/* 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([-1, 3, 4, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1]) primes_array = [ [3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3],\ [9, 3, -w^4 + 5*w^2 - 3],\ [9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2],\ [13, 13, -w^4 + w^3 + 4*w^2 - 3*w - 1],\ [17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1],\ [19, 19, -w^3 + w^2 + 4*w - 2],\ [23, 23, -w^2 + 3],\ [31, 31, w^3 - 4*w + 2],\ [32, 2, 2],\ [37, 37, w^3 - 3*w - 1],\ [53, 53, -2*w^4 + w^3 + 9*w^2 - 3*w - 2],\ [59, 59, -w^4 + 5*w^2 + w - 4],\ [61, 61, -w^4 + w^3 + 5*w^2 - 4*w],\ [67, 67, -w^4 + 6*w^2 + 2*w - 4],\ [71, 71, 2*w^4 - w^3 - 9*w^2 + 4*w + 5],\ [79, 79, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\ [83, 83, -w^4 + 2*w^3 + 5*w^2 - 7*w - 2],\ [83, 83, -w^4 + w^3 + 4*w^2 - 3*w + 3],\ [83, 83, w^4 - w^3 - 5*w^2 + 4*w - 1],\ [83, 83, -w^4 + w^3 + 4*w^2 - 4*w - 2],\ [83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\ [97, 97, -w^4 - w^3 + 6*w^2 + 4*w - 4],\ [101, 101, -w^4 + 4*w^2 + 2*w - 2],\ [107, 107, -2*w^4 + w^3 + 11*w^2 - 3*w - 7],\ [127, 127, w^3 - w^2 - 4*w],\ [131, 131, w^4 - w^3 - 4*w^2 + 2*w - 1],\ [137, 137, w^4 - w^3 - 6*w^2 + 3*w + 3],\ [139, 139, -2*w^4 + w^3 + 9*w^2 - 3*w + 1],\ [157, 157, 2*w^4 - w^3 - 9*w^2 + 4*w + 2],\ [163, 163, -w^2 - 2*w + 3],\ [167, 167, w^4 - 5*w^2 + 2*w + 1],\ [169, 13, -2*w^4 + 2*w^3 + 9*w^2 - 7*w - 5],\ [169, 13, w^4 - 2*w^3 - 5*w^2 + 8*w + 2],\ [191, 191, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\ [193, 193, 2*w^4 - 2*w^3 - 8*w^2 + 7*w],\ [199, 199, -w^4 + 2*w^3 + 5*w^2 - 9*w - 3],\ [211, 211, -3*w^4 + w^3 + 13*w^2 - 2*w - 1],\ [227, 227, 2*w^3 - w^2 - 9*w + 1],\ [233, 233, -w^3 + w^2 + 4*w + 1],\ [251, 251, -3*w^4 + 14*w^2 + w - 2],\ [257, 257, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 5],\ [257, 257, -w^4 + w^3 + 5*w^2 - 6*w - 1],\ [257, 257, 2*w^4 - 2*w^3 - 11*w^2 + 9*w + 9],\ [257, 257, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 3],\ [257, 257, 2*w^4 - w^3 - 10*w^2 + 5*w + 5],\ [269, 269, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\ [271, 271, -w^4 + 4*w^2 + w - 3],\ [277, 277, -2*w^4 + 9*w^2 + w - 4],\ [281, 281, w^4 - w^3 - 3*w^2 + 3*w - 4],\ [283, 283, 2*w^4 - 3*w^3 - 8*w^2 + 13*w],\ [289, 17, -w^4 + w^3 + 7*w^2 - 5*w - 5],\ [289, 17, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 6],\ [293, 293, -2*w^4 + 11*w^2 - 7],\ [317, 317, w^3 - 6*w],\ [337, 337, -w^4 + 2*w^3 + 5*w^2 - 9*w - 1],\ [337, 337, w^4 - 2*w^3 - 5*w^2 + 6*w + 3],\ [337, 337, -w^4 + w^3 + 5*w^2 - 4*w - 6],\ [337, 337, -2*w^3 + 8*w + 1],\ [337, 337, w^2 + w - 5],\ [347, 347, -2*w^4 + w^3 + 9*w^2 - 5*w - 3],\ [349, 349, 3*w^4 - 2*w^3 - 13*w^2 + 8*w + 2],\ [353, 353, w^4 - 3*w^3 - 4*w^2 + 12*w + 2],\ [359, 359, 2*w^3 - w^2 - 7*w + 3],\ [361, 19, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\ [361, 19, w^4 - w^3 - 3*w^2 + 3*w - 3],\ [367, 