/*
  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([5, -1, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([7, 7, -w^3 + 2*w^2 + 4*w - 3])

primes_array = [
[3, 3, -w^3 + 2*w^2 + 5*w - 3],\
[5, 5, w],\
[7, 7, -w^3 + 2*w^2 + 4*w - 3],\
[13, 13, -w^2 + w + 4],\
[13, 13, -w^3 + 2*w^2 + 5*w - 2],\
[16, 2, 2],\
[17, 17, -w + 2],\
[19, 19, -w^3 + 2*w^2 + 3*w - 2],\
[27, 3, w^3 - 3*w^2 - 4*w + 7],\
[31, 31, w^3 - 3*w^2 - 3*w + 7],\
[31, 31, -w^3 + w^2 + 6*w + 1],\
[41, 41, w^2 - w - 1],\
[43, 43, 2*w^3 - 5*w^2 - 6*w + 4],\
[47, 47, -w^3 + 2*w^2 + 5*w - 1],\
[53, 53, -w - 3],\
[53, 53, -w^3 + 3*w^2 + 3*w - 6],\
[59, 59, 2*w^2 - 3*w - 6],\
[59, 59, w^3 - w^2 - 7*w - 3],\
[79, 79, 2*w^3 - 4*w^2 - 8*w + 3],\
[79, 79, w^2 - 2*w - 1],\
[101, 101, 2*w^3 - 4*w^2 - 9*w + 4],\
[103, 103, -w^3 + 3*w^2 + 4*w - 2],\
[103, 103, w^2 - 3*w - 2],\
[107, 107, -w^3 + w^2 + 5*w - 1],\
[109, 109, -w^3 + 2*w^2 + 4*w - 6],\
[121, 11, -w^3 + 2*w^2 + 6*w - 3],\
[121, 11, w^2 - 3*w - 3],\
[125, 5, -w^3 + w^2 + 7*w + 1],\
[127, 127, 2*w^3 - 5*w^2 - 5*w + 7],\
[127, 127, 2*w^3 - 5*w^2 - 7*w + 6],\
[167, 167, -2*w^3 + 5*w^2 + 7*w - 11],\
[169, 13, -w^2 + w + 8],\
[181, 181, -2*w^3 + 5*w^2 + 8*w - 7],\
[193, 193, -w^3 + 3*w^2 + 3*w - 1],\
[197, 197, 2*w^3 - 4*w^2 - 7*w + 8],\
[197, 197, 3*w^3 - 7*w^2 - 10*w + 9],\
[199, 199, w^3 - 2*w^2 - 3*w - 3],\
[211, 211, -w^3 + w^2 + 7*w - 2],\
[211, 211, w^3 - w^2 - 6*w + 1],\
[227, 227, 2*w^3 - 3*w^2 - 9*w + 3],\
[229, 229, 3*w^3 - 6*w^2 - 13*w + 8],\
[239, 239, 2*w^3 - 4*w^2 - 9*w + 3],\
[239, 239, 2*w^3 - 4*w^2 - 6*w + 1],\
[241, 241, 3*w^3 - 7*w^2 - 9*w + 6],\
[241, 241, -2*w^3 + 4*w^2 + 6*w - 3],\
[251, 251, -4*w^3 + 10*w^2 + 15*w - 16],\
[251, 251, -w^3 + 3*w^2 - 3],\
[271, 271, -w^3 + 4*w^2 + 4*w - 11],\
[271, 271, -3*w^3 + 9*w^2 + 6*w - 13],\
[277, 277, -w^3 + 3*w^2 + 2*w - 9],\
[281, 281, -w^3 + 4*w^2 + w - 8],\
[293, 293, 3*w^3 - 7*w^2 - 11*w + 13],\
[293, 293, w^2 - 6],\
[293, 293, -4*w^3 + 11*w^2 + 9*w - 14],\
[293, 293, 3*w^3 - 5*w^2 - 15*w + 6],\
[311, 311, -2*w^3 + 4*w^2 + 7*w - 4],\
