/*
  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([16, 2, 2])

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^4 + 4*x^3 - 20*x^2 - 48*x - 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, 1/6*e^3 + 1/2*e^2 - 10/3*e - 14/3, -1/6*e^3 - 1/2*e^2 + 10/3*e + 8/3, 1/6*e^3 + 1/2*e^2 - 13/3*e - 14/3, -1/6*e^3 - 1/2*e^2 + 13/3*e + 14/3, -1/2*e^2 - e + 6, 1/2*e^2 + e - 6, -1/3*e^3 - e^2 + 26/3*e + 28/3, -1/3*e^3 - e^2 + 26/3*e + 28/3, 1/6*e^3 + 1/2*e^2 - 10/3*e - 14/3, -1/6*e^3 - 1/2*e^2 + 10/3*e + 8/3, 1/2*e^3 + 3/2*e^2 - 13*e - 14, 1/2*e^3 + 3/2*e^2 - 13*e - 14, -8, -1/6*e^3 - e^2 + 10/3*e + 32/3, -1/6*e^3 + 16/3*e - 4/3, 2/3*e^3 + 2*e^2 - 40/3*e - 68/3, -2/3*e^3 - 2*e^2 + 40/3*e + 20/3, 1/6*e^3 + 1/2*e^2 - 10/3*e - 56/3, -1/6*e^3 - 1/2*e^2 + 10/3*e - 34/3, -8, -8, 1/6*e^3 - 1/2*e^2 - 19/3*e + 22/3, 1/6*e^3 + 3/2*e^2 - 7/3*e - 50/3, 1/6*e^3 - 1/2*e^2 - 19/3*e + 22/3, 1/6*e^3 + 1/2*e^2 - 13/3*e - 14/3, 1/6*e^3 + 3/2*e^2 - 7/3*e - 50/3, 1/6*e^3 + 1/2*e^2 - 13/3*e - 14/3, 1/2*e^3 + 2*e^2 - 12*e - 20, 1/2*e^3 + e^2 - 14*e - 8, 2/3*e^3 + 2*e^2 - 40/3*e - 68/3, -2/3*e^3 - 2*e^2 + 40/3*e + 20/3, 4/3*e^3 + 4*e^2 - 80/3*e - 76/3, -4/3*e^3 - 4*e^2 + 80/3*e + 100/3, -1/2*e^3 - 3/2*e^2 + 10*e + 22, 1/2*e^3 + 3/2*e^2 - 10*e, 1/6*e^3 + 1/2*e^2 - 10/3*e - 62/3, -5/6*e^3 - 5/2*e^2 + 50/3*e + 46/3, 5/6*e^3 + 5/2*e^2 - 50/3*e - 64/3, -1/6*e^3 - 1/2*e^2 + 10/3*e - 40/3, -e^3 - 7/2*e^2 + 25*e + 34, -e^3 - 5/2*e^2 + 27*e + 22, -2/3*e^3 - 2*e^2 + 40/3*e + 98/3, 2/3*e^3 + 2*e^2 - 40/3*e + 10/3, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, -1/2*e^3 - 5/2*e^2 + 11*e + 26, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, -1/2*e^3 - 1/2*e^2 + 15*e + 2, -1/2*e^3 - e^2 + 14*e + 8, -1/2*e^3 - 2*e^2 + 12*e + 20, 0, 0, -3/2*e^3 - 9/2*e^2 + 30*e + 24, 3/2*e^3 + 9/2*e^2 - 30*e - 42, 11/6*e^3 + 11/2*e^2 - 110/3*e - 130/3, -11/6*e^3 - 11/2*e^2 + 110/3*e + 112/3, -3/2*e^2 - 3*e + 18, 3/2*e^2 + 3*e - 18, -1/2*e^3 - 5/2*e^2 + 11*e + 26, -1/2*e^3 - 1/2*e^2 + 15*e + 2, -1/6*e^3 - 3*e^2 - 2/3*e + 