/*
  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([8, 1, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([10, 10, -w^3 + 2*w^2 + 4*w - 3])

primes_array = [
[2, 2, -w^2 + 2],\
[2, 2, -w^3 + 2*w^2 + 4*w - 5],\
[5, 5, -w^3 + 2*w^2 + 3*w - 1],\
[13, 13, w^3 - 2*w^2 - 3*w + 5],\
[17, 17, -w^2 - w + 3],\
[19, 19, -w^3 + 3*w^2 + 2*w - 7],\
[23, 23, w^3 - 2*w^2 - 3*w + 3],\
[31, 31, -w^2 + w + 1],\
[47, 47, -w^3 + w^2 + 4*w - 3],\
[49, 7, 2*w^3 - 5*w^2 - 7*w + 11],\
[53, 53, -3*w^3 + 9*w^2 + 10*w - 31],\
[53, 53, w^3 - w^2 - 4*w + 1],\
[61, 61, 3*w^3 - 6*w^2 - 13*w + 13],\
[61, 61, 2*w^2 - 7],\
[71, 71, w^2 - 3*w - 5],\
[73, 73, 2*w - 3],\
[73, 73, -2*w^3 + 6*w^2 + 6*w - 19],\
[79, 79, 2*w^2 - 5],\
[81, 3, -3],\
[101, 101, 2*w^2 - 4*w - 9],\
[107, 107, 2*w - 1],\
[109, 109, 2*w^3 - 3*w^2 - 11*w + 7],\
[109, 109, 2*w^2 - 2*w - 7],\
[125, 5, -2*w^3 + 8*w^2 - 17],\
[127, 127, 2*w^2 - 4*w - 7],\
[127, 127, -w^2 + 3*w + 1],\
[131, 131, w^3 - w^2 - 4*w - 3],\
[137, 137, 4*w^3 - 10*w^2 - 14*w + 25],\
[139, 139, -w^3 + 2*w^2 + w - 5],\
[139, 139, 2*w^2 - 2*w - 5],\
[149, 149, -w^3 + 4*w^2 - w - 7],\
[149, 149, -2*w^3 + 5*w^2 + 9*w - 19],\
[151, 151, -w^3 + 4*w^2 + w - 11],\
[151, 151, w^2 + w + 1],\
[157, 157, -2*w + 5],\
[163, 163, 4*w^3 - 8*w^2 - 18*w + 19],\
[163, 163, w^3 - 4*w^2 - w + 9],\
[167, 167, -w^3 + 3*w^2 + 2*w - 9],\
[167, 167, w^3 - 2*w^2 - 5*w + 1],\
[173, 173, w^2 - 3*w - 7],\
[173, 173, w^3 - 3*w^2 - 4*w + 5],\
[181, 181, -w^3 + 4*w^2 + w - 13],\
[191, 191, -w^3 + 2*w^2 + 3*w + 1],\
[191, 191, -2*w^3 + 3*w^2 + 9*w - 3],\
[193, 193, -w^3 + 4*w^2 + 3*w - 13],\
[197, 197, 5*w^3 - 10*w^2 - 21*w + 21],\
[211, 211, -w^3 + 3*w^2 + 4*w - 13],\
[227, 227, w^3 - 4*w^2 + w + 5],\
[229, 229, -w^3 + 5*w^2 - 2*w - 11],\
[229, 229, -w^3 + 3*w^2 + 4*w - 3],\
[239, 239, -2*w^3 + 4*w^2 + 8*w - 13],\
[241, 241, 4*w^3 - 10*w^2 - 16*w + 31],\
[241, 241, -5*w^3 + 12*w^2 + 21*w - 31],\
[251, 251, -w^3 + 3*w^2 + 2*w - 11],\
[263, 263, -2*w^3 + 2*w^2 + 10*w + 1],\
[263, 263, -2*w - 5],\
[269, 269, w^2 + w - 5],\
[269, 269, 4*w^3 - 7*w^2 - 19*w + 15],\
[271, 271, 2*w^3 - 5*w^2 - 5*w + 11],\
[271, 271, -w^3 + 7*w + 3],\
[277, 277, -2*w^3 + 4*w^2 + 6*w - 5],\
[277, 277, 4*w^2 - 13],\
[281, 281, w^3 - 5*w^2 + 11],\
[307, 307, w^3 - 3*w - 3],\
[313, 313, 5*w^3 - 10*w^2 - 23*w + 27],\
[313, 313, -2*w^3 + 3*w^2 + 9*w - 7],\
