/*
  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([14, -4, -10, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([32, 4, -2*w - 4])

primes_array = [
[2, 2, -w - 2],\
[7, 7, -2/3*w^3 + 2/3*w^2 + 5*w - 7/3],\
[7, 7, -1/3*w^3 + 1/3*w^2 + w - 5/3],\
[9, 3, -1/3*w^3 + 1/3*w^2 + 3*w - 5/3],\
[9, 3, w + 1],\
[17, 17, w + 3],\
[17, 17, -1/3*w^3 + 1/3*w^2 + 3*w - 11/3],\
[31, 31, 1/3*w^3 - 1/3*w^2 - w - 1/3],\
[31, 31, -2/3*w^3 + 2/3*w^2 + 5*w - 1/3],\
[41, 41, -2/3*w^3 + 5/3*w^2 + 4*w - 19/3],\
[41, 41, w^2 - 5],\
[41, 41, 2*w + 3],\
[41, 41, 2/3*w^3 + 4/3*w^2 - 5*w - 29/3],\
[47, 47, -2/3*w^3 + 5/3*w^2 + 3*w - 19/3],\
[47, 47, 1/3*w^3 + 2/3*w^2 - 3*w - 13/3],\
[49, 7, -1/3*w^3 + 1/3*w^2 + 2*w - 11/3],\
[73, 73, -1/3*w^3 + 1/3*w^2 + 5*w + 19/3],\
[73, 73, -2/3*w^3 - 1/3*w^2 + 4*w + 11/3],\
[73, 73, -1/3*w^3 + 4/3*w^2 + 2*w - 17/3],\
[103, 103, -1/3*w^3 + 4/3*w^2 + w - 23/3],\
[103, 103, w^2 - w - 3],\
[113, 113, -2/3*w^3 + 2/3*w^2 + 5*w + 11/3],\
[113, 113, 1/3*w^3 - 1/3*w^2 - w - 13/3],\
[127, 127, 2/3*w^3 + 1/3*w^2 - 9*w - 41/3],\
[127, 127, -2/3*w^3 + 5/3*w^2 + 5*w - 31/3],\
[127, 127, -1/3*w^3 + 1/3*w^2 - 11/3],\
[127, 127, 4/3*w^3 + 5/3*w^2 - 10*w - 43/3],\
[151, 151, -1/3*w^3 + 4/3*w^2 + w - 29/3],\
[151, 151, 2/3*w^3 - 2/3*w^2 - 6*w - 5/3],\
[167, 167, -2/3*w^3 + 5/3*w^2 + 2*w - 19/3],\
[167, 167, 2/3*w^3 + 1/3*w^2 - 6*w - 11/3],\
[191, 191, -w^3 + 2*w^2 + 6*w - 5],\
[191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 19/3],\
[193, 193, -1/3*w^3 + 1/3*w^2 + 5*w + 13/3],\
[193, 193, 2/3*w^3 + 7/3*w^2 - 2*w - 23/3],\
[199, 199, 1/3*w^3 + 2/3*w^2 + 2*w + 11/3],\
[199, 199, 1/3*w^3 + 2/3*w^2 - 5*w - 31/3],\
[223, 223, -2/3*w^3 + 5/3*w^2 + 5*w - 13/3],\
[223, 223, 4/3*w^3 - 7/3*w^2 - 8*w + 17/3],\
[223, 223, 2/3*w^3 + 1/3*w^2 - 4*w - 17/3],\
[223, 223, w^3 - w^2 - 7*w - 1],\
[233, 233, -1/3*w^3 + 1/3*w^2 + w - 17/3],\
[233, 233, -2/3*w^3 + 2/3*w^2 + 5*w - 19/3],\
[239, 239, 5/3*w^3 + 7/3*w^2 - 10*w - 41/3],\
[239, 239, -5/3*w^3 - 7/3*w^2 + 12*w + 59/3],\
[241, 241, -1/3*w^3 + 7/3*w^2 + w - 23/3],\
[241, 241, 5/3*w^3 + 10/3*w^2 - 10*w - 59/3],\
[257, 257, -1/3*w^3 + 1/3*w^2 + 4*w - 5/3],\
[257, 257, 1/3*w^3 - 1/3*w^2 - 4*w - 1/3],\
[257, 257, 2/3*w^3 + 1/3*w^2 - 7*w - 23/3],\
[257, 257, -4/3*w^3 + 1/3*w^2 + 10*w + 13/3],\
[263, 263, -4/3*w^3 + 7/3*w^2 + 9*w - 23/3],\
[263, 263, 1/3*w^3 + 2/3*w^2 - w - 13/3],\
[271, 271, 5/3*w^3 - 5/3*w^2 - 12*w + 19/3],\
[271, 271, w^3 - w^2 - 4*w + 5],\
