/*
  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([-2, 1, 8, -1, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([34, 34, -w^5 + w^4 + 4*w^3 - 3*w^2 - 2*w + 2])

primes_array = [
[2, 2, -w],\
[13, 13, -w^2 + 3],\
[17, 17, -w^5 + w^4 + 5*w^3 - 3*w^2 - 5*w + 1],\
[23, 23, w^4 - w^3 - 4*w^2 + 2*w + 1],\
[31, 31, w^5 - w^4 - 6*w^3 + 5*w^2 + 7*w - 5],\
[32, 2, w^5 - 6*w^3 - w^2 + 8*w + 1],\
[43, 43, w^4 - 5*w^2 + 3],\
[47, 47, -w^4 + w^3 + 5*w^2 - 2*w - 5],\
[49, 7, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w - 1],\
[53, 53, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 5*w - 7],\
[59, 59, w^5 - w^4 - 6*w^3 + 4*w^2 + 7*w - 3],\
[71, 71, w^5 - w^4 - 5*w^3 + 4*w^2 + 4*w - 5],\
[79, 79, w^3 - w^2 - 4*w + 1],\
[83, 83, w^5 - 6*w^3 - w^2 + 7*w - 1],\
[83, 83, 2*w^5 - w^4 - 11*w^3 + 2*w^2 + 12*w + 1],\
[89, 89, -w^5 + w^4 + 4*w^3 - 2*w^2 - w - 1],\
[89, 89, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w + 3],\
[89, 89, w^5 + w^4 - 6*w^3 - 6*w^2 + 6*w + 3],\
[89, 89, 2*w^4 - w^3 - 9*w^2 + w + 5],\
[101, 101, w^5 - 5*w^3 - w^2 + 5*w - 1],\
[107, 107, w^4 - w^3 - 3*w^2 + 2*w - 1],\
[107, 107, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 1],\
[107, 107, -w^5 + 4*w^3 + 2*w^2 + 1],\
[113, 113, 2*w^5 - w^4 - 10*w^3 + 2*w^2 + 8*w - 3],\
[121, 11, 2*w^5 - w^4 - 10*w^3 + 2*w^2 + 8*w - 1],\
[125, 5, -w^3 + 4*w - 1],\
[125, 5, -2*w^5 + w^4 + 10*w^3 - 3*w^2 - 9*w + 3],\
[131, 131, w^5 + 2*w^4 - 7*w^3 - 10*w^2 + 9*w + 5],\
[137, 137, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 7],\
[137, 137, w^4 - 3*w^2 - 2*w + 1],\
[139, 139, -w^5 + w^4 + 5*w^3 - 4*w^2 - 5*w + 1],\
[139, 139, w^5 - w^4 - 5*w^3 + 4*w^2 + 3*w - 3],\
[149, 149, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 7],\
[151, 151, w^4 - 6*w^2 - w + 5],\
[163, 163, -w^5 + w^4 + 4*w^3 - 3*w^2 - w + 3],\
[167, 167, -w^5 + w^4 + 5*w^3 - 2*w^2 - 6*w + 1],\
[169, 13, -2*w^5 + 12*w^3 + w^2 - 13*w + 1],\
[179, 179, -w^5 + 6*w^3 + 2*w^2 - 9*w - 3],\
[179, 179, -w^3 + 5*w - 1],\
[191, 191, w^4 - 3*w^2 - 1],\
[193, 193, -w^5 - 3*w^4 + 6*w^3 + 17*w^2 - 5*w - 15],\
[197, 197, 2*w^5 - 11*w^3 - 2*w^2 + 10*w + 1],\
[197, 197, w^5 - 5*w^3 - 2*w^2 + 3*w - 1],\