[313, 313, -w^3 + 4*w^2 + 3*w - 13],\
[313, 313, -w^3 + w^2 + 6*w - 2],\
[317, 317, w^3 - 4*w^2 - w + 9],\
[337, 337, 3*w^3 - 7*w^2 - 8*w + 7],\
[343, 7, -2*w^3 + 3*w^2 + 9*w + 1],\
[359, 359, -w^3 + 2*w^2 + 4*w - 7],\
[359, 359, 2*w^3 - 3*w^2 - 10*w + 4],\
[367, 367, 2*w^3 - 4*w^2 - 5*w + 2],\
[367, 367, 2*w^3 - 3*w^2 - 11*w - 2],\
[367, 367, 2*w - 7],\
[367, 367, w^3 - 7*w - 4],\
[373, 373, -w^3 + 4*w^2 + w - 14],\
[373, 373, -2*w^3 + 4*w^2 + 10*w - 11],\
[379, 379, w^3 - 2*w^2 - 2*w - 1],\
[383, 383, w^3 - 8*w - 4],\
[397, 397, 4*w^3 - 10*w^2 - 12*w + 7],\
[397, 397, -2*w^3 + 3*w^2 + 9*w - 2],\
[401, 401, -w^3 + 6*w + 8],\
[409, 409, 2*w^3 - 3*w^2 - 11*w + 4],\
[419, 419, 3*w^3 - 6*w^2 - 15*w + 7],\
[419, 419, -w^2 + 4*w + 8],\
[431, 431, 5*w^3 - 15*w^2 - 10*w + 18],\
[431, 431, 3*w^3 - 4*w^2 - 16*w - 2],\
[439, 439, w^3 - w^2 - 4*w - 4],\
[443, 443, -4*w^3 + 9*w^2 + 15*w - 16],\
[461, 461, 2*w^3 - 2*w^2 - 13*w - 1],\
[467, 467, 2*w^3 - 6*w^2 - 2*w + 7],\
[467, 467, 3*w^3 - 3*w^2 - 19*w - 6],\
[479, 479, w^2 - 8],\
[479, 479, -3*w^3 + 7*w^2 + 14*w - 11],\
[491, 491, 3*w^3 - 5*w^2 - 16*w + 2],\
[499, 499, -w^2 + w - 2],\
[509, 509, -w^3 + 5*w^2 - w - 11],\
[509, 509, w^3 - 5*w - 1],\
[521, 521, -w^3 + 4*w^2 + 3*w - 7],\
[521, 521, -w^3 + 2*w^2 + 7*w - 4],\
[541, 541, -2*w^3 + 4*w^2 + 11*w - 6],\
[557, 557, -w^3 + w^2 + 8*w + 3],\
[557, 557, w^3 - 2*w^2 - 2*w - 2],\
[563, 563, 2*w^3 - 2*w^2 - 10*w - 3],\
[563, 563, 3*w^3 - 5*w^2 - 15*w + 1],\
[569, 569, 2*w^2 - 3*w - 4],\
[569, 569, 3*w^3 - 8*w^2 - 9*w + 7],\
[571, 571, -w^3 + 4*w^2 - 11],\
[571, 571, 3*w^3 - 8*w^2 - 11*w + 11],\
[577, 577, 3*w^3 - 8*w^2 - 5*w + 11],\
[577, 577, -4*w^3 + 11*w^2 + 9*w - 9],\
[593, 593, 2*w^3 - 7*w^2 - 2*w + 9],\
[601, 601, -w^3 + 3*w^2 + 5*w - 9],\
[613, 613, 3*w^3 - 5*w^2 - 14*w + 8],\
[613, 613, -w^3 + 2*w^2 + 7*w - 3],\
[617, 617, -2*w^3 + 6*w^2 + 5*w - 4],\
[617, 617, -w^3 + 3*w^2 - w - 6],\
[641, 641, 4*w^3 - 9*w^2 - 17*w + 14],\
[641, 641, -5*w^3 + 12*w^2 + 18*w - 17],\
[643, 643, -3*w^3 + 8*w^2 + 10*w - 13],\
[647, 647, 3*w - 4],\
[647, 647, -w^3 + 4*w^2 + 2*w - 9],\
