/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([5, -1, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13, 13, -w^2 + 3]) primes_array = [ [5, 5, w],\ [5, 5, -w^2 + w + 2],\ [7, 7, -w^2 + 2],\ [13, 13, -w^2 + 3],\ [13, 13, w^2 - w - 4],\ [16, 2, 2],\ [19, 19, -w^2 + w + 1],\ [23, 23, -w^3 + 4*w + 2],\ [25, 5, -w^3 + w^2 + 3*w - 1],\ [29, 29, w^3 - w^2 - 4*w + 1],\ [29, 29, -w + 3],\ [31, 31, -w^3 + w^2 + 5*w - 2],\ [37, 37, w^3 - 4*w - 1],\ [37, 37, w^3 - 3*w + 1],\ [53, 53, -w^3 + 2*w^2 + 4*w - 6],\ [59, 59, w^2 + w - 4],\ [61, 61, -2*w^2 + w + 8],\ [73, 73, -w^3 + 5*w - 1],\ [79, 79, 2*w^2 + w - 6],\ [79, 79, 2*w^3 - w^2 - 9*w + 3],\ [81, 3, -3],\ [83, 83, -w^3 + w^2 + 3*w - 4],\ [97, 97, -w^3 + 6*w + 2],\ [97, 97, -2*w^3 + w^2 + 10*w - 1],\ [97, 97, 3*w^3 - 4*w^2 - 15*w + 13],\ [97, 97, w^3 - w^2 - 6*w + 2],\ [103, 103, -2*w^3 + 3*w^2 + 11*w - 9],\ [109, 109, w^2 + 3*w - 3],\ [137, 137, -w^2 + 7],\ [149, 149, w^3 - 2*w^2 - 5*w + 4],\ [149, 149, w^3 + 2*w^2 - 6*w - 7],\ [151, 151, w^3 + w^2 - 5*w - 3],\ [163, 163, w^3 - 3*w - 4],\ [163, 163, -w^3 + 6*w - 3],\ [167, 167, w^3 - 2*w^2 - 6*w + 4],\ [169, 13, w^2 + 2*w - 4],\ [191, 191, w^3 - w^2 - 5*w - 2],\ [191, 191, 2*w^3 - 9*w - 2],\ [197, 197, w^3 - 4*w + 4],\ [211, 211, -w^3 + 2*w^2 + 6*w - 8],\ [223, 223, -w^3 + 3*w^2 + 4*w - 6],\ [229, 229, w^3 - w^2 - 5*w - 1],\ [251, 251, 2*w^3 - 2*w^2 - 7*w + 3],\ [257, 257, 3*w^2 - 14],\ [263, 263, w^2 - 3*w - 1],\ [263, 263, w^2 - 2*w - 7],\ [269, 269, -w^3 + w^2 + 2*w - 4],\ [269, 269, 2*w^3 - 11*w - 1],\ [271, 271, -w^3 + w^2 + 4*w - 7],\ [277, 277, w^3 - w^2 - 3*w + 8],\ [311, 311, w^3 + 2*w^2 - 7*w - 11],\ [311, 311, -3*w^2 - 2*w + 8],\ [317, 317, -2*w^3 + 2*w^2 + 7*w - 4],\ [331, 331, w^2 - w - 8],\ [331, 331, 3*w^3 - 2*w^2 - 12*w + 9],\ [337, 337, -2*w^3 + 2*w^2 + 11*w - 8],\ [343, 7, w^3 - 3*w^2 - 4*w + 11],\ [347, 347, -2*w^3 + 2*w^2 + 9*w - 4],\ [349, 349, -w^3 + 2*w^2 + 2*w - 6],\ [353, 353, 2*w^2 - w - 12],\ [353, 353, 2*w^3 - w^2 - 9*w - 1],\ [367, 367, -2*w^3 + w^2 + 10*w - 6],\ [367, 367, 2*w^3 - 11*w - 3],\ [379, 379, -3*w - 1],\ [379, 379, w^3 - 2*w - 3],\ [383, 383, -w^3 + 2*w^2 + 4*w - 11],\ [383, 383, -w^3 - w^2 + 7*w + 4],\ [389, 389, 2*w^3 - w^2 - 11*w + 4],\ [401, 401, w^3 + 2*w^2 - 7*w - 6],\ [401, 401, 2*w^3 - 11*w - 6],\ [419, 419, -2*w^3 + w^2 + 8*w - 1],\ [421, 421, -w^3 + 3*w^2 + 3*w - 12],\ [421, 421, -w^3 - 2*w^2 + 2*w + 6],\ [433, 433, w^3 - 2*w^2 - 6*w + 11],\ [433, 433, w^2 - 8],\ [439, 439, -w^3 + 3*w^2 + 3*w - 7],\ [443, 443, w^3 - w^2 - 2*w - 4],\ [443, 443, 2*w^3 + w^2 - 7*w - 2],\ [443, 443, 2*w^3 - w^2 - 8*w + 2],\ [443, 443, -w^2 - 2],\ [467, 467, 3*w^3 - 5*w^2 - 15*w + 19],\ [467, 467, 2*w^3 - 3*w^2 - 8*w + 13],\ [467, 467, -w^3 + 2*w^2 + 3*w - 9],\ [467, 467, -w^3 + 3*w^2 + 3*w - 8],\ [479, 479, -w^3 - 3*w^2 + 5*w + 13],\ [479, 479, -w^3 + w^2 + w - 4],\ [487, 487, 3*w^3 - w^2 - 13*w - 2],\ [491, 491, w^2 + w - 9],\ [499, 499, -3*w^3 + 3*w^2 + 13*w - 7],\ [503, 503, 2*w^2 + w - 9],\ [509, 509, -2*w^2 - 3*w + 6],\ [509, 509, -w^3 + w^2 - 4],\ [521, 521, -3*w^2 + w + 12],\ [523, 523, 2*w^3 - 8*w - 3],\ [529, 23, 2*w^3 - w^2 - 6*w - 1],\ [541, 541, -w^3 + w^2 + 7*w - 4],\ [547, 547, 2*w^3 - 3*w^2 - 9*w + 7],\ [557, 557, 3*w^2 - 2*w - 9],\ [557, 557, w^3 - 6*w - 7],\ [563, 563, -2*w^3 + w^2 + 6*w - 6],\ [577, 577, -w^3 + 4*w^2 + 2*w - 13],\ [587, 587, w^2 - 2*w + 3],\ [587, 587, w^2 + 2*w - 6],\ [593, 593, -2*w^3 + 2*w^2 + 11*w - 3],\ [599, 599, w^3 + 3*w^2 - 6*w - 12],\ [601, 601, -2*w^3 + w^2 + 9*w + 2],\ [607, 607, -w^3 + 3*w^2 + 4*w - 9],\ [617, 617, -2*w^3 + w^2 + 7*w - 3],\ [619, 619, -2*w^3 + 4*w^2 + 9*w - 11],\ [631, 631, 3*w^2 - w - 7],\ [631, 631, -w^3 - w^2 + 6*w + 1],\ [641, 641, -w^3 + 2*w^2 + 5*w - 1],\ [641, 641, -w^3 + 2*w^2 + 2*w - 7],\ [643, 643, -3*w^3 + w^2 + 14*w - 4],\ [647, 647, -3*w^3 + 5*w^2 + 14*w - 18],\ [647, 647, -w^3 + 7*w + 2],\ [647, 647, -2*w^3 + 7*w - 1],\ [647, 647, 2*w^3 - w^2 - 10*w - 1],\ [653, 653, -2*w^3 - w^2 + 11*w + 4],\ [659, 659, -w^3 - w^2 + 5*w - 1],\ [673, 673, -w^3 + w^2 + 7*w - 2],\ [673, 673, -w^3 + w^2 + 2*w - 8],\ [683, 683, 2*w^3 - 11*w - 8],\ [683, 683, 2*w^3 - 7*w - 3],\ [701, 701, 2*w^3 - 4*w^2 - 10*w + 17],\ [727, 727, -w^3 + w^2 + 4*w - 8],\ [727, 727, 3*w^2 - 11],\ [739, 739, 2*w^3 + 3*w^2 - 8*w - 13],\ [743, 743, 2*w^2 + w - 12],\ [743, 743, 3*w^2 - 2*w - 14],\ [751, 751, w^3 + w^2 - 3*w - 7],\ [757, 757, -2*w^3 + 10*w - 1],\ [761, 761, -2*w^3 + w^2 + 7*w - 1],\ [761, 761, 3*w^2 + w - 7],\ [773, 773, -2*w^3 + 2*w^2 + 8*w - 1],\ [797, 797, -2*w^3 + w^2 + 9*w + 3],\ [797, 797, 3*w^3 - 14*w - 8],\ [809, 809, 5*w^3 - 5*w^2 - 24*w + 16],\ [821, 821, -4*w^3 + 3*w^2 + 18*w - 9],\ [821, 821, w^3 - w - 3],\ [823, 823, 3*w^2 + w - 8],\ [829, 829, -2*w^3 + 3*w^2 + 10*w - 7],\ [829, 829, 3*w^2 - 2*w - 16],\ [841, 29, 2*w^2 + w - 11],\ [853, 853, 3*w^3 - 2*w^2 - 14*w + 3],\ [853, 853, 3*w^3 - 5*w^2 - 14*w + 17],\ [857, 857, 3*w^2 - w - 8],\ [857, 857, 3*w^3 - w^2 - 13*w + 3],\ [859, 859, w^3 - 3*w^2 - 6*w + 12],\ [877, 877, w^3 + 2*w^2 - 5*w - 4],\ [877, 877, w^2 - w - 9],\ [881, 881, w^3 + 2*w^2 - 4*w - 12],\ [881, 881, w^2 - 4*w - 4],\ [883, 883, -3*w^3 + 2*w^2 + 11*w - 8],\ [887, 887, -2*w^3 + w^2 + 6*w - 1],\ [911, 911, 3*w^2 - w - 17],\ [911, 911, 2*w^3 - 2*w^2 - 12*w + 3],\ [919, 919, 5*w^3 - 6*w^2 - 22*w + 24],\ [919, 919, -2*w^3 + w^2 + 6*w - 7],\ [929, 929, 2*w^3 - 7*w - 1],\ [937, 937, -w^3 - w^2 + 8*w - 2],\ [947, 947, 3*w^3 + w^2 - 15*w - 6],\ [947, 947, -2*w^3 + 9*w + 9],\ [953, 953, w^3 - 2*w^2 - 6*w + 1],\ [977, 977, w^3 - w^2 - 3*w + 9],\ [977, 977, w^3 + w^2 - 3*w - 8],\ [983, 983, w^3 - 5*w - 7],\ [991, 991, -w^3 + 2*w^2 + 2*w - 8],\ [991, 991, w^2 + 4*w - 1],\ [997, 997, 2*w^3 + w^2 - 12*w - 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 + 2*x^8 - 24*x^7 - 34*x^6 + 173*x^5 + 154*x^4 - 444*x^3 - 306*x^2 + 368*x + 245 K. = NumberField(heckePol) hecke_eigenvalues_array = [49787/798007*e^8 + 188199/798007*e^7 - 130483/114001*e^6 - 3378358/798007*e^5 + 3830616/798007*e^4 + 15002032/798007*e^3 - 2900951/798007*e^2 - 18763825/798007*e - 789127/114001, e, 56307/798007*e^8 + 167084/798007*e^7 - 156881/114001*e^6 - 2770342/798007*e^5 + 5122178/798007*e^4 + 10396889/798007*e^3 - 4181843/798007*e^2 - 11055246/798007*e - 875003/114001, 1, 18976/798007*e^8 + 41357/798007*e^7 - 61303/114001*e^6 - 556872/798007*e^5 + 3052054/798007*e^4 + 645896/798007*e^3 - 9302245/798007*e^2 + 2397956/798007*e + 1243547/114001, -146439/798007*e^8 - 416172/798007*e^7 + 412420/114001*e^6 + 6743584/798007*e^5 - 13891106/798007*e^4 - 24052818/798007*e^3 + 13459300/798007*e^2 + 24933215/798007*e + 1338415/114001, 8027/798007*e^8 - 53534/798007*e^7 - 41137/114001*e^6 + 1417309/798007*e^5 + 2725656/798007*e^4 - 10153691/798007*e^3 - 7827353/798007*e^2 + 16080101/798007*e + 1421259/114001, -79661/798007*e^8 - 347255/798007*e^7 + 177790/114001*e^6 + 6084539/798007*e^5 - 2502229/798007*e^4 - 25183838/798007*e^3 - 8108710/798007*e^2 + 28227487/798007*e + 2376046/114001, -26433/798007*e^8 - 8028/798007*e^7 + 109574/114001*e^6 + 64161/798007*e^5 - 6450565/798007*e^4 - 215083/798007*e^3 + 15191504/798007*e^2 + 793577/798007*e - 1281921/114001, 1237/114001*e^8 + 1152/114001*e^7 - 30827/114001*e^6 - 30678/114001*e^5 + 180801/114001*e^4 + 335037/114001*e^3 + 11633/114001*e^2 - 1129150/114001*e - 701469/114001, -101777/798007*e^8 - 361308/798007*e^7 + 265794/114001*e^6 + 6280053/798007*e^5 - 7517728/798007*e^4 - 26351091/798007*e^3 + 3567980/798007*e^2 + 32689486/798007*e + 1616572/114001, -45506/798007*e^8 - 318949/798007*e^7 + 59262/114001*e^6 + 5920937/798007*e^5 + 3106994/798007*e^4 - 26797826/798007*e^3 - 18610416/798007*e^2 + 32025986/798007*e + 3174251/114001, -5818/114001*e^8 + 2231/114001*e^7 + 179088/114001*e^6 - 88506/114001*e^5 - 1658232/114001*e^4 + 707922/114001*e^3 + 4909629/114001*e^2 - 1269792/114001*e - 3935088/114001, -83942/798007*e^8 - 216505/798007*e^7 + 249011/114001*e^6 + 3541960/798007*e^5 - 9439839/798007*e^4 - 13388044/798007*e^3 + 14200664/798007*e^2 + 16561340/798007*e - 465082/114001, 156874/798007*e^8 + 193280/798007*e^7 - 539820/114001*e^6 - 2221061/798007*e^5 + 25660349/798007*e^4 + 883278/798007*e^3 - 50438034/798007*e^2 + 6192105/798007*e + 3690907/114001, 24205/114001*e^8 + 