[227, 227, w^5 - w^4 - 5*w^3 + 5*w^2 + 4*w - 5],\
[229, 229, -2*w^4 + w^3 + 10*w^2 - w - 9],\
[241, 241, 3*w^5 - 2*w^4 - 16*w^3 + 6*w^2 + 17*w - 3],\
[263, 263, -2*w^5 + 11*w^3 + w^2 - 11*w - 1],\
[269, 269, -w^5 + w^4 + 5*w^3 - 4*w^2 - 7*w + 3],\
[277, 277, 2*w^5 - w^4 - 10*w^3 + w^2 + 7*w + 1],\
[277, 277, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 11*w - 5],\
[283, 283, -w^4 + w^3 + 4*w^2 - 3],\
[289, 17, -w^5 - w^4 + 7*w^3 + 4*w^2 - 10*w - 1],\
[293, 293, -3*w^5 + 16*w^3 + 3*w^2 - 15*w - 1],\
[293, 293, -2*w^5 - w^4 + 10*w^3 + 7*w^2 - 6*w - 5],\
[307, 307, -2*w^5 + w^4 + 9*w^3 - w^2 - 4*w - 1],\
[311, 311, w^4 - w^3 - 5*w^2 + 4*w + 1],\
[311, 311, -3*w^5 + 17*w^3 + 4*w^2 - 18*w - 7],\
[311, 311, -w^5 - w^4 + 5*w^3 + 6*w^2 - 2*w - 5],\
[311, 311, 2*w^4 - w^3 - 10*w^2 + w + 5],\
[313, 313, w^5 - 5*w^3 - 3*w^2 + 3*w + 3],\
[313, 313, -w^5 - w^4 + 5*w^3 + 7*w^2 - 3*w - 3],\
[317, 317, -w^5 + 2*w^4 + 3*w^3 - 8*w^2 + w + 5],\
[337, 337, 3*w^5 + w^4 - 16*w^3 - 10*w^2 + 14*w + 11],\
[337, 337, -w^5 - 2*w^4 + 6*w^3 + 10*w^2 - 6*w - 7],\
[337, 337, 2*w^5 + w^4 - 11*w^3 - 7*w^2 + 10*w + 3],\
[337, 337, w^4 - w^3 - 6*w^2 + 4*w + 7],\
[347, 347, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 7*w + 3],\
[347, 347, -w^5 - w^4 + 5*w^3 + 7*w^2 - 2*w - 7],\
[347, 347, -w^5 - w^4 + 6*w^3 + 7*w^2 - 5*w - 7],\
[349, 349, 3*w^5 - w^4 - 17*w^3 + 3*w^2 + 19*w - 3],\
[349, 349, w^4 + w^3 - 6*w^2 - 4*w + 7],\
[359, 359, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 13*w + 1],\
[373, 373, -2*w^5 + 10*w^3 + 2*w^2 - 9*w - 1],\
[379, 379, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 9],\
[389, 389, -2*w^5 + w^4 + 11*w^3 - 2*w^2 - 13*w - 1],\
[397, 397, w^5 - 3*w^4 - 5*w^3 + 14*w^2 + 7*w - 11],\
[419, 419, w^5 - 6*w^3 + w^2 + 7*w - 1],\
[419, 419, -w^5 + w^4 + 3*w^3 - 2*w^2 + w - 1],\
[433, 433, -w^5 + w^4 + 4*w^3 - 4*w^2 - w + 5],\
[433, 433, w^5 + w^4 - 7*w^3 - 4*w^2 + 9*w - 1],\
[439, 439, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\
[443, 443, -w^3 + w^2 + 3*w - 5],\
[443, 443, w^5 - w^4 - 5*w^3 + 2*w^2 + 5*w + 3],\
[449, 449, 2*w^5 - 2*w^4 - 11*w^3 + 8*w^2 + 12*w - 5],\
[457, 457, -2*w^5 - 2*w^4 + 11*w^3 + 13*w^2 - 10*w - 11],\
