/*
  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, 4, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([17, 17, -w^3 + w^2 + 3*w - 1])

primes_array = [
[2, 2, w],\
[4, 2, -w^3 + 4*w + 1],\
[5, 5, w + 1],\
[13, 13, -w^2 + 3],\
[17, 17, -w^3 + w^2 + 3*w - 1],\
[19, 19, -w^3 + 3*w - 1],\
[23, 23, -w + 3],\
[31, 31, -w^2 - 2*w + 1],\
[41, 41, w^3 + w^2 - 5*w - 3],\
[43, 43, 2*w - 1],\
[53, 53, -w - 3],\
[53, 53, w^3 - w^2 - 4*w + 1],\
[61, 61, w^3 - 3*w - 5],\
[67, 67, w^3 + w^2 - 5*w - 1],\
[81, 3, -3],\
[83, 83, -w^3 + 5*w - 3],\
[89, 89, w^2 + 1],\
[97, 97, w^3 - w^2 - 5*w + 1],\
[97, 97, 3*w^3 - 5*w^2 - 14*w + 21],\
[97, 97, w^3 - 3*w - 3],\
[97, 97, w^3 - 7*w - 3],\
[103, 103, w^3 - w^2 - 3*w + 5],\
[107, 107, -2*w^3 + 2*w^2 + 8*w - 7],\
[109, 109, 3*w^3 - 3*w^2 - 13*w + 11],\
[113, 113, 2*w^3 - 2*w^2 - 10*w + 7],\
[113, 113, w^3 + w^2 - 5*w - 7],\
[121, 11, 2*w^2 - w - 9],\
[121, 11, 2*w^2 - w - 7],\
[125, 5, -w^3 + 2*w^2 + 3*w - 7],\
[131, 131, 4*w^3 - 5*w^2 - 18*w + 19],\
[137, 137, w^3 + w^2 - 6*w - 5],\
[137, 137, 3*w^3 - 13*w - 3],\
[139, 139, 3*w^3 - 5*w^2 - 13*w + 19],\
[149, 149, 2*w^3 - 9*w + 1],\
[163, 163, -2*w^2 + 11],\
[163, 163, -w^3 + w^2 + 6*w - 3],\
[163, 163, w^3 - 2*w^2 - 5*w + 5],\
[163, 163, 3*w^3 - 3*w^2 - 14*w + 15],\
[173, 173, 2*w^3 - 10*w + 1],\
[173, 173, 2*w^3 - 3*w^2 - 8*w + 13],\
[179, 179, 2*w^3 + w^2 - 8*w - 1],\
[181, 181, 2*w^3 - 4*w^2 - 9*w + 15],\
[193, 193, w^2 - 7],\
[199, 199, 2*w^2 - 5],\
[211, 211, -2*w^3 + 8*w - 3],\
[211, 211, -2*w^3 + w^2 + 8*w - 3],\
[223, 223, 3*w - 1],\
[223, 223, -2*w^3 - w^2 + 8*w + 5],\
[229, 229, -w^3 + 3*w^2 + 4*w - 11],\
[233, 233, -w^3 + 3*w^2 - 5],\
[233, 233, w^3 + 2*w^2 - 5*w - 3],\
[239, 239, 2*w^3 - 7*w - 1],\
[241, 241, w^3 - 2*w^2 - 3*w + 11],\
[251, 251, 2*w^2 - w - 5],\
[251, 251, 2*w^2 + 2*w - 7],\
[271, 271, -2*w^3 + 2*w^2 + 7*w - 9],\
[283, 283, 6*w^3 - 6*w^2 - 28*w + 23],\
[293, 293, 4*w^3 - 4*w^2 - 17*w + 17],\
[293, 293, 2*w^3 - 2*w^2 - 7*w + 5],\
[307, 307, 6*w^3 - 7*w^2 - 28*w + 29],\
[311, 311, w^3 - 2*w^2 - 3*w + 1],\
[311, 311, 2*w^2 - 2*w - 7],\
[311, 311, 2*w^3 - 4*w^2 - 8*w + 17],\
[311, 311, -w^3 + 3*w^2 + 4*w - 9],\
[347, 347, -w^3 - w^2 + 6*w - 1],\
[347, 347, -3*w^3 + 5*w^2 + 15*w - 21],\
[349, 349, 2*w^3 + 2*w^2 - 11*w - 7],\
[349, 349, 3*w^3 - w^2 - 15*w + 3],\
[353, 353, w^3 + w^2 - 3*w - 5],\
[353, 353, -4*w^3 + 16*w + 5],\
[361, 19, 6*w^3 - 8*w^2 - 27*w + 31],\
[367, 367, 3*w^3 - 3*w^2 - 13*w + 9],\
[367, 367, -2*w^2 - w + 9],\
[373, 373, -2*w^3 + w^2 + 10*w - 7],\
[379, 379, w^3 + 2*w^2 - 7*w - 7],\
[383, 383, -w^3 + 2*w^2 + 3*w - 9],\
[389, 389, -2*w^3 + 3*w^2 + 10*w - 9],\
[389, 389, w^2 - 2*w - 5],\
[397, 397, 2*w^3 - w^2 - 10*w - 1],\
[397, 397, w - 5],\
[409, 409, w^3 - w^2 - 6*w - 3],\
[419, 419, w^3 - 7*w + 1],\
[419, 419, -3*w^3 + 2*w^2 + 13*w - 11],\
[421, 421, w^3 + w^2 - 4*w + 3],\
[421, 421, 3*w^3 + w^2 - 14*w - 3],\
[431, 431, w^2 + 2*w - 7],\
[449, 449, w^3 + w^2 - 3*w - 9],\
[457, 457, -2*w^3 + w^2 + 8*w - 9],\
[457, 457, 2*w^3 - 2*w^2 - 7*w + 11],\
[463, 463, -w^3 - w^2 + 8*w - 3],\
[463, 463, 3*w^3 - 3*w^2 - 15*w + 13],\
[487, 487, 2*w^3 - 2*w^2 - 7*w + 1],\
[487, 487, w^2 - 2*w - 7],\
[499, 499, 3*w^3 - 3*w^2 - 12*w + 11],\
[503, 503, -3*w^3 + w^2 + 13*w + 5],\
[509, 509, -w^3 - w^2 + 7*w + 5],\
[521, 521, 2*w^3 + 2*w^2 - 9*w - 5],\
[523, 523, -2*w^2 - 1],\
[541, 541, 2*w^3 - 2*w^2 - 8*w + 3],\
[541, 541, w^3 - 2*w^2 - 7*w + 5],\
[547, 547, 3*w^3 - 4*w^2 - 13*w + 13],\
[563, 563, w^3 + 3*w^2 - 3*w - 11],\
[571, 571, -w^3 + w - 3],\
[571, 571, 2*w^3 + w^2 - 10*w - 1],\
[587, 587, 3*w^3 - 15*w + 1],\
[587, 587, 3*w^3 - w^2 - 14*w - 1],\
[593, 593, 3*w^3 - 2*w^2 - 15*w + 7],\
[593, 593, -2*w^3 + w^2 + 6*w - 1],\
[599, 599, -w^3 + w^2 + 4*w + 3],\
[599, 599, 2*w^3 + 2*w^2 - 11*w - 3],\
[607, 607, -w - 5],\
[607, 607, -w^3 + 4*w^2 + 5*w - 19],\
[613, 613, 2*w^3 + w^2 - 8*w + 1],\
[617, 617, 3*w^3 - w^2 - 12*w + 5],\
[617, 617, -2*w^3 + 12*w - 3],\
[619, 619, w^2 - 4*w - 3],\
[631, 631, -3*w^2 - 4*w + 7],\
[631, 631, -6*w^3 + 4*w^2 + 27*w - 15],\
[643, 643, -w^3 + 2*w^2 + 7*w - 7],\
[643, 643, 3*w^2 - 11],\
[647, 647, 4*w^3 - 4*w^2 - 17*w + 15],\
