -0.00012634090084984173}, {1157/200, -0.00012310276494842398}, 
     {579/100, -0.00011981367949065458}, {1159/200, -0.00011658695919680717}, 
     {29/5, -0.00011345200406287503}, {1161/200, -0.00011026704310901358}, 
     {581/100, -0.00010710425393201106}, {1163/200, -0.00010396542458956937}, 
     {291/50, -0.00010082691033796998}, {233/40, -0.00009769551146754374}, 
     {583/100, -0.00009463515194818584}, {1167/200, -0.0000915841563493558}, 
     {146/25, -0.0000885353877511097}, {1169/200, -0.00008539184092848373}, 
     {117/20, -0.00008239214249683435}, {1171/200, -0.00007943134698895626}, 
     {293/50, -0.00007644787817318033}, {1173/200, -0.0000734807994478004}, 
     {587/100, -0.00007053183374683414}, {47/8, -0.00006752498336370927}, 
     {147/25, -0.00006466309945296622}, {1177/200, -0.00006177656143857568}, 
     {589/100, -0.000058872521992325844}, 
     {1179/200, -0.00005597827041348147}, {59/10, -0.00005308816715476894}, 
     {1181/200, -0.00005027467414686626}, 
     {591/100, -0.000047415812436391036}, 
     {1183/200, -0.000044602956262185245}, 
     {148/25, -0.000041736479707399354}, {237/40, -0.00003903228614365872}, 
     {593/100, -0.000036207638456353664}, 
     {1187/200, -0.00003343605285799356}, {297/50, -0.000030691027415041816}, 
     {1189/200, -0.000027919634019379913}, 
     {119/20, -0.000025184836450975467}, {1191/200, 
      -0.000022500477438569533}, {149/25, -0.000019792652093730823}, 
     {1193/200, -0.00001708305390080156}, 
     {597/100, -0.000014409511004398468}, {239/40, -0.00001177261415508113}, 
     {299/50, -9.114600617365909*^-6}, {1197/200, -6.447126299047312*^-6}, 
     {599/100, -3.7887863992835946*^-6}, {1199/200, -1.2277206162814025*^-6}, 
     {6, 1.4034809985297159*^-6}}
 
ReFRfind = {{6, 1.4034809985297159*^-6}, {151/25, 0.000021860106511173427}, 
     {152/25, 0.00004167961000600684}, {153/25, 0.000060642721575909775}, 
     {154/25, 0.00007893257100555218}, {31/5, 0.00009636675876301126}, 
     {156/25, 0.00011290098317351394}, {157/25, 0.00012849440011386548}, 
     {158/25, 0.00014306779198802744}, {159/25, 0.0001566282126250762}, 
     {32/5, 0.0001691545145225959}, {161/25, 0.0001806976032359131}, 
     {162/25, 0.00019133102190460605}, {163/25, 0.0002011077530310601}, 
     {164/25, 0.00021013610716424935}, {33/5, 0.0002184327780696549}, 
     {166/25, 0.00022607654836415136}, {167/25, 0.00023306080222673664}, 
     {168/25, 0.00023939384945026454}, {169/25, 0.00024503686707744166}, 
     {34/5, 0.0002499632067372026}, {171/25, 0.0002540619378783582}, 
     {172/25, 0.0002573209327838555}, {173/25, 0.0002597068434702088}, 
     {174/25, 0.0002611992477850045}, {7, 0.0002617948753904642}, 
     {176/25, 0.0002615591274515161}, {177/25, 0.00026054993686230876}, 
     {178/25, 0.000258838578437004}, {179/25, 0.0002564884486560004}, 
     {36/5, 0.00025356730938930205}, {181/25, 0.0002501246316176653}, 
     {182/25, 0.0002462186708203362}, {183/25, 0.00024181110483025015}, 
     {184/25, 0.00023695568179515902}, {37/5, 0.0002315822136736978}, 
     {186/25, 0.00022566147467972808}, {187/25, 0.0002191644656357461}, 
     {188/25, 0.00021210214757405588}, {189/25, 0.00020446743811175505}, 
     {38/5, 0.00019629110941177252}, {191/25, 0.00018764991332531622}, 
     {192/25, 0.00017854275376083528}, {193/25, 0.00016910554324600646}, 
     {194/25, 0.00015944410610302384}, {39/5, 0.0001495713476928895}, 
     {196/25, 0.00013957250806084787}, {197/25, 0.00012949385523675083}, 
     {198/25, 0.00011935612078217694}, {199/25, 0.00010916452655851394}, 
     {8, 0.00009891309100940049}, {201/25, 0.00008859139875383448}, 
     {202/25, 0.00007818855032404315}, {203/25, 0.00006770150504875616}, 
     {204/25, 0.000057156044718453813}, {41/5, 0.00004656280697545867}, 
     {206/25, 0.00003598275076566182}, {207/25, 0.00002548044219796708}, 
     {208/25, 0.000015127875049536499}, {209/25, 4.983253379275965*^-6}, 
     {42/5, -4.8593988459799675*^-6}, {211/25, -0.00001436518054909186}, 
     {212/25, -0.0000234901064621873}, {213/25, -0.000032221196651249784}, 
     {214/25, -0.00004057922199729447}, {43/5, -0.000048502912058268066}, 
     {216/25, -0.00005612891318307334}, {217/25, -0.00006334685580045019}, 
     {218/25, -0.00007023575316500441}, {219/25, -0.0000767946926680807}, 
     {44/5, -0.00008296657046491518}, {221/25, -0.00008879259978744614}, 
     {222/25, -0.00009417731020722186}, {223/25, -0.00009909815858755167}, 
     {224/25, -0.00010349906103734874}, {9, -0.00010734444167148638}, 
     {226/25, -0.00011061224765507305}, {227/25, -0.00011325494169245331}, 
     {228/25, -0.00011535087770098151}, {229/25, -0.00011682356757125589}, 
     {46/5, -0.00011777656818723337}, {231/25, -0.00011817350353182654}, 
     {232/25, -0.00011820742897128422}, {233/25, -0.00011774733844849283}, 
     {234/25, -0.00011683688690466987}, {47/5, -0.00011560246094144411}, 
     {236/25, -0.00011394826796412572}, {237/25, -0.0001118955146868772}, 
     {238/25, -0.00010940853133700745}, {239/25, -0.00010646221158819129}, 
     {48/5, -0.00010300942058946716}, {241/25, -0.00009917400651560104}, 
     {242/25, -0.00009490693531521988}, {243/25, -0.00009013346945363487}, 
     {244/25, -0.00008506361454241329}, {49/5, -0.00007965834002376937}, 
     {246/25, -0.00007392886540191768}, {247/25, -0.00006800645698379348}, 
     {248/25, -0.00006190519486715118}, {249/25, -0.00005566353717600947}, 
     {10, -0.00004931326209112186}, {251/25, -0.00004287180014661551}, 
     {252/25, -0.00003634075330349873}, {253/25, -0.00002972334054796022}, 
     {254/25, -0.00002303371735501436}, {51/5, -0.000016251622944274402}, 
     {256/25, -9.395697654124291*^-6}, {257/25, -2.4738530415291393*^-6}, 
     {258/25, 4.474137063059658*^-6}, {259/25, 0.000011432401029853878}, 
     {52/5, 0.000018305945302277138}, {261/25, 0.000025068960683327646}, 
     {262/25, 0.000031673444487179125}, {263/25, 0.000038070078546059705}, 
     {264/25, 0.000044213573922924354}, {53/5, 0.000050097749539901315}, 
     {266/25, 0.00005570410300226314}, {267/25, 0.000061016347371545265}, 
     {268/25, 0.00006607857861506972}, {269/25, 0.00007083854451783722}, 
     {54/5, 0.00007534395848463049}, {271/25, 0.0000796086485337355}, 
     {272/25, 0.00008359537215074653}, {273/25, 0.00008729126269635401}, 
     {274/25, 0.00009069146663254202}, {11, 0.00009374313897980713}, 
     {276/25, 0.00009644065856750927}, {277/25, 0.00009873457928089024}, 
     {278/25, 0.00010061657604332197}, {279/25, 0.00010205046108313631}, 
     {56/5, 0.00010303017566881678}, {281/25, 0.0001035889590690342}, 
     {282/25, 0.00010371682937604376}, {283/25, 0.00010344251704719198}, 
     {284/25, 0.00010281346558738136}, {57/5, 0.0001018248895219287}, 
     {286/25, 0.00010050248982573784}, {287/25, 0.00009885734012082814}, 
     {288/25, 0.00009694459101017294}, {289/25, 0.00009471339718669647}, 
     {58/5, 0.00009214787385813938}, {291/25, 0.00008926670678099935}, 
     {292/25, 0.00008607672363164509}, {293/25, 0.00008251815711285415}, 
     {294/25, 0.00007865881583621337}, {59/5, 0.00007449624901663399}, 
     {296/25, 0.00006999164087616305}, {297/25, 0.00006526322759575764}, 
     {298/25, 0.00006032231320568515}, {299/25, 0.00005516153891893527}, 
     {12, 0.00004984989200584877}, {301/25, 0.000044470635952365}, 
     {302/25, 0.000038990307297037674}, {303/25, 0.00003342440995457441}, 
     {304/25, 0.00002780755401343704}, {61/5, 0.000022150352805283546}, 
     {306/25, 0.000016447480569503625}, {307/25, 0.000010708611995147166}, 
     {308/25, 4.912297225434514*^-6}, {309/25, -9.063905930251082*^-7}, 
     {62/5, -6.735992510220612*^-6}, {311/25, -0.00001254956200558155}, 
     {312/25, -0.000018310919383202062}, {313/25, -0.000023990428082543147}, 
     {314/25, -0.000029551117474380106}, {63/5, -0.00003496465393526549}, 
     {316/25, -0.00004017436611203351}, {317/25, -0.00004519173074024607}, 
     {318/25, -0.0000499481568887461}, {319/25, -0.000054489464941021026}, 
     {64/5, -0.00005880456657347821}, {321/25, -0.00006287675391591918}, 
     {322/25, -0.00006672989317824118}, {323/25, -0.00007032561730868636}, 
     {324/25, -0.00007372088720014602}, {13, -0.00007693957640286797}, 
     {326/25, -0.0000797960700884559}, {327/25, -0.00008248070274374797}, 
     {328/25, -0.00008484109049433641}, {329/25, -0.00008689107572434907}, 
     {66/5, -0.00008861021296491245}, {331/25, -0.00008994296558428871}, 
     {332/25, -0.0000909909610542492}, {333/25, -0.00009166731574872244}, 
     {334/25, -0.0000919977063125188}, {67/5, -0.00009197828414420073}, 
     {336/25, -0.00009162536942719512}, {337/25, -0.00009100035420361863}, 
     {338/25, -0.00009009483005661956}, {339/25, -0.00008891850880354824}, 
     {68/5, -0.000087509174820255}, {341/25, -0.000085836204971379}, 
     {342/25, -0.00008391781121774855}, {343/25, -0.00008169479081643338}, 
     {344/25, -0.00007925074012860023}, {69/5, -0.0000765468740235864}, 
     {346/25, -0.00007358348208852394}, {347/25, -0.00007036180206054787}, 
     {348/25, -0.00006687554424278375}, {349/25, -0.00006321380180840386}, 
     {14, -0.00005929346441219119}, {351/25, -0.00005521389136500798}, 
     {352/25, -0.000050997966129257}, {353/25, -0.000046697614896430706}, 
     {354/25, -0.00004228136378264802}, {71/5, -0.0000377925236151877}, 
     {356/25, -0.000033247312363759995}, {357/25, -0.000028635328109427594}, 
     {358/25, -0.000024008486271931417}, {359/25, -0.000019348257331852636}, 
     {72/5, -0.000014633277191644645}, {361/25, -9.870258205202376*^-6}, 
     {362/25, -5.111575671845614*^-6}, {363/25, -3.416230915931351*^-7}, 
     {364/25, 4.434168066502764*^-6}, {73/5, 9.145113343489442*^-6}, 
     {366/25, 0.000013805152325518932}, {367/25, 0.000018340860441057316}, 
     {368/25, 0.00002279037956753882}, {369/25, 0.000027083472020406063}, 
     {74/5, 0.0000312051206026176}, {371/25, 0.00003515742557347323}, 
     {372/25, 0.00003893377925145991}, {373/25, 0.000042551575702542976}, 
     {374/25, 0.000045978774604549244}, {15, 0.00004920450142220645}, 
     {376/25, 0.00005230091961960781}, {377/25, 0.00005522546617231505}, 
     {378/25, 0.000057956373301415454}, {379/25, 0.00006049840491595404}, 
     {76/5, 0.00006283710238919049}, {381/25, 0.00006494791303035541}, 
     {382/25, 0.00006683816658248354}, {383/25, 0.00006847234251017298}, 
     {384/25, 0.00006980674757173233}, {77/5, 0.00007092513497242159}, 
     {386/25, 0.00007175191197417163}, {387/25, 0.00007232069083284998}, 
     {388/25, 0.00007258340714400013}, {389/25, 0.00007267477075001416}, 
     {78/5, 0.00007251626528481658}, {391/25, 0.00007215378512803738}, 
     {392/25, 0.00007158705742793536}, {393/25, 0.00007081792733698578}, 
     {394/25, 0.00006984661004727499}, {79/5, 0.00006870949270787463}, 
     {396/25, 0.00006737707610326993}, {397/25, 0.00006577537843055481}, 
     {398/25, 0.00006400933292494138}, {399/25, 0.0000620361619514398}, 
     {16, 0.00005987373130711404}, {401/25, 0.000057468389907833206}, 
     {402/25, 0.000054928519831021205}, {403/25, 0.00005221525332621546}, 
     {404/25, 0.000049379087159850954}, {81/5, 0.000046433604679707585}, 
     {406/25, 0.00004337829666356541}, {407/25, 0.00004025442706984128}, 
     {408/25, 0.00003706198204345146}, {409/25, 0.00003384091216299123}, 
     {82/5, 0.00003053757873991425}, {411/25, 0.000027185960055291225}, 
     {412/25, 0.000023810879694649567}, {413/25, 0.0000203884825312195}, 
     {414/25, 0.000016908345182253814}, {83/5, 0.000013386047162888826}, 
     {416/25, 9.868797974044163*^-6}, {417/25, 6.340388736980618*^-6}, 
     {418/25, 2.8083063022821264*^-6}, {419/25, -6.647002028792315*^-7}, 
     {84/5, -4.079042515092723*^-6}, {421/25, -7.4322514618252455*^-6}, 
     {422/25, -0.000010709854922130724}, {423/25, -0.000013835148786833784}, 
     {424/25, -0.000016923008336222622}, {17, -0.000019812616393721783}, 
     {426/25, -0.000022702209677927243}, {427/25, -0.000025382723118916317}, 
     {428/25, -0.00002802644550836675}, {429/25, -0.000030523152392936126}, 
     {86/5, -0.00003289781245574552}, {431/25, -0.00003522313961701329}, 
     {432/25, -0.00003735792837566976}, {433/25, -0.00003942377451782164}, 
     {434/25, -0.00004129763399474129}, {87/5, -0.00004303102306413287}, 
     {436/25, -0.000044568268797728905}, {437/25, -0.0000459431190309445}, 
     {438/25, -0.00004712806801676628}, {439/25, -0.0000481230379494324}, 
     {88/5, -0.00004894930192977931}, {441/25, -0.00004961577721496191}, 
     {442/25, -0.000050119258397707256}, {443/25, -0.00005047880675168592}, 
     {444/25, -0.00005065280898075564}, {89/5, -0.000050730535293030954}, 
     {446/25, -0.00005067458476037956}, {447/25, -0.00005048684735275977}, 
     {448/25, -0.000050120145839605}, {449/25, -0.00004967043974590801}, 
     {18, -0.00004899885001119486}, {451/25, -0.000048237674496132144}, 
     {452/25, -0.00004730057417168254}, {453/25, -0.000046246856800991054}, 
     {454/25, -0.00004500654216421651}, {91/5, -0.00004368532323351104}, 
     {456/25, -0.00004220196444038038}, {457/25, -0.00004066205198083317}, 
     {458/25, -0.00003900550248425727}, {459/25, -0.00003730490366404826}, 
     {92/5, -0.000035521817463801675}, {461/25, -0.0000336483635029472}, 
     {462/25, -0.000031811314574969884}, {463/25, -0.000029845787604676488}, 
     {464/25, -0.00002789212686460374}, {93/5, -0.000025806108342851797}, 
     {466/25, -0.00002375651918540278}, {467/25, -0.00002160410714374672}, 
     {468/25, -0.000019441551868726314}, {469/25, -0.000017216886715742952}, 
     {94/5, -0.000014950533578722558}, {471/25, -0.00001269641113660347}, 
     {472/25, -0.000010468645407464908}, {473/25, -8.209857867064185*^-6}, 
     {474/25, -6.030174599158666*^-6}, {19, -3.86174472358225*^-6}, 
     {476/25, -1.7473537778922577*^-6}, {477/25, 2.5962596417183903*^-7}, 
     {478/25, 2.297917491012047*^-6}, {479/25, 4.230332402710424*^-6}, 
     {96/5, 6.145724512407469*^-6}, {481/25, 8.042638299343707*^-6}, 
     {482/25, 9.840110650305434*^-6}, {483/25, 0.000011629496204479395}, 
     {484/25, 0.000013328071137852504}, {97/5, 0.000015059148972373926}, 
     {486/25, 0.000016655168528778574}, {487/25, 0.00001817822856686746}, 
     {488/25, 0.00001961728466748358}, {489/25, 0.000020948216899907557}, 
     {98/5, 0.0000222333593323798}, {491/25, 0.000023346159826798107}, 
     {492/25, 0.00002438075069455259}, {493/25, 0.00002530983079340743}, 
     {494/25, 0.00002618132701615039}, {99/5, 0.00002692482715449529}, 
     {496/25, 0.000027623231940276938}, {497/25, 0.000028276887293898767}, 
     {498/25, 0.00002876910862581461}, {499/25, 0.000029248571833173642}, 
     {20, 0.000029645406078637748}, {501/25, 0.00002997916286906488}, 
     {502/25, 0.00003017872787247633}, {503/25, 0.000030347768804617203}, 
     {504/25, 0.000030432694706927776}, {101/5, 0.000030315750729537072}, 
     {506/25, 0.000030240687055593796}, {507/25, 0.000029964835043250204}, 
     {508/25, 0.000029627264858334}, {509/25, 0.000029259540756942926}, 
     {102/5, 0.000028843403750089536}, {511/25, 0.00002830660738462054}, 
     {512/25, 0.000027805006004744115}, {513/25, 0.000027211036429886093}, 
     {514/25, 0.000026590533455106424}, {103/5, 0.00002593966054476038}, 
     {516/25, 0.000025223427848386493}, {517/25, 0.000024503168398415376}, 
     {518/25, 0.000023668776242824485}, {519/25, 0.000022863585499632855}, 
     {104/5, 0.00002193505711689525}, {521/25, 0.00002101193656356415}, 
     {522/25, 0.000019998222132278087}, {523/25, 0.00001897478812118436}, 
     {524/25, 0.000017946710970329072}, {21, 0.00001689667599785727}, 
     {526/25, 0.000015799713391717596}, {527/25, 0.000014765711682240834}, 
     {528/25, 0.00001368166621362743}, {529/25, 0.000012659954763571957}, 
     {106/5, 0.000011604367763567991}, {531/25, 0.00001057992806791086}, 
     {532/25, 9.533839192110705*^-6}, {533/25, 8.510612189593925*^-6}, 
     {534/25, 7.443899147308031*^-6}, {107/5, 6.400391033972719*^-6}, 
     {536/25, 5.341497601379225*^-6}, {537/25, 4.274794718192587*^-6}, 
     {538/25, 3.2023449464541054*^-6}, {539/25, 2.162156055085518*^-6}, 
     {108/5, 1.132772651790681*^-6}, {541/25, 1.475725156241392*^-7}, 
     {542/25, -8.293378759294256*^-7}, {543/25, -1.7527867072208991*^-6}, 
     {544/25, -2.6392173936296004*^-6}, {109/5, -3.5248661287567984*^-6}, 
     {546/25, -4.335753278905674*^-6}, {547/25, -5.184912437339317*^-6}, 
     {548/25, -5.977708397997272*^-6}, {549/25, -6.74122533317334*^-6}, 
     {22, -7.504646012512772*^-6}, {551/25, -8.266061064965413*^-6}, 
     {552/25, -8.96274767825389*^-6}, {553/25, -9.720523297063188*^-6}, 
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     {978/25, -9.063124811581336*^-6}, {979/25, -8.832060618940707*^-6}, 
     {196/5, -8.465021663128791*^-6}, {981/25, -8.151922835986092*^-6}, 
     {982/25, -7.78016339467169*^-6}, {983/25, -7.443294707365489*^-6}, 
     {984/25, -7.0422620571386485*^-6}, {197/5, -6.632452325572302*^-6}, 
     {986/25, -6.212199567284804*^-6}, {987/25, -5.774324797924724*^-6}, 
     {988/25, -5.3183596248063125*^-6}, {989/25, -4.883449800457962*^-6}, 
     {198/5, -4.371554914187059*^-6}, {991/25, -3.930125733131451*^-6}, 
     {992/25, -3.4482473853861273*^-6}, {993/25, -2.9321988928403264*^-6}, 
     {994/25, -2.4430987712806274*^-6}, {199/5, -1.9158647961356468*^-6}, 
     {996/25, -1.4014753962586501*^-6}, {997/25, -8.479849907122583*^-7}, 
     {998/25, -2.4735716962209775*^-7}, {999/25, 2.5775146310358377*^-7}, 
     {40, 8.393888920599224*^-7}, {1001/25, 1.3421203281099858*^-6}, 
     {1002/25, 1.8491552140897927*^-6}, {1003/25, 2.40217767910611*^-6}, 
     {1004/25, 2.8937337220868997*^-6}, {201/5, 3.4093938883483776*^-6}, 
     {1006/25, 3.898421625680992*^-6}, {1007/25, 4.386789632077059*^-6}, 
     {1008/25, 4.850924685079194*^-6}, {1009/25, 5.336829311974878*^-6}, 
     {202/5, 5.774974237954256*^-6}, {1011/25, 6.24513079841571*^-6}, 
     {1012/25, 6.661173919508823*^-6}, {1013/25, 7.095758045194689*^-6}, 
     {1014/25, 7.515907173905045*^-6}, {203/5, 7.900350559975067*^-6}, 
     {1016/25, 8.26484752092238*^-6}, {1017/25, 8.600861485519307*^-6}, 
     {1018/25, 8.90884619708654*^-6}, {1019/25, 9.187096082663437*^-6}, 
     {204/5, 9.451710310193207*^-6}, {1021/25, 9.683577346930594*^-6}, 
     {1022/25, 9.884571116169916*^-6}, {1023/25, 0.000010067014281411879}, 
     {1024/25, 0.000010227074141055947}, {41, 0.000010348142103822067}, 
     {1026/25, 0.00001044545116712925}, {1027/25, 0.000010554094568404615}, 
     {1028/25, 0.000010608146553514608}, {1029/25, 0.000010668378641331966}, 
     {206/5, 0.000010661963664282403}, {1031/25, 0.000010684220590195803}, 
     {1032/25, 0.000010638880235391834}, {1033/25, 0.000010514597021171745}, 
     {1034/25, 0.000010431548562617188}, {207/5, 0.000010246644770839364}, 
     {1036/25, 0.000010099356301196405}, {1037/25, 9.88121145595322*^-6}, 
     {1038/25, 9.66244122285742*^-6}, {1039/25, 9.408649143005654*^-6}, 
     {208/5, 9.159273710923621*^-6}, {1041/25, 8.844985546541118*^-6}, 
     {1042/25, 8.565067134591597*^-6}, {1043/25, 8.199443569389953*^-6}, 
     {1044/25, 7.85766285185674*^-6}, {209/5, 7.4869557090684324*^-6}, 
     {1046/25, 7.110449474045932*^-6}, {1047/25, 6.69596606667211*^-6}, 
     {1048/25, 6.2856988551074355*^-6}, {1049/25, 5.795373340888865*^-6}, 
     {42, 5.3303578466668*^-6}, {1051/25, 4.849307735407815*^-6}, 
     {1052/25, 4.367101869837131*^-6}, {1053/25, 3.857187970940368*^-6}, 
     {1054/25, 3.3579044367154642*^-6}, {211/5, 2.833903819762784*^-6}, 
     {1056/25, 2.3465211316867074*^-6}, {1057/25, 1.8078310552206711*^-6}, 
     {1058/25, 1.3229936516243046*^-6}, {1059/25, 7.700862170965939*^-7}, 
     {212/5, 2.2664416855777691*^-7}, {1061/25, -2.888006596507564*^-7}, 
     {1062/25, -7.855300860198922*^-7}, {1063/25, -1.297513140166573*^-6}, 
     {1064/25, -1.826372745372673*^-6}, {213/5, -2.343473001154006*^-6}, 
     {1066/25, -2.8569629826058485*^-6}, {1067/25, -3.364064070449091*^-6}, 
     {1068/25, -3.855436280286728*^-6}, {1069/25, -4.332116970345856*^-6}, 
     {214/5, -4.786410676610453*^-6}, {1071/25, -5.2115595747248555*^-6}, 
     {1072/25, -5.638530962415178*^-6}, {1073/25, -6.013858589060117*^-6}, 
     {1074/25, -6.399466152995359*^-6}, {43, -6.74732875549644*^-6}, 
     {1076/25, -7.080912819756868*^-6}, {1077/25, -7.407911294027292*^-6}, 
     {1078/25, -7.747703142324536*^-6}, {1079/25, -8.017365043189173*^-6}, 
     {216/5, -8.273446446271926*^-6}, {1081/25, -8.534537590643154*^-6}, 
     {1082/25, -8.692603624516071*^-6}, {1083/25, -8.910570450659794*^-6}, 
     {1084/25, -9.075542349301635*^-6}, {217/5, -9.199869739795474*^-6}, 
     {1086/25, -9.305062486975046*^-6}, {1087/25, -9.38917652171245*^-6}, 
     {1088/25, -9.419238662988771*^-6}, {1089/25, -9.448279416679473*^-6}, 
     {218/5, -9.434027734733785*^-6}, {1091/25, -9.434022229970473*^-6}, 
     {1092/25, -9.357016053868072*^-6}, {1093/25, -9.289484178442997*^-6}, 
     {1094/25, -9.20617031324733*^-6}, {219/5, -9.082350565070563*^-6}, 
     {1096/25, -8.91106626799143*^-6}, {1097/25, -8.785684908696467*^-6}, 
     {1098/25, -8.618020506445667*^-6}, {1099/25, -8.367006118059628*^-6}, 
     {44, -8.109760878172168*^-6}, {1101/25, -7.869339687327503*^-6}, 
     {1102/25, -7.6111962475367*^-6}, {1103/25, -7.293064681640482*^-6}, 
     {1104/25, -6.988937143903584*^-6}, {221/5, -6.6321610437403145*^-6}, 
     {1106/25, -6.260481760639314*^-6}, {1107/25, -5.95309822809531*^-6}, 
     {1108/25, -5.533224037429507*^-6}, {1109/25, -5.151168757128177*^-6}, 
     {222/5, -4.767245524534003*^-6}, {1111/25, -4.371224516241945*^-6}, 
     {1112/25, -3.967114842517994*^-6}, {1113/25, -3.5768812532838146*^-6}, 
     {1114/25, -3.126507426273739*^-6}, {223/5, -2.688404522527277*^-6}, 
     {1116/25, -2.2439470196700118*^-6}, {1117/25, -1.7908138082722846*^-6}, 
     {1118/25, -1.3718789045255586*^-6}, {1119/25, -9.134001822674875*^-7}, 
     {224/5, -4.505292658385507*^-7}, {1121/25, -4.300719353908522*^-8}, 
