/*
  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.<x> = PolynomialRing(QQ)
g = P([5, -1, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 25, -w^3 + 5*w + 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 - 29*x^7 - 18*x^6 + 239*x^5 + 275*x^4 - 441*x^3 - 669*x^2 - 27*x + 144
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 0, -139/1545*e^8 + 244/1545*e^7 + 3659/1545*e^6 - 1348/515*e^5 - 9193/515*e^4 + 4132/515*e^3 + 10151/309*e^2 - 1039/515*e - 747/103, -7/103*e^8 + 128/1545*e^7 + 2887/1545*e^6 - 1598/1545*e^5 - 23042/1545*e^4 - 1852/1545*e^3 + 46898/1545*e^2 + 1411/103*e - 4482/515, 139/1545*e^8 - 244/1545*e^7 - 3659/1545*e^6 + 1348/515*e^5 + 9193/515*e^4 - 4132/515*e^3 - 10151/309*e^2 + 1554/515*e + 850/103, 1/1545*e^8 + 13/515*e^7 - 52/515*e^6 - 283/515*e^5 + 922/515*e^4 + 4531/1545*e^3 - 2671/309*e^2 - 1004/515*e + 819/103, 23/1545*e^8 - 2/103*e^7 - 601/1545*e^6 + 91/309*e^5 + 1327/515*e^4 - 1259/1545*e^3 - 637/1545*e^2 + 1113/515*e - 3562/515, -118/515*e^8 + 511/1545*e^7 + 3164/515*e^6 - 7321/1545*e^5 - 73382/1545*e^4 + 8903/1545*e^3 + 47164/515*e^2 + 9851/515*e - 11853/515, 106/309*e^8 - 217/515*e^7 - 14494/1545*e^6 + 8071/1545*e^5 + 114929/1545*e^4 + 7504/1545*e^3 - 229886/1545*e^2 - 5175/103*e + 20019/515, 118/515*e^8 - 511/1545*e^7 - 3164/515*e^6 + 7321/1545*e^5 + 73382/1545*e^4 - 8903/1545*e^3 - 47164/515*e^2 - 10366/515*e + 11853/515, 91/309*e^8 - 589/1545*e^7 - 12476/1545*e^6 + 2663/515*e^5 + 33157/515*e^4 - 3854/1545*e^3 - 67753/515*e^2 - 2887/103*e + 21276/515, 112/309*e^8 - 239/515*e^7 - 5121/515*e^6 + 9587/1545*e^5 + 122513/1545*e^4 - 2002/1545*e^3 - 250157/1545*e^2 - 4195/103*e + 25758/515, 139/1545*e^8 - 244/1545*e^7 - 3659/1545*e^6 + 1348/515*e^5 + 9193/515*e^4 - 4132/515*e^3 - 9842/309*e^2 + 1039/515*e + 232/103, 49/309*e^8 - 111/515*e^7 - 2234/515*e^6 + 4793/1545*e^5 + 53387/1545*e^4 - 6013/1545*e^3 - 109463/1545*e^2 - 1507/103*e + 8707/515, -797/1545*e^8 + 351/515*e^7 + 21641/1545*e^6 - 14168/1545*e^5 - 169531/1545*e^4 + 1433/515*e^3 + 109907/515*e^2 + 30263/515*e - 25704/515, -231/515*e^8 + 886/1545*e^7 + 3782/309*e^6 - 3907/515*e^5 - 29851/309*e^4 + 5/103*e^3 + 98726/515*e^2 + 30907/515*e - 25317/515, -316/1545*e^8 + 23/103*e^7 + 2939/515*e^6 - 263/103*e^5 - 23964/515*e^4 - 8542/1545*e^3 + 150959/1545*e^2 + 15989/515*e - 12391/515, -1012/1545*e^8 + 88/103*e^7 + 9158/515*e^6 - 1163/103*e^5 - 71778/515*e^4 + 806/1545*e^3 + 418913/1545*e^2 + 41668/515*e - 31762/515, -1036/1545*e^8 + 437/515*e^7 + 28231/1545*e^6 - 17051/1545*e^5 - 74027/515*e^4 - 822/515*e^3 + 86890/309*e^2 + 40529/515*e - 7077/103, 251/1545*e^8 - 202/1545*e^7 - 468/103*e^6 + 449/515*e^5 + 11195/309*e^4 + 1233/103*e^3 - 103691/1545*e^2 - 17164/515*e + 3304/515, -128/1545*e^8 + 158/1545*e^7 + 3488/1545*e^6 - 2053/1545*e^5 - 27023/1545*e^4 - 593/1545*e^3 + 3272/103*e^2 + 5942/515*e - 493/103, -458/1545*e^8 + 226/515*e^7 + 12223/1545*e^6 - 