/*
  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([16, 4, -w^3 + w^2 + 4*w - 2])

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^3 + 3*x^2 - 5*x - 11
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, -e - 2, 5, e^2 + 2*e - 6, e^2 - 5, 2*e^2 + 2*e - 10, -e^2 - 2*e + 1, e + 8, e^2 + 2*e - 5, e^2 + 3*e - 1, e^2 + 3*e - 1, e^2 - e - 11, e^2 - 11, -3*e^2 + 22, -2*e^2 + 8, 2*e^2 + 4*e - 12, -4*e^2 - 6*e + 15, -2*e^2 + 13, -2*e^2 + e + 20, e^2 + 2*e - 5, -4*e^2 - 6*e + 20, -e^2 - 4*e + 5, 2*e^2 + 6*e - 9, -3*e^2 - 2*e + 23, e^2 + e + 1, e^2 - 2*e - 13, -3*e^2 - 2*e + 15, -5*e + 2, e^2 - 2*e - 5, e^2 + 2*e + 6, 3, 2*e^2 - 10, 3*e^2 + 2*e - 14, e^2 - 4*e - 7, -e^2 - 8*e + 1, 2, 4*e^2 + 8*e - 8, 2*e^2 + 3*e - 2, e^2 + 2*e - 12, -2*e^2 - 2*e + 22, -5*e, -4*e^2 - 10*e + 19, -2*e^2 - 8*e + 12, e^2 + 2*e + 7, -2*e^2 - 2*e - 10, -3*e^2 + 29, -3*e^2 - 4*e + 9, 2*e^2, -2*e^2 - 4*e + 12, -e^2 + 5*e + 5, e^2 + 8*e + 3, e^2 + 5*e + 1, 2*e^2 + 2*e - 22, -e^2 - 8*e + 3, 4*e^2 + 4*e - 28, e^2 - 2*e - 13, 4*e^2 + 8*e - 18, -e^2 - 4*e + 2, 16, -e^2 + 31, -3*e^2 - 4*e + 25, 4*e^2 + 4*e - 38, -2*e^2 + 20, 3*e^2 + 8*e - 23, 3*e^2 + 6*e - 15, e^2 + 11*e - 5, 2*e + 9, e^2 + 6*e + 11, -6*e^2 - 7*e + 40, e^2 - 4*e + 2, 2*e^2 - 4*e - 8, -3*e^2 - 8*e - 9, 3*e^2 + 7*e - 9, -4*e^2 - 6*e + 32, -2*e^2 + 4*e + 10, -5*e^2 - e + 45, -4*e + 1, -e^2 - e + 9, -5*e^2 - 14*e + 17, -2*e^2 - 2*e + 9, 9*e^2 + 16*e - 31, 2*e^2 - 4*e - 28, -8*e - 14, 3*e - 20, 2*e^2 + 8*e - 10, 5*e^2 + 5*e - 37, e^2 - 6*e - 2, 5*e^2 + 6*e - 13, 3*e^2 + 10*e - 3, -3*e^2 + 17, 4*e + 4, -3*e^2 - 4*e + 3, -6*e^2 - 6*e + 34, -e^2 + 4*e + 9, 3*e^2 + 6*e - 15, -6*e^2 - 7*e + 34, e^2 + 8*e - 19, 5*e^2 - 6*e - 49, -5*e^2 + 46, -3*e^2 + 4*e + 13, -2*e^2 - 10*e - 6, -7*e^2 - 2*e + 43, 2*e^2 + 10*e - 14, 7*e^2 + 12*e - 31, -e^2 + 10*e + 9, -4*e^2 - 6*e + 7, e^2 + 13*e + 13, e^2 + 16*e + 7, -3*e^2 - 8*e + 5, e^2 - 2*e - 13, -3*e^2 + 43, -2*e^2 + 7*e + 38, e^2 - 2*e - 5, -7*e^2 - 7*e + 35, 2*e^2 - 8*e - 28, -4*e^2 - 8*e + 40, -5*e^2 - 16*e + 11, -e^2 - 8*e - 19, -4*e + 12, 9*e^2 + 8*e - 41, e^2 + 8*e + 12, -4*e^2 - 13*e + 2, -e^2 - 12*e - 5, 5*e^2 + 6*e - 49, 7*e^2 + 6*e - 31, 2*e^2 + 2*e - 37, -5*e^2 - 4*e + 14, 4*e - 2, 5*e^2 - 6*e - 49, e^2 - 2*e + 12, -2*e^2 - 11*e + 16, -10*e^2 - 12*e + 42, -4*e^2 - 2, e^2 - 14*e - 14, -6*e^2 - 8*e + 32, -2*e^2 + 4*e + 30, 2*e^2 + 22, 4*e + 2, -2*e^2 - 8*e + 1, 8*e^2 + 4*e - 66, -7*e^2 + 4*e + 77, e^2 + 19, -4*e^2 - 8*e - 18, 8*e^2 + 4*e - 34, -6*e^2 - 14*e + 42, -13*e^2 - 18*e + 53, -12*e + 14, -4*e^2 + 4*e + 54, -2*e^2 - 14*e + 22, 5*e^2 - 41, -8*e^2 - 4*e + 52, 5*e^2 + 4*e - 31, -5*e^2 - 12*e + 41, -5*e^2 - 12*e - 1, 14*e^2 + 18*e - 58, 5*e^2 + 24*e - 13, -7*e^2 + 4*e + 59, -4*e^2 - 2*e + 28, 4*e^2 + 8*e - 16, 9*e^2 + 23*e - 29, -5*e^2 - 2*e + 25, 20*e + 12, -7*e^2 + 48, 7*e^2 + 8*e - 35, -7*e^2 + 43, -3*e^2 + 4*e + 17, 3*e^2 + 22*e - 15, -6*e^2 - 9*e + 10, 5*e^2 + 16*e - 4, -4*e^2 + 42, 6*e + 41, 3*e^2 + 10*e - 3, 5*e + 20, 3*e^2 + 8*e - 23, 2*e^2 - 2, 7*e^2 + 16*e - 39, -e^2 + 4*e + 29, -4*e^2 - e + 20, -5*e^2 - 10*e - 15, 7*e^2 + 24*e - 19, e^2 - 3*e - 9, 4*e^2 - e + 4, -5*e^2 - 14*e + 18, 3*e^2 + 4*e + 20, 5*e^2 + 14*e - 37, 6*e^2 - 2*e - 70, -9*e^2 - 20*e + 50, 5*e^2 + 22*e - 21, 7*e^2 - 10*e - 59, -11*e^2 - 17*e + 59, 7*e^2 + 13*e - 1, 3*e^2 - 7*e - 55, -4*e^2 - 11*e + 28, -6*e^2 - 3*e + 28, -12*e^2 - 20*e + 65, -2*e + 24, 7*e^2 + 10*e - 55, -10*e^2 - 24*e + 42, -2*e^2 - 4*e - 4, -4*e^2 - 4*e + 14, 15*e^2 + 24*e - 51, -13*e^2 - 20*e + 49, -8*e^2 - 20*e + 6, 2*e^2 + 12*e - 20, 7*e^2 + 10*e - 23, -11*e^2 - 12*e + 59, -8*e^2 - 27*e + 30, -8*e^2 - 12*e + 58, -5*e^2 - 6*e + 65, -12*e^2 - 14*e + 71, -3*e^2 - 2*e + 11, 20*e + 6, 2*e^2 - 2, -3*e^2 + 4*e + 35, 8*e^2 - 50, -8*e^2 - 8*e + 22, 4*e^2 - 2*e - 3, 13*e^2 + 6*e - 73, 9*e^2 + 12*e - 9, -10*e^2 - 16*e + 14, 5*e^2 + 6*e + 11, 2*e^2 - 4*e + 6, 2*e^2 - 4*e + 10, -3*e^2 + 4*e + 15, -2*e^2 + 2*e - 6, -5*e^2 + 6*e + 52, e^2 + 4*e + 4, -5*e^2 - 2*e + 25, 5*e^2 + 20*e - 37, 5*e^2 - 41, -7*e^2 - 16*e - 1, -2*e^2 - 