367, -2*w^4 + w^3 + 9*w^2 - w - 2],\ [379, 379, -2*w^3 + w^2 + 7*w + 2],\ [379, 379, -2*w^4 + w^3 + 10*w^2 - 4*w],\ [379, 379, 2*w^3 - w^2 - 6*w - 2],\ [379, 379, -2*w^3 + 2*w^2 + 6*w - 3],\ [379, 379, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\ [383, 383, 2*w^4 + w^3 - 10*w^2 - 7*w + 4],\ [383, 383, -2*w^3 + w^2 + 10*w],\ [383, 383, w^3 + w^2 - 5*w - 1],\ [383, 383, 3*w^4 + 3*w^3 - 15*w^2 - 15*w + 4],\ [383, 383, -2*w^4 + 3*w^3 + 10*w^2 - 10*w - 2],\ [389, 389, 3*w^4 - w^3 - 14*w^2 + 3*w + 3],\ [397, 397, w^4 - 6*w^2 - 2*w + 5],\ [397, 397, w^4 - 2*w^3 - 2*w^2 + 6*w - 5],\ [397, 397, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 6],\ [397, 397, w^4 - w^3 - 3*w^2 + 4*w - 6],\ [397, 397, w^3 + w^2 - 3*w - 4],\ [401, 401, w^3 - w^2 - 6*w + 3],\ [401, 401, -w^4 + 4*w^2 + 2*w - 3],\ [401, 401, -w^4 + 6*w^2 - w - 7],\ [421, 421, -w^4 - w^3 + 5*w^2 + 5*w - 4],\ [421, 421, -w^4 + w^3 + 6*w^2 - 3*w - 2],\ [421, 421, -w^4 - w^3 + 6*w^2 + 6*w - 5],\ [421, 421, 3*w^4 - w^3 - 15*w^2 + w + 10],\ [421, 421, 2*w^4 - 9*w^2 + 2*w + 4],\ [431, 431, 2*w^4 - 11*w^2 - 2*w + 11],\ [439, 439, 2*w^4 - 3*w^3 - 9*w^2 + 10*w + 6],\ [443, 443, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 2],\ [449, 449, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\ [461, 461, 3*w^4 - 4*w^3 - 14*w^2 + 14*w + 5],\ [463, 463, w^3 - 6*w - 1],\ [467, 467, 3*w^4 - 3*w^3 - 13*w^2 + 10*w],\ [487, 487, 3*w^4 - w^3 - 14*w^2 + w + 3],\ [487, 487, 2*w^2 - w - 4],\ [487, 487, -2*w^4 + 2*w^3 + 9*w^2 - 8*w - 5],\ [487, 487, 2*w^4 - 10*w^2 - 3*w + 4],\ [487, 487, -2*w^4 + w^3 + 8*w^2 - 3*w - 1],\ [499, 499, -w^4 + 2*w^3 + 4*w^2 - 8*w - 2],\ [499, 499, -2*w^4 + w^3 + 10*w^2 - w - 9],\ [499, 499, -w^3 - 2*w^2 + 2*w + 5],\ [499, 499, -w^4 + 4*w^2 + 4*w],\ [499, 499, -2*w^4 + w^3 + 12*w^2 - 4*w - 9],\ [509, 509, 3*w^4 - 2*w^3 - 16*w^2 + 6*w + 9],\ [521, 521, -2*w^4 + w^3 + 10*w^2 - 5*w - 4],\ [523, 523, w - 4],\ [529, 23, -w^3 + 2*w^2 + 4*w - 4],\ [529, 23, w^4 + 2*w^3 - 6*w^2 - 11*w + 4],\ [569, 569, -2*w^4 + 11*w^2 - 10],\ [571, 571, -2*w^4 + w^3 + 10*w^2 - 3*w - 2],\ [593, 593, -2*w^4 + 3*w^3 + 10*w^2 - 11*w - 8],\ [613, 613, -2*w^3 + 2*w^2 + 9*w - 5],\ [617, 617, -2*w^4 + 10*w^2 - w - 7],\ [631, 631, -2*w^4 + 2*w^3 + 7*w^2 - 8*w + 3],\ [641, 641, -2*w^4 + 2*w^3 + 8*w^2 - 9*w + 3],\ [643, 643, -3*w^4 + w^3 + 13*w^2 - w + 1],\ [643, 643, w^4 + w^3 - 3*w^2 - 6*w - 2],\ [643, 643, -w^4 - w^3 + 6*w^2 + 3*w - 4],\ [643, 643, 2*w^4 - w^3 - 10*w^2 + 4*w + 1],\ [643, 643, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 5],\ [647, 647, -2*w^3 + w^2 + 6*w - 4],\ [659, 659, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 10],\ [661, 661, 2*w^4 + 3*w^3 - 11*w^2 - 14*w + 6],\ [673, 673, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\ [683, 683, w^4 - 2*w^3 - 4*w^2 + 6*w - 4],\ [701, 701, w^3 - w^2 - 2*w + 4],\ [727, 727, -w^4 + 6*w^2 + 2*w - 7],\ [743, 743, w^4 - w^3 - 7*w^2 + 5*w + 9],\ [769, 769, w^4 + 2*w^3 - 5*w^2 - 9*w + 4],\ [787, 787, w^4 + w^3 - 7*w^2 - 3*w + 5],\ [797, 797, -2*w^4 - w^3 + 10*w^2 + 4*w - 4],\ [797, 797, w^4 - 3*w^3 - 5*w^2 + 12*w + 5],\ [797, 797, -3*w^4 + 2*w^3 + 13*w^2 - 8*w],\ [797, 797, -w^4 + w^3 + 3*w^2 - 5*w - 1],\ [797, 797, 2*w^4 - 11*w^2 + 2*w + 7],\ [809, 809, -4*w^4 + 2*w^3 + 18*w^2 - 6*w + 1],\ [809, 809, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 8],\ [809, 809, w^4 - 2*w^3 - 2*w^2 + 8*w - 4],\ [809, 809, 2*w^4 - 8*w^2 - 2*w + 3],\ [809, 809, 2*w^4 - 3*w^3 - 9*w^2 + 13*w + 4],\ [821, 821, -2*w^4 + 2*w^3 + 8*w^2 - 6*w + 3],\ [823, 823, -2*w^4 + 3*w^3 + 8*w^2 - 12*w - 1],\ [829, 829, 2*w^4 - 3*w^3 - 10*w^2 + 13*w + 4],\ [839, 839, -2*w^4 + 12*w^2 - w - 10],\ [863, 863, 2*w^4 - w^3 - 9*w^2 + 5],\ [877, 877, -w^4 + w^3 + 5*w^2 - 5*w - 7],\ [881, 881, 2*w^4 - w^3 - 9*w^2 + w - 1],\ [887, 887, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 6],\ [907, 907, -3*w^4 + w^3 + 13*w^2 - w - 5],\ [919, 919, w^4 + w^3 - 3*w^2 - 5*w - 3],\ [929, 929, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 4],\ [937, 937, -2*w^4 + 10*w^2 + 3*w - 7],\ [941, 941, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\ [961, 31, 2*w^4 + 2*w^3 - 10*w^2 - 12*w + 5],\ [961, 31, -w^4 + 5*w^2 - w - 7],\ [967, 967, -2*w^4 + w^3 + 9*w^2 - 3*w + 2],\ [991, 991, -3*w^4 + w^3 + 15*w^2 - 4*w - 5],\ [997, 997, -3*w^4 + 15*w^2 - 5],\ [997, 997, 2*w^4 - w^3 - 9*w^2 + 6*w + 2],\ [997, 997, 2*w^4 - w^3 - 11*w^2 + w + 7],\ [997, 997, 2*w^3 - 5*w - 1],\ [997, 997, 2*w^4 - 3*w^3 - 6*w^2 + 5*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^14 - 3*x^13 - 27*x^12 + 80*x^11 + 274*x^10 - 781*x^9 - 1378*x^8 + 3558*x^7 + 3692*x^6 - 7584*x^5 - 5070*x^4 + 6046*x^3 + 2807*x^2 - 332*x - 152 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -338713/1563066*e^13 + 361651/1563066*e^12 + 9467465/1563066*e^11 - 3985109/781533*e^10 - 16480532/260511*e^9 + 54797287/1563066*e^8 + 81580142/260511*e^7 - 20470291/260511*e^6 - 569318224/781533*e^5 - 10555019/781533*e^4 + 484679894/781533*e^3 + 85217987/781533*e^2 - 20803715/521022*e - 1517354/781533, -63704/781533*e^13 - 55378/781533*e^12 + 2140621/781533*e^11 + 1250116/781533*e^10 - 8873197/260511*e^9 - 10064680/781533*e^8 + 50214470/260511*e^7 + 13488794/260511*e^6 - 385511851/781533*e^5 - 84171758/781533*e^4 + 354992666/781533*e^3 + 61258379/781533*e^2 - 10849088/260511*e - 2021246/781533, 456040/781533*e^13 - 357256/781533*e^12 - 12919538/781533*e^11 + 7289260/781533*e^10 + 45666820/260511*e^9 - 40118641/781533*e^8 - 229024372/260511*e^7 + 3219893/260511*e^6 + 1611113351/781533*e^5 + 372498034/781533*e^4 - 1368653278/781533*e^3 - 523766002/781533*e^2 + 26273936/260511*e + 29739178/781533, 1, 60748/260511*e^13 - 23996/260511*e^12 - 1788496/260511*e^11 + 432757/260511*e^10 + 19726693/260511*e^9 - 361036/86837*e^8 - 33989304/86837*e^7 - 4817426/86837*e^6 + 243396329/260511*e^5 + 