[461, 461, w^5 + 2*w^4 - 6*w^3 - 10*w^2 + 5*w + 7],\
[479, 479, -2*w^5 + 10*w^3 + w^2 - 6*w + 1],\
[479, 479, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 1],\
[491, 491, w^5 - w^4 - 4*w^3 + w^2 + w + 3],\
[499, 499, -w^3 + 5*w - 3],\
[499, 499, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 6*w - 1],\
[509, 509, -2*w^5 + 2*w^4 + 10*w^3 - 9*w^2 - 9*w + 11],\
[521, 521, -w^5 + 4*w^3 + 2*w^2 - w - 3],\
[521, 521, 2*w^5 + 2*w^4 - 11*w^3 - 13*w^2 + 9*w + 13],\
[521, 521, -w^4 + 2*w^3 + 4*w^2 - 5*w - 3],\
[523, 523, -w^5 + w^4 + 6*w^3 - 5*w^2 - 8*w + 3],\
[523, 523, w^5 + w^4 - 5*w^3 - 8*w^2 + 3*w + 7],\
[541, 541, w^5 + 3*w^4 - 7*w^3 - 16*w^2 + 8*w + 13],\
[547, 547, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 7*w - 3],\
[557, 557, 3*w^5 - w^4 - 15*w^3 + w^2 + 11*w - 1],\
[557, 557, 2*w^5 - w^4 - 11*w^3 + 2*w^2 + 11*w + 1],\
[563, 563, w^5 - 3*w^4 - 4*w^3 + 13*w^2 + 3*w - 9],\
[569, 569, -w^5 - w^4 + 5*w^3 + 6*w^2 - 4*w - 1],\
[571, 571, -3*w^5 + 2*w^4 + 15*w^3 - 7*w^2 - 10*w + 3],\
[577, 577, 2*w^5 - 11*w^3 - 2*w^2 + 9*w + 3],\
[587, 587, w^4 - 6*w^2 - 2*w + 7],\
[599, 599, -2*w^5 + 2*w^4 + 10*w^3 - 7*w^2 - 10*w + 3],\
[599, 599, w^5 - 2*w^4 - 4*w^3 + 9*w^2 + 3*w - 7],\
[601, 601, 2*w^2 - 5],\
[607, 607, -w^5 - w^4 + 4*w^3 + 7*w^2 - 5],\
[613, 613, -w^5 + 5*w^3 + w^2 - 3*w + 3],\
[617, 617, -2*w^4 + 11*w^2 + 2*w - 9],\
[619, 619, -2*w^5 + 10*w^3 + w^2 - 7*w + 1],\
[619, 619, -2*w^5 + 4*w^4 + 8*w^3 - 15*w^2 - 5*w + 7],\
[643, 643, -2*w^5 - w^4 + 12*w^3 + 6*w^2 - 12*w - 3],\
[647, 647, 3*w^5 - w^4 - 18*w^3 + w^2 + 23*w + 3],\
[647, 647, 2*w^5 + w^4 - 10*w^3 - 9*w^2 + 9*w + 9],\
[653, 653, -w^4 + 7*w^2 + w - 7],\
[673, 673, -2*w^4 + w^3 + 8*w^2 - w - 5],\
[673, 673, -2*w^5 + 11*w^3 + w^2 - 9*w + 1],\
[677, 677, 4*w^5 - w^4 - 20*w^3 + w^2 + 15*w - 3],\
[683, 683, 3*w^5 - 2*w^4 - 14*w^3 + 6*w^2 + 11*w - 5],\
[683, 683, 2*w^5 - w^4 - 11*w^3 + 3*w^2 + 10*w - 3],\
[683, 683, -w^5 + 5*w^3 + w^2 - 4*w + 3],\
[691, 691, w^5 + w^4 - 6*w^3 - 6*w^2 + 8*w + 3],\
[709, 709, -2*w^5 + 2*w^4 + 11*w^3 - 7*w^2 - 13*w + 3],\
[719, 719, 2*w^5 - 2*w^4 - 10*w^3 + 8*w^2 + 9*w - 9],\
[719, 719, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 12*w + 3],\