12*e + 14, -2*e^2 - 8*e - 2, -4*e - 26, -13*e^2 - 12*e + 89, -4*e^2 - 12*e, 3*e^2 + 27, 4*e^2 - 14*e - 56, 11*e^2 + 20*e - 61, 10*e^2 + 28*e - 24, -12*e^2 - 22*e + 32, -4*e^2 - 8*e + 24, -8*e^2 - 4*e + 41, -4*e - 2, e^2 - 11*e - 35, -10*e^2 - 4*e + 56, -2*e^2 + 9*e - 12, 7*e^2 + 16*e - 24, 7*e^2 + 19*e - 47, -8*e^2 - 16*e + 50, 5*e^2 + 12*e, 8*e^2 + 12*e - 40, 13*e^2 + 24*e - 53, -3*e^2 - 21*e + 33, 8*e^2 + 8*e - 41, 2*e^2 - 10*e - 35, -3*e^2 - 8*e + 43, -2*e^2 + 10*e - 2, 9*e^2 + 31*e - 39, 11*e^2 - 6*e - 78, 4*e^2 + 11*e - 38, -10*e^2 - 13*e + 68, e^2 + e - 41, -10*e^2 - 24*e + 24, -2*e^2 + 20*e + 44, -9*e^2 - 19*e + 5, 4*e^2 + 20*e + 12, 8*e^2 - 4*e - 64, 4*e^2 + 4*e + 9, 7*e^2 + 2*e - 94, -3*e - 26, 2*e^2 + 8*e + 20, -9*e^2 - 14*e + 77, -2*e^2 - 16*e - 16, 10*e^2 + 18*e + 6, -7*e^2 + 4*e + 51, -2*e^2 - 7*e + 58, 13*e^2 + 38*e - 53, -4*e^2 - 14*e + 39, 4*e^2 + 16*e - 56, -2*e^2 - 24*e - 16, 4*e^2 + e + 16, 4*e^2 + 22*e + 7, -10*e^2 - 32*e + 35, -5*e^2 - 17*e + 5, -9*e^2 - 24*e + 25, 7*e^2 + 4*e - 19, 5*e^2 + 24*e + 16, 4*e^2 + 10*e - 32, 5*e^2 + 9, -5*e^2 - 6*e + 9, 5*e^2 + 4*e - 46, 14*e^2 + 16*e - 72, -10*e^2 - 16*e + 42, -8*e^2 - 20*e + 24, -12*e - 48, 7*e^2 + 4*e - 35, -7*e^2 - 5*e + 85, 12*e^2 - 66, 5*e^2 + 10*e - 57, -6*e^2 - 9*e + 6, -4*e^2 - 10*e + 41, -14*e^2 - 8*e + 97, -9*e^2 - 3*e + 99, 4*e^2 + 28*e - 8, 3*e^2 - 16*e - 59, -e^2 + 2*e - 43, 3*e^2 - 3*e - 33, 5*e^2 + 34*e - 9, 16*e^2 + 12*e - 94, -e^2 - 3*e + 61, -3*e^2 - 15*e + 33, 10*e^2 + 8*e - 63, -5*e^2 + 2*e + 25, -6*e^2 - 22*e + 38, -9*e^2 - 20*e - 3, 2*e^2 - 4*e - 41, -e^2 + 22*e + 1, 8*e^2 - 10*e - 96, 6*e^2 + 2*e + 10, 7*e^2 + 8*e - 10, 11*e^2 + 6*e - 91, -e^2 + 11*e - 25, 11*e^2 + 32*e - 51, 3*e^2 - 4*e - 15, -4*e^2 - 20, 15*e^2 + 24*e - 91, 5*e^2 - 51, 7*e^2 + 40*e - 29, 14*e^2 - 6*e - 117, -10*e^2 - 32*e + 24, -12*e^2 - 15*e + 58, -14*e^2 - 4*e + 98, -3*e^2 - 12*e - 5, 3*e^2 - 2*e - 51, 4*e - 32, 4*e^2 + 16*e - 30, e^2 - 17*e - 55, -e^2 + 8*e + 10, -e^2 + 14*e - 3, -9*e^2 - 17*e + 35, -7*e^2 - 20*e + 67, -2*e^2 + 10*e + 31, e^2 - 13*e - 29, -5*e^2 + 11*e + 43, -5*e^2 + 4*e + 101, 5*e^2 + 8*e + 51, -e^2 - 20*e + 5, -16*e - 18, -5*e^2 - 20*e + 1, 2*e^2 + 12*e - 44, 2*e^2 - e - 64, -6*e^2 - 8*e - 20, -7*e^2 - 20*e + 71, 7*e^2 + 18*e - 51, 10*e^2 + 4*e - 48, -4*e^2 - 10*e - 28, 8*e^2 + 28*e - 25, -36, 14*e^2 + 6*e - 71, 8*e^2 + 12*e - 8, -8*e^2 - 9*e - 6, 16*e^2 + 16*e - 78, -3*e^2 - 6*e - 17, -5*e^2 + 12*e + 58, 4*e^2 + 4*e + 4, 13*e^2 + 32*e - 63, -13*e^2 - 14*e + 73, -3*e^2 - 26*e + 27, 8*e^2 + 10*e - 80, -4*e^2 - 14*e - 13, 7*e^2 - 8*e - 47, 15*e^2 + 16*e - 41, -13*e^2 - 24*e + 13, 11*e^2 + 23*e - 37, -8*e^2 + 7*e + 88, -3*e^2 - 6*e + 31, -2*e^2 + 26*e + 47, -6*e^2 - 16*e - 14, -8*e^2 - 20*e + 46, 17*e^2 + 25*e - 39, -10*e^2 - 7*e, e^2 + 5*e + 3, -8*e^2 - 4*e + 50, 10*e^2 + 6*e - 90, -9*e^2 - 32*e + 47, 3*e^2 - 12*e - 11, 16*e + 28, 11*e^2 - 4*e - 67, -3*e^2 + 6*e + 63, 8*e^2 - 4*e - 70, -e^2 + 8*e + 53, -15*e^2 - 22*e + 52, -e^2 + 18*e + 13, -5*e^2 - 4*e - 23, -e^2 + 2*e + 5, 5*e^2 - 4*e - 34, 7*e^2 + 7*e - 101, -4*e^2 - 28*e + 2, -8*e^2 - 20*e + 6, 4*e^2 - 12*e - 2, -7*e^2 + 10*e + 63, 4*e^2 + 2*e - 63, 6*e^2 + 4*e - 6, 7*e^2 + 16*e - 57, -6*e^2 - 6*e + 82, 5*e^2 + 4*e - 67, -2*e^2 + 80, 4*e^2 + 4*e - 86, 4*e^2 - 20*e - 52, 2*e^2 + 4*e + 8, -17*e^2 - 24*e + 83, -10*e^2 - 30*e + 81, 2*e^2 + 22*e + 6, -21*e^2 - 28*e + 79, 9*e^2 + 6*e - 60, 11*e^2 + 6*e - 83, 2*e^2 + 20*e - 22, e^2 + 4*e - 15, 2*e^2 + 2*e + 78, e^2 - 20*e - 41, 3*e^2 + 36*e + 21, -10*e^2 - 8*e + 5, -3*e^2 - 20*e - 1, -5*e^2 + 2*e + 49, 10*e^2 + 38*e - 37, -8*e^2 - 13*e + 94, 12*e^2 + 12*e - 6, 7*e^2 - 20*e - 68, -6*e^2 - 26*e + 29, -8*e^2 - 28*e + 42, -3*e^2 + 14*e + 90, -3*e^2 - 12*e + 5, e^2 - 10*e + 43, 2*e^2 + 12*e - 6, 5*e^2 + 16*e - 61, 11*e^2 + 32*e - 27, -4*e^2 - 28*e + 12, -19*e^2 - 26*e + 99, 8*e^2 + 40*e - 6, 17*e^2 + 34*e - 52, -2*e^2 - 8*e - 48, 6*e^2 + 22*e - 10, -7*e^2 + 19, -2*e^2 + 8*e + 60, e^2 - 14*e + 31, -8*e^2 - 8*e - 20, -e^2 - 6*e + 29, e^2 - 2*e - 48, 13*e^2 + 46*e - 61, -9*e^2 - 28*e - 7, -6*e^2 + 4*e + 32, -11*e^2 - 8*e + 67, -10*e^2 - 24*e + 4, 2*e^2 + 39*e + 20, -4*e^2 - 6*e + 69, 7*e^2 + 33*e - 19, -e^2 + 16*e + 83, -4*e^2 - 4*e + 48, 7*e^2 - 63, 3*e^2 + 20*e + 3, -4*e^2 + 8*e - 16, 6*e^2 + 8*e - 68, -4*e^2 - 14*e + 65, 13*e^2 - 12*e - 101, 16*e^2 + 8*e - 94, 6*e^2 + 5*e + 8, -6*e^2 + 6*e + 42, -7*e^2 - 32*e + 75, 3*e^2 - 16*e - 11, e^2 - 6*e - 45, -3*e^2 - e + 35, 12*e^2 - 12*e - 102, 11*e^2 - 26, 11*e^2 + 20*e - 5, 2*e^2 + 4*e - 40, -8*e^2 + 10*e + 39, -e^2 - 31*e - 45, 6*e^2 + 33*e - 60, -3*e + 72, 6*e^2 + 28*e - 18, 2*e^2 + 12*e - 54, 6*e^2 + 16*e - 40, -15*e^2 - 30*e + 31, 17*e^2 + 40*e - 45, -2*e^2 - 32*e + 6, -9*e^2 + 6*e + 85, -3*e^2 + 10*e - 21, 6*e^2 + 16*e + 22, -9*e^2 - 17*e - 3, 8*e^2 - 4*e - 94, e^2 + 5*e - 83, -4*e^2 + 21*e + 50, 2*e + 16, 9*e^2 - 12*e - 45, -e^2 - 26*e - 11, 8*e^2 + 32*e + 12, -15*e^2 - 4*e + 88, -e^2 + 8*e - 71, 4*e^2 - 25*e - 36, -5*e^2 + 10*e + 37, -6*e^2 - 2*e + 53, 2*e^2 + 12*e - 18, -17*e^2 - 8*e + 123, 2*e^2 - 11*e - 42, -15*e^2 - 26*e + 74, 5*e^2 - 4*e - 85, -13*e^2 - 16*e + 97, 3*e^2 - 24*e - 55, -13*e^2 - 9*e + 71, 5*e^2 - 18*e - 73, e^2 - 8*e - 53, -3*e^2 - 22*e - 5, -2*e^2 + 12*e - 50, -15*e^2 - 34*e + 35, 19*e^2 + 16*e - 77, -e^2 + 10*e + 2, 12*e^2 + 3*e - 122, -12*e^2 - 18*e + 60, -e^2 - 24*e - 35, 10*e^2 + 13*e - 82, -11*e^2 + 10*e + 114, 21*e^2 + 39*e - 51, 16*e^2 + 20*e - 75, -9*e^2 - 16*e + 49, -21*e^2 - 20*e + 89, 7*e^2 + 20*e - 47, -e^2 + 14*e + 41, -6*e^2 - 16*e + 38, 5*e^2 + 28*e - 39, 14*e^2 + 14*e - 82, 7*e^2 + 11*e - 59, -9*e^2 - 22*e + 13, -17*e^2 - 16*e + 60, 15*e^2 + 36*e - 40, -10*e^2 - 24*e + 33, -16*e^2 - 32*e + 62, -14*e^2 - 12*e + 76, 3*e^2 + 16*e - 11, -15*e^2 - 10*e + 115, -18*e^2 - 13*e + 94, -12*e^2 - 36*e + 42, 17*e^2 - 6*e - 164, -7*e^2 - 20*e + 39, -9*e^2 - 16*e + 37, 14*e^2 + 12*e - 66, -10*e^2 - 2*e + 54, 11*e^2 + 20*e - 19, -5*e^2 + 2*e + 93, -6*e^2 - 14*e + 38]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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