[317, 317, -3*w^3 + 6*w^2 + 11*w - 15],\
[347, 347, -w^3 - w^2 + 1],\
[347, 347, -2*w^3 + 6*w^2 + 6*w - 17],\
[353, 353, -2*w^3 + 4*w^2 + 8*w - 5],\
[353, 353, w^3 - 5*w - 1],\
[359, 359, -2*w^2 + 1],\
[367, 367, -w^3 + 4*w^2 + 3*w - 17],\
[373, 373, 2*w^2 - 2*w - 13],\
[397, 397, 5*w^3 - 13*w^2 - 18*w + 39],\
[397, 397, 2*w^3 - 5*w^2 - 7*w + 9],\
[401, 401, -4*w^3 + 12*w^2 + 8*w - 25],\
[401, 401, -3*w^3 + 7*w^2 + 8*w - 13],\
[421, 421, -4*w^3 + 11*w^2 + 13*w - 31],\
[433, 433, 2*w^3 - 12*w - 15],\
[433, 433, w^3 - w^2 - 6*w + 5],\
[439, 439, 5*w^3 - 13*w^2 - 12*w + 19],\
[439, 439, -2*w^3 + 3*w^2 + 7*w + 1],\
[449, 449, -w^3 + 4*w^2 + 3*w - 11],\
[461, 461, -4*w^3 + 11*w^2 + 7*w - 19],\
[461, 461, -w^3 + w^2 + 2*w + 1],\
[463, 463, -w^3 + 2*w^2 + 7*w - 1],\
[463, 463, -4*w^3 + 11*w^2 + 7*w - 13],\
[467, 467, 2*w^2 - 2*w - 3],\
[467, 467, 2*w^3 - 4*w^2 - 6*w + 11],\
[487, 487, -3*w^3 + 11*w^2 + 2*w - 23],\
[487, 487, w^3 - w + 5],\
[491, 491, w^3 - 2*w^2 - 3*w + 9],\
[499, 499, w^3 - 3*w^2 - 4*w + 1],\
[503, 503, -6*w^3 + 11*w^2 + 27*w - 21],\
[503, 503, -3*w^3 + 8*w^2 + 5*w - 9],\
[521, 521, 2*w^2 - 4*w - 11],\
[541, 541, -3*w^3 + 7*w^2 + 8*w - 11],\
[557, 557, 5*w^3 - 11*w^2 - 18*w + 21],\
[557, 557, 4*w^3 - 7*w^2 - 17*w + 9],\
[557, 557, 4*w^3 - 8*w^2 - 16*w + 15],\
[557, 557, -3*w^3 + 6*w^2 + 11*w - 9],\
[563, 563, -2*w^3 + 6*w^2 + 8*w - 13],\
[569, 569, -2*w^3 + 3*w^2 + 7*w - 11],\
[587, 587, 3*w^3 - 8*w^2 - 9*w + 15],\
[601, 601, -3*w^2 + 5*w + 9],\
[607, 607, -w^3 + w^2 - 5],\
[619, 619, -2*w^3 + 4*w^2 + 6*w - 13],\
[631, 631, -2*w^3 + 7*w^2 + 5*w - 23],\
[643, 643, 2*w^3 - 2*w^2 - 12*w - 5],\
[659, 659, -w^3 + 6*w^2 + 3*w - 11],\
[659, 659, -3*w^2 + w + 9],\
[661, 661, -2*w^3 + 4*w^2 + 8*w - 3],\
[661, 661, -w^3 + 4*w^2 + 5*w - 7],\
[673, 673, w^2 - w - 9],\
[673, 673, 2*w^3 - 7*w^2 - 3*w + 17],\
[677, 677, 9*w^3 - 20*w^2 - 37*w + 51],\
[701, 701, -7*w^3 + 18*w^2 + 27*w - 57],\
[709, 709, 4*w^3 - 6*w^2 - 14*w + 17],\
[709, 709, w^3 + w^2 - 6*w - 17],\
[719, 719, -2*w^3 + 6*w^2 + 4*w - 15],\
[719, 719, -2*w^3 + 3*w^2 + 7*w + 3],\
[727, 727, -w^3 + 3*w^2 + 6*w - 3],\
[743, 743, -2*w^3 + 2*w^2 + 6*w - 1],\
[757, 757, 6*w^3 - 16*w^2 - 22*w + 51],\
[757, 757, w^3 + w^2 - 10*w - 11],\
[761, 761, w^2 + w - 7],\
[761, 761, 2*w^2 - 17],\
[761, 761, 2*w^3 - 6*w^2 - 2*w + 13],\
[761, 761, 2*w^2 - 4*w - 3],\