104/3, -1/6*e^3 + 2*e^2 + 28/3*e - 76/3, 2/3*e^3 + 2*e^2 - 40/3*e - 32/3, -2/3*e^3 - 2*e^2 + 40/3*e + 56/3, 1/3*e^3 + e^2 - 20/3*e + 2/3, -1/3*e^3 - e^2 + 20/3*e + 46/3, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, -1/2*e^3 - 7/2*e^2 + 9*e + 38, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, -1/2*e^3 + 1/2*e^2 + 17*e - 10, 2/3*e^3 + 2*e^2 - 40/3*e - 32/3, -2/3*e^3 - 2*e^2 + 40/3*e + 56/3, -1/6*e^3 - 1/2*e^2 + 10/3*e - 34/3, 1/6*e^3 + 1/2*e^2 - 10/3*e - 56/3, 1/2*e^3 + e^2 - 14*e - 8, 1/2*e^3 + 2*e^2 - 12*e - 20, -1/3*e^3 - e^2 + 26/3*e + 28/3, -1/3*e^3 - e^2 + 26/3*e + 28/3, -3/2*e^3 - 11/2*e^2 + 37*e + 54, -3/2*e^3 - 7/2*e^2 + 41*e + 30, 2/3*e^3 + 3*e^2 - 46/3*e - 92/3, 2/3*e^3 + e^2 - 58/3*e - 20/3, 5/3*e^3 + 5*e^2 - 100/3*e - 74/3, -5/3*e^3 - 5*e^2 + 100/3*e + 146/3, -4/3*e^3 - 4*e^2 + 80/3*e + 136/3, 4/3*e^3 + 4*e^2 - 80/3*e - 40/3, 13/6*e^3 + 13/2*e^2 - 130/3*e - 110/3, -13/6*e^3 - 13/2*e^2 + 130/3*e + 176/3, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, 5/6*e^3 + 5/2*e^2 - 65/3*e - 70/3, -2/3*e^3 - 2*e^2 + 40/3*e + 92/3, 4/3*e^3 + 4*e^2 - 80/3*e - 58/3, 2/3*e^3 + 2*e^2 - 40/3*e + 4/3, -4/3*e^3 - 4*e^2 + 80/3*e + 118/3, -1/2*e^3 - e^2 + 14*e + 8, -1/2*e^3 - 2*e^2 + 12*e + 20, 3/2*e^3 + 9/2*e^2 - 30*e - 56, -3/2*e^3 - 9/2*e^2 + 30*e + 10, 4/3*e^3 + 4*e^2 - 104/3*e - 112/3, 4/3*e^3 + 4*e^2 - 104/3*e - 112/3, -7/6*e^3 - 7/2*e^2 + 91/3*e + 98/3, -7/6*e^3 - 7/2*e^2 + 91/3*e + 98/3, -20, -1/6*e^3 - 2*e^2 + 4/3*e + 68/3, -1/6*e^3 + e^2 + 22/3*e - 40/3, -e^3 - 4*e^2 + 24*e + 40, -e^3 - 2*e^2 + 28*e + 16, 2/3*e^3 + 2*e^2 - 40/3*e + 22/3, -2/3*e^3 - 2*e^2 + 40/3*e + 110/3, -11/6*e^3 - 11/2*e^2 + 110/3*e + 82/3, 11/6*e^3 + 11/2*e^2 - 110/3*e - 160/3, -e^3 - 1/2*e^2 + 31*e - 2, -e^3 - 11/2*e^2 + 21*e + 58, -18, 5/6*e^3 + 5/2*e^2 - 50/3*e + 32/3, -5/6*e^3 - 5/2*e^2 + 50/3*e + 142/3, 1/6*e^3 + 1/2*e^2 - 10/3*e + 82/3, -1/6*e^3 - 1/2*e^2 + 10/3*e + 104/3, -2*e^3 - 11/2*e^2 + 53*e + 50, -2*e^3 - 13/2*e^2 + 51*e + 62, -e^3 - 3*e^2 + 20*e + 10, e^3 + 3*e^2 - 20*e - 34, 