78204878/260511*e^4 - 206445815/260511*e^3 - 90701935/260511*e^2 + 8251052/260511*e + 2056570/86837, -37994/781533*e^13 - 10831/781533*e^12 + 1153795/781533*e^11 + 455731/781533*e^10 - 4400428/260511*e^9 - 6787102/781533*e^8 + 23578526/260511*e^7 + 14679341/260511*e^6 - 172483891/781533*e^5 - 123826250/781533*e^4 + 139502186/781533*e^3 + 114787193/781533*e^2 + 4265161/260511*e - 4848320/781533, 404800/781533*e^13 - 447862/781533*e^12 - 11150990/781533*e^11 + 9583174/781533*e^10 + 12737504/86837*e^9 - 61854418/781533*e^8 - 186753061/260511*e^7 + 37322018/260511*e^6 + 1292290199/781533*e^5 + 135855718/781533*e^4 - 1095883081/781533*e^3 - 327993163/781533*e^2 + 8191066/86837*e + 22825840/781533, -51671/86837*e^13 + 121126/260511*e^12 + 1472336/86837*e^11 - 2508025/260511*e^10 - 15721999/86837*e^9 + 14398045/260511*e^8 + 79413098/86837*e^7 - 2941468/86837*e^6 - 187442035/86837*e^5 - 111174160/260511*e^4 + 159892698/86837*e^3 + 163779523/260511*e^2 - 8506892/86837*e - 9250783/260511, -266758/781533*e^13 + 538762/781533*e^12 + 6672485/781533*e^11 - 11869471/781533*e^10 - 20169419/260511*e^9 + 83929636/781533*e^8 + 86580202/260511*e^7 - 73980869/260511*e^6 - 533734415/781533*e^5 + 135649451/781533*e^4 + 410522548/781533*e^3 + 99785725/781533*e^2 - 6719923/260511*e - 10096654/781533, -128701/1563066*e^13 - 151997/1563066*e^12 + 4174139/1563066*e^11 + 1982545/781533*e^10 - 8374937/260511*e^9 - 38910305/1563066*e^8 + 46008959/260511*e^7 + 31159424/260511*e^6 - 341229877/781533*e^5 - 215593721/781533*e^4 + 294179249/781533*e^3 + 175561817/781533*e^2 - 9559031/521022*e - 6479978/781533, -14129/86837*e^13 + 60805/260511*e^12 + 1163450/260511*e^11 - 1424075/260511*e^10 - 11913037/260511*e^9 + 3752536/86837*e^8 + 19369619/86837*e^7 - 12384775/86837*e^6 - 44943502/86837*e^5 + 47865578/260511*e^4 + 118431076/260511*e^3 - 18989056/260511*e^2 - 12462272/260511*e + 133978/86837, -344563/1563066*e^13 + 931813/1563066*e^12 + 7796993/1563066*e^11 - 10233479/781533*e^10 - 9929303/260511*e^9 + 145026697/1563066*e^8 + 32718032/260511*e^7 - 65923861/260511*e^6 - 132936700/781533*e^5 + 154406281/781533*e^4 + 35435642/781533*e^3 + 37146281/781533*e^2 + 19234591/521022*e - 2708630/781533, 513685/1563066*e^13 - 580963/1563066*e^12 - 14257877/1563066*e^11 + 6359660/781533*e^10 + 8220050/86837*e^9 - 86752831/1563066*e^8 - 121731068/260511*e^7 + 32233948/260511*e^6 + 851643322/781533*e^5 + 18144476/781533*e^4 - 736632761/781533*e^3 - 147167948/781533*e^2 + 13904043/173674*e + 12929408/781533, -206078/781533*e^13 - 57787/781533*e^12 + 6362443/781533*e^11 + 1918729/781533*e^10 - 24539054/260511*e^9 - 25273456/781533*e^8 + 131924357/260511*e^7 + 53322683/260511*e^6 - 971410057/781533*e^5 - 455874110/781533*e^4 + 833779631/781533*e^3 + 423425873/781533*e^2 - 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66815179/260511*e - 94582646/781533, 201874/260511*e^13 - 584228/260511*e^12 - 4605631/260511*e^11 + 13301957/260511*e^10 + 35793517/260511*e^9 - 101604824/260511*e^8 - 40870018/86837*e^7 + 109333916/86837*e^6 + 187100687/260511*e^5 - 432484846/260511*e^4 - 103369805/260511*e^3 + 192215161/260511*e^2 + 1630118/260511*e - 16463032/260511, 288733/260511*e^13 - 202330/260511*e^12 - 8179438/260511*e^11 + 1274831/86837*e^10 + 86908381/260511*e^9 - 15983534/260511*e^8 - 145964486/86837*e^7 - 14404487/86837*e^6 + 1031184902/260511*e^5 + 351418948/260511*e^4 - 869004116/260511*e^3 - 143536320/86837*e^2 + 29949773/260511*e + 25552592/260511, -678044/781533*e^13 + 155369/781533*e^12 + 20142775/781533*e^11 - 2192381/781533*e^10 - 24886742/86837*e^9 - 9293398/781533*e^8 + 387960707/260511*e^7 + 79395833/260511*e^6 - 2790855973/781533*e^5 - 996213032/781533*e^4 + 2398902374/781533*e^3 + 1088007644/781533*e^2 - 13471277/86837*e - 53908856/781533, -434767/260511*e^13 + 491176/260511*e^12 + 12143021/260511*e^11 - 11154707/260511*e^10 - 42219445/86837*e^9 + 27369373/86837*e^8 + 208643357/86837*e^7 - 75299390/86837*e^6 - 1456530878/260511*e^5 + 148169324/260511*e^4 + 1258858672/260511*e^3 + 70177781/260511*e^2 - 38863948/86837*e - 528426/86837, -2424340/781533*e^13 + 739294/781533*e^12 + 71868065/781533*e^11 - 12123520/781533*e^10 - 88773493/86837*e^9 + 3262915/781533*e^8 + 1387351012/260511*e^7 + 230659510/260511*e^6 - 10002520976/781533*e^5 - 3185652610/781533*e^4 + 8532083953/781533*e^3 + 3499355047/781533*e^2 - 37931119/86837*e - 190559308/781533, -201964/86837*e^13 + 539234/260511*e^12 + 17077007/260511*e^11 - 11612681/260511*e^10 - 179913532/260511*e^9 + 75106826/260511*e^8 + 298673907/86837*e^7 - 43410999/86837*e^6 - 696177136/86837*e^5 - 197907998/260511*e^4 + 1772652211/260511*e^3 + 419851157/260511*e^2 - 106779989/260511*e - 17294120/260511, 66998/781533*e^13 + 184015/781533*e^12 - 2715790/781533*e^11 - 3247210/781533*e^10 + 12629879/260511*e^9 + 11605261/781533*e^8 - 75393542/260511*e^7 + 13635718/260511*e^6 + 595830826/781533*e^5 - 272334946/781533*e^4 - 595668590/781533*e^3 + 334118311/781533*e^2 + 41930698/260511*e - 34716688/781533, -98985/86837*e^13 + 136778/86837*e^12 + 7868702/260511*e^11 - 8639725/260511*e^10 - 77087611/260511*e^9 + 53951996/260511*e^8 + 119646697/86837*e^7 - 28797791/86837*e^6 - 263714019/86837*e^5 - 53896295/86837*e^4 + 631347715/260511*e^3 + 335011987/260511*e^2 - 11855765/260511*e - 20876390/260511, -193841/173674*e^13 + 838189/521022*e^12 + 15152035/521022*e^11 - 8725990/260511*e^10 - 72580162/260511*e^9 + 35493211/173674*e^8 + 109981847/86837*e^7 - 26053508/86837*e^6 - 237252992/86837*e^5 - 183240986/260511*e^4 + 560959255/260511*e^3 + 355015786/260511*e^2 - 25959091/521022*e - 9126726/86837, 2114908/781533*e^13 - 953584/781533*e^12 - 62095724/781533*e^11 + 18326554/781533*e^10 + 75966957/86837*e^9 - 73026604/781533*e^8 - 1179005713/260511*e^7 - 102175750/260511*e^6 + 8487873791/781533*e^5 + 2179960282/781533*e^4 - 