[653, 653, -2*w^3 - 2*w^2 + 10*w + 7],\
[653, 653, w^3 - 3*w^2 - 6*w + 7],\
[659, 659, -3*w^3 + 2*w^2 + 15*w - 11],\
[673, 673, w^3 + w^2 - 3*w - 7],\
[677, 677, w^3 - 3*w^2 - 3*w + 13],\
[677, 677, 2*w^3 - 2*w^2 - 11*w + 9],\
[709, 709, w^3 + w^2 - 2*w - 5],\
[751, 751, w^3 - 5*w^2 - 4*w + 21],\
[757, 757, -2*w^3 + 2*w^2 + 12*w - 1],\
[757, 757, -w^3 + w^2 + 2*w - 7],\
[761, 761, 4*w^3 - w^2 - 20*w + 3],\
[787, 787, 4*w + 3],\
[797, 797, 5*w^3 - 4*w^2 - 23*w + 17],\
[809, 809, -2*w^3 + 9*w - 5],\
[821, 821, 3*w^2 - 2*w - 9],\
[823, 823, -w^2 - 3],\
[863, 863, -w^3 + w^2 + 5*w - 9],\
[881, 881, -4*w^3 + 5*w^2 + 16*w - 21],\
[881, 881, -5*w^3 + 4*w^2 + 23*w - 13],\
[887, 887, 2*w^3 - 2*w^2 - 11*w + 7],\
[907, 907, -3*w^3 + 2*w^2 + 13*w - 3],\
[907, 907, 2*w^2 + 2*w - 9],\
[911, 911, -3*w^3 + w^2 + 15*w + 3],\
[919, 919, 3*w^2 - 7],\
[919, 919, 2*w^3 - 7*w + 7],\
[937, 937, 4*w^3 - 4*w^2 - 18*w + 13],\
[937, 937, 3*w^3 - w^2 - 13*w + 7],\
[977, 977, -4*w^3 + 2*w^2 + 19*w - 9],\
[983, 983, -w^3 + 4*w^2 + 5*w - 13],\
[983, 983, -2*w^3 + 2*w^2 + 9*w - 3],\
[991, 991, -w^3 + 4*w^2 + 3*w - 19],\
[991, 991, 2*w - 7],\
[1019, 1019, -5*w^3 + 5*w^2 + 23*w - 23],\
[1031, 1031, -2*w^3 + 4*w + 3],\
[1039, 1039, -3*w^3 + w^2 + 12*w - 3],\
[1051, 1051, -4*w^3 - 2*w^2 + 23*w + 9],\
[1051, 1051, 5*w^3 - 5*w^2 - 21*w + 21],\
[1051, 1051, 4*w^3 - 6*w^2 - 20*w + 23],\
[1051, 1051, 4*w^2 + 2*w - 11],\
[1061, 1061, -w^3 + 3*w^2 + 8*w - 7],\
[1061, 1061, 5*w^3 - 3*w^2 - 24*w + 13],\
[1063, 1063, -w^3 - w^2 + 8*w + 5],\
[1069, 1069, 2*w^2 - 4*w - 5],\
[1087, 1087, 2*w^3 - 2*w^2 - 10*w + 3],\
[1091, 1091, 3*w^3 - 17*w + 3],\
[1091, 1091, 3*w^3 + w^2 - 12*w - 7],\
[1093, 1093, 6*w^3 - 8*w^2 - 26*w + 29],\
[1093, 1093, 6*w^3 - 6*w^2 - 26*w + 25],\
[1093, 1093, -w^3 + 3*w^2 + 6*w - 15],\
[1093, 1093, 2*w^3 - 4*w^2 - 6*w + 13],\
[1117, 1117, 2*w^3 + w^2 - 12*w - 7],\
[1129, 1129, -w^3 + 3*w^2 + 7*w - 13],\
[1129, 1129, 2*w^2 - 3*w + 3],\
[1163, 1163, 2*w^3 + 3*w^2 - 10*w - 13],\
[1163, 1163, -2*w^3 + 2*w^2 + 6*w - 9],\
[1171, 1171, 3*w^2 - 2*w - 7],\
[1171, 1171, -3*w^3 + 11*w + 1],\
[1181, 1181, -5*w^3 + 6*w^2 + 23*w - 29],\
[1187, 1187, 4*w^3 - 2*w^2 - 20*w + 5],\
[1187, 1187, 2*w^3 - 3*w^2 - 10*w + 17],\
[1201, 1201, 5*w^3 - 3*w^2 - 22*w + 9],\
[1213, 1213, 2*w^3 + 2*w^2 - 13*w - 7],\
[1213, 1213, 3*w^3 - 11*w + 1],\
[1217, 1217, -2*w^3 + 4*w^2 + 11*w - 11],\
[1223, 1223, 2*w^3 - w^2 - 12*w + 7],\
[1223, 1223, w^3 + 2*w^2 - 5*w - 13],\
[1229, 1229, 2*w^3 - 6*w - 5],\
[1229, 1229, 3*w^3 + 2*w^2 - 11*w - 7],\
[1237, 1237, -w^3 + w^2 + w - 5],\
[1237, 1237, -2*w^3 + 10*w - 5],\
[1249, 1249, -3*w^3 + 3*w^2 + 13*w - 17],\
[1249, 1249, 2*w^3 - 12*w + 1],\
[1249, 1249, 4*w^3 - 5*w^2 - 18*w + 17],\
[1249, 1249, 4*w^3 - 3*w^2 - 18*w + 15],\
[1277, 1277, -3*w^3 + 2*w^2 + 11*w - 3],\
[1279, 1279, w^3 + w^2 - 3*w - 11],\
[1279, 1279, w^2 - 6*w - 1],\
[1279, 1279, -3*w^3 + 4*w^2 + 11*w - 9],\
[1279, 1279, 2*w^3 - 11*w + 5],\
[1283, 1283, 2*w^3 + 2*w^2 - 9*w - 1],\
[1283, 1283, -2*w^3 + 13*w - 5],\
[1291, 1291, 3*w^3 - 5*w^2 - 16*w + 19],\
[1291, 1291, -2*w^3 + 13*w + 3],\
[1301, 1301, -w^3 + 3*w^2 + 2*w - 11],\
[1301, 1301, w^3 + 3*w^2 - 7*w - 5],\
[1319, 1319, 2*w^3 - 2*w^2 - 8*w + 13],\
[1321, 1321, w^3 + 2*w^2 - 7*w - 9],\
[1321, 1321, -6*w^3 + 8*w^2 + 28*w - 37],\
[1361, 1361, -w^3 + w + 7],\
[1361, 1361, -4*w^3 + 2*w^2 + 17*w - 5],\
[1367, 1367, -w^3 + w^2 + 8*w - 1],\
[1381, 1381, 3*w^3 - w^2 - 11*w + 5],\
[1427, 1427, w^3 + 3*w^2 - 5*w - 5],\
[1427, 1427, -w^3 + 4*w^2 + 3*w - 13],\
[1427, 1427, 6*w^3 - 7*w^2 - 26*w + 33],\
[1427, 1427, -4*w^3 + w^2 + 18*w + 7],\
[1429, 1429, 3*w^3 - 3*w^2 - 17*w + 17],\
[1433, 1433, -w^3 + 5*w - 7],\
[1451, 1451, -3*w^3 + w^2 + 15*w - 7],\
[1451, 1451, -w^3 + 5*w^2 + 5*w - 19],\
[1459, 1459, -5*w + 9],\
[1471, 1471, -4*w^3 + 8*w^2 + 19*w - 29],\
[1483, 1483, w^3 + 3*w^2 - 6*w - 5],\
[1483, 1483, -3*w^3 - w^2 + 12*w - 1],\
[1487, 1487, -2*w^3 + 2*w^2 + 11*w - 15],\
[1489, 1489, 2*w^3 - 5*w^2 - 10*w + 23],\
[1493, 1493, 3*w^3 - 5*w^2 - 12*w + 25],\
[1493, 1493, 3*w^3 - 6*w^2 - 15*w + 25],\
[1499, 1499, 2*w^2 + 2*w - 13],\
[1499, 1499, w^3 + 3*w^2 - 5*w - 11],\
[1523, 1523, -w^3 + 3*w^2 + 5*w - 5],\