3256/515*e^5 - 93658/1545*e^4 + 11582/1545*e^3 + 11669/103*e^2 + 14872/515*e - 1830/103, 121/1545*e^8 - 328/1545*e^7 - 3014/1545*e^6 + 2116/515*e^5 + 7223/515*e^4 - 9482/515*e^3 - 41497/1545*e^2 + 5206/515*e + 5318/515, -11/1545*e^8 + 86/1545*e^7 + 57/515*e^6 - 1991/1545*e^5 - 556/1545*e^4 + 12989/1545*e^3 + 644/309*e^2 - 6466/515*e - 769/103, 92/103*e^8 - 120/103*e^7 - 2507/103*e^6 + 1614/103*e^5 + 19735/103*e^4 - 504/103*e^3 - 38598/103*e^2 - 10128/103*e + 9580/103, -45/103*e^8 + 194/309*e^7 + 3653/309*e^6 - 935/103*e^5 - 28669/309*e^4 + 1178/103*e^3 + 19025/103*e^2 + 3906/103*e - 4556/103, 86/309*e^8 - 637/1545*e^7 - 11563/1545*e^6 + 9232/1545*e^5 + 29986/515*e^4 - 11657/1545*e^3 - 175912/1545*e^2 - 2811/103*e + 16133/515, -196/515*e^8 + 758/1545*e^7 + 5341/515*e^6 - 10123/1545*e^5 - 42071/515*e^4 + 1927/1545*e^3 + 50165/309*e^2 + 22822/515*e - 5197/103, -98/515*e^8 + 92/515*e^7 + 8372/1545*e^6 - 2641/1545*e^5 - 23559/515*e^4 - 14332/1545*e^3 + 54559/515*e^2 + 18106/515*e - 21078/515, 289/309*e^8 - 368/309*e^7 - 7901/309*e^6 + 4826/309*e^5 + 20906/103*e^4 + 226/309*e^3 - 42326/103*e^2 - 11541/103*e + 11727/103, -137/515*e^8 + 152/309*e^7 + 10762/1545*e^6 - 860/103*e^5 - 80252/1545*e^4 + 13836/515*e^3 + 46808/515*e^2 - 1931/515*e - 7956/515, 235/309*e^8 - 311/309*e^7 - 2126/103*e^6 + 4219/309*e^5 + 16644/103*e^4 - 662/103*e^3 - 32347/103*e^2 - 8310/103*e + 8236/103, -26/103*e^8 + 446/1545*e^7 + 10679/1545*e^6 - 4876/1545*e^5 - 84584/1545*e^4 - 5638/515*e^3 + 167321/1545*e^2 + 6418/103*e - 10129/515, 854/1545*e^8 - 331/515*e^7 - 4747/309*e^6 + 4076/515*e^5 + 38638/309*e^4 + 822/103*e^3 - 413834/1545*e^2 - 40111/515*e + 45291/515, 59/1545*e^8 + 7/309*e^7 - 596/515*e^6 - 398/309*e^5 + 5061/515*e^4 + 7671/515*e^3 - 8822/515*e^2 - 15976/515*e - 651/515, -514/515*e^8 + 2177/1545*e^7 + 41762/1545*e^6 - 31387/1545*e^5 - 327482/1545*e^4 + 13286/515*e^3 + 129595/309*e^2 + 42823/515*e - 10830/103, 286/1545*e^8 - 97/309*e^7 - 7742/1545*e^6 + 1660/309*e^5 + 20509/515*e^4 - 28508/1545*e^3 - 43803/515*e^2 + 3831/515*e + 10566/515, -1174/1545*e^8 + 257/309*e^7 + 32558/1545*e^6 - 2885/309*e^5 - 262138/1545*e^4 - 12106/515*e^3 + 177437/515*e^2 + 65266/515*e - 44604/515, 521/1545*e^8 - 899/1545*e^7 - 13708/1545*e^6 + 14579/1545*e^5 + 103013/1545*e^4 - 13289/515*e^3 - 61421/515*e^2 - 359/515*e + 10047/515, 353/309*e^8 - 149/103*e^7 - 3215/103*e^6 + 5801/309*e^5 + 76487/309*e^4 + 986/309*e^3 - 154505/309*e^2 - 14100/103*e + 14556/103, -83/1545*e^8 + 53/309*e^7 + 1721/1545*e^6 - 1027/309*e^5 - 6686/1545*e^4 + 24494/1545*e^3 - 23093/1545*e^2 - 8338/515*e + 11242/515, -404/515*e^8 + 518/515*e^7 + 6626/309*e^6 - 20479/1545*e^5 - 52396/309*e^4 - 46/309*e^3 + 514192/1545*e^2 + 50373/515*e - 35723/515, -1669/1545*e^8 + 2477/1545*e^7 + 14997/515*e^6 - 36967/1545*e^5 - 116697/515*e^4 + 20813/515*e^3 + 225531/515*e^2 + 38491/515*e - 48297/515, 7/515*e^8 - 36/515*e^7 - 289/1545*e^6 + 