[653, 653, -w^3 + 2*w^2 + 5*w - 8],\
[661, 661, 2*w^3 - 7*w^2 - 5*w + 21],\
[661, 661, -w^3 + 2*w^2 + 3*w - 8],\
[673, 673, 2*w^3 - 7*w^2 - 5*w + 9],\
[673, 673, w^3 - 2*w^2 - 3*w - 4],\
[677, 677, -w^3 + 4*w^2 + 3*w - 8],\
[683, 683, -3*w^3 + 4*w^2 + 17*w - 1],\
[683, 683, -3*w^3 + 7*w^2 + 8*w - 2],\
[691, 691, w^2 - 4*w - 2],\
[701, 701, 3*w^3 - 6*w^2 - 11*w + 3],\
[709, 709, -w^3 + 4*w^2 + 3*w - 17],\
[709, 709, w^3 + w^2 - 10*w - 8],\
[709, 709, -3*w^3 + 10*w^2 + 2*w - 16],\
[709, 709, w^3 - w^2 - 8*w + 1],\
[727, 727, -w^3 + 5*w^2 - w - 13],\
[727, 727, 2*w^3 - 4*w^2 - 11*w + 2],\
[733, 733, -2*w^3 + 3*w^2 + 10*w - 6],\
[733, 733, 2*w^3 - 5*w^2 - 5*w + 9],\
[739, 739, -3*w^3 + 6*w^2 + 12*w - 8],\
[743, 743, 3*w^3 - 4*w^2 - 17*w - 4],\
[743, 743, 2*w^3 - 3*w^2 - 8*w + 1],\
[743, 743, -3*w^3 + 7*w^2 + 11*w - 7],\
[743, 743, -3*w^3 + 6*w^2 + 11*w - 9],\
[757, 757, 2*w^3 - 5*w^2 - 6*w + 11],\
[757, 757, -w^3 + w^2 + 8*w + 2],\
[761, 761, -5*w^3 + 14*w^2 + 13*w - 12],\
[769, 769, -3*w^2 + 4*w + 13],\
[773, 773, 3*w^3 - 4*w^2 - 18*w + 3],\
[797, 797, 4*w^3 - 7*w^2 - 21*w + 8],\
[797, 797, -3*w^3 + 7*w^2 + 11*w - 16],\
[809, 809, -2*w^2 + 5*w + 11],\
[827, 827, w - 6],\
[829, 829, -w^3 - w^2 + 11*w + 8],\
[841, 29, -3*w^3 + 6*w^2 + 14*w - 6],\
[841, 29, -2*w^3 + 5*w^2 + 8*w - 4],\
[853, 853, 3*w^3 - 6*w^2 - 9*w + 8],\
[857, 857, 2*w^2 - 3*w - 3],\
[859, 859, -w^3 + w^2 + 4*w + 7],\
[863, 863, 2*w^3 - 3*w^2 - 7*w - 2],\
[863, 863, -3*w^3 + 6*w^2 + 10*w - 11],\
[881, 881, -3*w^2 + 4*w + 12],\
[881, 881, w^2 - 2*w + 3],\
[883, 883, 4*w^3 - 13*w^2 - 6*w + 17],\
[883, 883, -2*w^3 + 4*w^2 + 12*w - 3],\
[887, 887, -3*w^3 + 5*w^2 + 16*w - 8],\
[887, 887, 3*w^3 - 5*w^2 - 14*w + 3],\
[911, 911, -w^3 + 10*w + 1],\
[919, 919, 5*w^3 - 13*w^2 - 14*w + 11],\
[929, 929, 2*w^3 - 3*w^2 - 12*w - 4],\
[937, 937, -3*w - 7],\
[941, 941, -w^3 + 3*w^2 + 3*w - 12],\
[947, 947, 2*w^3 - 6*w^2 - 9*w + 8],\
[947, 947, -4*w^3 + 7*w^2 + 19*w - 6],\
[953, 953, 3*w^2 - w - 9],\
[961, 31, 4*w^3 - 12*w^2 - 5*w + 17],\
[971, 971, 3*w^3 - 6*w^2 - 16*w + 12],\