[1523, 1523, 4*w^3 - w^2 - 14*w + 9],\
[1523, 1523, -3*w^3 + w^2 + 14*w - 7],\
[1523, 1523, -2*w^3 + 3*w^2 + 6*w - 11],\
[1543, 1543, -w^3 + 3*w^2 + w - 9],\
[1543, 1543, -4*w^3 + 7*w^2 + 20*w - 29],\
[1559, 1559, 2*w^2 - 13],\
[1559, 1559, -4*w^2 - w + 17],\
[1571, 1571, 5*w - 3],\
[1579, 1579, 2*w^2 + 2*w - 11],\
[1579, 1579, w^3 + w^2 - 7*w - 11],\
[1583, 1583, 2*w^3 - 3*w^2 - 10*w + 7],\
[1597, 1597, -3*w^3 + w^2 + 7*w + 1],\
[1601, 1601, -5*w^3 + 3*w^2 + 23*w - 13],\
[1601, 1601, 5*w^3 - w^2 - 20*w + 9],\
[1607, 1607, 2*w^3 - w^2 - 10*w - 5],\
[1609, 1609, 3*w^3 - 8*w^2 - 13*w + 37],\
[1609, 1609, 3*w^3 - 2*w^2 - 11*w + 7],\
[1613, 1613, 2*w^3 - 4*w^2 - 12*w + 13],\
[1621, 1621, 5*w - 1],\
[1621, 1621, -2*w^3 + 5*w^2 + 8*w - 17],\
[1627, 1627, 3*w^3 + w^2 - 14*w - 1],\
[1627, 1627, -2*w^3 + 2*w^2 + 9*w + 1],\
[1637, 1637, 7*w^3 - 12*w^2 - 31*w + 49],\
[1657, 1657, -2*w^3 + 2*w^2 + 9*w - 1],\
[1657, 1657, -5*w^3 + w^2 + 21*w - 7],\
[1663, 1663, 9*w^3 - 11*w^2 - 39*w + 45],\
[1667, 1667, -4*w^3 + 3*w^2 + 16*w - 7],\
[1669, 1669, -w^3 - w^2 - w - 3],\
[1693, 1693, -3*w^3 + w^2 + 11*w - 1],\
[1693, 1693, w^3 + 2*w^2 - 11*w - 5],\
[1709, 1709, 3*w^3 + 3*w^2 - 16*w - 5],\
[1721, 1721, w^3 - 4*w^2 - 3*w + 11],\
[1747, 1747, 2*w^3 - 2*w^2 - 11*w + 1],\
[1747, 1747, w^3 + 3*w^2 - 4*w - 7],\
[1753, 1753, -6*w^3 + 6*w^2 + 28*w - 21],\
[1787, 1787, w^3 + 3*w^2 - 7*w - 13],\
[1787, 1787, -w^3 + w^2 + 8*w - 5],\
[1789, 1789, 2*w^3 + 3*w^2 - 12*w - 7],\
[1789, 1789, 4*w^2 - 15],\
[1801, 1801, w^3 + 3*w^2 - 7*w - 7],\
[1811, 1811, -3*w^3 + 2*w^2 + 11*w - 5],\
[1823, 1823, -w^3 + 3*w^2 + 6*w - 5],\
[1831, 1831, 5*w^3 - 4*w^2 - 21*w + 17],\
[1867, 1867, 3*w^3 - w^2 - 10*w + 5],\
[1871, 1871, 2*w^3 + 2*w^2 - 6*w - 7],\
[1873, 1873, -3*w^3 + 3*w^2 + 10*w - 7],\
[1879, 1879, 2*w^3 - 4*w^2 - 7*w + 17],\
[1889, 1889, 3*w^3 - 17*w - 3],\
[1907, 1907, -4*w^3 - 2*w^2 + 19*w + 5],\
[1907, 1907, 6*w^3 - 8*w^2 - 29*w + 33],\
[1913, 1913, -w^3 + w^2 + 8*w - 3],\
[1913, 1913, w^3 + 2*w^2 - 9*w + 3],\
[1933, 1933, w^2 + 4*w - 9],\
[1933, 1933, 6*w^3 - 6*w^2 - 26*w + 23],\
[1951, 1951, w^3 + 2*w^2 - 3*w - 11],\
[1951, 1951, -2*w^3 + 2*w^2 + 10*w - 1],\
[1973, 1973, -5*w^3 + 7*w^2 + 23*w - 25],\
[1979, 1979, -3*w^3 + 5*w^2 + 11*w - 19],\
[1987, 1987, 2*w^3 - 2*w^2 - 6*w + 11],\
[1993, 1993, -w^3 + 3*w - 7],\
[1993, 1993, w^3 + w^2 - 2*w - 9],\
[1997, 1997, 5*w^3 - w^2 - 19*w - 5],\
[1999, 1999, -3*w^3 + 3*w^2 + 15*w - 19],\
[2011, 2011, 5*w^3 - 6*w^2 - 23*w + 21],\
[2039, 2039, -2*w^3 + 4*w^2 + 8*w - 9],\
[2039, 2039, -3*w^3 + 4*w^2 + 11*w - 17],\
[2053, 2053, -2*w^3 + 3*w^2 + 8*w - 5],\
[2069, 2069, 5*w^3 - 6*w^2 - 21*w + 19],\
[2069, 2069, w^3 - 2*w^2 - 5*w - 3],\
[2069, 2069, 5*w^3 - 10*w^2 - 23*w + 43],\
[2069, 2069, 3*w^3 - 2*w^2 - 13*w + 1],\
[2081, 2081, 7*w^3 - 10*w^2 - 31*w + 37],\
[2081, 2081, -3*w^3 + 2*w^2 + 11*w - 15],\
[2099, 2099, -4*w^3 + 5*w^2 + 14*w - 13],\
[2111, 2111, w^3 + 3*w^2 - 6*w - 9],\
[2129, 2129, 4*w^3 - 4*w^2 - 20*w + 15],\
[2129, 2129, 4*w^2 - 3*w - 15],\
[2141, 2141, -w^3 + w^2 + w - 7],\
[2153, 2153, 7*w^3 - 11*w^2 - 30*w + 45],\
[2153, 2153, -4*w^3 + 8*w^2 + 17*w - 37],\
[2153, 2153, 4*w^3 + w^2 - 14*w - 3],\
[2153, 2153, -3*w^3 + 4*w^2 + 13*w - 11],\
[2161, 2161, 3*w^3 - 7*w^2 - 11*w + 27],\
[2179, 2179, w^3 + 3*w^2 - 5*w - 9],\
[2179, 2179, -2*w^3 + 14*w - 7],\
[2197, 13, w^3 + 3*w^2 - 6*w - 7],\
[2203, 2203, 6*w^3 - 9*w^2 - 28*w + 33],\
[2203, 2203, 3*w^3 + 3*w^2 - 13*w - 7],\
[2207, 2207, -4*w^3 + 16*w - 5],\
[2221, 2221, 5*w^3 - 3*w^2 - 21*w + 13],\
[2221, 2221, -3*w^3 + 3*w^2 + 16*w - 13],\
[2237, 2237, w^3 - w^2 - 3*w - 5],\
[2239, 2239, 3*w^3 - w^2 - 16*w + 9],\
[2239, 2239, -4*w^3 + 8*w^2 + 18*w - 31],\
[2243, 2243, -2*w^3 + 2*w^2 + 12*w - 5],\
[2251, 2251, 3*w^3 + 3*w^2 - 14*w - 7],\
[2251, 2251, 4*w^3 + 2*w^2 - 15*w - 1],\
[2267, 2267, w^3 - 5*w^2 + 15],\
[2269, 2269, 3*w^3 - 3*w^2 - 11*w + 3],\
[2273, 2273, -w^3 + 5*w^2 + 2*w - 17],\
[2281, 2281, -3*w^3 - w^2 + 11*w + 7],\
[2287, 2287, -3*w^3 + 4*w^2 + 17*w - 19],\
[2287, 2287, 4*w^2 + w - 11],\
[2287, 2287, w^3 - 5*w - 7],\
[2287, 2287, -5*w^3 + 21*w - 3],\
[2293, 2293, w^3 + w^2 - 8*w - 7],\
[2293, 2293, -2*w^3 - 2*w^2 + 7*w + 9],\
