/*
  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([7, 2, -7, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([17, 17, -w^3 + 3*w^2 + 4*w - 3])

primes_array = [
[4, 2, w^3 - 3*w^2 - 3*w + 4],\
[7, 7, w],\
[7, 7, w^3 - 3*w^2 - 4*w + 5],\
[9, 3, w^3 - 4*w^2 - w + 9],\
[17, 17, 2*w^3 - 6*w^2 - 7*w + 8],\
[17, 17, -w^3 + 3*w^2 + 4*w - 3],\
[17, 17, -w + 2],\
[23, 23, 2*w^3 - 7*w^2 - 4*w + 12],\
[23, 23, -w^2 + 2*w + 3],\
[31, 31, -2*w^3 + 7*w^2 + 5*w - 12],\
[31, 31, -w^3 + 4*w^2 + 2*w - 8],\
[41, 41, 3*w^3 - 10*w^2 - 7*w + 16],\
[41, 41, 2*w^3 - 7*w^2 - 5*w + 10],\
[49, 7, 2*w^3 - 6*w^2 - 6*w + 9],\
[71, 71, w^2 - 2*w - 2],\
[71, 71, 2*w^3 - 7*w^2 - 4*w + 13],\
[73, 73, 3*w^3 - 11*w^2 - 5*w + 19],\
[73, 73, -4*w^3 + 13*w^2 + 10*w - 17],\
[79, 79, 3*w^3 - 9*w^2 - 10*w + 13],\
[79, 79, -2*w^3 + 6*w^2 + 5*w - 8],\
[97, 97, 2*w^3 - 6*w^2 - 8*w + 9],\
[97, 97, 2*w - 1],\
[113, 113, 2*w^3 - 6*w^2 - 7*w + 6],\
[113, 113, -w^3 + 3*w^2 + 2*w - 1],\
[137, 137, w^3 - 2*w^2 - 5*w + 2],\
[137, 137, 2*w^3 - 7*w^2 - 3*w + 12],\
[137, 137, -3*w^3 + 10*w^2 + 7*w - 17],\
[137, 137, -w^3 + 2*w^2 + 6*w - 2],\
[167, 167, -2*w^3 + 7*w^2 + 6*w - 10],\
[167, 167, 3*w^3 - 9*w^2 - 10*w + 10],\
[169, 13, -2*w^3 + 7*w^2 + 2*w - 9],\
[169, 13, -2*w^3 + 5*w^2 + 10*w - 4],\
[193, 193, -2*w^3 + 8*w^2 + 3*w - 13],\
[193, 193, -3*w^3 + 11*w^2 + 6*w - 22],\
[199, 199, 5*w^3 - 16*w^2 - 14*w + 26],\
[199, 199, w^3 - 2*w^2 - 7*w + 3],\
[223, 223, -3*w^3 + 8*w^2 + 12*w - 8],\
[223, 223, 3*w^3 - 11*w^2 - 6*w + 17],\
[223, 223, 2*w^3 - 8*w^2 - 3*w + 18],\
[223, 223, -4*w^3 + 13*w^2 + 9*w - 18],\
[233, 233, -3*w^3 + 10*w^2 + 6*w - 16],\
[233, 233, -2*w^3 + 5*w^2 + 9*w - 6],\
[241, 241, -3*w^3 + 9*w^2 + 8*w - 10],\
[241, 241, 4*w^3 - 12*w^2 - 13*w + 15],\
[257, 257, 2*w^3 - 8*w^2 - w + 16],\
[257, 257, 4*w^3 - 13*w^2 - 11*w + 18],\
[257, 257, -w^3 + 5*w^2 - 2*w - 9],\
[257, 257, -w^3 + 2*w^2 + 4*w + 2],\
[263, 263, 4*w^3 - 14*w^2 - 9*w + 27],\
[263, 263, 5*w^3 - 15*w^2 - 17*w + 25],\
[263, 263, -2*w^3 + 7*w^2 + 6*w - 16],\
[263, 263, -2*w^3 + 7*w^2 + 6*w - 9],\
[271, 271, -w - 4],\
[271, 271, -w^3 + 3*w^2 + 4*w - 9],\
[271, 271, 5*w^3 - 16*w^2 - 14*w + 24],\
[271, 271, -4*w^3 + 14*w^2 + 9*w - 24],\
[281, 281, -2*w^3 + 6*w^2 + 5*w - 4],\
[281, 281, -3*w^3 + 9*w^2 + 10*w - 9],\
[281, 281, 3*w^3 - 10*w^2 - 8*w + 12],\
[281, 281, w^2 - w - 8],\
[311, 311, w^2 - 5],\
[311, 311, -4*w^3 + 13*w^2 + 12*w - 20],\
[313, 313, 6*w^3 - 19*w^2 - 18*w + 31],\
[313, 313, -2*w^3 + 5*w^2 + 6*w - 6],\
[337, 337, 3*w^3 - 11*w^2 - 3*w + 15],\
[337, 337, w^3 - w^2 - 9*w - 5],\
[353, 353, -w^3 + 2*w^2 + 5*w - 4],\
[353, 353, w^3 - w^2 - 8*w - 3],\
[353, 353, 3*w^3 - 10*w^2 - 7*w + 19],\
[353, 353, -4*w^3 + 14*w^2 + 7*w - 22],\
[361, 19, -3*w^3 + 11*w^2 + 6*w - 18],\
[361, 19, 2*w^3 - 8*w^2 - 3*w + 17],\
[367, 367, -4*w^3 + 12*w^2 + 13*w - 18],\
