/*
  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([45, 15, -14, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 5, 2/3*w^2 - 2/3*w - 5])

primes_array = [
[5, 5, 2/3*w^2 + 1/3*w - 5],\
[5, 5, 2/3*w^2 - 5/3*w - 4],\
[9, 3, -w + 3],\
[9, 3, w + 2],\
[11, 11, 2/3*w^2 + 1/3*w - 4],\
[16, 2, 2],\
[19, 19, 1/3*w^3 - 10/3*w - 3],\
[19, 19, 1/3*w^3 - w^2 - 7/3*w + 6],\
[29, 29, -1/3*w^3 + 2/3*w^2 + 8/3*w - 2],\
[29, 29, 1/3*w^3 - 1/3*w^2 - 3*w + 1],\
[31, 31, -1/3*w^3 + 1/3*w^2 + 3*w + 1],\
[31, 31, -1/3*w^3 + 2/3*w^2 + 8/3*w - 4],\
[49, 7, 1/3*w^3 - 10/3*w - 1],\
[49, 7, -1/3*w^3 + w^2 + 7/3*w - 4],\
[59, 59, -1/3*w^3 + 5/3*w^2 + 5/3*w - 11],\
[59, 59, -2/3*w^3 + 5/3*w^2 + 5*w - 13],\
[61, 61, -1/3*w^3 + 5/3*w^2 + 2/3*w - 9],\
[61, 61, -1/3*w^3 + 1/3*w^2 + 4*w + 2],\
[61, 61, 2/3*w^2 - 5/3*w - 1],\
[61, 61, -1/3*w^2 + 4/3*w + 6],\
[71, 71, -4/3*w^2 + 7/3*w + 11],\
[79, 79, -1/3*w^2 + 7/3*w - 3],\
[79, 79, -2/3*w^3 + 1/3*w^2 + 16/3*w - 4],\
[101, 101, 2/3*w^2 - 5/3*w - 6],\
[101, 101, -2/3*w^2 - 1/3*w + 7],\
[109, 109, -4/3*w^2 + 1/3*w + 9],\
[109, 109, 1/3*w^3 - 1/3*w^2 - 3*w - 4],\
[121, 11, -1/3*w^2 + 1/3*w + 6],\
[131, 131, -2/3*w^3 + 2/3*w^2 + 5*w - 7],\
[131, 131, 2/3*w^3 - 4/3*w^2 - 13/3*w - 2],\
[151, 151, -1/3*w^3 - 2/3*w^2 + 5*w + 7],\
[151, 151, 1/3*w^3 - 10/3*w + 2],\
[169, 13, 5/3*w^2 + 1/3*w - 11],\
[169, 13, 5/3*w^2 - 11/3*w - 9],\
[181, 181, -1/3*w^3 + 4/3*w^2 + 3*w - 8],\
[181, 181, -1/3*w^3 - 1/3*w^2 + 14/3*w + 4],\
[191, 191, -2/3*w^3 + w^2 + 17/3*w - 9],\
[191, 191, 1/3*w^3 - 2*w^2 - 7/3*w + 13],\
[191, 191, 2/3*w^3 - 1/3*w^2 - 22/3*w - 7],\
[191, 191, 2/3*w^3 - w^2 - 17/3*w - 3],\
[199, 199, 1/3*w^3 + w^2 - 13/3*w - 9],\
[199, 199, 2/3*w^2 - 5/3*w - 7],\
[199, 199, 1/3*w^3 - w^2 - 4/3*w + 6],\
[199, 199, -1/3*w^3 + 2*w^2 + 4/3*w - 12],\
[269, 269, -1/3*w^3 - 4/3*w^2 + 11/3*w + 14],\
[269, 269, 1/3*w^3 - 7/3*w^2 + 16],\
[271, 271, 2/3*w^2 + 1/3*w - 9],\
[271, 271, 2/3*w^2 - 5/3*w - 8],\
[281, 281, 1/3*w^3 + w^2 - 13/3*w - 11],\
[281, 281, -2/3*w^3 + 20/3*w + 3],\
[281, 281, -w^2 + 3*w + 2],\
[281, 281, -1/3*w^3 + 2*w^2 + 4/3*w - 14],\
[289, 17, w^3 - 8/3*w^2 - 16/3*w + 4],\
[289, 17, -w^3 + 1/3*w^2 + 23/3*w - 3],\
[331, 331, -2/3*w^3 + 2*w^2 + 11/3*w - 7],\
[331, 331, 2/3*w^3 - 17/3*w - 2],\
[359, 359, -1/3*w^3 - 1/3*w^2 + 11/3*w - 2],\