[281, 281, w^2 + 5*w + 5],\
[281, 281, -1/3*w^3 - 5/3*w^2 + 2*w + 25/3],\
[289, 17, w^3 - w^2 - 6*w + 3],\
[311, 311, 1/3*w^3 - 7/3*w^2 + 41/3],\
[311, 311, -2*w + 5],\
[311, 311, -w^3 - 2*w^2 + 7*w + 15],\
[311, 311, 2/3*w^3 - 2/3*w^2 - 6*w - 11/3],\
[313, 313, w^3 - w^2 - 5*w + 1],\
[313, 313, -4/3*w^3 + 4/3*w^2 + 9*w - 5/3],\
[337, 337, 4/3*w^3 - 4/3*w^2 - 11*w + 5/3],\
[337, 337, 2/3*w^3 + 1/3*w^2 - 6*w - 29/3],\
[359, 359, -w^3 - w^2 + 12*w + 19],\
[359, 359, -1/3*w^3 + 4/3*w^2 + 5*w + 1/3],\
[359, 359, -1/3*w^3 - 8/3*w^2 - 4*w + 1/3],\
[359, 359, w^2 - 3*w - 9],\
[361, 19, 2*w^2 - w - 13],\
[361, 19, -w^3 + 3*w^2 + 5*w - 9],\
[409, 409, -w - 5],\
[409, 409, -1/3*w^3 + 1/3*w^2 + 3*w - 17/3],\
[431, 431, -w^3 - 3*w^2 + 2*w + 9],\
[431, 431, 2/3*w^3 + 7/3*w^2 - w - 23/3],\
[433, 433, -1/3*w^3 + 1/3*w^2 + 6*w + 19/3],\
[433, 433, 2/3*w^3 + 7/3*w^2 - 3*w - 29/3],\
[439, 439, 2/3*w^3 + 4/3*w^2 - 8*w - 47/3],\
[439, 439, 4/3*w^3 - 10/3*w^2 - 8*w + 29/3],\
[439, 439, 2*w^2 - 13],\
[439, 439, 5*w + 9],\
[449, 449, w^2 - 11],\
[449, 449, 2/3*w^3 - 5/3*w^2 - 4*w + 1/3],\
[457, 457, -w^3 - w^2 + 10*w + 17],\
[457, 457, -4/3*w^3 + 4/3*w^2 + 7*w + 1/3],\
[457, 457, 4/3*w^3 + 5/3*w^2 - 5*w - 19/3],\
[457, 457, -w^3 + 2*w^2 + 7*w - 13],\
[463, 463, w^3 - 2*w^2 - 5*w + 9],\
[463, 463, 2/3*w^3 + 1/3*w^2 - 5*w - 5/3],\
[463, 463, 5/3*w^3 - 11/3*w^2 - 9*w + 43/3],\
[463, 463, 2/3*w^3 + 4/3*w^2 - 5*w - 23/3],\
[487, 487, -4/3*w^3 - 8/3*w^2 + 7*w + 37/3],\
[487, 487, w^3 + w^2 - 8*w - 9],\
[487, 487, -2/3*w^3 - 4/3*w^2 + 4*w + 17/3],\
[487, 487, 5/3*w^3 - 11/3*w^2 - 8*w + 37/3],\
[503, 503, 2/3*w^3 + 4/3*w^2 - 4*w - 29/3],\
[503, 503, 2/3*w^3 + 1/3*w^2 - 10*w - 47/3],\
[503, 503, 1/3*w^3 - 1/3*w^2 + w + 17/3],\
[503, 503, -4/3*w^3 - 8/3*w^2 + 5*w + 31/3],\
[521, 521, -1/3*w^3 + 4/3*w^2 + 9*w + 31/3],\
[521, 521, w^3 - 6*w - 3],\
[529, 23, -1/3*w^3 + 1/3*w^2 + 2*w - 17/3],\
[529, 23, 1/3*w^3 - 1/3*w^2 - 2*w - 13/3],\
[569, 569, -4/3*w^3 - 5/3*w^2 + 7*w + 25/3],\
[569, 569, -1/3*w^3 - 5/3*w^2 - 2*w - 5/3],\
[577, 577, -1/3*w^3 + 7/3*w^2 + 3*w - 23/3],\
[577, 577, -4/3*w^3 + 10/3*w^2 + 9*w - 47/3],\
[599, 599, -4/3*w^3 - 8/3*w^2 + 6*w + 37/3],\
[599, 599, 2/3*w^3 + 4/3*w^2 - 3*w - 23/3],\
[601, 601, -2/3*w^3 + 8/3*w^2 + 4*w - 43/3],\
[601, 601, -2/3*w^3 + 8/3*w^2 + 4*w - 25/3],\
[617, 617, -1/3*w^3 + 7/3*w^2 + 2*w - 23/3],\
[617, 617, w^3 - 3*w^2 - 6*w + 15],\
[625, 5, -5],\
[631, 631, -2*w^3 + 2*w^2 + 14*w - 1],\