2153/1545*e^5 - 517/515*e^4 - 10321/1545*e^3 + 8176/515*e^2 + 2091/515*e - 9177/515, -95/103*e^8 + 633/515*e^7 + 38651/1545*e^6 - 25969/1545*e^5 - 100922/515*e^4 + 16154/1545*e^3 + 197203/515*e^2 + 8967/103*e - 47496/515, 158/1545*e^8 - 121/1545*e^7 - 892/309*e^6 + 297/515*e^5 + 2417/103*e^4 + 1637/309*e^3 - 24971/515*e^2 - 5162/515*e + 16032/515, -416/515*e^8 + 1592/1545*e^7 + 34214/1545*e^6 - 6904/515*e^5 - 273079/1545*e^4 - 1953/515*e^3 + 186908/515*e^2 + 58192/515*e - 53466/515, 1784/1545*e^8 - 704/515*e^7 - 16342/515*e^6 + 25852/1545*e^5 + 389566/1545*e^4 + 28601/1545*e^3 - 257321/515*e^2 - 86486/515*e + 63447/515, 352/515*e^8 - 1252/1545*e^7 - 1939/103*e^6 + 15212/1545*e^5 + 15527/103*e^4 + 3950/309*e^3 - 474641/1545*e^2 - 57004/515*e + 40344/515, 1706/1545*e^8 - 454/309*e^7 - 15479/515*e^6 + 6199/309*e^5 + 365707/1545*e^4 - 16538/1545*e^3 - 721339/1545*e^2 - 58129/515*e + 65706/515, -145/309*e^8 + 257/515*e^7 + 20194/1545*e^6 - 2782/515*e^5 - 163504/1545*e^4 - 27394/1545*e^3 + 111262/515*e^2 + 8590/103*e - 22869/515, -1799/1545*e^8 + 818/515*e^7 + 16298/515*e^6 - 34129/1545*e^5 - 385324/1545*e^4 + 24871/1545*e^3 + 51491/103*e^2 + 66526/515*e - 13974/103, 522/515*e^8 - 1859/1545*e^7 - 43343/1545*e^6 + 7653/515*e^5 + 350503/1545*e^4 + 7821/515*e^3 - 245616/515*e^2 - 77734/515*e + 73017/515, 416/1545*e^8 - 154/515*e^7 - 2329/309*e^6 + 5462/1545*e^5 + 19043/309*e^4 + 707/103*e^3 - 66972/515*e^2 - 27294/515*e + 16174/515, 769/1545*e^8 - 223/309*e^7 - 20878/1545*e^6 + 3262/309*e^5 + 165728/1545*e^4 - 23017/1545*e^3 - 346666/1545*e^2 - 20691/515*e + 36704/515, -797/1545*e^8 + 351/515*e^7 + 21641/1545*e^6 - 14168/1545*e^5 - 169531/1545*e^4 + 1948/515*e^3 + 109392/515*e^2 + 23568/515*e - 29824/515, 544/1545*e^8 - 344/515*e^7 - 14206/1545*e^6 + 5904/515*e^5 + 106891/1545*e^4 - 19923/515*e^3 - 204058/1545*e^2 + 3844/515*e + 16167/515, -32/515*e^8 + 479/1545*e^7 + 666/515*e^6 - 10784/1545*e^5 - 11023/1545*e^4 + 65707/1545*e^3 + 5781/515*e^2 - 26186/515*e - 3162/515, 388/515*e^8 - 1469/1545*e^7 - 10573/515*e^6 + 6368/515*e^5 + 249104/1545*e^4 + 4604/1545*e^3 - 96706/309*e^2 - 52651/515*e + 8394/103, -728/515*e^8 + 3404/1545*e^7 + 58484/1545*e^6 - 17438/515*e^5 - 452164/1545*e^4 + 36572/515*e^3 + 58352/103*e^2 + 33856/515*e - 13800/103, 844/1545*e^8 - 358/515*e^7 - 22999/1545*e^6 + 13714/1545*e^5 + 181289/1545*e^4 + 2328/515*e^3 - 23815/103*e^2 - 37796/515*e + 5565/103, 12/103*e^8 - 29/515*e^7 - 1841/515*e^6 + 32/1545*e^5 + 50963/1545*e^4 + 5296/515*e^3 - 131617/1545*e^2 - 2772/103*e + 16203/515, -139/103*e^8 + 3248/1545*e^7 + 18604/515*e^6 - 49948/1545*e^5 - 143869/515*e^4 + 105703/1545*e^3 + 840223/1545*e^2 + 5638/103*e - 75492/515, 34/103*e^8 - 401/1545*e^7 - 14464/1545*e^6 + 797/515*e^5 + 39783/515*e^4 + 42544/1545*e^3 - 254791/1545*e^2 - 8266/103*e + 32364/515, 291/515*e^8 - 1076/1545*e^7 - 4763/309*e^6 + 4467/515*e^5 + 12517/103*e^4 + 2318/309*e^3 - 