     {1122/25, 4.2419861133479765*^-7}, {1123/25, 7.917991852873785*^-7}, 
     {1124/25, 1.2457571338768403*^-6}, {45, 1.629878432635179*^-6}, 
     {1126/25, 2.037380173278147*^-6}, {1127/25, 2.398293068153756*^-6}, 
     {1128/25, 2.7870677323516002*^-6}, {1129/25, 3.14989072282279*^-6}, 
     {226/5, 3.518519968895295*^-6}, {1131/25, 3.8734335993384494*^-6}, 
     {1132/25, 4.208291929597152*^-6}, {1133/25, 4.4718246779151816*^-6}, 
     {1134/25, 4.7811067197811585*^-6}, {227/5, 5.10025489203203*^-6}, 
     {1136/25, 5.408465435230436*^-6}, {1137/25, 5.628477016378364*^-6}, 
     {1138/25, 5.8592292202785945*^-6}, {1139/25, 6.025243548923864*^-6}, 
     {228/5, 6.226679739818053*^-6}, {1141/25, 6.384121551544775*^-6}, 
     {1142/25, 6.525437373977594*^-6}, {1143/25, 6.643026642771943*^-6}, 
     {1144/25, 6.786313188317239*^-6}, {229/5, 6.868353726291465*^-6}, 
     {1146/25, 6.931224547868098*^-6}, {1147/25, 6.950157267038293*^-6}, 
     {1148/25, 7.0441629532180805*^-6}, {1149/25, 7.035937003990744*^-6}, 
     {46, 7.05404904044471*^-6}, {1151/25, 7.0424740541696895*^-6}, 
     {1152/25, 6.937846925320068*^-6}, {1153/25, 6.919093665708198*^-6}, 
     {1154/25, 6.850108646261344*^-6}, {231/5, 6.72789082575842*^-6}, 
     {1156/25, 6.564853220286659*^-6}, {1157/25, 6.436420080607741*^-6}, 
     {1158/25, 6.292401075497223*^-6}, {1159/25, 6.113172789867782*^-6}, 
     {232/5, 5.944980361383134*^-6}, {1161/25, 5.754077065461827*^-6}, 
     {1162/25, 5.556879392687453*^-6}, {1163/25, 5.330468893255391*^-6}, 
     {1164/25, 5.112158038250714*^-6}, {233/5, 4.897154489591493*^-6}, 
     {1166/25, 4.639277205037429*^-6}, {1167/25, 4.349752035670562*^-6}, 
     {1168/25, 4.130032058291544*^-6}, {1169/25, 3.859619646218171*^-6}, 
     {234/5, 3.569863977759269*^-6}, {1171/25, 3.2867697696559173*^-6}, 
     {1172/25, 2.9300882110061544*^-6}, {1173/25, 2.6776983617637917*^-6}, 
     {1174/25, 2.3808389114921003*^-6}, {47, 2.08919686633946*^-6}, 
     {1176/25, 1.7956398658675043*^-6}, {1177/25, 1.4848580730808525*^-6}, 
     {1178/25, 1.1839148377212894*^-6}, {1179/25, 9.652896670042654*^-7}, 
     {236/5, 6.80509092076953*^-7}, {1181/25, 4.015807844801045*^-7}, 
     {1182/25, 1.217267570075009*^-7}, {1183/25, -1.916223744645451*^-7}, 
     {1184/25, -4.2773303738155577*^-7}, {237/5, -7.035157022303867*^-7}, 
     {1186/25, -9.446381935914079*^-7}, {1187/25, -1.2159509818294653*^-6}, 
     {1188/25, -1.466336571408211*^-6}, {1189/25, -1.7053698562891073*^-6}, 
     {238/5, -1.931516503801689*^-6}, {1191/25, -2.113516383517311*^-6}, 
     {1192/25, -2.3417366235983783*^-6}, {1193/25, -2.4843942604615976*^-6}, 
     {1194/25, -2.7127526843334637*^-6}, {239/5, -2.885285188797271*^-6}, 
     {1196/25, -2.987502480608639*^-6}, {1197/25, -3.1582992600920345*^-6}, 
     {1198/25, -3.3189368200264857*^-6}, {1199/25, -3.4011972827457937*^-6}, 
     {48, -3.562927955183537*^-6}, {1201/25, -3.6492704390267416*^-6}, 
     {1202/25, -3.7568326649028982*^-6}, {1203/25, -3.831273988896822*^-6}, 
     {1204/25, -3.8969064449223545*^-6}, {241/5, -3.980791119018168*^-6}, 
     {1206/25, -4.011865213843224*^-6}, {1207/25, -4.038292398866883*^-6}, 
     {1208/25, -4.039066867606023*^-6}, {1209/25, -4.04030731851468*^-6}, 
     {242/5, -4.040040032599057*^-6}, {1211/25, -4.040738594501825*^-6}, 
     {1212/25, -3.986347828971448*^-6}, {1213/25, -3.943558206376263*^-6}, 
     {1214/25, -3.936753326327924*^-6}, {243/5, -3.89503469344632*^-6}, 
     {1216/25, -3.821921451652166*^-6}, {1217/25, -3.7567899311141684*^-6}, 
     {1218/25, -3.705618851712611*^-6}, {1219/25, -3.650980492764244*^-6}, 
     {244/5, -3.552495749681306*^-6}, {1221/25, -3.4351276543553855*^-6}, 
     {1222/25, -3.3164239465754974*^-6}, {1223/25, -3.252141539789033*^-6}, 
     {1224/25, -3.100520236193338*^-6}, {49, -3.017080104611436*^-6}, 
     {1226/25, -2.8965794467428196*^-6}, {1227/25, -2.7187760437141772*^-6}, 
     {1228/25, -2.6197543540606993*^-6}, {1229/25, -2.5025648236198794*^-6}, 
     {246/5, -2.350393649958038*^-6}, {1231/25, -2.239470828030443*^-6}, 
     {1232/25, -2.1118167341238614*^-6}, {1233/25, -2.0041957519978393*^-6}, 
     {1234/25, -1.832163825168931*^-6}, {247/5, -1.7588929379919183*^-6}, 
     {1236/25, -1.6086783677232708*^-6}, {1237/25, -1.4313899953100062*^-6}, 
     {1238/25, -1.320052664399718*^-6}, {1239/25, -1.2104772595944446*^-6}, 
     {248/5, -1.0470588980016071*^-6}, {1241/25, -9.321136270612485*^-7}, 
     {1242/25, -7.772976536729592*^-7}, {1243/25, -6.837518984198487*^-7}, 
     {1244/25, -5.342269231642383*^-7}, {249/5, -4.4107088367772995*^-7}, 
     {1246/25, -2.973481823542734*^-7}, {1247/25, -2.2242060362248628*^-7}, 
     {1248/25, -7.002531744043639*^-8}, {1249/25, -4.1401960679254834*^-10}, 
     {50, 1.0536754767656586*^-7}}
 
ReFRfine = {{50, 1.0536754767656586*^-7}, {1001/20, 2.092177472171053*^-7}, 
     {501/10, 2.8525999385374534*^-7}, {1003/20, 4.62368255408057*^-7}, 
     {251/5, 5.591059840902302*^-7}, {201/4, 6.628247033423074*^-7}, 
     {503/10, 7.532580404423506*^-7}, {1007/20, 8.374095373277213*^-7}, 
     {252/5, 9.052995394859265*^-7}, {1009/20, 9.202275464692544*^-7}, 
     {101/2, 1.0430432441504989*^-6}, {1011/20, 1.0667581809981064*^-6}, 
     {253/5, 1.1428598318263816*^-6}, {1013/20, 1.1640420193442802*^-6}, 
     {507/10, 1.192284241308128*^-6}, {203/4, 1.2562513081182392*^-6}, 
     {254/5, 1.3086564627229347*^-6}, {1017/20, 1.3482256372571166*^-6}, 
     {509/10, 1.3497640999338145*^-6}, {1019/20, 1.3981092254755634*^-6}, 
     {51, 1.371141346684368*^-6}, {1021/20, 1.4344561292400915*^-6}, 
     {511/10, 1.446608507149616*^-6}, {1023/20, 1.4463140306508748*^-6}, 
     {256/5, 1.441772360069593*^-6}, {205/4, 1.4014204987589096*^-6}, 
     {513/10, 1.4055394569056912*^-6}, {1027/20, 1.4203632220655127*^-6}, 
     {257/5, 1.4758721436775035*^-6}, {1029/20, 1.4095914616374383*^-6}, 
     {103/2, 1.459315915219861*^-6}, {1031/20, 1.4635137101925988*^-6}, 
     {258/5, 1.4505867288183705*^-6}, {1033/20, 1.407394727787059*^-6}, 
     {517/10, 1.4412004073621754*^-6}, {207/4, 1.4164954619810821*^-6}, 
     {259/5, 1.3562551777618337*^-6}, {1037/20, 1.4239728881038083*^-6}, 
     {519/10, 1.422361560726726*^-6}, {1039/20, 1.4057018816321376*^-6}, 
     {52, 1.375845360779282*^-6}, {1041/20, 1.378965207868288*^-6}, 
     {521/10, 1.3964146827610824*^-6}, {1043/20, 1.3690627389539856*^-6}, 
     {261/5, 1.3569694130993737*^-6}, {209/4, 1.3659423093309586*^-6}, 
     {523/10, 1.3476255844857565*^-6}, {1047/20, 1.3512001090509873*^-6}, 
     {262/5, 1.3020177588238258*^-6}, {1049/20, 1.2857437665242388*^-6}, 
     {105/2, 1.2878234274746325*^-6}, {1051/20, 1.2796947669937997*^-6}, 
     {263/5, 1.2572739535032795*^-6}, {1053/20, 1.2295567665132623*^-6}, 
     {527/10, 1.2080355729915393*^-6}, {211/4, 1.2027294648275788*^-6}, 
     {264/5, 1.1720725342674598*^-6}, {1057/20, 1.137988498267628*^-6}, 
     {529/10, 1.0745672871723122*^-6}, {1059/20, 1.0530858104047802*^-6}, 
     {53, 9.998144945887535*^-7}, {1061/20, 9.59116283410122*^-7}, 
     {531/10, 8.88323195124413*^-7}, {1063/20, 8.506314668060844*^-7}, 
     {266/5, 8.343647708922153*^-7}, {213/4, 7.823080525812265*^-7}, 
     {533/10, 6.911380850266324*^-7}, {1067/20, 6.687093087737184*^-7}, 
     {267/5, 5.998535175244513*^-7}, {1069/20, 4.889676319466685*^-7}, 
     {107/2, 4.1834141854824036*^-7}, {1071/20, 3.0910956311247517*^-7}, 
     {268/5, 2.3643141944251767*^-7}, {1073/20, 1.7618854093043312*^-7}, 
     {537/10, 8.296419314740566*^-8}, {215/4, 7.275610489076989*^-9}, 
     {269/5, -1.3240620092697108*^-7}, {1077/20, -2.0150009179265016*^-7}, 
     {539/10, -2.5355911315028123*^-7}, {1079/20, -3.7887564069416513*^-7}, 
     {54, -5.172835431666023*^-7}, {1081/20, -5.67236076123856*^-7}, 
     {541/10, -7.529060640082408*^-7}, {1083/20, -8.153463895571589*^-7}, 
     {271/5, -9.430293754636443*^-7}, {217/4, -1.033516665860379*^-6}, 
     {543/10, -1.083152766506723*^-6}, {1087/20, -1.2063170291565228*^-6}, 
     {272/5, -1.2912405879667022*^-6}, {1089/20, -1.4022946158986915*^-6}, 
     {109/2, -1.4718112576889153*^-6}, {1091/20, -1.5868725522227844*^-6}, 
     {273/5, -1.6480641653604522*^-6}, {1093/20, -1.7606906033001968*^-6}, 
     {547/10, -1.8461623799981286*^-6}, {219/4, -1.9280809601118776*^-6}, 
     {274/5, -1.9730597767830815*^-6}, {1097/20, -2.0900664169376526*^-6}, 
     {549/10, -2.139606910686598*^-6}, {1099/20, -2.2002983494084916*^-6}, 
     {55, -2.2067817441462356*^-6}, {1101/20, -2.2506056035626054*^-6}, 
     {551/10, -2.2909886199101726*^-6}, {1103/20, -2.31925409989453*^-6}, 
     {276/5, -2.357871583286153*^-6}, {221/4, -2.3732382319341383*^-6}, 
     {553/10, -2.39116320976257*^-6}, {1107/20, -2.3897613090906322*^-6}, 
     {277/5, -2.388450987031443*^-6}, {1109/20, -2.363258540097335*^-6}, 
     {111/2, -2.3702454287760633*^-6}, {1111/20, -2.3200417460858547*^-6}, 
     {278/5, -2.276579618432084*^-6}, {1113/20, -2.2010545859679764*^-6}, 
     {557/10, -2.1537320697359585*^-6}, {223/4, -2.126999212155589*^-6}, 
     {279/5, -2.0525661748108104*^-6}, {1117/20, -1.94743626877672*^-6}, 
     {559/10, -1.8830420102713963*^-6}, {1119/20, -1.8041239089466865*^-6}, 
     {56, -1.69199366425489*^-6}, {1121/20, -1.5706246078604422*^-6}, 
     {561/10, -1.4676957874810211*^-6}, {1123/20, -1.3521668742692144*^-6}, 
     {281/5, -1.2324606491198598*^-6}, {225/4, -1.0895108557996275*^-6}, 
     {563/10, -9.297401366223368*^-7}, {1127/20, -7.93208616824137*^-7}, 
     {282/5, -6.423467502937596*^-7}, {1129/20, -5.10245054811953*^-7}, 
     {113/2, -3.386349298264979*^-7}, {1131/20, -2.172046951395834*^-7}, 
     {283/5, -5.552604775971304*^-8}, {1133/20, 8.200875252495354*^-8}, 
     {567/10, 2.658829813956265*^-7}, {227/4, 4.842720917469512*^-7}, 
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     {569/10, 9.833689739724427*^-7}, {1139/20, 1.1459545374292723*^-6}, 
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     {583/10, 3.24469029465424*^-6}, {1167/20, 3.187541600571664*^-6}, 
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     {589/10, 1.7106516881776335*^-6}, {1179/20, 1.5233592412155703*^-6}, 
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     {296/5, 4.3244579565893115*^-7}, {237/4, 2.0938046852575498*^-7}, 
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     {297/5, -5.160634998502278*^-7}, {1189/20, -7.341813612268822*^-7}, 
     {119/2, -9.99945788372758*^-7}, {1191/20, -1.2608400070668324*^-6}, 
     {298/5, -1.4616217243884622*^-6}, {1193/20, -1.710637860141695*^-6}, 
     {597/10, -1.91507964868165*^-6}, {239/4, -2.1673717170711537*^-6}, 
     {299/5, -2.373812543116083*^-6}, {1197/20, -2.597133741663593*^-6}, 
     {599/10, -2.8087946947197295*^-6}, {1199/20, -3.015677290413299*^-6}, 
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     {601/10, -3.545255603920605*^-6}, {1203/20, -3.7379214892496737*^-6}, 
     {301/5, -3.881279555029149*^-6}, {241/4, -4.051368069593608*^-6}, 
     {603/10, -4.146019513470711*^-6}, {1207/20, -4.3317310830515154*^-6}, 
     {302/5, -4.31212904915268*^-6}, {1209/20, -4.390473029483588*^-6}, 
     {121/2, -4.441490590423314*^-6}, {1211/20, -4.498819269532772*^-6}, 
     {303/5, -4.516619987821047*^-6}, {1213/20, -4.5308022110640556*^-6}, 
     {607/10, -4.547920967656882*^-6}, {243/4, -4.52065548157965*^-6}, 
     {304/5, -4.458244349650475*^-6}, {1217/20, -4.408177918996392*^-6}, 
     {609/10, -4.337836482293245*^-6}, {1219/20, -4.203799750912562*^-6}, 
     {61, -4.124950473527456*^-6}, {1221/20, -3.9952928522352105*^-6}, 
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     {306/5, -3.4845299016900144*^-6}, {245/4, -3.23837740500571*^-6}, 
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     {307/5, -2.6136799892231832*^-6}, {1229/20, -2.3670833919908763*^-6}, 
     {123/2, -2.099036837614754*^-6}, {1231/20, -1.8046928948849128*^-6}, 
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     {617/10, -9.053676533420617*^-7}, {247/4, -6.371570810976418*^-7}, 
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     {62, 9.763909022825201*^-7}, {1241/20, 1.304094196921679*^-6}, 
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     {311/5, 2.266262649971984*^-6}, {249/4, 2.516092850624041*^-6}, 
     {623/10, 2.8145005340346474*^-6}, {1247/20, 3.150394670997647*^-6}, 
     {312/5, 3.3800009816425947*^-6}, {1249/20, 3.654061980482015*^-6}, 
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     {627/10, 4.768294801726913*^-6}, {251/4, 4.938468522952544*^-6}, 
     {314/5, 5.071090107999776*^-6}, {1257/20, 5.239104659104932*^-6}, 
     {629/10, 5.3906508384604646*^-6}, {1259/20, 5.484227525720531*^-6}, 
     {63, 5.4875543129828674*^-6}, {1261/20, 5.541280078430466*^-6}, 
     {631/10, 5.542172739902984*^-6}, {1263/20, 5.528764888296234*^-6}, 
     {316/5, 5.564199495933231*^-6}, {253/4, 5.504046505871996*^-6}, 
     {633/10, 5.3806070808570805*^-6}, {1267/20, 5.304198322841902*^-6}, 
     {317/5, 5.217212645514113*^-6}, {1269/20, 5.056659352783988*^-6}, 
     {127/2, 4.92828120852995*^-6}, {1271/20, 4.738373648977001*^-6}, 
     {318/5, 4.531269265029003*^-6}, {1273/20, 4.307706328240957*^-6}, 
     {637/10, 4.047755629649208*^-6}, {255/4, 3.817056960259135*^-6}, 
     {319/5, 3.536215059427028*^-6}, {1277/20, 3.212860045051502*^-6}, 
     {639/10, 2.850347256347363*^-6}, {1279/20, 2.590823296295952*^-6}, 
     {64, 2.2766138950552905*^-6}, {1281/20, 1.926996992467067*^-6}, 
     {641/10, 1.5733484934540853*^-6}, {1283/20, 1.2292035305450089*^-6}, 
     {321/5, 8.476505991474731*^-7}, {257/4, 4.933714045926921*^-7}, 
     {643/10, 7.65412069038407*^-8}, {1287/20, -3.001327804966203*^-7}, 
     {322/5, -6.543785778453937*^-7}, {1289/20, -1.0359002229690106*^-6}, 
     {129/2, -1.4364990812004708*^-6}, {1291/20, -1.7516370128256575*^-6}, 
     {323/5, -2.129955682508844*^-6}, {1293/20, -2.481238730894786*^-6}, 
     {647/10, -2.8406438912775833*^-6}, {259/4, -3.181259432064043*^-6}, 
     {324/5, -3.501176078085644*^-6}, {1297/20, -3.791498047439612*^-6}, 
     {649/10, -4.107772791861475*^-6}, {1299/20, -4.375074700940784*^-6}, 
     {65, -4.638153229638564*^-6}, {1301/20, -4.88986721691731*^-6}, 
     {651/10, -5.048488247755278*^-6}, {1303/20, -5.2800994695401116*^-6}, 
     {326/5, -5.442268384642235*^-6}, {261/4, -5.610722716042904*^-6}, 
     {653/10, -5.71355036826926*^-6}, {1307/20, -5.8288760306501874*^-6}, 
     {327/5, -5.909046431468168*^-6}, {1309/20, -5.9870505039194555*^-6}, 
     {131/2, -5.99795890790511*^-6}, {1311/20, -6.032616966078486*^-6}, 
     {328/5, -5.97215401620943*^-6}, {1313/20, -5.948588841925284*^-6}, 
     {657/10, -5.8751356250275055*^-6}, {263/4, -5.768343795703457*^-6}, 
     {329/5, -5.670151694781023*^-6}, {1317/20, -5.510261534946714*^-6}, 
     {659/10, -5.32558421401097*^-6}, {1319/20, -5.13983450814437*^-6}, 
     {66, -4.936725056484126*^-6}, {1321/20, -4.63847996640121*^-6}, 
     {661/10, -4.43774112138251*^-6}, {1323/20, -4.175090831753936*^-6}, 
     {331/5, -3.876134578861823*^-6}, {265/4, -3.5992596515155295*^-6}, 
     {663/10, -3.24027323708731*^-6}, {1327/20, -2.894278510245929*^-6}, 
     {332/5, -2.591995454284679*^-6}, {1329/20, -2.2179717839784785*^-6}, 
     {133/2, -1.8359967491332618*^-6}, {1331/20, -1.4592780605074407*^-6}, 
     {333/5, -1.1118848727564856*^-6}, {1333/20, -7.166148178819332*^-7}, 
     {667/10, -3.298289825703904*^-7}, {267/4, 1.578719773892524*^-8}, 
     {334/5, 4.480033614501222*^-7}, {1337/20, 8.090322970444319*^-7}, 
     {669/10, 1.1673989103108684*^-6}, {1339/20, 1.540105018932314*^-6}, 
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     {677/10, 5.484198645794303*^-6}, {271/4, 5.537998546162326*^-6}, 
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     {679/10, 5.749384489106557*^-6}, {1359/20, 5.739786954589432*^-6}, 
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     {341/5, 5.365645131261143*^-6}, {273/4, 5.230131000677485*^-6}, 
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     {342/5, 4.697185469831888*^-6}, {1369/20, 4.49140543595794*^-6}, 
     {137/2, 4.267708812802362*^-6}, {1371/20, 4.043131372463704*^-6}, 
     {343/5, 3.730815843899782*^-6}, {1373/20, 3.4689124186471076*^-6}, 
     {687/10, 3.166016858208165*^-6}, {275/4, 2.831309185408193*^-6}, 
     {344/5, 2.590522825307584*^-6}, {1377/20, 2.2263380229370355*^-6}, 
     {689/10, 1.8479338126098366*^-6}, {1379/20, 1.5786396512576517*^-6}, 
     {69, 1.238336183768951*^-6}, {1381/20, 8.701453936207915*^-7}, 
     {691/10, 5.376357129320553*^-7}, {1383/20, 1.8953011100136807*^-7}, 
     {346/5, -1.4047218683740925*^-7}, {277/4, -4.4908448848697546*^-7}, 
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     {347/5, -1.4065563796565594*^-6}, {1389/20, -1.7816813650678442*^-6}, 
     {139/2, -2.0684567183168467*^-6}, {1391/20, -2.3740526717136445*^-6}, 
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     {697/10, -3.104766489639421*^-6}, {279/4, -3.3715660494454402*^-6}, 
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     {351/5, -4.7128522040612575*^-6}, {281/4, -4.722458389699868*^-6}, 
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     {352/5, -4.8357001565246804*^-6}, {1409/20, -4.7583884082713634*^-6}, 
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     {353/5, -4.564415247362841*^-6}, {1413/20, -4.4608754447006405*^-6}, 
     {707/10, -4.346738940508299*^-6}, {283/4, -4.2245898580067776*^-6}, 
     {354/5, -4.033367012962197*^-6}, {1417/20, -3.943204142708989*^-6}, 
     {709/10, -3.7374058029920887*^-6}, {1419/20, -3.485065751665517*^-6}, 
     {71, -3.3250325881389875*^-6}, {1421/20, -3.150891756745211*^-6}, 
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     {356/5, -2.4770393369510924*^-6}, {285/4, -2.1729333113673643*^-6}, 
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     {357/5, -1.4285570394401148*^-6}, {1429/20, -1.1748334462213794*^-6}, 
     {143/2, -9.104125580847167*^-7}, {1431/20, -6.90347814955028*^-7}, 
     {358/5, -4.4088940967523804*^-7}, {1433/20, -1.324914949488165*^-7}, 
     {717/10, 4.0562656046516654*^-8}, {287/4, 2.9912531678867593*^-7}, 
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     {361/5, 2.3458524064864927*^-6}, {289/4, 2.4725138483908116*^-6}, 
     {723/10, 2.621636705030239*^-6}, {1447/20, 2.758941080475974*^-6}, 
     {362/5, 2.936439017983683*^-6}, {1449/20, 3.04678893102428*^-6}, 
     {145/2, 3.188057672492972*^-6}, {1451/20, 3.254935455082597*^-6}, 
     {363/5, 3.3727757025731053*^-6}, {1453/20, 3.419378818744767*^-6}, 
     {727/10, 3.4632859271938043*^-6}, {291/4, 3.531370332349182*^-6}, 
     {364/5, 3.504571447654481*^-6}, {1457/20, 3.5518145122953593*^-6}, 
     {729/10, 3.558471744574687*^-6}, {1459/20, 3.5577279116905114*^-6}, 
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     {371/5, 4.197478525314047*^-7}, {297/4, 2.4286410889307053*^-7}, 
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     {377/5, -2.6421843830892744*^-6}, {1509/20, -2.6677177334122337*^-6}, 
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     {383/5, -1.425509871075259*^-6}, {1533/20, -1.305575091668787*^-6}, 
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     {769/10, -5.526143703124542*^-7}, {1539/20, -4.4921866876324046*^-7}, 
     {77, -3.1002286450532157*^-7}, {1541/20, -1.7048515677312026*^-7}, 
     {771/10, -2.3806548506838388*^-8}, {1543/20, 1.5591685732785354*^-7}, 
     {386/5, 3.0528048620623305*^-7}, {309/4, 4.528472138092682*^-7}, 
     {773/10, 6.051569035542617*^-7}, {1547/20, 7.569924988140141*^-7}, 
     {387/5, 9.023015930271355*^-7}, {1549/20, 1.015863902944017*^-6}, 
     {155/2, 1.1445650480741004*^-6}, {1551/20, 1.3025192725397983*^-6}, 
     {388/5, 1.3872588874135061*^-6}, {1553/20, 1.5281879938537635*^-6}, 
     {777/10, 1.6307161245197876*^-6}, {311/4, 1.7332905672406973*^-6}, 
     {389/5, 1.8919314366955264*^-6}, {1557/20, 1.9557182545093532*^-6}, 
     {779/10, 2.0466061711327255*^-6}, {1559/20, 2.132049974575001*^-6}, 
     {78, 2.2214326287142705*^-6}, {1561/20, 2.2854885806666836*^-6}, 
     {781/10, 2.347938675803518*^-6}, {1563/20, 2.4039420506369313*^-6}, 
     {391/5, 2.4396069693566336*^-6}, {313/4, 2.489996088900215*^-6}, 
     {783/10, 2.523972317272638*^-6}, {1567/20, 2.5599683354804448*^-6}, 
     {392/5, 2.5423183862560705*^-6}, {1569/20, 2.5331990473609345*^-6}, 
     {157/2, 2.5597179849762286*^-6}, {1571/20, 2.535861171951148*^-6}, 
     {393/5, 2.549841758764382*^-6}, {1573/20, 2.5245215478503225*^-6}, 
     {787/10, 2.4925159831518107*^-6}, {315/4, 2.426670840424694*^-6}, 
     {394/5, 2.3769009268870267*^-6}, {1577/20, 2.2752048711854878*^-6}, 
     {789/10, 2.177463184219186*^-6}, {1579/20, 2.1333309747073592*^-6}, 
     {79, 2.022456648750892*^-6}, {1581/20, 2.008803157260708*^-6}, 
     {791/10, 1.836473453711851*^-6}, {1583/20, 1.747974922652884*^-6}, 
     {396/5, 1.6416318697060062*^-6}, {317/4, 1.5231277522981257*^-6}, 
     {793/10, 1.4577883680477743*^-6}, {1587/20, 1.262886805297736*^-6}, 
     {397/5, 1.115072578813936*^-6}, {1589/20, 9.230811332389122*^-7}, 
     {159/2, 8.271209692919945*^-7}, {1591/20, 6.713634747856911*^-7}, 
     {398/5, 5.362453825569213*^-7}, {1593/20, 4.2784420922759026*^-7}, 
     {797/10, 2.6904745774325445*^-7}, {319/4, 1.1591958291867765*^-7}, 
     {399/5, -1.0848592857382044*^-9}, {1597/20, -1.9847970962952322*^-7}, 
     {799/10, -3.1933569553249663*^-7}, {1599/20, -5.078786923795597*^-7}, 
     {80, -6.534102713288276*^-7}, {1601/20, -8.166377064421776*^-7}, 
     {801/10, -9.73342837846578*^-7}, {1603/20, -1.0733938790299588*^-6}, 
     {401/5, -1.2165207542904483*^-6}, {321/4, -1.3539403752420298*^-6}, 
     {803/10, -1.4729090397069822*^-6}, {1607/20, -1.5959629994580227*^-6}, 
     {402/5, -1.7376127745896697*^-6}, {1609/20, -1.8278416493086591*^-6}, 
     {161/2, -1.915162369102441*^-6}, {1611/20, -2.012619114241665*^-6}, 
     {403/5, -2.0945243628528454*^-6}, {1613/20, -2.1725004375888757*^-6}, 