[631, 631, -w^3 + 10*w - 1],\
[641, 641, -w^2 - 1],\
[641, 641, -2/3*w^3 + 5/3*w^2 + 4*w - 37/3],\
[641, 641, 2/3*w^3 - 8/3*w^2 - 5*w + 37/3],\
[641, 641, w^3 - 3*w^2 - 7*w + 11],\
[647, 647, -1/3*w^3 - 2/3*w^2 - 3*w - 17/3],\
[647, 647, 1/3*w^3 + 2/3*w^2 - 6*w - 37/3],\
[673, 673, 2/3*w^3 - 2/3*w^2 - 7*w - 5/3],\
[673, 673, 2/3*w^3 - 5/3*w^2 - 3*w + 1/3],\
[673, 673, -1/3*w^3 + 1/3*w^2 + 5*w - 11/3],\
[673, 673, 1/3*w^3 + 2/3*w^2 - 3*w - 31/3],\
[719, 719, -w^3 - 2*w^2 + 4*w + 9],\
[719, 719, -w^3 - 2*w^2 + 5*w + 11],\
[727, 727, -w^3 + 3*w^2 + 4*w - 13],\
[727, 727, -1/3*w^3 + 4/3*w^2 + 4*w - 23/3],\
[727, 727, 1/3*w^3 + 5/3*w^2 - 4*w - 25/3],\
[727, 727, -2/3*w^3 - 1/3*w^2 + 4*w + 23/3],\
[743, 743, 1/3*w^3 + 2/3*w^2 + 3*w + 23/3],\
[743, 743, -1/3*w^3 + 7/3*w^2 + 2*w - 53/3],\
[751, 751, -2/3*w^3 + 5/3*w^2 + 2*w - 25/3],\
[751, 751, -2/3*w^3 - 1/3*w^2 + 6*w + 5/3],\
[761, 761, -1/3*w^3 + 7/3*w^2 + w - 29/3],\
[761, 761, -2/3*w^3 + 8/3*w^2 + 3*w - 37/3],\
[769, 769, -4/3*w^3 + 13/3*w^2 + 6*w - 59/3],\
[769, 769, -7/3*w^3 + 7/3*w^2 + 16*w - 5/3],\
[823, 823, -4/3*w^3 + 1/3*w^2 + 11*w + 25/3],\
[823, 823, w^3 - 2*w^2 - 3*w + 1],\
[857, 857, w^2 - 3*w - 5],\
[857, 857, -2/3*w^3 - 1/3*w^2 + 8*w - 1/3],\
[857, 857, 1/3*w^3 + 2/3*w^2 - 5*w - 13/3],\
[857, 857, w^2 - 4*w - 9],\
[863, 863, -4/3*w^3 + 7/3*w^2 + 8*w - 5/3],\
[863, 863, 2/3*w^3 + 1/3*w^2 - 4*w - 29/3],\
[881, 881, -5/3*w^3 - 4/3*w^2 + 11*w + 41/3],\
[881, 881, -4/3*w^3 - 5/3*w^2 + 6*w + 19/3],\
[887, 887, -4/3*w^3 + 4/3*w^2 + 10*w + 1/3],\
[887, 887, 2/3*w^3 - 2/3*w^2 - 2*w - 5/3],\
[911, 911, w^3 - 9*w - 1],\
[911, 911, 5/3*w^3 + 10/3*w^2 - 12*w - 65/3],\
[911, 911, 1/3*w^3 - 1/3*w^2 + w + 23/3],\
[911, 911, -2/3*w^3 + 5/3*w^2 + w - 25/3],\
[919, 919, -2/3*w^3 + 8/3*w^2 - 37/3],\
[919, 919, 2/3*w^3 + 4/3*w^2 - 8*w - 23/3],\
[929, 929, -2*w^3 - 3*w^2 + 11*w + 17],\
[929, 929, 1/3*w^3 - 1/3*w^2 - 4*w - 19/3],\
[937, 937, 4/3*w^3 - 1/3*w^2 - 9*w - 13/3],\
[937, 937, 3*w - 1],\
[937, 937, -w^3 + w^2 + 7*w - 9],\
[937, 937, w^3 - w^2 - 9*w + 1],\
[961, 31, 4/3*w^3 - 4/3*w^2 - 8*w + 11/3],\
[967, 967, w^2 - 3*w - 11],\
[967, 967, 1/3*w^3 + 2/3*w^2 - w - 19/3],\
[967, 967, 1/3*w^3 + 5/3*w^2 + 6*w + 23/3],\
[967, 967, 4/3*w^3 - 7/3*w^2 - 9*w + 17/3],\
[977, 977, w^3 - 4*w^2 - 5*w + 23],\
[977, 977, 2/3*w^3 - 11/3*w^2 - 3*w + 31/3],\
[983, 983, 4/3*w^3 - 4/3*w^2 - 6*w + 23/3],\
[983, 983, -2*w^3 + 2*w^2 + 14*w - 9],\
[991, 991, 2/3*w^3 + 1/3*w^2 - 5*w + 1/3],\