7341451522/781533*e^3 - 2595117190/781533*e^2 + 48154462/86837*e + 164746714/781533, 162604/781533*e^13 + 440336/781533*e^12 - 6490244/781533*e^11 - 9326252/781533*e^10 + 30121666/260511*e^9 + 63979055/781533*e^8 - 180849634/260511*e^7 - 60939718/260511*e^6 + 1417547921/781533*e^5 + 205466824/781533*e^4 - 1268855914/781533*e^3 - 13732321/781533*e^2 + 17625419/260511*e - 19660910/781533, 41654/260511*e^13 - 19913/260511*e^12 - 1416578/260511*e^11 + 285549/86837*e^10 + 17676662/260511*e^9 - 11676271/260511*e^8 - 33116883/86837*e^7 + 20987628/86837*e^6 + 250038715/260511*e^5 - 139692211/260511*e^4 - 220162438/260511*e^3 + 37237233/86837*e^2 + 8285788/260511*e - 11020442/260511, 5397289/1563066*e^13 - 4714879/1563066*e^12 - 153073475/1563066*e^11 + 50898941/781533*e^10 + 90234817/86837*e^9 - 657580153/1563066*e^8 - 1357453775/260511*e^7 + 182130124/260511*e^6 + 9553599166/781533*e^5 + 1010537360/781533*e^4 - 8154930392/781533*e^3 - 2032061978/781533*e^2 + 109330357/173674*e + 105443864/781533, 254615/1563066*e^13 - 141515/1563066*e^12 - 7586653/1563066*e^11 + 1291606/781533*e^10 + 14229080/260511*e^9 - 8077985/1563066*e^8 - 75593116/260511*e^7 - 10739077/260511*e^6 + 553230305/781533*e^5 + 191438935/781533*e^4 - 456293803/781533*e^3 - 226297849/781533*e^2 - 6840145/521022*e + 14311384/781533, 1532594/781533*e^13 - 1081325/781533*e^12 - 43529887/781533*e^11 + 21053963/781533*e^10 + 51448027/86837*e^9 - 97797437/781533*e^8 - 776330468/260511*e^7 - 51173180/260511*e^6 + 5470047109/781533*e^5 + 1682695430/781533*e^4 - 4633717619/781533*e^3 - 2116780187/781533*e^2 + 27117978/86837*e + 114781442/781533, -468679/521022*e^13 - 213905/521022*e^12 + 14764627/521022*e^11 + 2842892/260511*e^10 - 86646539/260511*e^9 - 20031951/173674*e^8 + 155870503/86837*e^7 + 55068838/86837*e^6 - 1142594854/260511*e^5 - 438849254/260511*e^4 + 970248841/260511*e^3 + 386337709/260511*e^2 - 31574213/521022*e - 4939046/86837, 2462317/781533*e^13 - 1631425/781533*e^12 - 70785251/781533*e^11 + 32916781/781533*e^10 + 84701720/86837*e^9 - 170520850/781533*e^8 - 1290169870/260511*e^7 - 30775858/260511*e^6 + 9142771103/781533*e^5 + 2226589387/781533*e^4 - 7757158867/781533*e^3 - 2977876852/781533*e^2 + 42497155/86837*e + 202901818/781533, 2514754/781533*e^13 - 2123998/781533*e^12 - 71416835/781533*e^11 + 45576208/781533*e^10 + 253110122/260511*e^9 - 290597353/781533*e^8 - 1272591127/260511*e^7 + 152765444/260511*e^6 + 8981760191/781533*e^5 + 993113200/781533*e^4 - 7700944597/781533*e^3 - 1903599016/781533*e^2 + 173015647/260511*e + 83752030/781533, 596413/173674*e^13 - 1674077/521022*e^12 - 49985123/521022*e^11 + 17546029/260511*e^10 + 260816483/260511*e^9 - 211965815/521022*e^8 - 429566749/86837*e^7 + 41553378/86837*e^6 + 994219557/86837*e^5 + 539746618/260511*e^4 - 2496510161/260511*e^3 - 906744913/260511*e^2 + 243538781/521022*e + 60477994/260511] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]