[2293, 2293, -4*w^3 + 6*w^2 + 16*w - 25],\
[2293, 2293, -5*w^3 + w^2 + 20*w - 7],\
[2309, 2309, 2*w^3 + 2*w^2 - 12*w - 1],\
[2311, 2311, -2*w^3 - w^2 + 10*w - 3],\
[2333, 2333, -5*w^3 + 7*w^2 + 25*w - 29],\
[2341, 2341, 6*w^3 - 7*w^2 - 24*w + 27],\
[2341, 2341, -w^3 + 5*w^2 + 6*w - 11],\
[2347, 2347, -5*w^3 + 7*w^2 + 23*w - 33],\
[2347, 2347, 4*w^3 - 2*w^2 - 16*w + 3],\
[2347, 2347, -6*w^3 + 8*w^2 + 26*w - 37],\
[2347, 2347, -w^3 - w^2 + 4*w - 5],\
[2351, 2351, -3*w^2 - 2*w + 13],\
[2357, 2357, 6*w^3 - 4*w^2 - 29*w + 15],\
[2357, 2357, 3*w^3 - 4*w^2 - 13*w + 21],\
[2371, 2371, 3*w^3 - 13*w + 9],\
[2371, 2371, -7*w^3 + 29*w + 9],\
[2377, 2377, w^3 - 3*w^2 - 7*w + 15],\
[2377, 2377, 4*w^3 - 6*w^2 - 21*w + 25],\
[2399, 2399, -3*w^3 + w^2 + 10*w - 1],\
[2401, 7, -7],\
[2411, 2411, 4*w^3 + w^2 - 16*w + 1],\
[2417, 2417, 3*w^3 + 2*w^2 - 15*w - 3],\
[2423, 2423, 5*w^3 + w^2 - 20*w - 3],\
[2437, 2437, -2*w^3 + 3*w^2 + 12*w - 11],\
[2437, 2437, 7*w^3 - 13*w^2 - 32*w + 55],\
[2437, 2437, -3*w^3 + w^2 + 14*w - 9],\
[2437, 2437, 3*w^3 - 3*w^2 - 9*w + 5],\
[2459, 2459, 5*w^2 - 2*w - 23],\
[2459, 2459, 5*w^3 - 4*w^2 - 23*w + 19],\
[2467, 2467, 4*w^3 + 4*w^2 - 15*w - 11],\
[2473, 2473, -w - 7],\
[2503, 2503, -4*w^3 + w^2 + 16*w - 11],\
[2521, 2521, 3*w^3 - 7*w^2 - 16*w + 27],\
[2531, 2531, -2*w^2 + w - 3],\
[2539, 2539, w^3 - 3*w^2 - 2*w + 13],\
[2543, 2543, -w^3 + 3*w^2 + 5*w - 3],\
[2549, 2549, 3*w^3 - 9*w - 5],\
[2549, 2549, -3*w^3 + w^2 + 10*w - 3],\
[2551, 2551, 2*w^3 - 4*w^2 - 9*w + 21],\
[2557, 2557, 3*w^3 - 4*w^2 - 15*w + 11],\
[2579, 2579, 6*w^3 - 8*w^2 - 27*w + 29],\
[2591, 2591, 2*w^3 - 6*w^2 - 8*w + 23],\
[2609, 2609, 6*w^3 - 5*w^2 - 26*w + 17],\
[2617, 2617, 7*w^3 - 7*w^2 - 32*w + 31],\
[2633, 2633, -5*w^3 + 3*w^2 + 22*w - 15],\
[2659, 2659, -6*w^3 - w^2 + 26*w + 13],\
[2659, 2659, w^3 + 3*w^2 - 7*w - 17],\
[2663, 2663, 2*w^3 - 2*w^2 - 12*w - 5],\
[2683, 2683, 4*w^3 - 3*w^2 - 22*w + 21],\
[2683, 2683, -w^3 + 3*w^2 + 5*w - 1],\
[2687, 2687, -w^3 - w^2 + 3*w - 5],\
[2687, 2687, -2*w^3 - w^2 + 12*w - 3],\
[2687, 2687, -3*w^3 + 5*w^2 + 15*w - 15],\
[2687, 2687, 3*w^3 + 3*w^2 - 16*w - 9],\
[2693, 2693, 2*w^3 + 3*w^2 - 10*w - 7],\
[2711, 2711, 6*w^3 - 8*w^2 - 28*w + 29],\
[2719, 2719, w^3 - 5*w^2 + w + 13],\
[2729, 2729, 4*w^3 - 3*w^2 - 16*w + 9],\
[2729, 2729, 2*w^2 + 5*w - 5],\
[2741, 2741, 3*w^3 + w^2 - 12*w + 3],\
[2741, 2741, w^3 - 9*w + 3],\
[2749, 2749, w^3 - w^2 - 4*w - 5],\
[2749, 2749, -2*w^3 + 13*w - 3],\
[2789, 2789, -3*w^3 + 4*w^2 + 11*w - 19],\
[2789, 2789, 3*w^3 - w^2 - 17*w + 11],\
[2791, 2791, 2*w^3 + 2*w^2 - 9*w - 15],\
[2791, 2791, w^3 - 9*w + 1],\
[2791, 2791, 7*w^3 - 11*w^2 - 33*w + 47],\
[2791, 2791, 3*w^3 - 17*w - 1],\
[2801, 2801, 2*w^2 - 4*w - 7],\
[2801, 2801, 3*w^3 - w^2 - 7*w + 1],\
[2803, 2803, -w^3 + 2*w^2 - w - 5],\
[2809, 53, -2*w^3 + 4*w^2 + 7*w - 7],\
[2819, 2819, 4*w^2 - 2*w - 13],\
[2833, 2833, 2*w^3 + w^2 - 6*w - 7],\
[2843, 2843, 6*w^3 - 8*w^2 - 25*w + 35],\
[2843, 2843, 4*w^3 - 2*w^2 - 19*w + 11],\
[2861, 2861, 8*w^3 - 11*w^2 - 36*w + 49],\
[2879, 2879, w^3 - w^2 - 5*w - 5],\
[2879, 2879, w^3 + w^2 - w - 13],\
[2887, 2887, 7*w^3 + 2*w^2 - 35*w - 9],\
[2887, 2887, -4*w^3 + 5*w^2 + 20*w - 15],\
[2939, 2939, 4*w^3 - 2*w^2 - 18*w + 1],\
[2939, 2939, -w^3 + w^2 + 9*w - 7],\
[2953, 2953, -5*w^3 + 9*w^2 + 22*w - 33],\
[2963, 2963, w^3 - 5*w^2 - 5*w + 17],\
[3001, 3001, 4*w^2 + w - 19],\
[3037, 3037, w^3 + w^2 - 7],\
[3037, 3037, w^3 + 4*w^2 - 9*w - 9],\
[3041, 3041, -5*w^3 + 7*w^2 + 22*w - 33],\
[3041, 3041, -4*w^3 - w^2 + 16*w + 9],\
[3041, 3041, -2*w^3 - 4*w^2 + 14*w + 13],\
[3041, 3041, -2*w^3 + 3*w^2 + 6*w - 13],\
[3049, 3049, -w^3 + 3*w^2 + 7*w - 3],\
[3067, 3067, w^3 + w^2 - 4*w - 11],\
[3067, 3067, -3*w^3 + 6*w^2 + 13*w - 29],\
[3079, 3079, 2*w^3 + 5*w^2 - 6*w - 17],\
[3079, 3079, 2*w^3 + 3*w^2 - 10*w - 9],\
[3079, 3079, w^3 + 3*w^2 - 7*w - 15],\
[3079, 3079, -5*w^3 + w^2 + 21*w + 9],\
[3089, 3089, -4*w^3 + w^2 + 16*w - 3],\
[3089, 3089, 5*w^3 - 2*w^2 - 25*w + 5],\
[3109, 3109, -w^2 - 5],\
[3109, 3109, w^2 - 2*w - 11],\
[3119, 3119, 5*w^3 - 9*w^2 - 24*w + 31],\
[3119, 3119, 2*w^3 - 4*w - 5],\
[3137, 3137, -w^3 + 3*w^2 + 2*w - 15],\
[3167, 3167, -2*w^3 - 2*w^2 + 15*w + 7],\