371248/1545*e^2 - 42192/515*e + 31632/515, -589/1545*e^8 + 1028/1545*e^7 + 3071/309*e^6 - 5426/515*e^5 - 7548/103*e^4 + 7781/309*e^3 + 62928/515*e^2 + 5286/515*e - 1446/515, 342/515*e^8 - 1289/1545*e^7 - 9371/515*e^6 + 16889/1545*e^5 + 224188/1545*e^4 - 202/1545*e^3 - 154066/515*e^2 - 36154/515*e + 50982/515, -5/309*e^8 + 38/103*e^7 - 44/309*e^6 - 954/103*e^5 + 1826/309*e^4 + 19781/309*e^3 - 2187/103*e^2 - 9091/103*e + 228/103, -1439/1545*e^8 + 353/309*e^7 + 13131/515*e^6 - 4444/309*e^5 - 103736/515*e^4 - 5151/515*e^3 + 201812/515*e^2 + 64556/515*e - 43644/515, -1409/1545*e^8 + 1802/1545*e^7 + 12807/515*e^6 - 7794/515*e^5 - 303521/1545*e^4 - 6316/1545*e^3 + 200411/515*e^2 + 66366/515*e - 46557/515, -13/515*e^8 + 8/515*e^7 + 934/1545*e^6 + 151/1545*e^5 - 1453/515*e^4 - 5729/1545*e^3 - 1018/103*e^2 + 1046/515*e + 2049/103, 50/103*e^8 - 241/515*e^7 - 21107/1545*e^6 + 7103/1545*e^5 + 173017/1545*e^4 + 35197/1545*e^3 - 362678/1545*e^2 - 8872/103*e + 43977/515, 1552/1545*e^8 - 2302/1545*e^7 - 41777/1545*e^6 + 11409/515*e^5 + 108424/515*e^4 - 19641/515*e^3 - 127877/309*e^2 - 30203/515*e + 12222/103, -1879/1545*e^8 + 911/515*e^7 + 10153/309*e^6 - 40163/1545*e^5 - 79544/309*e^4 + 12365/309*e^3 + 795109/1545*e^2 + 41271/515*e - 73226/515, -59/309*e^8 + 443/1545*e^7 + 7807/1545*e^6 - 6118/1545*e^5 - 59332/1545*e^4 + 2458/1545*e^3 + 110288/1545*e^2 + 2895/103*e - 5397/515, 889/515*e^8 - 3622/1545*e^7 - 72547/1545*e^6 + 50642/1545*e^5 + 572227/1545*e^4 - 14691/515*e^3 - 229664/309*e^2 - 81553/515*e + 22612/103, 649/1545*e^8 - 318/515*e^7 - 17299/1545*e^6 + 13954/1545*e^5 + 131684/1545*e^4 - 6877/515*e^3 - 16030/103*e^2 - 15571/515*e + 2832/103, -258/515*e^8 + 341/515*e^7 + 4208/309*e^6 - 14228/1545*e^5 - 10968/103*e^4 + 2462/309*e^3 + 105918/515*e^2 + 20046/515*e - 32871/515, -577/515*e^8 + 2222/1545*e^7 + 9470/309*e^6 - 29752/1545*e^5 - 75044/309*e^4 + 1129/309*e^3 + 251107/515*e^2 + 73444/515*e - 66729/515, 887/1545*e^8 - 1354/1545*e^7 - 4726/309*e^6 + 6788/515*e^5 + 11988/103*e^4 - 7408/309*e^3 - 109269/515*e^2 - 17623/515*e + 19128/515, -353/309*e^8 + 2647/1545*e^7 + 15766/515*e^6 - 13239/515*e^5 - 364513/1545*e^4 + 73762/1545*e^3 + 231209/515*e^2 + 5345/103*e - 56403/515, 368/1545*e^8 - 68/1545*e^7 - 3686/515*e^6 - 1144/515*e^5 + 97583/1545*e^4 + 62668/1545*e^3 - 15175/103*e^2 - 43992/515*e + 4752/103, 761/1545*e^8 - 809/1545*e^7 - 6921/515*e^6 + 2688/515*e^5 + 161213/1545*e^4 + 38173/1545*e^3 - 95701/515*e^2 - 54889/515*e + 16407/515, -2683/1545*e^8 + 1274/515*e^7 + 72674/1545*e^6 - 18464/515*e^5 - 570854/1545*e^4 + 74371/1545*e^3 + 380973/515*e^2 + 70322/515*e - 109776/515, -628/1545*e^8 + 743/1545*e^7 + 17113/1545*e^6 - 3041/515*e^5 - 44446/515*e^4 - 8333/1545*e^3 + 16388/103*e^2 + 25387/515*e - 1083/103, 142/515*e^8 - 587/1545*e^7 - 2332/309*e^6 + 2939/515*e^5 + 18395/309*e^4 - 1182/103*e^3 - 58272/515*e^2 + 2321/515*e + 6654/515, -379/1545*e^8 + 154/1545*e^7 + 3743/515*e^6 + 1441/1545*e^5 - 32713/515*e^4 - 48134/1545*e^3 + 46169/309*e^2 + 27741/515*e - 6448/103, 383/309*e^8 - 2359/1545*e^7 - 52261/1545*e^6 + 29684/1545*e^5 + 412321/1545*e^4 + 18376/1545*e^3 - 270453/515*e^2 - 16719/103*e + 65631/515, -51/515*e^8 + 7/1545*e^7 + 4504/1545*e^6 + 2383/1545*e^5 - 37669/1545*e^4 - 12103/515*e^3 + 67054/1545*e^2 + 24862/515*e - 4106/515, -2128/1545*e^8 + 1073/515*e^7 + 19089/515*e^6 - 49079/1545*e^5 - 445382/1545*e^4 + 98948/1545*e^3 + 290422/515*e^2 + 31707/515*e - 76374/515, -505/309*e^8 + 3598/1545*e^7 + 68317/1545*e^6 - 51823/1545*e^5 - 178234/515*e^4 + 63913/1545*e^3 + 349101/515*e^2 + 14886/103*e - 75822/515, 106/515*e^8 - 74/309*e^7 - 2837/515*e^6 + 779/309*e^5 + 64961/1545*e^4 + 13381/1545*e^3 - 39344/515*e^2 - 16967/515*e + 14298/515, 207/515*e^8 - 707/1545*e^7 - 3472/309*e^6 + 2859/515*e^5 + 28316/309*e^4 + 865/103*e^3 - 99772/515*e^2 - 35354/515*e + 35769/515, -76/1545*e^8 + 641/1545*e^7 + 347/515*e^6 - 15301/1545*e^5 + 483/515*e^4 + 33878/515*e^3 - 1997/103*e^2 - 52446/515*e + 380/103, -832/1545*e^8 + 1336/1545*e^7 + 22363/1545*e^6 - 21121/1545*e^5 - 58361/515*e^4 + 51302/1545*e^3 + 354349/1545*e^2 + 8753/515*e - 32451/515, 161/1545*e^8 - 107/1545*e^7 - 965/309*e^6 + 169/515*e^5 + 2929/103*e^4 + 827/103*e^3 - 116111/1545*e^2 - 11264/515*e + 15339/515, 976/515*e^8 - 1282/515*e^7 - 15937/309*e^6 + 17212/515*e^5 + 125425/309*e^4 - 3037/309*e^3 - 1235593/1545*e^2 - 105667/515*e + 105402/515, 601/1545*e^8 - 766/1545*e^7 - 5502/515*e^6 + 3472/515*e^5 + 130756/1545*e^4 - 5854/1545*e^3 - 17069/103*e^2 - 14244/515*e + 4926/103, -356/515*e^8 + 1711/1545*e^7 + 1899/103*e^6 - 26551/1545*e^5 - 43867/309*e^4 + 11935/309*e^3 + 141216/515*e^2 + 9827/515*e - 40662/515, 520/309*e^8 - 3866/1545*e^7 - 70129/1545*e^6 + 57776/1545*e^5 + 548924/1545*e^4 - 33552/515*e^3 - 366972/515*e^2 - 11715/103*e + 104229/515, 41/309*e^8 - 451/1545*e^7 - 4994/1545*e^6 + 2652/515*e^5 + 10923/515*e^4 - 10437/515*e^3 - 43501/1545*e^2 + 2611/103*e + 7029/515, -326/1545*e^8 - 148/1545*e^7 + 1993/309*e^6 + 8768/1545*e^5 - 17665/309*e^4 - 19855/309*e^3 + 65962/515*e^2 + 63109/515*e - 14304/515, -14/1545*e^8 - 31/1545*e^7 + 213/515*e^6 + 357/515*e^5 - 8339/1545*e^4 - 12964/1545*e^3 + 2302/103*e^2 + 14056/515*e - 2196/103, 247/515*e^8 - 662/1545*e^7 - 4126/309*e^6 + 1859/515*e^5 + 32900/309*e^4 + 2917/103*e^3 - 104552/515*e^2 - 44079/515*e + 18864/515, 796/515*e^8 - 3173/1545*e^7 - 21691/515*e^6 + 43403/1545*e^5 + 512758/1545*e^4 - 20722/1545*e^3 - 67249/103*e^2 - 94987/515*e + 14943/103, -1789/1545*e^8 + 2432/1545*e^7 + 48776/1545*e^6 - 33967/1545*e^5 - 387431/1545*e^4 + 29084/1545*e^3 + 797023/1545*e^2 + 53911/515*e - 79802/515, -602/1545*e^8 + 208/515*e^7 + 3353/309*e^6 - 6889/1545*e^5 - 27034/309*e^4 - 3464/309*e^3 + 271862/1545*e^2 + 26578/515*e - 22648/515, 572/309*e^8 - 1136/515*e^7 - 78347/1545*e^6 + 13796/515*e^5 + 619802/1545*e^4 + 