     {807/10, -2.2492016598027464*^-6}, {323/4, -2.3290432687103624*^-6}, 
     {404/5, -2.3540225422766237*^-6}, {1617/20, -2.381424551861633*^-6}, 
     {809/10, -2.4348276436575444*^-6}, {1619/20, -2.4844875959606494*^-6}, 
     {81, -2.4738809013824525*^-6}, {1621/20, -2.4377214452864227*^-6}, 
     {811/10, -2.496844769356299*^-6}, {1623/20, -2.490709134356228*^-6}, 
     {406/5, -2.4951155094682376*^-6}, {325/4, -2.417574798352362*^-6}, 
     {813/10, -2.3744041069417854*^-6}, {1627/20, -2.334899634609533*^-6}, 
     {407/5, -2.325248823237258*^-6}, {1629/20, -2.249710425977769*^-6}, 
     {163/2, -2.1205035962007512*^-6}, {1631/20, -2.0813422171028773*^-6}, 
     {408/5, -1.9745021643952088*^-6}, {1633/20, -1.9311088034212887*^-6}, 
     {817/10, -1.7856731624465993*^-6}, {327/4, -1.7088370178608425*^-6}, 
     {409/5, -1.5965674098478155*^-6}, {1637/20, -1.4859290680818704*^-6}, 
     {819/10, -1.3486293119896464*^-6}, {1639/20, -1.219531890611636*^-6}, 
     {82, -1.1049594294681997*^-6}, {1641/20, -9.354544593109804*^-7}, 
     {821/10, -8.311855034595639*^-7}, {1643/20, -6.487355825451901*^-7}, 
     {411/5, -5.249126010450911*^-7}, {329/4, -3.860230216937155*^-7}, 
     {823/10, -2.4498652192311843*^-7}, {1647/20, -1.1062078279777676*^-7}, 
     {412/5, 2.829001091719796*^-8}, {1649/20, 1.9631006393378003*^-7}, 
     {165/2, 3.1166849483871273*^-7}, {1651/20, 4.291136773346138*^-7}, 
     {413/5, 5.90285896641396*^-7}, {1653/20, 7.336683208215844*^-7}, 
     {827/10, 8.491253038565155*^-7}, {331/4, 9.61129406405574*^-7}, 
     {414/5, 1.1060342982715382*^-6}, {1657/20, 1.2086004735380185*^-6}, 
     {829/10, 1.3862696226166898*^-6}, {1659/20, 1.4504839269194325*^-6}, 
     {83, 1.5255385094684049*^-6}, {1661/20, 1.6327286379569372*^-6}, 
     {831/10, 1.7335289321657177*^-6}, {1663/20, 1.8281304613870786*^-6}, 
     {416/5, 1.8539990308819032*^-6}, {333/4, 1.9175201669136*^-6}, 
     {833/10, 1.9642353347379404*^-6}, {1667/20, 2.111537200893965*^-6}, 
     {417/5, 2.1080720060268066*^-6}, {1669/20, 2.1295243464308777*^-6}, 
     {167/2, 2.1589806879079854*^-6}, {1671/20, 2.1698657155511114*^-6}, 
     {418/5, 2.1930059747043984*^-6}, {1673/20, 2.193587566173827*^-6}, 
     {837/10, 2.21714009961127*^-6}, {335/4, 2.2068036012873327*^-6}, 
     {419/5, 2.16250086593206*^-6}, {1677/20, 2.1457474016078892*^-6}, 
     {839/10, 2.0939063281322223*^-6}, {1679/20, 2.0737497505307623*^-6}, 
     {84, 2.0731780620009133*^-6}, {1681/20, 1.9447919071269304*^-6}, 
     {841/10, 1.9050839626111316*^-6}, {1683/20, 1.8775515836511047*^-6}, 
     {421/5, 1.7639498119115249*^-6}, {337/4, 1.6733445462047136*^-6}, 
     {843/10, 1.6194389947099541*^-6}, {1687/20, 1.496248709223491*^-6}, 
     {422/5, 1.4036494757480034*^-6}, {1689/20, 1.3456825832536268*^-6}, 
     {169/2, 1.1909549324923274*^-6}, {1691/20, 1.128807695122136*^-6}, 
     {423/5, 1.02855096806298*^-6}, {1693/20, 8.952075347123944*^-7}, 
     {847/10, 7.936065856001262*^-7}, {339/4, 6.500813567664188*^-7}, 
     {424/5, 5.391873494006716*^-7}, {1697/20, 4.4110866544849747*^-7}, 
     {849/10, 3.151995346395431*^-7}, {1699/20, 1.9345602930709305*^-7}, 
     {85, 4.680274112017768*^-8}, {1701/20, -6.564067688702435*^-8}, 
     {851/10, -2.1762634035485395*^-7}, {1703/20, -2.8013727899553476*^-7}, 
     {426/5, -3.823204992661755*^-7}, {341/4, -5.066606277720487*^-7}, 
     {853/10, -6.232355264706654*^-7}, {1707/20, -6.969455174489578*^-7}, 
     {427/5, -7.978771619679241*^-7}, {1709/20, -9.365633804100243*^-7}, 
     {171/2, -1.0463765348980858*^-6}, {1711/20, -1.1204503599648863*^-6}, 
     {428/5, -1.2268578156449106*^-6}, {1713/20, -1.2960790151325674*^-6}, 
     {857/10, -1.3819030749082084*^-6}, {343/4, -1.418743188208449*^-6}, 
     {429/5, -1.5059175133141922*^-6}, {1717/20, -1.5528496231514977*^-6}, 
     {859/10, -1.6161417848437054*^-6}, {1719/20, -1.6914451118690832*^-6}, 
     {86, -1.760394818736688*^-6}, {1721/20, -1.829776340819822*^-6}, 
     {861/10, -1.8618662314257017*^-6}, {1723/20, -1.8607409622978244*^-6}, 
     {431/5, -1.8691714867430376*^-6}, {345/4, -1.930986040676874*^-6}, 
     {863/10, -1.916208222069171*^-6}, {1727/20, -1.8922466368809232*^-6}, 
     {432/5, -1.8961871872391622*^-6}, {1729/20, -1.8818291442346258*^-6}, 
     {173/2, -1.8917974997090248*^-6}, {1731/20, -1.9171077224877653*^-6}, 
     {433/5, -1.8619118143520241*^-6}, {1733/20, -1.7932985949403735*^-6}, 
     {867/10, -1.759243685395262*^-6}, {347/4, -1.759803045398023*^-6}, 
     {434/5, -1.6689610238401764*^-6}, {1737/20, -1.6215411490078102*^-6}, 
     {869/10, -1.5602200699599278*^-6}, {1739/20, -1.4793274088209518*^-6}, 
     {87, -1.4252825003002734*^-6}, {1741/20, -1.3273732023533213*^-6}, 
     {871/10, -1.2392905340968818*^-6}, {1743/20, -1.1879509551893097*^-6}, 
     {436/5, -1.0911176464289962*^-6}, {349/4, -1.0062954431261373*^-6}, 
     {873/10, -9.38171055439585*^-7}, {1747/20, -8.250733008335898*^-7}, 
     {437/5, -7.298702150576597*^-7}, {1749/20, -6.229628830498046*^-7}, 
     {175/2, -5.266062016728856*^-7}, {1751/20, -3.964106772211262*^-7}, 
     {438/5, -3.3536401464889787*^-7}, {1753/20, -2.1155422590124484*^-7}, 
     {877/10, -2.949084372538824*^-9}, {351/4, 2.314315430962388*^-8}, 
     {439/5, 1.2059062527540465*^-7}, {1757/20, 2.037897110229725*^-7}, 
     {879/10, 3.508507159973029*^-7}, {1759/20, 4.5247443820656437*^-7}, 
     {88, 5.233526998542348*^-7}, {1761/20, 6.447977002159433*^-7}, 
     {881/10, 7.513297038547195*^-7}, {1763/20, 8.927039698673755*^-7}, 
     {441/5, 9.710602407869695*^-7}, {353/4, 1.0021327311593442*^-6}, 
     {883/10, 1.1264852794873326*^-6}, {1767/20, 1.2162117084615898*^-6}, 
     {442/5, 1.3296968407114362*^-6}, {1769/20, 1.3801763459400651*^-6}, 
     {177/2, 1.4358649247508959*^-6}, {1771/20, 1.469093885340944*^-6}, 
     {443/5, 1.5710656613918128*^-6}, {1773/20, 1.628400496805904*^-6}, 
     {887/10, 1.6675635270135825*^-6}, {355/4, 1.733191495628672*^-6}, 
     {444/5, 1.7744594807966863*^-6}, {1777/20, 1.7983779519864518*^-6}, 
     {889/10, 1.823402123429796*^-6}, {1779/20, 1.863190900716627*^-6}, 
     {89, 1.8720802925364932*^-6}, {1781/20, 1.8685468157753071*^-6}, 
     {891/10, 1.848672872090118*^-6}, {1783/20, 1.8206583561053424*^-6}, 
     {446/5, 1.8650105614442802*^-6}, {357/4, 1.7926525894274015*^-6}, 
     {893/10, 1.7710421838096346*^-6}, {1787/20, 1.7564153696747464*^-6}, 
     {447/5, 1.702408971987479*^-6}, {1789/20, 1.7010484237162116*^-6}, 
     {179/2, 1.6009020421814402*^-6}, {1791/20, 1.529009012499194*^-6}, 
     {448/5, 1.447381657374014*^-6}, {1793/20, 1.4378822489058418*^-6}, 
     {897/10, 1.3282608876397095*^-6}, {359/4, 1.263793241793043*^-6}, 
     {449/5, 1.1445637683460408*^-6}, {1797/20, 1.0934615199548192*^-6}, 
     {899/10, 1.0264694366574068*^-6}, {1799/20, 8.021078626782585*^-7}, 
     {90, 7.839247658791848*^-7}, {1801/20, 7.099307767557961*^-7}, 
     {901/10, 5.807275478206253*^-7}, {1803/20, 5.03720862188306*^-7}, 
     {451/5, 3.6886625939119844*^-7}, {361/4, 2.6874129153975357*^-7}, 
     {903/10, 1.5982885992471552*^-7}, {1807/20, 5.440127486336377*^-8}, 
     {452/5, -1.0536912725331304*^-7}, {1809/20, -1.6451006134947377*^-7}, 
     {181/2, -2.7214153175587896*^-7}, {1811/20, -4.040360077890541*^-7}, 
     {453/5, -5.108482072991097*^-7}, {1813/20, -6.102512232382395*^-7}, 
     {907/10, -6.967050057808677*^-7}, {363/4, -8.128375060464932*^-7}, 
     {454/5, -9.299223802800016*^-7}, {1817/20, -1.018655866828061*^-6}, 
     {909/10, -1.0910285673654263*^-6}, {1819/20, -1.1897372174940468*^-6}, 
     {91, -1.2850458699781298*^-6}, {1821/20, -1.3867512447113262*^-6}, 
     {911/10, -1.4206511543199407*^-6}, {1823/20, -1.4919998795048794*^-6}, 
     {456/5, -1.529206756799295*^-6}, {365/4, -1.596971147259374*^-6}, 
     {913/10, -1.643801045156379*^-6}, {1827/20, -1.6878498232952843*^-6}, 
     {457/5, -1.694930950771334*^-6}, {1829/20, -1.7654822374868484*^-6}, 
     {183/2, -1.8030847777489312*^-6}, {1831/20, -1.7809083433240058*^-6}, 
     {458/5, -1.791599218203821*^-6}, {1833/20, -1.8056600060711858*^-6}, 
     {917/10, -1.774746549110251*^-6}, {367/4, -1.7799852299049679*^-6}, 
     {459/5, -1.7447568520650991*^-6}, {1837/20, -1.7153361144828239*^-6}, 
     {919/10, -1.7019749151692132*^-6}, {1839/20, -1.6549878933957984*^-6}, 
     {92, -1.6226210837327892*^-6}, {1841/20, -1.5657053394901865*^-6}, 
     {921/10, -1.506719312621696*^-6}, {1843/20, -1.4159596467416824*^-6}, 
     {461/5, -1.3598273268800032*^-6}, {369/4, -1.300398454792684*^-6}, 
     {923/10, -1.1930243847824151*^-6}, {1847/20, -1.0887311488391727*^-6}, 
     {462/5, -9.96742151940233*^-7}, {1849/20, -9.357401495324602*^-7}, 
     {185/2, -8.176519184499575*^-7}, {1851/20, -7.292892783700156*^-7}, 
     {463/5, -6.042435184080985*^-7}, {1853/20, -5.180012537520096*^-7}, 
     {927/10, -3.766913905453584*^-7}, {371/4, -3.193864659828405*^-7}, 
     {464/5, -2.0761379569689264*^-7}, {1857/20, -7.786222224609451*^-8}, 
     {929/10, -1.3809132774766919*^-8}, {1859/20, 1.3242956080523893*^-7}, 
     {93, 2.0219466005666487*^-7}, {1861/20, 2.950064425400606*^-7}, 
     {931/10, 4.314687577779922*^-7}, {1863/20, 5.438826273726494*^-7}, 
     {466/5, 6.116917253499304*^-7}, {373/4, 6.73248062989934*^-7}, 
     {933/10, 8.134253700053939*^-7}, {1867/20, 8.727101777836199*^-7}, 
     {467/5, 9.367549002603504*^-7}, {1869/20, 9.93243945153488*^-7}, 
     {187/2, 1.0877524907297598*^-6}, {1871/20, 1.1560080233757875*^-6}, 
     {468/5, 1.279975393050914*^-6}, {1873/20, 1.263876697209232*^-6}, 
     {937/10, 1.333197093292271*^-6}, {375/4, 1.3590060798998604*^-6}, 
     {469/5, 1.4366243060448536*^-6}, {1877/20, 1.4409284539093625*^-6}, 
     {939/10, 1.452917849968649*^-6}, {1879/20, 1.455783554864254*^-6}, 
     {94, 1.484567567086592*^-6}, {1881/20, 1.5292122260146535*^-6}, 
     {941/10, 1.4989452936930991*^-6}, {1883/20, 1.4725792414002625*^-6}, 
     {471/5, 1.4813849831124548*^-6}, {377/4, 1.4381662857693156*^-6}, 
     {943/10, 1.4493300723311675*^-6}, {1887/20, 1.438288480495875*^-6}, 
     {472/5, 1.4168743369541437*^-6}, {1889/20, 1.3536934654889698*^-6}, 
     {189/2, 1.3042555293135694*^-6}, {1891/20, 1.2566027574947847*^-6}, 
     {473/5, 1.240506593537527*^-6}, {1893/20, 1.124221457558805*^-6}, 
     {947/10, 1.0959987358227785*^-6}, {379/4, 1.0360418974744712*^-6}, 
     {474/5, 1.0237211261129864*^-6}, {1897/20, 8.966259399736942*^-7}, 
     {949/10, 7.927371864641097*^-7}, {1899/20, 7.643213066621524*^-7}, 
     {95, 7.234976436704121*^-7}, {1901/20, 5.832649477288676*^-7}, 
     {951/10, 5.066767926539817*^-7}, {1903/20, 4.306577742543838*^-7}, 
     {476/5, 3.599375399052085*^-7}, {381/4, 2.795791823051452*^-7}, 
     {953/10, 2.0176280463718443*^-7}, {1907/20, 1.0837668088306551*^-7}, 
     {477/5, 5.0966649893513516*^-8}, {1909/20, -3.884503995549293*^-8}, 
     {191/2, -9.201628161162323*^-8}, {1911/20, -1.8331946139218958*^-7}, 
     {478/5, -2.698921765624529*^-7}, {1913/20, -3.321530516933041*^-7}, 
     {957/10, -3.957114961729985*^-7}, {383/4, -4.266611065441685*^-7}, 
     {479/5, -5.157143321207758*^-7}, {1917/20, -5.384865508764256*^-7}, 
     {959/10, -6.31763042975228*^-7}, {1919/20, -6.519465217142556*^-7}, 
     {96, -7.271739128275612*^-7}, {1921/20, -7.368529820472869*^-7}, 
     {961/10, -7.580662175731001*^-7}, {1923/20, -8.319281118232547*^-7}, 
     {481/5, -8.762082753938083*^-7}, {385/4, -9.160969985898271*^-7}, 
     {963/10, -9.015045291452251*^-7}, {1927/20, -9.336668993636943*^-7}, 
     {482/5, -9.39930747873019*^-7}, {1929/20, -9.723518034701617*^-7}, 
     {193/2, -1.0113500718417212*^-6}, {1931/20, -9.82642251096122*^-7}, 
     {483/5, -1.0078994876067116*^-6}, {1933/20, -9.874233298234891*^-7}, 
     {967/10, -9.888821451142782*^-7}, {387/4, -9.424753419640108*^-7}, 
     {484/5, -9.450636508992472*^-7}, {1937/20, -8.924756706024661*^-7}, 
     {969/10, -9.63887983040923*^-7}, {1939/20, -9.079776057130395*^-7}, 
     {97, -9.026524248403889*^-7}, {1941/20, -8.380452337641842*^-7}, 
     {971/10, -8.148810920552418*^-7}, {1943/20, -7.805589697928994*^-7}, 
     {486/5, -7.840867154440545*^-7}, {389/4, -7.62017300239004*^-7}, 
     {973/10, -6.663197369416451*^-7}, {1947/20, -6.339268366697959*^-7}, 
     {487/5, -6.566211957423351*^-7}, {1949/20, -6.063084091040283*^-7}, 
     {195/2, -5.755076904270795*^-7}, {1951/20, -5.100418123751838*^-7}, 
     {488/5, -5.019468911557357*^-7}, {1953/20, -4.2117018573401*^-7}, 
     {977/10, -4.1492529450487536*^-7}, {391/4, -3.4135726183909254*^-7}, 
     {489/5, -3.347679789350577*^-7}, {1957/20, -2.7741185106011645*^-7}, 
     {979/10, -2.643479621866618*^-7}, {1959/20, -2.270382085979572*^-7}, 
     {98, -1.8940066510292342*^-7}, {1961/20, -1.1982743477328972*^-7}, 
     {981/10, -1.0728071431903574*^-7}, {1963/20, -4.930469859817932*^-8}, 
     {491/5, -6.328688661148829*^-8}, {393/4, -1.9537400419711304*^-8}, 
     {983/10, 9.163138043472019*^-9}, {1967/20, 2.999258648384018*^-8}, 
     {492/5, 7.533342460258607*^-8}, {1969/20, 8.949001774945925*^-8}, 
     {197/2, 1.2618635371402728*^-7}, {1971/20, 1.5758086437068705*^-7}, 
     {493/5, 1.9196676740058927*^-7}, {1973/20, 2.2034396472865592*^-7}, 
     {987/10, 2.3652254920250582*^-7}, {395/4, 2.3129640204164192*^-7}, 
     {494/5, 2.788739681125474*^-7}, {1977/20, 2.868537429707996*^-7}, 
     {989/10, 3.477173411564616*^-7}, {1979/20, 3.7769375796359306*^-7}, 
     {99, 3.762161487549931*^-7}, {1981/20, 3.7913080108004094*^-7}, 
     {991/10, 4.108600561089637*^-7}, {1983/20, 4.5156174459382026*^-7}, 
     {496/5, 4.3430778775416234*^-7}, {397/4, 4.478520836057043*^-7}, 
     {993/10, 4.725965202512228*^-7}, {1987/20, 4.987952511165128*^-7}, 
     {497/5, 4.9768247326748*^-7}, {1989/20, 5.508564055733967*^-7}, 
     {199/2, 5.429935800993491*^-7}, {1991/20, 5.672244995022502*^-7}, 
     {498/5, 5.555582489602529*^-7}, {1993/20, 5.584503409636343*^-7}, 
     {997/10, 5.627384963569071*^-7}, {399/4, 5.871851269934059*^-7}, 
     {499/5, 6.100734748076819*^-7}, {1997/20, 6.140625215395046*^-7}, 
     {999/10, 6.199819490848579*^-7}, {1999/20, 6.448348253973446*^-7}, 
     {100, 6.692886762443839*^-7}}
 
ImFRfin = {{1/10000, -5722.895802791449}, {11/100000, -5202.628471740969}, 
     {3/25000, -4769.0756583954535}, {13/100000, -4402.223914176731}, 
     {7/50000, -4087.779256321406}, {3/20000, -3815.260636206509}, 
     {1/6250, -3576.8067999589684}, {17/100000, -3366.406361073812}, 
     {9/50000, -3179.383918111951}, {19/100000, -3012.047795462705}, 
     {1/5000, -2861.4454143656376}, {21/100000, -2725.188509096127}, 
     {11/50000, -2601.3139223696908}, {23/100000, -2488.213328595626}, 
     {3/12500, -2384.537809450924}, {1/4000, -2289.1562230259287}, 
     {13/50000, -2201.1117478290653}, {27/100000, -2119.589100209695}, 
     {7/25000, -2043.8911284419528}, {29/100000, -1973.410442273118}, 
     {3/10000, -1907.6300788910448}, {31/100000, -1846.093664018876}, 
     {1/3125, -1788.404515888416}, {33/100000, -1734.2091690406573}, 
     {17/50000, -1683.2030146404459}, {7/20000, -1635.111367963364}, 
     {9/25000, -1589.69158702383}, {37/100000, -1546.7270307834324}, 
     {19/50000, -1506.02473711958}, {39/100000, -1467.4087079103397}, 
     {1/2500, -1430.7223715295327}, {41/100000, -1395.8267481194034}, 
     {21/50000, -1362.5926488951914}, {43/100000, -1330.9045206442706}, 
     {11/25000, -1300.6567012729188}, {9/20000, -1271.7542666182421}, 
     {23/50000, -1244.1062890103053}, {47/100000, -1217.6359336127998}, 
     {3/6250, -1192.2684773588142}, {49/100000, -1167.9364943975943}, 
     {1/2000, -1144.577815782561}, {51/100000, -1122.1350750933934}, 
     {13/25000, -1100.5555556738866}, {53/100000, -1079.7903235276372}, 
     {27/50000, -1059.7941948267512}, {11/20000, -1040.5251648004114}, 
     {7/12500, -1021.9443227352781}, {57/100000, -1004.0163749445328}, 
     {29/50000, -986.7056906794571}, {59/100000, -969.9810570935044}, 
     {3/5000, -953.8146464976653}, {61/100000, -938.1783693351986}, 
     {31/50000, -923.0463816881086}, {63/100000, -908.3948800072617}, 
     {2/3125, -894.2015928483224}, {13/20000, -880.4449437332692}, 
     {33/50000, -867.1041562350081}, {67/100000, -854.162272086794}, 
     {17/25000, -841.6017439146183}, {69/100000, -829.4045853245364}, 
     {7/10000, -817.5552285722072}, {71/100000, -806.0410812141938}, 
     {9/12500, -794.845342384539}, {73/100000, -783.9570710828275}, 
     {37/50000, -773.3630027011043}, {3/4000, -763.0514166811838}, 
     {19/25000, -753.0113302454324}, {77/100000, -743.2319486955414}, 
     {39/50000, -733.7033034428521}, {79/100000, -724.4158830529664}, 
     {1/1250, -715.3612057330645}, {81/100000, -706.5290783472076}, 
     {41/50000, -697.9128206161538}, {83/100000, -689.5047987561982}, 
     {21/25000, -681.295819901932}, {17/20000, -673.2805427468256}, 
     {43/50000, -665.4517124855652}, {87/100000, -657.802791928033}, 
     {11/12500, -650.3282155864831}, {89/100000, -643.0206729464153}, 
     {9/10000, -635.87595245693}, {91/100000, -628.8887988929825}, 
     {23/25000, -622.0525613450607}, {93/100000, -615.3638291625244}, 
     {47/50000, -608.8173881989408}, {19/20000, -602.4092770384632}, 
     {3/3125, -596.1336331745615}, {97/100000, -589.9884512117003}, 
     {49/50000, -583.9676419748162}, {99/100000, -578.0689277274923}, 
     {1/1000, -572.2881978102912}, {101/100000, -566.6219754122046}, 
     {51/50000, -561.0668753922066}, {103/100000, -555.6195935413398}, 
     {13/12500, -550.277045106662}, {21/20000, -545.0363114725433}, 
     {53/50000, -539.8944679411079}, {107/100000, -534.8486931019986}, 
     {27/25000, -529.8963889062816}, {109/100000, -525.0353857678476}, 
     {11/10000, -520.2618349733023}, {111/100000, -515.5751835601432}, 
     {7/6250, -510.9714272510514}, {113/100000, -506.4499556011915}, 
     {57/50000, -502.00700635518035}, {23/20000, -497.6416945317869}, 
     {29/25000, -493.3516621619133}, {117/100000, -489.1353102704952}, 
     {59/50000, -484.98974404214323}, {119/100000, -480.9141574486848}, 
     {3/2500, -476.90649331839245}, {121/100000, -472.96554578429743}, 
     {61/50000, -469.0883855812755}, {123/100000, -465.2749976713359}, 
     {31/25000, -461.52239093706044}, {1/800, -457.83052213374697}, 
     {63/50000, -454.1969637273919}, {127/100000, -450.6206187001808}, 
     {4/3125, -447.09975409722085}, {129/100000, -443.6338526365481}, 
     {13/10000, -440.221264161876}, {131/100000, -436.8607744504768}, 
     {33/25000, -433.55153449467434}, {133/100000, -430.2917588276806}, 
     {67/50000, -427.08059434134316}, {27/20000, -423.9166851436005}, 
     {17/12500, -420.7999252314271}, {137/100000, -417.7280844976598}, 
     {69/50000, -414.7010525502077}, {139/100000, -411.7175465995773}, 
     {7/5000, -408.77670721390166}, {141/100000, -405.87791007949204}, 
     {71/50000, -403.0192677818434}, {143/100000, -400.20088937840546}, 
     {9/6250, -397.4217356168384}, {29/20000, -394.6811680151891}, 
     {73/50000, -391.9778586740314}, {147/100000, -389.3113353595272}, 
     {37/25000, -386.6805135284892}, {149/100000, -384.08568686916954}, 
     {3/2000, -381.52508475536627}, {151/100000, -378.99805410172814}, 
     {19/12500, -376.50461162146746}, {153/100000, -374.04415694063164}, 
     {77/50000, -371.614956158512}, {31/20000, -369.21742240395565}, 
     {39/25000, -366.85089871807884}, {157/100000, -364.5139747990951}, 
     {79/50000, -362.20687619375553}, {159/100000, -359.92912171908574}, 
     {1/625, -357.6795596817914}, {161/100000, -355.45791787554367}, 
     {81/50000, -353.2637358602734}, {163/100000, -351.0964426079115}, 
     {41/25000, -348.95530262606997}, {33/20000, -346.84044728413437}, 
     {83/50000, -344.75102802469735}, {167/100000, -342.68686630279433}, 
     {21/12500, -340.6470729849975}, {169/100000, -338.63139485033446}, 
     {17/10000, -336.639157829208}, {171/100000, -334.6704975461066}, 
     {43/25000, -332.7247033312224}, {173/100000, -330.80143322999675}, 
     {87/50000, -328.9005379779851}, {7/4000, -327.0207912084536}, 
     {11/6250, -325.16293655724223}, {177/100000, -323.3258648415257}, 
     {89/50000, -321.50916714992707}, {179/100000, -319.7130245651863}, 
     {9/5000, -317.9368175289886}, {181/100000, -316.1802484975882}, 
     {91/50000, -314.44322694791947}, {183/100000, -312.7249069384418}, 
     {23/12500, -311.0253224225022}, {37/20000, -309.3438250014917}, 
     {93/50000, -307.68090779217243}, {187/100000, -306.035545151824}, 
     {47/25000, -304.4077053232505}, {189/100000, -302.796803503136}, 
     {19/10000, -301.20311018630287}, {191/100000, -299.626378876054}, 
     {6/3125, -298.06583007921114}, {193/100000, -296.5211660902469}, 
     {97/50000, -294.99293000965804}, {39/20000, -293.4801020642835}, 
     {49/25000, -291.9825222417237}, {197/100000, -290.50062196986914}, 
     {99/50000, -289.0333949206721}, {199/100000, -287.58095180299847}, 
     {1/500, -286.14302918267816}, {201/100000, -284.7191736614865}, 
     {101/50000, -283.3099143827267}, {203/100000, -281.914046980061}, 
     {51/25000, -280.53232133658935}, {41/20000, -279.163829604708}, 
     {103/50000, -277.808426156726}, {207/100000, -276.46634743352934}, 
     {13/6250, -275.13716809007155}, {209/100000, -273.8209499752851}, 
     {21/10000, -272.51679800789327}, {211/100000, -271.2251955387566}, 
     {53/25000, -269.9458300744119}, {213/100000, -268.6784597305757}, 
     {107/50000, -267.4229067423264}, {43/20000, -266.17907871253135}, 
     {27/12500, -264.94677591972913}, {217/100000, -263.7258031851673}, 
     {109/50000, -262.51602031554614}, {219/100000, -261.31730620428664}, 
     {11/5000, -260.1294810787159}, {221/100000, -258.9526183575135}, 
     {111/50000, -257.7859483732286}, {223/100000, -256.6299324848266}, 
     {7/3125, -255.4842448149326}, {9/4000, -254.3489688172815}, 
     {113/50000, -253.22346962833888}, {227/100000, -252.10796761663073}, 
     {57/25000, -251.00220420269864}, {229/100000, -249.90591227852428}, 