[3167, 3167, 4*w^3 - 4*w^2 - 21*w + 19],\
[3169, 3169, -5*w^2 - 4*w + 9],\
[3181, 3181, -3*w^3 + 2*w^2 + 9*w - 3],\
[3187, 3187, -4*w^3 + 2*w^2 + 16*w - 7],\
[3187, 3187, 2*w^3 + 2*w^2 - 10*w + 1],\
[3191, 3191, -5*w^3 + 4*w^2 + 23*w - 23],\
[3191, 3191, 5*w^3 + w^2 - 18*w - 5],\
[3203, 3203, -2*w^3 + 6*w^2 + 10*w - 27],\
[3229, 3229, 4*w^3 + w^2 - 18*w - 1],\
[3229, 3229, 7*w^3 - 5*w^2 - 31*w + 17],\
[3257, 3257, 5*w^3 - 11*w^2 - 23*w + 47],\
[3271, 3271, 6*w^3 - 11*w^2 - 30*w + 43],\
[3271, 3271, 6*w - 1],\
[3271, 3271, -5*w^3 - w^2 + 21*w + 11],\
[3271, 3271, 2*w^3 - 13*w + 1],\
[3299, 3299, -w^3 + 3*w^2 + 8*w - 15],\
[3299, 3299, -2*w^2 + 6*w + 5],\
[3301, 3301, -8*w^3 - w^2 + 34*w + 13],\
[3307, 3307, -w^3 + 2*w^2 + 9*w - 3],\
[3307, 3307, -8*w^3 + 6*w^2 + 35*w - 25],\
[3313, 3313, 6*w^3 - 6*w^2 - 25*w + 31],\
[3323, 3323, -6*w^3 + w^2 + 26*w - 3],\
[3323, 3323, -2*w^2 - 3*w + 15],\
[3347, 3347, 2*w^3 - 6*w^2 - 5*w + 17],\
[3373, 3373, 4*w^3 - 4*w^2 - 18*w + 11],\
[3373, 3373, 4*w^3 - 6*w^2 - 20*w + 19],\
[3389, 3389, 4*w^2 - 11],\
[3389, 3389, 3*w^3 - 7*w^2 - 15*w + 21],\
[3391, 3391, 4*w^3 - 15*w + 1],\
[3391, 3391, 4*w^3 - 7*w^2 - 16*w + 29],\
[3433, 3433, -5*w^2 + 2*w + 19],\
[3433, 3433, -w^3 + 4*w^2 + 7*w - 17],\
[3449, 3449, 2*w^2 - 3*w - 11],\
[3449, 3449, 3*w^3 - w^2 - 15*w - 7],\
[3463, 3463, 4*w^2 - w - 13],\
[3463, 3463, -5*w^3 - 3*w^2 + 23*w + 7],\
[3467, 3467, 3*w^3 + 2*w^2 - 13*w - 1],\
[3469, 3469, 4*w^2 - 3*w - 9],\
[3491, 3491, w^3 - 5*w^2 - 7*w + 11],\
[3499, 3499, 5*w^3 - 2*w^2 - 23*w + 1],\
[3499, 3499, -8*w^3 + 9*w^2 + 34*w - 37],\
[3511, 3511, w^3 - 5*w^2 - 8*w + 11],\
[3511, 3511, -2*w^3 + 6*w^2 + 4*w - 13],\
[3517, 3517, w^3 + 4*w^2 - 3*w - 9],\
[3527, 3527, w^2 - 4*w - 7],\
[3529, 3529, -8*w^3 + 10*w^2 + 38*w - 39],\
[3529, 3529, 2*w^3 - 5*w - 7],\
[3539, 3539, 6*w^3 - 4*w^2 - 28*w + 11],\
[3539, 3539, 4*w^2 - w - 9],\
[3541, 3541, 6*w^3 - 23*w - 9],\
[3547, 3547, -3*w^3 - 2*w^2 + 11*w + 9],\
[3557, 3557, -3*w^3 + 2*w^2 + 15*w + 3],\
[3571, 3571, 3*w^3 - w^2 - 15*w + 11],\
[3581, 3581, 6*w^3 - 2*w^2 - 28*w + 1],\
[3593, 3593, 5*w^3 - w^2 - 24*w + 5],\
[3593, 3593, -2*w^3 + 3*w^2 + 4*w - 9],\
[3607, 3607, 3*w^3 - 4*w^2 - 17*w + 11],\
[3607, 3607, -w^3 - 5*w^2 + 6*w + 21],\
[3617, 3617, 2*w^3 + 4*w^2 - 7*w - 7],\
[3617, 3617, 2*w^2 + 4*w - 11],\
[3623, 3623, -5*w^3 + 4*w^2 + 25*w - 17],\
[3631, 3631, 8*w^3 - 14*w^2 - 36*w + 57],\
[3631, 3631, -2*w^3 + 4*w^2 + 13*w - 7],\
[3637, 3637, 6*w^3 - 3*w^2 - 26*w + 7],\
[3637, 3637, w^3 + 2*w^2 - w - 9],\
[3659, 3659, 4*w^3 - 4*w^2 - 14*w + 13],\
[3677, 3677, -w^3 + w^2 + 3*w - 11],\
[3691, 3691, -4*w^3 + 5*w^2 + 14*w - 19],\
[3697, 3697, -4*w^3 + 18*w - 3],\
[3719, 3719, w^3 + 5*w^2 - 2*w - 9],\
[3733, 3733, 3*w^2 + 2*w - 15],\
[3733, 3733, -5*w^3 + 5*w^2 + 22*w - 15],\
[3767, 3767, w^3 + w^2 - w - 9],\
[3767, 3767, -3*w^3 + 3*w^2 + 13*w - 5],\
[3793, 3793, 2*w^2 + 3*w - 13],\
[3793, 3793, 5*w^3 - 3*w^2 - 25*w + 9],\
[3797, 3797, -9*w^3 - w^2 + 39*w + 15],\
[3797, 3797, 4*w^3 - 6*w^2 - 21*w + 21],\
[3803, 3803, -6*w^3 + 4*w^2 + 26*w - 15],\
[3803, 3803, 2*w - 9],\
[3823, 3823, -5*w^3 + 10*w^2 + 23*w - 39],\
[3833, 3833, w^3 + w^2 - 5*w - 11],\
[3847, 3847, 3*w^3 - 5*w^2 - 11*w + 21],\
[3851, 3851, 4*w^2 - 2*w - 9],\
[3851, 3851, -2*w^3 + 6*w^2 + 9*w - 21],\
[3853, 3853, -w^3 + w^2 + 7*w - 13],\
[3863, 3863, 4*w^3 - 6*w^2 - 18*w + 19],\
[3881, 3881, -4*w^3 + 14*w + 7],\
[3889, 3889, -3*w^3 + w^2 + 12*w - 13],\
[3889, 3889, -4*w^3 + 2*w^2 + 21*w - 9],\
[3889, 3889, 5*w^3 - 6*w^2 - 25*w + 25],\
[3889, 3889, 3*w^3 - 7*w^2 - 12*w + 21],\
[3907, 3907, -3*w^3 + 9*w^2 + 14*w - 39],\
[3917, 3917, 3*w^3 + 3*w^2 - 13*w - 17],\
[3917, 3917, 9*w^3 - 11*w^2 - 40*w + 41],\
[3917, 3917, -w^3 + w^2 + 4*w - 11],\
[3917, 3917, 3*w^3 - 3*w^2 - 11*w - 1],\
[3923, 3923, -2*w^3 + 4*w^2 + 12*w - 21],\
[3923, 3923, w^3 + 3*w^2 - 11*w - 7],\
[3931, 3931, -3*w^3 + 19*w - 7],\
[3947, 3947, -4*w^3 + 4*w^2 + 22*w - 9],\
[3947, 3947, -5*w^3 - w^2 + 17*w + 7],\
[3947, 3947, -w^3 - 4*w^2 + 3*w + 17],\
[3947, 3947, -2*w^3 - 4*w^2 + 12*w + 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^12 - 2*x^11 - 19*x^10 + 36*x^9 + 134*x^8 - 235*x^7 - 435*x^6 + 669*x^5 + 677*x^4 - 784*x^3 - 552*x^2 + 320*x + 200