[991, 991, -w^3 + 2*w^2 + 5*w - 11],\
[1009, 1009, -1/3*w^3 + 1/3*w^2 + 9*w + 37/3],\
[1009, 1009, 2/3*w^3 + 7/3*w^2 - 6*w - 47/3],\
[1031, 1031, -4/3*w^3 + 10/3*w^2 + 7*w - 47/3],\
[1031, 1031, w^3 - w^2 - 9*w - 3],\
[1031, 1031, 1/3*w^3 - 7/3*w^2 + 53/3],\
[1031, 1031, 1/3*w^3 + 5/3*w^2 - 3*w - 19/3],\
[1033, 1033, -4/3*w^3 - 5/3*w^2 + 5*w + 13/3],\
[1033, 1033, 2*w^3 + 2*w^2 - 14*w - 19],\
[1039, 1039, -4/3*w^3 + 10/3*w^2 + 10*w - 53/3],\
[1039, 1039, -2/3*w^3 + 8/3*w^2 + 6*w - 19/3],\
[1063, 1063, -1/3*w^3 - 8/3*w^2 + 4*w + 37/3],\
[1063, 1063, -2/3*w^3 + 5/3*w^2 + 2*w - 43/3],\
[1063, 1063, -5/3*w^3 + 14/3*w^2 + 8*w - 61/3],\
[1063, 1063, 2/3*w^3 + 4/3*w^2 - 5*w - 41/3],\
[1097, 1097, -4/3*w^3 + 7/3*w^2 + 8*w - 47/3],\
[1097, 1097, 5/3*w^3 - 8/3*w^2 - 8*w + 19/3],\
[1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 31/3],\
[1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 37/3],\
[1129, 1129, 2/3*w^3 + 10/3*w^2 - w - 29/3],\
[1129, 1129, -2/3*w^3 + 2/3*w^2 + 10*w + 29/3],\
[1151, 1151, -w^3 + w^2 + 15*w + 17],\
[1151, 1151, -2/3*w^3 + 5/3*w^2 + 6*w - 1/3],\
[1153, 1153, w^3 - w^2 - 9*w + 3],\
[1153, 1153, -3*w - 1],\
[1201, 1201, 1/3*w^3 + 8/3*w^2 - 4*w - 43/3],\
[1201, 1201, -5/3*w^3 - 13/3*w^2 + 7*w + 53/3],\
[1231, 1231, 2/3*w^3 + 1/3*w^2 - 3*w - 17/3],\
[1231, 1231, -5/3*w^3 + 8/3*w^2 + 11*w - 19/3],\
[1279, 1279, 4/3*w^3 - 1/3*w^2 - 10*w - 1/3],\
[1279, 1279, -4/3*w^3 + 7/3*w^2 + 6*w - 29/3],\
[1279, 1279, 2/3*w^3 + 1/3*w^2 - 7*w + 1/3],\
[1279, 1279, -1/3*w^3 + 4/3*w^2 - w - 29/3],\
[1297, 1297, -2*w^3 - 3*w^2 + 9*w + 11],\
[1297, 1297, w^3 + 3*w^2 - 1],\
[1303, 1303, 8/3*w^3 - 11/3*w^2 - 17*w + 19/3],\
[1303, 1303, 4/3*w^3 + 2/3*w^2 - 13*w - 19/3],\
[1319, 1319, 5/3*w^3 - 8/3*w^2 - 9*w + 37/3],\
[1319, 1319, 4/3*w^3 - 1/3*w^2 - 9*w + 5/3],\
[1321, 1321, -1/3*w^3 + 1/3*w^2 + 5*w - 5/3],\
[1321, 1321, 2/3*w^3 - 2/3*w^2 - 7*w + 1/3],\
[1327, 1327, 2/3*w^3 + 1/3*w^2 - 11*w - 53/3],\
[1327, 1327, -1/3*w^3 + 1/3*w^2 - 2*w - 23/3],\
[1361, 1361, 2/3*w^3 + 1/3*w^2 - 8*w - 41/3],\
[1361, 1361, -5/3*w^3 - 7/3*w^2 + 7*w + 29/3],\
[1367, 1367, -1/3*w^3 + 7/3*w^2 + 3*w - 41/3],\
[1367, 1367, 4/3*w^3 - 10/3*w^2 - 9*w + 29/3],\
[1369, 37, -4/3*w^3 + 10/3*w^2 + 9*w - 65/3],\
[1369, 37, 1/3*w^3 - 7/3*w^2 - 3*w + 5/3],\
[1409, 1409, -2/3*w^3 - 13/3*w^2 - w + 29/3],\
[1409, 1409, -4/3*w^3 - 2/3*w^2 + 5*w + 1/3],\
[1423, 1423, 2/3*w^3 + 1/3*w^2 + 19/3],\
[1423, 1423, 7/3*w^3 - 16/3*w^2 - 12*w + 59/3],\