     {23/10000, -248.8195451651261}, {231/100000, -247.74237224470022}, 
     {29/12500, -246.67451144924297}, {233/100000, -245.61578174735962}, 
     {117/50000, -244.56611847123958}, {47/20000, -243.52520908493614}, 
     {59/25000, -242.49350179185404}, {237/100000, -241.47032384144774}, 
     {119/50000, -240.45572113215133}, {239/100000, -239.4496051461523}, 
     {3/1250, -238.45186087367063}, {241/100000, -237.46225430231596}, 
     {121/50000, -236.4809849581303}, {243/100000, -235.5079889229301}, 
     {61/25000, -234.54276904425507}, {49/20000, -233.58524657644108}, 
     {123/50000, -232.63588026051121}, {247/100000, -231.69381410795626}, 
     {31/12500, -230.7595704771931}, {249/100000, -229.83279153027678}, 
     {1/400, -228.91362723603578}, {251/100000, -228.0014136435795}, 
     {63/25000, -227.09663286361285}, {253/100000, -226.19916569540226}, 
     {127/50000, -225.3086260422159}, {51/20000, -224.4249582292926}, 
     {8/3125, -223.54838372254733}, {257/100000, -222.67833493386115}, 
     {129/50000, -221.81542450635237}, {259/100000, -220.95895437099142}, 
     {13/5000, -220.10891715260425}, {261/100000, -219.26556784313658}, 
     {131/50000, -218.42866006968097}, {263/100000, -217.59811840961942}, 
     {33/12500, -216.77385308618653}, {53/20000, -215.95600520398295}, 
     {133/50000, -215.14394346698572}, {267/100000, -214.33814327300104}, 
     {67/25000, -213.53834139443563}, {269/100000, -212.74450850191238}, 
     {27/10000, -211.95656189934203}, {271/100000, -211.17457088248256}, 
     {17/6250, -210.39800154459203}, {273/100000, -209.62731578781666}, 
     {137/50000, -208.86222796462079}, {11/4000, -208.10289942604425}, 
     {69/25000, -207.3488678844555}, {277/100000, -206.6001368549471}, 
     {139/50000, -205.85694688457318}, {279/100000, -205.11918160340184}, 
     {7/2500, -204.386523039473}, {281/100000, -203.65912271534125}, 
     {141/50000, -202.93693074014698}, {283/100000, -202.21999180927946}, 
     {71/25000, -201.50774835272517}, {57/20000, -200.8006904843179}, 
     {143/50000, -200.0985820253838}, {287/100000, -199.40149276831414}, 
     {9/3125, -198.70905010896632}, {289/100000, -198.02152711924856}, 
     {29/10000, -197.33868187453646}, {291/100000, -196.66036191667706}, 
     {73/25000, -195.98686819661236}, {293/100000, -195.31795357629397}, 
     {147/50000, -194.65373701428047}, {59/20000, -193.99371903875306}, 
     {37/12500, -193.33830861415572}, {297/100000, -192.68747739891575}, 
     {149/50000, -192.0408648220954}, {299/100000, -191.3984052855639}, 
     {3/1000, -190.76057178743105}, {301/100000, -190.12677164506118}, 
     {151/50000, -189.49719498529862}, {303/100000, -188.8717986577626}, 
     {19/6250, -188.250481853545}, {61/20000, -187.63324121837695}, 
     {153/50000, -187.01988369325477}, {307/100000, -186.4107087492847}, 
     {77/25000, -185.80545304203764}, {309/100000, -185.20410065256772}, 
     {31/10000, -184.6068236821033}, {311/100000, -184.01318890673406}, 
     {39/12500, -183.42326926521497}, {313/100000, -182.83735407283405}, 
     {157/50000, -182.25491597417215}, {63/20000, -181.6764844180522}, 
     {79/25000, -181.10152732550551}, {317/100000, -180.53005140835995}, 
     {159/50000, -179.9623372508686}, {319/100000, -179.39830170597787}, 
     {2/625, -178.8376586350372}, {321/100000, -178.2803867681095}, 
     {161/50000, -177.72671008318702}, {323/100000, -177.17646905038362}, 
     {81/25000, -176.6296026218099}, {13/4000, -176.0861017933537}, 
     {163/50000, -175.54608555349728}, {327/100000, -175.00923587792204}, 
     {41/12500, -174.4755016112502}, {329/100000, -173.94516143766094}, 
     {33/10000, -173.4181721355326}, {331/100000, -172.8941026598489}, 
     {83/25000, -172.3734462640806}, {333/100000, -171.85567514486962}, 
     {167/50000, -171.3412615727604}, {67/20000, -170.8297752402073}, 
     {21/6250, -170.32120025793915}, {337/100000, -169.8159072169948}, 
     {169/50000, -169.3133406835051}, {339/100000, -168.81400284976195}, 
     {17/5000, -168.31746233776335}, {341/100000, -167.82386330246362}, 
     {171/50000, -167.33300716815899}, {343/100000, -166.84511924456967}, 
     {43/12500, -166.3602125807614}, {69/20000, -165.877884067899}, 
     {173/50000, -165.39856653162786}, {347/100000, -164.92176217930785}, 
     {87/25000, -164.4478293598077}, {349/100000, -163.9766357029618}, 
     {7/2000, -163.5082410758419}, {351/100000, -163.04238547051534}, 
     {11/3125, -162.57904684353718}, {353/100000, -162.11857490845102}, 
     {177/50000, -161.66060277665412}, {71/20000, -161.2052091971388}, 
     {89/25000, -160.75235272896174}, {357/100000, -160.301942172258}, 
     {179/50000, -159.85427317376661}, {359/100000, -159.408981262407}, 
     {9/2500, -158.966047655554}, {361/100000, -158.5256856299265}, 
     {181/50000, -158.08774868684287}, {363/100000, -157.65233636615915}, 
     {91/25000, -157.2192218215735}, {73/20000, -156.78832940757115}, 
     {183/50000, -156.3600703204134}, {367/100000, -155.93385990662682}, 
     {23/6250, -155.51012095922198}, {369/100000, -155.08866061498213}, 
     {37/10000, -154.66947700177093}, {371/100000, -154.25268738818545}, 
     {93/25000, -153.83788809245925}, {373/100000, -153.42544416080514}, 
     {187/50000, -153.01531509169627}, {3/800, -152.60725462507003}, 
     {47/12500, -152.2012499260114}, {377/100000, -151.79752314309005}, 
     {189/50000, -151.39601658082626}, {379/100000, -150.99643918020706}, 
     {19/5000, -150.59906896180996}, {381/100000, -150.20389512788077}, 
     {191/50000, -149.81056169800317}, {383/100000, -149.41938549153923}, 
     {12/3125, -149.03025377109793}, {77/20000, -148.64326511381847}, 
     {193/50000, -148.25805049467795}, {387/100000, -147.87505863937884}, 
     {97/25000, -147.49379000639047}, {389/100000, -147.11473657431662}, 
     {39/10000, -146.73747944666457}, {391/100000, -146.3620755041145}, 
     {49/12500, -145.98868356659108}, {393/100000, -145.61732203367887}, 
     {197/50000, -145.24758726016006}, {79/20000, -144.8798516383261}, 
     {99/25000, -144.5139629574689}, {397/100000, -144.1500526038813}, 
     {199/50000, -143.78785515491927}, {399/100000, -143.42735708367832}, 
     {1/250, -143.0688969704891}, {401/100000, -142.71209265157106}, 
     {201/50000, -142.35695448835375}, {403/100000, -142.00369182014865}, 
     {101/25000, -141.65228500422933}, {81/20000, -141.30249779288175}, 
     {203/50000, -140.95433685282592}, {407/100000, -140.6081172955848}, 
     {51/12500, -140.26336996262387}, {409/100000, -139.9204000179675}, 
     {41/10000, -139.57921308093412}, {411/100000, -139.23958488529178}, 
     {103/25000, -138.90160407990487}, {413/100000, -138.56527254439578}, 
     {207/50000, -138.2304595821928}, {83/20000, -137.89735050840963}, 
     {13/3125, -137.56596487603065}, {417/100000, -137.23593359171238}, 
     {209/50000, -136.90759926505302}, {419/100000, -136.5808432720148}, 
     {21/5000, -136.2556321450665}, {421/100000, -135.93195132093817}, 
     {211/50000, -135.6098319482402}, {423/100000, -135.2893302131343}, 
     {53/12500, -134.97022211708534}, {17/4000, -134.65253553558745}, 
     {213/50000, -134.33653393652975}, {427/100000, -134.02191335658432}, 
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     {9/1000, -63.57983281690994}, {901/100000, -63.509205561054756}, 
     {451/50000, -63.43882561179555}, {903/100000, -63.36850361641494}, 
     {113/12500, -63.29838818420515}, {181/20000, -63.22842451302746}, 
     {453/50000, -63.158675283314636}, {907/100000, -63.08897007192772}, 
     {227/25000, -63.01952243633984}, {909/100000, -62.95018522393161}, 
     {91/10000, -62.880979416654796}, {911/100000, -62.81189029749737}, 
     {57/6250, -62.74300366266881}, {913/100000, -62.674268408611326}, 
     {457/50000, -62.60572480405992}, {183/20000, -62.53723591827176}, 
     {229/25000, -62.46895093488763}, {917/100000, -62.40084891498688}, 
     {459/50000, -62.33281791326597}, {919/100000, -62.26496294858288}, 
     {23/2500, -62.19732256455268}, {921/100000, -62.129725042879414}, 
     {461/50000, -62.06231846573739}, {923/100000, -61.99505991905434}, 
     {231/25000, -61.92800010996562}, {37/4000, -61.86103186401358}, 
     {463/50000, -61.794204024243086}, {927/100000, -61.72748119770746}, 
     {29/3125, -61.66094944087811}, {929/100000, -61.59455563331687}, 
     {93/10000, -61.52836050639888}, {931/100000, -61.46225346196154}, 
     {233/25000, -61.39629533319898}, {933/100000, -61.330462978529965}, 
     {467/50000, -61.26478990467507}, {187/20000, -61.19924133991603}, 
     {117/12500, -61.133848650265946}, {937/100000, -61.06853540241107}, 
     {469/50000, -61.003452228590916}, {939/100000, -60.93847555288832}, 
     {47/5000, -60.873626842211976}, {941/100000, -60.808919483375746}, 
     {471/50000, -60.74434856135598}, {943/100000, -60.67991402955502}, 
     {59/6250, -60.61561994254254}, {189/20000, -60.551452413730786}, 
     {473/50000, -60.48738332096032}, {947/100000, -60.423539454939856}, 
     {237/25000, -60.359782751265556}, {949/100000, -60.29616433580054}, 
     {19/2000, -60.232631616673444}, {951/100000, -60.169277506716924}, 
     {119/12500, -60.1060537650622}, {953/100000, -60.04297240294393}, 
     {477/50000, -59.980057468941396}, {191/20000, -59.91723768919334}, 
     {239/25000, -59.85454468989093}, {957/100000, -59.791986205286776}, 
     {479/50000, -59.72950348786833}, {959/100000, -59.66720475154824}, 
     {6/625, -59.60503015614472}, {961/100000, -59.54299031208026}, 
     {481/50000, -59.48107483508625}, {963/100000, -59.419296408533086}, 
     {241/25000, -59.35763971556895}, {193/20000, -59.296158154693956}, 
     {483/50000, -59.23471008716899}, {967/100000, -59.17344041810891}, 
     {121/12500, -59.11228554450376}, {969/100000, -59.05127212864889}, 
     {97/10000, -58.99036901894614}, {971/100000, -58.92959947078707}, 
     {243/25000, -58.868962116095815}, {973/100000, -58.808440889675666}, 
     {487/50000, -58.74808933803196}, {39/4000, -58.68776468877168}, 
     {61/6250, -58.627621072095295}, {977/100000, -58.56759899686871}, 
     {489/50000, -58.50773788935436}, {979/100000, -58.44795729392342}, 
     {49/5000, -58.38825542458788}, {981/100000, -58.328716944107384}, 
     {491/50000, -58.269301168256916}, {983/100000, -58.2100556773985}, 
     {123/12500, -58.15088425369005}, {197/20000, -58.0917823803601}, 
     {493/50000, -58.032895049511694}, {987/100000, -57.974036558568145}, 
     {247/25000, -57.91537913387778}, {989/100000, -57.85680483309869}, 
     {99/10000, -57.79830392252494}, {991/100000, -57.73996186873835}, 
     {31/3125, -57.68173169162404}, {993/100000, -57.62363176376141}, 
     {497/50000, -57.56569217982414}, {199/20000, -57.50781775038004}, 
     {249/25000, -57.45005412028681}, {997/100000, -57.39242215498675}, 
     {499/50000, -57.334851425310404}, {999/100000, -57.277437560376185}, 
     {1/100, -57.220188806496054}}
 
ImFRfinb = {{1/100, -57.220188806496054}, {11/1000, -52.01668146577818}, 
     {3/250, -47.68024105081747}, {13/1000, -44.01084375044874}, 
     {7/500, -40.86552303268249}, {3/200, -38.13945990120184}, 
     {2/125, -35.754047062796616}, {17/1000, -33.64919153071777}, 
     {9/500, -31.778064645766413}, {19/1000, -30.10385309954853}, 
     {1/50, -28.596949919520874}, {21/1000, -27.233480200910442}, 
     {11/500, -25.993889934318346}, {23/1000, -24.862005798817734}, 
     {3/125, -23.824374779435402}, {1/40, -22.86966578890253}, 
     {13/500, -21.988346734730435}, {27/1000, -21.172263134593045}, 
     {7/250, -20.414377293167483}, {29/1000, -19.708726269740474}, 
     {3/100, -19.050049326512084}, {31/1000, -18.433811494521315}, 
     {4/125, -17.856019178599105}, {33/1000, -17.31322012993831}, 
     {17/500, -16.80227350164452}, {7/200, -16.32049735774899}, 
     {9/250, -15.86541930314825}, {37/1000, -15.434907964613263}, 
     {19/500, -15.026992380047759}, {39/1000, -14.639959618818907}, 
     {1/25, -14.272236516881492}, {41/1000, -13.922408231027529}, 
     {21/500, -13.589209625596485}, {43/1000, -13.27145661672387}, 
     {11/250, -12.968109359119211}, {9/200, -12.678204965095567}, 
     {23/500, -12.400865143422322}, {47/1000, -12.135286058637362}, 
     {6/125, -11.880741784548633}, {49/1000, -11.636552275310219}, 
     {1/20, -11.402097665752244}, {51/1000, -11.176811532183091}, 
     {13/250, -10.960139817774003}, {53/1000, -10.751623292593813}, 
     {27/500, -10.55080245325722}, {11/200, -10.35724044298841}, 
     {7/125, -10.170572237814206}, {57/1000, -9.990420085332765}, 
     {29/500, -9.816441185518464}, {59/1000, -9.648345293192282}, 
     {3/50, -9.485817553603885}, {61/1000, -9.328590326789776}, 
     {31/500, -9.176401689501741}, {63/1000, -9.029030271465547}, 
     {8/125, -8.886224214866424}, {13/200, -8.747792449692582}, 
     {33/500, -8.613537484917947}, {67/1000, -8.483259532811012}, 
     {17/250, -8.356777874949248}, {69/1000, -8.233949645622147}, 
     {7/100, -8.114601421053244}, {71/1000, -7.998594764320558}, 
     {9/125, -7.88579355118576}, {73/1000, -7.776045744000179}, 
     {37/500, -7.669253417169244}, {3/40, -7.565281858086902}, 
     {19/250, -7.464018184506269}, {77/1000, -7.365375698385138}, 
     {39/500, -7.2692340098978665}, {79/1000, -7.175498270997}, 
     {2/25, -7.084098648012866}, {81/1000, -6.994923330278507}, 
     {41/500, -6.907912422374688}, {83/1000, -6.82297406932503}, 
     {21/250, -6.74003945908113}, {17/200, -6.659035841499678}, 
     {43/500, -6.57989743428274}, {87/1000, -6.502554911471561}, 
     {11/125, -6.426957988297557}, {89/1000, -6.353039097709727}, 
     {9/100, -6.280742979409638}, {91/1000, -6.210015217067328}, 
     {23/250, -6.140814918678217}, {93/1000, -6.073077990311992}, 
     {47/500, -6.006771776958656}, {19/200, -5.941840213256011}, 
     {12/125, -5.8782444846222965}, {97/1000, -5.815945471707616}, 
     {49/500, -5.754899621630008}, {99/1000, -5.6950649982825485}, 
     {1/10, -5.6364170478908076}, {101/1000, -5.57891850727632}, 
     {51/500, -5.5225267072542685}, {103/1000, -5.467209924068541}, 
     {13/125, -5.412950058869871}, {21/200, -5.359704959930948}, 
     {53/500, -5.307445350924988}, {107/1000, -5.256153664147828}, 
     {27/250, -5.205796210989927}, {109/1000, -5.156347868101237}, 
     {11/100, -5.107781657325175}, {111/1000, -5.060078169286253}, 
     {14/125, -5.013213353927581}, {113/1000, -4.967157622815643}, 
     {57/500, -4.921904422569854}, {23/200, -4.877416797806923}, 
     {29/250, -4.833687927648292}, {117/1000, -4.790690752191948}, 
     {59/500, -4.748415161263036}, {119/1000, -4.70683312497523}, 
     {3/25, -4.66592960302367}, {121/1000, -4.6256863432016}, 
     {61/500, -4.586098519141768}, {123/1000, -4.54713681602308}, 
     {31/250, -4.508791212511143}, {1/8, -4.471047489167101}, 
     {63/500, -4.433885842334564}, {127/1000, -4.397302707194781}, 
     {16/125, -4.361281496663276}, {129/1000, -4.325800761009733}, 
     {13/100, -4.290859976442695}, {131/1000, -4.256436619345017}, 
     {33/250, -4.222522027318927}, {133/1000, -4.189111891867633}, 
     {67/500, -4.156183959284338}, {27/200, -4.12373844589216}, 
     {17/125, -4.09175550121328}, {137/1000, -4.06022703433646}, 
     {69/500, -4.029143186028547}, {139/1000, -3.9985018443505957}, 
     {7/50, -3.968285467796008}, {141/1000, -3.93848502474159}, 
     {71/500, -3.909091663917107}, {143/1000, -3.880102857956178}, 
     {18/125, -3.8515085137537}, {29/200, -3.823292605742507}, 
     {73/500, -3.795459945979074}, {147/1000, -3.7679934821719065}, 
     {37/250, -3.740882723490796}, {149/1000, -3.7141307316202257}, 
     {3/20, -3.687728596340733}, {151/1000, -3.6616641458555534}, 
     {19/125, -3.635931871154141}, {153/1000, -3.610528431674749}, 
     {77/500, -3.585444983457762}, {31/200, -3.5606750239356}, 
     {39/250, -3.536210707404072}, {157/1000, -3.512055204780097}, 
     {79/500, -3.4881932370711066}, {159/1000, -3.4646223715592956}, 
     {4/25, -3.4413381306510766}, {161/1000, -3.4183340466701795}, 
     {81/500, -3.3956055526839046}, {163/1000, -3.3731462049089975}, 
     {41/250, -3.350950097187197}, {33/200, -3.3290193880816696}, 
     {83/500, -3.3073422428960955}, {167/1000, -3.285917248000472}, 
     {21/125, -3.2647361010849494}, {169/1000, -3.2437990759072584}, 
     {17/100, -3.2231003310696718}, {171/1000, -3.202640324521046}, 
     {43/250, -3.1824028261214616}, {173/1000, -3.1623978957296295}, 
     {87/500, -3.1426085376458355}, {7/40, -3.123041453593183}, 
     {22/125, -3.1036919729011965}, {177/1000, -3.084547075208608}, 
     {89/500, -3.065614064298705}, {179/1000, -3.04688319884112}, 
     {9/50, -3.0283532891146825}, {181/1000, -3.010024232791463}, 
     {91/500, -2.9918839204147005}, {183/1000, -2.9739400978760067}, 
     {23/125, -2.9561814112384983}, {37/200, -2.9386044880053337}, 
     {93/500, -2.9212152091381993}, {187/1000, -2.904000696995525}, 
     {47/250, -2.886966595540583}, {189/1000, -2.8701030786427193}, 
     {19/100, -2.853407191388218}, {191/1000, -2.836886061153163}, 
     {24/125, -2.820523802854158}, {193/1000, -2.8043300677575456}, 
     {97/500, -2.7882943281615464}, {39/200, -2.7724141458690967}, 
     {49/250, -2.7566919590370738}, {197/1000, -2.741123064842075}, 
     {99/500, -2.7257052094440803}, {199/1000, -2.710438187726292}, 
     {1/5, -2.695312913053539}, {201/1000, -2.680335029135308}, 
     {101/500, -2.665500788960193}, {203/1000, -2.650803679988705}, 
     {51/250, -2.6362464505589056}, {41/200, -2.621823115326281}, 
     {103/500, -2.6075361730570297}, {207/1000, -2.5933796614622926}, 
     {26/125, -2.5793548064819474}, {209/1000, -2.5654566453141046}, 
     {21/100, -2.551686016394435}, {211/1000, -2.5380383315222814}, 
     {53/250, -2.5245158757466957}, {213/1000, -2.511116444091865}, 
     {107/500, -2.4978353220333203}, {43/200, -2.4846708509553643}, 
     {27/125, -2.4716251172094053}, {217/1000, -2.4586909961640027}, 
     {109/500, -2.445875157368726}, {219/1000, -2.433167157996844}, 
     {11/50, -2.420571587832896}, {221/1000, -2.4080808498322552}, 
     {111/500, -2.3957005625971792}, {223/1000, -2.383427978693737}, 
     {28/125, -2.37125802881134}, {9/40, -2.359191555152109}, 
     {113/500, -2.347223731184468}, {227/1000, -2.335360818144241}, 
     {57/250, -2.3235955027130393}, {229/1000, -2.311926282769452}, 
     {23/100, -2.3003573338974106}, {231/1000, -2.288882637369606}, 
     {29/125, -2.277501434743745}, {233/1000, -2.2662121992252526}, 
     {117/500, -2.255017088160421}, {47/200, -2.24390822560849}, 
     {59/250, -2.2328922026915254}, {237/1000, -2.221966392713715}, 
     {119/500, -2.211126354007205}, {239/1000, -2.200369812796654}, 
     {6/25, -2.189700854844351}, {241/1000, -2.179116024197982}, 
     {121/500, -2.168615615327597}, {243/1000, -2.1581964550513124}, 
     {61/250, -2.147856360664372}, {49/200, -2.1376001980541854}, 
     {123/500, -2.127421980375054}, {247/1000, -2.117319206460569}, 
     {31/125, -2.1072952767621356}, {249/1000, -2.0973500181204265}, 
     {1/4, -2.0874783658748886}, {251/1000, -2.0776801160120444}, 
     {63/250, -2.0679595289958654}, {253/1000, -2.0583089918200828}, 
     {127/500, -2.0487291675266612}, {51/200, -2.039224615469592}, 
     {32/125, -2.029788348071577}, {257/1000, -2.020421943161676}, 
     {129/500, -2.011121849640153}, {259/1000, -2.0018939551449595}, 
     {13/50, -1.9927319657664548}, {261/1000, -1.9836337961218864}, 
     {131/500, -1.974605649978618}, {263/1000, -1.9656403131841005}, 
     {33/125, -1.9567402059991958}, {53/200, -1.947901151079023}, 
     {133/500, -1.9391286915661565}, {267/1000, -1.9304151279931947}, 
     {67/250, -1.9217668087697106}, {269/1000, -1.9131767011837106}, 
     {27/100, -1.9046464793463471}, {271/1000, -1.8961790854631353}, 
     {34/125, -1.8877664200352489}, {273/1000, -1.8794161241406098}, 
     {137/500, -1.8711215294943861}, {11/40, -1.8628834391682876}, 
     {69/250, -1.8547036027786796}, {277/1000, -1.846576529190251}, 
     {139/500, -1.8385083341698198}, {279/1000, -1.8304917154758993}, 
     {7/25, -1.8225328809332684}, {281/1000, -1.8146256096510585}, 
     {141/500, -1.806771308974005}, {283/1000, -1.7989690323864709}, 
     {71/250, -1.791220021725279}, {57/200, -1.7835219426821967}, 
     {143/500, -1.775873910523205}, {287/1000, -1.7682778618595045}, 
     {36/125, -1.7607305073790211}, {289/1000, -1.753233301999769}, 
     {29/100, -1.7457831531964647}, {291/1000, -1.7383825670714694}, 
     {73/250, -1.7310317988479667}, {293/1000, -1.7237270719393525}, 
     {147/500, -1.7164678098147004}, {59/200, -1.709257987198873}, 
     {37/125, -1.7020927839495639}, {297/1000, -1.6949712686609946}, 
     {149/500, -1.6878967089981471}, {299/1000, -1.6808686050242962}, 
     {3/10, -1.673883272483648}, {301/1000, -1.6669409808702742}, 
     {151/500, -1.6600433994474817}, {303/1000, -1.6531879534844638}, 
     {38/125, -1.6463763173957506}, {61/200, -1.6396048988062746}, 
     {153/500, -1.6328779909704867}, {307/1000, -1.6261912140007029}, 
     {77/250, -1.6195457668441224}, {309/1000, -1.612940791851056}, 
     {31/100, -1.606376093399136}, {311/1000, -1.5998509961748688}, 
     {39/125, -1.5933652229387159}, {313/1000, -1.5869185002264037}, 
     {157/500, -1.5805127688301621}, {63/200, -1.57414421205814}, 
     {79/250, -1.5678130570727307}, {317/1000, -1.5615194655523963}, 
     {159/500, -1.5552653241421024}, {319/1000, -1.5490473830888871}, 
     {8/25, -1.5428656505175726}, {321/1000, -1.5367194667413009}, 
     {161/500, -1.530612022216017}, {323/1000, -1.5245377936210285}, 
     {81/250, -1.5185015914801558}, {13/40, -1.5124993545965455}, 
     {163/500, -1.5065307137294406}, {327/1000, -1.5005976294794694}, 
     {41/125, -1.4946999640640621}, {329/1000, -1.4888355762677639}, 
     {33/100, -1.483004392376738}, {331/1000, -1.4772072112579382}, 
     {83/250, -1.4714412079476973}, {333/1000, -1.4657093366954803}, 
     {167/500, -1.4600113971011264}, {67/200, -1.4543439892532657}, 
     {42/125, -1.448708501642808}, {337/1000, -1.4431058627351638}, 