[769, 769, -w^3 - w^2 + 4*w + 7],\
[769, 769, w^3 + w^2 - 4*w - 1],\
[787, 787, 3*w^3 - 6*w^2 - 11*w + 3],\
[809, 809, -w^3 + 3*w^2 + 2*w - 1],\
[809, 809, 2*w^3 - w^2 - 9*w - 3],\
[809, 809, 2*w^3 - 7*w^2 - 3*w + 15],\
[809, 809, 2*w^3 - 2*w^2 - 8*w - 1],\
[811, 811, -8*w^3 + 19*w^2 + 33*w - 57],\
[811, 811, -2*w^3 + 2*w^2 + 4*w - 11],\
[823, 823, 2*w^3 - w^2 - 7*w + 1],\
[823, 823, -3*w^3 + 8*w^2 + 7*w - 9],\
[829, 829, -w^3 + 5*w - 1],\
[853, 853, -w^3 + 5*w^2 - 2*w - 15],\
[853, 853, -2*w^3 + 4*w^2 + 4*w - 9],\
[853, 853, 2*w^3 - w^2 - 11*w - 3],\
[853, 853, 2*w^3 - 5*w^2 - 7*w + 5],\
[857, 857, -2*w^3 + 5*w^2 + 7*w - 7],\
[859, 859, w^3 - 2*w^2 - w + 9],\
[859, 859, w^3 - 2*w^2 - w - 1],\
[877, 877, 2*w^3 - 6*w^2 - 8*w + 25],\
[877, 877, -4*w^3 + 8*w^2 + 16*w - 19],\
[881, 881, -4*w^2 + 6*w + 13],\
[881, 881, w^3 + 2*w^2 - 7*w - 9],\
[887, 887, -4*w^2 + 4*w + 11],\
[887, 887, -w^3 - w^2 + 6*w + 11],\
[887, 887, w^3 - 6*w^2 - w + 29],\
[887, 887, 4*w^3 - 9*w^2 - 19*w + 31],\
[907, 907, -3*w^3 + 9*w^2 + 12*w - 25],\
[907, 907, -w^3 + 2*w^2 + 7*w - 7],\
[929, 929, -7*w^3 + 13*w^2 + 32*w - 29],\
[941, 941, -2*w^3 + 10*w^2 - 2*w - 23],\
[941, 941, 4*w^3 - 9*w^2 - 13*w + 13],\
[967, 967, -w^3 + 2*w^2 - w - 1],\
[977, 977, w^3 - 5*w^2 + 15],\
[983, 983, w^3 + 2*w^2 - 9*w - 11],\
[983, 983, 2*w^3 - 5*w^2 - 5*w + 13],\
[997, 997, -4*w^3 + 10*w^2 + 12*w - 23],\
[1009, 1009, 2*w^2 + 2*w + 1],\
[1019, 1019, 2*w^3 - 2*w^2 - 6*w + 3],\
[1031, 1031, w^3 - 9*w - 7],\
[1033, 1033, 2*w^3 - 2*w^2 - 8*w + 1],\
[1063, 1063, -w^3 - w - 7],\
[1063, 1063, 4*w^3 - 8*w^2 - 12*w + 5],\
[1091, 1091, 2*w^3 - 2*w^2 - 4*w + 1],\
[1093, 1093, 3*w^3 - 4*w^2 - 13*w - 1],\
[1093, 1093, w^3 - w^2 - 4*w - 7],\
[1097, 1097, w^3 + 3*w^2 - 2*w - 9],\
[1109, 1109, w^2 + w - 9],\
[1109, 1109, -2*w^3 + 5*w^2 + 3*w - 11],\
[1123, 1123, -5*w^3 + 16*w^2 + 7*w - 27],\
[1123, 1123, 8*w^3 - 17*w^2 - 35*w + 47],\
[1163, 1163, 3*w^3 - 3*w^2 - 14*w - 5],\
[1171, 1171, 2*w^3 - w^2 - 7*w - 1],\
[1171, 1171, -3*w^3 + 6*w^2 + 9*w - 7],\
[1181, 1181, 3*w^3 - 7*w^2 - 10*w + 21],\
[1187, 1187, w^3 - 2*w^2 - 7*w + 3],\
[1201, 1201, -3*w^3 + 5*w^2 + 10*w - 3],\
[1201, 1201, -3*w^2 + 3*w + 19],\
[1213, 1213, w^3 - 5*w^2 + 4*w + 7],\
[1217, 1217, w^3 - 4*w^2 - 5*w + 5],\
[1223, 1223, -w^3 - w^2 + 2*w + 5],\
[1223, 1223, w^3 - 5*w^2 + 4*w + 5],\
[1231, 1231, 7*w^3 - 15*w^2 - 28*w + 33],\
