In this version I am using fits to get p^b_w for large values of T  The fits were computed in fits_integrands_September_2022.  They ended up in the folder below even though Zach didn’t compute them.

SetDirectory["C:\\MyPath\\Wolfram Mathematica\\PaulAnderson"]

<<"Fits_for_chib.m";

fit1 = fit1/.{wp->omegap};

fit2 = fit2/.{wp->omegap};

fit3 = fit3/.{wp->omegap};

fit4 = fit4/.{wp->omegap};

fit5 = fit5/.{wp->omegap};

Notes

This program is computing PBW using fits for chi^b_w’.  There are 5 bands of frequencies between  w’ = 10^-4 and 100.  For larger frequencies we are assuming that the contribution is negligible.  This needs to be checked.  For smaller frequencies we should be able to just use the fit for the smallest band - if we only integrate using chi^b for the massive field which is infrared finite.  So for that part only, we don’t subtract chi^b for the massless field.

Definitions

xb = 1/10;

xc = ((-xb)/2)+Sqrt[1-(3*xb^2)/4];

x0=(101*xb)/100;

x1=(((10^9)-1)*xc)/(10^9);

(* r1 and r2 are the values of x that we want to compute the mode functions *)

r1 = 3/10;

r2 = 6/10;

m=1;

f = -(1/x)*(x-xc)*(x-xb)*(x+xc+xb);

fp = D[f,x];

κb=(1/(2*xb))*(xc-xb)*(xc+(2*xb));

κc=(1/(2*xc))*(xc-xb)*((2*xc)+xb);

κN=(1/(2(xc+xb)))*((2*xc)+xb)*(xc+(2*xb));

xstar = (1/(2*κb))*Log[(x-xb)/(xc-xb)]-(1/(2*κc))*Log[-(x-xc)/(xc-xb)]+(1/(2*κN))*Log[(x+xc+xb)/(xc+(2*xb))]-(xc/(4*xb*κb))*Log[((2*xc)+xb)/(xc+(2*xb))]-(xb*xc)/(2*(xc-xb))*Log[(xb/xc)];

xstar1 = N[xstar/.{x-> x1}];

xstarp = D[xstar,x];

xstarp1 = N[D[xstar,x]/.{x->x1}];

These are the Bogolubov coefficients.  These should be checked.
We have only fit chi^b.  We have not yet fit chi^c so we can’t compute p^c.

xstar1 = N[xstar/.{x-> 3/10}]

(* αcw = (1/(2*Pi))*Sqrt[omegap/omega]*(κc^(-1-(I*(omegap/κc))))*((Gamma[δ-(I*(omegap/κc))])/(((-I*omega)+ϵ)^(-I*(omegap/κc)))); *)

(* βcw = (1/(2*Pi))*Sqrt[omegap/omega]*(κc^(-1+(I*(omegap/κc))))*((Gamma[δ+(I*(omegap/κc))])/(((-I*omega)+ϵ)^(I*(omegap/κc)))); *)

αbw = (1/(2*Pi))*Sqrt[omegap/omega]*(κb^(-1-(I*(omegap/κb))))*((Gamma[δ-(I*(omegap/κb))])/(((-I*omega)+ϵ)^(-I*(omegap/κb))));

βbw =(1/(2*Pi))*Sqrt[omegap/omega]*(κb^(-1+(I*(omegap/κb))))*((Gamma[δ+(I*(omegap/κb))])/(((-I*omega)+ϵ)^(I*(omegap/κb))));

We are going to use the usual time t and not the well-behaved time T, but I’ll keep the hx for T just in case we change our minds.

hx = (1/(2*κb))*Log[Abs[(x-xb)]/(xc-xb)]+(1/(2*κc))*Log[Abs[(x-xc)]/(xc-xb)]+(1/2)*((xc)/(xb*κb)-(1/κN))*Log[(x+xc+xb)/(xc + 2*xb)]-((xb*xc)/(2*(xc-xb)))*Log[(x^2)/(xc*xb)]+(xc/(4*xb*κb))*Log[(xc+2*xb)/(2*xc+xb)];

(* u=(T-hx)-xstar;  *)

u=t-xstar;

(* v=(T-hx)+xstar; *)

v = t + xstar;

The fits are for the following ranges:  
Band 1.  w’ = 10^(-4) to 10^(-2)
Band 2.  w’ = 10^(-2) to 1
Band 3:  w’ = 1 to 6
Band 4:  w’ = 6 to 50
Band 5: w’ = 50 to 100

Pbw Calculations:

Exact integrand for p^b_w  at r = r1 for the integral from w’ = 0 to w’ = 10^(-4).  I’ll call this Band 0.  There will be no subtraction of the massless modes and I’ll use the fit for Band 1.  At some point we should check this and make sure it is accurate.

Int0r1 =  Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*fit1+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*Conjugate[fit1]];

Int0r1 = Expand[Int0r1/.{Conjugate[omegap]->omegap}];

Next, I’ll write the integrands for bands 1 - 5.  These have the massless chi^b subtracted.  
a=-0.0677511;

Int1r1 =Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*(fit1-Exp[I*omegap*(-0.0677510672722334)])+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*(Conjugate[fit1]-Exp[I*omegap*(-0.0677510672722334)])];

Int1r1 = Expand[Int1r1/.{Conjugate[omegap]->omegap}];

Int2r1 =  Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*(fit2-Exp[I*omegap*(-0.0677510672722334)])+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*(Conjugate[fit2]-Exp[-I*omegap*(-0.0677510672722334)])];

Int2r1 = Expand[Int2r1/.{Conjugate[omegap]->omegap}];

Int3r1 =  Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*(fit3-Exp[I*omegap*(-0.0677510672722334)])+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*(Conjugate[fit3]-Exp[-I*omegap*(-0.0677510672722334)])];

Int3r1 = Expand[Int3r1/.{Conjugate[omegap]->omegap}];

Int4r1 =  Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*(fit4-Exp[I*omegap*(-0.0677510672722334)])+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*(Conjugate[fit4]-Exp[-I*omegap*((-0.0677510672722334))])];

Int4r1 = Expand[Int4r1/.{Conjugate[omegap]->omegap}];

Int5r1 =  Expand[(αbw/.{δ->0,ϵ->0})*(Exp[-I*omegap*t]/Sqrt[4*Pi*omegap])*(fit5-Exp[I*omegap*(-0.0677510672722334)])+(βbw/.{δ->0,ϵ->0})*(Exp[I*omegap*t]/Sqrt[4*Pi*omegap])*(Conjugate[fit5]-Exp[-I*omegap*(-0.0677510672722334)])];

Int5r1 = Expand[Int5r1/.{Conjugate[omegap]->omegap}];

Next we can look at the integrands for t = 0 and then we can numerically compute the integrals.

N[Int0r1/.{omega->1/10,omegap->10^(-4),t->0}]

N[xstar/.{x-> 3/10}]

(* Here, we numerically compute the contribution of each band to the mode function pb. *)

Table[{j,Re[NIntegrate[Int1r1/.{omega->1/10,t->j},{omegap,10^(-4),10^(-2)}]]},{j,1,200}]

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ListLinePlot[T30]

Table[{j,Re[NIntegrate[Int1r1/.{omega->1/10,t->j},{omegap,10^(-4),10^(-2)}]]},{j,1,500}]

T31={{1,0.002842595142089151`},{2,0.000031599100424075434`},{3,-0.0027793979987967626`},{4,-0.005590301513181822`},{5,-0.008401016805954663`},{6,-0.011211449251631977`},{7,-0.014021504241700795`},{8,-0.016831087190294487`},{9,-0.019640103539867147`},{10,-0.022448458766865947`},{11,-0.025256058387401092`},{12,-0.0280628079629129`},{13,-0.03086861310583566`},{14,-0.033673379485257886`},{15,-0.03647701283257844`},{16,-0.0392794189471583`},{17,-0.04208050370196741`},{18,-0.0448801730492263`},{19,-0.047678333026042054`},{20,-0.05047488976003813`},{21,-0.053269749474977916`},{22,-0.05606281849638119`},{23,-0.058854003257133455`},{24,-0.06164321030308757`},{25,-0.0644303462986573`},{26,-0.06721531803240245`},{27,-0.06999803242260506`},{28,-0.07277839652283648`},{29,-0.07555631752751454`},{30,-0.07833170277745094`},{31,-0.08110445976538798`},{32,-0.08387449614152472`},{33,-0.08664171971903135`},{34,-0.0894060384795528`},{35,-0.0921673605786993`},{36,-0.09492559435152544`},{37,-0.0976806483179959`},{38,-0.10043243118843816`},{39,-0.10318085186898139`},{40,-0.10592581946698194`},{41,-0.10866724329643387`},{42,-0.11140503288336503`},{43,-0.11413909797121799`},{44,-0.11686934852621549`},{45,-0.11959569474270983`},{46,-0.12231804704851633`},{47,-0.1250363161102298`},{48,-0.12775041283852423`},{49,-0.13046024839343479`},{50,-0.13316573418962258`},{51,-0.13586678190162055`},{52,-0.13856330346906162`},{53,-0.14125521110188716`},{54,-0.14394241728553694`},{55,-0.146624834786119`},{56,-0.1493023766555596`},{57,-0.15197495623673277`},{58,-0.15464248716856951`},{59,-0.15730488339114548`},{60,-0.15996205915074724`},{61,-0.1626139290049171`},{62,-0.16526040782747559`},{63,-0.16790141081352108`},{64,-0.17053685348440717`},{65,-0.17316665169269638`},{66,-0.17579072162709058`},{67,-0.17840897981733733`},{68,-0.18102134313911192`},{69,-0.1836277288188752`},{70,-0.18622805443870563`},{71,-0.18882223794110728`},{72,-0.1914101976337909`},{73,-0.19399185219443024`},{74,-0.19656712067539087`},{75,-0.19913592250843362`},{76,-0.20169817750939006`},{77,-0.2042538058828113`},{78,-0.2068027282265889`},{79,-0.2093448655365479`},{80,-0.2118801392110119`},{81,-0.2144084710553389`},{82,-0.21692978328642898`},{83,-0.2194439985372024`},{84,-0.2219510398610483`},{85,-0.2244508307362434`},{86,-0.22694329507034086`},{87,-0.2294283572045284`},{88,-0.23190594191795588`},{89,-0.23437597443203204`},{90,-0.23683838041468921`},{91,-0.23929308598461713`},{92,-0.24174001771546452`},{93,-0.24417910264000844`},{94,-0.24661026825429097`},{95,-0.2490334425217237`},{96,-0.25144855387715814`},{97,-0.253855531230924`},{98,-0.2562543039728329`},{99,-0.25864480197614814`},{100,-0.26102695560152134`},{101,-0.26340069570089303`},{102,-0.26576595362136035`},{103,-0.26812266120900785`},{104,-0.2704707508127047`},{105,-0.2728101552878653`},{106,-0.2751408080001745`},{107,-0.27746264282927713`},{108,-0.2797755941724303`},{109,-0.28207959694812046`},{110,-0.2843745865996428`},{111,-0.2866604990986437`},{112,-0.2889372709486262`},{113,-0.29120483918841794`},{114,-0.2934631413956014`},{115,-0.29571211568990585`},{116,-0.29795170073656174`},{117,-0.30018183574961593`},{118,-0.30240246049520897`},{119,-0.3046135152948131`},{120,-0.30681494102843143`},{121,-0.30900667913775764`},{122,-0.3111886716292962`},{123,-0.3133608610774434`},{124,-0.31552319062752715`},{125,-0.31767560399880884`},{126,-0.3198180454874426`},{127,-0.3219504599693955`},{128,-0.3240727929033265`},{129,-0.3261849903334253`},{130,-0.32828699889220836`},{131,-0.3303787658032757`},{132,-0.3324602388840252`},{133,-0.33453136654832544`},{134,-0.33659209780914673`},{135,-0.3386423822811503`},{136,-0.3406821701832353`},{137,-0.342711412341044`},{138,-0.34473006018942337`},{139,-0.34673806577484534`},{140,-0.34873538175778374`},{141,-0.35072196141504847`},{142,-0.3526977586420758`},{143,-0.3546627279551775`},{144,-0.3566168244937444`},{145,-0.3585600040224076`},{146,-0.3604922229331564`},{147,-0.3624134382474113`},{148,-0.3643236076180545`},{149,-0.36622268933141544`},{150,-0.3681106423092127`},{151,-0.36998742611045177`},{152,-0.3718530009332775`},{153,-0.37370732761678377`},{154,-0.3755503676427775`},{155,-0.3773820831374977`},{156,-0.3792024368732911`},{157,-0.3810113922702413`},{158,-0.3828089133977543`},{159,-0.38459496497609863`},{160,-0.38636951237789957`},{161,-0.3881325216295895`},{162,-0.3898839594128118`},{163,-0.39162379306577993`},{164,-0.3933519905845913`},{165,-0.3950685206244951`},{166,-0.3967733525011149`},{167,-0.3984664561916253`},{168,-0.40014780233588354`},{169,-0.40181736223751463`},{170,-0.4034751078649511`},{171,-0.40512101185242694`},{172,-0.4067550475009251`},{173,-0.40837718877908025`},{174,-0.4099874103240337`},{175,-0.41158568744224455`},{176,-0.41317199611025285`},{177,-0.41474631297539816`},{178,-0.41630861535649066`},{179,-0.4178588812444376`},{180,-0.4193970893028225`},{181,-0.4209232188684387`},{182,-0.42243724995177667`},{183,-0.42393916323746544`},{184,-0.42542894008466736`},{185,-0.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ListLinePlot[T31]