     {169/500, -1.4375345634753125}, {339/1000, -1.4319927879595016}, 
     {17/50, -1.426484174466609}, {341/1000, -1.421004565535303}, 
     {171/500, -1.4155564658267568}, {343/1000, -1.410136870022501}, 
     {43/125, -1.4047489807630549}, {69/200, -1.3993904767700736}, 
     {173/500, -1.3940601363836467}, {347/1000, -1.388759390179008}, 
     {87/250, -1.3834894435389078}, {349/1000, -1.37824671138472}, 
     {7/20, -1.3730312244933138}, {351/1000, -1.3678451596085612}, 
     {44/125, -1.3626880095801628}, {353/1000, -1.357558322082302}, 
     {177/500, -1.3524552972838209}, {71/200, -1.3473790228729428}, 
     {89/250, -1.3423317820587546}, {357/1000, -1.3373104439360433}, 
     {179/500, -1.3323159362876098}, {359/1000, -1.327346803512107}, 
     {9/25, -1.3224061746380278}, {361/1000, -1.317490342860752}, 
     {181/500, -1.312600316159596}, {363/1000, -1.3077356742766852}, 
     {91/250, -1.3028976281903635}, {73/200, -1.298083691260822}, 
     {183/500, -1.2932957898715047}, {367/1000, -1.2885316595117449}, 
     {46/125, -1.2837933555017391}, {369/1000, -1.279079205195226}, 
     {37/100, -1.2743890386293306}, {371/1000, -1.2697234017316616}, 
     {93/250, -1.2650816289849067}, {373/1000, -1.260463569150157}, 
     {187/500, -1.2558685168055668}, {3/8, -1.2512979793464845}, 
     {47/125, -1.2467491506122967}, {377/1000, -1.2422254934807548}, 
     {189/500, -1.2377228592445357}, {379/1000, -1.2332443608653545}, 
     {19/50, -1.2287873345510494}, {381/1000, -1.2243530104135274}, 
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     {106/125, -0.3101583405200947}, {849/1000, -0.30938616948463116}, 
     {17/20, -0.30861636580242213}, {851/1000, -0.3078489338075223}, 
     {213/250, -0.30708383172109044}, {853/1000, -0.30632128114703994}, 
     {427/500, -0.3055609662334018}, {171/200, -0.3048029378290513}, 
     {107/125, -0.30404739472883047}, {857/1000, -0.3032941247665917}, 
     {429/500, -0.30254310592811073}, {859/1000, -0.3017944877108272}, 
     {43/50, -0.30104818403961775}, {861/1000, -0.30030417511474017}, 
     {431/500, -0.29956246980313583}, {863/1000, -0.29882312930080257}, 
     {108/125, -0.29808601609836405}, {173/200, -0.2973511459008067}, 
     {433/500, -0.29661837710748307}, {867/1000, -0.2958880345880046}, 
     {217/250, -0.2951599954651758}, {869/1000, -0.2944340270881822}, 
     {87/100, -0.29371035604074325}, {871/1000, -0.29298908063701856}, 
     {109/125, -0.2922698644869697}, {873/1000, -0.29155271709409947}, 
     {437/500, -0.2908380597468452}, {7/8, -0.29012543656763423}, 
     {219/250, -0.28941484498278136}, {877/1000, -0.28870673320170237}, 
     {439/500, -0.28800062359556144}, {879/1000, -0.2872967132865121}, 
     {22/25, -0.2865948381245269}, {881/1000, -0.28589522732227834}, 
     {441/500, -0.28519774899713335}, {883/1000, -0.28450238365795455}, 
     {221/250, -0.28380910806657145}, {177/200, -0.2831177788979218}, 
     {443/500, -0.2824287708487634}, {887/1000, -0.28174185873850566}, 
     {111/125, -0.2810571400446964}, {889/1000, -0.2803743548775819}, 
     {89/100, -0.2796934569179934}, {891/1000, -0.27901487168390426}, 
     {223/250, -0.27833852751206356}, {893/1000, -0.2776638966634726}, 
     {447/500, -0.276991400998998}, {179/200, -0.2763211560806096}, 
     {112/125, -0.27565279340392124}, {897/1000, -0.2749863341904508}, 
     {449/500, -0.27432202154872076}, {899/1000, -0.27365975607119797}, 
     {9/10, -0.27299943814131766}, {901/1000, -0.2723411458971985}, 
     {451/500, -0.27168473228931855}, {903/1000, -0.2710304905159826}, 
     {113/125, -0.270378005917014}, {181/200, -0.269727623888091}, 
     {453/500, -0.26907918478177106}, {907/1000, -0.2684327146496901}, 
     {227/250, -0.26778813813092484}, {909/1000, -0.26714552041327244}, 
     {91/100, -0.2665049611622261}, {911/1000, -0.2658663573882889}, 
     {114/125, -0.2652294624790943}, {913/1000, -0.264594551894066}, 
     {457/500, -0.26396155062953564}, {183/200, -0.26333056828009505}, 
     {229/250, -0.2627014745843146}, {917/1000, -0.26207401632937954}, 
     {459/500, -0.26144862107337685}, {919/1000, -0.2608250745280942}, 
     {23/25, -0.26020357995531396}, {921/1000, -0.25958376259175964}, 
     {461/500, -0.258965917755583}, {923/1000, -0.2583497374272996}, 
     {231/250, -0.2577353649903711}, {37/40, -0.2571229820605141}, 
     {463/500, -0.2565125371547057}, {927/1000, -0.25590386545129595}, 
     {116/125, -0.25529688357828806}, {929/1000, -0.25469165510751357}, 
     {93/100, -0.2540885220948086}, {931/1000, -0.2534870542572185}, 
     {233/250, -0.2528873309032378}, {933/1000, -0.25228942625154893}, 
     {467/500, -0.25169317921600376}, {187/200, -0.25109874835906054}, 
     {117/125, -0.2505060768838958}, {937/1000, -0.24991548022223742}, 
     {469/500, -0.2493262032050061}, {939/1000, -0.2487390465503707}, 
     {47/50, -0.2481535062843503}, {941/1000, -0.24756940968645624}, 
     {471/500, -0.24698751825702314}, {943/1000, -0.24640712006066168}, 
     {118/125, -0.24582839274961454}, {189/200, -0.24525154932941984}, 
     {473/500, -0.24467610826463404}, {947/1000, -0.24410273079642741}, 
     {237/250, -0.24353082439496165}, {949/1000, -0.24296073484692182}, 
     {19/20, -0.2423921234393005}, {951/1000, -0.24182535132331773}, 
     {119/125, -0.24126039513382103}, {953/1000, -0.24069695139431646}, 
     {477/500, -0.24013517716408517}, {191/200, -0.23957481754370868}, 
     {239/250, -0.23901639431778832}, {957/1000, -0.23845978729591333}, 
     {479/500, -0.23790459598571956}, {959/1000, -0.23735095863706612}, 
     {24/25, -0.23679893081358294}, {961/1000, -0.23624881465579728}, 
     {481/500, -0.23570014638551195}, {963/1000, -0.23515307189873447}, 
     {241/250, -0.23460767332555132}, {193/200, -0.23406377133069034}, 
     {483/500, -0.2335215210576389}, {967/1000, -0.2329807648674984}, 
     {121/125, -0.23244154185382992}, {969/1000, -0.23190423039083496}, 
     {97/100, -0.23136808024322075}, {971/1000, -0.2308336956706767}, 
     {243/250, -0.23030107734151395}, {973/1000, -0.2297698379967379}, 
     {487/500, -0.22924003083573496}, {39/40, -0.22871199440881185}, 
     {122/125, -0.22818539683007666}, {977/1000, -0.2276604084873044}, 
     {489/500, -0.22713688601490922}, {979/1000, -0.22661466493679905}, 
     {49/50, -0.22609436939719219}, {981/1000, -0.22557544499220383}, 
     {491/500, -0.22505796752258167}, {983/1000, -0.2245419430482083}, 
     {123/125, -0.2240273841228726}, {197/200, -0.22351460176241256}, 
     {493/500, -0.22300319253196577}, {987/1000, -0.222492957485815}, 
     {247/250, -0.22198469120700448}, {989/1000, -0.22147764726685226}, 
     {99/100, -0.22097197583373984}, {991/1000, -0.2204680817191047}, 
     {124/125, -0.2199654931689916}, {993/1000, -0.21946429861443906}, 
     {497/500, -0.2189646508422154}, {199/200, -0.2184663083824967}, 
     {249/250, -0.21796946801236627}, {997/1000, -0.21747389527005812}, 
     {499/500, -0.21697992617532735}, {999/1000, -0.21648765623014343}, 
     {1, -0.21599652302419692}}
 
ImFRfinc = {{1, -0.21601042006888216}, {201/200, -0.21357406190614414}, 
     {101/100, -0.21117256456639577}, {203/200, -0.20880535336528627}, 
     {51/50, -0.20647186390861538}, {41/40, -0.2041715990228803}, 
     {103/100, -0.20190391978161237}, {207/200, -0.19966832936026813}, 
     {26/25, -0.19746430607334942}, {209/200, -0.19529132448314002}, 
     {21/20, -0.1931488898047795}, {211/200, -0.19103650928358107}, 
     {53/50, -0.18895369972897336}, {213/200, -0.18689996059511982}, 
     {107/100, -0.18487485943207083}, {43/40, -0.1828778873538175}, 
     {27/25, -0.18090860990397428}, {217/200, -0.17896657370096936}, 
     {109/100, -0.1770513277071064}, {219/200, -0.17516248162064496}, 
     {11/10, -0.17329956216244513}, {221/200, -0.17146217322468216}, 
     {111/100, -0.16964991131374907}, {223/200, -0.16786237043423702}, 
     {28/25, -0.1660991634377751}, {9/8, -0.16435989283673313}, 
     {113/100, -0.16264415067683258}, {227/200, -0.1609516059632612}, 
     {57/50, -0.15928186867481786}, {229/200, -0.15763456970768086}, 
     {23/20, -0.15600934960246304}, {231/200, -0.1544058563547237}, 
     {29/25, -0.15282374506639873}, {233/200, -0.15126267687617978}, 
     {117/100, -0.14972231921048018}, {47/40, -0.1482023742310623}, 
     {59/50, -0.14670247132464453}, {237/200, -0.14522231960780108}, 
     {119/100, -0.14376160147213457}, {239/200, -0.14232000746164797}, 
     {6/5, -0.1408972281160723}, {241/200, -0.13949296619297313}, 
     {121/100, -0.13810693003521424}, {243/200, -0.13673883430363376}, 
     {61/50, -0.13538839824996218}, {49/40, -0.1340553857120983}, 
     {123/100, -0.13273946803487813}, {247/200, -0.1314403894015903}, 
     {31/25, -0.13015788149031282}, {249/200, -0.1288916851456936}, 
     {5/4, -0.1276415467943821}, {251/200, -0.12640721680191414}, 
     {63/50, -0.1251884492122104}, {253/200, -0.12398504180751235}, 
     {127/100, -0.12279669321749598}, {51/40, -0.1216232050772903}, 
     {32/25, -0.1204643376277239}, {257/200, -0.11931985741114626}, 
     {129/100, -0.11818953307067925}, {259/200, -0.1170731536082017}, 
     {13/10, -0.11597050769168127}, {261/200, -0.1148813989716091}, 
     {131/100, -0.11380558970495147}, {263/200, -0.11274288711673908}, 
     {33/25, -0.11169309383527914}, {53/40, -0.11065600959521582}, 
     {133/100, -0.10963144079880838}, {267/200, -0.1086192040886107}, 
     {67/50, -0.10761911224143184}, {269/200, -0.10663098421995199}, 
     {27/20, -0.1056546129098721}, {271/200, -0.104689820511489}, 
     {34/25, -0.10373644844406593}, {273/200, -0.10279433231637669}, 
     {137/100, -0.10186328762594443}, {11/8, -0.1009431523118769}, 
     {69/50, -0.10003376661705543}, {277/200, -0.09913498410568478}, 
     {139/100, -0.09824664713386255}, {279/200, -0.09736856236045832}, 
     {7/5, -0.09650058899726988}, {281/200, -0.09564259602394354}, 
     {141/100, -0.09479442905486968}, {283/200, -0.09395594904341298}, 
     {71/50, -0.09312701660066369}, {57/40, -0.0923074795872334}, 
     {143/100, -0.09149724495773848}, {287/200, -0.09069612014710171}, 
     {36/25, -0.08990399119735049}, {289/200, -0.08912072162099172}, 
     {29/20, -0.08834619052811998}, {291/200, -0.08758027985281203}, 
     {73/50, -0.08682288204493727}, {293/200, -0.0860738601046549}, 
     {147/100, -0.085333060822395}, {59/40, -0.08460043062238198}, 
     {37/25, -0.08387581220835694}, {297/200, -0.08315910550748429}, 
     {149/100, -0.08245020385272328}, {299/200, -0.08174899930397594}, 
     {3/2, -0.08105538391776879}, {301/200, -0.0803692520837167}, 
     {151/100, -0.07969049454259802}, {303/200, -0.0790190079896429}, 
     {38/25, -0.07835469563387032}, {61/40, -0.07769745842839848}, 
     {153/100, -0.07704720060852854}, {307/200, -0.07640382827964953}, 
     {77/50, -0.07576725096839887}, {309/200, -0.07513737078177196}, 
     {31/20, -0.07451410729245}, {311/200, -0.07389736433188032}, 
     {39/25, -0.07328707067277906}, {313/200, -0.07268311769048252}, 
     {157/100, -0.0720854311638166}, {63/40, -0.07149392782863417}, 
     {79/50, -0.07090852462360497}, {317/200, -0.07032914000192547}, 
     {159/100, -0.06975569433238449}, {319/200, -0.06918810974586975}, 
     {8/5, -0.06862630845911255}, {321/200, -0.06807019446215157}, 
     {161/100, -0.06751973411792034}, {323/200, -0.06697483822775929}, 
     {81/50, -0.06643543461838086}, {13/8, -0.06590143929758252}, 
     {163/100, -0.06537278429322302}, {327/200, -0.06484942138046712}, 
     {41/25, -0.06433127156895058}, {329/200, -0.06381826598749663}, 
     {33/20, -0.06331033635557004}, {331/200, -0.06280741667983958}, 
     {83/50, -0.062309442288726924}, {333/200, -0.061816328492984685}, 
     {167/100, -0.061328062640855}, {67/40, -0.06084455514360654}, 
     {42/25, -0.06036574938339889}, {337/200, -0.059891567221083575}, 
     {169/100, -0.059421977596588516}, {339/200, -0.05895691180788165}, 
     {17/10, -0.05849632386817638}, {341/200, -0.05804012420523419}, 
     {171/100, -0.05758827459911453}, {343/200, -0.057140720221214636}, 
     {43/25, -0.05669740859776384}, {69/40, -0.05625828914966169}, 
     {173/100, -0.05582330200358632}, {347/200, -0.05539240803869605}, 
     {87/50, -0.05496554356455419}, {349/200, -0.05454265778627909}, 
     {7/4, -0.05412369973131592}, {351/200, -0.05370861983649}, 
     {44/25, -0.0532973700840178}, {353/200, -0.052889904952246436}, 
     {177/100, -0.05248616806041162}, {71/40, -0.05208612537412893}, 
     {89/50, -0.051689725378144424}, {357/200, -0.051296923441757736}, 
     {179/100, -0.050907676029101956}, {359/200, -0.050521957212973145}, 
     {9/5, -0.050139670397656544}, {361/200, -0.0497608100260325}, 
     {181/100, -0.04938532956566588}, {363/200, -0.04901318071020688}, 
     {91/50, -0.048644322828822806}, {73/40, -0.04827871850674981}, 
     {183/100, -0.047916329204872765}, {367/200, -0.047557110150668214}, 
     {46/25, -0.04720102438602669}, {369/200, -0.04684803851083075}, 
     {37/20, -0.04649810852079517}, {371/200, -0.046151192822370124}, 
     {93/50, -0.0458072542387824}, {373/200, -0.04546625816662553}, 
     {187/100, -0.045128190488881725}, {15/8, -0.04479297654805858}, 
     {47/25, -0.0444606004746686}, {377/200, -0.044131029405549915}, 
     {189/100, -0.043804226008171576}, {379/200, -0.04348016539524313}, 
     {19/10, -0.04315880861790755}, {381/200, -0.042840125465599566}, 
     {191/100, -0.04252407975998118}, {383/200, -0.042210637482287594}, 
     {48/25, -0.04189976903675985}, {77/40, -0.04159145115750129}, 
     {193/100, -0.04128564390040901}, {387/200, -0.0409823308826367}, 
     {97/50, -0.04068147851984616}, {389/200, -0.0403830648805521}, 
     {39/20, -0.04008704671309182}, {391/200, -0.039793397441635014}, 
     {49/25, -0.03950209082417239}, {393/200, -0.03921311067343569}, 
     {197/100, -0.03892642390027862}, {79/40, -0.038642011931557196}, 
     {99/50, -0.038359837560870635}, {397/200, -0.03807988627646319}, 
     {199/100, -0.037802128085174524}, {399/200, -0.03752654868481037}, 
     {2, -0.0372531139801785}, {401/200, -0.03698180667435258}, 
     {201/100, -0.03671260071403121}, {403/200, -0.03644547517838059}, 
     {101/50, -0.03618040463248673}, {81/40, -0.035917368351064516}, 
     {203/100, -0.03565634584138844}, {407/200, -0.035397317453266686}, 
     {51/25, -0.03514026164587769}, {409/200, -0.03488516321301788}, 
     {41/20, -0.0346320008282594}, {411/200, -0.034380758735310796}, 
     {103/50, -0.03413141665965008}, {413/200, -0.033883945584750996}, 
     {207/100, -0.033638331499496965}, {83/40, -0.03339454933502442}, 
     {52/25, -0.033152600303287094}, {417/200, -0.032912453276612186}, 
     {209/100, -0.03267409368620844}, {419/200, -0.03243750603370196}, 
     {21/10, -0.03220267487912511}, {421/200, -0.03196958494170235}, 
     {211/100, -0.03173822008522113}, {423/200, -0.031508564821476175}, 
     {53/25, -0.03128060573641869}, {17/8, -0.03105431641162227}, 
     {213/100, -0.030829678854170966}, {427/200, -0.030606694573064943}, 
     {107/50, -0.030385339582044472}, {429/200, -0.030165598421122895}, 
     {43/20, -0.02994746550310272}, {431/200, -0.0297309183936105}, 
     {54/25, -0.029515951883837134}, {433/200, -0.029302555741050076}, 
     {217/100, -0.02909070703518786}, {87/40, -0.028880376728073254}, 
     {109/50, -0.028671582604846757}, {437/200, -0.02846429200245415}, 
     {219/100, -0.028258494191599037}, {439/200, -0.028054178128884416}, 
     {11/5, -0.027851325343847988}, {441/200, -0.027649943592495785}, 
     {221/100, -0.027450002654055283}, {443/200, -0.027251501876762896}, 
     {111/50, -0.027054431043638305}, {89/40, -0.026858774222301096}, 
     {223/100, -0.02666450761523831}, {447/200, -0.026471612656886467}, 
     {56/25, -0.02628009956860683}, {449/200, -0.026089950621261737}, 
     {9/4, -0.02590115892524969}, {451/200, -0.02571370417098856}, 
     {113/50, -0.025527583471051107}, {453/200, -0.02534278847652993}, 
     {227/100, -0.02515931607026206}, {91/40, -0.024977104274757134}, 
     {57/25, -0.02479619289889734}, {457/200, -0.02461656542673807}, 
     {229/100, -0.0244381893885105}, {459/200, -0.024261060110642274}, 
     {23/10, -0.024085180373709603}, {461/200, -0.02391055447363799}, 
     {231/100, -0.023737145944467186}, {463/200, -0.023564955968770396}, 
     {58/25, -0.023393928574480638}, {93/40, -0.023224124626322284}, 
     {233/100, -0.023055489064708334}, {467/200, -0.022888018145706956}, 
     {117/50, -0.02272171774330367}, {469/200, -0.022556566826437585}, 
     {47/20, -0.022392552175586777}, {471/200, -0.022229681550952396}, 
     {59/25, -0.022067927210206895}, {473/200, -0.021907313123045835}, 
     {237/100, -0.021747772429129064}, {19/8, -0.021589306391777252}, 
     {119/50, -0.021431957452869743}, {477/200, -0.02127565898896422}, 
     {239/100, -0.02112044666510915}, {479/200, -0.020966269994241116}, 
     {12/5, -0.020813161948042724}, {481/200, -0.02066105739631341}, 
     {241/100, -0.020510001030087377}, {483/200, -0.02036000230457935}, 
     {121/50, -0.020210984890828287}, {97/40, -0.020062958018167154}, 
     {243/100, -0.019915919851499653}, {487/200, -0.01976986617534615}, 
     {61/25, -0.019624786105876257}, {489/200, -0.019480677894011422}, 
     {49/20, -0.019337530138117565}, {491/200, -0.019195338694610653}, 
     {123/50, -0.019054086999485964}, {493/200, -0.018913785019093243}, 
     {247/100, -0.018774398304205908}, {99/40, -0.01863592447179452}, 
     {62/25, -0.018498353704858528}, {497/200, -0.018361678580277707}, 
     {249/100, -0.01822589222308091}, {499/200, -0.018091001829869224}, 
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     {19/4, 0.0005399766268534556}, {951/200, 0.0005428439852808165}, 
     {119/25, 0.0005456353298647354}, {953/200, 0.0005483845741491855}, 
     {477/100, 0.0005510932682943892}, {191/40, 0.0005537927938539244}, 
     {239/50, 0.0005564328768301596}, {957/200, 0.0005590155700678778}, 
     {479/100, 0.000561554586692381}, {959/200, 0.0005640401991071631}, 
     {24/5, 0.0005664821360196193}, {961/200, 0.0005688922248485717}, 
     {481/100, 0.0005712601564298314}, {963/200, 0.0005735984845622877}, 
     {241/50, 0.0005758953944663414}, {193/40, 0.0005781503868453886}, 
     {483/100, 0.0005803500098338077}, {967/200, 0.0005825104150607441}, 
     {121/25, 0.000584637474013272}, {969/200, 0.0005867327651378762}, 
     {97/20, 0.0005888013581629714}, {971/200, 0.0005908373477430118}, 
     {243/50, 0.0005928251705304977}, {973/200, 0.0005947742932381761}, 
     {487/100, 0.0005967002551543477}, {39/8, 0.0005985798814893695}, 
     {122/25, 0.0006004062437543478}, {977/200, 0.0006022243645726899}, 
     {489/100, 0.0006040201090784514}, {979/200, 0.0006057816919082804}, 
     {49/10, 0.0006075135531686815}, {981/200, 0.0006091910150609614}, 
     {491/100, 0.0006108557849571206}, {983/200, 0.000612457444942649}, 
     {123/25, 0.0006140624132804362}, {197/40, 0.0006156397907521871}, 
     {493/100, 0.0006171999413440155}, {987/200, 0.0006187211527035608}, 
     {247/50, 0.0006201917056589679}, {989/200, 0.0006216515961878777}, 
     {99/20, 0.0006230774690862972}, {991/200, 0.0006244807653494888}, 
     {124/25, 0.00062586167436951}, {993/200, 0.0006272184367355216}, 
     {497/100, 0.0006285527087595}, {199/40, 0.0006298615956334963}, 
     {249/50, 0.0006311424619505068}, {997/200, 0.0006323933921610347}, 
     {499/100, 0.0006336128378006123}, {999/200, 0.0006348020237947338}, 
     {5, 0.0006359673876268346}, {1001/200, 0.0006371118017076682}, 
     {501/100, 0.0006382375852327371}, {1003/200, 0.0006393423006159082}, 
     {251/50, 0.000640432614908093}, {201/40, 0.000641502448888609}, 
     {503/100, 0.0006425478843512522}, {1007/200, 0.0006435631240928608}, 
     {126/25, 0.0006445475800087586}, {1009/200, 0.0006455056221916777}, 
     {101/20, 0.0006464307235556355}, {1011/200, 0.0006473443616608066}, 
     {253/50, 0.0006482435910060147}, {1013/200, 0.0006491298712183458}, 
     {507/100, 0.0006499956223597891}, {203/40, 0.0006508421558124589}, 
     {127/25, 0.0006516389970157022}, {1017/200, 0.0006524071701599077}, 
     {509/100, 0.0006532845362774431}, {1019/200, 0.0006539057804615389}, 
     {51/10, 0.0006546312000041965}, {1021/200, 0.0006553246882199382}, 
     {511/100, 0.0006560048659731699}, {1023/200, 0.0006566633600413319}, 
     {128/25, 0.0006573326694572224}, {41/8, 0.0006579181276546997}, 
     {513/100, 0.0006584970250460565}, {1027/200, 0.0006590161435280351}, 
     {257/50, 0.0006595516158305337}, {1029/200, 0.0006600793570576968}, 
     {103/20, 0.000660566715354971}, {1031/200, 0.0006610420163806197}, 
     {129/25, 0.000661528916406251}, {1033/200, 0.000661945460310065}, 
     {517/100, 0.0006623789802540081}, {207/40, 0.0006626863721983511}, 
     {259/50, 0.0006630547960968514}, {1037/200, 0.000663369398480107}, 
     {519/100, 0.0006636810092235379}, {1039/200, 0.0006640171731335798}, 
     {26/5, 0.0006642787349164792}, {1041/200, 0.0006645715488180493}, 
     {521/100, 0.0006647099605707751}, {1043/200, 0.0006648935866118144}, 
     {261/50, 0.0006650702075741144}, {209/40, 0.0006651970693360987}, 
     {523/100, 0.0006653607611766255}, {1047/200, 0.0006654718603034127}, 
     {131/25, 0.0006655170471550065}, {1049/200, 0.0006655427175679129}, 
     {21/4, 0.0006655973777900392}, {1051/200, 0.0006656306378252097}, 
     {263/50, 0.0006656327201275403}, {1053/200, 0.0006655944688658266}, 
     {527/100, 0.0006655979305087989}, {211/40, 0.0006654402754699973}, 
     {132/25, 0.0006653137290348887}, {1057/200, 0.0006652004113560928}, 
     {529/100, 0.0006651277220610652}, {1059/200, 0.0006649506647571357}, 
     {53/10, 0.0006647264003016851}, {1061/200, 0.000664501520061922}, 
     {531/100, 0.0006643149800034109}, {1063/200, 0.0006640706391620732}, 
     {133/25, 0.0006637893178274012}, {213/40, 0.0006634820923783202}, 
     {533/100, 0.0006631470083378055}, {1067/200, 0.0006628396481334065}, 
     {267/50, 0.0006624798635743723}, {1069/200, 0.0006621264917154868}, 