[727, 727, w^5 - w^4 - 6*w^3 + 4*w^2 + 7*w - 1],\
[729, 3, -3],\
[739, 739, 2*w^4 - w^3 - 9*w^2 + 5],\
[739, 739, -w^5 + w^4 + 4*w^3 - 3*w^2 - 3*w - 1],\
[751, 751, -2*w^4 + w^3 + 9*w^2 - 3*w - 3],\
[761, 761, -w^5 - 2*w^4 + 7*w^3 + 12*w^2 - 9*w - 13],\
[773, 773, -w^5 + 5*w^3 + 2*w^2 - 2*w - 3],\
[787, 787, 2*w^5 - 12*w^3 - 2*w^2 + 13*w + 3],\
[787, 787, -2*w^5 + w^4 + 10*w^3 - 3*w^2 - 10*w + 1],\
[797, 797, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 7*w + 3],\
[811, 811, -2*w^5 + 12*w^3 + w^2 - 15*w - 1],\
[821, 821, 4*w^5 + w^4 - 22*w^3 - 8*w^2 + 21*w + 3],\
[821, 821, w^5 - 2*w^4 - 3*w^3 + 8*w^2 - 3*w - 3],\
[821, 821, -w^5 + 7*w^3 - 9*w - 1],\
[827, 827, w^5 - 7*w^3 - w^2 + 10*w + 1],\
[829, 829, -2*w^4 + 10*w^2 + w - 7],\
[839, 839, -w^5 + 2*w^4 + 6*w^3 - 10*w^2 - 8*w + 9],\
[853, 853, -w^5 + w^4 + 3*w^3 - 3*w^2 + 2*w + 1],\
[859, 859, -w^5 + 6*w^3 - 9*w + 1],\
[859, 859, -2*w^5 + 3*w^4 + 8*w^3 - 10*w^2 - 6*w + 5],\
[859, 859, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 2*w - 7],\
[859, 859, 2*w^5 - 2*w^4 - 10*w^3 + 6*w^2 + 10*w - 3],\
[863, 863, 3*w^5 - 4*w^4 - 14*w^3 + 14*w^2 + 13*w - 7],\
[877, 877, w^3 + w^2 - 4*w - 1],\
[881, 881, -w^5 + w^4 + 4*w^3 - 4*w^2 - 2*w + 5],\
[881, 881, -2*w^5 + 10*w^3 + 4*w^2 - 7*w - 5],\
[907, 907, -w^4 + w^3 + 4*w^2 - w + 1],\
[937, 937, w^5 - 7*w^3 + w^2 + 11*w - 3],\
[941, 941, -2*w^5 + w^4 + 11*w^3 - w^2 - 12*w - 1],\
[947, 947, -w^5 + 5*w^3 + 3*w^2 - 5*w - 7],\
[953, 953, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 10*w - 7],\
[971, 971, w^5 - w^4 - 5*w^3 + 3*w^2 + 7*w + 1],\
[983, 983, -2*w^5 + 9*w^3 + 3*w^2 - 5*w - 3],\
[997, 997, 3*w^5 - 18*w^3 - 2*w^2 + 22*w + 1]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 + 16*x^4 + 80*x^3 + 87*x^2 - 243*x - 266
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [1, e, -1, -1/5*e^4 - 12/5*e^3 - 32/5*e^2 + 31/5*e + 54/5, 29/25*e^4 + 308/25*e^3 + 658/25*e^2 - 1089/25*e - 1426/25, 4/25*e^4 + 33/25*e^3 + 33/25*e^2 - 114/25*e + 49/25, 4/25*e^4 + 58/25*e^3 + 183/25*e^2 - 189/25*e - 526/25, -13/25*e^4 - 126/25*e^3 - 226/25*e^2 + 433/25*e + 322/25, -6/25*e^4 - 62/25*e^3 - 137/25*e^2 + 171/25*e + 264/25, 26/25*e^4 + 277/25*e^3 + 577/25*e^2 - 1041/25*e - 1244/25, 6/25*e^4 + 62/25*e^3 + 137/25*e^2 - 196/25*e - 464/25, -46/25*e^4 - 492/25*e^3 - 1067/25*e^2 + 1736/25*e + 2324/25, -32/25*e^4 - 339/25*e^3 - 714/25*e^2 + 1212/25*e + 1408/25, -26/25*e^4 - 277/25*e^3 - 577/25*e^2 + 1041/25*e + 1094/25, -21/25*e^4 - 242/25*e^3 - 617/25*e^2 + 636/25*e + 1324/25, 19/25*e^4 + 213/25*e^3 + 488/25*e^2 - 779/25*e - 1036/25, 4/5*e^4 + 43/5*e^3 + 98/5*e^2 - 149/5*e - 296/5, 16/25*e^4 + 182/25*e^3 + 407/25*e^2 - 781/25*e - 1004/25, -6/25*e^4 - 62/25*e^3 - 162/25*e^2 + 71/25*e + 564/25, -51/25*e^4 - 527/25*e^3 - 1052/25*e^2 + 2016/25*e + 2294/25, 1/5*e^4 + 7/5*e^3 + 7/5*e^2 - 16/5*e - 84/5, -16/25*e^4 - 157/25*e^3 - 307/25*e^2 + 456/25*e + 704/25, -14/25*e^4 - 153/25*e^3 - 303/25*e^2 + 724/25*e + 616/25, 14/25*e^4 + 153/25*e^3 + 378/25*e^2 - 424/25*e - 1166/25, -59/25*e^4 - 618/25*e^3 - 1293/25*e^2 + 2219/25*e + 2796/25, 32/25*e^4 + 339/25*e^3 + 764/25*e^2 - 962/25*e - 1658/25, -41/25*e^4 - 432/25*e^3 - 957/25*e^2 + 1281/25*e + 1904/25, -3/5*e^4 - 31/5*e^3 - 61/5*e^2 + 113/5*e + 102/5, 17/25*e^4 + 184/25*e^3 + 434/25*e^2 - 447/25*e - 748/25, -21/25*e^4 - 242/25*e^3 - 567/25*e^2 + 911/25*e + 1124/25, 12/25*e^4 + 124/25*e^3 + 299/25*e^2 - 217/25*e - 778/25, -1/5*e^4 - 12/5*e^3 - 32/5*e^2 + 31/5*e + 74/5, -3/5*e^4 - 31/5*e^3 - 66/5*e^2 + 93/5*e + 112/5, 12/25*e^4 + 149/25*e^3 + 424/25*e^2 - 317/25*e - 978/25, 44/25*e^4 + 463/25*e^3 + 938/25*e^2 - 1829/25*e - 2086/25, -24/25*e^4 - 273/25*e^3 - 648/25*e^2 + 1009/25*e + 1606/25, 36/25*e^4 + 372/25*e^3 + 822/25*e^2 - 1001/25*e - 1784/25, 33/25*e^4 + 341/25*e^3 + 691/25*e^2 - 1203/25*e - 1502/25, 73/25*e^4 + 771/25*e^3 + 1696/25*e^2 - 2443/25*e - 3862/25, -1/25*e^4 - 2/25*e^3 + 73/25*e^2 + 241/25*e - 306/25, 39/25*e^4 + 403/25*e^3 + 853/25*e^2 - 1199/25*e - 1616/25, 14/25*e^4 + 153/25*e^3 + 403/25*e^2 - 274/25*e - 1166/25, -2/5*e^4 - 14/5*e^3 + 1/5*e^2 + 92/5*e + 18/5, -76/25*e^4 - 827/25*e^3 - 1902/25*e^2 + 2666/25*e + 4544/25, -48/25*e^4 - 521/25*e^3 - 1221/25*e^2 + 1543/25*e + 2712/25, 37/25*e^4 + 399/25*e^3 + 874/25*e^2 - 1367/25*e - 2128/25, 1/5*e^4 + 7/5*e^3 - 3/5*e^2 - 66/5*e + 16/5, -3/5*e^4 - 31/5*e^3 - 76/5*e^2 + 43/5*e + 172/5, 54/25*e^4 + 608/25*e^3 + 1458/25*e^2 - 1939/25*e - 3676/25, 19/5*e^4 + 208/5*e^3 + 488/5*e^2 - 619/5*e - 1076/5, 47/25*e^4 + 469/25*e^3 + 869/25*e^2 - 1877/25*e - 2118/25, 2/5*e^4 + 29/5*e^3 + 99/5*e^2 - 47/5*e - 228/5, -e^2 - 3*e + 16, 6/25*e^4 + 37/25*e^3 - 88/25*e^2 - 521/25*e + 36/25, -13/25*e^4 - 126/25*e^3 - 276/25*e^2 + 183/25*e + 522/25, -88/25*e^4 - 951/25*e^3 - 2201/25*e^2 + 2858/25*e + 5072/25, 66/25*e^4 + 707/25*e^3 + 1557/25*e^2 - 2256/25*e - 3004/25, 11/25*e^4 + 122/25*e^3 + 297/25*e^2 - 451/25*e - 1034/25, 81/25*e^4 + 862/25*e^3 + 1837/25*e^2 - 3121/25*e - 3914/25, -7/5*e^4 - 79/5*e^3 - 194/5*e^2 + 237/5*e + 448/5, 91/25*e^4 + 957/25*e^3 + 2007/25*e^2 - 3356/25*e - 3954/25, -e^3 - 4*e^2 + 8*e - 10, -57/25*e^4 - 614/25*e^3 - 1289/25*e^2 + 2287/25*e + 2408/25, 53/25*e^4 + 581/25*e^3 + 1281/25*e^2 - 2148/25*e - 2782/25, -91/25*e^4 - 982/25*e^3 - 2257/25*e^2 + 2906/25*e + 4754/25, -3/25*e^4 - 31/25*e^3 - 81/25*e^2 + 148/25*e + 282/25, -6/5*e^4 - 67/5*e^3 - 177/5*e^2 + 126/5*e + 384/5, -7/25*e^4 - 64/25*e^3 - 64/25*e^2 + 462/25*e + 508/25, -29/25*e^4 - 333/25*e^3 - 783/25*e^2 + 1289/25*e + 2226/25, -32/25*e^4 - 364/25*e^3 - 889/25*e^2 + 1037/25*e + 1508/25, 93/25*e^4 + 961/25*e^3 + 1986/25*e^2 - 3338/25*e - 4542/25, 8/25*e^4 + 91/25*e^3 + 166/25*e^2 - 503/25*e - 102/25, 4/25*e^4 + 33/25*e^3 + 8/25*e^2 - 239/25*e + 324/25, 54/25*e^4 + 583/25*e^3 + 1283/25*e^2 - 1989/25*e - 2326/25, -54/25*e^4 - 583/25*e^3 - 1358/25*e^2 + 1789/25*e + 3376/25, -13/25*e^4 - 151/25*e^3 - 351/25*e^2 + 558/25*e + 522/25, 12/5*e^4 + 129/5*e^3 + 284/5*e^2 - 437/5*e - 598/5, 4/5*e^4 + 48/5*e^3 + 123/5*e^2 - 139/5*e - 206/5, -94/25*e^4 - 988/25*e^3 - 2038/25*e^2 + 3729/25*e + 4136/25, 46/25*e^4 + 492/25*e^3 + 1117/25*e^2 - 1611/25*e - 3224/25, 57/25*e^4 + 614/25*e^3 + 1414/25*e^2 - 1812/25*e - 3608/25, 14/25*e^4 + 153/25*e^3 + 428/25*e^2 - 49/25*e - 966/25, 52/25*e^4 + 529/25*e^3 + 1004/25*e^2 - 2207/25*e - 2238/25, 84/25*e^4 + 918/25*e^3 + 2118/25*e^2 - 2844/25*e - 4546/25, 16/25*e^4 + 132/25*e^3 + 107/25*e^2 - 781/25*e - 504/25, -38/25*e^4 - 401/25*e^3 - 851/25*e^2 + 1283/25*e + 1572/25, 24/25*e^4 + 298/25*e^3 + 748/25*e^2 - 1234/25*e - 1756/25, -127/25*e^4 - 1354/25*e^3 - 2929/25*e^2 + 4707/25*e + 6338/25, 37/25*e^4 + 374/25*e^3 + 699/25*e^2 - 1617/25*e - 1978/25, -2/25*e^4 - 4/25*e^3 + 71/25*e^2 + 57/25*e - 562/25, 99/25*e^4 + 1073/25*e^3 + 2448/25*e^2 - 3309/25*e - 5406/25, -3*e^4 - 31*e^3 - 64*e^2 + 110*e + 142, -51/25*e^4 - 552/25*e^3 - 1277/25*e^2 + 1741/25*e + 3244/25, 7/25*e^4 + 39/25*e^3 - 11/25*e^2 - 12/25*e + 42/25, 58/25*e^4 + 616/25*e^3 + 1366/25*e^2 - 1903/25*e - 3152/25, -56/25*e^4 - 587/25*e^3 - 1237/25*e^2 + 1996/25*e + 2064/25, -27/25*e^4 - 304/25*e^3 - 829/25*e^2 + 607/25*e + 2138/25, -62/25*e^4 - 649/25*e^3 - 1349/25*e^2 + 2367/25*e + 2628/25, 31/25*e^4 + 362/25*e^3 + 912/25*e^2 - 1096/25*e - 2164/25, 27/25*e^4 + 279/25*e^3 + 554/25*e^2 - 857/25*e - 488/25, 6/25*e^4 + 62/25*e^3 + 87/25*e^2 - 646/25*e - 514/25, -23/5*e^4 - 246/5*e^3 - 531/5*e^2 + 883/5*e + 1142/5, 21/25*e^4 + 267/25*e^3 + 842/25*e^2 - 461/25*e - 2024/25, -e^4 - 10*e^3 - 18*e^2 + 45*e + 54, 74/25*e^4 + 773/25*e^3 + 1573/25*e^2 - 2809/25*e - 3056/25, -23/25*e^4 - 221/25*e^3 - 321/25*e^2 + 1093/25*e + 162/25, 38/25*e^4 + 451/25*e^3 + 1176/25*e^2 - 1383/25*e - 2822/25, 39/25*e^4 + 403/25*e^3 + 753/25*e^2 - 1774/25*e - 1116/25, -2*e^4 - 21*e^3 - 43*e^2 + 79*e + 84, -14/5*e^4 - 143/5*e^3 - 288/5*e^2 + 459/5*e + 446/5, 14/5*e^4 + 148/5*e^3 + 338/5*e^2 - 404/5*e - 746/5, -4/5*e^4 - 53/5*e^3 - 168/5*e^2 + 64/5*e + 346/5, -113/25*e^4 - 1201/25*e^3 - 2551/25*e^2 + 4383/25*e + 5622/25, 86/25*e^4 + 947/25*e^3 + 2272/25*e^2 - 2776/25*e - 5084/25, -137/25*e^4 - 1449/25*e^3 - 3049/25*e^2 + 5242/25*e + 6428/25, -37/25*e^4 - 399/25*e^3 - 899/25*e^2 + 1217/25*e + 1678/25, 58/25*e^4 + 591/25*e^3 + 1191/25*e^2 - 2128/25*e - 3352/25, 14/5*e^4 + 158/5*e^3 + 368/5*e^2 - 539/5*e - 716/5, 3/5*e^4 + 36/5*e^3 + 96/5*e^2 - 108/5*e - 222/5, -104/25*e^4 - 1133/25*e^3 - 2558/25*e^2 + 3639/25*e + 4876/25, 14/5*e^4 + 148/5*e^3 + 323/5*e^2 - 499/5*e - 836/5, 119/25*e^4 + 1288/25*e^3 + 2788/25*e^2 - 4729/25*e - 5886/25, 87/25*e^4 + 924/25*e^3 + 1949/25*e^2 - 3217/25*e - 3578/25, -64/25*e^4 - 678/25*e^3 - 1528/25*e^2 + 2099/25*e + 3666/25, -54/25*e^4 - 608/25*e^3 - 1433/25*e^2 + 1939/25*e + 2526/25, -22/25*e^4 - 269/25*e^3 - 769/25*e^2 + 702/25*e + 1918/25, -53/25*e^4 - 