[359, 359, 1/3*w^3 + 4/3*w^2 - 17/3*w - 12],\
[361, 19, 4/3*w^2 - 4/3*w - 11],\
[389, 389, 5/3*w^2 - 8/3*w - 13],\
[389, 389, 5/3*w^2 - 2/3*w - 14],\
[401, 401, -1/3*w^3 + 5/3*w^2 + 11/3*w - 12],\
[401, 401, 1/3*w^3 + 2/3*w^2 - 6*w - 7],\
[409, 409, 1/3*w^3 + 1/3*w^2 - 14/3*w - 3],\
[409, 409, -1/3*w^3 + 4/3*w^2 + 3*w - 7],\
[421, 421, -1/3*w^3 + 5/3*w^2 + 11/3*w - 13],\
[421, 421, 1/3*w^3 + 2/3*w^2 - 6*w - 8],\
[431, 431, 2/3*w^2 + 4/3*w - 9],\
[431, 431, 2/3*w^2 - 8/3*w - 7],\
[449, 449, 2/3*w^3 - 17/3*w + 2],\
[449, 449, 1/3*w^3 + 4/3*w^2 - 20/3*w - 11],\
[461, 461, 1/3*w^2 + 5/3*w - 8],\
[461, 461, 1/3*w^3 + 1/3*w^2 - 17/3*w - 3],\
[461, 461, -1/3*w^3 + 4/3*w^2 + 4*w - 8],\
[461, 461, 1/3*w^2 - 7/3*w - 6],\
[479, 479, -1/3*w^3 + 2/3*w^2 + 5/3*w - 9],\
[479, 479, 4/3*w^3 + w^2 - 40/3*w - 18],\
[479, 479, 4/3*w^3 - 5*w^2 - 22/3*w + 29],\
[479, 479, 1/3*w^3 - 1/3*w^2 - 2*w - 7],\
[491, 491, 2/3*w^3 - 5/3*w^2 - 5*w + 8],\
[491, 491, -1/3*w^3 + 3*w^2 + 10/3*w - 24],\
[491, 491, 1/3*w^3 + 2*w^2 - 25/3*w - 18],\
[491, 491, 2/3*w^3 - 1/3*w^2 - 19/3*w - 2],\
[499, 499, -1/3*w^3 + 10/3*w^2 - 4*w - 17],\
[499, 499, 1/3*w^3 - 7/3*w - 9],\
[499, 499, -1/3*w^3 + w^2 + 4/3*w - 11],\
[499, 499, -w^3 + 5/3*w^2 + 22/3*w - 14],\
[509, 509, w^3 - 14/3*w^2 - 10/3*w + 24],\
[509, 509, -2/3*w^2 + 5/3*w + 11],\
[509, 509, 2/3*w^2 + 1/3*w - 12],\
[509, 509, -2/3*w^3 + 3*w^2 + 8/3*w - 18],\
[521, 521, 1/3*w^3 - 13/3*w + 1],\
[521, 521, w^3 + 2/3*w^2 - 32/3*w - 12],\
[521, 521, 2/3*w^3 + 7/3*w^2 - 13*w - 23],\
[521, 521, -1/3*w^3 + w^2 + 10/3*w - 3],\
[541, 541, 2/3*w^3 - 17/3*w - 3],\
[541, 541, -1/3*w^3 + 4/3*w^2 + 2*w - 14],\
[541, 541, -1/3*w^3 + 4/3*w^2 + w - 1],\
[541, 541, -1/3*w^3 + 1/3*w^2 + 5*w - 4],\
[569, 569, 1/3*w^3 + 11/3*w^2 - 12*w - 26],\
[569, 569, -w^3 + 10/3*w^2 + 23/3*w - 21],\
[571, 571, w^3 - 7/3*w^2 - 23/3*w + 17],\
[571, 571, 2/3*w^3 - 3*w^2 - 11/3*w + 17],\
[599, 599, 1/3*w^3 + 2/3*w^2 - 4*w - 1],\
[599, 599, 1/3*w^3 - 5/3*w^2 - 5/3*w + 4],\
[601, 601, 1/3*w^3 - 7/3*w - 6],\
[601, 601, -2/3*w^3 + 2*w^2 + 11/3*w - 9],\
[601, 601, 2/3*w^3 - 17/3*w - 4],\
[601, 601, -1/3*w^3 + w^2 + 4/3*w - 8],\
[619, 619, -2/3*w^3 + 10/3*w^2 + 19/3*w - 26],\
[619, 619, 2/3*w^3 + 4/3*w^2 - 11*w - 17],\
[631, 631, 1/3*w^3 - 7/3*w^2 - w + 14],\
[631, 631, 1/3*w^3 + 4/3*w^2 - 14/3*w - 11],\
[659, 659, -2/3*w^3 + 2/3*w^2 + 6*w + 1],\