Table[{j,Re[NIntegrate[Int5r1/.{omega->1/10,t->j},{omegap,50,100}]]},{j,1,10}]

T32={{1,-0.000017085898238438846`},{2,-7.549884205907253`*^-6},{3,-2.3156035730184755`*^-6},{4,5.819701413846844`*^-7},{5,2.0231040219467366`*^-6},{6,2.567752572402246`*^-6},{7,2.6334512499672307`*^-6},{8,2.5287169617799446`*^-6},{9,2.451109299617387`*^-6},{10,2.4863279413890607`*^-6}};

ListLinePlot[T32]

Table[{j/10,Re[NIntegrate[Int1r1/.{omega->1/10,t->j/10},{omegap,10^(-4),10^(-2)}]]},{j,1,100}]

T1={{(1/10),0.005372412453400439`},{(1/5),0.005091327614189363`},{(3/10),0.004810241060870953`},{(2/5),0.0045291528880801735`},{(1/2),0.004248063190452964`},{(3/5),0.003966972062626177`},{(7/10),0.003685879599237522`},{(4/5),0.0034047858949255135`},{(9/10),0.0031236910443294087`},{1,0.002842595142089151`},{(11/10),0.0025614982828453168`},{(6/5),0.0022804005612390545`},{(13/10),0.0019993020719120333`},{(7/5),0.0017182029095063804`},{(3/2),0.0014371031686646267`},{(8/5),0.001156002944029651`},{(17/10),0.0008749023302446231`},{(9/5),0.0005938014219529453`},{(19/10),0.00031270031379819626`},{2,0.000031599100424075434`},{(21/10),-0.0002495021235256566`},{(11/5),-0.0005306032634072287`},{(23/10),-0.0008117042245769224`},{(12/5),-0.001092804912391132`},{(5/2),-0.0013739052322064064`},{(13/5),-0.00165500508937952`},{(27/10),-0.0019361043892675259`},{(14/5),-0.0022172030372278077`},{(29/10),-0.0024983009386181456`},{3,-0.0027793979987967626`},{(31/10),-0.0030604941231223894`},{(16/5),-0.003341589216954318`},{(33/10),-0.0036226831856524568`},{(17/5),-0.0039037759345773907`},{(7/2),-0.004184867369090438`},{(18/5),-0.004465957394553702`},{(37/10),-0.004747045916330134`},{(19/5),-0.005028132839783587`},{(39/10),-0.005309218070278873`},{4,-0.005590301513181822`},{(41/10),-0.0058713830738593275`},{(21/5),-0.006152462657679428`},{(43/10),-0.006433540170011331`},{(22/5),-0.006714615516225503`},{(9/2),-0.006995688601693693`},{(23/5),-0.007276759331789024`},{(47/10),-0.007557827611886019`},{(24/5),-0.007838893347360676`},{(49/10),-0.008119956443590521`},{5,-0.008401016805954663`},{(51/10),-0.008682074339833848`},{(26/5),-0.008963128950610525`},{(53/10),-0.009244180543668887`},{(27/5),-0.009525229024394951`},{(11/2),-0.009806274298176586`},{(28/5),-0.010087316270403601`},{(57/10),-0.010368354846467776`},{(29/5),-0.010649389931762928`},{(59/10),-0.010930421431684975`},{6,-0.011211449251631977`},{(61/10),-0.011492473297004212`},{(31/5),-0.011773493473204222`},{(63/10),-0.012054509685636854`},{(32/5),-0.012335521839709354`},{(13/2),-0.012616529840831395`},{(33/5),-0.012897533594415134`},{(67/10),-0.013178533005875293`},{(34/5),-0.013459527980629181`},{(69/10),-0.013740518424096782`},{7,-0.014021504241700795`},{(71/10),-0.01430248533886669`},{(36/5),-0.014583461621022777`},{(73/10),-0.014864432993600248`},{(37/5),-0.015145399362033242`},{(15/2),-0.015426360631758902`},{(38/5),-0.015707316708217428`},{(77/10),-0.015988267496852143`},{(39/5),-0.016269212903109526`},{(79/10),-0.01655015283243931`},{8,-0.016831087190294487`},{(81/10),-0.01711201588213141`},{(41/5),-0.017392938813409822`},{(83/10),-0.017673855889592936`},{(42/5),-0.017954767016147455`},{(17/2),-0.018235672098543664`},{(43/5),-0.018516571042255483`},{(87/10),-0.018797463752760504`},{(44/5),-0.01907835013554007`},{(89/10),-0.019359230096079275`},{9,-0.019640103539867147`},{(91/10),-0.019920970372396547`},{(46/5),-0.020201830499164346`},{(93/10),-0.020482683825671432`},{(47/5),-0.020763530257422756`},{(19/2),-0.02104436969992742`},{(48/5),-0.021325202058698714`},{(97/10),-0.02160602723925417`},{(49/5),-0.021886845147115665`},{(99/10),-0.022167655687809377`},{10,-0.022448458766865947`}};

Table[{j/10,Re[NIntegrate[Int2r1/.{omega->1/10,t->j/10},{omegap,10^(-2),1}]]},{j,1,100}]

T2={{(1/10),0.2981948388252674`},{(1/5),0.2834764813931134`},{(3/10),0.26820658834666`},{(2/5),0.252414035296862`},{(1/2),0.23613011972076076`},{(3/5),0.2193884100203258`},{(7/10),0.20222458051430886`},{(4/5),0.18467623343232348`},{(9/10),0.16678270907438053`},{1,0.14858488538108522`},{(11/10),0.1301249682356157`},{(6/5),0.11144627388296738`},{(13/10),0.09259300490579975`},{(7/5),0.07361002124151915`},{(3/2),0.05454260775602767`},{(8/5),0.03543623991244545`},{(17/10),0.016336349082689848`},{(9/5),-0.002711910951600595`},{(19/10),-0.021663894775436295`},{2,-0.04047569188462369`},{(21/10),-0.05910434752362827`},{(11/5),-0.07750807638927659`},{(23/10),-0.09564646782873354`},{(12/5),-0.11348068122731228`},{(5/2),-0.13097363035671822`},{(13/5),-0.14809015553973445`},{(27/10),-0.16479718257946724`},{(14/5),-0.18106386750253253`},{(29/10),-0.19686172627146797`},{3,-0.212164748733775`},{(31/10),-0.22694949619356747`},{(16/5),-0.2411951821114454`},{(33/10),-0.2548837355636127`},{(17/5),-0.2679998472159322`},{(7/2),-0.28053099769700673`},{(18/5),-0.29246746838002546`},{(37/10),-0.3038023347098525`},{(19/5),-0.3145314423358311`},{(39/10),-0.32465336643087817`},{4,-0.33416935469607156`},{(41/10),-0.3430832546610493`},{(21/5),-0.35140142599787166`},{(43/10),-0.35913263866708994`},{(22/5),-0.3662879578067114`},{(9/2),-0.37288061595383554`},{(23/5),-0.3789258761101052`},{(47/10),-0.38444088072875876`},{(24/5),-0.3894444958710132`},{(49/10),-0.39395714577922153`},{5,-0.3980006415435011`},{(51/10),-0.4015980047846958`},{(26/5),-0.4047732876903244`},{(53/10),-0.4075513907463399`},{(27/5),-0.4099578795073567`},{(11/2),-0.4120188017330106`},{(28/5),-0.41376050661389285`},{(57/10),-0.4152094648419125`},{(29/5),-0.41639209707186786`},{(59/10),-0.4173346035007314`},{6,-0.41806280204292046`},{(61/10),-0.4186019736003622`},{(31/5),-0.4189767158293679`},{(63/10),-0.4192108062978311`},{(32/5),-0.4193270758380758`},{(13/2),-0.4193472928086193`},{(33/5),-0.419292058879839`},{(67/10),-0.4191807168589899`},{(34/5),-0.4190312709654676`},{(69/10),-0.4188603198633584`},{7,-0.4186830026509336`},{(71/10),-0.41851295790254056`},{(36/5),-0.4183622957513988`},{(73/10),-0.41824158289977686`},{(37/5),-0.41815984034168246`},{(15/2),-0.4181245534858002`},{(38/5),-0.41814169427225206`},{(77/10),-0.4182157547902118`},{(39/5),-0.4183497918171856`},{(79/10),-0.4185454816274866`},{8,-0.4188031843426548`},{(81/10),-0.4191220170386614`},{(41/5),-0.41949993476379815`},{(83/10),-0.4199338185771384`},{(42/5),-0.42041956967729843`},{(17/2),-0.4209522086581474`},{(43/5),-0.4215259789091619`},{(87/10),-0.422134453161117`},{(44/5),-0.42277064217517796`},{(89/10),-0.42342710457492877`},{9,-0.4240960568343041`},{(91/10),-0.4247694824541914`},{(46/5),-0.4254392393864412`},{(93/10),-0.4260971648037861`},{(47/5),-0.42673517635163793`},{(19/2),-0.42734536907135545`},{(48/5),-0.42792010723759566`},{(97/10),-0.4284521104140098`},{(49/5),-0.428934533097869`},{(99/10),-0.42936103739364717`},{10,-0.42972585823038173`}};