556/25*e^3 - 1206/25*e^2 + 1773/25*e + 2882/25, 3*e^2 + 9*e - 6, -14/5*e^4 - 143/5*e^3 - 278/5*e^2 + 529/5*e + 506/5, -8/25*e^4 - 91/25*e^3 - 241/25*e^2 + 353/25*e + 1152/25, -99/25*e^4 - 1023/25*e^3 - 2098/25*e^2 + 3459/25*e + 3506/25, -34/5*e^4 - 363/5*e^3 - 803/5*e^2 + 1219/5*e + 1926/5, 2/25*e^4 + 4/25*e^3 + 4/25*e^2 + 218/25*e + 212/25, -47/25*e^4 - 469/25*e^3 - 994/25*e^2 + 1152/25*e + 2018/25, -41/25*e^4 - 407/25*e^3 - 657/25*e^2 + 1981/25*e + 1104/25, 89/25*e^4 + 928/25*e^3 + 2003/25*e^2 - 2924/25*e - 4116/25, e^4 + 8*e^3 + 5*e^2 - 47*e - 10, 24/25*e^4 + 248/25*e^3 + 523/25*e^2 - 559/25*e - 356/25, 24/25*e^4 + 223/25*e^3 + 423/25*e^2 - 359/25*e - 206/25, -6/5*e^4 - 67/5*e^3 - 162/5*e^2 + 201/5*e + 244/5, 31/5*e^4 + 327/5*e^3 + 702/5*e^2 - 1091/5*e - 1464/5, -6/25*e^4 - 62/25*e^3 - 162/25*e^2 - 4/25*e + 314/25, 9/5*e^4 + 98/5*e^3 + 213/5*e^2 - 339/5*e - 366/5, -32/25*e^4 - 314/25*e^3 - 489/25*e^2 + 1537/25*e + 908/25, -32/25*e^4 - 389/25*e^3 - 1064/25*e^2 + 862/25*e + 2108/25, -158/25*e^4 - 1716/25*e^3 - 3941/25*e^2 + 5328/25*e + 8602/25, 21/5*e^4 + 227/5*e^3 + 492/5*e^2 - 831/5*e - 994/5, -91/25*e^4 - 1007/25*e^3 - 2382/25*e^2 + 3031/25*e + 5154/25, 142/25*e^4 + 1509/25*e^3 + 3184/25*e^2 - 5597/25*e - 6898/25, 34/25*e^4 + 343/25*e^3 + 593/25*e^2 - 1644/25*e - 1496/25, -8*e^4 - 86*e^3 - 195*e^2 + 269*e + 438, -59/25*e^4 - 668/25*e^3 - 1718/25*e^2 + 1619/25*e + 3896/25, 3/25*e^4 + 31/25*e^3 + 31/25*e^2 - 223/25*e - 332/25, -59/25*e^4 - 618/25*e^3 - 1243/25*e^2 + 2219/25*e + 1796/25, -59/25*e^4 - 643/25*e^3 - 1368/25*e^2 + 2444/25*e + 2596/25, -12/5*e^4 - 134/5*e^3 - 319/5*e^2 + 427/5*e + 648/5, 22/25*e^4 + 169/25*e^3 + 69/25*e^2 - 902/25*e + 282/25, -91/25*e^4 - 907/25*e^3 - 1732/25*e^2 + 3131/25*e + 3254/25, 79/25*e^4 + 808/25*e^3 + 1533/25*e^2 - 3064/25*e - 2426/25, 68/25*e^4 + 761/25*e^3 + 1861/25*e^2 - 2113/25*e - 4042/25, 59/25*e^4 + 593/25*e^3 + 1218/25*e^2 - 1869/25*e - 3446/25, -18/25*e^4 - 161/25*e^3 - 186/25*e^2 + 1113/25*e + 692/25]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([2, 2, -w])] = -1
AL_eigenvalues[ZF.ideal([17, 17, -w^5 + w^4 + 5*w^3 - 3*w^2 - 5*w + 1])] = 1

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