     {107/20, 0.0006617401232218434}, {1071/200, 0.0006613042889940246}, 
     {134/25, 0.0006608539596300034}, {1073/200, 0.0006604107941892146}, 
     {537/100, 0.0006599680801882002}, {43/8, 0.0006595196352678911}, 
     {269/50, 0.0006590074610559604}, {1077/200, 0.0006585406226178314}, 
     {539/100, 0.0006579289896966323}, {1079/200, 0.0006573576622193045}, 
     {27/5, 0.0006567875413177049}, {1081/200, 0.0006562790176483091}, 
     {541/100, 0.0006556722429222894}, {1083/200, 0.0006550302476413528}, 
     {271/50, 0.000654380855342751}, {217/40, 0.0006537340335341923}, 
     {543/100, 0.0006530547730347891}, {1087/200, 0.0006524345923475394}, 
     {136/25, 0.0006517684770019905}, {1089/200, 0.0006510082415349672}, 
     {109/20, 0.0006502823151097736}, {1091/200, 0.0006495636328245347}, 
     {273/50, 0.0006488201266332538}, {1093/200, 0.0006480535882120719}, 
     {547/100, 0.0006472965860422342}, {219/40, 0.0006465047000254742}, 
     {137/25, 0.0006457130915702436}, {1097/200, 0.000644922726174002}, 
     {549/100, 0.0006441636959890751}, {1099/200, 0.0006432937949467643}, 
     {11/2, 0.0006424629723889019}, {1101/200, 0.0006416203572832124}, 
     {551/100, 0.0006407500939560329}, {1103/200, 0.0006399469903286548}, 
     {138/25, 0.0006390535554212651}, {221/40, 0.0006381664416243993}, 
     {553/100, 0.0006372658320599189}, {1107/200, 0.0006363494129024705}, 
     {277/50, 0.0006354436049755829}, {1109/200, 0.0006345122598905295}, 
     {111/20, 0.0006335801792247686}, {1111/200, 0.0006326491110659749}, 
     {139/25, 0.0006317120800585219}, {1113/200, 0.0006307540302989967}, 
     {557/100, 0.0006297931524998912}, {223/40, 0.0006288343229805538}, 
     {279/50, 0.0006278674021991115}, {1117/200, 0.0006268866325156441}, 
     {559/100, 0.0006258904794727016}, {1119/200, 0.0006248859142303775}, 
     {28/5, 0.000623938256846257}, {1121/200, 0.00062291182505958}, 
     {561/100, 0.0006218812331701962}, {1123/200, 0.000620842776680286}, 
     {281/50, 0.0006198063697662182}, {45/8, 0.0006187633590502006}, 
     {563/100, 0.0006177102792539468}, {1127/200, 0.0006166587446532201}, 
     {141/25, 0.000615598384577698}, {1129/200, 0.0006145383624733824}, 
     {113/20, 0.000613447273078549}, {1131/200, 0.0006123669261053344}, 
     {283/50, 0.0006112875306767407}, {1133/200, 0.0006101929577666532}, 
     {567/100, 0.0006090821529585178}, {227/40, 0.00060796052150347}, 
     {142/25, 0.0006068329288391183}, {1137/200, 0.0006057023432042286}, 
     {569/100, 0.0006045712954940718}, {1139/200, 0.0006034269153909477}, 
     {57/10, 0.0006022774906191408}, {1141/200, 0.0006011191283432638}, 
     {571/100, 0.00059994418900855}, {1143/200, 0.000598766639115178}, 
     {143/25, 0.0005975839319449783}, {229/40, 0.0005963981293859444}, 
     {573/100, 0.0005951973057289894}, {1147/200, 0.0005939880088989824}, 
     {287/50, 0.0005927686274256327}, {1149/200, 0.0005915380992720376}, 
     {23/4, 0.0005902986926165088}, {1151/200, 0.0005890457161816798}, 
     {144/25, 0.0005877827627123189}, {1153/200, 0.0005865719568625138}, 
     {577/100, 0.000585255245704408}, {231/40, 0.0005839748078448892}, 
     {289/50, 0.0005826653231217893}, {1157/200, 0.0005813691694989132}, 
     {579/100, 0.0005800772978499236}, {1159/200, 0.0005787555768681507}, 
     {29/5, 0.0005773868367247026}, {1161/200, 0.0005760479416827557}, 
     {581/100, 0.0005746939021795683}, {1163/200, 0.0005733314986997584}, 
     {291/50, 0.0005719627113809356}, {233/40, 0.0005705622803549026}, 
     {583/100, 0.0005691814526813666}, {1167/200, 0.0005677668209671527}, 
     {146/25, 0.0005663517802934059}, {1169/200, 0.0005649386081951757}, 
     {117/20, 0.0005634827674088072}, {1171/200, 0.000562031104105909}, 
     {293/50, 0.0005605691752692543}, {1173/200, 0.000559118113356849}, 
     {587/100, 0.0005576048904873954}, {47/8, 0.0005561260719477712}, 
     {147/25, 0.000554623454801062}, {1177/200, 0.0005531109149390367}, 
     {589/100, 0.0005515938577254076}, {1179/200, 0.0005500526196193789}, 
     {59/10, 0.0005484816035021822}, {1181/200, 0.0005469485847930944}, 
     {591/100, 0.0005453863488835697}, {1183/200, 0.0005437998399806521}, 
     {148/25, 0.0005422116612054939}, {237/40, 0.000540628161604495}, 
     {593/100, 0.0005390033338263933}, {1187/200, 0.0005373937473622803}, 
     {297/50, 0.0005357686451989974}, {1189/200, 0.0005341680549990624}, 
     {119/20, 0.0005325211923179474}, {1191/200, 0.000530833270300124}, 
     {149/25, 0.0005291675260983286}, {1193/200, 0.0005275469306808}, 
     {597/100, 0.0005258683817465082}, {239/40, 0.0005241513309457435}, 
     {299/50, 0.000522453380782717}, {1197/200, 0.0005207520835424084}, 
     {599/100, 0.0005190196174809092}, {1199/200, 0.0005173135806499918}, 
     {6, 0.0005156017090320875}}
 
ImFRfind = {{6, 0.0005156017090320875}, {151/25, 0.000501516674397906}, 
     {152/25, 0.00048707606365439027}, {153/25, 0.00047239296741119485}, 
     {154/25, 0.0004575222098179288}, {31/5, 0.00044252381206477676}, 
     {156/25, 0.00042745487732970266}, {157/25, 0.0004123014707259204}, 
     {158/25, 0.00039697829480286884}, {159/25, 0.00038147601943594456}, 
     {32/5, 0.0003657672867352635}, {161/25, 0.0003497933580269841}, 
     {162/25, 0.0003335474386388926}, {163/25, 0.000316987414747838}, 
     {164/25, 0.00030017950385974324}, {33/5, 0.0002832068172353708}, 
     {166/25, 0.00026611545296795214}, {167/25, 0.0002490106485601995}, 
     {168/25, 0.0002319816868956437}, {169/25, 0.0002151127083138693}, 
     {34/5, 0.0001984648126338584}, {171/25, 0.00018201136931650375}, 
     {172/25, 0.0001658844021186212}, {173/25, 0.00014995775129400535}, 
     {174/25, 0.0001342429451831606}, {7, 0.0001186727691067091}, 
     {176/25, 0.00010325598516258694}, {177/25, 0.00008798757151629033}, 
     {178/25, 0.00007281195053598921}, {179/25, 0.00005781636743051877}, 
     {36/5, 0.00004306838014134229}, {181/25, 0.000028612717423381895}, 
     {182/25, 0.000014532612885531648}, {183/25, 9.314250712932903*^-7}, 
     {184/25, -0.000012184940846537984}, {37/5, -0.000024697345962110262}, 
     {186/25, -0.00003659973516390025}, {187/25, -0.000047899378475158016}, 
     {188/25, -0.00005864959935353298}, {189/25, -0.00006881882442799636}, 
     {38/5, -0.00007845956189989067}, {191/25, -0.00008758297481215038}, 
     {192/25, -0.0000962829602135784}, {193/25, -0.00010449769477371973}, 
     {194/25, -0.00011219878408619266}, {39/5, -0.00011939416004791426}, 
     {196/25, -0.00012607109101003822}, {197/25, -0.00013209319785612017}, 
     {198/25, -0.00013744314690899984}, {199/25, -0.00014207873144522765}, 
     {8, -0.0001459761998647835}, {201/25, -0.00014912962363977655}, 
     {202/25, -0.00015155743259609444}, {203/25, -0.0001532926371610177}, 
     {204/25, -0.00015439234923553258}, {41/5, -0.00015489203646157357}, 
     {206/25, -0.0001548473278524254}, {207/25, -0.00015429984413828368}, 
     {208/25, -0.0001533041769820609}, {209/25, -0.00015176573481401334}, 
     {42/5, -0.0001498021902981428}, {211/25, -0.0001473506353196971}, 
     {212/25, -0.00014438695245423683}, {213/25, -0.00014089110376552805}, 
     {214/25, -0.00013687334993911504}, {43/5, -0.0001322728268537965}, 
     {216/25, -0.00012723635119205046}, {217/25, -0.00012159370618569643}, 
     {218/25, -0.00011557118783755982}, {219/25, -0.00010917545692668007}, 
     {44/5, -0.00010248333513684926}, {221/25, -0.00009555946140316074}, 
     {222/25, -0.00008840640624852014}, {223/25, -0.00008116634936583544}, 
     {224/25, -0.00007372838557317962}, {9, -0.00006622592607619104}, 
     {226/25, -0.000058625140231916006}, {227/25, -0.00005092543934992477}, 
     {228/25, -0.000043105468302773176}, {229/25, -0.00003514860893538696}, 
     {46/5, -0.000027146324608651184}, {231/25, -0.000019072207894765825}, 
     {232/25, -0.000010916320987597317}, {233/25, -2.7802040580837684*^-6}, 
     {234/25, 5.228023356451672*^-6}, {47/5, 0.000013181198415423978}, 
     {236/25, 0.0000209062888689715}, {237/25, 0.00002837165571811795}, 
     {238/25, 0.00003554151938223171}, {239/25, 0.00004242400396359258}, 
     {48/5, 0.00004891541516727216}, {241/25, 0.00005518124550452086}, 
     {242/25, 0.00006119435319806854}, {243/25, 0.00006676802184335529}, 
     {244/25, 0.0000722187454007539}, {49/5, 0.00007729416899771024}, 
     {246/25, 0.00008212453084066595}, {247/25, 0.00008655920392053318}, 
     {248/25, 0.00009069692789465122}, {249/25, 0.00009443986434076734}, 
     {10, 0.00009777049064751964}, {251/25, 0.00010062818556222375}, 
     {252/25, 0.0001030042021177291}, {253/25, 0.00010488974184186262}, 
     {254/25, 0.00010625436954603273}, {51/5, 0.00010713803732276261}, 
     {256/25, 0.00010755339238621708}, {257/25, 0.0001075213288883603}, 
     {258/25, 0.00010707892220551685}, {259/25, 0.00010625519343432366}, 
     {52/5, 0.00010506761608608528}, {261/25, 0.00010354265004752783}, 
     {262/25, 0.00010167397570759462}, {263/25, 0.00009943077063767625}, 
     {264/25, 0.0000968639828232698}, {53/5, 0.0000939272704734706}, 
     {266/25, 0.00009058146275894852}, {267/25, 0.00008687192152930998}, 
     {268/25, 0.00008277364911814244}, {269/25, 0.00007835122485128077}, 
     {54/5, 0.00007356169142280766}, {271/25, 0.00006849390026530955}, 
     {272/25, 0.00006315519251298696}, {273/25, 0.00005763832262961621}, 
     {274/25, 0.00005195190653650705}, {11, 0.000046173339788069256}, 
     {276/25, 0.00004030071364269361}, {277/25, 0.00003432193493480007}, 
     {278/25, 0.00002832718210066254}, {279/25, 0.000022232774178121417}, 
     {56/5, 0.000016082954550578066}, {281/25, 9.87265028817852*^-6}, 
     {282/25, 3.6024014742341848*^-6}, {283/25, -2.6875179057750387*^-6}, 
     {284/25, -9.000759847666018*^-6}, {57/5, -0.00001528175216103378}, 
     {286/25, -0.000021542915711769695}, {287/25, -0.00002766493628536537}, 
     {288/25, -0.000033659871805813424}, {289/25, -0.000039499776015361476}, 
     {58/5, -0.000045095142729323356}, {291/25, -0.00005045134781456184}, 
     {292/25, -0.00005556768640513354}, {293/25, -0.00006038491652748945}, 
     {294/25, -0.00006498065986715318}, {59/5, -0.00006932214826793626}, 
     {296/25, -0.00007338344172413969}, {297/25, -0.0000772124920205286}, 
     {298/25, -0.00008083060517583007}, {299/25, -0.00008415446257270531}, 
     {12, -0.00008719073084950679}, {301/25, -0.00008997041082015045}, 
     {302/25, -0.00009241405071014341}, {303/25, -0.0000944603923009879}, 
     {304/25, -0.00009615174836774543}, {61/5, -0.00009748488651339926}, 
     {306/25, -0.00009839847596726514}, {307/25, -0.00009894449627800839}, 
     {308/25, -0.00009905956679134853}, {309/25, -0.00009879761534792308}, 
     {62/5, -0.00009826697259396333}, {311/25, -0.00009736325397668999}, 
     {312/25, -0.00009615721614220085}, {313/25, -0.00009466355182841113}, 
     {314/25, -0.00009290069672962531}, {63/5, -0.00009090323181526472}, 
     {316/25, -0.00008854863752705278}, {317/25, -0.00008600076582354621}, 
     {318/25, -0.00008305148084652991}, {319/25, -0.00007986088761635646}, 
     {64/5, -0.00007639516121182854}, {321/25, -0.000072611391560784}, 
     {322/25, -0.00006856492552703708}, {323/25, -0.00006429447298164637}, 
     {324/25, -0.00005981037757174165}, {13, -0.00005517063966951896}, 
     {326/25, -0.00005032429069587452}, {327/25, -0.0000454329787297203}, 
     {328/25, -0.000040425225973916845}, {329/25, -0.00003535227511786143}, 
     {66/5, -0.000030227574583707728}, {331/25, -0.000025037839795460926}, 
     {332/25, -0.00001984940208732411}, {333/25, -0.000014593603469226224}, 
     {334/25, -9.29426662032995*^-6}, {67/5, -3.979364882500391*^-6}, 
     {336/25, 1.348420888946933*^-6}, {337/25, 6.6727997287685525*^-6}, 
     {338/25, 0.000011963234156198155}, {339/25, 0.00001719943997380291}, 
     {68/5, 0.000022321610224862454}, {341/25, 0.000027318021615263532}, 
     {342/25, 0.000032164614656160495}, {343/25, 0.000036830745006710686}, 
     {344/25, 0.00004130588176054495}, {69/5, 0.000045577754850256724}, 
     {346/25, 0.00004963873006946784}, {347/25, 0.00005349175166280418}, 
     {348/25, 0.00005712028394455615}, {349/25, 0.00006056024783651637}, 
     {14, 0.00006381458573700982}, {351/25, 0.00006687021655160663}, 
     {352/25, 0.00006971253177256997}, {353/25, 0.00007229087617144359}, 
     {354/25, 0.00007463864233248074}, {71/5, 0.00007675384543537334}, 
     {356/25, 0.00007855635650289017}, {357/25, 0.00008003381328514081}, 
     {358/25, 0.00008122584208081207}, {359/25, 0.00008211848475214722}, 
     {72/5, 0.00008269009496375546}, {361/25, 0.00008295929966273263}, 
     {362/25, 0.00008291083185385517}, {363/25, 0.00008262829083216516}, 
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     {32, -0.000017190582819015532}, {801/25, -0.00001719297468660841}, 
     {802/25, -0.000017104488751806812}, {803/25, -0.000016966209557878198}, 
     {804/25, -0.000016795324442764326}, {161/5, -0.000016593778995710462}, 
     {806/25, -0.00001632531035578033}, {807/25, -0.00001599395884221977}, 
     {808/25, -0.000015660624332780593}, {809/25, -0.000015294189627979016}, 
     {162/5, -0.000014876134434460564}, {811/25, -0.000014487892882719677}, 
     {812/25, -0.000014018263913229134}, {813/25, -0.00001350907534686252}, 
     {814/25, -0.000013002489533897599}, {163/5, -0.000012465703616626467}, 
     {816/25, -0.000011883971282600214}, {817/25, -0.000011285534742722092}, 
     {818/25, -0.00001064111449544658}, {819/25, -9.985004591706037*^-6}, 
     {164/5, -9.350026760113206*^-6}, {821/25, -8.598497232059632*^-6}, 
     {822/25, -7.904640014266828*^-6}, {823/25, -7.15698781295071*^-6}, 
     {824/25, -6.4597162397206365*^-6}, {33, -5.719363632861185*^-6}, 
     {826/25, -4.989263266544364*^-6}, {827/25, -4.241302268857827*^-6}, 
     {828/25, -3.5204475234557053*^-6}, {829/25, -2.7981902497916517*^-6}, 
     {166/5, -2.0453755246886*^-6}, {831/25, -1.3368121499490737*^-6}, 
     {832/25, -5.383166071307177*^-7}, {833/25, 1.6170066766130198*^-7}, 
     {834/25, 8.804600255957196*^-7}, {167/5, 1.6380676004235095*^-6}, 
     {836/25, 2.3561498607715947*^-6}, {837/25, 3.0779601336572426*^-6}, 
     {838/25, 3.739494128685017*^-6}, {839/25, 4.380859932706649*^-6}, 
     {168/5, 5.026915916445107*^-6}, {841/25, 5.675531912913145*^-6}, 
     {842/25, 6.228845829014951*^-6}, {843/25, 6.7903039554506606*^-6}, 
     {844/25, 7.350731177246939*^-6}, {169/5, 7.878914428216532*^-6}, 
     {846/25, 8.361168457371448*^-6}, {847/25, 8.900215460239114*^-6}, 
     {848/25, 9.336797155146126*^-6}, {849/25, 9.80933118754912*^-6}, 
     {34, 0.00001018645678957375}, {851/25, 0.000010627063817936211}, 
     {852/25, 0.000010945022559494255}, {853/25, 0.000011289399669656142}, 
     {854/25, 0.000011573591942037886}, {171/5, 0.000011890555454030505}, 
     {856/25, 0.000012112647249207242}, {857/25, 0.000012318835468594358}, 
     {858/25, 0.000012431183716354877}, {859/25, 0.000012598651177864184}, 
     {172/5, 0.00001265763083502236}, {861/25, 0.000012772534665306257}, 
     {862/25, 0.000012766178987988486}, {863/25, 0.00001281782222828376}, 
     {864/25, 0.000012837742339066871}, {173/5, 0.000012801937891049331}, 
     {866/25, 0.000012760235145403698}, {867/25, 0.000012695116047956034}, 
     {868/25, 0.000012650575539452369}, {869/25, 0.000012434434084052093}, 
     {174/5, 0.00001225483397893079}, {871/25, 0.000012087673781191466}, 
     {872/25, 0.000011880796128238558}, {873/25, 0.000011634590009301782}, 
     {874/25, 0.000011302016020175998}, {35, 0.000011010623023111066}, 
     {876/25, 0.000010679998351470488}, {877/25, 0.000010354455404315566}, 
     {878/25, 0.000010043171043916388}, {879/25, 9.628689108698296*^-6}, 
     {176/5, 9.2762378228195*^-6}, {881/25, 8.882298103696229*^-6}, 
     {882/25, 8.506027804833227*^-6}, {883/25, 8.090457414622332*^-6}, 
     {884/25, 7.604934646271433*^-6}, {177/5, 7.1577140134393424*^-6}, 
     {886/25, 6.733661376712163*^-6}, {887/25, 6.230741366047843*^-6}, 
     {888/25, 5.722606968683319*^-6}, {889/25, 5.1959740912516095*^-6}, 
     {178/5, 4.660258091954139*^-6}, {891/25, 4.191254242363884*^-6}, 
     {892/25, 3.675436448608016*^-6}, {893/25, 3.13418042008351*^-6}, 
     {894/25, 2.6321857166181073*^-6}, {179/5, 2.0718402455755652*^-6}, 
     {896/25, 1.612284367008901*^-6}, {897/25, 1.0774096566579239*^-6}, 
     {898/25, 5.778983422285999*^-7}, {899/25, 2.580502207055746*^-8}, 
     {36, -4.778701198637769*^-7}, {901/25, -9.827024783221061*^-7}, 
     {902/25, -1.4778278215887841*^-6}, {903/25, -2.0338648200890486*^-6}, 
     {904/25, -2.5133160914125874*^-6}, {181/5, -3.0346485343779595*^-6}, 
     {906/25, -3.527809621983735*^-6}, {907/25, -3.986197791849833*^-6}, 
     {908/25, -4.4308145600302495*^-6}, {909/25, -4.919158728633466*^-6}, 
     {182/5, -5.3640611082372835*^-6}, {911/25, -5.7800451856437896*^-6}, 
     {912/25, -6.150204234889323*^-6}, {913/25, -6.507787167819856*^-6}, 
     {914/25, -6.9034503279441495*^-6}, {183/5, -7.3113809363478666*^-6}, 
     {916/25, -7.654695868608563*^-6}, {917/25, -7.987469950176962*^-6}, 
     {918/25, -8.277075704388182*^-6}, {919/25, -8.620258592884067*^-6}, 
     {184/5, -8.935981564484052*^-6}, {921/25, -9.169136881648221*^-6}, 
     {922/25, -9.470665614186302*^-6}, {923/25, -9.63243053264673*^-6}, 
     {924/25, -9.860494499913663*^-6}, {37, -0.000010042559081935298}, 
     {926/25, -0.000010163709995181236}, {927/25, -0.00001028273133757418}, 
     {928/25, -0.000010431061305271605}, {929/25, -0.000010486762758943335}, 
     {186/5, -0.000010553379513444927}, {931/25, -0.00001062351706698772}, 
     {932/25, -0.000010641319773241342}, {933/25, -0.000010686919143076956}, 
     {934/25, -0.000010651709180964364}, {187/5, -0.000010641716836568005}, 
     {936/25, -0.000010580346772148808}, {937/25, -0.000010496939181536824}, 
     {938/25, -0.00001038503721140227}, {939/25, -0.00001026708451373759}, 
     {188/5, -0.000010098428661953207}, {941/25, -9.937209367705258*^-6}, 
     {942/25, -9.70554446427796*^-6}, {943/25, -9.487494171511734*^-6}, 
     {944/25, -9.250121614068352*^-6}, {189/5, -8.988856331548778*^-6}, 
     {946/25, -8.716753415627387*^-6}, {947/25, -8.425345910195725*^-6}, 
     {948/25, -8.121199491839537*^-6}, {949/25, -7.812375861310228*^-6}, 
     {38, -7.491870131354217*^-6}, {951/25, -7.1176419008667224*^-6}, 
     {952/25, -6.745247933592768*^-6}, {953/25, -6.356618814207238*^-6}, 
     {954/25, -5.9729867127322755*^-6}, {191/5, -5.485458744888816*^-6}, 
     {956/25, -5.099083036738672*^-6}, {957/25, -4.617771788173464*^-6}, 
     {958/25, -4.1736817637111345*^-6}, {959/25, -3.6613633383891786*^-6}, 
     {192/5, -3.179568157818391*^-6}, {961/25, -2.678689362808906*^-6}, 
     {962/25, -2.1787685796892907*^-6}, {963/25, -1.7024162580585311*^-6}, 
     {964/25, -1.1905930314068391*^-6}, {193/5, -7.245420579338191*^-7}, 
     {966/25, -2.5407626150220075*^-7}, {967/25, 2.8851249567196646*^-7}, 
     {968/25, 7.504417608994451*^-7}, {969/25, 1.319914348249518*^-6}, 
     {194/5, 1.866714250120527*^-6}, {971/25, 2.3500983171165224*^-6}, 
     {972/25, 2.883312497425905*^-6}, {973/25, 3.3764457622598165*^-6}, 
     {974/25, 3.829923449411021*^-6}, {39, 4.3733323763783805*^-6}, 
     {976/25, 4.7828543101036125*^-6}, {977/25, 5.292105645204881*^-6}, 
     {978/25, 5.688047923779749*^-6}, {979/25, 6.154659938584217*^-6}, 
     {196/5, 6.53343730028233*^-6}, {981/25, 6.8985120125208965*^-6}, 
     {982/25, 7.310092389745115*^-6}, {983/25, 7.681703141804164*^-6}, 
     {984/25, 8.055929191785882*^-6}, {197/5, 8.396349091943645*^-6}, 
     {986/25, 8.790737413166827*^-6}, {987/25, 9.022413254622386*^-6}, 
     {988/25, 9.388733261506133*^-6}, {989/25, 9.561737371377443*^-6}, 
     {198/5, 9.875351156041212*^-6}, {991/25, 0.000010053973018064877}, 
     {992/25, 0.000010185460922684797}, {993/25, 0.000010382457172719572}, 
     {994/25, 0.000010460274018186944}, {199/5, 0.000010566397445732623}, 
     {996/25, 0.00001062528639206306}, {997/25, 0.000010711721875167335}, 
     {998/25, 0.000010748241880575993}, {999/25, 0.000010735320277954763}, 
     {40, 0.000010721936012370037}, {1001/25, 0.000010667193938440622}, 
     {1002/25, 0.000010585213873259836}, {1003/25, 0.000010516900627921544}, 
     {1004/25, 0.000010379109383840124}, {201/5, 0.000010233964650496752}, 
     {1006/25, 0.000010046849016676074}, {1007/25, 9.833373500467424*^-6}, 
     {1008/25, 9.59851423898428*^-6}, {1009/25, 9.32033921613451*^-6}, 
     {202/5, 9.039974730451483*^-6}, {1011/25, 8.709541080870187*^-6}, 
     {1012/25, 8.39560014259666*^-6}, {1013/25, 8.02898927773632*^-6}, 
     {1014/25, 7.661062593034007*^-6}, {203/5, 7.260395471053727*^-6}, 
     {1016/25, 6.868865446041372*^-6}, {1017/25, 6.448933104530319*^-6}, 
     {1018/25, 6.027096290550649*^-6}, {1019/25, 5.5615438223077795*^-6}, 
     {204/5, 5.1208822862552905*^-6}, {1021/25, 4.664900270415218*^-6}, 
     {1022/25, 4.149070950795752*^-6}, {1023/25, 3.649060180091479*^-6}, 
     {1024/25, 3.1116497762190276*^-6}, {41, 2.5783737726478573*^-6}, 
     {1026/25, 2.0376957348654245*^-6}, {1027/25, 1.483476804914059*^-6}, 
     {1028/25, 9.291723398335838*^-7}, {1029/25, 3.984273642676506*^-7}, 
     {206/5, -1.3707048249211873*^-7}, {1031/25, -6.768893189984526*^-7}, 
     {1032/25, -1.2051428961712407*^-6}, {1033/25, -1.7219369958937358*^-6}, 
     {1034/25, -2.253592031292717*^-6}, {207/5, -2.7514813594753385*^-6}, 
     {1036/25, -3.2896111984148657*^-6}, {1037/25, -3.7646856776152315*^-6}, 
     {1038/25, -4.272718114872731*^-6}, {1039/25, -4.769708345397916*^-6}, 
     {208/5, -5.257014130233273*^-6}, {1041/25, -5.717300536889347*^-6}, 
     {1042/25, -6.172513782043421*^-6}, {1043/25, -6.577219157172243*^-6}, 
     {1044/25, -6.975561119032525*^-6}, {209/5, -7.346036269839651*^-6}, 
     {1046/25, -7.70440485642343*^-6}, {1047/25, -8.031792052332065*^-6}, 
     {1048/25, -8.36300403195267*^-6}, {1049/25, -8.67572541818351*^-6}, 
     {42, -8.92997606460888*^-6}, {1051/25, -9.175602436295449*^-6}, 