Table[{j/10,Re[NIntegrate[Int3r1/.{omega->1/10,t->j/10},{omegap,1,6}]]},{j,1,100}]

T3={{(1/10),0.024700689062948`},{(1/5),0.02136985031287569`},{(3/10),0.0180019459707181`},{(2/5),0.014466470108924982`},{(1/2),0.010685995243017691`},{(3/5),0.0066716965718548096`},{(7/10),0.0025261648334008605`},{(4/5),-0.0015835944499785854`},{(9/10),-0.005471539490171869`},{1,-0.008980524896802702`},{(11/10),-0.012017713524667947`},{(6/5),-0.014567655083373203`},{(13/10),-0.016681044668579063`},{(7/5),-0.018444963137693206`},{(3/2),-0.01994574474633455`},{(8/5),-0.021237028021724516`},{(17/10),-0.022322866308242498`},{(9/5),-0.02316014306249355`},{(19/10),-0.023677951344598977`},{2,-0.023806229559644662`},{(21/10),-0.023503443400589366`},{(11/5),-0.022774091104486208`},{(23/10),-0.021670748844541315`},{(12/5),-0.020280800897516778`},{(5/2),-0.01870305525463314`},{(13/5),-0.017022491991499453`},{(27/10),-0.015291541150016491`},{(14/5),-0.013523648652691352`},{(29/10),-0.011700483099890894`},{3,-0.009789514767322564`},{(31/10),-0.0077654044537865535`},{(16/5),-0.005627703512157142`},{(33/10),-0.003408983090181841`},{(17/5),-0.0011710202385422793`},{(7/2),0.0010091910146097609`},{(18/5),0.003058478766800341`},{(37/10),0.004924974544715165`},{(19/5),0.006588235363056675`},{(39/10),0.008058932544090508`},{4,0.00936868266767098`},{(41/10),0.010553901160343906`},{(21/5),0.011639418714855205`},{(43/10),0.012627444891547452`},{(22/5),0.013495423228498843`},{(9/2),0.014203158947540807`},{(23/5),0.014706427685491682`},{(47/10),0.014972165279213738`},{(24/5),0.014989972232121979`},{(49/10),0.014776102988107368`},{5,0.014368799989673919`},{(51/10),0.013816818520990369`},{(26/5),0.013165244827131335`},{(53/10),0.012443495081095893`},{(27/5),0.011659475841561278`},{(11/2),0.0108016520882407`},{(28/5),0.009848009863435246`},{(57/10),0.008778574141677894`},{(29/5),0.007587028442844328`},{(59/10),0.006287425459354854`},{6,0.00491377844818695`},{(61/10),0.003512827722466431`},{(31/5),0.0021326079652398784`},{(63/10),0.0008108085109411047`},{(32/5),-0.00043311975039644803`},{(13/2),-0.001599548787473261`},{(33/5),-0.002703618077805375`},{(67/10),-0.0037654921089376606`},{(34/5),-0.004799436867655277`},{(69/10),-0.0058055303040026925`},{7,-0.006766814725971744`},{(71/10),-0.007652752958045048`},{(36/5),-0.008427658256367062`},{(73/10),-0.009061087068822669`},{(37/5),-0.009536579116308432`},{(15/2),-0.009855781388230817`},{(38/5),-0.010036647550914666`},{(77/10),-0.010106469845498482`},{(39/5),-0.010092256868981414`},{(79/10),-0.010011822388776216`},{8,-0.009868624309177664`},{(81/10),-0.009652029821853628`},{(41/5),-0.009342773003546684`},{(83/10),-0.008921585148956166`},{(42/5),-0.008377927032944524`},{(17/2),-0.007715781597635544`},{(43/5),-0.006954542477760256`},{(87/10),-0.006124764388389374`},{(44/5),-0.005260316903091791`},{(89/10),-0.00438969009661689`},{9,-0.003529436170558696`},{(91/10),-0.002681933143464102`},{(46/5),-0.0018381217382757793`},{(93/10),-0.0009841380929621227`},{(47/5),-0.00010944259563343183`},{(19/2),0.0007864230901366383`},{(48/5),0.0016907881220744768`},{(97/10),0.0025795239973743314`},{(49/5),0.003422795268799662`},{(99/10),0.004192850445039082`},{10,0.004871145516838181`}};

Table[{j/10,Re[NIntegrate[Int4r1/.{omega->1/10,t->j/10},{omegap,6,50}]]},{j,1,100}]

T4={{(1/10),0.0009539221097538006`},{(1/5),0.0005037412509611579`},{(3/10),-0.0000376057195529116`},{(2/5),-0.0004747882736924951`},{(1/2),-0.0006987046367555033`},{(3/5),-0.0006777426921337614`},{(7/10),-0.0004345090394531143`},{(4/5),-0.000053902490772286966`},{(9/10),0.0003188762757912247`},{1,0.0005380818684167393`},{(11/10),0.000537955900025177`},{(6/5),0.0003556668853587448`},{(13/10),0.00008300414955412597`},{(7/5),-0.00018984748597625196`},{(3/2),-0.0003888475766652416`},{(8/5),-0.00045172212694909815`},{(17/10),-0.00034871684241862244`},{(9/5),-0.00011779961892400504`},{(19/10),0.0001392361537529353`},{2,0.00031554118921091996`},{(21/10),0.0003606502821669818`},{(11/5),0.00028825981841326535`},{(23/10),0.0001392711872870852`},{(12/5),-0.000045321729762701896`},{(5/2),-0.00021807606581026798`},{(13/5),-0.0003183383901961778`},{(27/10),-0.0002987641313321664`},{(14/5),-0.00016491912885579113`},{(29/10),0.00002051186529091678`},{3,0.0001794257947873729`},{(31/10),0.00026295927217103224`},{(16/5),0.0002594872642144079`},{(33/10),0.00017668468312466245`},{(17/5),0.000034323885539011575`},{(7/2),-0.00012526334454425036`},{(18/5),-0.00023934309580485484`},{(37/10),-0.00025709426449116706`},{(19/5),-0.00017534734630833375`},{(39/10),-0.00003884233254666953`},{4,0.00009467625459689667`},{(41/10),0.00018602715594642777`},{(21/5),0.00021704799025464063`},{(43/10),0.00017958765766602793`},{(22/5),0.00007855620521429949`},{(9/2),-0.00005438486517481723`},{(23/5),-0.0001647784387739225`},{(47/10),-0.0002060215537499288`},{(24/5),-0.00016884633590279189`},{(49/10),-0.00007986514502611921`},{5,0.000024335889631851767`},{(51/10),0.00011572743545769433`},{(26/5),0.00017231845448277`},{(53/10),0.0001732016830286956`},{(27/5),0.00011007862943215916`},{(11/2),3.8914694898720625`*^-6},{(28/5),-0.00009971106822372007`},{(57/10),-0.0001584409681513798`},{(29/5),-0.0001576386373157093`},{(59/10),-0.00010843276021640401`},{6,-0.000030141811737394195`},{(61/10),0.00005801485013184336`},{(31/5),0.00013147267829843748`},{(63/10),0.00016065727550691703`},{(32/5),0.00012825090860943753`},{(13/2),0.000046746907263558066`},{(33/5),-0.00004666769226340561`},{(67/10),-0.00011506520589855927`},{(34/5),-0.00014079265787669452`},{(69/10),-0.00012328283444882132`},{7,-0.00006835008746112315`},{(71/10),0.000012173416808871157`},{(36/5),0.00009331587034891623`},{(73/10),0.00014117671849638605`},{(37/5),0.00013327897042003553`},{(15/2),0.00007539676918406888`},{(38/5),-3.9613116024080726`*^-6},{(77/10),-0.00007460842381318531`},{(39/5),-0.00011825614233046228`},{(79/10),-0.0001258441884937137`},{8,-0.00009259737358993857`},{(81/10),-0.00002376493278115699`},{(41/5),0.00005729196265744587`},{(83/10),0.00011593276510649532`},{(42/5),0.00012746949007982057`},{(17/2),0.00009220092868593046`},{(43/5),0.000029798866526519794`},{(87/10),-0.00003721982004607618`},{(44/5),-0.00009168163951202944`},{(89/10),-0.00011864430474311964`},{9,-0.00010523704107734653`},{(91/10),-0.00005091347484590369`},{(46/5),0.000024095025687686823`},{(93/10),0.00008711835071817163`},{(47/5),0.00011350983127671631`},{(19/2),0.00009917368422419283`},{(48/5),0.000055198548747894796`},{(97/10),-3.884921319931745`*^-6},{(49/5),-0.00006321607149676424`},{(99/10),-0.00010419615629202132`},{10,-0.00010818497094512602`}};

ListLinePlot[T1+T2+T3+T4]

Table[{j/10,Re[NIntegrate[Int5r1/.{omega->1/10,t->j/10},{omegap,50,100}]]},{j,1,100}]