[983, 983, w^3 + w^2 - 7*w - 12],\
[991, 991, -2*w^3 + 7*w^2 + 3*w - 12],\
[991, 991, -2*w^3 + 4*w^2 + 12*w - 9],\
[997, 997, 3*w^3 - 5*w^2 - 14*w + 9],\
[997, 997, -2*w^3 + 3*w^2 + 11*w - 7],\
[1013, 1013, -2*w^3 + 6*w^2 + 3*w - 11],\
[1019, 1019, -w^3 + 5*w^2 + 2*w - 8],\
[1021, 1021, -w^3 + 5*w^2 - w - 17],\
[1021, 1021, 3*w^3 - 6*w^2 - 8*w + 3],\
[1033, 1033, -2*w^3 + 5*w^2 + 6*w - 13],\
[1033, 1033, 3*w^3 - 6*w^2 - 11*w + 4],\
[1051, 1051, 3*w^3 - 7*w^2 - 10*w + 13],\
[1061, 1061, 2*w^2 - 5*w - 13],\
[1063, 1063, -w^3 + w^2 + 5*w + 8],\
[1069, 1069, -5*w^3 + 12*w^2 + 19*w - 18],\
[1069, 1069, w^3 - 5*w^2 - w + 9],\
[1097, 1097, -3*w^3 + 9*w^2 + 8*w - 12],\
[1097, 1097, -2*w^3 + 6*w^2 + 7*w - 12],\
[1103, 1103, -3*w^3 + 4*w^2 + 15*w - 3],\
[1103, 1103, -w^3 + 3*w^2 + 5*w - 11],\
[1109, 1109, 5*w^3 - 11*w^2 - 16*w + 6],\
[1129, 1129, -w^2 + 3*w - 4],\
[1129, 1129, 2*w^3 - 2*w^2 - 10*w - 9],\
[1151, 1151, 4*w^3 - 10*w^2 - 14*w + 13],\
[1153, 1153, -2*w^3 + 5*w^2 + 11*w - 12],\
[1153, 1153, -2*w^3 + 8*w^2 - 13],\
[1153, 1153, -w^3 + 3*w^2 + 5*w - 12],\
[1153, 1153, 2*w^3 - w^2 - 11*w - 4],\
[1163, 1163, -w^3 + w^2 + 9*w - 4],\
[1163, 1163, 2*w^3 - 4*w^2 - 10*w - 1],\
[1171, 1171, 3*w^3 - 4*w^2 - 18*w - 1],\
[1193, 1193, w^3 - 4*w^2 + 2*w + 6],\
[1193, 1193, w^3 - 2*w^2 - 5*w - 4],\
[1201, 1201, 2*w^3 - 4*w^2 - 9*w - 3],\
[1201, 1201, 4*w^3 - 10*w^2 - 13*w + 11],\
[1213, 1213, -4*w^3 + 7*w^2 + 19*w - 11],\
[1217, 1217, -2*w^3 + 8*w^2 + 2*w - 13],\
[1229, 1229, -4*w^3 + 13*w^2 + 6*w - 19],\
[1229, 1229, -4*w^3 + 8*w^2 + 16*w - 13],\
[1229, 1229, -3*w^3 + 9*w^2 + 6*w - 16],\
[1229, 1229, 2*w^3 - 3*w^2 - 6*w - 1],\
[1231, 1231, -3*w^3 + 6*w^2 + 16*w - 8],\
[1231, 1231, -3*w^2 + w + 12],\
[1237, 1237, -2*w^3 + 5*w^2 + 4*w - 9],\
[1237, 1237, -w^2 - 3],\
[1237, 1237, -w^3 + 6*w - 3],\
[1237, 1237, -4*w - 1],\
[1249, 1249, -2*w^3 + 4*w^2 + 5*w - 8],\
[1283, 1283, 3*w - 8],\
[1289, 1289, 2*w^3 - w^2 - 14*w - 6],\
[1289, 1289, 4*w^3 - 9*w^2 - 13*w + 8],\
[1291, 1291, w^3 - w^2 - 3*w - 4],\
[1297, 1297, 4*w^3 - 9*w^2 - 15*w + 9],\