[1423, 1423, -4/3*w^3 - 2/3*w^2 + 9*w + 37/3],\
[1423, 1423, 7/3*w^3 - 13/3*w^2 - 13*w + 29/3],\
[1433, 1433, 1/3*w^3 - 1/3*w^2 - w - 19/3],\
[1433, 1433, -2*w^3 - 2*w^2 + 13*w + 15],\
[1433, 1433, 2/3*w^3 - 2/3*w^2 - 5*w - 17/3],\
[1433, 1433, -2/3*w^3 + 11/3*w^2 + 2*w - 61/3],\
[1439, 1439, 2/3*w^3 + 4/3*w^2 - 6*w - 23/3],\
[1439, 1439, -4/3*w^3 + 10/3*w^2 + 6*w - 41/3],\
[1447, 1447, -5/3*w^3 + 11/3*w^2 + 7*w - 37/3],\
[1447, 1447, 2/3*w^3 - 5/3*w^2 - 8*w + 31/3],\
[1471, 1471, 5/3*w^3 - 2/3*w^2 - 14*w + 1/3],\
[1471, 1471, -w^3 + 2*w^2 + 2*w - 9],\
[1481, 1481, -1/3*w^3 - 5/3*w^2 + 7*w + 43/3],\
[1481, 1481, -8/3*w^3 + 17/3*w^2 + 17*w - 73/3],\
[1489, 1489, 4*w + 5],\
[1489, 1489, 4/3*w^3 - 4/3*w^2 - 12*w + 23/3],\
[1511, 1511, w^3 - 4*w^2 - 3*w + 9],\
[1511, 1511, 3*w^2 - 3*w - 23],\
[1543, 1543, 2/3*w^3 + 1/3*w^2 - 6*w + 1/3],\
[1543, 1543, -2/3*w^3 + 5/3*w^2 + 2*w - 31/3],\
[1553, 1553, -7/3*w^3 + 10/3*w^2 + 13*w - 41/3],\
[1553, 1553, 2*w^3 - w^2 - 13*w + 3],\
[1559, 1559, 2*w^2 - 15],\
[1559, 1559, -4/3*w^3 + 10/3*w^2 + 8*w - 23/3],\
[1567, 1567, -1/3*w^3 - 2/3*w^2 - 4*w - 23/3],\
[1567, 1567, -1/3*w^3 - 2/3*w^2 + 7*w + 43/3],\
[1601, 1601, -2/3*w^3 + 2/3*w^2 + 5*w - 25/3],\
[1601, 1601, -1/3*w^3 + 1/3*w^2 + w - 23/3],\
[1607, 1607, -7/3*w^3 + 10/3*w^2 + 18*w - 29/3],\
[1607, 1607, -2*w^3 + 4*w^2 + 12*w - 19],\
[1607, 1607, -2/3*w^3 - 4/3*w^2 + 4*w + 11/3],\
[1607, 1607, -4/3*w^3 - 5/3*w^2 + 11*w + 43/3],\
[1657, 1657, -4/3*w^3 + 1/3*w^2 + 6*w - 5/3],\
[1657, 1657, 8/3*w^3 - 11/3*w^2 - 18*w + 43/3],\
[1697, 1697, 2/3*w^3 - 2/3*w^2 - 8*w - 11/3],\
[1697, 1697, -2/3*w^3 - 1/3*w^2 + 10*w + 41/3],\
[1697, 1697, -w^3 - 3*w^2 + 7*w + 17],\
[1697, 1697, -2/3*w^3 - 1/3*w^2 + 13*w + 59/3],\
[1721, 1721, -2/3*w^3 - 7/3*w^2 - 4*w - 19/3],\
[1721, 1721, -5/3*w^3 - 7/3*w^2 + 5*w + 11/3],\
[1753, 1753, -7/3*w^3 - 14/3*w^2 + 15*w + 85/3],\
[1753, 1753, -5/3*w^3 - 13/3*w^2 + 11*w + 71/3],\
[1753, 1753, 1/3*w^3 + 2/3*w^2 - 6*w - 25/3],\
[1753, 1753, 1/3*w^3 + 8/3*w^2 - 2*w - 43/3],\
[1759, 1759, -1/3*w^3 + 4/3*w^2 + 4*w - 29/3],\
[1759, 1759, -w^3 + 2*w^2 + 8*w - 3],\
[1777, 1777, -2/3*w^3 + 11/3*w^2 + 4*w - 31/3],\
[1777, 1777, -5/3*w^3 + 14/3*w^2 + 12*w - 67/3],\
[1777, 1777, -4/3*w^3 + 13/3*w^2 + 8*w - 71/3],\
[1777, 1777, w^3 - 4*w^2 - 8*w + 13],\
[1783, 1783, -5/3*w^3 + 2/3*w^2 + 13*w + 29/3],\
[1783, 1783, 4/3*w^3 - 7/3*w^2 - 5*w - 1/3],\
[1831, 1831, -1/3*w^3 - 5/3*w^2 + 25/3],\