[367, 367, 3*w^3 - 9*w^2 - 8*w + 13],\
[383, 383, 5*w^3 - 17*w^2 - 12*w + 30],\
[383, 383, 2*w^2 - 3*w - 5],\
[383, 383, 3*w^3 - 9*w^2 - 11*w + 11],\
[383, 383, -w^3 + 3*w^2 + w - 1],\
[401, 401, 3*w^3 - 11*w^2 - 8*w + 23],\
[401, 401, 4*w^3 - 14*w^2 - 11*w + 22],\
[431, 431, 2*w^3 - 5*w^2 - 10*w + 8],\
[431, 431, 6*w^3 - 20*w^2 - 15*w + 29],\
[433, 433, -4*w^3 + 12*w^2 + 13*w - 17],\
[433, 433, -3*w^3 + 9*w^2 + 8*w - 12],\
[433, 433, 3*w^3 - 11*w^2 - 6*w + 20],\
[433, 433, -2*w^3 + 8*w^2 + 3*w - 15],\
[439, 439, -3*w^3 + 11*w^2 + 6*w - 19],\
[439, 439, -2*w^3 + 8*w^2 + 3*w - 16],\
[449, 449, w^3 - 4*w^2 + w + 11],\
[449, 449, -w^3 + 2*w^2 + 7*w - 6],\
[457, 457, w^2 - 4*w - 3],\
[457, 457, 4*w^3 - 15*w^2 - 6*w + 27],\
[457, 457, w^2 - 4*w - 2],\
[457, 457, -2*w^3 + 6*w^2 + 8*w - 15],\
[479, 479, -4*w^3 + 14*w^2 + 9*w - 29],\
[479, 479, -w^3 + 5*w^2 - 6],\
[487, 487, -w^3 + 6*w^2 - 3*w - 16],\
[487, 487, -5*w^3 + 18*w^2 + 9*w - 29],\
[503, 503, -2*w^3 + 7*w^2 + 8*w - 15],\
[503, 503, 4*w^3 - 13*w^2 - 14*w + 20],\
[521, 521, 3*w^3 - 10*w^2 - 9*w + 10],\
[521, 521, -2*w^3 + 7*w^2 + 3*w - 16],\
[529, 23, w^3 - 3*w^2 - 3*w - 1],\
[599, 599, -4*w^3 + 12*w^2 + 14*w - 15],\
[599, 599, 2*w^3 - 6*w^2 - 4*w + 5],\
[599, 599, 4*w^3 - 13*w^2 - 12*w + 19],\
[599, 599, w^2 - 6],\
[601, 601, -4*w^3 + 12*w^2 + 11*w - 19],\
[601, 601, 5*w^3 - 15*w^2 - 16*w + 24],\
[607, 607, -w^3 + 4*w^2 + w - 13],\
[607, 607, -w^3 + 4*w^2 + w - 2],\
[617, 617, -4*w^3 + 13*w^2 + 11*w - 16],\
[617, 617, 4*w^3 - 13*w^2 - 13*w + 20],\
[625, 5, -5],\
[631, 631, -3*w^3 + 8*w^2 + 11*w - 9],\
[631, 631, 5*w^3 - 16*w^2 - 13*w + 24],\
[631, 631, w^3 - 3*w^2 - 4*w - 1],\
[631, 631, w - 6],\
[641, 641, -3*w^3 + 12*w^2 + w - 17],\
[641, 641, w^3 - 6*w^2 + 5*w + 18],\
[673, 673, 4*w^3 - 15*w^2 - 6*w + 26],\
[673, 673, -2*w^3 + 9*w^2 - 19],\
[719, 719, 2*w^2 - 4*w - 5],\
[719, 719, 4*w^3 - 14*w^2 - 8*w + 25],\
[727, 727, 3*w^3 - 8*w^2 - 11*w + 8],\
[727, 727, 6*w^3 - 18*w^2 - 19*w + 20],\
[727, 727, -5*w^3 + 14*w^2 + 19*w - 17],\
[727, 727, -5*w^3 + 16*w^2 + 13*w - 23],\
[743, 743, 4*w^3 - 14*w^2 - 7*w + 23],\
[743, 743, w^3 - w^2 - 8*w - 2],\
[751, 751, 3*w^3 - 12*w^2 - 3*w + 23],\
[751, 751, 3*w^3 - 12*w^2 - 3*w + 22],\
[761, 761, 3*w^3 - 10*w^2 - 6*w + 22],\
[761, 761, 3*w^3 - 10*w^2 - 6*w + 18],\
[761, 761, -5*w^3 + 16*w^2 + 17*w - 25],\
[761, 761, -2*w^3 + 5*w^2 + 9*w - 8],\
[809, 809, -3*w^3 + 8*w^2 + 13*w - 3],\
[809, 809, -2*w^3 + 6*w^2 + 3*w - 12],\
[823, 823, -w^3 + 4*w^2 + 2*w - 2],\
[823, 823, 2*w^3 - 7*w^2 - 5*w + 18],\
[839, 839, 4*w^3 - 13*w^2 - 14*w + 27],\
[839, 839, -7*w^3 + 23*w^2 + 19*w - 41],\
[857, 857, -3*w^3 + 10*w^2 + 9*w - 12],\
[857, 857, -w^3 + 4*w^2 + 3*w - 13],\
[863, 863, 3*w^3 - 11*w^2 - 2*w + 20],\
[863, 863, -2*w^3 + 4*w^2 + 13*w - 5],\
[863, 863, 6*w^3 - 19*w^2 - 18*w + 27],\
[863, 863, -2*w^3 + 5*w^2 + 6*w - 2],\