[1303, 1303, -w^3 + 4*w^2 - 13],\
[1321, 1321, 3*w^3 - 6*w^2 - 13*w + 3],\
[1321, 1321, -3*w^3 + 6*w^2 + 11*w - 7],\
[1367, 1367, -2*w^3 + 6*w^2 + 4*w - 13],\
[1369, 37, 2*w^2 - w - 11],\
[1369, 37, w^3 - 2*w^2 - w - 2],\
[1373, 1373, -w^3 + 3*w^2 + 8*w - 6],\
[1381, 1381, -w^3 + 3*w^2 - 9],\
[1381, 1381, 3*w^3 - 8*w^2 - 8*w + 14],\
[1427, 1427, 3*w^3 - 7*w^2 - 9*w + 12],\
[1429, 1429, 4*w^3 - 9*w^2 - 11*w + 8],\
[1433, 1433, -w^3 + 8*w + 12],\
[1447, 1447, -4*w^3 + 10*w^2 + 15*w - 14],\
[1447, 1447, 6*w^3 - 14*w^2 - 21*w + 19],\
[1451, 1451, w^3 - w^2 - 9*w - 4],\
[1459, 1459, 3*w^3 - 7*w^2 - 13*w + 9],\
[1481, 1481, -3*w^2 + 3*w + 19],\
[1481, 1481, -w^3 + 5*w^2 - 3*w - 14],\
[1487, 1487, -2*w^3 + 6*w^2 + w - 6],\
[1489, 1489, -3*w^3 + 3*w^2 + 19*w + 3],\
[1499, 1499, 3*w^2 - 4*w - 7],\
[1511, 1511, 4*w^3 - 6*w^2 - 20*w + 3],\
[1523, 1523, 8*w^3 - 23*w^2 - 17*w + 27],\
[1531, 1531, -w^3 + 2*w^2 + 3*w - 9],\
[1531, 1531, 3*w^3 - 9*w^2 - 8*w + 19],\
[1549, 1549, -5*w^3 + 11*w^2 + 17*w - 18],\
[1553, 1553, 2*w^2 - 9],\
[1567, 1567, 2*w^3 - 7*w^2 - 4*w + 22],\
[1579, 1579, -2*w^3 + 4*w^2 + 8*w + 3],\
[1579, 1579, -3*w^3 + 5*w^2 + 13*w - 1],\
[1607, 1607, w^3 - w^2 - 6*w - 8],\
[1609, 1609, -4*w^3 + 7*w^2 + 19*w - 2],\
[1619, 1619, -5*w^3 + 11*w^2 + 13*w - 9],\
[1627, 1627, 4*w^3 - 9*w^2 - 16*w + 11],\
[1657, 1657, 2*w^3 - 8*w^2 - w + 12],\
[1657, 1657, -4*w^3 + 11*w^2 + 15*w - 17],\
[1667, 1667, -w^3 + 5*w^2 - 6],\
[1667, 1667, -3*w^3 + 6*w^2 + 10*w - 6],\
[1697, 1697, w^3 + w^2 - 9*w - 7],\
[1697, 1697, 3*w^3 - 6*w^2 - 13*w + 2],\
[1697, 1697, w^3 - 6*w + 1],\
[1697, 1697, -5*w^3 + 11*w^2 + 22*w - 17],\
[1709, 1709, w^3 - w^2 - 8*w - 9],\
[1709, 1709, -w^3 + 3*w^2 - 13],\
[1723, 1723, 2*w^3 - 3*w^2 - 7*w - 3],\
[1733, 1733, -w^3 + 4*w^2 + 3*w - 19],\
[1741, 1741, -w^3 + 5*w^2 - 14],\
[1747, 1747, -4*w^3 + 6*w^2 + 22*w + 1],\
[1747, 1747, 2*w^3 - 5*w^2 - 9*w + 2],\
[1753, 1753, -2*w^3 + 5*w^2 + 3*w - 1],\
[1759, 1759, -w^3 + 2*w^2 + 4*w - 9],\
[1783, 1783, -3*w^3 + 8*w^2 + 5*w - 12],\
[1783, 1783, -2*w^3 + 6*w^2 + 3*w - 12],\