T5={{(1/10),7.781050863858478`*^-6},{(1/5),0.000018378616641705033`},{(3/10),0.000023021585847518435`},{(2/5),-0.000018615618548826793`},{(1/2),-0.000025154984628313575`},{(3/5),7.788629147339817`*^-6},{(7/10),0.000014538605478584129`},{(4/5),0.000016438841037271996`},{(9/10),-0.0000180784774543487`},{1,-0.000017085898238438846`},{(11/10),7.408847338791259`*^-6},{(6/5),0.000012377216316519683`},{(13/10),0.000011808831309818275`},{(7/5),-0.00001736747132797964`},{(3/2),-0.000011559213986541074`},{(8/5),6.879895890002128`*^-6},{(17/10),0.00001101850750500441`},{(9/5),8.20282372172938`*^-6},{(19/10),-0.000016452923550349282`},{2,-7.549884205907253`*^-6},{(21/10),6.316198931940453`*^-6},{(11/5),0.000010075436660553642`},{(23/10),5.224430519564434`*^-6},{(12/5),-0.000015347258836707527`},{(5/2),-4.560861491104761`*^-6},{(13/5),5.7805725361531305`*^-6},{(27/10),9.342781850269509`*^-6},{(14/5),2.6879755796078257`*^-6},{(29/10),-0.000014078725295017057`},{3,-2.3156035730184755`*^-6},{(31/10),5.309859266779253`*^-6},{(16/5),8.698912384028057`*^-6},{(33/10),5.036469444571968`*^-7},{(17/5),-0.0000126836911110112`},{(7/2),-6.412992659978987`*^-7},{(18/5),4.924406965057886`*^-6},{(37/10),8.067639908895282`*^-6},{(19/5),-1.3712004170513395`*^-6},{(39/10),-0.00001120286852326123`},{4,5.819701413846844`*^-7},{(41/10),4.632406248753122`*^-6},{(21/5),7.401085927293849`*^-6},{(43/10),-2.955738649127482`*^-6},{(22/5),-9.678567740124574`*^-6},{(9/2),1.445327902996825`*^-6},{(23/5),4.432282997902767`*^-6},{(47/10),6.671212125236528`*^-6},{(24/5),-4.258342157477892`*^-6},{(49/10),-8.152639966795312`*^-6},{5,2.0231040219467366`*^-6},{(51/10),4.314602942255987`*^-6},{(26/5),5.865126944249471`*^-6},{(53/10),-5.283880135902231`*^-6},{(27/5),-6.6644984627342234`*^-6},{(11/2),2.378755066731153`*^-6},{(28/5),4.263693537825939`*^-6},{(57/10),4.981989148436802`*^-6},{(29/5),-6.038118313675825`*^-6},{(59/10),-5.249546556976264`*^-6},{6,2.567752572402246`*^-6},{(61/10),4.259368752550755`*^-6},{(31/5),4.030741771459434`*^-6},{(63/10),-6.530224242600903`*^-6},{(32/5),-3.9377947180509926`*^-6},{(13/2),2.6386563612615987`*^-6},{(33/5),4.278597959219377`*^-6},{(67/10),3.028044121540251`*^-6},{(34/5),-6.77415342089474`*^-6},{(69/10),-2.752871730577203`*^-6},{7,2.6334512499672307`*^-6},{(71/10),4.297247231224075`*^-6},{(36/5),1.996361690212217`*^-6},{(73/10),-6.7891149701850155`*^-6},{(37/5),-1.7113844242521863`*^-6},{(15/2),2.5873768940373163`*^-6},{(38/5),4.291729600815341`*^-6},{(77/10),9.620635257993249`*^-7},{(39/5),-6.599407648124916`*^-6},{(79/10),-8.226587313506841`*^-7},{8,2.5287169617799446`*^-6},{(81/10),4.240518074540193`*^-6},{(41/5),-4.646349518306577`*^-8},{(83/10),-6.233721927461278`*^-6},{(42/5),-8.886394204013935`*^-8},{(17/2),2.4786196932475484`*^-6},{(43/5),4.125510467129347`*^-6},{(87/10),-1.0006412197922188`*^-6},{(44/5),-5.724138811686829`*^-6},{(89/10),4.945141803721285`*^-7},{9,2.451109299617387`*^-6},{(91/10),3.933085121389366`*^-6},{(46/5),-1.873376936409462`*^-6},{(93/10),-5.104842721359828`*^-6},{(47/5),9.378480594545595`*^-7},{(19/2),2.453385237211615`*^-6},{(48/5),3.6548883238025777`*^-6},{(97/10),-2.6405861294311704`*^-6},{(49/5),-4.410682444620538`*^-6},{(99/10),1.2563254343425332`*^-6},{10,2.4863279413890607`*^-6}};

(*Since the integral were not converging very fast, we subtracted off the corresponding 2D modes-massless case- to the integral in the previous integral. Here we add them back. *)

Table[{j/10,Re[(1/Sqrt[4*Pi/10])*Exp[(I/(10*κb))*Exp[-κb*((j/10)+0.0677511)]]-0.44603102903]},{j,1,100}]

N[1/(2*Sqrt[4*Pi*(1/10)])]

T6={{(1/10),0.4459937726526595`},{(1/5),0.44601690571842134`},{(3/10),0.44602567512354074`},{(2/5),0.44602899946378727`},{(1/2),0.44603025966586696`},{(3/5),0.44603073738725507`},{(7/10),0.4460309184833525`},{(4/5),0.4460309871338146`},{(9/10),0.44603101315804083`},{1,0.4460310230233836`},{(11/10),0.44603102676316764`},{(6/5),0.4460310281808565`},{(13/10),0.44603102871827816`},{(7/5),0.44603102892200563`},{(3/2),0.4460310289992353`},{(8/5),0.44603102902851166`},{(17/10),0.4460310290396099`},{(9/5),0.446031029043817`},{(19/10),0.4460310290454119`},{2,0.44603102904601644`},{(21/10),0.4460310290462457`},{(11/5),0.4460310290463325`},{(23/10),0.4460310290463655`},{(12/5),0.4460310290463779`},{(5/2),0.4460310290463827`},{(13/5),0.4460310290463845`},{(27/10),0.44603102904638514`},{(14/5),0.44603102904638536`},{(29/10),0.4460310290463855`},{3,0.4460310290463856`},{(31/10),0.4460310290463856`},{(16/5),0.4460310290463856`},{(33/10),0.4460310290463856`},{(17/5),0.4460310290463856`},{(7/2),0.4460310290463856`},{(18/5),0.4460310290463856`},{(37/10),0.4460310290463856`},{(19/5),0.4460310290463856`},{(39/10),0.4460310290463856`},{4,0.4460310290463856`},{(41/10),0.4460310290463856`},{(21/5),0.4460310290463856`},{(43/10),0.4460310290463856`},{(22/5),0.4460310290463856`},{(9/2),0.4460310290463856`},{(23/5),0.4460310290463856`},{(47/10),0.4460310290463856`},{(24/5),0.4460310290463856`},{(49/10),0.4460310290463856`},{5,0.4460310290463856`},{(51/10),0.4460310290463856`},{(26/5),0.4460310290463856`},{(53/10),0.4460310290463856`},{(27/5),0.4460310290463856`},{(11/2),0.4460310290463856`},{(28/5),0.4460310290463856`},{(57/10),0.4460310290463856`},{(29/5),0.4460310290463856`},{(59/10),0.4460310290463856`},{6,0.4460310290463856`},{(61/10),0.4460310290463856`},{(31/5),0.4460310290463856`},{(63/10),0.4460310290463856`},{(32/5),0.4460310290463856`},{(13/2),0.4460310290463856`},{(33/5),0.4460310290463856`},{(67/10),0.4460310290463856`},{(34/5),0.4460310290463856`},{(69/10),0.4460310290463856`},{7,0.4460310290463856`},{(71/10),0.4460310290463856`},{(36/5),0.4460310290463856`},{(73/10),0.4460310290463856`},{(37/5),0.4460310290463856`},{(15/2),0.4460310290463856`},{(38/5),0.4460310290463856`},{(77/10),0.4460310290463856`},{(39/5),0.4460310290463856`},{(79/10),0.4460310290463856`},{8,0.4460310290463856`},{(81/10),0.4460310290463856`},{(41/5),0.4460310290463856`},{(83/10),0.4460310290463856`},{(42/5),0.4460310290463856`},{(17/2),0.4460310290463856`},{(43/5),0.4460310290463856`},{(87/10),0.4460310290463856`},{(44/5),0.4460310290463856`},{(89/10),0.4460310290463856`},{9,0.4460310290463856`},{(91/10),0.4460310290463856`},{(46/5),0.4460310290463856`},{(93/10),0.4460310290463856`},{(47/5),0.4460310290463856`},{(19/2),0.4460310290463856`},{(48/5),0.4460310290463856`},{(97/10),0.4460310290463856`},{(49/5),0.4460310290463856`},{(99/10),0.4460310290463856`},{10,0.4460310290463856`}};

T1+T2+T3+T4+T5+T6

{{(3/5)*(1/6),0.775223416154893`},{(6/5)*(1/6),0.7564766849062026`},{(9/5)*(1/6),0.7370298663680843`},{(12/5)*(1/6),0.7169452538654131`},{3*(1/6),0.6963705781987145`},{(18/5)*(1/6),0.6753878619790754`},{(21/5)*(1/6),0.6540475729963253`},{(24/5)*(1/6),0.63249094836135`},{(27/5)*(1/6),0.6107666715849158`},{6*(1/6),0.5889989746199336`},{(33/5)*(1/6),0.5672451445043246`},{(36/5)*(1/6),0.545558091643365`},{(39/5)*(1/6),0.5240371040082749`},{(42/5)*(1/6),0.5027070749780337`},{9*(1/6),0.48166458838694126`},{(48/5)*(1/6),0.4609414016322031`},{(51/5)*(1/6),0.44058171580938826`},{(54/5)*(1/6),0.42064317965647346`},{(57/5)*(1/6),0.40112466646937744`},{12*(1/6),0.38208869800717715`},{(63/5)*(1/6),0.36354070247960135`},{(66/5)*(1/6),0.3455165935442363`},{(69/5)*(1/6),0.3280466037663204`},{(72/5)*(1/6),0.3111160730205583`},{15*(1/6),0.2947578012755236`},{(78/5)*(1/6),0.278950818608111`},{(81/5)*(1/6),0.263716779578152`},{(84/5)*(1/6),0.2490640787006575`},{(87/5)*(1/6),0.23497695187640436`},{18*(1/6),0.22147447773770562`},{(93/5)*(1/6),0.20852390340734694`},{(96/5)*(1/6),0.19613474038242718`},{(99/5)*(1/6),0.18429281553700771`},{(102/5)*(1/6),0.17297802585176175`},{21*(1/6),0.16219845035108793`},{(108/5)*(1/6),0.15192166334976698`},{(111/5)*(1/6),0.14215759634033587`},{(114/5)*(1/6),0.1328829706871022`},{(117/5)*(1/6),0.1240773318882491`},{24*(1/6),0.11573531372954143`},{(123/5)*(1/6),0.10782095203401604`},{(126/5)*(1/6),0.10034100818187158`},{(129/5)*(1/6),0.09326892701984862`},{(132/5)*(1/6),0.08659275658942167`},{27*(1/6),0.08030494390112536`},{(138/5)*(1/6),0.07437447513420703`},{(141/5)*(1/6),0.06880513564332985`},{(144/5)*(1/6),0.06356450738207348`},{(147/5)*(1/6),0.058642012026688006`},{30*(1/6),0.054024529680257505`},{(153/5)*(1/6),0.04968781048124621`},{(156/5)*(1/6),0.04563804081400902`},{(159/5)*(1/6),0.04184687064036546`},{(162/5)*(1/6),0.03831081048716467`},{33*(1/6),0.035013875327995714`},{(168/5)*(1/6),0.03193576865083847`},{(171/5)*(1/6),0.029078324520680265`},{(174/5)*(1/6),0.02641289372996969`},{(177/5)*(1/6),0.023939747266550626`},{36*(1/6),0.021642982140855138`},{(183/5)*(1/6),0.019511684090369963`},{(186/5)*(1/6),0.017548931129123257`},{(189/5)*(1/6),0.015730648625123078`},{(192/5)*(1/6),0.014059624732095322`},{39*(1/6),0.01251704317308644`},{(198/5)*(1/6),0.011095429400021839`},{(201/5)*(1/6),0.009794249910805686`},{(204/5)*(1/6),0.008593226421335975`},{(207/5)*(1/6),0.007498624748748239`},{42*(1/6),0.006493990791568316`},{(213/5)*(1/6),0.005579303510973355`},{(216/5)*(1/6),0.004752925649636086`},{(219/5)*(1/6),0.003998313687711974`},{(222/5)*(1/6),0.003320777812357234`},{45*(1/6),0.002702317686673783`},{(228/5)*(1/6),0.002145700932999872`},{(231/5)*(1/6),0.0016468905535358402`},{(234/5)*(1/6),0.001194911907130447`},{(237/5)*(1/6),0.0007969053504583434`},{48*(1/6),0.0004380645476305123`},{(243/5)*(1/6),0.00012544188903251818`},{(246/5)*(1/6),-0.0001473720352068164`},{(249/5)*(1/6),-0.00038853152612289277`},{(252/5)*(1/6),-0.0005938540538670822`},{51*(1/6),-0.0007779537595618558`},{(258/5)*(1/6),-0.0009321390057984158`},{(261/5)*(1/6),-0.0010638727171471407`},{(264/5)*(1/6),-0.0011756859457479618`},{(267/5)*(1/6),-0.0012631455118020662`},{54*(1/6),-0.0013373534301220902`},{(273/5)*(1/6),-0.0013883373133909416`},{(276/5)*(1/6),-0.0014259409287444846`},{(279/5)*(1/6),-0.0014509441680372603`},{(282/5)*(1/6),-0.0014626724789724155`},{57*(1/6),-0.0014706595652991816`},{(288/5)*(1/6),-0.0014646386907626319`},{(291/5)*(1/6),-0.0014541101169533999`},{(294/5)*(1/6),-0.0014351806837407666`},{(297/5)*(1/6),-0.001407753420889557`},{60*(1/6),-0.0013778410770276528`}};