[881, 881, -3*w^3 + 10*w^2 + 5*w - 17],\
[881, 881, -3*w^3 + 8*w^2 + 13*w - 12],\
[887, 887, -3*w^3 + 9*w^2 + 11*w - 9],\
[887, 887, w^3 - 3*w^2 - w - 1],\
[911, 911, 4*w^3 - 14*w^2 - 10*w + 17],\
[911, 911, 5*w^3 - 17*w^2 - 12*w + 22],\
[919, 919, -4*w^3 + 15*w^2 + 7*w - 30],\
[919, 919, -2*w^2 + 7*w + 2],\
[919, 919, w^3 - 5*w^2 + 4*w + 13],\
[919, 919, 3*w^3 - 12*w^2 - 4*w + 20],\
[929, 929, -4*w^3 + 13*w^2 + 9*w - 22],\
[929, 929, 3*w^3 - 8*w^2 - 12*w + 12],\
[961, 31, 4*w^3 - 12*w^2 - 12*w + 17],\
[967, 967, -2*w^3 + 6*w^2 + 7*w - 2],\
[967, 967, -3*w^3 + 8*w^2 + 15*w - 6],\
[967, 967, w^3 - 2*w^2 - 5*w - 6],\
[967, 967, 7*w^3 - 22*w^2 - 21*w + 36],\
[983, 983, 5*w^3 - 17*w^2 - 13*w + 25],\
[983, 983, w^3 - 5*w^2 - w + 15],\
[991, 991, -6*w^3 + 21*w^2 + 13*w - 34],\
[991, 991, 7*w^3 - 22*w^2 - 21*w + 33],\
[1009, 1009, w^2 - 2*w + 3],\
[1009, 1009, -2*w^3 + 7*w^2 + 4*w - 18],\
[1031, 1031, -4*w^3 + 15*w^2 + 4*w - 26],\
[1031, 1031, 3*w^2 - 8*w - 9],\
[1033, 1033, 2*w^3 - 4*w^2 - 13*w + 3],\
[1033, 1033, -5*w^3 + 15*w^2 + 19*w - 23],\
[1033, 1033, w^3 - w^2 - 8*w - 10],\
[1033, 1033, 4*w^3 - 14*w^2 - 7*w + 15],\
[1049, 1049, -7*w^3 + 24*w^2 + 16*w - 34],\
[1049, 1049, -5*w^3 + 16*w^2 + 18*w - 24],\
[1063, 1063, w^3 - 4*w^2 + 2*w + 8],\
[1063, 1063, w^3 - 2*w^2 - 4*w - 8],\
[1063, 1063, 7*w^3 - 24*w^2 - 17*w + 39],\
[1063, 1063, w^3 - 2*w^2 - 7*w - 6],\
[1103, 1103, w^3 - 5*w^2 + 3*w + 17],\
[1103, 1103, -w^3 + 5*w^2 - 3*w - 3],\
[1103, 1103, -w^3 + 5*w^2 - 2*w - 6],\
[1103, 1103, -2*w^3 + 8*w^2 + w - 19],\
[1129, 1129, -6*w^3 + 18*w^2 + 20*w - 27],\
[1129, 1129, -4*w^3 + 12*w^2 + 10*w - 17],\
[1151, 1151, w^3 - w^2 - 7*w - 1],\
[1151, 1151, 5*w^3 - 17*w^2 - 11*w + 29],\
[1153, 1153, -2*w^3 + 8*w^2 + 3*w - 23],\
[1153, 1153, -6*w^3 + 18*w^2 + 20*w - 25],\
[1193, 1193, -2*w^3 + 5*w^2 + 9*w - 10],\
[1193, 1193, 3*w^3 - 10*w^2 - 6*w + 20],\
[1201, 1201, 6*w^3 - 19*w^2 - 16*w + 24],\
[1201, 1201, 4*w^3 - 11*w^2 - 14*w + 9],\
[1217, 1217, 7*w^3 - 22*w^2 - 21*w + 30],\
[1217, 1217, 7*w^3 - 23*w^2 - 18*w + 39],\
[1223, 1223, -2*w^3 + 9*w^2 - 15],\
[1223, 1223, -3*w^3 + 9*w^2 + 13*w - 9],\
[1223, 1223, -5*w^3 + 17*w^2 + 12*w - 34],\
[1223, 1223, 4*w^3 - 15*w^2 - 6*w + 30],\
[1231, 1231, -3*w^3 + 7*w^2 + 12*w - 3],\
[1231, 1231, -8*w^3 + 26*w^2 + 21*w - 38],\
[1289, 1289, -4*w^3 + 14*w^2 + 7*w - 24],\
[1289, 1289, -w^3 + w^2 + 8*w + 1],\
[1297, 1297, -4*w^3 + 12*w^2 + 11*w - 15],\
[1297, 1297, -5*w^3 + 15*w^2 + 16*w - 20],\
[1303, 1303, -3*w^3 + 10*w^2 + 7*w - 23],\
[1303, 1303, -w^3 + 2*w^2 + 5*w - 8],\
[1319, 1319, -8*w^3 + 28*w^2 + 15*w - 43],\
[1319, 1319, w^3 + w^2 - 12*w - 12],\
[1321, 1321, w^2 - 2*w - 10],\
[1321, 1321, 2*w^3 - 7*w^2 - 4*w + 5],\
[1367, 1367, -5*w^3 + 17*w^2 + 14*w - 26],\
[1367, 1367, 2*w^3 - 8*w^2 - 5*w + 19],\
[1399, 1399, -2*w^3 + 7*w^2 + 3*w - 4],\