     {1052/25, -9.401880039783261*^-6}, {1053/25, -9.5993947737405*^-6}, 
     {1054/25, -9.816672174145502*^-6}, {211/5, -9.946250251913202*^-6}, 
     {1056/25, -0.00001008157215287575}, {1057/25, -0.000010176356901148154}, 
     {1058/25, -0.000010228500190834211}, {1059/25, -0.0000102728671952379}, 
     {212/5, -0.000010275872261433783}, {1061/25, -0.000010246215601583675}, 
     {1062/25, -0.000010199109815700602}, {1063/25, -0.00001007597992702669}, 
     {1064/25, -9.998255922294419*^-6}, {213/5, -9.825268506791218*^-6}, 
     {1066/25, -9.689052771100215*^-6}, {1067/25, -9.488133813018162*^-6}, 
     {1068/25, -9.292978026209653*^-6}, {1069/25, -9.063444172952018*^-6}, 
     {214/5, -8.818893228623725*^-6}, {1071/25, -8.591545649694332*^-6}, 
     {1072/25, -8.251443072981868*^-6}, {1073/25, -7.930794600791158*^-6}, 
     {1074/25, -7.591514322724535*^-6}, {43, -7.209903470084544*^-6}, 
     {1076/25, -6.828433946837187*^-6}, {1077/25, -6.490843948492309*^-6}, 
     {1078/25, -6.032265485234056*^-6}, {1079/25, -5.629428109582557*^-6}, 
     {216/5, -5.176675531709529*^-6}, {1081/25, -4.715504015345706*^-6}, 
     {1082/25, -4.260766532787619*^-6}, {1083/25, -3.7999211470463035*^-6}, 
     {1084/25, -3.339296332754982*^-6}, {217/5, -2.8575416117226915*^-6}, 
     {1086/25, -2.367266500324927*^-6}, {1087/25, -1.9238951631944667*^-6}, 
     {1088/25, -1.3963496496294248*^-6}, {1089/25, -9.046022172998214*^-7}, 
     {218/5, -3.9487576928426416*^-7}, {1091/25, 8.315932541885784*^-8}, 
     {1092/25, 5.545216643018658*^-7}, {1093/25, 1.0413817114890422*^-6}, 
     {1094/25, 1.5859654252450839*^-6}, {219/5, 2.042609529004369*^-6}, 
     {1096/25, 2.4814100967190944*^-6}, {1097/25, 2.9185702371259392*^-6}, 
     {1098/25, 3.3559708651209608*^-6}, {1099/25, 3.7698655640655554*^-6}, 
     {44, 4.166247879411333*^-6}, {1101/25, 4.57805727721583*^-6}, 
     {1102/25, 4.924594716682051*^-6}, {1103/25, 5.315798789401471*^-6}, 
     {1104/25, 5.6202443862729545*^-6}, {221/5, 6.004167969503316*^-6}, 
     {1106/25, 6.314508132654328*^-6}, {1107/25, 6.598431175813824*^-6}, 
     {1108/25, 6.892363274169089*^-6}, {1109/25, 7.131661198117589*^-6}, 
     {222/5, 7.3862562242899*^-6}, {1111/25, 7.5542947479689815*^-6}, 
     {1112/25, 7.77553533715114*^-6}, {1113/25, 7.911849491115674*^-6}, 
     {1114/25, 8.043874455299083*^-6}, {223/5, 8.134870395359872*^-6}, 
     {1116/25, 8.219289358013526*^-6}, {1117/25, 8.265972981202907*^-6}, 
     {1118/25, 8.353495198176741*^-6}, {1119/25, 8.36495068889942*^-6}, 
     {224/5, 8.34324784731999*^-6}, {1121/25, 8.320172402598303*^-6}, 
     {1122/25, 8.273377395784376*^-6}, {1123/25, 8.185634114088458*^-6}, 
     {1124/25, 8.165220429456888*^-6}, {45, 7.988891263188691*^-6}, 
     {1126/25, 7.889885701994892*^-6}, {1127/25, 7.704464819680013*^-6}, 
     {1128/25, 7.5984318360644565*^-6}, {1129/25, 7.346345127001719*^-6}, 
     {226/5, 7.108412119510854*^-6}, {1131/25, 6.893960115467168*^-6}, 
     {1132/25, 6.616844023893398*^-6}, {1133/25, 6.365366523097826*^-6}, 
     {1134/25, 6.065415000700014*^-6}, {227/5, 5.8574000674216364*^-6}, 
     {1136/25, 5.515726428928502*^-6}, {1137/25, 5.206536271451512*^-6}, 
     {1138/25, 4.887035325945588*^-6}, {1139/25, 4.539195664038376*^-6}, 
     {228/5, 4.21013680784732*^-6}, {1141/25, 3.841329883985667*^-6}, 
     {1142/25, 3.505006197584981*^-6}, {1143/25, 3.151182191074575*^-6}, 
     {1144/25, 2.7680376738503654*^-6}, {229/5, 2.384528607041192*^-6}, 
     {1146/25, 2.028526722847035*^-6}, {1147/25, 1.6383534599817562*^-6}, 
     {1148/25, 1.2473750584662824*^-6}, {1149/25, 9.031574310508494*^-7}, 
     {46, 5.143600330173581*^-7}, {1151/25, 1.4791001849701058*^-7}, 
     {1152/25, -1.4759896409255457*^-7}, {1153/25, -5.298009554156879*^-7}, 
     {1154/25, -8.671989338303364*^-7}, {231/5, -1.2165301743090329*^-6}, 
     {1156/25, -1.5574648067756547*^-6}, {1157/25, -1.831006019060999*^-6}, 
     {1158/25, -2.185830475426309*^-6}, {1159/25, -2.430138224950029*^-6}, 
     {232/5, -2.7714104440385023*^-6}, {1161/25, -3.0683913901374815*^-6}, 
     {1162/25, -3.320223100830577*^-6}, {1163/25, -3.603064106613707*^-6}, 
     {1164/25, -3.838888936721907*^-6}, {233/5, -4.083979424876483*^-6}, 
     {1166/25, -4.24530645555532*^-6}, {1167/25, -4.478338389735104*^-6}, 
     {1168/25, -4.5930103301228264*^-6}, {1169/25, -4.772156236371172*^-6}, 
     {234/5, -4.9277504493017155*^-6}, {1171/25, -5.017606249768658*^-6}, 
     {1172/25, -5.148529997001106*^-6}, {1173/25, -5.284114468762091*^-6}, 
     {1174/25, -5.362141232145845*^-6}, {47, -5.415730791880069*^-6}, 
     {1176/25, -5.503369449155748*^-6}, {1177/25, -5.529821806959934*^-6}, 
     {1178/25, -5.568931985888703*^-6}, {1179/25, -5.564757448200952*^-6}, 
     {236/5, -5.553258454749077*^-6}, {1181/25, -5.518284617284097*^-6}, 
     {1182/25, -5.489389201140948*^-6}, {1183/25, -5.4446929857454585*^-6}, 
     {1184/25, -5.34892531772746*^-6}, {237/5, -5.285335759414034*^-6}, 
     {1186/25, -5.16881237055955*^-6}, {1187/25, -5.075708852025906*^-6}, 
     {1188/25, -4.980379728097839*^-6}, {1189/25, -4.868656015372119*^-6}, 
     {238/5, -4.730228447241691*^-6}, {1191/25, -4.604405548613855*^-6}, 
     {1192/25, -4.428980381193659*^-6}, {1193/25, -4.312699850739232*^-6}, 
     {1194/25, -4.107947856796246*^-6}, {239/5, -3.92467227605664*^-6}, 
     {1196/25, -3.7729217866044884*^-6}, {1197/25, -3.558376911072525*^-6}, 
     {1198/25, -3.323294929719056*^-6}, {1199/25, -3.164716256498501*^-6}, 
     {48, -2.9006381420670913*^-6}, {1201/25, -2.722679399130845*^-6}, 
     {1202/25, -2.518533503498288*^-6}, {1203/25, -2.3175882497006306*^-6}, 
     {1204/25, -2.108367505526676*^-6}, {241/5, -1.8479592033132652*^-6}, 
     {1206/25, -1.644156001290309*^-6}, {1207/25, -1.4507584015222008*^-6}, 
     {1208/25, -1.2316085910013541*^-6}, {1209/25, -1.0422638478113644*^-6}, 
     {242/5, -8.270992581937975*^-7}, {1211/25, -6.343188432705871*^-7}, 
     {1212/25, -4.4411592804022293*^-7}, {1213/25, -2.3984740853133513*^-7}, 
     {1214/25, -3.043892613657784*^-8}, {243/5, 1.834476096654325*^-7}, 
     {1216/25, 3.563471155931808*^-7}, {1217/25, 5.040699379947611*^-7}, 
     {1218/25, 7.209557196241612*^-7}, {1219/25, 8.146298334276228*^-7}, 
     {244/5, 1.0068783947063745*^-6}, {1221/25, 1.1653855136635471*^-6}, 
     {1222/25, 1.2777888162632256*^-6}, {1223/25, 1.40050676553094*^-6}, 
     {1224/25, 1.5193338969293757*^-6}, {49, 1.6522412563876876*^-6}, 
     {1226/25, 1.8003861721321845*^-6}, {1227/25, 1.8945092810293551*^-6}, 
     {1228/25, 1.977983350109902*^-6}, {1229/25, 2.078821339623893*^-6}, 
     {246/5, 2.1696196584181093*^-6}, {1231/25, 2.2991342588790653*^-6}, 
     {1232/25, 2.3160342046968374*^-6}, {1233/25, 2.379791198950376*^-6}, 
     {1234/25, 2.4541963975638348*^-6}, {247/5, 2.48247171676097*^-6}, 
     {1236/25, 2.510115174630956*^-6}, {1237/25, 2.552709770495265*^-6}, 
     {1238/25, 2.5645539413476914*^-6}, {1239/25, 2.587460654193685*^-6}, 
     {248/5, 2.6028643926867545*^-6}, {1241/25, 2.5461593502612567*^-6}, 
     {1242/25, 2.599822629761883*^-6}, {1243/25, 2.6338343260823294*^-6}, 
     {1244/25, 2.627920504677528*^-6}, {249/5, 2.6120619469882644*^-6}, 
     {1246/25, 2.600272397512704*^-6}, {1247/25, 2.527915243549783*^-6}, 
     {1248/25, 2.484338862795976*^-6}, {1249/25, 2.453235390109665*^-6}, 
     {50, 2.44870571106115*^-6}}
 
ImFRfine = {{50, 2.44870571106115*^-6}, {1001/20, 2.3699896068984927*^-6}, 
     {501/10, 2.310870126726039*^-6}, {1003/20, 2.225994156002109*^-6}, 
     {251/5, 2.1593172867262478*^-6}, {201/4, 2.0904610448513328*^-6}, 
     {503/10, 2.0219032550172766*^-6}, {1007/20, 1.995041425867372*^-6}, 
     {252/5, 1.886996440908506*^-6}, {1009/20, 1.8204177048841697*^-6}, 
     {101/2, 1.7287747919036978*^-6}, {1011/20, 1.6534033004805826*^-6}, 
     {253/5, 1.573324916070984*^-6}, {1013/20, 1.4999325981396305*^-6}, 
     {507/10, 1.4348107187506232*^-6}, {203/4, 1.2988272653363664*^-6}, 
     {254/5, 1.2254114975518426*^-6}, {1017/20, 1.1670666588137202*^-6}, 
     {509/10, 1.0928029335610656*^-6}, {1019/20, 1.0686771931556205*^-6}, 
     {51, 9.684522460501332*^-7}, {1021/20, 8.905054871971574*^-7}, 
     {511/10, 8.369233958915867*^-7}, {1023/20, 7.503901568173266*^-7}, 
     {256/5, 7.195880463994886*^-7}, {205/4, 6.297647058076117*^-7}, 
     {513/10, 5.637668821223407*^-7}, {1027/20, 5.074663104141786*^-7}, 
     {257/5, 4.538296909037398*^-7}, {1029/20, 3.854709281908564*^-7}, 
     {103/2, 3.5199796086932134*^-7}, {1031/20, 3.12379668299112*^-7}, 
     {258/5, 2.771939736105275*^-7}, {1033/20, 2.0699566675996817*^-7}, 
     {517/10, 1.513350542468178*^-7}, {207/4, 1.314673326521798*^-7}, 
     {259/5, 5.670469726062888*^-8}, {1037/20, -4.119191714113679*^-8}, 
     {519/10, -5.568492981999906*^-8}, {1039/20, -1.1723986091671801*^-7}, 
     {52, -1.73723410518134*^-7}, {1041/20, -1.757055801340779*^-7}, 
     {521/10, -2.570331134252313*^-7}, {1043/20, -2.5830763430295667*^-7}, 
     {261/5, -3.0943611986633535*^-7}, {209/4, -3.5460404010367874*^-7}, 
     {523/10, -4.039651021192636*^-7}, {1047/20, -4.86525183945874*^-7}, 
     {262/5, -5.170874305682194*^-7}, {1049/20, -5.736590210220216*^-7}, 
     {105/2, -6.473853806782115*^-7}, {1051/20, -7.112068610287681*^-7}, 
     {263/5, -7.440800944003012*^-7}, {1053/20, -8.389374333284128*^-7}, 
     {527/10, -8.605074647005662*^-7}, {211/4, -9.017313271353355*^-7}, 
     {264/5, -9.65990961679375*^-7}, {1057/20, -1.0168816354794163*^-6}, 
     {529/10, -1.0866036105477983*^-6}, {1059/20, -1.1379889306717406*^-6}, 
     {53, -1.1917857105914198*^-6}, {1061/20, -1.2770489222907466*^-6}, 
     {531/10, -1.3069389479813953*^-6}, {1063/20, -1.3774164151769686*^-6}, 
     {266/5, -1.4118756064551707*^-6}, {213/4, -1.467209393854474*^-6}, 
     {533/10, -1.5151009102182256*^-6}, {1067/20, -1.5729260159080827*^-6}, 
     {267/5, -1.5921204000179934*^-6}, {1069/20, -1.6451724205168716*^-6}, 
     {107/2, -1.6833046851127964*^-6}, {1071/20, -1.7250137088059558*^-6}, 
     {268/5, -1.7760397487132096*^-6}, {1073/20, -1.7912394138508425*^-6}, 
     {537/10, -1.8233914418075425*^-6}, {215/4, -1.861846032069625*^-6}, 
     {269/5, -1.8843564692019865*^-6}, {1077/20, -1.8839246856347525*^-6}, 
     {539/10, -1.8728807949439097*^-6}, {1079/20, -1.8430797451562952*^-6}, 
     {54, -1.8759141722640704*^-6}, {1081/20, -1.846806160638037*^-6}, 
     {541/10, -1.8228801220709911*^-6}, {1083/20, -1.7960688198925823*^-6}, 
     {271/5, -1.7515295593802105*^-6}, {217/4, -1.761962449768617*^-6}, 
     {543/10, -1.7375276063456846*^-6}, {1087/20, -1.6701392549327287*^-6}, 
     {272/5, -1.6277285229925054*^-6}, {1089/20, -1.549964895906225*^-6}, 
     {109/2, -1.5193177354752563*^-6}, {1091/20, -1.404376549058741*^-6}, 
     {273/5, -1.3592862090146436*^-6}, {1093/20, -1.2171062395392729*^-6}, 
     {547/10, -1.1509381930407264*^-6}, {219/4, -1.091674881339988*^-6}, 
     {274/5, -9.893394599495842*^-7}, {1097/20, -8.743632831757775*^-7}, 
     {549/10, -7.614628007163171*^-7}, {1099/20, -7.056886524581252*^-7}, 
     {55, -5.774357530671792*^-7}, {1101/20, -4.508616620185757*^-7}, 
     {551/10, -3.2177799672017393*^-7}, {1103/20, -1.9919912575688814*^-7}, 
     {276/5, -6.946957987336022*^-8}, {221/4, 8.378313096774059*^-8}, 
     {553/10, 2.4653398942448*^-7}, {1107/20, 3.479028414868357*^-7}, 
     {277/5, 4.967954269630148*^-7}, {1109/20, 6.491599034014195*^-7}, 
     {111/2, 7.58098846725952*^-7}, {1111/20, 9.354394098770591*^-7}, 
     {278/5, 1.0728799254289267*^-6}, {1113/20, 1.1367790241356701*^-6}, 
     {557/10, 1.277563700552431*^-6}, {223/4, 1.432705855508587*^-6}, 
     {279/5, 1.582805866928716*^-6}, {1117/20, 1.6812990519532445*^-6}, 
     {559/10, 1.8103476194658574*^-6}, {1119/20, 1.9391491516279613*^-6}, 
     {56, 2.0415836800985465*^-6}, {1121/20, 2.1358703177903893*^-6}, 
     {561/10, 2.2413540333027226*^-6}, {1123/20, 2.3296004324491193*^-6}, 
     {281/5, 2.4061651951873264*^-6}, {225/4, 2.499957078128112*^-6}, 
     {563/10, 2.5680067688577113*^-6}, {1127/20, 2.6232470436426958*^-6}, 
     {282/5, 2.7293838955610994*^-6}, {1129/20, 2.7574928689599876*^-6}, 
     {113/2, 2.806534785460002*^-6}, {1131/20, 2.8307951938644216*^-6}, 
     {283/5, 2.871210360300136*^-6}, {1133/20, 2.8578566481918255*^-6}, 
     {567/10, 2.8728349844020507*^-6}, {227/4, 2.8428328661678215*^-6}, 
     {284/5, 2.8314884171765087*^-6}, {1137/20, 2.8362161292525*^-6}, 
     {569/10, 2.7891485529646376*^-6}, {1139/20, 2.7524344855811567*^-6}, 
     {57, 2.68258731535298*^-6}, {1141/20, 2.639246864687139*^-6}, 
     {571/10, 2.5838512889286847*^-6}, {1143/20, 2.5257343020321232*^-6}, 
     {286/5, 2.3842931224857256*^-6}, {229/4, 2.2939173369672383*^-6}, 
     {573/10, 2.1270487375602*^-6}, {1147/20, 2.0509815280393695*^-6}, 
     {287/5, 1.9304851935388057*^-6}, {1149/20, 1.7352416073479482*^-6}, 
     {115/2, 1.6511230080335296*^-6}, {1151/20, 1.508508566207701*^-6}, 
     {288/5, 1.3199684083249445*^-6}, {1153/20, 1.1734502179359951*^-6}, 
     {577/10, 1.0290078616848747*^-6}, {231/4, 8.327453565500076*^-7}, 
     {289/5, 6.363531340480844*^-7}, {1157/20, 4.186262304098354*^-7}, 
     {579/10, 2.717015798597844*^-7}, {1159/20, 5.667615900206702*^-8}, 
     {58, -1.4250231578083472*^-7}, {1161/20, -2.90613347067592*^-7}, 
     {581/10, -5.038939695223288*^-7}, {1163/20, -7.465949636298319*^-7}, 
     {291/5, -9.379108735843578*^-7}, {233/4, -1.1183548952187206*^-6}, 
     {583/10, -1.3207596887832018*^-6}, {1167/20, -1.4923700212554625*^-6}, 
     {292/5, -1.7295541406836534*^-6}, {1169/20, -1.916152207834254*^-6}, 
     {117/2, -2.1002593123820024*^-6}, {1171/20, -2.2926898682607*^-6}, 
     {293/5, -2.481761375836*^-6}, {1173/20, -2.6434784020923363*^-6}, 
     {587/10, -2.7950696357137428*^-6}, {235/4, -2.9564967118783647*^-6}, 
     {294/5, -3.0867016296565186*^-6}, {1177/20, -3.1907479740300726*^-6}, 
     {589/10, -3.355586699144153*^-6}, {1179/20, -3.4770444613113627*^-6}, 
     {59, -3.5825234050712584*^-6}, {1181/20, -3.6675611465863955*^-6}, 
     {591/10, -3.7347786682462303*^-6}, {1183/20, -3.847788567101773*^-6}, 
     {296/5, -3.869245450677239*^-6}, {237/4, -3.939633012678412*^-6}, 
     {593/10, -3.956667022742*^-6}, {1187/20, -3.955656665582952*^-6}, 
     {297/5, -3.9419800058337895*^-6}, {1189/20, -3.911805967829474*^-6}, 
     {119/2, -3.912299904262895*^-6}, {1191/20, -3.865751837542342*^-6}, 
     {298/5, -3.786430946367547*^-6}, {1193/20, -3.7572054594758875*^-6}, 
     {597/10, -3.631102531709285*^-6}, {239/4, -3.547004995427261*^-6}, 
     {299/5, -3.452491865146845*^-6}, {1197/20, -3.311512006040629*^-6}, 
     {599/10, -3.1829080497369766*^-6}, {1199/20, -2.970877354617485*^-6}, 
     {60, -2.8093157117686784*^-6}, {1201/20, -2.614558945603085*^-6}, 
     {601/10, -2.403953495822009*^-6}, {1203/20, -2.2005090188001453*^-6}, 
     {301/5, -1.9642917000115*^-6}, {241/4, -1.7560557497992013*^-6}, 
     {603/10, -1.5270412331951089*^-6}, {1207/20, -1.270111188366287*^-6}, 
     {302/5, -1.0111083409963112*^-6}, {1209/20, -7.29953037887851*^-7}, 
     {121/2, -4.718689188693004*^-7}, {1211/20, -1.8942416999540024*^-7}, 
     {303/5, 7.509302329261613*^-8}, {1213/20, 3.8521410278269386*^-7}, 
     {607/10, 6.755539393790699*^-7}, {243/4, 9.60900681232224*^-7}, 
     {304/5, 1.1924640421767663*^-6}, {1217/20, 1.4976325717896977*^-6}, 
     {609/10, 1.721759566281067*^-6}, {1219/20, 2.043162811632415*^-6}, 
     {61, 2.288506378983479*^-6}, {1221/20, 2.6048576906856358*^-6}, 
     {611/10, 2.867848841209275*^-6}, {1223/20, 3.0886050259165687*^-6}, 
     {306/5, 3.3507686050121555*^-6}, {245/4, 3.532199310679607*^-6}, 
     {613/10, 3.7486656344482006*^-6}, {1227/20, 3.981558072255198*^-6}, 
     {307/5, 4.163494166709025*^-6}, {1229/20, 4.355089311486315*^-6}, 
     {123/2, 4.493244349701442*^-6}, {1231/20, 4.646408958225434*^-6}, 
     {308/5, 4.781250868057807*^-6}, {1233/20, 4.855440906587072*^-6}, 
     {617/10, 4.9436694218862876*^-6}, {247/4, 5.025948436709893*^-6}, 
     {309/5, 5.0309539282866744*^-6}, {1237/20, 5.118054853092691*^-6}, 
     {619/10, 5.124234620262902*^-6}, {1239/20, 5.1090032063549895*^-6}, 
     {62, 5.053867175891513*^-6}, {1241/20, 5.03478732755136*^-6}, 
     {621/10, 4.916633238385981*^-6}, {1243/20, 4.836322739121268*^-6}, 
     {311/5, 4.721082325839787*^-6}, {249/4, 4.66826243727958*^-6}, 
     {623/10, 4.443288706815207*^-6}, {1247/20, 4.343786518173909*^-6}, 
     {312/5, 4.088611340810622*^-6}, {1249/20, 3.857968862111538*^-6}, 
     {125/2, 3.668594904804312*^-6}, {1251/20, 3.4169575927195384*^-6}, 
     {313/5, 3.1201725383331325*^-6}, {1253/20, 2.884255205656827*^-6}, 
     {627/10, 2.5784787023724887*^-6}, {251/4, 2.2399885309318246*^-6}, 
     {314/5, 1.9377108864820913*^-6}, {1257/20, 1.6568247033915684*^-6}, 
     {629/10, 1.2549529951090543*^-6}, {1259/20, 9.61172173209561*^-7}, 
     {63, 6.039892929011331*^-7}, {1261/20, 2.787770326737049*^-7}, 
     {631/10, -1.0139159498448458*^-7}, {1263/20, -4.5265530498536655*^-7}, 
     {316/5, -7.878040071962467*^-7}, {253/4, -1.1657954350832722*^-6}, 
     {633/10, -1.4901341021181236*^-6}, {1267/20, -1.8611824780800923*^-6}, 
     {317/5, -2.1746132928268658*^-6}, {1269/20, -2.587288297051238*^-6}, 
     {127/2, -2.893728407504792*^-6}, {1271/20, -3.151915722088283*^-6}, 
     {318/5, -3.477263987472501*^-6}, {1273/20, -3.7647612300267808*^-6}, 
     {637/10, -4.032959393399094*^-6}, {255/4, -4.279665799827859*^-6}, 
     {319/5, -4.559376742818699*^-6}, {1277/20, -4.78564317077379*^-6}, 
     {639/10, -5.015211158032606*^-6}, {1279/20, -5.188405054062928*^-6}, 
     {64, -5.349719214509108*^-6}, {1281/20, -5.476193167763821*^-6}, 
     {641/10, -5.595570794880711*^-6}, {1283/20, -5.707802641030657*^-6}, 
     {321/5, -5.777052045630171*^-6}, {257/4, -5.849570142352212*^-6}, 
     {643/10, -5.848178078360355*^-6}, {1287/20, -5.839626177006618*^-6}, 
     {322/5, -5.827525787260868*^-6}, {1289/20, -5.813800598941654*^-6}, 
     {129/2, -5.740752753280454*^-6}, {1291/20, -5.6389102390252965*^-6}, 
     {323/5, -5.534957158992437*^-6}, {1293/20, -5.384860524815238*^-6}, 
     {647/10, -5.22829949586856*^-6}, {259/4, -5.029212203619404*^-6}, 
     {324/5, -4.799958740031585*^-6}, {1297/20, -4.587640642816915*^-6}, 
     {649/10, -4.304550901279569*^-6}, {1299/20, -4.026182283428659*^-6}, 
     {65, -3.7910770519788972*^-6}, {1301/20, -3.454943807601474*^-6}, 
     {651/10, -3.1724027700907875*^-6}, {1303/20, -2.806739999403063*^-6}, 
     {326/5, -2.4820285431381706*^-6}, {261/4, -2.1347615830752398*^-6}, 
     {653/10, -1.7439941759275768*^-6}, {1307/20, -1.371467323867115*^-6}, 
     {327/5, -9.680980356877034*^-7}, {1309/20, -5.898193606562047*^-7}, 
     {131/2, -2.0099089507118716*^-7}, {1311/20, 2.0637314047597388*^-7}, 
     {328/5, 5.846638874394683*^-7}, {1313/20, 9.54140644715551*^-7}, 
     {657/10, 1.3054641793269761*^-6}, {263/4, 1.6854563685969604*^-6}, 
     {329/5, 2.018094623024158*^-6}, {1317/20, 2.4487931091915494*^-6}, 
     {659/10, 2.795332905008996*^-6}, {1319/20, 3.0865434373361644*^-6}, 
     {66, 3.4559224479091544*^-6}, {1321/20, 3.7410255898234768*^-6}, 
     {661/10, 4.0511974161439035*^-6}, {1323/20, 4.361331323088358*^-6}, 
     {331/5, 4.5957253827361155*^-6}, {265/4, 4.8302339704514585*^-6}, 
     {663/10, 5.048757388326219*^-6}, {1327/20, 5.255590992098158*^-6}, 
     {332/5, 5.391172324981097*^-6}, {1329/20, 5.503293706715651*^-6}, 
     {133/2, 5.651956537150449*^-6}, {1331/20, 5.786639819038708*^-6}, 
     {333/5, 5.891299026533625*^-6}, {1333/20, 5.938343196454365*^-6}, 
     {667/10, 5.9771002855202315*^-6}, {267/4, 5.996963727633586*^-6}, 
     {334/5, 5.945939949847379*^-6}, {1337/20, 5.901015514647723*^-6}, 
     {669/10, 5.824234649232096*^-6}, {1339/20, 5.74249919707559*^-6}, 
     {67, 5.595626716314861*^-6}, {1341/20, 5.424909066742423*^-6}, 
     {671/10, 5.2874803554980865*^-6}, {1343/20, 5.116831580803671*^-6}, 
     {336/5, 4.8442654763392046*^-6}, {269/4, 4.651961759083445*^-6}, 
     {673/10, 4.423709604114978*^-6}, {1347/20, 4.152218032196786*^-6}, 
     {337/5, 3.895073809809246*^-6}, {1349/20, 3.5698886647894668*^-6}, 
     {135/2, 3.2549652530522444*^-6}, {1351/20, 2.925531623190758*^-6}, 
     {338/5, 2.590967902824093*^-6}, {1353/20, 2.2226889614118672*^-6}, 
     {677/10, 1.853107572363788*^-6}, {271/4, 1.529274913633638*^-6}, 
     {339/5, 1.1302272402285984*^-6}, {1357/20, 7.753097483916005*^-7}, 
     {679/10, 4.287436364963648*^-7}, {1359/20, 6.532130257877466*^-8}, 
     {68, -2.924671238970075*^-7}, {1361/20, -6.72600921115124*^-7}, 
     {681/10, -1.0068226663217938*^-6}, {1363/20, -1.4160571207427752*^-6}, 
     {341/5, -1.779155680017852*^-6}, {273/4, -2.0300754741131577*^-6}, 
     {683/10, -2.4130947428452343*^-6}, {1367/20, -2.733614966540787*^-6}, 
     {342/5, -3.0311959764439678*^-6}, {1369/20, -3.319994973854934*^-6}, 
     {137/2, -3.5617094932272053*^-6}, {1371/20, -3.844482802481397*^-6}, 
     {343/5, -4.085200814823997*^-6}, {1373/20, -4.261532197402662*^-6}, 
     {687/10, -4.490391504394231*^-6}, {275/4, -4.679247851566148*^-6}, 
     {344/5, -4.791848601859439*^-6}, {1377/20, -5.006943876575964*^-6}, 
     {689/10, -5.078629232685428*^-6}, {1379/20, -5.165215483382557*^-6}, 
     {69, -5.234861254699297*^-6}, {1381/20, -5.301810085706071*^-6}, 
     {691/10, -5.3019002347887145*^-6}, {1383/20, -5.309527352420629*^-6}, 
     {346/5, -5.294834459435016*^-6}, {277/4, -5.251163323172214*^-6}, 
     {693/10, -5.209336757794336*^-6}, {1387/20, -5.093033131786662*^-6}, 
     {347/5, -5.0284346465312435*^-6}, {1389/20, -4.90411712456007*^-6}, 
     {139/2, -4.774845720423304*^-6}, {1391/20, -4.631901767221391*^-6}, 
     {348/5, -4.420676592037376*^-6}, {1393/20, -4.2061589795722165*^-6}, 
     {697/10, -3.97845608764158*^-6}, {279/4, -3.840995164733352*^-6}, 
     {349/5, -3.532542268230854*^-6}, {1397/20, -3.2864171000956954*^-6}, 
     {699/10, -3.025548025906155*^-6}, {1399/20, -2.8000067166245035*^-6}, 