(* This is the real part of the mode function.*)

TRe={{(1/10),0.775223416154893`},{(1/5),0.7564766849062026`},{(3/10),0.7370298663680843`},{(2/5),0.7169452538654131`},{(1/2),0.6963705781987145`},{(3/5),0.6753878619790754`},{(7/10),0.6540475729963253`},{(4/5),0.63249094836135`},{(9/10),0.6107666715849158`},{1,0.5889989746199336`},{(11/10),0.5672451445043246`},{(6/5),0.545558091643365`},{(13/10),0.5240371040082749`},{(7/5),0.5027070749780337`},{(3/2),0.48166458838694126`},{(8/5),0.4609414016322031`},{(17/10),0.44058171580938826`},{(9/5),0.42064317965647346`},{(19/10),0.40112466646937744`},{2,0.38208869800717715`},{(21/10),0.36354070247960135`},{(11/5),0.3455165935442363`},{(23/10),0.3280466037663204`},{(12/5),0.3111160730205583`},{(5/2),0.2947578012755236`},{(13/5),0.278950818608111`},{(27/10),0.263716779578152`},{(14/5),0.2490640787006575`},{(29/10),0.23497695187640436`},{3,0.22147447773770562`},{(31/10),0.20852390340734694`},{(16/5),0.19613474038242718`},{(33/10),0.18429281553700771`},{(17/5),0.17297802585176175`},{(7/2),0.16219845035108793`},{(18/5),0.15192166334976698`},{(37/10),0.14215759634033587`},{(19/5),0.1328829706871022`},{(39/10),0.1240773318882491`},{4,0.11573531372954143`},{(41/10),0.10782095203401604`},{(21/5),0.10034100818187158`},{(43/10),0.09326892701984862`},{(22/5),0.08659275658942167`},{(9/2),0.08030494390112536`},{(23/5),0.07437447513420703`},{(47/10),0.06880513564332985`},{(24/5),0.06356450738207348`},{(49/10),0.058642012026688006`},{5,0.054024529680257505`},{(51/10),0.04968781048124621`},{(26/5),0.04563804081400902`},{(53/10),0.04184687064036546`},{(27/5),0.03831081048716467`},{(11/2),0.035013875327995714`},{(28/5),0.03193576865083847`},{(57/10),0.029078324520680265`},{(29/5),0.02641289372996969`},{(59/10),0.023939747266550626`},{6,0.021642982140855138`},{(61/10),0.019511684090369963`},{(31/5),0.017548931129123257`},{(63/10),0.015730648625123078`},{(32/5),0.014059624732095322`},{(13/2),0.01251704317308644`},{(33/5),0.011095429400021839`},{(67/10),0.009794249910805686`},{(34/5),0.008593226421335975`},{(69/10),0.007498624748748239`},{7,0.006493990791568316`},{(71/10),0.005579303510973355`},{(36/5),0.004752925649636086`},{(73/10),0.003998313687711974`},{(37/5),0.003320777812357234`},{(15/2),0.002702317686673783`},{(38/5),0.002145700932999872`},{(77/10),0.0016468905535358402`},{(39/5),0.001194911907130447`},{(79/10),0.0007969053504583434`},{8,0.0004380645476305123`},{(81/10),0.00012544188903251818`},{(41/5),-0.0001473720352068164`},{(83/10),-0.00038853152612289277`},{(42/5),-0.0005938540538670822`},{(17/2),-0.0007779537595618558`},{(43/5),-0.0009321390057984158`},{(87/10),-0.0010638727171471407`},{(44/5),-0.0011756859457479618`},{(89/10),-0.0012631455118020662`},{9,-0.0013373534301220902`},{(91/10),-0.0013883373133909416`},{(46/5),-0.0014259409287444846`},{(93/10),-0.0014509441680372603`},{(47/5),-0.0014626724789724155`},{(19/2),-0.0014706595652991816`},{(48/5),-0.0014646386907626319`},{(97/10),-0.0014541101169533999`},{(49/5),-0.0014351806837407666`},{(99/10),-0.001407753420889557`},{10,-0.0013778410770276528`}};

ListLinePlot[TRe]

(* Here, we just look at the imaginary part of the modes (Figure1, right plot)*)

Table[{j/10,Im[NIntegrate[Int1r1/.{omega->1/10,t->j/10},{omegap,10^(-4),10^(-2)}]]},{j,1,100}]

T11={{(1/10),-0.0009096096054283367`},{(1/5),-0.0009095191316327716`},{(3/10),-0.0009094283517636453`},{(2/5),-0.0009093372658659895`},{(1/2),-0.0009092458739849813`},{(3/5),-0.0009091541761658034`},{(7/10),-0.0009090621724537703`},{(4/5),-0.000908969862894278`},{(9/10),-0.000908877247533465`},{1,-0.0009087843264171043`},{(11/10),-0.0009086910995912441`},{(6/5),-0.0009085975671024657`},{(13/10),-0.0009085037289971036`},{(7/5),-0.0009084095853217675`},{(3/2),-0.0009083151361235506`},{(8/5),-0.0009082203814493997`},{(17/10),-0.0009081253213463905`},{(9/5),-0.0009080299558623022`},{(19/10),-0.0009079342850443861`},{2,-0.0009078383089405704`},{(21/10),-0.0009077420275990509`},{(11/5),-0.0009076454410675773`},{(23/10),-0.0009075485493947223`},{(12/5),-0.0009074513526289379`},{(5/2),-0.0009073538508190249`},{(13/5),-0.0009072560440137756`},{(27/10),-0.0009071579322624466`},{(14/5),-0.0009070595156137937`},{(29/10),-0.0009069607941177537`},{3,-0.0009068617678236832`},{(31/10),-0.0009067624367815955`},{(16/5),-0.0009066628010411936`},{(33/10),-0.0009065628606530245`},{(17/5),-0.0009064626156669477`},{(7/2),-0.0009063620661340431`},{(18/5),-0.00090626121210454`},{(37/10),-0.0009061600536296309`},{(19/5),-0.0009060585907602047`},{(39/10),-0.0009059568235477641`},{4,-0.000905854752043517`},{(41/10),-0.0009057523762990554`},{(21/5),-0.0009056496963664977`},{(43/10),-0.000905546712297523`},{(22/5),-0.0009054434241444853`},{(9/2),-0.0009053398319596327`},{(23/5),-0.00090523593579565`},{(47/10),-0.0009051317357052116`},{(24/5),-0.000905027231741064`},{(49/10),-0.0009049224239562871`},{5,-0.0009048173124043588`},{(51/10),-0.0009047118971386612`},{(26/5),-0.00090460617821283`},{(53/10),-0.0009045001556805459`},{(27/5),-0.0009043938295960263`},{(11/2),-0.0009042872000130309`},{(28/5),-0.0009041802669864232`},{(57/10),-0.000904073030570378`},{(29/5),-0.0009039654908201088`},{(59/10),-0.0009038576477898378`},{6,-0.0009037495015349983`},{(61/10),-0.00090364105211104`},{(31/5),-0.0009035322995730108`},{(63/10),-0.0009034232439768774`},{(32/5),-0.0009033138853781548`},{(13/2),-0.0009032042238332655`},{(33/5),-0.0009030942593979433`},{(67/10),-0.0009029839921287394`},{(34/5),-0.0009028734220822129`},{(69/10),-0.0009027625493150646`},{7,-0.0009026513738841972`},{(71/10),-0.0009025398958465012`},{(36/5),-0.0009024281152594942`},{(73/10),-0.0009023160321805495`},{(37/5),-0.0009022036466673111`},{(15/2),-0.0009020909587775101`},{(38/5),-0.000901977968569227`},{(77/10),-0.000901864676100554`},{(39/5),-0.0009017510814300278`},{(79/10),-0.0009016371846159159`},{8,-0.0009015229857169687`},{(81/10),-0.0009014084847922077`},{(41/5),-0.0009012936819007252`},{(83/10),-0.0009011785771013827`},{(42/5),-0.0009010631704542105`},{(17/2),-0.00090094746201853`},{(43/5),-0.0009008314518540401`},{(87/10),-0.0009007151400209271`},{(44/5),-0.00090059852657917`},{(89/10),-0.0009004816115894422`},{9,-0.0009003643951117964`},{(91/10),-0.0009002468772072578`},{(46/5),-0.000900129057936535`},{(93/10),-0.0009000109373607537`},{(47/5),-0.0008998925155412329`},{(19/2),-0.0008997737925391739`},{(48/5),-0.0008996547684164773`},{(97/10),-0.0008995354432346846`},{(49/5),-0.0008994158170558505`},{(99/10),-0.0008992958899422576`},{10,-0.0008991756619558098`}};

Table[{j/10,Im[NIntegrate[Int2r1/.{omega->1/10,t->j/10},{omegap,10^(-2),1}]]},{j,1,100}]