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 9/50*e^11 - 23/50*e^10 - 161/50*e^9 + 369/50*e^8 + 538/25*e^7 - 407/10*e^6 - 334/5*e^5 + 2223/25*e^4 + 2399/25*e^3 - 3091/50*e^2 - 1324/25*e - 1/5, 1/5*e^11 - 2/5*e^10 - 19/5*e^9 + 36/5*e^8 + 129/5*e^7 - 46*e^6 - 73*e^5 + 609/5*e^4 + 372/5*e^3 - 579/5*e^2 - 112/5*e + 32, 11/25*e^11 - 17/25*e^10 - 194/25*e^9 + 276/25*e^8 + 1229/25*e^7 - 313/5*e^6 - 672/5*e^5 + 3584/25*e^4 + 3742/25*e^3 - 2714/25*e^2 - 1492/25*e + 72/5, -1, -14/25*e^11 + 33/25*e^10 + 256/25*e^9 - 524/25*e^8 - 1746/25*e^7 + 562/5*e^6 + 1093/5*e^5 - 5666/25*e^4 - 7708/25*e^3 + 2811/25*e^2 + 4183/25*e + 172/5, -1/5*e^11 + 2/5*e^10 + 14/5*e^9 - 36/5*e^8 - 49/5*e^7 + 48*e^6 - 13*e^5 - 709/5*e^4 + 513/5*e^3 + 869/5*e^2 - 458/5*e - 86, 21/25*e^11 - 12/25*e^10 - 409/25*e^9 + 136/25*e^8 + 3019/25*e^7 - 53/5*e^6 - 2102/5*e^5 - 1476/25*e^4 + 17037/25*e^3 + 5521/25*e^2 - 9862/25*e - 938/5, 1/2*e^11 - 21/2*e^9 - e^8 + 83*e^7 + 31/2*e^6 - 607/2*e^5 - 173/2*e^4 + 1001/2*e^3 + 202*e^2 - 291*e - 154, 23/25*e^11 - 6/25*e^10 - 467/25*e^9 + 68/25*e^8 + 3522/25*e^7 - 14/5*e^6 - 2416/5*e^5 - 1563/25*e^4 + 18356/25*e^3 + 5773/25*e^2 - 9956/25*e - 974/5, -3/10*e^11 + 3/5*e^10 + 47/10*e^9 - 49/5*e^8 - 121/5*e^7 + 113/2*e^6 + 85/2*e^5 - 1347/10*e^4 - 51/10*e^3 + 571/5*e^2 - 47/5*e - 28, -1/2*e^11 + 23/2*e^9 - 97*e^7 - 11/2*e^6 + 731/2*e^5 + 135/2*e^4 - 1195/2*e^3 - 234*e^2 + 351*e + 194, 1/50*e^11 - 11/25*e^10 + 71/50*e^9 + 183/25*e^8 - 618/25*e^7 - 463/10*e^6 + 1303/10*e^5 + 7119/50*e^4 - 12803/50*e^3 - 5362/25*e^2 + 4089/25*e + 606/5, 33/25*e^11 - 1/25*e^10 - 682/25*e^9 - 22/25*e^8 + 5237/25*e^7 + 111/5*e^6 - 3661/5*e^5 - 3873/25*e^4 + 28426/25*e^3 + 10533/25*e^2 - 15851/25*e - 1654/5, -18/25*e^11 + 21/25*e^10 + 397/25*e^9 - 413/25*e^8 - 3177/25*e^7 + 554/5*e^6 + 2221/5*e^5 - 6992/25*e^4 - 16171/25*e^3 + 4082/25*e^2 + 8446/25*e + 284/5, -22/25*e^11 + 9/25*e^10 + 438/25*e^9 - 52/25*e^8 - 3333/25*e^7 - 104/5*e^6 + 2409/5*e^5 + 4432/25*e^4 - 20259/25*e^3 - 9697/25*e^2 + 11959/25*e + 1356/5, -12/25*e^11 + 14/25*e^10 + 223/25*e^9 - 267/25*e^8 - 1468/25*e^7 + 366/5*e^6 + 804/5*e^5 - 5153/25*e^4 - 4089/25*e^3 + 4838/25*e^2 + 1414/25*e - 224/5, -9/25*e^11 - 2/25*e^10 + 211/25*e^9 + 56/25*e^8 - 1826/25*e^7 - 123/5*e^6 + 1423/5*e^5 + 3129/25*e^4 - 12123/25*e^3 - 6884/25*e^2 + 7298/25*e + 972/5, -1/25*e^11 + 22/25*e^10 + 29/25*e^9 - 366/25*e^8 - 339/25*e^7 + 413/5*e^6 + 357/5*e^5 - 4519/25*e^4 - 3972/25*e^3 + 3074/25*e^2 + 2872/25*e + 18/5, -12/25*e^11 + 14/25*e^10 + 198/25*e^9 - 242/25*e^8 - 1093/25*e^7 + 306/5*e^6 + 434/5*e^5 - 4203/25*e^4 - 639/25*e^3 + 4563/25*e^2 - 886/25*e - 364/5, 21/50*e^11 - 6/25*e^10 - 409/50*e^9 + 193/25*e^8 + 1347/25*e^7 - 753/10*e^6 - 1317/10*e^5 + 13849/50*e^4 + 3487/50*e^3 - 8577/25*e^2 + 669/25*e + 656/5, 11/25*e^11 + 8/25*e^10 - 219/25*e^9 - 199/25*e^8 + 1654/25*e^7 + 342/5*e^6 - 1182/5*e^5 - 6266/25*e^4 + 9842/25*e^3 + 9511/25*e^2 - 5692/25*e - 998/5, -53/25*e^11 + 91/25*e^10 + 987/25*e^9 - 1498/25*e^8 - 6742/25*e^7 + 1699/5*e^6 + 4101/5*e^5 - 18707/25*e^4 - 26841/25*e^3 + 11297/25*e^2 + 13366/25*e + 274/5, 18/25*e^11 - 21/25*e^10 - 322/25*e^9 + 263/25*e^8 + 2177/25*e^7 - 174/5*e^6 - 1411/5*e^5 - 133/25*e^4 + 11096/25*e^3 + 3443/25*e^2 - 6446/25*e - 634/5, -2/5*e^11 + 9/5*e^10 + 33/5*e^9 - 172/5*e^8 - 163/5*e^7 + 235*e^6 + 21*e^5 - 3383/5*e^4 + 831/5*e^3 + 3713/5*e^2 - 786/5*e - 276, 1/5*e^11 + 3/5*e^10 - 34/5*e^9 - 54/5*e^8 + 374/5*e^7 + 74*e^6 - 347*e^5 - 1206/5*e^4 + 3362/5*e^3 + 1871/5*e^2 - 2092/5*e - 236, 38/25*e^11 - 61/25*e^10 - 702/25*e^9 + 958/25*e^8 + 4807/25*e^7 - 1019/5*e^6 - 3001/5*e^5 + 10197/25*e^4 + 21036/25*e^3 - 4787/25*e^2 - 11236/25*e - 424/5, 23/10*e^11 - 8/5*e^10 - 457/10*e^9 + 124/5*e^8 + 1686/5*e^7 - 247/2*e^6 - 2263/2*e^5 + 1657/10*e^4 + 16861/10*e^3 + 1179/5*e^2 - 4563/5*e - 376, -33/50*e^11 + 13/25*e^10 + 707/50*e^9 - 214/25*e^8 - 2806/25*e^7 + 439/10*e^6 + 4011/10*e^5 - 2527/50*e^4 - 31301/50*e^3 - 3229/25*e^2 + 9063/25*e + 832/5, -23/25*e^11 + 31/25*e^10 + 492/25*e^9 - 568/25*e^8 - 3847/25*e^7 + 714/5*e^6 + 2641/5*e^5 - 8487/25*e^4 - 18931/25*e^3 + 4602/25*e^2 + 9806/25*e + 394/5, -3/5*e^11 + 6/5*e^10 + 47/5*e^9 - 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238/5*e^7 - 444*e^6 + 545*e^5 + 6802/5*e^4 - 7884/5*e^3 - 8497/5*e^2 + 5714/5*e + 870, -159/25*e^11 + 148/25*e^10 + 3061/25*e^9 - 2419/25*e^8 - 21626/25*e^7 + 2662/5*e^6 + 13668/5*e^5 - 25221/25*e^4 - 94448/25*e^3 - 284/25*e^2 + 49948/25*e + 3572/5, -207/50*e^11 - 23/25*e^10 + 4453/50*e^9 + 394/25*e^8 - 17649/25*e^7 - 1109/10*e^6 + 25139/10*e^5 + 23167/50*e^4 - 194679/50*e^3 - 27716/25*e^2 + 53227/25*e + 4438/5, 202/25*e^11 - 544/25*e^10 - 3583/25*e^9 + 8957/25*e^8 + 23278/25*e^7 - 10211/5*e^6 - 13494/5*e^5 + 116363/25*e^4 + 84819/25*e^3 - 87073/25*e^2 - 42294/25*e + 1764/5, -8/5*e^11 + 6/5*e^10 + 212/5*e^9 - 138/5*e^8 - 1952/5*e^7 + 189*e^6 + 1531*e^5 - 1867/5*e^4 - 12401/5*e^3 - 1128/5*e^2 + 7176/5*e + 554, 44/25*e^11 + 7/25*e^10 - 1101/25*e^9 - 146/25*e^8 + 10016/25*e^7 + 318/5*e^6 - 8103/5*e^5 - 9464/25*e^4 + 70543/25*e^3 + 25619/25*e^2 - 41743/25*e - 4452/5, -101/25*e^11 + 47/25*e^10 + 1929/25*e^9 - 1066/25*e^8 - 13014/25*e^7 + 1673/5*e^6 + 7312/5*e^5 - 25044/25*e^4 - 39022/25*e^3 + 20024/25*e^2 + 15672/25*e - 472/5, 17/50*e^11 + 38/25*e^10 - 343/50*e^9 - 1039/25*e^8 + 1769/25*e^7 + 3649/10*e^6 - 4089/10*e^5 - 62477/50*e^4 + 52149/50*e^3 + 37671/25*e^2 - 16687/25*e - 2988/5, 33/25*e^11 + 99/25*e^10 - 757/25*e^9 - 1672/25*e^8 + 6362/25*e^7 + 1976/5*e^6 - 4856/5*e^5 - 24798/25*e^4 + 41176/25*e^3 + 26933/25*e^2 - 22726/25*e - 2534/5, 291/25*e^11 - 252/25*e^10 - 5789/25*e^9 + 3856/25*e^8 + 43049/25*e^7 - 3808/5*e^6 - 29357/5*e^5 + 27779/25*e^4 + 223877/25*e^3 + 21291/25*e^2 - 123077/25*e - 8668/5, -93/25*e^11 + 171/25*e^10 + 1672/25*e^9 - 3038/25*e^8 - 10502/25*e^7 + 3819/5*e^6 + 5286/5*e^5 - 49067/25*e^4 - 21946/25*e^3 + 42857/25*e^2 + 6421/25*e - 1966/5, -92/25*e^11 + 99/25*e^10 + 1693/25*e^9 - 1272/25*e^8 - 11863/25*e^7 + 916/5*e^6 + 7994/5*e^5 - 1598/25*e^4 - 64699/25*e^3 - 13117/25*e^2 + 37599/25*e + 3086/5, -112/25*e^11 - 136/25*e^10 + 2498/25*e^9 + 2633/25*e^8 - 20768/25*e^7 - 3754/5*e^6 + 15804/5*e^5 + 60872/25*e^4 - 133564/25*e^3 - 89237/25*e^2 + 76264/25*e + 9936/5, -259/50*e^11 + 249/25*e^10 + 4011/50*e^9 - 4222/25*e^8 - 9888/25*e^7 + 10357/10*e^6 + 5643/10*e^5 - 137471/50*e^4 + 20477/50*e^3 + 73108/25*e^2 - 17751/25*e - 5794/5, 254/25*e^11 - 238/25*e^10 - 4891/25*e^9 + 4164/25*e^8 + 34256/25*e^7 - 5092/5*e^6 - 21068/5*e^5 + 60076/25*e^4 + 136263/25*e^3 - 33846/25*e^2 - 65238/25*e - 1642/5, 329/50*e^11 + 31/25*e^10 - 6941/50*e^9 - 1193/25*e^8 + 27778/25*e^7 + 5303/10*e^6 - 41613/10*e^5 - 120099/50*e^4 + 356313/50*e^3 + 112602/25*e^2 - 107419/25*e - 14306/5, 314/25*e^11 - 483/25*e^10 - 5656/25*e^9 + 7924/25*e^8 + 36971/25*e^7 - 9052/5*e^6 - 21308/5*e^5 + 102616/25*e^4 + 131708/25*e^3 - 69411/25*e^2 - 63133/25*e - 12/5, -248/25*e^11 + 156/25*e^10 + 4742/25*e^9 - 2493/25*e^8 - 33172/25*e^7 + 2739/5*e^6 + 20636/5*e^5 - 27237/25*e^4 - 137706/25*e^3 + 3977/25*e^2 + 65756/25*e + 3104/5, -56/5*e^11 + 57/5*e^10 + 1049/5*e^9 - 936/5*e^8 - 7164/5*e^7 + 1067*e^6 + 4327*e^5 - 11694/5*e^4 - 27892/5*e^3 + 5854/5*e^2 + 13352/5*e + 480, 8*e^11 - 10*e^10 - 145*e^9 + 155*e^8 + 969*e^7 - 824*e^6 - 2950*e^5 + 1699*e^4 + 4048*e^3 - 922*e^2 - 2022*e - 282, -219/25*e^11 + 243/25*e^10 + 3926/25*e^9 - 3829/25*e^8 - 25516/25*e^7 + 4202/5*e^6 + 14643/5*e^5 - 46211/25*e^4 - 89918/25*e^3 + 31431/25*e^2 + 39168/25*e + 112/5, 137/25*e^11 - 289/25*e^10 - 2248/25*e^9 + 5092/25*e^8 + 12193/25*e^7 - 6491/5*e^6 - 4384/5*e^5 + 89203/25*e^4 - 3336/25*e^3 - 97613/25*e^2 + 18136/25*e + 7594/5, -76/25*e^11 - 28/25*e^10 + 1629/25*e^9 + 634/25*e^8 - 12964/25*e^7 - 1107/5*e^6 + 9357/5*e^5 + 23406/25*e^4 - 74597/25*e^3 - 46451/25*e^2 + 43347/25*e + 6128/5, -11/50*e^11 + 271/25*e^10 - 431/50*e^9 - 4663/25*e^8 + 4173/25*e^7 + 11483/10*e^6 - 9443/10*e^5 - 153409/50*e^4 + 101783/50*e^3 + 86357/25*e^2 - 32629/25*e - 6996/5, 143/25*e^11 - 146/25*e^10 - 2722/25*e^9 + 2213/25*e^8 + 19277/25*e^7 - 2204/5*e^6 - 12496/5*e^5 + 18267/25*e^4 + 90546/25*e^3 + 1918/25*e^2 - 46796/25*e - 3094/5, 211/50*e^11 - 171/25*e^10 - 3519/50*e^9 + 2563/25*e^8 + 10427/25*e^7 - 5203/10*e^6 - 10627/10*e^5 + 51459/50*e^4 + 55817/50*e^3 - 16682/25*e^2 - 9171/25*e + 266/5, 18/25*e^11 + 29/25*e^10 - 472/25*e^9 - 412/25*e^8 + 4202/25*e^7 + 451/5*e^6 - 3106/5*e^5 - 7658/25*e^4 + 22846/25*e^3 + 17418/25*e^2 - 11896/25*e - 2364/5, 259/25*e^11 - 248/25*e^10 - 5086/25*e^9 + 4169/25*e^8 + 36751/25*e^7 - 4812/5*e^6 - 23753/5*e^5 + 51421/25*e^4 + 166023/25*e^3 - 17566/25*e^2 - 84798/25*e - 4122/5, -138/25*e^11 + 111/25*e^10 + 2752/25*e^9 - 1708/25*e^8 - 20432/25*e^7 + 1669/5*e^6 + 13806/5*e^5 - 10547/25*e^4 - 102911/25*e^3 - 16563/25*e^2 + 54661/25*e + 4894/5, -226/25*e^11 + 147/25*e^10 + 4454/25*e^9 - 1716/25*e^8 - 33214/25*e^7 + 703/5*e^6 + 23227/5*e^5 + 19181/25*e^4 - 187497/25*e^3 - 73601/25*e^2 + 109422/25*e + 11938/5, 41/25*e^11 + 73/25*e^10 - 1039/25*e^9 - 1119/25*e^8 + 9299/25*e^7 + 1237/5*e^6 - 7242/5*e^5 - 16896/25*e^4 + 60177/25*e^3 + 27241/25*e^2 - 36002/25*e - 3428/5, -e^11 + 9*e^10 - 2*e^9 - 158*e^8 + 199*e^7 + 1024*e^6 - 1363*e^5 - 3010*e^4 + 3133*e^3 + 3917*e^2 - 2114*e - 1906, 68/25*e^11 - 46/25*e^10 - 1247/25*e^9 + 138/25*e^8 + 9002/25*e^7 + 856/5*e^6 - 6581/5*e^5 - 28433/25*e^4 + 60271/25*e^3 + 53543/25*e^2 - 38071/25*e - 6384/5, -e^11 + 22*e^9 - 11*e^8 - 163*e^7 + 144*e^6 + 466*e^5 - 562*e^4 - 402*e^3 + 665*e^2 + 72*e - 314, -111/10*e^11 + 31/5*e^10 + 2159/10*e^9 - 378/5*e^8 - 7877/5*e^7 + 403/2*e^6 + 10665/2*e^5 + 5521/10*e^4 - 82507/10*e^3 - 13623/5*e^2 + 23211/5*e + 2384, 2*e^11 - 3*e^10 - 46*e^9 + 47*e^8 + 396*e^7 - 229*e^6 - 1544*e^5 + 284*e^4 + 2620*e^3 + 413*e^2 - 1546*e - 662, 18/5*e^11 - 41/5*e^10 - 322/5*e^9 + 638/5*e^8 + 2157/5*e^7 - 668*e^6 - 1349*e^5 + 6542/5*e^4 + 9816/5*e^3 - 3037/5*e^2 - 5436/5*e - 266, 111/25*e^11 - 167/25*e^10 - 2119/25*e^9 + 2601/25*e^8 + 15054/25*e^7 - 2673/5*e^6 - 9747/5*e^5 + 23459/25*e^4 + 70217/25*e^3 - 1364/25*e^2 - 37492/25*e - 2878/5, 214/25*e^11 - 483/25*e^10 - 3781/25*e^9 + 7824/25*e^8 + 24246/25*e^7 - 8747/5*e^6 - 13633/5*e^5 + 97291/25*e^4 + 80258/25*e^3 - 70761/25*e^2 - 36258/25*e + 1678/5, -7*e^11 + 13*e^10 + 115*e^9 - 201*e^8 - 665*e^7 + 1075*e^6 + 1621*e^5 - 2352*e^4 - 1556*e^3 + 1933*e^2 + 442*e - 446, 213/25*e^11 - 311/25*e^10 - 4102/25*e^9 + 5158/25*e^8 + 29132/25*e^7 - 5844/5*e^6 - 18546/5*e^5 + 61897/25*e^4 + 128061/25*e^3 - 26612/25*e^2 - 67036/25*e - 3034/5, -46/25*e^11 + 37/25*e^10 + 1009/25*e^9 - 261/25*e^8 - 8719/25*e^7 - 352/5*e^6 + 7282/5*e^5 + 17851/25*e^4 - 70537/25*e^3 - 41171/25*e^2 + 46987/25*e + 5658/5, 129/25*e^11 - 138/25*e^10 - 2441/25*e^9 + 2114/25*e^8 + 17031/25*e^7 - 2107/5*e^6 - 10713/5*e^5 + 16276/25*e^4 + 74338/25*e^3 + 7929/25*e^2 - 39188/25*e - 3632/5, 433/50*e^11 - 88/25*e^10 - 8157/50*e^9 + 764/25*e^8 + 28856/25*e^7 + 461/10*e^6 - 38361/10*e^5 - 49423/50*e^4 + 299601/50*e^3 + 64979/25*e^2 - 85813/25*e - 9472/5, -37/5*e^11 + 44/5*e^10 + 668/5*e^9 - 652/5*e^8 - 4423/5*e^7 + 635*e^6 + 2640*e^5 - 5318/5*e^4 - 17444/5*e^3 + 523/5*e^2 + 8344/5*e + 538, -3/25*e^11 + 116/25*e^10 + 37/25*e^9 - 2173/25*e^8 + 83/25*e^7 + 2879/5*e^6 - 539/5*e^5 - 39782/25*e^4 + 9884/25*e^3 + 41472/25*e^2 - 6284/25*e - 2886/5, 159/25*e^11 - 148/25*e^10 - 3286/25*e^9 + 2419/25*e^8 + 25201/25*e^7 - 2557/5*e^6 - 17458/5*e^5 + 19696/25*e^4 + 132598/25*e^3 + 17034/25*e^2 - 74148/25*e - 6452/5, -34/25*e^11 - 102/25*e^10 + 936/25*e^9 + 1806/25*e^8 - 8976/25*e^7 - 2363/5*e^6 + 7448/5*e^5 + 35504/25*e^4 - 64898/25*e^3 - 49109/25*e^2 + 36648/25*e + 5182/5, 14/25*e^11 + 17/25*e^10 - 156/25*e^9 - 276/25*e^8 + 46/25*e^7 + 228/5*e^6 + 862/5*e^5 + 691/25*e^4 - 14542/25*e^3 - 9336/25*e^2 + 13342/25*e + 1848/5, 7/5*e^11 - 4/5*e^10 - 108/5*e^9 - 3/5*e^8 + 608/5*e^7 + 107*e^6 - 344*e^5 - 2927/5*e^4 + 2839/5*e^3 + 4677/5*e^2 - 1714/5*e - 462, -101/25*e^11 + 322/25*e^10 + 1529/25*e^9 - 5616/25*e^8 - 7139/25*e^7 + 7043/5*e^6 + 1472/5*e^5 - 94569/25*e^4 + 17703/25*e^3 + 100024/25*e^2 - 20278/25*e - 7262/5, -51/25*e^11 + 147/25*e^10 + 654/25*e^9 - 2341/25*e^8 - 1964/25*e^7 + 2658/5*e^6 - 688/5*e^5 - 33044/25*e^4 + 19553/25*e^3 + 36274/25*e^2 - 14978/25*e - 3162/5, -34/25*e^11 + 73/25*e^10 + 661/25*e^9 - 1344/25*e^8 - 4651/25*e^7 + 1732/5*e^6 + 2813/5*e^5 - 22146/25*e^4 - 16973/25*e^3 + 16941/25*e^2 + 8048/25*e - 178/5]
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 + w^2 + 3*w - 1])] = 1

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