117005/114001*e^7 - 363409/114001*e^6 - 2115390/114001*e^5 + 560527/114001*e^4 + 9308542/114001*e^3 + 3165758/114001*e^2 - 11025028/114001*e - 6920035/114001, -210519/798007*e^8 - 580726/798007*e^7 + 612417/114001*e^6 + 9438239/798007*e^5 - 22878781/798007*e^4 - 33884313/798007*e^3 + 35536150/798007*e^2 + 34812926/798007*e - 525625/114001, -345073/798007*e^8 - 851185/798007*e^7 + 1041586/114001*e^6 + 13760312/798007*e^5 - 40656415/798007*e^4 - 50091819/798007*e^3 + 59768939/798007*e^2 + 54383043/798007*e - 712111/114001, -28776/798007*e^8 + 54025/798007*e^7 + 136650/114001*e^6 - 1409603/798007*e^5 - 9291826/798007*e^4 + 9325996/798007*e^3 + 29155743/798007*e^2 - 16212036/798007*e - 4323283/114001, 52180/798007*e^8 + 166374/798007*e^7 - 132933/114001*e^6 - 2859498/798007*e^5 + 2664820/798007*e^4 + 12364137/798007*e^3 + 10125040/798007*e^2 - 19471888/798007*e - 3862514/114001, 225429/798007*e^8 + 766212/798007*e^7 - 587808/114001*e^6 - 12972945/798007*e^5 + 16366408/798007*e^4 + 51590680/798007*e^3 - 7019914/798007*e^2 - 63272224/798007*e - 3117364/114001, -3674/798007*e^8 + 172234/798007*e^7 + 69218/114001*e^6 - 3697182/798007*e^5 - 6793134/798007*e^4 + 20843152/798007*e^3 + 23107099/798007*e^2 - 29985488/798007*e - 3445495/114001, 333131/798007*e^8 + 1106496/798007*e^7 - 899447/114001*e^6 - 19092128/798007*e^5 + 27453078/798007*e^4 + 78809907/798007*e^3 - 17041751/798007*e^2 - 94677892/798007*e - 5482343/114001, 260621/798007*e^8 + 862760/798007*e^7 - 678957/114001*e^6 - 14363653/798007*e^5 + 18462487/798007*e^4 + 54391271/798007*e^3 - 2463828/798007*e^2 - 60314790/798007*e - 5874332/114001, -73761/798007*e^8 - 388393/798007*e^7 + 119632/114001*e^6 + 6722861/798007*e^5 + 3469245/798007*e^4 - 26969287/798007*e^3 - 32845724/798007*e^2 + 32782094/798007*e + 5882024/114001, -79647/114001*e^8 - 203750/114001*e^7 + 1639360/114001*e^6 + 3208823/114001*e^5 - 8758810/114001*e^4 - 10656116/114001*e^3 + 12627070/114001*e^2 + 10189463/114001*e - 1504080/114001, 376088/798007*e^8 + 906795/798007*e^7 - 1133413/114001*e^6 - 14285272/798007*e^5 + 44302193/798007*e^4 + 48754481/798007*e^3 - 67896200/798007*e^2 - 51704659/798007*e + 1424384/114001, -31952/798007*e^8 - 43396/798007*e^7 + 113700/114001*e^6 + 640265/798007*e^5 - 5752727/798007*e^4 - 2038985/798007*e^3 + 12735628/798007*e^2 - 1354356/798007*e - 608521/114001, -9273/798007*e^8 - 406303/798007*e^7 - 125659/114001*e^6 + 7823251/798007*e^5 + 15797331/798007*e^4 - 36554635/798007*e^3 - 53655418/798007*e^2 + 39460440/798007*e + 7421907/114001, -28726/114001*e^8 - 133749/114001*e^7 + 444926/114001*e^6 + 2423535/114001*e^5 - 872774/114001*e^4 - 10789057/114001*e^3 - 2906545/114001*e^2 + 12928699/114001*e + 6962478/114001, -179068/798007*e^8 - 78567/798007*e^7 + 