T22={{(1/10),-0.046468886068677065`},{(1/5),-0.04827026986489232`},{(3/10),-0.04998361953170744`},{(2/5),-0.051601033176304045`},{(1/2),-0.053115063829087206`},{(3/5),-0.054518765489116716`},{(7/10),-0.05580573594531698`},{(4/5),-0.05697015606864654`},{(9/10),-0.058006825297318265`},{1,-0.058911193064991374`},{(11/10),-0.05967938595174163`},{(6/5),-0.06030823036907795`},{(13/10),-0.06079527062459111`},{(7/5),-0.06113878224450227`},{(3/2),-0.06133778046868238`},{(8/5),-0.06139202386844542`},{(17/10),-0.061302013072911596`},{(9/5),-0.06106898462657965`},{(19/10),-0.060694900036335535`},{2,-0.06018243010169627`},{(21/10),-0.05953493465644151`},{(11/5),-0.05875643788359483`},{(23/10),-0.057851599397691925`},{(12/5),-0.056825681318953776`},{(5/2),-0.05568451159251354`},{(13/5),-0.05443444383310231`},{(27/10),-0.05308231399907695`},{(14/5),-0.051635394222858615`},{(29/10),-0.05010134414311587`},{3,-0.04848816010133877`},{(31/10),-0.046804122579370465`},{(16/5),-0.04505774226395773`},{(33/10),-0.043257705134233465`},{(17/5),-0.04141281697051076`},{(7/2),-0.03953194768603306`},{(18/5),-0.037623975880362134`},{(37/10),-0.03569773400967747`},{(19/5),-0.0337619545603459`},{(39/10),-0.03182521760256079`},{4,-0.029895900086483566`},{(41/10),-0.027982127227648233`},{(21/5),-0.026091726309143005`},{(43/10),-0.024232183207356574`},{(22/5),-0.022410601924171117`},{(9/2),-0.020633667347999086`},{(23/5),-0.01890761168924373`},{(47/10),-0.01723818424123715`},{(24/5),-0.015630625387422572`},{(49/10),-0.014089644420918087`},{5,-0.012619401517799774`},{(51/10),-0.011223493899969794`},{(26/5),-0.00990494622896103`},{(53/10),-0.008666205240531001`},{(27/5),-0.007509138595557754`},{(11/2),-0.006435037891939195`},{(28/5),-0.005444625722046969`},{(57/10),-0.004538066819679075`},{(29/5),-0.003714982755979177`},{(59/10),-0.0029744705189581576`},{6,-0.002315124405554321`},{(61/10),-0.0017350611444493479`},{(31/5),-0.0012319479794473034`},{(63/10),-0.0008030334467554936`},{(32/5),-0.0004451805612819392`},{(13/2),-0.00015490211352829804`},{(33/5),0.00007160223577016601`},{(67/10),0.0002384073837745932`},{(34/5),0.0003498230650089921`},{(69/10),0.0004103533155858097`},{7,0.00042465545495957296`},{(71/10),0.0003974989193432539`},{(36/5),0.00033372427475866946`},{(73/10),0.00023820273246564702`},{(37/5),0.00011579647968193787`},{(15/2),-0.000028679872963371066`},{(38/5),-0.00019049643985783425`},{(77/10),-0.00036504353299793204`},{(39/5),-0.0005478652061307386`},{(79/10),-0.0007346906369168709`},{8,-0.0009214631358297623`},{(81/10),-0.0011043665936278932`},{(41/5),-0.001279849203232636`},{(83/10),-0.0014446443180088767`},{(42/5),-0.0015957883339693874`},{(17/2),-0.0017306355106967359`},{(43/5),-0.0018468696726575483`},{(87/10),-0.0019425127600657278`},{(44/5),-0.0020159302253825685`},{(89/10),-0.002065833298455987`},{9,-0.002091278169234041`},{(91/10),-0.0020916621626661984`},{(46/5),-0.00206671700470089`},{(93/10),-0.0020164993008283377`},{(47/5),-0.0019413783718297403`},{(19/2),-0.001842021609621474`},{(48/5),-0.0017193775365799795`},{(97/10),-0.0015746567666585047`},{(49/5),-0.0014093110824035648`},{(99/10),-0.0012250108541904904`},{10,-0.0010236210381722793`}};

Table[{j/10,Im[NIntegrate[Int3r1/.{omega->1/10,t->j/10},{omegap,1,6}]]},{j,1,100}]

T33={{(1/10),-0.01066687935863704`},{(1/5),-0.010915087676506764`},{(3/10),-0.011260173801445547`},{(2/5),-0.011691046274448533`},{(1/2),-0.012105368702683689`},{(3/5),-0.012358702574612183`},{(7/10),-0.012319907433338238`},{(4/5),-0.011915736243704931`},{(9/10),-0.011152439180017147`},{1,-0.010110249702088672`},{(11/10),-0.008915230128472725`},{(6/5),-0.007699469287772566`},{(13/10),-0.006563229543096745`},{(7/5),-0.005550830392791221`},{(3/2),-0.004646717288364329`},{(8/5),-0.003791219376602392`},{(17/10),-0.0029092427932887084`},{(9/5),-0.0019415054142102308`},{(19/10),-0.0008678720364503167`},{2,0.00028433104556208804`},{(21/10),0.001448742528641234`},{(11/5),0.002541249459580913`},{(23/10),0.003486263088102106`},{(12/5),0.0042389640830641185`},{(5/2),0.0047963683040679085`},{(13/5),0.005194183345697409`},{(27/10),0.005491311497350916`},{(14/5),0.005747855230379489`},{(29/10),0.0060043239962749425`},{3,0.006268928282067977`},{(31/10),0.006516783616164763`},{(16/5),0.006700663266941197`},{(33/10),0.006769080832307213`},{(17/5),0.0066852237884299295`},{(7/2),0.006440276820934208`},{(18/5),0.00605685938780424`},{(37/10),0.0055818269496096745`},{(19/5),0.005071308236423702`},{(39/10),0.00457335086428641`},{4,0.004114130841618574`},{(41/10),0.0036922303699649787`},{(21/5),0.0032825742478763227`},{(43/10),0.002848278710660086`},{(22/5),0.0023560514849354118`},{(9/2),0.0017897439341166856`},{(23/5),0.0011574882132150543`},{(47/10),0.0004902034214192154`},{(24/5),-0.00016772706753777507`},{(49/10),-0.0007721657903550219`},{5,-0.0012925018295867812`},{(51/10),-0.0017199940791199388`},{(26/5),-0.0020685037751885234`},{(53/10),-0.0023676262842952894`},{(27/5),-0.002650824821648196`},{(11/2),-0.002942790262902165`},{(28/5),-0.003250380266449811`},{(57/10),-0.0035601300412775715`},{(29/5),-0.0038429860845103424`},{(59/10),-0.004064421799532402`},{6,-0.004196305007446242`},{(61/10),-0.0042263925685741`},{(31/5),-0.004162258010889572`},{(63/10),-0.004028455350531105`},{(32/5),-0.0038580731883019964`},{(13/2),-0.0036817235713867058`},{(33/5),-0.003517805914791477`},{(67/10),-0.0033673442835932413`},{(34/5),-0.003215038385772578`},{(69/10),-0.003035991892726653`},{7,-0.002805645517995531`},{(71/10),-0.0025094046137999135`},{(36/5),-0.002148644570951919`},{(73/10),-0.001741104923215101`},{(37/5),-0.0013156611034604335`},{(15/2),-0.0009033964423043272`},{(38/5),-0.0005281234214555456`},{(77/10),-0.00019961829411361095`},{(39/5),0.00008817695041704956`},{(79/10),0.00035349217189488457`},{8,0.0006190036788311`},{(81/10),0.0009028094402874391`},{(41/5),0.0012112531961771932`},{(83/10),0.0015360380414789969`},{(42/5),0.001856537834512632`},{(17/2),0.002146403253144879`},{(43/5),0.002382097536262889`},{(87/10),0.0025503812679811264`},{(44/5),0.0026521894707829175`},{(89/10),0.0027016404218098214`},{9,0.002720619328527805`},{(91/10),0.0027308962020409265`},{(46/5),0.002746547279419714`},{(93/10),0.0027692882267515762`},{(47/5),0.002788270066018831`},{(19/2),0.0027843173407774207`},{(48/5),0.0027370543337316353`},{(97/10),0.0026323973100549664`},{(49/5),0.0024678116292672497`},{(99/10),0.002253553009750177`},{10,0.0020095315500869683`}};

Table[{j/10,Im[NIntegrate[Int4r1/.{omega->1/10,t->j/10},{omegap,6,50}]]},{j,1,100}]

T44={{(1/10),-0.00031791056932278886`},{(1/5),-0.0007454435385264465`},{(3/10),-0.000872385573127867`},{(2/5),-0.0006517302041368337`},{(1/2),-0.0002087909568969729`},{(3/5),0.00023660606137263852`},{(7/10),0.0005169002813470037`},{(4/5),0.0005855826057618791`},{(9/10),0.00047527520108332083`},{1,0.00023497363783953838`},{(11/10),-0.00007520190231607902`},{(6/5),-0.00035831083562286504`},{(13/10),-0.0004994100906172673`},{(7/5),-0.0004373203186667236`},{(3/2),-0.0002143679007236958`},{(8/5),0.0000553990463455644`},{(17/10),0.00026603922610417226`},{(9/5),0.00036710039615105427`},{(19/10),0.00035110850325410656`},{2,0.00022761368645167232`},{(21/10),0.000027331408522975464`},{(11/5),-0.00018237327673933885`},{(23/10),-0.0003161798743974437`},{(12/5),-0.00032204664757233775`},{(5/2),-0.0002132831877667793`},{(13/5),-0.000048197522546658815`},{(27/10),0.00011430245331065024`},{(14/5),0.00023458062320159354`},{(29/10),0.00028254129602663076`},{3,0.0002349085509951008`},{(31/10),0.00009735414645396764`},{(16/5),-0.00007805206958384883`},{(33/10),-0.00021463424985794006`},{(17/5),-0.00025923147201418117`},{(7/2),-0.0002095126502431946`},{(18/5),-0.0000987825879342216`},{(37/10),0.00003408227428823881`},{(19/5),0.00015457389068908718`},{(39/10),0.0002261279317462264`},{4,0.00021651569564650985`},{(41/10),0.00012287981497168833`},{(21/5),-0.000014710115977271349`},{(43/10),-0.00013499930928540793`},{(22/5),-0.00019450463652964203`},{(9/2),-0.00018541879683138347`},{(23/5),-0.00012231994013346814`},{(47/10),-0.000024395379369549927`},{(24/5),0.00008419870158312171`},{(49/10),0.00016741677067682895`},{5,0.00018836844648307017`},{(51/10),0.00013576451979772686`},{(26/5),0.000035936135765821304`},{(53/10),-0.00006587153451394171`},{(27/5),-0.00013519142077885303`},{(11/2),-0.00015906032495844802`},{(28/5),-0.00013597862588463452`},{(57/10),-0.00006890589677812953`},{(29/5),0.000026587165798537993`},{(59/10),0.0001158012384691049`},{6,0.0001594122108106716`},{(61/10),0.0001400111422965935`},{(31/5),0.00007256059352875308`},{(63/10),-0.000011328510260584644`},{(32/5),-0.00008500297642975927`},{(13/2),-0.00013201307000160008`},{(33/5),-0.00013918105136679796`},{(67/10),-0.00009784875896581048`},{(34/5),-0.00001696525690775172`},{(69/10),0.00007144847452929959`},{7,0.000128757108211761`},{(71/10),0.0001345483168778529`},{(36/5),0.00009492301169031195`},{(73/10),0.000029621972471794843`},{(37/5),-0.000042315066591116265`},{(15/2),-0.00010315741870871734`},{(38/5),-0.00013216202227073337`},{(77/10),-0.00011277143053517501`},{(39/5),-0.00004848434215404077`},{(79/10),0.00003294119050182773`},{8,0.00009627870392564073`},{(81/10),0.00012063752661253585`},{(41/5),0.00010516906118850018`},{(83/10),0.00005908927593666707`},{(42/5),-6.032994638903711`*^-6},{(17/2),-0.00007305691352471773`},{(43/5),-0.00011698373122073242`},{(87/10),-0.00011628271223421545`},{(44/5),-0.0000698685060716552`},{(89/10),-6.711364694645038`*^-8},{9,0.00006328304495131925`},{(91/10),0.0001005946725447337`},{(46/5),0.00010567832125712168`},{(93/10),0.00007860763236289968`},{(47/5),0.0000238959579857385`},{(19/2),-0.000043206990998020826`},{(48/5),-0.00009613267229022271`},{(97/10),-0.00011079890951214715`},{(49/5),-0.00008241049254029969`},{(99/10),-0.0000272218879591654`},{10,0.000031517127875071226`}};