[1399, 1399, w^3 - 2*w^2 - 6*w - 6],\
[1409, 1409, w^3 - 2*w^2 - 3*w - 3],\
[1409, 1409, 3*w^3 - 10*w^2 - 5*w + 18],\
[1409, 1409, -5*w^3 + 16*w^2 + 15*w - 22],\
[1409, 1409, -3*w^3 + 8*w^2 + 13*w - 13],\
[1423, 1423, 7*w^3 - 24*w^2 - 18*w + 44],\
[1423, 1423, -8*w^3 + 26*w^2 + 21*w - 40],\
[1433, 1433, -7*w^3 + 24*w^2 + 17*w - 45],\
[1433, 1433, -3*w^3 + 12*w^2 + 3*w - 29],\
[1439, 1439, -2*w^3 + 6*w^2 + 4*w - 3],\
[1439, 1439, -4*w^3 + 12*w^2 + 14*w - 13],\
[1471, 1471, -w - 6],\
[1471, 1471, -w^3 + 3*w^2 + 4*w - 11],\
[1471, 1471, w^3 - 2*w^2 - 8*w + 4],\
[1471, 1471, w^2 - 5*w - 4],\
[1489, 1489, -2*w^3 + 9*w^2 + 2*w - 17],\
[1489, 1489, -6*w^3 + 21*w^2 + 14*w - 38],\
[1543, 1543, -7*w^3 + 24*w^2 + 19*w - 45],\
[1543, 1543, 2*w^3 - 3*w^2 - 15*w - 4],\
[1543, 1543, -5*w^3 + 18*w^2 + 6*w - 26],\
[1543, 1543, -3*w^3 + 12*w^2 + 7*w - 20],\
[1553, 1553, -4*w^3 + 14*w^2 + 11*w - 20],\
[1553, 1553, -3*w^3 + 11*w^2 + 8*w - 25],\
[1559, 1559, 2*w^2 - 4*w - 3],\
[1559, 1559, 4*w^3 - 14*w^2 - 8*w + 27],\
[1567, 1567, -4*w^3 + 15*w^2 + 3*w - 20],\
[1567, 1567, w^3 - 12*w - 10],\
[1601, 1601, -3*w^3 + 10*w^2 + 10*w - 12],\
[1601, 1601, 2*w^3 - 7*w^2 - 7*w + 18],\
[1607, 1607, -7*w^3 + 23*w^2 + 20*w - 36],\
[1607, 1607, -6*w^3 + 19*w^2 + 18*w - 26],\
[1607, 1607, 2*w^2 - w - 9],\
[1607, 1607, -2*w^3 + 5*w^2 + 6*w - 1],\
[1609, 1609, -4*w^3 + 15*w^2 + 8*w - 24],\
[1609, 1609, 4*w^3 - 15*w^2 - 8*w + 31],\
[1663, 1663, -6*w^3 + 19*w^2 + 13*w - 26],\
[1663, 1663, -7*w^3 + 20*w^2 + 26*w - 26],\
[1681, 41, -5*w^3 + 15*w^2 + 15*w - 17],\
[1697, 1697, -w^3 + 9*w + 6],\
[1697, 1697, -7*w^3 + 24*w^2 + 15*w - 39],\
[1721, 1721, -5*w^3 + 18*w^2 + 13*w - 38],\
[1721, 1721, -w^3 + 6*w^2 - 5*w - 20],\
[1721, 1721, -w^3 + w^2 + 6*w + 11],\
[1721, 1721, 6*w^3 - 20*w^2 - 15*w + 24],\
[1753, 1753, -3*w^3 + 9*w^2 + 13*w - 17],\
[1753, 1753, w^3 - 3*w^2 - 7*w + 3],\
[1753, 1753, -6*w^3 + 22*w^2 + 12*w - 45],\
[1753, 1753, -6*w^3 + 21*w^2 + 16*w - 40],\
[1759, 1759, -2*w^3 + 6*w^2 + w - 8],\
[1759, 1759, 7*w^3 - 21*w^2 - 26*w + 33],\
[1759, 1759, -3*w^3 + 10*w^2 + 10*w - 26],\
[1759, 1759, -5*w^3 + 17*w^2 + 12*w - 37],\
[1783, 1783, -5*w^3 + 18*w^2 + 11*w - 29],\
[1783, 1783, 4*w^3 - 15*w^2 - 7*w + 26],\
[1783, 1783, 3*w^3 - 12*w^2 - 5*w + 26],\
[1783, 1783, -3*w^3 + 12*w^2 + 4*w - 24],\
[1801, 1801, 8*w^3 - 24*w^2 - 27*w + 33],\
[1801, 1801, 4*w^3 - 12*w^2 - 16*w + 19],\
[1801, 1801, 4*w - 1],\
[1801, 1801, 7*w^3 - 21*w^2 - 23*w + 33],\
[1831, 1831, w^3 - 2*w^2 - 8*w + 2],\
[1831, 1831, w^2 - 5*w - 2],\
[1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25],\
[1847, 1847, w^3 - w^2 - 6*w - 10],\
[1849, 43, -6*w^3 + 21*w^2 + 14*w - 37],\
[1849, 43, -2*w^3 + 9*w^2 + 2*w - 18],\
[1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22],\
[1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15],\