[1237, 1237, w^3 - 5*w^2 + 2*w + 9],\
[1249, 1249, -2*w^3 + 2*w^2 + 10*w - 3],\
[1259, 1259, -4*w^3 + 8*w^2 + 16*w - 13],\
[1283, 1283, w^3 - 2*w^2 - 3*w - 3],\
[1289, 1289, -w^3 + w^2 + 4*w - 7],\
[1291, 1291, 2*w^3 - 5*w^2 - 9*w + 9],\
[1297, 1297, -10*w^3 + 24*w^2 + 38*w - 63],\
[1301, 1301, 3*w^3 - 8*w^2 - 11*w + 17],\
[1301, 1301, 2*w^2 - 4*w - 1],\
[1307, 1307, w^3 - w^2 + 7],\
[1327, 1327, -6*w^3 + 12*w^2 + 24*w - 31],\
[1327, 1327, -w^3 + 2*w^2 - w - 5],\
[1327, 1327, 8*w^3 - 16*w^2 - 34*w + 35],\
[1327, 1327, 3*w^3 - 8*w^2 - 3*w + 15],\
[1367, 1367, -w^3 + 2*w^2 + 7*w - 5],\
[1369, 37, 7*w^3 - 17*w^2 - 18*w + 19],\
[1369, 37, w^3 - 7*w^2 + 6*w + 19],\
[1381, 1381, 6*w^2 - 6*w - 35],\
[1427, 1427, -2*w^3 + 3*w^2 + 11*w + 1],\
[1427, 1427, -2*w^3 + 7*w^2 + 7*w - 13],\
[1427, 1427, 3*w^3 - 8*w^2 - 9*w + 9],\
[1427, 1427, -12*w^3 + 26*w^2 + 50*w - 65],\
[1433, 1433, w^3 - 7*w^2 - 4*w + 11],\
[1439, 1439, -5*w^3 + 12*w^2 + 21*w - 39],\
[1453, 1453, -w^3 - w^2 - 2*w - 7],\
[1453, 1453, 2*w^3 - 4*w^2 - 6*w - 1],\
[1459, 1459, 3*w^2 - 7*w - 15],\
[1483, 1483, 4*w^3 - 15*w^2 - 9*w + 55],\
[1483, 1483, w^3 - 3*w - 5],\
[1493, 1493, -2*w^3 + 8*w^2 + 2*w - 23],\
[1499, 1499, -w^3 + 9*w + 1],\
[1499, 1499, w^3 - 4*w^2 + 3*w + 3],\
[1499, 1499, 5*w^3 - 12*w^2 - 13*w + 17],\
[1499, 1499, w^3 + w^2 - 8*w - 15],\
[1511, 1511, -7*w^3 + 17*w^2 + 26*w - 47],\
[1531, 1531, w^3 - 4*w^2 - 7*w + 13],\
[1543, 1543, 4*w^3 - 7*w^2 - 21*w + 21],\
[1543, 1543, 5*w^2 + 3*w - 7],\
[1579, 1579, 4*w^3 - 9*w^2 - 13*w + 17],\
[1583, 1583, -2*w^3 + 6*w^2 + 6*w - 23],\
[1597, 1597, -4*w^3 + 11*w^2 + 13*w - 25],\
[1609, 1609, 4*w^3 - 11*w^2 - 11*w + 27],\
[1609, 1609, -4*w^3 + 13*w^2 + 5*w - 21],\
[1637, 1637, -6*w^3 + 16*w^2 + 20*w - 45],\
[1667, 1667, 5*w^2 - 3*w - 13],\
[1667, 1667, -5*w^2 - w + 11],\
[1697, 1697, -w^3 + 3*w^2 + 8*w + 1],\
[1699, 1699, -w^3 + 4*w^2 - w - 13],\
[1699, 1699, 5*w^3 - 14*w^2 - 9*w + 25],\
[1721, 1721, 2*w^3 - 7*w^2 - w + 17],\
[1723, 1723, -3*w^3 + 6*w^2 + 9*w - 11],\
[1733, 1733, w^3 - w^2 - 8*w + 3],\
[1747, 1747, w^3 - 2*w^2 - 7*w - 5],\
[1753, 1753, -w^3 + 3*w^2 - 11],\
[1759, 1759, -w^3 + 6*w^2 - w - 15],\
[1759, 1759, -4*w^3 + 8*w^2 + 14*w - 19],\
[1783, 1783, 3*w^3 - 6*w^2 - 7*w + 13],\
[1783, 1783, -5*w^2 - 3*w + 13],\
[1787, 1787, -2*w^3 + 7*w^2 + 5*w - 21],\
[1787, 1787, w^2 - 3*w - 11],\