Table[{j/10,Im[NIntegrate[Int5r1/.{omega->1/10,t->j/10},{omegap,50,100}]]},{j,1,100}]

T55={{(1/10),-0.00002695056250232419`},{(1/5),-8.471955878012506`*^-6},{(3/10),0.00001679086397520685`},{(2/5),0.000028722358005745353`},{(1/2),-0.000016836225461588648`},{(3/5),-0.000018224378592206877`},{(7/10),-5.578493332976818`*^-6},{(4/5),0.000015817729607766155`},{(9/10),0.000019968864868074034`},{1,-0.000015858230493513744`},{(11/10),-0.000013021973506251`},{(6/5),-3.717467631763152`*^-6},{(13/10),0.000015193918922654952`},{(7/5),0.00001381440994069262`},{(3/2),-0.000014713205447261157`},{(8/5),-9.620863941140347`*^-6},{(17/10),-2.3134750528565545`*^-6},{(9/5),0.000014624438489800618`},{(19/10),9.149278713712937`*^-6},{2,-0.00001345297952892969`},{(21/10),-7.287144341033631`*^-6},{(11/5),-1.1277701086717717`*^-6},{(23/10),0.000013988249706790932`},{(12/5),5.469875839129325`*^-6},{(5/2),-0.00001212659044028677`},{(13/5),-5.642880294701473`*^-6},{(27/10),-5.286251711061174`*^-8},{(14/5),0.000013231020104049789`},{(29/10),2.5184804199102346`*^-6},{3,-0.000010779342626431915`},{(31/10),-4.46468846239862`*^-6},{(16/5),9.57726663756729`*^-7},{(33/10),0.000012332032300749342`},{(17/5),1.4988388399419234`*^-7},{(7/2),-9.452181892948974`*^-6},{(18/5),-3.6058792499094064`*^-6},{(37/10),1.918300388253532`*^-6},{(19/5),0.000011290839447855998`},{(39/10),-1.726128636369449`*^-6},{4,-8.180723251775354`*^-6},{(41/10),-2.962431367192265`*^-6},{(21/5),2.824957426492571`*^-6},{(43/10),0.000010120766957284768`},{(22/5),-3.172413549930814`*^-6},{(9/2),-6.9943408956628904`*^-6},{(23/5),-2.4568765430258056`*^-6},{(47/10),3.6634608430036106`*^-6},{(24/5),8.844862097508447`*^-6},{(49/10),-4.238667439689518`*^-6},{5,-5.915435234229835`*^-6},{(51/10),-2.030226727780891`*^-6},{(26/5),4.414328062373317`*^-6},{(53/10),7.493009497940332`*^-6},{(27/5),-4.968854684482952`*^-6},{(11/2),-4.958965245014188`*^-6},{(28/5),-1.6378413070283576`*^-6},{(57/10),5.0564284632452686`*^-6},{(29/5),6.099407707366339`*^-6},{(59/10),-5.4050756123183575`*^-6},{6,-4.132383931064177`*^-6},{(61/10),-1.2471008786597052`*^-6},{(31/5),5.569697986690669`*^-6},{(63/10),4.70038378882431`*^-6},{(32/5),-5.589230133538706`*^-6},{(13/2),-3.435919990109702`*^-6},{(33/5),-8.360601422446307`*^-7},{(67/10),5.9372143457635845`*^-6},{(34/5),3.33230135579461`*^-6},{(69/10),-5.563454903348907`*^-6},{7,-2.8631785005476283`*^-6},{(71/10),-3.9235812993738287`*^-7},{(36/5),6.146736391249619`*^-6},{(73/10),2.0296761736387375`*^-6},{(37/5),-5.369771887152578`*^-6},{(15/2),-2.402096543940122`*^-6},{(38/5),8.775747475477617`*^-8},{(77/10),6.191778042458443`*^-6},{(39/5),8.235768624533997`*^-7},{(79/10),-5.049241932337299`*^-6},{8,-2.036104030426252`*^-6},{(81/10),6.005125954601089`*^-7},{(41/5),6.0722048124017276`*^-6},{(83/10),-2.597787589005924`*^-7},{(42/5),-4.640929455515465`*^-6},{(17/2),-1.745497828074792`*^-6},{(43/5),1.135811159345712`*^-6},{(87/10),5.794377121055984`*^-6},{(44/5),-1.2000487197818158`*^-6},{(89/10),-4.180750040785918`*^-6},{9,-1.508897701073742`*^-6},{(91/10),1.6786188456672531`*^-6},{(46/5),5.370937213485938`*^-6},{(93/10),-1.983449784102133`*^-6},{(47/5),-3.700466889150318`*^-6},{(19/2),-1.3047227598810066`*^-6},{(48/5),2.2104325361200224`*^-6},{(97/10),4.820144056410967`*^-6},{(49/5),-2.603079636127717`*^-6},{(99/10),-3.226790195855967`*^-6},{10,-1.1125817733894562`*^-6}};

(* We add back the imaginary part of the 2D modes- massless case-to the imaginary part of the 2D modes-massive case.*)

Table[{j/10,Im[(1/Sqrt[4*Pi/10])*Exp[(I/(10*κb))*Exp[-κb*((j/10)+0.0677511)]]]},{j,1,100}]

T66={{(1/10),0.008152830336074309`},{(1/5),0.005019718174666245`},{(3/10),0.0030906365362119302`},{(2/5),0.0019028986153337673`},{(1/2),0.0011716098948928897`},{(3/5),0.000721357056755082`},{(7/10),0.0004441375477647933`},{(4/5),0.0002734542501512911`},{(9/10),0.00016836501689867323`},{1,0.00010366186931981798`},{(11/10),0.00006382432244074762`},{(6/5),0.00003929645643296518`},{(13/10),0.000024194718073405183`},{(7/5),0.000014896620095431784`},{(3/2),9.171807234284544`*^-6},{(8/5),5.647056003473166`*^-6},{(17/10),3.4768765513237697`*^-6},{(9/5),2.1407031461488862`*^-6},{(19/10),1.3180249261891413`*^-6},{2,8.11504252320289`*^-7},{(21/10),4.996408933159422`*^-7},{(11/5),3.0762749740343897`*^-7},{(23/10),1.8940538779891223`*^-7},{(12/5),1.16616366319843`*^-7},{(5/2),7.180036983996449`*^-8},{(13/5),4.420728643710511`*^-8},{(27/10),2.7218302335881392`*^-8},{(14/5),1.675823244888501`*^-8},{(29/10),1.0317996741502767`*^-8},{3,6.352761669966287`*^-9},{(31/10),3.911377551909829`*^-9},{(16/5),2.4082241941976356`*^-9},{(33/10),1.482736885547417`*^-9},{(17/5),9.129169439705518`*^-10},{(7/2),5.620804032812849`*^-10},{(18/5),3.460713286564262`*^-10},{(37/10),2.1307514693425338`*^-10},{(19/5),1.3118977066755804`*^-10},{(39/10),8.077317404416496`*^-11},{4,4.973181683274611`*^-11},{(41/10),3.0619740213916686`*^-11},{(21/5),1.8852488215359164`*^-11},{(43/10),1.1607424146228365`*^-11},{(22/5),7.146658508486858`*^-12},{(9/2),4.400177609907004`*^-12},{(23/5),2.7091770196847158`*^-12},{(47/10),1.6680326965581013`*^-12},{(24/5),1.0270030553819874`*^-12},{(49/10),6.323229022670436`*^-13},{5,3.8931943837567744`*^-13},{(51/10),2.3970288685375053`*^-13},{(26/5),1.4758439549216094`*^-13},{(53/10),9.086729859067513`*^-14},{(27/5),5.5946741019821794`*^-14},{(11/2),3.444625161400185`*^-14},{(28/5),2.1208460557778108`*^-14},{(57/10),1.3057989713109895`*^-14},{(29/5),8.039767661738639`*^-15},{(59/10),4.950062411968616`*^-15},{6,3.0477395508573456`*^-15},{(61/10),1.8764846979305106`*^-15},{(31/5),1.155346368286892`*^-15},{(63/10),7.113435202460371`*^-16},{(32/5),4.379722113519223`*^-16},{(13/2),2.696582627900338`*^-16},{(33/5),1.660278364841508`*^-16},{(67/10),1.0222287350813081`*^-16},{(34/5),6.293833666414628`*^-17},{(69/10),3.8750957453121714`*^-17},{7,2.3858855875819133`*^-17},{(71/10),1.468983068074494`*^-17},{(36/5),9.04448757107659`*^-18},{(73/10),5.568665643681278`*^-18},{(37/5),3.4286118265321477`*^-18},{(15/2),2.11098669038872`*^-18},{(38/5),1.2997285876790516`*^-18},{(77/10),8.002392479883959`*^-19},{(39/5),4.927050617272152`*^-19},{(79/10),3.033571253370207`*^-19},{8,1.8677613168847298`*^-19},{(81/10),1.1499754070307068`*^-19},{(41/5),7.080366344566741`*^-20},{(83/10),4.359361710413934`*^-20},{(42/5),2.6840467847834007`*^-20},{(17/2),1.652560081375345`*^-20},{(43/5),1.017476609587352`*^-20},{(87/10),6.2645749629616646`*^-21},{(44/5),3.857081243615196`*^-21},{(89/10),2.3747941093859804`*^-21},{9,1.462154076041286`*^-21},{(91/10),9.002441658560938`*^-22},{(46/5),5.542778093209994`*^-22},{(93/10),3.4126729342758845`*^-22},{(47/5),2.101173159106996`*^-22},{(19/2),1.2936864239785445`*^-22},{(48/5),7.965191047355971`*^-23},{(97/10),4.904145799549124`*^-23},{(49/5),3.019468821305698`*^-23},{(99/10),1.8590784889950927`*^-23},{10,1.144629414239054`*^-23}};