52142/1545*e^3 - 405791/515*e^2 - 28285/103*e + 103497/515, -724/1545*e^8 + 398/1545*e^7 + 4193/309*e^6 + 487/1545*e^5 - 35320/309*e^4 - 16603/309*e^3 + 376669/1545*e^2 + 65636/515*e - 28971/515, 353/1545*e^8 - 110/309*e^7 - 3112/515*e^6 + 579/103*e^5 + 69586/1545*e^4 - 8083/515*e^3 - 113717/1545*e^2 + 10723/515*e + 1578/515, -1954/1545*e^8 + 2486/1545*e^7 + 17869/515*e^6 - 33241/1545*e^5 - 142464/515*e^4 + 3501/515*e^3 + 290804/515*e^2 + 57861/515*e - 92878/515, 1438/1545*e^8 - 2422/1545*e^7 - 38104/1545*e^6 + 39137/1545*e^5 + 290314/1545*e^4 - 106601/1545*e^3 - 181258/515*e^2 - 3297/515*e + 37386/515, 173/1545*e^8 - 223/515*e^7 - 3607/1545*e^6 + 4498/515*e^5 + 17902/1545*e^4 - 66608/1545*e^3 - 2342/515*e^2 + 18403/515*e - 411/515, -709/515*e^8 + 176/103*e^7 + 58244/1545*e^6 - 6772/309*e^5 - 460744/1545*e^4 - 14044/1545*e^3 + 904673/1545*e^2 + 91473/515*e - 78562/515, 1819/1545*e^8 - 661/515*e^7 - 3344/103*e^6 + 21578/1545*e^5 + 79930/309*e^4 + 13397/309*e^3 - 262818/515*e^2 - 110296/515*e + 63396/515, 1858/1545*e^8 - 422/309*e^7 - 51506/1545*e^6 + 5027/309*e^5 + 416266/1545*e^4 + 12187/515*e^3 - 289349/515*e^2 - 87137/515*e + 91158/515, -3146/1545*e^8 + 4099/1545*e^7 + 85883/1545*e^6 - 18348/515*e^5 - 226526/515*e^4 + 13652/1545*e^3 + 453611/515*e^2 + 126779/515*e - 120552/515, -2317/1545*e^8 + 1088/515*e^7 + 12571/309*e^6 - 15643/515*e^5 - 98830/309*e^4 + 11402/309*e^3 + 326224/515*e^2 + 69023/515*e - 78138/515, 3607/1545*e^8 - 932/309*e^7 - 32858/515*e^6 + 4151/103*e^5 + 781534/1545*e^4 - 11641/1545*e^3 - 523766/515*e^2 - 147238/515*e + 132717/515, -4421/1545*e^8 + 5668/1545*e^7 + 120704/1545*e^6 - 24821/515*e^5 - 318413/515*e^4 - 1759/1545*e^3 + 637629/515*e^2 + 175514/515*e - 177978/515, -132/103*e^8 + 937/515*e^7 + 53234/1545*e^6 - 13267/515*e^5 - 411449/1545*e^4 + 40811/1545*e^3 + 776536/1545*e^2 + 11746/103*e - 50204/515, 173/515*e^8 - 154/515*e^7 - 14426/1545*e^6 + 1134/515*e^5 + 114476/1545*e^4 + 42226/1545*e^3 - 213688/1545*e^2 - 51396/515*e + 8552/515, -147/103*e^8 + 2482/1545*e^7 + 60833/1545*e^6 - 28202/1545*e^5 - 487178/1545*e^4 - 65363/1545*e^3 + 329934/515*e^2 + 23863/103*e - 86088/515, -252/515*e^8 + 369/515*e^7 + 3976/309*e^6 - 15502/1545*e^5 - 9750/103*e^4 + 2479/309*e^3 + 76567/515*e^2 + 26179/515*e - 1494/515, -55/309*e^8 - 116/1545*e^7 + 2867/515*e^6 + 7081/1545*e^5 - 26332/515*e^4 - 27787/515*e^3 + 63158/515*e^2 + 12166/103*e - 16506/515, 451/515*e^8 - 2132/1545*e^7 - 35659/1545*e^6 + 10664/515*e^5 + 89128/515*e^4 - 58106/1545*e^3 - 466924/1545*e^2 - 28167/515*e + 15306/515, -739/515*e^8 + 547/309*e^7 + 60439/1545*e^6 - 2279/103*e^5 - 158453/515*e^4 - 24769/1545*e^3 + 923668/1545*e^2 + 97888/515*e - 74252/515, 798/515*e^8 - 629/309*e^7 - 65288/1545*e^6 + 8630/309*e^5 + 515758/1545*e^4 - 27217/1545*e^3 - 1035511/1545*e^2 - 78351/515*e + 108864/515, -2048/1545*e^8 + 485/309*e^7 + 56426/1545*e^6 - 1977/103*e^5 - 150337/515*e^4 - 