[1787, 1787, -2*w - 7],\
[1787, 1787, -w^3 + 3*w^2 + 4*w - 15],\
[1789, 1789, w^3 - w^2 - 8*w - 1],\
[1789, 1789, -4*w^2 + 8*w + 13],\
[1801, 1801, -3*w^3 + 9*w^2 + 6*w - 11],\
[1823, 1823, -2*w^3 + 5*w^2 + 5*w - 15],\
[1831, 1831, 3*w^3 - 5*w^2 - 12*w + 9],\
[1831, 1831, 3*w^3 - 3*w^2 - 18*w + 1],\
[1831, 1831, w^3 - 5*w^2 - 2*w + 5],\
[1831, 1831, w^3 - 5*w^2 - 2*w + 13],\
[1847, 1847, 2*w^3 - 2*w^2 - 8*w - 9],\
[1847, 1847, -3*w^3 + 5*w^2 + 14*w - 17],\
[1849, 43, 3*w^3 - 3*w^2 - 12*w + 5],\
[1849, 43, 3*w^3 - 2*w^2 - 19*w - 5],\
[1861, 1861, 4*w^3 - 13*w^2 - 5*w + 27],\
[1867, 1867, w^3 + 2*w^2 - 5*w - 5],\
[1871, 1871, -w^3 + 5*w^2 + 2*w - 15],\
[1871, 1871, 2*w^3 - w^2 - 15*w + 1],\
[1873, 1873, w^3 - 7*w - 11],\
[1873, 1873, -4*w^3 + 9*w^2 + 11*w - 17],\
[1877, 1877, -4*w - 1],\
[1877, 1877, 4*w + 9],\
[1889, 1889, -3*w^3 + 7*w^2 + 6*w - 7],\
[1901, 1901, 2*w^3 - 8*w^2 - 2*w + 17],\
[1901, 1901, -3*w^2 + 7*w + 7],\
[1913, 1913, 4*w^3 - 14*w^2 - 2*w + 27],\
[1931, 1931, w^2 + 3*w - 7],\
[1931, 1931, 3*w^3 - 3*w^2 - 12*w - 5],\
[1933, 1933, -2*w^3 + 7*w^2 + 7*w - 17],\
[1951, 1951, -2*w^3 + 6*w^2 + 4*w - 17],\
[1951, 1951, -5*w^3 + 13*w^2 + 20*w - 43],\
[1973, 1973, -2*w^3 + 9*w^2 - w - 19],\
[1979, 1979, -4*w^3 + 10*w^2 + 18*w - 37],\
[1979, 1979, -2*w^3 + 6*w^2 + 8*w - 11],\
[1987, 1987, -w^3 + 3*w^2 + 6*w - 13],\
[1997, 1997, -4*w^3 + 11*w^2 + 13*w - 29],\
[1997, 1997, 4*w - 1],\
[1997, 1997, 9*w^3 - 23*w^2 - 22*w + 35],\
[1997, 1997, -6*w^3 + 18*w^2 + 8*w - 31],\
[1999, 1999, 6*w^3 - 19*w^2 - 9*w + 37]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 - 6*x^2 + 3*x + 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -1, 1, -e^2 - 2*e + 4, e^3 + e^2 - 6*e - 3, e^2 + 2*e - 5, -3*e^3 - 4*e^2 + 11*e + 6, 3*e^3 + 5*e^2 - 12*e - 8, -e^3 + 8*e - 3, e^3 + e^2 - 3*e - 8, 5*e^3 + 7*e^2 - 19*e - 9, -3*e^3 - 4*e^2 + 13*e + 3, e^3 - 2*e^2 - 8*e + 4, 2*e^3 + 2*e^2 - 9*e - 5, -2*e^3 + e^2 + 11*e - 6, 4*e^3 - 21*e + 4, -2*e^3 - 3*e^2 + 7*e + 4, -4*e^3 - 4*e^2 + 18*e + 5, -2*e^3 - e^2 + 10*e - 5, -5*e^3 - 6*e^2 + 24*e + 6, -3*e^3 - 2*e^2 + 12*e - 3, -2*e^3 - 2*e^2 + 9*e - 4, -e^3 + 4*e^2 + 6*e - 13, -4*e^3 - 6*e^2 + 13*e + 6, e^3 - 3*e^2 - 10*e + 14, 3*e^2 + 2*e - 13, -3*e^3 - 4*e^2 + 10*e, -2*e^3 - 2*e^2 + 13*e - 3, 5*e^3 + 6*e^2 - 24*e - 2, 4*e^3 + 10*e^2 - 9*e - 29, 4*e^3 + 3*e^2 - 17*e - 6, -e^3 - 5*e^2 + 8*e + 21, -4*e^3 + 19*e - 7, -e^3 - e^2 + 5*e + 2, 5*e^3 + 3*e^2 - 20*e - 8, -2*e^3 - 5*e^2 + 8*e + 14, -e^3 - 6*e^2 + 5*e + 17, -3*e^3 - 8*e^2 + 16*e + 18, 8*e^3 + 5*e^2 - 33*e + 3, -5*e^3 - 3*e^2 + 23*e + 3, -3*e^3 - e^2 + 11*e - 12, -6*e^3 - 9*e^2 + 24*e + 13, e^3 + 6*e^2 - 3*e - 18, 5*e^3 + 3*e^2 - 26*e - 6, 4*e^3 + e^2 - 17*e + 11, 3*e^2 + e - 9, 2*e^3 - 6*e + 8, -4*e^3 - 8*e^2 + 17*e + 12, e^3 + 8*e^2 + 6*e - 26, -12*e^3 - 13*e^2 + 51*e + 1, -e^2 - 5*e - 3, -3*e^3 - 7*e^2 + 11*e + 13, -3*e^3 + e^2 + 19*e - 8, 4*e^3 - 15*e + 6, 8*e^3 + 11*e^2 - 25*e - 24, 4*e^2 + 4*e - 6, -e^3 + 3*e - 9, -3*e^3 - 6*e^2 + 9*e + 9, -3*e^3 - 2*e^2 + 14*e + 1, 3*e^3 + 6*e^2 - 12*e - 11, 8*e^3 + 5*e^2 - 37*e - 1, 17, -3*e^3 - 6*e^2 + 12*e + 6, -8*e^3 - 8*e^2 + 33*e + 1, 4*e^2 - 2*e - 14, -2*e^3 + 2*e^2 + 3*e - 20, 7*e^3 + 11*e^2 - 36*e - 15, 7*e^3 + 8*e^2 - 24*e - 12, 9*e^3 + 14*e^2 - 31*e - 27, 2*e^3 + 3*e^2 - 9*e - 12, -6*e^3 - 7*e^2 + 20*e - 9, 3*e^3 - 2*e^2 - 23*e + 9, 5*e^3 + 3*e^2 - 18*e - 5, 4*e^3 + 9*e^2 - 18*e - 19, -6*e^3 - 16*e^2 + 24*e + 37, -2*e^3 + e^2 - 8, 9*e^2 + 14*e - 33, 4*e^3 + 9*e^2 - 22*e - 27, -3*e^3 + 6*e^2 + 21*e - 13, 5*e^3 + 11*e^2 - 12*e - 47, 4*e^3 - 4*e^2 - 14*e + 25, 12*e^3 + 13*e^2 - 57*e - 8, 3*e^3 - 2*e^2 - 7*e + 28, 7*e^3 + 6*e^2 - 40*e - 3, -4*e^3 + 18*e - 21, -4*e^3 + 3*e^2 + 13*e - 21, 3*e^3 + 3*e^2 - 17*e - 16, 2*e^3 - 8*e^2 - 21*e + 23, -7*e^3 - 9*e^2 + 26*e - 6, -3*e^3 + 7*e - 12, 6*e^3 + 8*e^2 - 20*e - 13, -8*e^3 - 8*e^2 + 22*e - 1, -9*e^2 - 2*e + 27, -5*e^3 - 9*e^2 + 9*e + 14, -4*e^3 - 9*e^2 + 16*e + 12, 7*e^3 + 2*e^2 - 35*e + 9, -6*e^3 - e^2 + 23*e + 6, -2*e^3 - 14*e^2 + 5*e + 47, 12*e^3 + 9*e^2 - 43*e, 3*e^3 - e^2 - 21*e + 3, -3*e^3 - 10*e^2 + e + 24, -8*e^3 - 3*e^2 + 52*e - 18, -11*e^3 - 11*e^2 + 46*e - 6, -2*e^3 - 4*e^2 + 4*e - 27, -7*e^3 - 13*e^2 + 21*e + 30, 3*e^3 + 6*e^2 - 14*e - 14, 3*e^3 + 11*e^2 - 3*e - 44, 7*e^3 - 4*e^2 - 37*e + 19, 8*e^3 + 4*e^2 - 45*e + 17, 4*e^3 + 6*e^2 - 9*e - 14, 7*e^3 + 16*e^2 - 24*e - 39, -e^3 - 6*e^2 + 2*e + 39, -3*e^3 + 3*e^2 + 21*e + 1, -10*e^3 - 8*e^2 + 42*e - 2, -e^3 + 2*e^2 + 8*e - 28, 4*e^3 + 9*e^2 - 9*e - 43, -9*e^3 - 14*e^2 + 25*e + 21, 9*e^3 + 10*e^2 - 40*e - 6, -2*e^3 - 8*e^2 + 8*e + 29, 12*e^3 + 7*e^2 - 66*e - 1, 7*e^3 + 8*e^2 - 17*e - 15, -5*e^3 - 10*e^2 + 21*e - 12, -9*e^3 - 10*e^2 + 42*e - 5, -e^3 + 6*e^2 + 6*e - 18, 16*e^3 + 10*e^2 - 71*e - 4, 5*e^3 + 