[1783, 1783, 2*w^3 - 7*w^2 - 4*w + 17],\
[1783, 1783, 2*w^3 - 6*w^2 - w + 7],\
[1787, 1787, -5*w^3 + 8*w^2 + 25*w - 3],\
[1823, 1823, w^3 - 8*w - 1],\
[1823, 1823, -3*w^3 + 5*w^2 + 14*w + 6],\
[1831, 1831, -3*w^3 + 8*w^2 + 14*w - 18],\
[1847, 1847, w^3 - 3*w^2 - w + 14],\
[1847, 1847, -2*w^3 + 2*w^2 + 11*w + 11],\
[1861, 1861, 2*w^2 - w - 12],\
[1871, 1871, 4*w^3 - 8*w^2 - 19*w + 9],\
[1871, 1871, -w^3 + 5*w^2 - w - 7],\
[1873, 1873, -3*w^3 + 5*w^2 + 13*w - 4],\
[1877, 1877, -4*w^3 + 8*w^2 + 16*w - 7],\
[1877, 1877, 3*w^3 - 5*w^2 - 15*w - 2],\
[1879, 1879, -w^3 + 4*w^2 - w - 12],\
[1907, 1907, w^3 - w^2 - 10*w - 6],\
[1931, 1931, -w^3 + 5*w^2 - w - 19],\
[1931, 1931, -6*w^3 + 17*w^2 + 12*w - 22],\
[1951, 1951, 4*w^3 - 10*w^2 - 14*w + 21],\
[1951, 1951, -2*w^3 + 4*w^2 + 13*w - 13],\
[1993, 1993, 2*w^3 - 2*w^2 - 11*w + 1],\
[1993, 1993, -w^3 + 6*w + 14]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 + x^2 - 7*x - 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, 1, -e^2 + 4, -e^2 + 2*e + 6, -1, -e^2 + 2, 2*e^2 - 2*e - 12, -2*e^2 + 8, 2*e^2 - 2*e - 10, 2*e^2 - 2*e - 12, -3*e - 2, 2, -2*e^2 + 2*e + 12, -3*e - 2, -e + 2, -4, 2*e^2 + 2*e - 10, 2*e^2 - 10, -2*e^2 - 2*e + 4, 2*e^2 + 3*e - 16, 2*e^2 - 2*e - 8, 2*e, 4*e + 4, -4*e^2 + e + 14, 2*e^2 - 2*e - 4, -e^2 - 2*e - 2, 4*e^2 - e - 22, 4*e^2 + 2*e - 16, -2*e^2 + 4*e + 18, -2*e^2 - 2*e + 18, 6*e^2 - e - 34, -e^2 - 2*e - 2, e^2 - 2*e - 14, -2*e^2 - e + 24, -3*e^2 + 6*e + 18, 6*e^2 - 8*e - 38, -2*e - 20, -4*e^2 - 2*e + 18, -2*e^2 - 6*e + 8, 2*e^2 - 3*e - 18, -2*e^2 + 26, 4*e^2 - 4*e - 40, 6*e^2 + e - 32, e^2 - 14, -2*e^2 - 2*e + 12, -10*e^2 + 4*e + 48, 2*e^2 - 2*e - 32, -2*e, -e^2 - 4*e + 12, -2*e^2 + e + 6, 2*e^2 - 2*e + 8, 7*e^2 - 2*e - 42, e^2 + 2*e - 14, 2*e^2 + 6*e - 12, -4*e^2 + 18, 4*e^2 + e - 38, 2*e^2 + 5*e - 26, 10*e^2 - 3*e - 42, 2*e^2 - 11*e - 12, -6*e^2 + 20, -6*e^2 + 32, 4*e^2 - 2*e - 34, -8*e^2 + 4*e + 32, -2*e^2 + 8*e + 16, -8*e + 12, -4*e^2 + 4*e + 30, 3*e^2 + 8*e - 10, -e^2 - 6*e + 12, -6*e^2 + 2*e + 32, 2*e^2 - 10*e - 12, -5*e^2 + 2*e + 30, -6*e^2 + 3*e + 40, -2*e^2 + 5*e, -2*e^2 + 3*e + 6, -10*e^2 + 2*e + 36, -8*e - 4, -4*e^2 - 2*e + 8, -2*e^2 - 12, 6*e^2 + 2*e - 32, -2*e^2 - 4*e + 24, 3*e^2 - 38, -6*e - 16, 6*e^2 - 40, 4*e^2 - 2*e - 24, -8*e^2 + 4*e + 50, 2*e^2 + 6*e - 2, 2*e^2 - 12, 2*e^2 - 5*e - 32, -9*e^2 + 14*e + 64, e^2 + 8*e, 8*e^2 - 4*e - 42, -e^2 - 2*e + 2, -8*e^2 + 11*e + 38, -7*e^2 + 6*e + 14, 4, -2*e^2 - 4, -3*e^2 + 10, -4*e^2 + 4*e + 26, -2*e^2 + 16*e + 8, -4*e^2 + 10*e + 46, e^2 + 6*e + 8, 6*e^2 - 5*e - 22, 6*e^2 + 11*e - 30, -6*e^2 + 7*e + 34, 8*e^2 - 8*e - 62, 7*e^2 + 2*e - 38, 5*e^2 - 8*e - 6, -10*e^2 + 3*e + 50, -5*e - 18, 5*e^2 - 6*e - 8, 10*e^2 - 8*e - 66, 2*e^2 + 8*e - 8, 4*e^2 + 8*e - 8, -e^2 - 4*e + 26, -6*e^2 + e + 42, -9*e^2 + 4*e + 34, 10*e^2 - 11*e - 44, 9*e^2 - 8*e - 58, -5*e^2 + 8*e + 22, 14*e^2 - 4*e - 54, -4*e^2 + 10*e + 12, 8*e^2 - 22, -3*e^2 + 22, -5*e^2 + 12*e + 44, 7*e^2 - 4*e - 34, -4*e^2 + 4*e + 34, 4*e^2 + 9*e - 20, -10*e^2 + 16*e + 54, 4*e^2 - 8*e + 2, -12*e^2 + 3*e + 50, -10*e^2 - 6*e + 44, -14*e^2 + 6*e + 76, -4*e^2 - 2*e + 34, -6*e - 4, 8*e^2 - 14*e - 56, 8*e^2 + 2*e - 32, 11*e - 18, -8*e^2 + 3*e + 62, -7*e - 22, 2*e^2 - 6*e, 4*e^2 - 7*e - 28, 8*e^2 + 4*e - 50, 10*e^2 + e - 54, 9*e^2 - 2*e - 70, 6*e^2 - 8*e - 14, 4*e^2 - 3*e - 24, -3*e^2 + 14*e + 22, 5*e^2 - 18*e - 22, -10, 12*e - 2, -12*e^2 - 2*e + 44, 2*e^2 + 6*e - 22, -6*e^2 + 12*e + 40, 9*e^2 + 6*e - 26, 3*e^2 + 2*e - 6, -6*e^2 + 6*e + 44, -2*e^2 - 2*e - 4, 4*e^2 + 14*e - 36, -14*e^2 + 8*e + 68, -4*e^2 + 20*e + 16, 10*e^2 + 6*e - 44, -3*e^2 - 6*e + 28, -16*e^2 - 7*e + 74, -7*e^2 + 10*e + 54, 2*e^2 - 22, -4*e^2 + 8*e, -12*e^2 - 5*e + 50, -6*e^2 - 9*e + 42, -10*e^2 + 20, 2*e^2 + 4*e - 40, 12*e^2 - 12*e - 64, -16*e^2 + 14*e + 92, -8*e^2 + 3*e + 66, 5*e^2 + 6*e - 26, -8*e^2 + 4*e + 22, 4*e^2 + 10*e - 16, 4*e^2 + 8*e - 54, 2*e^2 + 5*e - 42, -3*e^2 - 4*e + 34, -12*e^2 + 20*e + 86, -14*e^2 + 12*e + 68, 2*e^2 - 2*e + 4, -2*e^2 - 18*e + 14, 4*e^2 + 17*e - 40, 15*e^2 - 10*e - 70, -7*e^2 + 14*e + 70, 7*e^2 - 8*e - 46, 20*e^2 - 8*e - 96, 6*e^2 + 12*e - 34, 5*e + 12, e^2 + 12*e + 26, 10*e^2 - 2*e - 60, -2*e^2 + 12*e + 28, -4*e^2 + e + 22, 14*e^2 - 9*e - 86, -10*e^2 - 13*e + 58, 8*e^2 - e - 56, -20*e^2 + 2*e + 82, -10*e^2 - 4*e + 56, -10*e^2 + 6*e + 48, 5*e^2 - 6*e - 40, 15*e^2 - 6*e - 86, 9*e^2 - 76, 13*e^2 - 16*e - 76, 6*e^2 + 17*e - 26, 5*e^2 - 56, 8*e^2 + 8*e - 22, 9*e^2 + 8*e - 62, 12*e^2 - 15*e - 62, 5*e^2 - 34, 10*e^2 - 8*e - 84, -10*e^2 - 18*e + 56, 7*e^2 + 10*e - 12, -8*e^2 + 13*e + 18, 7*e^2 - 6, 2*e^2 - 17*e - 10, e^2 + 14*e - 18, 12*e^2 - 22*e - 64, 2*e^2 + 9*e - 26, -11*e^2 + 2*e + 70, 4*e^2 - 10*e - 36, -7*e^2 + 14*e + 54, 16*e^2 - 6*e - 80, 13*e^2 - 10*e - 86, -12*e^2 + 15*e + 58, -4*e + 16, -10*e^2 + 5*e + 42, 10*e^2 + e - 66, -4*e^2 + 8*e + 42, 19*e - 2, -4*e^2 + 16*e + 38, 16*e^2 - 12*e - 100, -11*e^2 + 2*e + 50, -3*e^2 + 4*e + 22, -8*e^2 - 2*e + 66, -6*e^2 + 2*e + 68, -4*e^2 - 12*e + 30, -10*e^2 + 12*e + 20, 16*e^2 - 20*e - 94, -15*e^2 - 4*e + 80, -6*e^2 + 10*e + 54, -8*e^2 - 5*e + 44, -8*e^2 + 18*e + 42, 6*e^2 + 4*e - 38, 8*e^2 - 24, -6*e^2 + 18*e + 68, 4*e^2 - 4*e + 12, 5*e^2 + 12*e - 34, 9*e^2 - 28*e - 60, 10*e^2 - 22*e - 64, 6*e - 52, 8*e^2 - 18*e - 28, -8*e - 8, 17*e^2 + 2*e - 72, 4*e^2 - 20*e - 44, -20*e^2 + 14*e + 100, -19*e^2 + 8*e + 84, 14*e^2 - 5*e - 86, -8*e^2 + 14*e + 76, -12*e^2 + 26*e + 80, -20*e + 22, 16*e^2 - 13*e - 66, -11*e^2 + 12*e + 78, 6*e^2 - 15*e - 26, -18*e^2 + 13*e + 106, -10*e^2 + 15*e + 86, -10*e^2 + 6*e + 16, -5*e^2 - 18*e + 26, 5*e^2 - 24*e - 10, -6*e^2 + 10*e + 44, -18*e^2 - 8*e + 72, -9*e^2 + 8*e + 98, 10*e^2 + 18*e - 66, 32, -6*e^2 - 6*e + 10, -2*e^2 + 2*e + 30, 8*e^2 - 14*e - 52, 12*e^2 - 16*e - 68, -4*e^2 + 6*e - 10, -10*e^2 - 18*e + 52, -2*e^2 - 16*e + 46, -10*e^2 + 4*e + 40, -6*e + 44, 19*e + 2, 8*e^2 - 18, -10*e^2 + 20*e + 98, -3*e^2 + 6*e + 56, 3*e^2 - 10*e - 76, 15*e^2 - 6*e - 102, -6*e^2 + 12*e + 46, 2*e^2 - 14*e - 24, 2*e^2 - 26*e - 4, -18*e^2 + 2*e + 52, 10*e^2 - 4*e - 64, -6*e^2 + 8*e + 26, -8*e^2 + 16*e + 18, 3*e^2 + 8*e + 18]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([7, 7, -w^3 + 2*w^2 + 4*w - 3])] = -1

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