5/2*e^3 + 8*e^2 - 64*e - 76, 5/2*e^3 + 7*e^2 - 66*e - 64, 1/6*e^3 + 1/2*e^2 - 10/3*e - 110/3, 7/2*e^3 + 21/2*e^2 - 70*e - 74, -7/2*e^3 - 21/2*e^2 + 70*e + 80, -1/6*e^3 - 1/2*e^2 + 10/3*e - 88/3, -1/3*e^3 + e^2 + 38/3*e - 44/3, -1/3*e^3 - 3*e^2 + 14/3*e + 100/3, -1/2*e^3 - 3/2*e^2 + 10*e + 6, 1/2*e^3 + 3/2*e^2 - 10*e - 16, 3/2*e^3 + 9/2*e^2 - 39*e - 42, 13/6*e^3 + 13/2*e^2 - 169/3*e - 182/3, 3/2*e^3 + 9/2*e^2 - 39*e - 42, 13/6*e^3 + 13/2*e^2 - 169/3*e - 182/3, -1/6*e^3 + 1/2*e^2 + 19/3*e - 22/3, -1/6*e^3 - 3/2*e^2 + 7/3*e + 50/3, -7/6*e^3 - 7/2*e^2 + 70/3*e + 8/3, 7/6*e^3 + 7/2*e^2 - 70/3*e - 146/3, -11/6*e^3 - 4*e^2 + 152/3*e + 100/3, -11/6*e^3 - 7*e^2 + 134/3*e + 208/3, -7/6*e^3 - 3/2*e^2 + 103/3*e + 26/3, -7/6*e^3 - 11/2*e^2 + 79/3*e + 170/3, -1/2*e^3 + 2*e^2 + 20*e - 28, -1/2*e^3 - 5*e^2 + 6*e + 56, 2*e^3 + 7*e^2 - 50*e - 68, 2*e^3 + 5*e^2 - 54*e - 44, 1/2*e^3 + 5/2*e^2 - 11*e - 26, 1/2*e^3 + 1/2*e^2 - 15*e - 2, 7/3*e^3 + 7*e^2 - 182/3*e - 196/3, 7/3*e^3 + 7*e^2 - 182/3*e - 196/3, 1/3*e^3 - 2*e^2 - 44/3*e + 80/3, 1/3*e^3 + 4*e^2 - 8/3*e - 136/3, -5/6*e^3 - 5/2*e^2 + 50/3*e - 2/3, 5/2*e^3 + 15/2*e^2 - 50*e - 54, -5/2*e^3 - 15/2*e^2 + 50*e + 56, 5/6*e^3 + 5/2*e^2 - 50/3*e - 112/3, 7/6*e^3 + 3/2*e^2 - 103/3*e - 26/3, 7/6*e^3 + 11/2*e^2 - 79/3*e - 170/3, -16, 7/6*e^3 + 7/2*e^2 - 70/3*e - 104/3, -5/2*e^3 - 15/2*e^2 + 50*e + 54, 5/2*e^3 + 15/2*e^2 - 50*e - 56, -7/6*e^3 - 7/2*e^2 + 70/3*e + 50/3, 1/2*e^3 + 5*e^2 - 6*e - 56, 1/2*e^3 - 2*e^2 - 20*e + 28, 7/6*e^3 + 7/2*e^2 - 70/3*e - 98/3, -7/6*e^3 - 7/2*e^2 + 70/3*e + 56/3, 7/3*e^3 + 7*e^2 - 140/3*e - 142/3, -7/3*e^3 - 7*e^2 + 140/3*e + 166/3, -3/2*e^3 - 3*e^2 + 42*e + 24, -3/2*e^3 - 6*e^2 + 36*e + 60, e^3 + 3*e^2 - 20*e - 18, -e^3 - 3*e^2 + 20*e + 26, -2/3*e^3 - 2*e^2 + 40/3*e - 16/3, 2/3*e^3 + 2*e^2 - 40/3*e - 104/3, 3/2*e^3 + 7/2*e^2 - 41*e - 30, 3/2*e^3 + 11/2*e^2 - 37*e - 54, 11/6*e^3 + 11/2*e^2 - 110/3*e - 130/3, 3/2*e^3 + 9/2*e^2 - 30*e - 24, -3/2*e^3 - 9/2*e^2 + 30*e + 42, -11/6*e^3 - 11/2*e^2 + 110/3*e + 112/3, 5/3*e^3 + 4*e^2 - 136/3*e - 104/3, 5/3*e^3 + 6*e^2 - 124/3*e - 176/3, 11/6*e^3 + 6*e^2 - 140/3*e - 172/3, 11/6*e^3 + 5*e^2 - 146/3*e - 136/3, 2/3*e^3 + 2*e^2 - 40/3*e + 64/3, -2/3*e^3 - 2*e^2 + 40/3*e + 152/3, -2*e^3 - 5*e^2 + 54*e + 44, -2*e^3 - 7*e^2 + 50*e + 68, -8/3*e^3 - 8*e^2 + 160/3*e + 140/3, 8/3*e^3 + 8*e^2 - 160/3*e - 212/3, 5/2*e^2 + 5*e - 30, -5/2*e^2 - 5*e + 30, 4/3*e^3 + 4*e^2 - 80/3*e - 208/3, -4/3*e^3 - 4*e^2 + 80/3*e - 32/3, -1/6*e^3 - 1/2*e^2 + 13/3*e + 14/3, -1/6*e^3 - 1/2*e^2 + 13/3*e + 14/3, 1/2*e^3 + 4*e^2 - 8*e - 44, -1/2*e^3 - 4*e^2 + 8*e + 44, -1/2*e^3 + e^2 + 18*e - 16, 1/2*e^3 - e^2 - 18*e + 16, 1/6*e^3 + 1/2*e^2 - 10/3*e - 104/3, -1/6*e^3 - 1/2*e^2 + 10/3*e - 82/3, -7/3*e^3 - 15/2*e^2 + 179/3*e + 214/3, -7/3*e^3 - 13/2*e^2 + 185/3*e + 178/3, 2*e^3 + 6*e^2 - 40*e - 70, -2*e^3 - 6*e^2 + 40*e + 18, -13/6*e^3 - 13/2*e^2 + 130/3*e + 206/3, 13/6*e^3 + 13/2*e^2 - 130/3*e - 80/3, -1/3*e^3 + e^2 + 38/3*e - 44/3, -1/3*e^3 - 3*e^2 + 14/3*e + 100/3, 4/3*e^3 + 4*e^2 - 80/3*e - 34/3, -4/3*e^3 - 4*e^2 + 80/3*e + 142/3, -e^3 - 2*e^2 + 28*e + 16, -e^3 - 4*e^2 + 24*e + 40, -7/6*e^3 - 7/2*e^2 + 70/3*e + 2/3, 7/6*e^3 + 7/2*e^2 - 70/3*e - 152/3, 1/2*e^3 + 9/2*e^2 - 7*e - 50, -5/3*e^3 - 17/2*e^2 + 109/3*e + 266/3, 1/2*e^3 - 3/2*e^2 - 19*e + 22, -5/3*e^3 - 3/2*e^2 + 151/3*e + 14/3, -1/2*e^3 - 3/2*e^2 + 10*e + 16, 1/2*e^3 + 3/2*e^2 - 10*e - 6, 5/6*e^3 - 3/2*e^2 - 89/3*e + 74/3, 5/6*e^3 + 13/2*e^2 - 41/3*e - 214/3, -1/3*e^3 - 3*e^2 + 14/3*e + 100/3, -1/3*e^3 + e^2 + 38/3*e - 44/3, 5/2*e^3 + 15/2*e^2 - 50*e - 40, -5/2*e^3 - 15/2*e^2 + 50*e + 70, 5/6*e^3 + 5/2*e^2 - 50/3*e - 46/3, -5/6*e^3 - 5/2*e^2 + 50/3*e + 64/3, 7/3*e^3 + 7*e^2 - 140/3*e - 70/3, -7/3*e^3 - 7*e^2 + 140/3*e + 238/3, -1/6*e^3 - 1/2*e^2 + 10/3*e + 158/3, -11/6*e^3 - 11/2*e^2 + 110/3*e + 64/3, 11/6*e^3 + 11/2*e^2 - 110/3*e - 178/3, 1/6*e^3 + 1/2*e^2 - 10/3*e + 136/3, -5/6*e^3 - 3/2*e^2 + 71/3*e + 34/3, -5/6*e^3 - 7/2*e^2 + 59/3*e + 106/3, 3*e^3 + 8*e^2 - 80*e - 72, 3*e^3 + 10*e^2 - 76*e - 96, 13/6*e^3 + 13/2*e^2 - 130/3*e - 224/3, -13/6*e^3 - 13/2*e^2 + 130/3*e + 62/3, 17/6*e^3 + 19/2*e^2 - 215/3*e - 274/3, 17/6*e^3 + 15/2*e^2 - 227/3*e - 202/3, -3/2*e^3 - e^2 + 46*e, -7/6*e^3 - e^2 + 106/3*e + 8/3, -3/2*e^3 - 8*e^2 + 32*e + 84, -7/6*e^3 - 6*e^2 + 76/3*e + 188/3, -5/3*e^3 - 5*e^2 + 100/3*e + 170/3, 5/3*e^3 + 5*e^2 - 100/3*e - 50/3, -11/6*e^3 - 11/2*e^2 + 110/3*e + 112/3, 11/6*e^3 + 11/2*e^2 - 110/3*e - 130/3, -34, -1/6*e^3 - 1/2*e^2 + 13/3*e + 14/3, -1/6*e^3 - 1/2*e^2 + 13/3*e + 14/3, 2*e^3 + 13/2*e^2 - 51*e - 62, 2*e^3 + 11/2*e^2 - 53*e - 50, 11/6*e^3 + 11/2*e^2 - 143/3*e - 154/3, 11/6*e^3 + 11/2*e^2 - 143/3*e - 154/3, -7/3*e^3 - 7*e^2 + 140/3*e + 262/3, 7/3*e^3 + 7*e^2 - 140/3*e - 46/3, -7/3*e^3 - 7*e^2 + 140/3*e + 142/3, 7/3*e^3 + 7*e^2 - 140/3*e - 166/3, -11/2*e^3 - 33/2*e^2 + 110*e + 122, 11/2*e^3 + 33/2*e^2 - 110*e - 120, -1/2*e^3 - 3/2*e^2 + 10*e + 16, 1/2*e^3 + 3/2*e^2 - 10*e - 6, -7/6*e^3 - 7/2*e^2 + 70/3*e + 194/3, 5/6*e^3 + 5/2*e^2 - 50/3*e + 2/3, 7/6*e^3 + 7/2*e^2 - 70/3*e + 40/3, -5/6*e^3 - 5/2*e^2 + 50/3*e + 112/3, -2/3*e^3 - 2*e^2 + 40/3*e + 122/3, 10/3*e^3 + 10*e^2 - 200/3*e - 196/3, -10/3*e^3 - 10*e^2 + 200/3*e + 244/3, 2/3*e^3 + 2*e^2 - 40/3*e + 34/3, -1/6*e^3 - 1/2*e^2 + 10/3*e + 62/3, 1/6*e^3 + 1/2*e^2 - 10/3*e + 40/3, -5/3*e^3 - 5*e^2 + 130/3*e + 140/3, -5/3*e^3 - 5*e^2 + 130/3*e + 140/3, -5/3*e^3 - 5*e^2 + 100/3*e + 2/3, 5/3*e^3 + 5*e^2 - 100/3*e - 218/3, -2/3*e^3 + e^2 + 70/3*e - 52/3, -4*e^3 - 12*e^2 + 104*e + 112, -2/3*e^3 - 5*e^2 + 34/3*e + 164/3, -4*e^3 - 12*e^2 + 104*e + 112, 16/3*e^3 + 16*e^2 - 320/3*e - 340/3, -16/3*e^3 - 16*e^2 + 320/3*e + 364/3, 4/3*e^3 + 9/2*e^2 - 101/3*e - 130/3, 4/3*e^3 + 7/2*e^2 - 107/3*e - 94/3, -1/3*e^3 + 3/2*e^2 + 41/3*e - 62/3, -1/3*e^3 - 7/2*e^2 + 11/3*e + 118/3, 10/3*e^3 + 10*e^2 - 200/3*e - 184/3, -10/3*e^3 - 10*e^2 + 200/3*e + 256/3, -e^3 - 3*e^2 + 20*e - 2, e^3 + 3*e^2 - 20*e - 46, -7/6*e^3 - 7/2*e^2 + 70/3*e + 98/3, 7/6*e^3 + 7/2*e^2 - 70/3*e - 56/3]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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