[1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17],\
[1871, 1871, w^2 - 10],\
[1873, 1873, -w^3 + 5*w^2 - 20],\
[1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15],\
[1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4],\
[1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19],\
[1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30],\
[1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45],\
[1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43],\
[1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19],\
[1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36],\
[1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19],\
[1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30],\
[1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 + 4*x^4 - 9*x^2 - 2*x + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e^3 - 3*e^2 + 2*e + 3, -e^4 - 3*e^3 + 3*e^2 + 7*e - 2, e^2 + 2*e - 3, -e^2 - 4*e, 1, 2*e^4 + 7*e^3 - 3*e^2 - 16*e - 2, e^4 + 3*e^3 - 2*e^2 - 5*e - 1, e^3 + 2*e^2 - 2*e - 3, 2*e^3 + 5*e^2 - 3*e - 4, -2*e^4 - 7*e^3 + e^2 + 10*e + 3, -3*e^4 - 14*e^3 - 5*e^2 + 29*e + 5, 3*e^4 + 10*e^3 - 3*e^2 - 19*e - 6, e^4 + 3*e^3 - 4*e^2 - 9*e + 5, -e^4 - 3*e^3 + 4*e^2 + 4*e - 11, e^3 + e^2 - 7*e - 1, 3*e^4 + 11*e^3 - e^2 - 21*e - 4, -e^2 - 5*e + 1, 2*e^4 + 10*e^3 + 5*e^2 - 22*e - 8, 3*e^4 + 11*e^3 - e^2 - 18*e - 4, e^4 + 4*e^3 - 4*e^2 - 15*e + 12, -4*e^4 - 16*e^3 + 3*e^2 + 42*e + 2, e^4 + 6*e^3 + 6*e^2 - 13*e - 11, -3*e^4 - 11*e^3 + 3*e^2 + 31*e + 5, 2*e^4 + 7*e^3 - e^2 - 10*e + 8, -3*e^4 - 11*e^3 + e^2 + 25*e + 4, e^4 + 3*e^3 - 4*e^2 - 10*e - 7, -2*e^4 - 3*e^3 + 10*e^2 - 2*e - 13, e^3 - 11*e - 4, -2*e^4 - 6*e^3 + 2*e^2 + 8*e + 11, -4*e^2 - 11*e - 2, -e^4 - 2*e^3 + 6*e^2 + 3*e + 1, -3*e^4 - 13*e^3 - 2*e^2 + 31*e + 13, 3*e^4 + 10*e^3 - 5*e^2 - 27*e - 13, -e^4 - 9*e^3 - 13*e^2 + 14*e + 15, 3*e^4 + 9*e^3 - e^2 - 8*e - 5, -e^4 + 9*e^2 - 3*e - 9, 2*e^4 + 6*e^3 - 2*e^2 - 7*e - 8, 3*e^4 + 13*e^3 + 5*e^2 - 22*e - 9, 2*e^4 + 7*e^3 - e^2 - 19*e - 5, -e^4 - 4*e^3 - 7*e^2 - e + 12, -2*e^4 - 9*e^3 + e^2 + 33*e + 1, 5*e^4 + 20*e^3 + 3*e^2 - 26*e - 9, -7*e^4 - 27*e^3 + 4*e^2 + 62*e + 13, e^4 + 8*e^3 + 13*e^2 - 20*e - 17, -8*e^4 - 27*e^3 + 16*e^2 + 58*e - 1, -8*e^4 - 31*e^3 + 3*e^2 + 72*e + 7, -5*e^4 - 20*e^3 - 7*e^2 + 33*e + 16, -6*e^4 - 24*e^3 - 3*e^2 + 42*e + 3, 7*e^4 + 25*e^3 - 8*e^2 - 57*e - 4, -4*e^3 - 12*e^2 + 11*e + 13, 3*e^4 + 8*e^3 - 9*e^2 - 20*e - 3, e^4 + 3*e^3 - 2*e^2 - 10*e - 7, -5*e^4 - 24*e^3 - 7*e^2 + 53*e - 2, -3*e^4 - 12*e^3 + 2*e^2 + 34*e + 7, 7*e^4 + 23*e^3 - 8*e^2 - 36*e + 2, 4*e^4 + 12*e^3 - 12*e^2 - 28*e - 2, -4*e^4 - 8*e^3 + 17*e^2 + 12*e - 12, 2*e^4 + 7*e^3 + 5*e^2 + 3*e - 12, 4*e^4 + 12*e^3 - 11*e^2 - 20*e + 5, 3*e^4 + 15*e^3 + 9*e^2 - 26*e - 26, e^4 + 8*e^3 + 4*e^2 - 36*e - 9, -e^4 - 4*e^3 + 3*e^2 + 13*e, 10*e^4 + 40*e^3 + e^2 - 85*e - 12, 9*e^4 + 35*e^3 + e^2 - 68*e - 14, -e^3 - 2*e^2 + 8*e - 4, 6*e^4 + 24*e^3 + 7*e^2 - 32*e - 15, 3*e^4 + 16*e^3 + 15*e^2 - 19*e - 27, 2*e^4 + 9*e^3 - e^2 - 25*e - 11, -9*e^4 - 34*e^3 + 6*e^2 + 68*e - 8, -7*e^4 - 22*e^3 + 13*e^2 + 49*e - 1, -2*e^4 - 6*e^3 + 12*e^2 + 21*e - 5, -10*e^3 - 26*e^2 + 20*e + 29, -3*e^4 - 8*e^3 + 7*e^2 + 13*e + 9, -8*e^4 - 29*e^3 + 11*e^2 + 66*e - 5, 5*e^4 + 15*e^3 - 13*e^2 - 24*e + 17, 4*e^4 + 16*e^3 + 3*e^2 - 25*e - 16, 3*e^4 + 14*e^3 + 15*e^2 - 14*e - 30, 3*e^2 + 9*e - 21, -6*e^4 - 23*e^3 + 40*e + 26, e^4 + 7*e^3 + 10*e^2 - 14*e - 15, -e^4 - 4*e^3 + 2*e^2 + 26*e - 3, -4*e^4 - 19*e^3 - 10*e^2 + 38*e + 8, -10*e^4 - 37*e^3 + 4*e^2 + 79*e + 17, -10*e^4 - 36*e^3 + 3*e^2 + 61*e + 13, 6*e^4 + 24*e^3 - 6*e^2 - 63*e - 7, 11*e^4 + 40*e^3 - 8*e^2 - 69*e, 5*e^4 + 9*e^3 - 29*e^2 - 25*e + 22, -e^4 - 5*e^3 - 9*e^2 - 9*e + 20, -e^3 + 13*e, 3*e^3 + 3*e^2 - 15*e - 16, -2*e^3 - 6*e^2 - 8*e - 2, 9*e^4 + 35*e^3 + e^2 - 64*e - 16, 8*e^4 + 34*e^3 + 3*e^2 - 71*e - 13, -3*e^4 - 5*e^3 + 21*e^2 + 12*e - 20, 3*e^4 + 5*e^3 - 16*e^2 - 10*e + 2, e^4 + 2*e^3 - 3*e^2 - 4*e - 34, -6*e^4 - 24*e^3 + 54*e + 8, -11*e^4 - 41*e^3 + 7*e^2 + 81*e + 8, 3*e^4 + 7*e^3 - 5*e^2 + 7*e - 2, -5*e^4 - 19*e^3 - 3*e^2 + 33*e + 7, 2*e^4 + 4*e^3 - e^2 + 8*e - 25, -8*e^4 - 32*e^3 - 3*e^2 + 61*e + 12, -8*e^4 - 34*e^3 + e^2 + 79*e + 7, -7*e^4 - 17*e^3 + 32*e^2 + 45*e - 30, 2*e^4 + e^3 - 22*e^2 + 39, -8*e^4 - 31*e^3 + 4*e^2 + 75*e - 3, 4*e^4 + 20*e^3 + 13*e^2 - 44*e - 21, -2*e^4 - 9*e^3 - 3*e^2 + 27*e + 19, -3*e^4 - 12*e^3 + e^2 + 23*e + 3, -11*e^4 - 42*e^3 + 84*e + 25, -13*e^4 - 42*e^3 + 23*e^2 + 84*e - 16, -12*e^4 - 47*e^3 - 2*e^2 + 88*e + 1, 7*e^4 + 23*e^3 - 5*e^2 - 27*e - 1, 2*e^3 + 4*e^2 - 24*e - 15, 14*e^4 + 46*e^3 - 25*e^2 - 91*e + 16, 5*e^4 + 16*e^3 - 13*e^2 - 34*e + 7, -e^3 - 7*e^2 + 9*e + 23, e^4 + e^3 + e^2 + 17*e - 14, 7*e^4 + 25*e^3 - 15*e^2 - 52*e + 29, -5*e^4 - 24*e^3 - 16*e^2 + 51*e + 29, 8*e^4 + 33*e^3 + 8*e^2 - 66*e - 32, -2*e^4 - 7*e^3 - 16*e^2 - 23*e + 33, -8*e^4 - 41*e^3 - 23*e^2 + 83*e + 19, -5*e^4 - 27*e^3 - 9*e^2 + 75*e + 1, 2*e^4 + 8*e^3 - 4*e^2 - 28*e - 7, 5*e^4 + 15*e^3 - 16*e^2 - 38*e - 13, -12*e^4 - 36*e^3 + 28*e^2 + 69*e - 14, -8*e^4 - 31*e^3 + e^2 + 63*e + 12, 3*e^4 + 13*e^3 + 10*e^2 - 7*e - 22, 9*e^4 + 36*e^3 + 5*e^2 - 71*e - 8, 3*e^4 + 21*e^3 + 15*e^2 - 63*e - 31, 4*e^4 + 25*e^3 + 22*e^2 - 55*e - 32, 3*e^4 + 12*e^3 - 6*e^2 - 32*e + 4, 2*e^4 + 17*e^3 + 27*e^2 - 38*e - 44, -2*e^4 - 9*e^3 + e^2 + 21*e - 8, -6*e^4 - 31*e^3 - 18*e^2 + 65*e + 22, 9*e^4 + 27*e^3 - 21*e^2 - 57*e + 24, e^4 + 8*e^3 + 15*e^2 - 4*e - 16, -14*e^4 - 45*e^3 + 30*e^2 + 108*e - 2, 3*e^4 + e^3 - 36*e^2 - 16*e + 57, 9*e^4 + 34*e^3 + 3*e^2 - 44*e - 16, -7*e^4 - 22*e^3 + 18*e^2 + 42*e - 12, -e^4 - 14*e^3 - 30*e^2 + 18*e + 17, 16*e^4 + 59*e^3 - 11*e^2 - 132*e - 12, 2*e^4 + 6*e^3 - 10*e - 12, -2*e^4 - 15*e^3 - 17*e^2 + 31*e + 35, 5*e^4 + 12*e^3 - 28*e^2 - 26*e + 