[1831, 1831, 4/3*w^3 + 2/3*w^2 - 7*w - 25/3],\
[1831, 1831, -7/3*w^3 + 13/3*w^2 + 16*w - 47/3],\
[1831, 1831, 3*w^3 - 5*w^2 - 19*w + 15],\
[1847, 1847, -4/3*w^3 - 2/3*w^2 + 8*w + 31/3],\
[1847, 1847, -8/3*w^3 - 10/3*w^2 + 19*w + 89/3],\
[1889, 1889, -2/3*w^3 - 1/3*w^2 + 10*w + 53/3],\
[1889, 1889, 2/3*w^3 + 7/3*w^2 + 3*w + 13/3],\
[1889, 1889, 3*w^3 - 2*w^2 - 24*w + 1],\
[1889, 1889, -5/3*w^3 - 7/3*w^2 + 5*w + 17/3],\
[1913, 1913, 5/3*w^3 - 5/3*w^2 - 9*w + 1/3],\
[1913, 1913, -4/3*w^3 + 7/3*w^2 + 9*w - 47/3],\
[1951, 1951, -7/3*w^3 - 8/3*w^2 + 17*w + 67/3],\
[1951, 1951, 4/3*w^3 - 10/3*w^2 - 10*w + 59/3],\
[1993, 1993, -8/3*w^3 + 8/3*w^2 + 19*w - 19/3],\
[1993, 1993, 5/3*w^3 - 5/3*w^2 - 7*w + 13/3],\
[1999, 1999, 2/3*w^3 + 1/3*w^2 - 3*w - 41/3],\
[1999, 1999, -5/3*w^3 + 8/3*w^2 + 11*w + 5/3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 + x^2 - 19*x - 37
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, -1/3*e^2 + e + 13/3, e, e^2 - 2*e - 15, -1/3*e^2 + 13/3, 2/3*e^2 - 2*e - 29/3, -2/3*e^2 + 2*e + 35/3, -2/3*e^2 + 32/3, -2, -2*e + 2, -4/3*e^2 + 2*e + 46/3, -e^2 + 2*e + 19, 1/3*e^2 - 25/3, -1/3*e^2 - 11/3, -7/3*e^2 + 4*e + 103/3, -2/3*e^2 + 2*e + 14/3, 1/3*e^2 - 2*e - 1/3, 5/3*e^2 - 4*e - 83/3, 4/3*e^2 - 4*e - 64/3, -5/3*e^2 + 4*e + 83/3, e^2 - 15, 13/3*e^2 - 6*e - 166/3, -7/3*e^2 + 4*e + 100/3, 7/3*e^2 - 6*e - 91/3, e^2 - 4*e - 19, e^2 - 2*e - 17, -1/3*e^2 - 29/3, -2/3*e^2 + 3*e + 50/3, e^2 - e - 25, 4/3*e^2 + e - 76/3, 5*e^2 - 11*e - 69, -e^2 + 2*e + 23, 19/3*e^2 - 10*e - 241/3, -4/3*e^2 + 6*e + 55/3, -4/3*e^2 + 2*e + 19/3, e^2 - 4*e - 11, e^2 - 11, 17/3*e^2 - 10*e - 221/3, -19/3*e^2 + 10*e + 247/3, 3*e^2 - 10*e - 43, -11/3*e^2 + 2*e + 131/3, -8/3*e^2 + 6*e + 80/3, -4/3*e^2 + 2*e + 88/3, 4/3*e^2 + 2*e - 88/3, -10/3*e^2 + 10*e + 142/3, 13/3*e^2 - 8*e - 172/3, -e^2 - 2*e + 10, -5/3*e^2 + 68/3, 5*e^2 - 10*e - 74, 7/3*e^2 - 2*e - 82/3, -5/3*e^2 + 4*e + 68/3, 2/3*e^2 + 5*e - 26/3, 3*e^2 - 3*e - 39, 4/3*e^2 - 4*e - 70/3, -2*e^2 + 4*e + 24, -6*e, -4*e^2 + 6*e + 56, -2/3*e^2 - 2*e + 14/3, 1/3*e^2 - 2*e - 85/3, 1/3*e^2 + 5*e - 19/3, 7*e^2 - 14*e - 95, -4*e^2 + 5*e + 62, 1/3*e^2 - 2*e + 47/3, 1/3*e^2 - 4*e - 31/3, -14/3*e^2 + 10*e + 191/3, -2/3*e^2 + 2*e + 35/3, 7/3*e^2 - 5*e - 157/3, 5*e^2 - 6*e - 61, -5/3*e^2 - 2*e + 65/3, 4/3*e^2 - e + 26/3, 5*e^2 - 8*e - 53, -1/3*e^2 - 2*e + 19/3, -13/3*e^2 + 169/3, 7/3*e^2 - 2*e - 121/3, 5/3*e^2 - 2*e - 47/3, -13/3*e^2 + 10*e + 139/3, -8/3*e^2 + 4*e + 35/3, -4*e^2 + 12*e + 69, 