6*e^2 - 26*e - 4, 9*e^3 + 12*e^2 - 45*e - 24, 3*e^3 - 5*e^2 - 5*e + 36, -7*e^3 - 15*e^2 + 23*e + 15, -3*e^3 + 8*e^2 + 27*e - 24, -5*e^3 - e^2 + 29*e - 32, 10*e^3 + 16*e^2 - 44*e - 29, -12*e^3 - 24*e^2 + 42*e + 43, 13*e^3 + 9*e^2 - 64*e - 3, 19*e^3 + 21*e^2 - 86*e - 3, e^3 - 5*e^2 + 4*e + 39, 3*e^3 - 15*e + 33, -6*e^3 - 6*e^2 + 18*e - 5, -4*e^3 - 13*e^2 + 3*e + 40, -6*e^3 - 3*e^2 + 17*e - 1, -13*e^3 - 22*e^2 + 57*e + 29, e^3 - 9*e - 8, 12*e^3 + 12*e^2 - 44*e - 29, 10*e^3 + 17*e^2 - 39*e - 20, -2*e^3 - 2*e^2 + 9*e - 5, 2*e^3 + 2*e^2 - 24*e - 5, 7*e^3 + 3*e^2 - 54*e + 18, -4*e^3 + 5*e^2 + 23*e - 17, -15*e^3 - 18*e^2 + 54*e + 16, 9*e^3 - 51*e + 11, 9*e^3 + 21*e^2 - 34*e - 52, -21*e^3 - 21*e^2 + 86*e + 21, 2*e^3 - 2*e^2 + 7*e + 24, 6*e^3 + 11*e^2 - 15*e - 21, 4*e^2 - e - 12, e^3 + 16*e^2 + 18*e - 48, -2*e^3 + 2*e^2 + 10*e - 24, 10*e^2 + 24*e - 37, 3*e^3 + 13*e^2 - 3*e - 40, -10*e^3 + 4*e^2 + 58*e - 15, 3*e^3 + e^2 - 31*e + 12, 7*e^3 + 12*e^2 - 38*e - 27, e^3 - 5*e^2 - 15*e - 10, 13*e^3 + 21*e^2 - 49*e - 24, -9*e^3 - 10*e^2 + 41*e + 6, 7*e^3 + 14*e^2 - 26*e - 24, 9*e^3 + 33*e^2 - 24*e - 71, 12*e^3 + 5*e^2 - 50*e + 14, -17*e^3 - 15*e^2 + 59*e + 12, -8*e^3 - 14*e^2 + 37*e - 3, -17*e^3 - 21*e^2 + 80*e + 11, 13*e^3 + 5*e^2 - 78*e + 19, 4*e^3 + 2*e^2 - 15*e - 14, 11*e^3 + 9*e^2 - 48*e + 33, -15*e^2 - 21*e + 41, 8*e^3 - 5*e^2 - 39*e + 47, e^3 + 8*e^2 - 12*e - 15, 13*e^3 + 6*e^2 - 46*e + 27, 10*e^3 + 18*e^2 - 52*e - 39, -2*e^3 + 11*e^2 + 20*e - 38, -11*e^2 - 3*e + 49, 3*e^3 + 14*e^2 - 5*e - 66, -9*e^3 - 17*e^2 + 35*e + 53, -2*e^3 - e^2 - 7*e - 28, 19*e^3 + 19*e^2 - 78*e - 15, 9*e^3 + 10*e^2 - 45*e + 18, -8*e^3 + 64*e - 1, -13*e^3 - 12*e^2 + 42*e - 13, -3*e^3 - 12*e^2 + e + 50, -3*e^3 + 6*e^2 + 33*e - 15, 26*e^3 + 36*e^2 - 104*e - 39, 13*e^3 + 8*e^2 - 72*e + 3, 10*e^3 + 3*e^2 - 33*e + 28, 6*e^3 + e^2 - 21*e + 58, 18*e^3 + 14*e^2 - 101*e + 4, -2*e^3 - 4*e^2 + 20*e - 9, 10*e^3 + 8*e^2 - 47*e - 12, 4*e^3 + 4*e^2 - 31*e + 24, -5*e^3 - 14*e^2 + 18*e + 16, -8*e^3 - 5*e^2 + 24*e - 13, -15*e^3 - 18*e^2 + 64*e + 30, 6*e^3 + 21*e^2 - e - 51, 8*e^3 + 3*e^2 - 26*e + 27, -27*e^3 - 23*e^2 + 105*e + 17, 14*e^3 + 10*e^2 - 66*e - 25, 9*e^3 + 18*e^2 - 22*e - 34, -2*e^3 + 9*e^2 - 2*e - 37, 11*e^3 + 11*e^2 - 38*e + 21, 5*e^3 - 9*e^2 - 27*e + 32, 6*e - 19, -24*e^3 - 25*e^2 + 90*e + 35, 3*e^3 - 14*e - 24, -8*e^3 + 3*e^2 + 20*e - 60, 2*e^3 - 7*e^2 - 3*e + 66, 17*e^3 + 10*e^2 - 100*e + 24, -24*e^3 - 21*e^2 + 89*e - 6, 10*e^3 + 2*e^2 - 53*e, 13*e^3 + 19*e^2 - 42*e - 31, 5*e^3 + 22*e^2 - 3*e - 61, -6*e - 41, -21*e^3 - 26*e^2 + 90*e + 16, -13*e^3 - 12*e^2 + 45*e + 16, 5*e^3 - 5*e^2 - 16*e + 15, 8*e^3 + 18*e^2 - 44*e - 30, -12*e^3 - 10*e^2 + 43*e - 27, -4*e^3 - 10*e^2 + 20*e - 12, 14*e^3 + 13*e^2 - 63*e - 18, 6*e^3 + 7*e^2 - 6*e - 6, -21*e^3 - 10*e^2 + 96*e - 23, -20*e^3 - 30*e^2 + 77*e + 55, 2*e^3 + 22*e^2 - 41, -8*e^3 + 5*e^2 + 51*e + 2, -11*e^3 - 28*e^2 + 10*e + 81, 25*e^3 + 31*e^2 - 111*e - 22, 3*e^3 - 4*e^2 - 15*e + 52, 23*e^2 + 7*e - 68, -5*e^3 - 12*e^2 + 36*e + 15, 13*e^3 - 43*e + 57, -14*e^3 + e^2 + 65*e - 30, -6*e^3 - 11*e^2 + 11*e + 15, -3*e^3 - 4*e^2 + 15*e + 49, -16*e^3 - 5*e^2 + 54*e - 23, 12*e^3 + 15*e^2 - 36*e - 39, -10*e^3 + e^2 + 39*e - 31, -6*e^3 - 4*e^2 + 24*e + 42, 15*e^3 + 21*e^2 - 60*e - 25, 11*e^3 + 9*e^2 - 51*e + 4, -3*e^3 + 15*e^2 + 35*e - 34, 17*e^3 + 11*e^2 - 75*e - 16, 8*e^3 + 11*e^2 - 27*e - 29, 4*e^2 - 12*e - 5, -2*e^3 - 14*e^2 - 23*e + 54, -10*e^3 - 2*e^2 + 68*e - 3, -3*e^3 - 5*e^2 + 31*e + 3, 6*e^3 + 15*e^2 - 25*e - 18, 24*e^3 + 20*e^2 - 96*e - 7, -4*e^3 - 3*e^2 + 30*e + 38, e^3 - 18*e^2 - 20*e + 38, -12*e^3 - 22*e^2 + 57*e + 45, 24*e^3 + 34*e^2 - 100*e - 28, -5*e^3 + 7*e^2 + 30*e + 2, 5*e^3 + 6*e^2 - 39*e - 37, 8*e^3 + 19*e^2 - 39*e - 40, -15*e^3 - 9*e^2 + 70*e + 36, -2*e^3 - 27*e^2 - 14*e + 54, 13*e^3 + 16*e^2 - 53*e - 10, -4*e^3 - 20*e^2 - 15*e + 62, 8*e^3 - e^2 - 66*e + 16, -11*e^3 - 19*e^2 + 49*e + 31, -10*e^3 - 23*e^2 + 34*e + 60, 12*e^3 - 44*e + 60, 8*e^3 + 21*e^2 - 29*e - 46, -9*e^2 + 8, -24*e^3 - 31*e^2 + 91*e + 48, 5*e^3 + 6*e^2 - 28*e + 3, 4*e^3 + 15*e^2 + 3*e - 30, 5*e^3 + 3*e^2 - 10*e + 3, -12*e^3 - 28*e^2 + 52*e + 81, -5*e^3 - 3*e^2 + 14*e - 42, 16*e^3 + 4*e^2 - 70*e + 12, 36*e^3 + 34*e^2 - 147*e - 6, -11*e^3 + 6*e^2 + 48*e - 46, -15*e^3 - 9*e^2 + 78*e + 7, 14*e^3 + 18*e^2 - 40*e - 8, -11*e^3 - 6*e^2 + 77*e - 3, 23*e^3 + 16*e^2 - 88*e + 3, -4*e^3 + 6*e^2 + 15*e - 36, 4*e^3 - 4*e^2 - 33*e - 23, 18*e^3 + 3*e^2 - 83*e + 36, -6*e^3 - 21*e^2 - 13*e + 63, 3*e^3 + 9*e^2 - 8*e - 30, 3*e^3 + 4*e^2 - 22*e + 6, 3*e^3 - 11*e^2 - 37*e + 41]
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^3 + 2*w^2 + 4*w - 5])] = 1
AL_eigenvalues[ZF.ideal([5, 5, -w^3 + 2*w^2 + 3*w - 1])] = -1

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