21, 5*e^4 + 14*e^3 - 10*e^2 - 18*e - 17, -6*e^4 - 23*e^3 + 3*e^2 + 55*e + 8, e^4 - 5*e^3 - 33*e^2 - 6*e + 36, 7*e^3 + 18*e^2 - 8*e - 10, -6*e^4 - 19*e^3 + 9*e^2 + 40*e + 3, -5*e^4 - 24*e^3 - 25*e^2 + 23*e + 53, -6*e^4 - 22*e^3 + 10*e^2 + 43*e - 32, -5*e^4 - 14*e^3 - 5*e + 6, -9*e^4 - 34*e^3 + 5*e^2 + 69*e - 7, -11*e^4 - 41*e^3 - e^2 + 80*e + 41, -5*e^4 - 7*e^3 + 34*e^2 + 14*e - 34, -4*e^4 - 22*e^3 - 3*e^2 + 75*e + 3, -5*e^4 - 26*e^3 - 20*e^2 + 46*e + 11, e^4 - e^3 - 15*e^2 - 7*e - 13, 5*e^4 + 17*e^3 - 14*e^2 - 59*e + 8, 11*e^4 + 42*e^3 + 13*e^2 - 61*e - 44, -3*e^4 - 15*e^3 - 16*e^2 + 22*e + 31, 10*e^4 + 46*e^3 + 18*e^2 - 88*e - 19, 8*e^4 + 30*e^3 - e^2 - 41*e - 18, 8*e^3 + 24*e^2 - 18*e - 23, 7*e^4 + 34*e^3 + 24*e^2 - 62*e - 21, -3*e^4 - 12*e^3 + 8*e^2 + 40*e - 11, 16*e^4 + 59*e^3 - 8*e^2 - 119*e - 6, -15*e^4 - 59*e^3 + 6*e^2 + 128*e + 9, 10*e^4 + 42*e^3 + e^2 - 102*e + 4, e^4 + 4*e^3 - 2*e^2 - 7*e + 36, -2*e^4 + e^3 + 22*e^2 + 8*e + 3, -3*e^4 - e^3 + 22*e^2 - 11*e - 35, -2*e^4 - 15*e^3 - 25*e^2 + 28*e + 45, -6*e^4 - 13*e^3 + 36*e^2 + 36*e - 37, -9*e^4 - 28*e^3 + 18*e^2 + 52*e - 24, -5*e^4 - 22*e^3 - 6*e^2 + 62*e + 47, 9*e^4 + 34*e^3 - 13*e^2 - 88*e + 3, -2*e^4 - 16*e^3 - 24*e^2 + 29*e + 20, 18*e^4 + 65*e^3 - 14*e^2 - 133*e - 7, -23*e^4 - 86*e^3 + 2*e^2 + 162*e + 19, -3*e^4 - 13*e^3 - 9*e^2 + 31*e + 21, -4*e^3 - 9*e^2 + 29*e + 25, 17*e^4 + 70*e^3 - 5*e^2 - 172*e - 12, -14*e^4 - 52*e^3 + 10*e^2 + 100*e + 15, -6*e^4 - 31*e^3 - 12*e^2 + 80*e + 24, 20*e^4 + 76*e^3 - 10*e^2 - 160*e - 10, 13*e^4 + 57*e^3 + 9*e^2 - 125*e - 24, 14*e^4 + 44*e^3 - 33*e^2 - 115*e - 2, -e^4 + 3*e^3 + 16*e^2 - 25*e - 23, -4*e^4 - 4*e^3 + 41*e^2 + 11*e - 42, -3*e^4 - 9*e^3 + 9*e^2 + 25*e - 20, 17*e^4 + 68*e^3 - 2*e^2 - 155*e - 7, 4*e^4 + 23*e^3 + 21*e^2 - 43*e - 7, 5*e^4 + 17*e^3 - 5*e^2 - 12*e + 29, -4*e^4 - 18*e^3 - 2*e^2 + 48*e + 30, -16*e^4 - 67*e^3 - 13*e^2 + 137*e + 30, 10*e^4 + 42*e^3 + 7*e^2 - 82*e - 18, -6*e^4 - 7*e^3 + 48*e^2 + 27*e - 31, -3*e^3 - 3*e^2 + 28*e + 22, -2*e^4 - 8*e^3 - 5*e^2 + 13*e - 4, -13*e^4 - 51*e^3 + 11*e^2 + 121*e + 2, -2*e^4 - 2*e^3 - 6*e^2 - 36*e + 30, -3*e^4 + 2*e^3 + 42*e^2 + 17*e - 41, 4*e^4 + 18*e^3 + 12*e^2 - 36*e - 35, 10*e^4 + 30*e^3 - 24*e^2 - 51*e + 37, 3*e^4 + 22*e^3 + 25*e^2 - 59*e - 45, -14*e^4 - 59*e^3 - 10*e^2 + 144*e + 36, -3*e^4 - 10*e^3 + 15*e^2 + 50*e - 2, -7*e^4 - 19*e^3 + 18*e^2 + 18*e - 15, 12*e^4 + 41*e^3 - 11*e^2 - 84*e - 9, 18*e^4 + 66*e^3 - 7*e^2 - 131*e - 35, -2*e^4 - 10*e^3 - 6*e^2 - 3*e - 2, 8*e^3 + 33*e^2 - 6*e - 55, 15*e^4 + 54*e^3 - 7*e^2 - 92*e - 14, 11*e^4 + 45*e^3 - 10*e^2 - 120*e + 10, 3*e^4 + 14*e^3 + 12*e^2 - 24*e - 43, -14*e^4 - 65*e^3 - 18*e^2 + 144*e + 15, 4*e^4 + 14*e^3 - 15*e + 10, 2*e^4 + 7*e^3 + 6*e^2 + 8*e + 10, 13*e^4 + 48*e^3 - 5*e^2 - 101*e - 11, -7*e^4 - 32*e^3 - 21*e^2 + 49*e + 26, 15*e^4 + 55*e^3 + 3*e^2 - 91*e - 27, -9*e^4 - 22*e^3 + 45*e^2 + 58*e - 33, 3*e^4 + 21*e^3 + 13*e^2 - 74*e - 45, 6*e^4 + 18*e^3 - 14*e^2 - 45*e + 20, -6*e^4 - 28*e^3 - 24*e^2 + 49*e + 53, -12*e^4 - 42*e^3 + 4*e^2 + 61*e - 10, 10*e^4 + 51*e^3 + 26*e^2 - 112*e - 11, 9*e^4 + 31*e^3 - 16*e^2 - 73*e - 9, 9*e^4 + 40*e^3 - 2*e^2 - 120*e + 2, -5*e^4 - 25*e^3 - e^2 + 87*e + 4, -5*e^4 - 20*e^3 - 4*e^2 + 51*e + 51, -6*e^4 - 17*e^3 + 21*e^2 + 16*e - 26, -8*e^4 - 33*e^3 - 13*e^2 + 28*e + 30, -17*e^4 - 63*e^3 - 6*e^2 + 102*e + 34, -18*e^4 - 81*e^3 - 23*e^2 + 166*e + 27, -e^4 + 8*e^3 + 21*e^2 - 47*e - 35, 11*e^4 + 38*e^3 - 5*e^2 - 52*e + 7, -6*e^4 - 30*e^3 - 21*e^2 + 60*e + 39, 13*e^4 + 40*e^3 - 15*e^2 - 50*e, -3*e^3 + 10*e^2 + 31*e - 43, 4*e^4 + 8*e^3 - 29*e^2 - 12*e + 33, 21*e^4 + 75*e^3 - 24*e^2 - 171*e - 21, -9*e^4 - 37*e^3 - 6*e^2 + 72*e + 23, -e^4 - 16*e^3 - 22*e^2 + 53*e + 12, -2*e^4 + 22*e^2 + 2*e - 57, 6*e^4 + 18*e^3 - 17*e^2 - 23*e + 24, 10*e^4 + 43*e^3 + 16*e^2 - 90*e - 29, -10*e^4 - 33*e^3 + 8*e^2 + 58*e + 2, -11*e^4 - 45*e^3 + 7*e^2 + 113*e + 5, 9*e^4 + 29*e^3 - 28*e^2 - 90*e + 41, e^4 + 19*e^3 + 49*e^2 - 36*e - 65, -21*e^4 - 83*e^3 - 3*e^2 + 149*e + 21, -8*e^4 - 17*e^3 + 46*e^2 + 60*e - 28, 14*e^4 + 48*e^3 - 23*e^2 - 96*e + 9, -2*e^4 - 5*e^3 - 7*e^2 + 9*e + 76, 4*e^4 + 17*e^3 + 10*e^2 - 14*e - 32, 13*e^4 + 49*e^3 - 20*e^2 - 117*e + 8, -9*e^4 - 40*e^3 - 14*e^2 + 78*e + 30, -11*e^4 - 51*e^3 - 31*e^2 + 74*e + 46, -8*e^4 - 36*e^3 - 10*e^2 + 100*e + 57, -15*e^4 - 51*e^3 + 33*e^2 + 134*e - 29, 10*e^4 + 33*e^3 - 8*e^2 - 70*e - 37, -5*e^4 - 21*e^3 + 3*e^2 + 39*e - 5, 13*e^4 + 48*e^3 - 4*e^2 - 85*e - 26, -13*e^4 - 48*e^3 - e^2 + 86*e + 48, 8*e^4 + 36*e^3 + 2*e^2 - 121*e - 21, 2*e^4 + 5*e^3 - 19*e^2 - 48*e + 21, -14*e^4 - 62*e^3 - 15*e^2 + 127*e + 30, -15*e^4 - 56*e^3 + 12*e^2 + 109*e + 1, 9*e^4 + 37*e^3 + 18*e^2 - 44*e - 44, 17*e^4 + 59*e^3 - 14*e^2 - 116*e - 13, -6*e^4 - 28*e^3 - 2*e^2 + 104*e + 23, 13*e^4 + 52*e^3 + e^2 - 93*e - 5, 12*e^4 + 57*e^3 + 38*e^2 - 92*e - 53, 9*e^4 + 35*e^3 + 3*e^2 - 62*e - 58, 13*e^4 + 36*e^3 - 35*e^2 - 70*e + 6, 3*e^4 + 13*e^3 + 10*e^2 - 35*e - 47, -11*e^4 - 37*e^3 + 8*e^2 + 63*e + 7, 12*e^4 + 41*e^3 - 10*e^2 - 72*e - 1, 5*e^4 + 17*e^3 + 5*e^2 - 18*e - 35, -15*e^4 - 62*e^3 - 12*e^2 + 140*e + 48, -18*e^4 - 67*e^3 + 10*e^2 + 107*e + 3, -12*e^4 - 34*e^3 + 27*e^2 + 38*e - 44, 3*e^4 + 16*e^3 + 17*e^2 - 25*e - 36, 10*e^4 + 34*e^3 - 34*e^2 - 109*e + 23, -4*e^4 - 13*e^3 + 11*e^2 + 14*e - 48, 18*e^4 + 78*e^3 + 9*e^2 - 174*e - 15, 7*e^4 + 26*e^3 - 4*e^2 - 68*e - 60, -32*e^4 - 113*e^3 + 28*e^2 + 216*e + 8, 8*e^4 + 46*e^3 + 36*e^2 - 95*e - 46, -22*e^4 - 73*e^3 + 42*e^2 + 170*e + 1, 7*e^3 + 24*e^2 - 66, -18*e^4 - 68*e^3 + 4*e^2 + 107*e + 22, 15*e^4 + 39*e^3 - 60*e^2 - 81*e + 62, -5*e^3 - 11*e^2 + 26*e + 10]
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^3 + 3*w^2 + 4*w - 3])] = -1

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