ListLinePlot[T11+T22+T33+T44+T55+T66]

(* I have missed a coefficient 1/6. So I multiply my data by 1/6 and call the new data TIm ( Imaginary part of the mode)*)

T11+T22+T33+T44+T55+T66

{{(3/5)*(1/6),-0.050237405828493245`},{(6/5)*(1/6),-0.055829073992770074`},{(9/5)*(1/6),-0.059918179857857364`},{(12/5)*(1/6),-0.06292152594741589`},{3*(1/6),-0.06518369569322155`},{(18/5)*(1/6),-0.0668468835003592`},{(21/5)*(1/6),-0.06807924621533018`},{(24/5)*(1/6),-0.06892000758972482`},{(27/5)*(1/6),-0.06940453264201882`},{6*(1/6),-0.06960744981683131`},{(33/5)*(1/6),-0.06952770673318719`},{(36/5)*(1/6),-0.06923902907077464`},{(39/5)*(1/6),-0.06872702535030617`},{(42/5)*(1/6),-0.06800663151124585`},{9*(1/6),-0.06711272219210693`},{(48/5)*(1/6),-0.0660400383880893`},{(51/5)*(1/6),-0.06485217855994405`},{(54/5)*(1/6),-0.06353465445886518`},{(57/5)*(1/6),-0.062109130550936226`},{12*(1/6),-0.06059096515389969`},{(63/5)*(1/6),-0.058973390250324075`},{(66/5)*(1/6),-0.057306027284432105`},{(69/5)*(1/6),-0.0555748870782874`},{(72/5)*(1/6),-0.05381062874388549`},{15*(1/6),-0.05202083511710188`},{(78/5)*(1/6),-0.0502013127269736`},{(81/5)*(1/6),-0.048383883624892605`},{(84/5)*(1/6),-0.04654677010655483`},{(87/5)*(1/6),-0.0447189108465154`},{18*(1/6),-0.04290195802596414`},{(93/5)*(1/6),-0.041101208030618175`},{(96/5)*(1/6),-0.03934083373275362`},{(99/5)*(1/6),-0.037597487897399584`},{(102/5)*(1/6),-0.03589313647296102`},{21*(1/6),-0.03421699720128864`},{(108/5)*(1/6),-0.03257576582577524`},{(111/5)*(1/6),-0.030986066325945787`},{(114/5)*(1/6),-0.029430840053355688`},{(117/5)*(1/6),-0.02793342167793911`},{24*(1/6),-0.026479288974781957`},{(123/5)*(1/6),-0.02507573181975807`},{(126/5)*(1/6),-0.02372668689733147`},{(129/5)*(1/6),-0.02241432973971471`},{(132/5)*(1/6),-0.021157670906313104`},{27*(1/6),-0.0199416763791689`},{(138/5)*(1/6),-0.01878013622579164`},{(141/5)*(1/6),-0.017673844472381656`},{(144/5)*(1/6),-0.016610336121993776`},{(147/5)*(1/6),-0.015603554531359934`},{30*(1/6),-0.014634267648152753`},{(153/5)*(1/6),-0.013714465582918745`},{(156/5)*(1/6),-0.012837705718386605`},{(159/5)*(1/6),-0.01199671020543197`},{(162/5)*(1/6),-0.011204517522209368`},{33*(1/6),-0.010446134645023405`},{(168/5)*(1/6),-0.009736802722653658`},{(171/5)*(1/6),-0.00906611935982885`},{(174/5)*(1/6),-0.008429247757795685`},{(177/5)*(1/6),-0.00783235380341866`},{36*(1/6),-0.007259899087652906`},{(183/5)*(1/6),-0.006726330723714678`},{(186/5)*(1/6),-0.006219607998393287`},{(189/5)*(1/6),-0.005741540167734525`},{(192/5)*(1/6),-0.0052971598415249505`},{39*(1/6),-0.00487527889873971`},{(198/5)*(1/6),-0.004489315049928131`},{(201/5)*(1/6),-0.004123832436567332`},{(204/5)*(1/6),-0.003781721698397693`},{(207/5)*(1/6),-0.0034625161068299183`},{42*(1/6),-0.003157747507208918`},{(213/5)*(1/6),-0.0028802896315552303`},{(216/5)*(1/6),-0.0026162786633711728`},{(219/5)*(1/6),-0.002373566574284564`},{(222/5)*(1/6),-0.002149753108924072`},{45*(1/6),-0.0019397267892978635`},{(228/5)*(1/6),-0.001752672094678584`},{(231/5)*(1/6),-0.0015731061557048129`},{(234/5)*(1/6),-0.0014091001024353039`},{(237/5)*(1/6),-0.0012549437010684116`},{48*(1/6),-0.0011097398428204163`},{(243/5)*(1/6),-0.0009817275989246657`},{(246/5)*(1/6),-0.000858648422955266`},{(249/5)*(1/6),-0.0007509553564534959`},{(252/5)*(1/6),-0.000650987594005385`},{51*(1/6),-0.0005599821309231794`},{(258/5)*(1/6),-0.0004814515083100864`},{(261/5)*(1/6),-0.0004033349672186878`},{(264/5)*(1/6),-0.0003354078359702579`},{(267/5)*(1/6),-0.00026892235192334`},{54*(1/6),-0.00020924908856778714`},{(273/5)*(1/6),-0.00015873954644212866`},{(276/5)*(1/6),-0.00010924952474710297`},{(279/5)*(1/6),-0.00007059782885871769`},{(282/5)*(1/6),-0.00003280533025555403`},{57*(1/6),-1.9897751411291915`*^-6},{(288/5)*(1/6),0.000024099788981075786`},{(291/5)*(1/6),0.00005222633470604093`},{(294/5)*(1/6),0.00007407115763140686`},{(297/5)*(1/6),0.00009879758746240768`},{60*(1/6),0.00011713939606056086`}}

TIm={{(1/10),-0.050237405828493245`},{(1/5),-0.055829073992770074`},{(3/10),-0.059918179857857364`},{(2/5),-0.06292152594741589`},{(1/2),-0.06518369569322155`},{(3/5),-0.0668468835003592`},{(7/10),-0.06807924621533018`},{(4/5),-0.06892000758972482`},{(9/10),-0.06940453264201882`},{1,-0.06960744981683131`},{(11/10),-0.06952770673318719`},{(6/5),-0.06923902907077464`},{(13/10),-0.06872702535030617`},{(7/5),-0.06800663151124585`},{(3/2),-0.06711272219210693`},{(8/5),-0.0660400383880893`},{(17/10),-0.06485217855994405`},{(9/5),-0.06353465445886518`},{(19/10),-0.062109130550936226`},{2,-0.06059096515389969`},{(21/10),-0.058973390250324075`},{(11/5),-0.057306027284432105`},{(23/10),-0.0555748870782874`},{(12/5),-0.05381062874388549`},{(5/2),-0.05202083511710188`},{(13/5),-0.0502013127269736`},{(27/10),-0.048383883624892605`},{(14/5),-0.04654677010655483`},{(29/10),-0.0447189108465154`},{3,-0.04290195802596414`},{(31/10),-0.041101208030618175`},{(16/5),-0.03934083373275362`},{(33/10),-0.037597487897399584`},{(17/5),-0.03589313647296102`},{(7/2),-0.03421699720128864`},{(18/5),-0.03257576582577524`},{(37/10),-0.030986066325945787`},{(19/5),-0.029430840053355688`},{(39/10),-0.02793342167793911`},{4,-0.026479288974781957`},{(41/10),-0.02507573181975807`},{(21/5),-0.02372668689733147`},{(43/10),-0.02241432973971471`},{(22/5),-0.021157670906313104`},{(9/2),-0.0199416763791689`},{(23/5),-0.01878013622579164`},{(47/10),-0.017673844472381656`},{(24/5),-0.016610336121993776`},{(49/10),-0.015603554531359934`},{5,-0.014634267648152753`},{(51/10),-0.013714465582918745`},{(26/5),-0.012837705718386605`},{(53/10),-0.01199671020543197`},{(27/5),-0.011204517522209368`},{(11/2),-0.010446134645023405`},{(28/5),-0.009736802722653658`},{(57/10),-0.00906611935982885`},{(29/5),-0.008429247757795685`},{(59/10),-0.00783235380341866`},{6,-0.007259899087652906`},{(61/10),-0.006726330723714678`},{(31/5),-0.006219607998393287`},{(63/10),-0.005741540167734525`},{(32/5),-0.0052971598415249505`},{(13/2),-0.00487527889873971`},{(33/5),-0.004489315049928131`},{(67/10),-0.004123832436567332`},{(34/5),-0.003781721698397693`},{(69/10),-0.0034625161068299183`},{7,-0.003157747507208918`},{(71/10),-0.0028802896315552303`},{(36/5),-0.0026162786633711728`},{(73/10),-0.002373566574284564`},{(37/5),-0.002149753108924072`},{(15/2),-0.0019397267892978635`},{(38/5),-0.001752672094678584`},{(77/10),-0.0015731061557048129`},{(39/5),-0.0014091001024353039`},{(79/10),-0.0012549437010684116`},{8,-0.0011097398428204163`},{(81/10),-0.0009817275989246657`},{(41/5),-0.000858648422955266`},{(83/10),-0.0007509553564534959`},{(42/5),-0.000650987594005385`},{(17/2),-0.0005599821309231794`},{(43/5),-0.0004814515083100864`},{(87/10),-0.0004033349672186878`},{(44/5),-0.0003354078359702579`},{(89/10),-0.00026892235192334`},{9,-0.00020924908856778714`},{(91/10),-0.00015873954644212866`},{(46/5),-0.00010924952474710297`},{(93/10),-0.00007059782885871769`},{(47/5),-0.00003280533025555403`},{(19/2),-1.9897751411291915`*^-6},{(48/5),0.000024099788981075786`},{(97/10),0.00005222633470604093`},{(49/5),0.00007407115763140686`},{(99/10),0.00009879758746240768`},{10,0.00011713939606056086`}};

ListLinePlot[TIm,Frame->True,FrameLabel->{"Ht",""},ImageSize->300,LabelStyle->{FontSize->12,FontFamily->"Courier New",Black},PlotRange->{{1/10,7},{-0.085,0.1}},PlotStyle->{{Black,Thickness[0.003]}},FrameTicks->Automatic,Axes->False]

ListLinePlot[TRe,Frame->True,FrameLabel->{"Ht",""},ImageSize->300,LabelStyle->{FontSize->12,FontFamily->"Courier New",Black},PlotRange->{{1/10,7},{-0.1,1}},PlotStyle->{{Black,Thickness[0.003]}},FrameTicks->Automatic,Axes->False]