653248/114001*e^6 - 1137179/798007*e^5 - 34447807/798007*e^4 + 26059403/798007*e^3 + 86563749/798007*e^2 - 57153340/798007*e - 10579670/114001, 290776/798007*e^8 + 864854/798007*e^7 - 829548/114001*e^6 - 14743607/798007*e^5 + 28625498/798007*e^4 + 59925470/798007*e^3 - 26343111/798007*e^2 - 73440790/798007*e - 4390492/114001, 273897/798007*e^8 + 1106167/798007*e^7 - 697599/114001*e^6 - 20176470/798007*e^5 + 18667007/798007*e^4 + 92415422/798007*e^3 - 3557231/798007*e^2 - 118962019/798007*e - 6945534/114001, 4666/114001*e^8 - 3396/114001*e^7 - 128814/114001*e^6 + 183062/114001*e^5 + 1152091/114001*e^4 - 1938857/114001*e^3 - 4410269/114001*e^2 + 4114772/114001*e + 5527090/114001, 620440/798007*e^8 + 1863244/798007*e^7 - 1744787/114001*e^6 - 31048288/798007*e^5 + 59940185/798007*e^4 + 118188457/798007*e^3 - 72608450/798007*e^2 - 131372600/798007*e - 3081039/114001, -183214/798007*e^8 - 477607/798007*e^7 + 540157/114001*e^6 + 7627323/798007*e^5 - 20523593/798007*e^4 - 26020130/798007*e^3 + 32519435/798007*e^2 + 25079631/798007*e - 1282169/114001, 190457/798007*e^8 + 1165870/798007*e^7 - 319904/114001*e^6 - 21529465/798007*e^5 - 4637533/798007*e^4 + 97677861/798007*e^3 + 45734473/798007*e^2 - 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175869254/798007*e^3 + 100333253/798007*e^2 + 208615702/798007*e + 9364030/114001, 10429/798007*e^8 + 155324/798007*e^7 - 2674/114001*e^6 - 3853683/798007*e^5 - 3805811/798007*e^4 + 27425649/798007*e^3 + 37827523/798007*e^2 - 55455497/798007*e - 9841365/114001, -372726/798007*e^8 - 1361972/798007*e^7 + 937889/114001*e^6 + 23717613/798007*e^5 - 22272629/798007*e^4 - 100001150/798007*e^3 - 16218192/798007*e^2 + 125733542/798007*e + 12160259/114001, -839931/798007*e^8 - 1873934/798007*e^7 + 2662516/114001*e^6 + 30144267/798007*e^5 - 114270361/798007*e^4 - 109755430/798007*e^3 + 201967835/798007*e^2 + 116853073/798007*e - 8253585/114001, -48579/114001*e^8 - 69018/114001*e^7 + 1188416/114001*e^6 + 1015019/114001*e^5 - 8286623/114001*e^4 - 3426628/114001*e^3 + 16374106/114001*e^2 + 4757284/114001*e - 4545159/114001, -578075/798007*e^8 - 1453955/798007*e^7 + 1657013/114001*e^6 + 21241940/798007*e^5 - 59360394/798007*e^4 - 51160173/798007*e^3 + 86509849/798007*e^2 + 12108734/798007*e - 2676592/114001, -751566/798007*e^8 - 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19249782/798007*e^2 - 82383582/798007*e - 6616366/114001, 260616/798007*e^8 + 1177940/798007*e^7 - 499018/114001*e^6 - 19215806/798007*e^5 - 1964790/798007*e^4 + 65032652/798007*e^3 + 65859772/798007*e^2 - 57585814/798007*e - 13117526/114001, -726146/798007*e^8 - 1938278/798007*e^7 + 2136608/114001*e^6 + 31159505/798007*e^5 - 81027095/798007*e^4 - 106872578/798007*e^3 + 127618812/798007*e^2 + 92106785/798007*e - 4145585/114001, 510767/798007*e^8 + 1277824/798007*e^7 - 1501017/114001*e^6 - 20196598/798007*e^5 + 55653216/798007*e^4 + 68653828/798007*e^3 - 82109918/798007*e^2 - 68476553/798007*e + 6217172/114001, -45706/798007*e^8 - 479861/798007*e^7 - 39242/114001*e^6 + 8942546/798007*e^5 + 16741201/798007*e^4 - 40844443/798007*e^3 - 87468993/798007*e^2 + 58192298/798007*e + 13155120/114001, 451875/798007*e^8 + 2861386/798007*e^7 - 656483/114001*e^6 - 52965664/798007*e^5 - 26953212/798007*e^4 + 244326289/798007*e^3 + 202491734/798007*e^2 - 322355415/798007*e - 37622667/114001, -499521/798007*e^8 - 2348471/798007*e^7 + 1120965/114001*e^6 + 43417198/798007*e^5 - 15336057/798007*e^4 - 202210394/798007*e^3 - 72340556/798007*e^2 + 265522104/798007*e + 26032950/114001, -65518/114001*e^8 - 263582/114001*e^7 + 1038793/114001*e^6 + 4502909/114001*e^5 - 2082146/114001*e^4 - 17889636/114001*e^3 - 8276422/114001*e^2 + 20484017/114001*e + 17692940/114001, -442685/798007*e^8 - 1213130/798007*e^7 + 1329508/114001*e^6 + 20776366/798007*e^5 - 52943705/798007*e^4 - 86027611/798007*e^3 + 93163618/798007*e^2 + 97731555/798007*e - 4261908/114001, 65052/114001*e^8 + 226100/114001*e^7 - 1250021/114001*e^6 - 4071198/114001*e^5 + 5770262/114001*e^4 + 18176848/114001*e^3 - 5170033/114001*e^2 - 21186491/114001*e - 7596766/114001, 66307/114001*e^8 + 118613/114001*e^7 - 1506073/114001*e^6 - 1545456/114001*e^5 + 9925850/114001*e^4 + 1817503/114001*e^3 - 23805366/114001*e^2 + 5548776/114001*e + 18299686/114001, -354265/798007*e^8 - 1575362/798007*e^7 + 828140/114001*e^6 + 27729406/798007*e^5 - 18087640/798007*e^4 - 113320748/798007*e^3 + 6904917/798007*e^2 + 114751443/798007*e + 5169296/114001, 540297/798007*e^8 + 2373082/798007*e^7 - 1161426/114001*e^6 - 40560532/798007*e^5 + 11764526/798007*e^4 + 157873718/798007*e^3 + 73741460/798007*e^2 - 169808319/798007*e - 16698510/114001, -1079173/798007*e^8 - 2549515/798007*e^7 + 3259845/114001*e^6 + 39810088/798007*e^5 - 126700358/798007*e^4 - 132358979/798007*e^3 + 180037161/798007*e^2 + 136691482/798007*e - 2034813/114001, 131486/798007*e^8 - 250794/798007*e^7 - 645169/114001*e^6 + 6454257/798007*e^5 + 45507458/798007*e^4 - 44821324/798007*e^3 - 147860659/798007*e^2 + 89399424/798007*e + 19859406/114001, 1461727/798007*e^8 + 3647111/798007*e^7 - 4323131/114001*e^6 - 57052568/798007*e^5 + 162991775/798007*e^4 + 188173126/798007*e^3 - 231121687/798007*e^2 - 189838160/798007*e + 2120301/114001, -17158/114001*e^8 - 69800/114001*e^7 + 253594/114001*e^6 + 1227033/114001*e^5 + 81939/114001*e^4 - 5377729/114001*e^3 - 7274946/114001*e^2 + 7939565/114001*e + 10403795/114001] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([13, 13, -w^2 + 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]