Maass forms from Figure 4.2.1 These Maass forms have no inherent symmetry, so they have a Fourier expansion of the form Sum[coeff[[n]] Sqrt[y] BesselK[i R, 2 Pi N y] ( A[n] Cos[2 Pi n x] + I B[n] Sin[2 Pi n x)], {n,1,??}] The lists of coefficients below are encoded in a somewhat unusual manner. If the coefficient list is {c[1],c[2],c[3],...} then A[n] = c[2n-1] + c[2n] and B[n] = c[2n-1] - c[2n] Not all of the given digits of the coefficients are accurate. The first few coefficients are probably accurate to 6 or 7 digits, and the accuracy decreases to one or two digits for the last coefficients. For each Maass form f[x,y] there is a compley number C such that C f[x,y] is real (to within approximately 1 part in 10^8). b = 0.1019120990012473 a = 5.324370182235845 R = 11.732824299262715 {1, -0.28607824766927714 - 0.9582062597426462*I, -0.025881229950467568 + 0.019282711726241786*I, -0.011072758169194561 + 0.030315920928916152*I, -0.3460511480223843 + 1.1590864554796372*I, -1.01164619119373 + 0.6631777983075713*I, 0.240615215215805 + 0.6587542843085783*I, -0.7000572579890806 - 0.04210373410947924*I, -1.7893664653072328 - 1.1730074929710141*I, 1.6358819453231184 + 1.379010219938477*I, 0.7101104054358167 - 0.042708102475730994*I, -0.16222396930480226 - 0.6926500947146694*I, -0.44381979757968504 + 0.37412991174341304*I, -0.23152643341688456 + 0.5323013377906104*I, -0.11853888152365315 + 0.5061299131604833*I, -0.4510654555269992 + 0.25837745694901765*I, -0.2651255348623876 - 0.6095472152267192*I, 0.6599186056651138 + 0.07966674791894907*I, 1.7447921073431556 + 0.9994450168408908*I, -1.4568215400222932 - 1.3859512401465968*I, -1.3322297294559968 + 0.1608301429680545*I, 0.22701349674865437 + 1.3225608716534678*I, 0.7451660884133489 - 0.7089146126490575*I, 0.46611061066671394 - 0.9168278605983872*I, -0.06864580338242005 + 0.39993340982993075*I, -0.3635806256399149 + 0.18018908757523358*I, 0.545905119596856 + 1.0737712038732026*I, -1.185065869095235 - 0.2159071184228586*I, 0.12186827715012359 + 0.060389898162798154*I, -0.09272984162490969 - 0.09949870979434804*I, 1.7168311631769204 - 0.3128041831656559*I, -0.1914171243230848 - 1.7345648400879448*I, 0.12616622368392377 - 0.13542762522014856*I, 0.09367418607989991 - 0.15963616306303371*I, -0.08204132719590623 + 0.7423684613706658*I, -0.6878718674530532 + 0.29098798178501994*I, -0.5074650998971462 - 0.8647825563837565*I, 0.9738147857082241 + 0.23886075709552404*I, 0.07430910753061148 + 0.03203049938255511*I, -0.0519500438487212 - 0.06204022219977946*I, -0.46706373946825436 + 0.11569741484704202*I, 0.022754788847612766 + 0.480641914269877*I, -1.0563857496550422 + 1.2837669174743054*I, -0.9279045148898731 + 1.3794932309865755*I, 0.013365641347732828 - 0.1439098416483936*I, 0.13407168330049513 - 0.053976515138353144*I, -0.6395477195196458 - 0.9787066915857703*I, 1.1207635525231998 + 0.33283192434901837*I, 0.05951515926852746 - 0.008667514994507065*I, -0.008720742213635994 - 0.05950742044813771*I, 0.2780613251365452 - 0.14249107645055287*I, 0.05698855975015855 - 0.30720377358885753*I, -0.30401519766910656 + 0.24672093284948582*I, -0.14943729775721717 + 0.3618906662342296*I, -0.2055338865167745 - 0.9344285786299312*I, 0.9541743628605376 - 0.07037584051133113*I, 0.015858711147029414 + 0.6637809729615312*I, -0.640575468635533 + 0.17469767755898202*I, 0.47318343065235224 + 0.8903719781553231*I, -0.9885271003246443 - 0.1986903950341855*I, -0.09473691531796002 + 1.2156147199673697*I, -1.1377076714500687 + 0.43853992222134086*I, 0.11780198672199031 + 2.0166486830545325*I, -1.9660670637550126 + 0.464042166270367*I, 0.7122961202505598 + 0.6301797130453801*I, -0.807615731594526 - 0.5022452733936051*I} (******************************) b = 0.09075668325928765 a = 5.156121436350612 R = 11.554437293941307 {1, -0.2161903473851285 - 0.9763512348010298*I, -2.0942870519854746 + 1.0531677500347048*I, -0.5754969879060933 + 2.272444450968648*I, 0.9883488207329435 - 1.4903213986119317*I, 1.2414056628932237 - 1.287168692418159*I, 0.2351460171691797 + 0.3592739537237008*I, -0.40161386748801936 - 0.15191354335971494*I, 0.9359336494012177 + 1.2078301742847342*I, -1.3816063028863221 - 0.6526787493238573*I, 0.6412755394658723 + 0.16460802171111155*I, -0.2993528269025105 - 0.5905234994090985*I, -1.5812412937809681 + 0.397201656238558*I, -0.04595922293131267 + 1.6297180537455895*I, -1.4693375470039025 + 1.2063151387782354*I, -0.860130680592519 + 1.6953832172651833*I, -0.14041370775462506 + 0.21022887878156696*I, -0.1749011371321119 + 0.18254255128339403*I, 0.24848822100170823 + 0.9097127973376162*I, -0.941919967814351 - 0.04594065573140777*I, 1.5026202692967696 + 1.0636435357093783*I, -1.3633416774851959 - 1.2371356898859955*I, -1.077794444209465 + 0.009749675177183345*I, 0.223489647905231 + 1.0544137221290473*I, -1.6897565846695575 + 0.5838265989532985*I, -0.2047107577617479 + 1.7760136031956348*I, 0.009812643368881248 - 0.08940428769651462*I, 0.08516858791035294 - 0.028908930484831313*I, 0.010460975295846631 - 0.2965504845157461*I, 0.28727586985489056 - 0.07432493841218403*I, 0.674198573698544 + 0.9993238397666138*I, -1.1214462887758825 - 0.4422104418621777*I, 0.3161040206198612 + 0.37529637972630003*I, -0.43475972178839856 - 0.227493096150987*I, 0.3846572612069105 + 0.0777978831852233*I, -0.159117246236675 - 0.3587414405582648*I, 0.6031122840773154 - 0.6466717861893271*I, 0.5009917427449541 - 0.7286536213730154*I, -0.1749030528648771 - 0.2617725050815015*I, 0.29339426030742743 + 0.11417412283742884*I, 1.1080696836610275 + 2.210734923687462*I, -2.398007742458025 - 0.6039256527694238*I, -1.9852999271256617 - 1.1301157094992043*I, 1.5325925492518306 + 1.6940299273801636*I, -0.730043817073128 - 0.624346854499786*I, 0.7674102487162551 + 0.577801418605528*I, -1.4213628414278998 + 1.2206586985481547*I, -0.8845067008567197 + 1.651643992861069*I, 1.3059162762055407 - 2.8121434892907824*I, 2.4633132759110175 - 1.8829912472259716*I, 0.2985098556356474 - 0.04523203905271158*I, -0.020372589781067044 - 0.3012291959679946*I, -0.5736146574987004 - 0.6637414042950026*I, 0.7720546950239761 + 0.4165548977299027*I, -0.587016876096734 - 0.1599344562585749*I, 0.2830595873976769 + 0.5385583746478411*I, 2.8560939812619104 - 1.2765622601838518*I, 0.6289131816373345 - 3.064531311327502*I, -0.038290552833519814 + 0.37075505094456324*I, -0.35370912595189286 + 0.1175386999448624*I, -0.5619461296843676 - 0.7858233735455216*I, 0.8887269240275103 + 0.378769360391241*I, 0.5477586810909345 + 1.4962782824422238*I, -1.579313300483524 - 0.21132396980828053*I, 0.6350421447307567 + 0.8579159399816404*I, -0.9749172679058775 - 0.43455105273183814*I} (***********************) b = 0.07705046927222699 a = 5.285983531460722 R = 11.672492062242371 {1, -0.33115525753858077 - 0.9435762795897898*I, -0.548964298293426 + 0.16636466293491903*I, 0.024814663873485802 + 0.5730822230108494*I, 0.4677774544463846 + 0.11836776329767174*I, -0.26659597711369704 - 0.40218560300338835*I, 0.7955920065295851 + 0.501906066291626*I, -0.7370511345529576 - 0.584492912949583*I, 0.4145502651777661 - 0.6676248150519815*I, 0.4926744393209236 - 0.6122472644871354*I, 0.9314951607253252 + 0.6184821765289872*I, -0.8920546309677612 - 0.6741231137616119*I, -0.46472899595430306 - 0.323109670106853*I, 0.4587760707598083 + 0.3315077910025986*I, -0.4388968283289769 + 0.4530169447826923*I, -0.2821130511310697 + 0.564151579417322*I, -0.9257759430382211 - 0.4182091286981912*I, 0.7011877845874119 + 0.7350480683467172*I, 0.4938168490661477 + 0.6823902420739546*I, -0.8074172916739483 - 0.23997674888475548*I, -0.47805449533231814 + 0.33686508936553977*I, -0.1595476482279068 + 0.5626355275714592*I, 0.4337555405464774 + 0.46180833059490806*I, -0.5793918142047367 - 0.2563511825486621*I, -0.9347243776653982 - 0.5135531554372982*I, 0.7941154677925445 + 0.7119179232709324*I, -0.8572265125771412 - 0.4734735809551809*I, 0.7306335065431068 + 0.6520653378645268*I, -0.5680617507670134 - 0.19267398178856787*I, 0.3699192342827353 + 0.4722045913059772*I, 0.28445966601575223 + 1.1670179905559521*I, -1.1953708077023646 + 0.11805474986211267*I, -0.5705835266558009 + 0.3019666852678438*I, -0.09597686672855765 + 0.638386936704322*I, -0.8215350756068132 + 0.287272928846436*I, 0.0009917381128220551 + 0.870312950928423*I, 0.44493571059116405 + 0.21805505710843817*I, -0.3530943793539969 - 0.34762070386038074*I, 0.3690377149581799 - 0.665095071470069*I, 0.5053591535919568 - 0.5684649637712352*I, 0.9553828808299544 + 0.32316191187325627*I, -0.6213079784422648 - 0.7944598580507599*I, -0.32406301187002884 - 0.09645345915408292*I, 0.1983263662447377 + 0.27383710118627924*I, 0.8711735187757135 - 0.03447578475676098*I, -0.2559631585464984 - 0.8334355047551297*I, -0.2644861677088771 - 0.3975917666812248*I, 0.46274414403384356 + 0.11789827050894706*I, -0.39822414269453293 + 0.4412932758049862*I, -0.2845198511766552 + 0.521891442849866*I, 0.6476013083818236 + 0.1658630611444763*I, -0.37096103227543265 - 0.5561348116289593*I, 0.46191688126257585 + 0.10453201990317101*I, -0.2516001428389945 - 0.40123749289593463*I, -0.4278980138834453 + 0.2427029124736382*I, -0.08730803469548791 + 0.48412674549147716*I, 0.32641321613940494 + 0.38462931438225273*I, -0.47102054139181904 - 0.18062377066810026*I, 1.473378247103657 + 0.8580142160532243*I, -1.2975188069898 - 1.1061088559933514*I, 1.636958398650765 + 1.1031940231876094*I, -1.5830350585635844 - 1.1792665671692288*I, 1.3971836889086648 + 0.07378615572869104*I, -0.5323075463082929 - 1.2939147316123945*I}