4/3*e^2 + e - 118/3, 1/3*e^2 - e - 1/3, -5*e - 8, -7/3*e^2 + 5*e + 121/3, 2*e^2 + 4*e - 27, -10/3*e^2 + 8*e + 115/3, -2/3*e^2 + 6*e + 2/3, 4/3*e^2 + 4*e - 64/3, 6*e^2 - 10*e - 78, -8/3*e^2 + 4*e + 116/3, 7/3*e^2 - 2*e - 85/3, 3*e^2 - 6*e - 53, -13/3*e^2 + 8*e + 109/3, 3*e^2 - 4*e - 47, -3*e^2 + 5*e + 43, 11/3*e^2 - 8*e - 185/3, -8/3*e^2 + 5*e + 68/3, 5*e^2 - 4*e - 55, -13/3*e^2 + 8*e + 199/3, 2/3*e^2 - 3*e + 4/3, 5*e^2 - 7*e - 63, e^2 - 4*e + 5, 14/3*e^2 - 4*e - 164/3, 2*e^2, -4*e - 14, -4*e^2 + 54, -11/3*e^2 + 4*e + 95/3, -5*e^2 + 6*e + 59, 2/3*e^2 - 17/3, -22/3*e^2 + 8*e + 271/3, 5*e^2 - 71, 5*e^2 - 12*e - 79, e^2 - 8*e - 23, 23/3*e^2 - 18*e - 311/3, -5/3*e^2 - 4*e + 95/3, -7*e^2 + 10*e + 99, -28/3*e^2 + 16*e + 367/3, 1/3*e^2 + 2*e - 85/3, -11/3*e^2 + 6*e + 179/3, 11/3*e^2 - 4*e - 224/3, -1/3*e^2 + 2*e + 22/3, 4/3*e^2 - 6*e - 124/3, 4*e^2 - 10*e - 80, -8/3*e^2 + 3*e + 134/3, 19/3*e^2 - 9*e - 265/3, -e^2 - 4*e + 38, -28/3*e^2 + 12*e + 346/3, -e^2 + 6*e + 16, -12*e^2 + 20*e + 158, -2*e^2 + 12*e + 16, -4/3*e^2 - 4*e + 82/3, -11/3*e^2 + 9*e + 137/3, -4*e^2 + 3*e + 72, 4*e^2 - 11*e - 86, -7/3*e^2 + 3*e + 7/3, -2/3*e^2 + 7*e + 68/3, 5/3*e^2 - 5*e - 119/3, -e^2 - 2*e + 3, -17/3*e^2 + 2*e + 191/3, 9*e^2 - 12*e - 109, e^2 - 6*e - 15, -10/3*e^2 + 6*e + 121/3, -2/3*e^2 + 6*e - 55/3, -5/3*e^2 + 9*e + 107/3, -10/3*e^2 + 5*e + 28/3, 35/3*e^2 - 16*e - 401/3, 7*e^2 - 8*e - 79, -13/3*e^2 + 6*e + 193/3, 37/3*e^2 - 30*e - 559/3, -10*e^2 + 16*e + 146, 10*e^2 - 16*e - 114, -28/3*e^2 + 16*e + 415/3, 4*e - 35, -8*e^2 + 13*e + 122, -7/3*e^2 + 5*e + 133/3, -8*e^2 + 14*e + 100, -29/3*e^2 + 18*e + 359/3, 1/3*e^2 - 2*e - 31/3, -2*e^2 + 6*e + 22, -4*e^2 + 13*e + 42, -11/3*e^2 + 9*e + 113/3, -7*e^2 + 20*e + 120, e^2 - 10*e - 6, 11/3*e^2 - 8*e - 71/3, -22/3*e^2 + 14*e + 244/3, 7/3*e^2 + 6*e - 145/3, 6*e^2 - 18*e - 108, -34/3*e^2 + 20*e + 463/3, -25/3*e^2 + 15*e + 307/3, -17/3*e^2 + 2*e + 257/3, 28/3*e^2 - 17*e - 370/3, e^2 - 2*e + 27, -10/3*e^2 + 4*e + 148/3, 10/3*e^2 - 8*e - 28/3, 10/3*e^2 - 11*e - 148/3, 19/3*e^2 - 7*e - 289/3, -25/3*e^2 + 16*e + 319/3, -29/3*e^2 + 12*e + 371/3, -4/3*e^2 - 2*e + 40/3, 10*e, 10*e^2 - 21*e - 160, 10/3*e^2 + 3*e - 136/3, -11/3*e^2 + 7*e + 233/3, 3*e^2 - 13*e - 25, 5/3*e^2 + 6*e - 161/3, -23/3*e^2 + 12*e + 245/3, -6*e^2 + 18*e + 108, -10/3*e^2 + 10*e + 160/3, 16/3*e^2 - 5*e - 250/3, 5/3*e^2 + 4*e + 13/3, 7/3*e^2 - 17*e - 109/3, -9*e^2 + 16*e + 111, 3*e^2 - 10*e - 7, 5/3*e^2 + 4*e - 23/3, -6*e^2 - 2*e + 80, 38/3*e^2 - 18*e - 488/3, 5/3*e^2 - 6*e - 11/3, -5*e^2 + 8*e + 89, -1/3*e^2 - 2*e + 67/3, 37/3*e^2 - 14*e - 451/3, 25/3*e^2 - 10*e - 232/3, -9*e^2 + 20*e + 114, 2/3*e^2 + 12*e - 35/3, 14/3*e^2 - 12*e - 143/3, -5/3*e^2 + 10*e + 65/3, 35/3*e^2 - 18*e - 467/3, -e^2 - 10*e + 1, -47/3*e^2 + 26*e + 611/3, 14*e^2 - 20*e - 184, -8/3*e^2 + 12*e + 110/3, 16/3*e^2 - 12*e - 166/3, -32/3*e^2 + 20*e + 506/3, 5*e^2 - 8*e - 75, -3*e^2 + 4*e + 45, -2*e^2 + 7*e + 4, 17/3*e^2 - 21*e - 287/3, 19/3*e^2 - 2*e - 277/3, e^2 + 3, 17/3*e^2 - 12*e - 329/3, 5*e^2 - 8*e - 97, -10*e^2 + 14*e + 113, 26/3*e^2 - 10*e - 389/3, 4*e^2 - 5*e - 68, -11/3*e^2 + 3*e + 215/3, 14*e^2 - 20*e - 166, -14/3*e^2 + 8*e + 122/3, -22/3*e^2 + 8*e + 283/3, 26/3*e^2 - 12*e - 329/3, 13/3*e^2 - 223/3, -35/3*e^2 + 20*e + 545/3, 6*e^2 - 2*e - 96, -2*e^2 + 6*e + 36, 4/3*e^2 - 8*e - 46/3, -4*e^2 + 4*e + 46, -20/3*e^2 + 24*e + 314/3, 4*e - 30, 16/3*e^2 + 4*e - 208/3, 8*e^2 - 4*e - 112, -13/3*e^2 + 187/3, 23/3*e^2 - 12*e - 353/3, 14/3*e^2 - 6*e - 332/3, 2/3*e^2 - 6*e - 68/3, -19/3*e^2 + 8*e + 235/3, -11/3*e^2 + 2*e + 185/3, -40/3*e^2 + 20*e + 538/3, 8/3*e^2 - 4*e - 62/3, -1/3*e^2 - 5*e - 41/3, 4*e^2 - e - 70, 4/3*e^2 - e - 166/3, -13/3*e^2 + 15*e + 259/3, -6*e^2 + 22*e + 81, 26/3*e^2 - 22*e - 293/3, 14/3*e^2 - 15*e - 236/3, e^2 - 3*e - 55, -5*e^2 + 14*e + 27, 5*e^2 - 22*e - 79, -7/3*e^2 - 2*e + 256/3, 1/3*e^2 - 8*e + 38/3, -32/3*e^2 + 19*e + 506/3, -20/3*e^2 + 13*e + 224/3, e^2 - 7*e - 5, 23/3*e^2 - 17*e - 425/3, -9*e^2 + 12*e + 143, -13*e^2 + 30*e + 189, 6*e^2 - 10*e - 57, -26/3*e^2 + 16*e + 452/3, 10/3*e^2 - 4*e - 196/3, -2/3*e^2 + 2*e - 163/3, -6*e^2 + 8*e + 36, -14/3*e^2 + 12*e + 332/3, -4*e - 34, -10/3*e^2 + 12*e + 142/3, -16/3*e^2 + 20*e + 178/3, -2/3*e^2 + 98/3, -41/3*e^2 + 18*e + 491/3, 11*e^2 - 18*e - 149, -31/3*e^2 + 10*e + 466/3, 19/3*e^2 - 6*e - 88/3, -7/3*e^2 + 100/3, -25/3*e^2 + 8*e + 310/3, 10/3*e^2 - 7*e - 148/3, 13*e^2 - 23*e - 171, 28/3*e^2 - 15*e - 436/3, -6*e^2 + 17*e + 94, -25/3*e^2 + 9*e + 301/3, 5/3*e^2 - 7*e + 55/3, 11/3*e^2 - 3*e - 137/3, -14/3*e^2 + 5*e + 200/3, 6*e^2 - 8*e - 95, 22/3*e^2 - 6*e - 355/3, -10*e^2 + 18*e + 123, 6*e^2 - 20*e - 91, -4/3*e^2 + 14*e - 2/3, -4/3*e^2 + 2*e - 134/3, -20/3*e^2 + 4*e + 266/3, 22/3*e^2 - 4*e - 268/3, -5/3*e^2 + 14*e - 19/3, -5/3*e^2 + 59/3, 10/3*e^2 + 4*e - 178/3, 14/3*e^2 - 12*e - 326/3]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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