33796/1545*e^3 + 303269/515*e^2 + 96617/515*e - 78168/515, 955/309*e^8 - 1991/515*e^7 - 130402/1545*e^6 + 25476/515*e^5 + 1030372/1545*e^4 + 31687/1545*e^3 - 679746/515*e^2 - 42120/103*e + 167892/515, -2318/1545*e^8 + 3328/1545*e^7 + 62908/1545*e^6 - 48758/1545*e^5 - 495268/1545*e^4 + 69577/1545*e^3 + 198220/309*e^2 + 63847/515*e - 17250/103, -2134/1545*e^8 + 892/515*e^7 + 19504/515*e^6 - 34921/1545*e^5 - 465892/1545*e^4 - 2707/1545*e^3 + 939757/1545*e^2 + 82536/515*e - 83228/515, 551/1545*e^8 - 193/309*e^7 - 4859/515*e^6 + 1073/103*e^5 + 112142/1545*e^4 - 50918/1545*e^3 - 74873/515*e^2 + 2996/515*e + 20421/515, -1469/1545*e^8 + 679/515*e^7 + 13352/515*e^6 - 29092/1545*e^5 - 318586/1545*e^4 + 32884/1545*e^3 + 219796/515*e^2 + 43691/515*e - 66687/515, 284/515*e^8 - 92/103*e^7 - 7533/515*e^6 + 1464/103*e^5 + 57128/515*e^4 - 19442/515*e^3 - 105111/515*e^2 + 7217/515*e + 22887/515, 518/1545*e^8 - 398/1545*e^7 - 4791/515*e^6 + 696/515*e^5 + 112328/1545*e^4 + 45523/1545*e^3 - 12868/103*e^2 - 42152/515*e + 2457/103, 1291/1545*e^8 - 395/309*e^7 - 11409/515*e^6 + 1934/103*e^5 + 259147/1545*e^4 - 43933/1545*e^3 - 155678/515*e^2 - 28749/515*e + 31791/515, 993/515*e^8 - 3917/1545*e^7 - 81461/1545*e^6 + 17714/515*e^5 + 648196/1545*e^4 - 7173/515*e^3 - 443371/515*e^2 - 111036/515*e + 131937/515, -931/1545*e^8 + 463/515*e^7 + 25138/1545*e^6 - 20809/1545*e^5 - 195743/1545*e^4 + 11709/515*e^3 + 124446/515*e^2 + 25234/515*e - 14217/515, 717/515*e^8 - 196/103*e^7 - 58177/1545*e^6 + 8197/309*e^5 + 150749/515*e^4 - 31918/1545*e^3 - 285038/515*e^2 - 73339/515*e + 49431/515, -211/1545*e^8 + 217/1545*e^7 + 1186/309*e^6 - 954/515*e^5 - 3188/103*e^4 + 275/103*e^3 + 89641/1545*e^2 - 4971/515*e - 2759/515, -1303/1545*e^8 + 777/515*e^7 + 2283/103*e^6 - 38701/1545*e^5 - 51917/309*e^4 + 23518/309*e^3 + 497308/1545*e^2 - 4008/515*e - 37362/515, 788/1545*e^8 - 992/1545*e^7 - 21679/1545*e^6 + 13157/1545*e^5 + 172859/1545*e^4 - 812/515*e^3 - 113823/515*e^2 - 28437/515*e + 21191/515, 341/1545*e^8 - 61/103*e^7 - 8597/1545*e^6 + 1217/103*e^5 + 64307/1545*e^4 - 30636/515*e^3 - 142874/1545*e^2 + 34616/515*e + 18976/515, 26/515*e^8 - 92/309*e^7 - 1456/1545*e^6 + 694/103*e^5 + 5216/1545*e^4 - 21038/515*e^3 + 3691/515*e^2 + 28293/515*e - 2362/515, 551/309*e^8 - 3589/1545*e^7 - 75151/1545*e^6 + 47824/1545*e^5 + 197787/515*e^4 - 5639/1545*e^3 - 1172329/1545*e^2 - 23166/103*e + 93041/515, 3449/1545*e^8 - 4333/1545*e^7 - 6288/103*e^6 + 56018/1545*e^5 + 49905/103*e^4 + 855/103*e^3 - 505593/515*e^2 - 137441/515*e + 150366/515, -462/515*e^8 + 1772/1545*e^7 + 7667/309*e^6 - 24472/1545*e^5 - 62174/309*e^4 + 3223/309*e^3 + 223202/515*e^2 + 48939/515*e - 70719/515, -1771/1545*e^8 + 2413/1545*e^7 + 16078/515*e^6 - 34108/1545*e^5 - 380594/1545*e^4 + 32671/1545*e^3 + 760367/1545*e^2 + 58499/515*e - 77883/515, 304/1545*e^8 - 13/103*e^7 - 3036/515*e^6 + 77/103*e^5 + 27011/515*e^4 + 21223/1545*e^3 - 195566/1545*e^2 - 20936/515*e + 21034/515, -1186/1545*e^8 + 287/309*e^7 + 32267/1545*e^6 - 1182/103*e^5 - 83474/515*e^4 - 5819/515*e^3 + 454744/1545*e^2 + 57229/515*e - 18966/515, -312/515*e^8 + 604/515*e^7 + 1618/103*e^6 - 10534/515*e^5 - 11939/103*e^4 + 7602/103*e^3 + 105882/515*e^2 - 19186/515*e - 24804/515, 1108/1545*e^8 - 634/515*e^7 - 29369/1545*e^6 + 10474/515*e^5 + 223679/1545*e^4 - 94426/1545*e^3 - 140818/515*e^2 + 7178/515*e + 42546/515, 2351/1545*e^8 - 1058/515*e^7 - 63833/1545*e^6 + 14673/515*e^5 + 500438/1545*e^4 - 11324/515*e^3 - 973568/1545*e^2 - 68654/515*e + 78112/515, -833/1545*e^8 + 1091/1545*e^7 + 1515/103*e^6 - 4972/515*e^5 - 35920/309*e^4 + 1588/309*e^3 + 119066/515*e^2 + 32417/515*e - 22332/515, 1016/1545*e^8 - 57/103*e^7 - 28922/1545*e^6 + 1306/309*e^5 + 240097/1545*e^4 + 23729/515*e^3 - 169358/515*e^2 - 80189/515*e + 41241/515, 223/1545*e^8 - 88/515*e^7 - 6257/1545*e^6 + 1163/515*e^5 + 52172/1545*e^4 - 3313/1545*e^3 - 38667/515*e^2 + 2193/515*e + 1944/515, -1363/1545*e^8 + 1639/1545*e^7 + 37837/1545*e^6 - 7113/515*e^5 - 308537/1545*e^4 - 697/1545*e^3 + 674531/1545*e^2 + 49537/515*e - 84684/515, -488/309*e^8 + 1034/515*e^7 + 66593/1545*e^6 - 40867/1545*e^5 - 174951/515*e^4 + 1822/1545*e^3 + 1025867/1545*e^2 + 18830/103*e - 68368/515, -286/515*e^8 + 279/515*e^7 + 7948/515*e^6 - 2429/515*e^5 - 64308/515*e^4 - 18048/515*e^3 + 132748/515*e^2 + 59062/515*e - 38496/515, 1678/1545*e^8 - 743/515*e^7 - 45262/1545*e^6 + 29429/1545*e^5 + 116549/515*e^4 - 216/515*e^3 - 646511/1545*e^2 - 65552/515*e + 45394/515, 529/309*e^8 - 587/309*e^7 - 14647/309*e^6 + 2218/103*e^5 + 39276/103*e^4 + 15848/309*e^3 - 80417/103*e^2 - 29094/103*e + 21795/103, 1616/1545*e^8 - 538/309*e^7 - 42697/1545*e^6 + 8503/309*e^5 + 323282/1545*e^4 - 34666/515*e^3 - 198408/515*e^2 - 13604/515*e + 40146/515, -4441/1545*e^8 + 2007/515*e^7 + 120631/1545*e^6 - 83851/1545*e^5 - 948656/1545*e^4 + 21943/515*e^3 + 125735/103*e^2 + 150274/515*e - 32694/103, 1511/1545*e^8 - 2047/1545*e^7 - 8168/309*e^6 + 28042/1545*e^5 + 21149/103*e^4 - 3557/309*e^3 - 198397/515*e^2 - 48779/515*e + 40299/515, 250/309*e^8 - 2029/1545*e^7 - 32981/1545*e^6 + 10458/515*e^5 + 82742/515*e^4 - 69539/1545*e^3 - 147058/515*e^2 - 2564/103*e + 24576/515, -2093/1545*e^8 + 2524/1545*e^7 + 57472/1545*e^6 - 31414/1545*e^5 - 152069/515*e^4 - 29837/1545*e^3 + 300272/515*e^2 + 107292/515*e - 76734/515, -1331/1545*e^8 + 392/309*e^7 + 11944/515*e^6 - 1936/103*e^5 - 278632/1545*e^4 + 16031/515*e^3 + 542369/1545*e^2 + 28224/515*e - 30276/515, -719/309*e^8 + 5128/1545*e^7 + 97217/1545*e^6 - 73483/1545*e^5 - 762247/1545*e^4 + 28871/515*e^3 + 506396/515*e^2 + 20961/103*e - 141772/515, -115/309*e^8 + 47/309*e^7 + 3314/309*e^6 + 203/103*e^5 - 27424/309*e^4 - 18013/309*e^3 + 54479/309*e^2 + 13387/103*e - 3202/103]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, -w^2 + w + 2])] = 1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]