     {70, -2.4897543234592145*^-6}, {1401/20, -2.203420604168782*^-6}, 
     {701/10, -1.9605685663143246*^-6}, {1403/20, -1.6250761102273859*^-6}, 
     {351/5, -1.3315104839886627*^-6}, {281/4, -9.989321334141765*^-7}, 
     {703/10, -7.11070912241818*^-7}, {1407/20, -3.920094895151771*^-7}, 
     {352/5, -1.460990105874027*^-7}, {1409/20, 1.9317692636494632*^-7}, 
     {141/2, 5.405737325200888*^-7}, {1411/20, 7.657107844009654*^-7}, 
     {353/5, 1.0283048333305927*^-6}, {1413/20, 1.3655230631202941*^-6}, 
     {707/10, 1.6354342562072133*^-6}, {283/4, 1.8695987585790053*^-6}, 
     {354/5, 2.106907891680221*^-6}, {1417/20, 2.379470265524708*^-6}, 
     {709/10, 2.5925597619824714*^-6}, {1419/20, 2.8403285080302876*^-6}, 
     {71, 3.006749656406238*^-6}, {1421/20, 3.1436905291448713*^-6}, 
     {711/10, 3.3636341854048624*^-6}, {1423/20, 3.5084735747203943*^-6}, 
     {356/5, 3.6035706466874817*^-6}, {285/4, 3.7667841426142212*^-6}, 
     {713/10, 3.8545156991476315*^-6}, {1427/20, 3.912564126726248*^-6}, 
     {357/5, 4.02080323674836*^-6}, {1429/20, 4.1057745118755484*^-6}, 
     {143/2, 4.1350750964314065*^-6}, {1431/20, 4.166744834124825*^-6}, 
     {358/5, 4.225328893880942*^-6}, {1433/20, 4.149972337622043*^-6}, 
     {717/10, 4.165289338831091*^-6}, {287/4, 4.12571064101197*^-6}, 
     {359/5, 4.088446511230082*^-6}, {1437/20, 3.990655844610114*^-6}, 
     {719/10, 3.901545392190342*^-6}, {1439/20, 3.844232155617022*^-6}, 
     {72, 3.6759950824138965*^-6}, {1441/20, 3.6506530139424065*^-6}, 
     {721/10, 3.4147520063532166*^-6}, {1443/20, 3.3412006572169917*^-6}, 
     {361/5, 3.1637905834602797*^-6}, {289/4, 2.971279153676787*^-6}, 
     {723/10, 2.7992292377931882*^-6}, {1447/20, 2.6524048689080537*^-6}, 
     {362/5, 2.441531550850806*^-6}, {1449/20, 2.22698919595532*^-6}, 
     {145/2, 2.0768138331433983*^-6}, {1451/20, 1.8018490887256045*^-6}, 
     {363/5, 1.6591412799749072*^-6}, {1453/20, 1.3988593655020476*^-6}, 
     {727/10, 1.151186089815015*^-6}, {291/4, 9.8108897199356*^-7}, 
     {364/5, 7.772685521462153*^-7}, {1457/20, 5.369029303925466*^-7}, 
     {729/10, 3.499886888566617*^-7}, {1459/20, 1.1153001479996538*^-7}, 
     {73, -1.5486841401651796*^-7}, {1461/20, -2.865849537195264*^-7}, 
     {731/10, -5.161633150523384*^-7}, {1463/20, -7.438806097638095*^-7}, 
     {366/5, -8.929069939874607*^-7}, {293/4, -1.0441017967068728*^-6}, 
     {733/10, -1.2726582237776451*^-6}, {1467/20, -1.4280595223847836*^-6}, 
     {367/5, -1.6356422267924109*^-6}, {1469/20, -1.7778552680279558*^-6}, 
     {147/2, -1.94216843601297*^-6}, {1471/20, -2.0793296313936782*^-6}, 
     {368/5, -2.282748569656934*^-6}, {1473/20, -2.3466867174609662*^-6}, 
     {737/10, -2.457814921009993*^-6}, {295/4, -2.5865404644775936*^-6}, 
     {369/5, -2.628584342481699*^-6}, {1477/20, -2.763143404582724*^-6}, 
     {739/10, -2.821694847943146*^-6}, {1479/20, -2.887088004846494*^-6}, 
     {74, -2.9224770707325654*^-6}, {1481/20, -2.9517533121359296*^-6}, 
     {741/10, -3.010052991067602*^-6}, {1483/20, -3.0399039990663956*^-6}, 
     {371/5, -3.128982912256606*^-6}, {297/4, -3.1156224672701516*^-6}, 
     {743/10, -3.081183474432092*^-6}, {1487/20, -3.023279941893886*^-6}, 
     {372/5, -2.9715428485899142*^-6}, {1489/20, -2.9774204918509017*^-6}, 
     {149/2, -2.939257881709456*^-6}, {1491/20, -2.870874053984007*^-6}, 
     {373/5, -2.8594328136122282*^-6}, {1493/20, -2.803778031690296*^-6}, 
     {747/10, -2.6739663971375727*^-6}, {299/4, -2.566449158927786*^-6}, 
     {374/5, -2.482843996301498*^-6}, {1497/20, -2.3671113393436416*^-6}, 
     {749/10, -2.316741364472019*^-6}, {1499/20, -2.2152086646270996*^-6}, 
     {75, -2.0683091756790173*^-6}, {1501/20, -1.9635163382020204*^-6}, 
     {751/10, -1.765013401433535*^-6}, {1503/20, -1.6493082941604342*^-6}, 
     {376/5, -1.5301997307384796*^-6}, {301/4, -1.3718105472404485*^-6}, 
     {753/10, -1.274332589534799*^-6}, {1507/20, -1.0645967494782305*^-6}, 
     {377/5, -9.468232146578326*^-7}, {1509/20, -8.261421767380428*^-7}, 
     {151/2, -6.600559191854982*^-7}, {1511/20, -5.109890234417103*^-7}, 
     {378/5, -3.3684445321230383*^-7}, {1513/20, -1.6879818951279213*^-7}, 
     {757/10, -8.000583552603135*^-8}, {303/4, 1.4055654488920322*^-7}, 
     {379/5, 2.76370180768426*^-7}, {1517/20, 4.5129401934213*^-7}, 
     {759/10, 5.599937671499702*^-7}, {1519/20, 7.224219225059232*^-7}, 
     {76, 8.870743631152547*^-7}, {1521/20, 9.713400019473878*^-7}, 
     {761/10, 1.1603352235434183*^-6}, {1523/20, 1.2520402977653222*^-6}, 
     {381/5, 1.3882421024194458*^-6}, {305/4, 1.488399299032217*^-6}, 
     {763/10, 1.5985237164055366*^-6}, {1527/20, 1.7504056973802196*^-6}, 
     {382/5, 1.8655545412221697*^-6}, {1529/20, 1.9591367201726717*^-6}, 
     {153/2, 2.0582410055342004*^-6}, {1531/20, 2.1790000382382324*^-6}, 
     {383/5, 2.196971659269853*^-6}, {1533/20, 2.224692380002613*^-6}, 
     {767/10, 2.3616365035297737*^-6}, {307/4, 2.390573335182833*^-6}, 
     {384/5, 2.481745775592681*^-6}, {1537/20, 2.5133408863287077*^-6}, 
     {769/10, 2.546613254911234*^-6}, {1539/20, 2.624592088912303*^-6}, 
     {77, 2.6108593160767413*^-6}, {1541/20, 2.5965565250002376*^-6}, 
     {771/10, 2.5552534382716763*^-6}, {1543/20, 2.5729994404255496*^-6}, 
     {386/5, 2.568479212011754*^-6}, {309/4, 2.5269628424196*^-6}, 
     {773/10, 2.5080211634165295*^-6}, {1547/20, 2.5135507475265717*^-6}, 
     {387/5, 2.418770414264193*^-6}, {1549/20, 2.388093589836271*^-6}, 
     {155/2, 2.3181475332645363*^-6}, {1551/20, 2.235299188843576*^-6}, 
     {388/5, 2.173157241464052*^-6}, {1553/20, 2.0674808783038845*^-6}, 
     {777/10, 1.9887101794235917*^-6}, {311/4, 1.9047054596182944*^-6}, 
     {389/5, 1.7963895106165584*^-6}, {1557/20, 1.674770262707903*^-6}, 
     {779/10, 1.5668282702802072*^-6}, {1559/20, 1.4520081530605689*^-6}, 
     {78, 1.2740141276668115*^-6}, {1561/20, 1.1922563377328443*^-6}, 
     {781/10, 1.0357725926807282*^-6}, {1563/20, 9.071265529639327*^-7}, 
     {391/5, 8.055533425449513*^-7}, {313/4, 6.090967041988415*^-7}, 
     {783/10, 5.101792946715644*^-7}, {1567/20, 3.3053928380488706*^-7}, 
     {392/5, 1.852243508432272*^-7}, {1569/20, -2.6512541724532657*^-8}, 
     {157/2, -1.4418239806940347*^-7}, {1571/20, -2.907429702755926*^-7}, 
     {393/5, -4.1483641043289776*^-7}, {1573/20, -5.714082688835359*^-7}, 
     {787/10, -7.255612380742751*^-7}, {315/4, -8.538523177769979*^-7}, 
     {394/5, -9.784025275312754*^-7}, {1577/20, -1.1390688401009819*^-6}, 
     {789/10, -1.2935388366795697*^-6}, {1579/20, -1.4115974996606329*^-6}, 
     {79, -1.5216141990397059*^-6}, {1581/20, -1.638356671527369*^-6}, 
     {791/10, -1.784489667450151*^-6}, {1583/20, -1.8703591717628143*^-6}, 
     {396/5, -1.9585269421390494*^-6}, {317/4, -2.0538752505266933*^-6}, 
     {793/10, -2.1432781723770833*^-6}, {1587/20, -2.216980281521952*^-6}, 
     {397/5, -2.2848201867708973*^-6}, {1589/20, -2.356881146262091*^-6}, 
     {159/2, -2.415651412103481*^-6}, {1591/20, -2.4445430159697468*^-6}, 
     {398/5, -2.4815848029130505*^-6}, {1593/20, -2.5649319419784877*^-6}, 
     {797/10, -2.554364185572422*^-6}, {319/4, -2.5476500157550763*^-6}, 
     {399/5, -2.5669103662084858*^-6}, {1597/20, -2.529550585786411*^-6}, 
     {799/10, -2.5098700286163567*^-6}, {1599/20, -2.489774435704417*^-6}, 
     {80, -2.454853158487258*^-6}, {1601/20, -2.3635730335008764*^-6}, 
     {801/10, -2.380809491026037*^-6}, {1603/20, -2.2508940055315785*^-6}, 
     {401/5, -2.2302852768218973*^-6}, {321/4, -2.173113734821319*^-6}, 
     {803/10, -2.045638216055523*^-6}, {1607/20, -1.9271544269700014*^-6}, 
     {402/5, -1.8492144921444797*^-6}, {1609/20, -1.7360415905526283*^-6}, 
     {161/2, -1.6461715988541625*^-6}, {1611/20, -1.5245095583704682*^-6}, 
     {403/5, -1.3738868335638754*^-6}, {1613/20, -1.2631971247067941*^-6}, 
     {807/10, -1.1442671345174293*^-6}, {323/4, -1.0234457715613265*^-6}, 
     {404/5, -8.18338472111102*^-7}, {1617/20, -7.315527480594719*^-7}, 
     {809/10, -5.382675964324402*^-7}, {1619/20, -4.2409073816584986*^-7}, 
     {81, -2.6813183373608496*^-7}, {1621/20, -1.0363451870276652*^-7}, 
     {811/10, 8.046565122543647*^-9}, {1623/20, 1.9113586782401604*^-7}, 
     {406/5, 3.5051325743273853*^-7}, {325/4, 5.039549018162615*^-7}, 
     {813/10, 6.415149348994176*^-7}, {1627/20, 7.90999501842915*^-7}, 
     {407/5, 9.213879808437145*^-7}, {1629/20, 1.0561935258260454*^-6}, 
     {163/2, 1.1639250313468658*^-6}, {1631/20, 1.3104142670711943*^-6}, 
     {408/5, 1.405066887410003*^-6}, {1633/20, 1.5273132953214086*^-6}, 
     {817/10, 1.636704514952625*^-6}, {327/4, 1.728810549377069*^-6}, 
     {409/5, 1.8375314611018823*^-6}, {1637/20, 1.9199192545227284*^-6}, 
     {819/10, 2.0063707229581174*^-6}, {1639/20, 2.0748104006679258*^-6}, 
     {82, 2.163685015175998*^-6}, {1641/20, 2.211775614331668*^-6}, 
     {821/10, 2.235178200159227*^-6}, {1643/20, 2.2621795825877866*^-6}, 
     {411/5, 2.3086923378046187*^-6}, {329/4, 2.3482423944509723*^-6}, 
     {823/10, 2.359497517631648*^-6}, {1647/20, 2.38627681814485*^-6}, 
     {412/5, 2.345686884744347*^-6}, {1649/20, 2.338993704664727*^-6}, 
     {165/2, 2.3400436768017396*^-6}, {1651/20, 2.3217452019830276*^-6}, 
     {413/5, 2.2482554080938133*^-6}, {1653/20, 2.1947408901101806*^-6}, 
     {827/10, 2.1517737041620855*^-6}, {331/4, 2.115709313660341*^-6}, 
     {414/5, 2.009725975041232*^-6}, {1657/20, 1.9774712376463555*^-6}, 
     {829/10, 1.8826544226080433*^-6}, {1659/20, 1.769923159408715*^-6}, 
     {83, 1.7175308259509414*^-6}, {1661/20, 1.6072023216184839*^-6}, 
     {831/10, 1.5072987426256734*^-6}, {1663/20, 1.3838777407210179*^-6}, 
     {416/5, 1.2574908265922113*^-6}, {333/4, 1.1736886743329844*^-6}, 
     {833/10, 1.0244497309214173*^-6}, {1667/20, 8.693645970614394*^-7}, 
     {417/5, 7.794220084761383*^-7}, {1669/20, 6.407106626568626*^-7}, 
     {167/2, 5.720355401583888*^-7}, {1671/20, 4.0744856265317875*^-7}, 
     {418/5, 2.5977046154423977*^-7}, {1673/20, 1.5325683049710603*^-7}, 
     {837/10, 2.8475244884251794*^-8}, {335/4, -1.1840189748091312*^-7}, 
     {419/5, -2.6357332470056116*^-7}, {1677/20, -3.967120771886101*^-7}, 
     {839/10, -5.325865267448437*^-7}, {1679/20, -6.54831025473368*^-7}, 
     {84, -7.43953833043029*^-7}, {1681/20, -8.644701770402566*^-7}, 
     {841/10, -1.0041606116374668*^-6}, {1683/20, -1.0909936809088555*^-6}, 
     {421/5, -1.1737013559075249*^-6}, {337/4, -1.311199052542178*^-6}, 
     {843/10, -1.3667809474898762*^-6}, {1687/20, -1.4910480697974404*^-6}, 
     {422/5, -1.5728838941297951*^-6}, {1689/20, -1.6308865432926312*^-6}, 
     {169/2, -1.6918460304105043*^-6}, {1691/20, -1.7590112568119376*^-6}, 
     {423/5, -1.8298404533406698*^-6}, {1693/20, -1.8853813723504476*^-6}, 
     {847/10, -1.9375344316174825*^-6}, {339/4, -1.9350378352711584*^-6}, 
     {424/5, -1.9553121986259914*^-6}, {1697/20, -1.998930357072215*^-6}, 
     {849/10, -2.037988879655117*^-6}, {1699/20, -1.989222420881176*^-6}, 
     {85, -2.027556889008797*^-6}, {1701/20, -2.0250447044650732*^-6}, 
     {851/10, -2.020923461215629*^-6}, {1703/20, -1.966573150491424*^-6}, 
     {426/5, -1.975004520926582*^-6}, {341/4, -1.9067968912156452*^-6}, 
     {853/10, -1.905330244578174*^-6}, {1707/20, -1.855452534171853*^-6}, 
     {427/5, -1.7904571336241348*^-6}, {1709/20, -1.7460307532024544*^-6}, 
     {171/2, -1.6901968280524926*^-6}, {1711/20, -1.618230718036795*^-6}, 
     {428/5, -1.5588955537548799*^-6}, {1713/20, -1.5042435321938052*^-6}, 
     {857/10, -1.3985920724740586*^-6}, {343/4, -1.3299231730601324*^-6}, 
     {429/5, -1.2382621115553105*^-6}, {1717/20, -1.144981021938829*^-6}, 
     {859/10, -1.0096735748449381*^-6}, {1719/20, -9.1140363485398*^-7}, 
     {86, -8.397448804792207*^-7}, {1721/20, -7.299830606724567*^-7}, 
     {861/10, -6.4062586289243*^-7}, {1723/20, -5.002082924532303*^-7}, 
     {431/5, -4.261042596612197*^-7}, {345/4, -3.1973566669979414*^-7}, 
     {863/10, -2.3465608141315375*^-7}, {1727/20, -9.092772022128992*^-8}, 
     {432/5, 3.467727163058987*^-8}, {1729/20, 1.3131484888004308*^-7}, 
     {173/2, 2.629456032215982*^-7}, {1731/20, 3.703139598350974*^-7}, 
     {433/5, 4.532854642937817*^-7}, {1733/20, 5.65597226242099*^-7}, 
     {867/10, 6.78747848288988*^-7}, {347/4, 7.669898761265143*^-7}, 
     {434/5, 8.875528955086531*^-7}, {1737/20, 9.789091176409803*^-7}, 
     {869/10, 1.053013395167779*^-6}, {1739/20, 1.1474792418128543*^-6}, 
     {87, 1.251854142896025*^-6}, {1741/20, 1.3046315325698776*^-6}, 
     {871/10, 1.3891810881835887*^-6}, {1743/20, 1.427857690430856*^-6}, 
     {436/5, 1.5501790703795204*^-6}, {349/4, 1.5924062475650147*^-6}, 
     {873/10, 1.6193832049760104*^-6}, {1747/20, 1.686746474938161*^-6}, 
     {437/5, 1.7109594819542107*^-6}, {1749/20, 1.7973611499827458*^-6}, 
     {175/2, 1.8215450569014635*^-6}, {1751/20, 1.8335692064108677*^-6}, 
     {438/5, 1.7892815507014603*^-6}, {1753/20, 1.8813302145731514*^-6}, 
     {877/10, 1.8513276263953937*^-6}, {351/4, 1.8722470042503714*^-6}, 
     {439/5, 1.8603288745172586*^-6}, {1757/20, 1.8236915091257577*^-6}, 
     {879/10, 1.832115397948364*^-6}, {1759/20, 1.8279871871335063*^-6}, 
     {88, 1.734072549108845*^-6}, {1761/20, 1.7124286564584867*^-6}, 
     {881/10, 1.6990651074272334*^-6}, {1763/20, 1.6054363040363118*^-6}, 
     {441/5, 1.609094469057215*^-6}, {353/4, 1.5269417865670931*^-6}, 
     {883/10, 1.4668304516851638*^-6}, {1767/20, 1.419324557466739*^-6}, 
     {442/5, 1.3255545580348471*^-6}, {1769/20, 1.2228813237452618*^-6}, 
     {177/2, 1.1403667176945742*^-6}, {1771/20, 1.0809570517855693*^-6}, 
     {443/5, 9.54998889177161*^-7}, {1773/20, 8.581614127922688*^-7}, 
     {887/10, 7.757359125892815*^-7}, {355/4, 6.72073113550109*^-7}, 
     {444/5, 6.057490260988341*^-7}, {1777/20, 4.479659967346339*^-7}, 
     {889/10, 3.6605592297622724*^-7}, {1779/20, 2.85864691550175*^-7}, 
     {89, 1.3263995672987972*^-7}, {1781/20, 8.8518545632299*^-8}, 
     {891/10, -7.855420659438894*^-8}, {1783/20, -2.1406710640388404*^-7}, 
     {446/5, -2.847793040428731*^-7}, {357/4, -3.616044797140512*^-7}, 
     {893/10, -5.373710808311005*^-7}, {1787/20, -5.954589556815548*^-7}, 
     {447/5, -7.187816097597999*^-7}, {1789/20, -8.28052875153501*^-7}, 
     {179/2, -9.177003456664612*^-7}, {1791/20, -1.0222231267356663*^-6}, 
     {448/5, -1.133389861740497*^-6}, {1793/20, -1.1841797556769174*^-6}, 
     {897/10, -1.2636728249498796*^-6}, {359/4, -1.3487997794214834*^-6}, 
     {449/5, -1.432665097916841*^-6}, {1797/20, -1.4908720968390132*^-6}, 
     {899/10, -1.580735115053189*^-6}, {1799/20, -1.6456830252420396*^-6}, 
     {90, -1.6765743171276437*^-6}, {1801/20, -1.7225217659039282*^-6}, 
     {901/10, -1.755245915696646*^-6}, {1803/20, -1.8131386274877759*^-6}, 
     {451/5, -1.788974179947611*^-6}, {361/4, -1.8237947840282764*^-6}, 
     {903/10, -1.8397900251043708*^-6}, {1807/20, -1.8674927273198971*^-6}, 
     {452/5, -1.8343933171904858*^-6}, {1809/20, -1.835504906261276*^-6}, 
     {181/2, -1.8061268310110012*^-6}, {1811/20, -1.8110253049152814*^-6}, 
     {453/5, -1.8114379234240863*^-6}, {1813/20, -1.7185868280561456*^-6}, 
     {907/10, -1.676953258561431*^-6}, {363/4, -1.6152534894064985*^-6}, 
     {454/5, -1.608400428024237*^-6}, {1817/20, -1.5470226083225125*^-6}, 
     {909/10, -1.4608197411170032*^-6}, {1819/20, -1.3672244568718739*^-6}, 
     {91, -1.2776601498593054*^-6}, {1821/20, -1.1949291707918919*^-6}, 
     {911/10, -1.1290621580797855*^-6}, {1823/20, -1.0657364119884272*^-6}, 
     {456/5, -9.300391607680591*^-7}, {365/4, -8.287843671489492*^-7}, 
     {913/10, -7.523209847939971*^-7}, {1827/20, -6.523775783473518*^-7}, 
     {457/5, -5.0268030795525*^-7}, {1829/20, -4.232268183551602*^-7}, 
     {183/2, -2.849115087535936*^-7}, {1831/20, -1.9969204372374816*^-7}, 
     {458/5, -8.650656667733014*^-8}, {1833/20, 1.6602756247943717*^-8}, 
     {917/10, 1.2822373105306206*^-7}, {367/4, 2.3238525619084793*^-7}, 
     {459/5, 3.404938216635062*^-7}, {1837/20, 4.269971078480969*^-7}, 
     {919/10, 5.704552613807617*^-7}, {1839/20, 7.118138469833224*^-7}, 
     {92, 7.359654043935515*^-7}, {1841/20, 8.349937100811389*^-7}, 
     {921/10, 9.375572016488698*^-7}, {1843/20, 1.0416395773774068*^-6}, 
     {461/5, 1.1573731498668027*^-6}, {369/4, 1.1893527068346232*^-6}, 
     {923/10, 1.2814234855926254*^-6}, {1847/20, 1.3631478440051525*^-6}, 
     {462/5, 1.4054897639476094*^-6}, {1849/20, 1.468062647419499*^-6}, 
     {185/2, 1.5137779927759665*^-6}, {1851/20, 1.5393309245811948*^-6}, 
     {463/5, 1.6002003700929524*^-6}, {1853/20, 1.641961410316084*^-6}, 
     {927/10, 1.6613953959243588*^-6}, {371/4, 1.6600280845768811*^-6}, 
     {464/5, 1.6850101574317211*^-6}, {1857/20, 1.726779190289185*^-6}, 
     {929/10, 1.6673820226464908*^-6}, {1859/20, 1.6697264067361273*^-6}, 
     {93, 1.6568991179632953*^-6}, {1861/20, 1.6467201188752334*^-6}, 
     {931/10, 1.6457559094129603*^-6}, {1863/20, 1.5811814276928127*^-6}, 
     {466/5, 1.5306513953955436*^-6}, {373/4, 1.5006778305570734*^-6}, 
     {933/10, 1.4321051827609343*^-6}, {1867/20, 1.3671541969073608*^-6}, 
     {467/5, 1.333337890527253*^-6}, {1869/20, 1.2619225823115587*^-6}, 
     {187/2, 1.1971486352513327*^-6}, {1871/20, 1.0752344138595382*^-6}, 
     {468/5, 9.849393125954675*^-7}, {1873/20, 9.244381493078713*^-7}, 
     {937/10, 8.344942416249612*^-7}, {375/4, 7.660357289052122*^-7}, 
     {469/5, 6.870090898114523*^-7}, {1877/20, 5.849829638818194*^-7}, 
     {939/10, 5.0740092002316*^-7}, {1879/20, 4.036332739640325*^-7}, 
     {94, 2.717582275116315*^-7}, {1881/20, 2.0345981377456468*^-7}, 
     {941/10, 1.0322068221685354*^-7}, {1883/20, 3.905484004251836*^-8}, 
     {471/5, -1.4670470761118937*^-7}, {377/4, -1.9423845867318212*^-7}, 
     {943/10, -2.698047603770515*^-7}, {1887/20, -3.4849589139809845*^-7}, 
     {472/5, -4.1018452996217014*^-7}, {1889/20, -5.240876404977342*^-7}, 
     {189/2, -6.069845432700449*^-7}, {1891/20, -6.68114651058288*^-7}, 
     {473/5, -7.699120566709294*^-7}, {1893/20, -7.860551052910059*^-7}, 
     {947/10, -9.059988780937833*^-7}, {379/4, -9.394870434768776*^-7}, 
     {474/5, -1.0090343268778779*^-6}, {1897/20, -1.0477012646961659*^-6}, 
     {949/10, -1.1010731809923957*^-6}, {1899/20, -1.1364750613640506*^-6}, 
     {95, -1.178342291657808*^-6}, {1901/20, -1.1984192730615795*^-6}, 
     {951/10, -1.1808501508558944*^-6}, {1903/20, -1.2361891913448275*^-6}, 
     {476/5, -1.2628512653309332*^-6}, {381/4, -1.2315880348334751*^-6}, 
     {953/10, -1.2527937551035095*^-6}, {1907/20, -1.2704781915395813*^-6}, 
     {477/5, -1.2648052324926162*^-6}, {1909/20, -1.2752856601364049*^-6}, 
     {191/2, -1.2663234147114455*^-6}, {1911/20, -1.2164036870196404*^-6}, 
     {478/5, -1.195617315513653*^-6}, {1913/20, -1.1880015529722177*^-6}, 
     {957/10, -1.1284317503953978*^-6}, {383/4, -1.0760673245513441*^-6}, 
     {479/5, -1.0734638024104126*^-6}, {1917/20, -1.0425074326164685*^-6}, 
     {959/10, -9.809602090210534*^-7}, {1919/20, -9.206436066694357*^-7}, 
     {96, -8.531334052749862*^-7}, {1921/20, -8.085646350519671*^-7}, 
     {961/10, -7.894108552883305*^-7}, {1923/20, -6.796292719435382*^-7}, 
     {481/5, -6.499942898849365*^-7}, {385/4, -5.983250550914421*^-7}, 
     {963/10, -5.677226482675435*^-7}, {1927/20, -4.183588065836963*^-7}, 
     {482/5, -3.74881918015213*^-7}, {1929/20, -3.5209449016082583*^-7}, 
     {193/2, -2.981442661781353*^-7}, {1931/20, -2.712266945481545*^-7}, 
     {483/5, -1.745024259154626*^-7}, {1933/20, -1.3033731754985567*^-7}, 
     {967/10, -5.971704332072281*^-8}, {387/4, 4.570657959751534*^-9}, 
     {484/5, 6.288731385639679*^-8}, {1937/20, 1.0443161868600725*^-7}, 
     {969/10, 1.645504036293377*^-7}, {1939/20, 2.2387257397026017*^-7}, 
     {97, 2.475241452403257*^-7}, {1941/20, 2.7815515712351774*^-7}, 
     {971/10, 3.226705643633829*^-7}, {1943/20, 3.5811825784904175*^-7}, 
     {486/5, 4.178687571356268*^-7}, {389/4, 4.3893492136792833*^-7}, 
     {973/10, 4.4873892444605157*^-7}, {1947/20, 5.301874478058632*^-7}, 
     {487/5, 5.446006811904436*^-7}, {1949/20, 5.888184882382741*^-7}, 
     {195/2, 6.022373728771513*^-7}, {1951/20, 6.448070886920509*^-7}, 
     {488/5, 6.194846331741832*^-7}, {1953/20, 6.59718054303593*^-7}, 
     {977/10, 6.577142437277916*^-7}, {391/4, 6.446054335029761*^-7}, 
     {489/5, 6.845964116986014*^-7}, {1957/20, 6.881495643179525*^-7}, 
     {979/10, 7.113875701431072*^-7}, {1959/20, 6.923826855673165*^-7}, 
     {98, 6.998028538179879*^-7}, {1961/20, 7.179631279011223*^-7}, 
     {981/10, 6.97160305561384*^-7}, {1963/20, 7.177511737316289*^-7}, 
     {491/5, 6.674600053838131*^-7}, {393/4, 6.808386698586855*^-7}, 
     {983/10, 6.757990962252824*^-7}, {1967/20, 6.741981042057699*^-7}, 
     {492/5, 6.549759751992013*^-7}, {1969/20, 6.446553886124695*^-7}, 
     {197/2, 6.367342250054864*^-7}, {1971/20, 6.062613712443099*^-7}, 
     {493/5, 6.396823802740093*^-7}, {1973/20, 6.169666223604375*^-7}, 
     {987/10, 5.546405039830171*^-7}, {395/4, 5.781496203033365*^-7}, 
     {494/5, 5.688744406581736*^-7}, {1977/20, 5.382010930740644*^-7}, 
     {989/10, 5.327750138978127*^-7}, {1979/20, 5.069998497142514*^-7}, 
     {99, 4.6488444561954*^-7}, {1981/20, 4.7252730017016686*^-7}, 
     {991/10, 4.787567501884915*^-7}, {1983/20, 4.3942875115055013*^-7}, 
     {496/5, 4.2295007273568386*^-7}, {397/4, 4.192651655229862*^-7}, 
     {993/10, 3.9418393248114025*^-7}, {1987/20, 3.614310775841567*^-7}, 
     {497/5, 3.310796912701919*^-7}, {1989/20, 3.2530345600231825*^-7}, 
     {199/2, 3.0334390516140175*^-7}, {1991/20, 2.874177334188932*^-7}, 
     {498/5, 2.4005010708372243*^-7}, {1993/20, 2.403534859161949*^-7}, 
     {997/10, 2.2599326576777656*^-7}, {399/4, 1.767397575427182*^-7}, 
     {499/5, 1.617569601866306*^-7}, {1997/20, 1.3188542047912546*^-7}, 
     {999/10, 1.0385098741334461*^-7}, {1999/20, 8.777123555302885*^-8}, 
     {100, 2.505204304940889*^-8}}