[659, 659, 2/3*w^3 - 4/3*w^2 - 16/3*w + 7],\
[661, 661, -2/3*w^3 + 13/3*w^2 + 16/3*w - 32],\
[661, 661, -2/3*w^3 - 7/3*w^2 + 12*w + 23],\
[691, 691, 1/3*w^3 - 11/3*w^2 - 11/3*w + 29],\
[691, 691, -2/3*w^3 + 10/3*w^2 + 10/3*w - 23],\
[701, 701, 2/3*w^3 - 4/3*w^2 - 13/3*w - 3],\
[701, 701, 2/3*w^3 - 4/3*w^2 - 16/3*w - 1],\
[701, 701, -2/3*w^3 + 2/3*w^2 + 6*w - 7],\
[701, 701, -2/3*w^3 + 2/3*w^2 + 5*w - 8],\
[709, 709, -4/3*w^3 + 31/3*w - 2],\
[709, 709, -w^3 + 1/3*w^2 + 32/3*w + 4],\
[719, 719, -2/3*w^3 + w^2 + 17/3*w - 2],\
[719, 719, 1/3*w^3 - 2*w^2 - 4/3*w + 9],\
[719, 719, 1/3*w^3 + w^2 - 13/3*w - 6],\
[719, 719, 2/3*w^3 - w^2 - 17/3*w + 4],\
[739, 739, 2/3*w^3 + 2/3*w^2 - 19/3*w - 11],\
[739, 739, -2/3*w^3 + 8/3*w^2 + 3*w - 16],\
[751, 751, -1/3*w^3 + w^2 + 4/3*w - 9],\
[751, 751, 1/3*w^3 - 7/3*w - 7],\
[761, 761, 1/3*w^3 - 16/3*w - 4],\
[761, 761, w^3 - 1/3*w^2 - 29/3*w - 12],\
[761, 761, -w^3 + 8/3*w^2 + 22/3*w - 21],\
[761, 761, -1/3*w^3 + w^2 + 13/3*w - 9],\
[769, 769, w^3 - 7/3*w^2 - 23/3*w + 8],\
[769, 769, 1/3*w^3 + 4/3*w^2 - 14/3*w - 14],\
[769, 769, -1/3*w^3 + 7/3*w^2 + w - 17],\
[769, 769, 1/3*w^3 - 3*w^2 + 11/3*w + 13],\
[811, 811, 1/3*w^3 + w^2 - 10/3*w - 12],\
[811, 811, -1/3*w^3 + 2*w^2 + 1/3*w - 14],\
[821, 821, -1/3*w^3 + 13/3*w - 3],\
[821, 821, -1/3*w^3 + w^2 + 10/3*w - 1],\
[839, 839, -w^3 - 5/3*w^2 + 32/3*w + 18],\
[839, 839, 1/3*w^3 + 3*w^2 - 7/3*w - 22],\
[839, 839, 1/3*w^3 - 4*w^2 + 14/3*w + 21],\
[839, 839, -w^3 + 14/3*w^2 + 13/3*w - 26],\
[841, 29, -5/3*w^2 + 5/3*w + 11],\
[859, 859, -w^3 + 5/3*w^2 + 25/3*w - 1],\
[859, 859, -w^3 + 4/3*w^2 + 26/3*w - 8],\
[911, 911, -1/3*w^3 + 1/3*w^2 + 5*w + 1],\
[911, 911, 1/3*w^3 - 2/3*w^2 - 14/3*w + 6],\
[919, 919, 2/3*w^3 - 2/3*w^2 - 5*w - 7],\
[919, 919, -2/3*w^3 + 7/3*w^2 + 10/3*w - 7],\
[919, 919, 2/3*w^3 + 1/3*w^2 - 6*w - 2],\
[919, 919, -2/3*w^3 + 4/3*w^2 + 13/3*w - 12],\
[941, 941, 5/3*w^2 + 1/3*w - 9],\
[941, 941, 5/3*w^2 - 11/3*w - 7],\
[961, 31, 5/3*w^2 - 5/3*w - 13],\
[971, 971, -1/3*w^3 + w^2 + 13/3*w - 8],\
[971, 971, 2/3*w^3 - 2/3*w^2 - 5*w + 2],\
[971, 971, -2/3*w^3 + 4/3*w^2 + 13/3*w - 3],\
[971, 971, 1/3*w^3 - 16/3*w - 3],\
[991, 991, 10/3*w^2 - 22/3*w - 19],\
[991, 991, 10/3*w^2 + 2/3*w - 23],\
[1009, 1009, -2*w^2 + 3*w + 16],\
[1009, 1009, 2*w^2 - w - 17],\
[1019, 1019, 1/3*w^3 + w^2 - 19/3*w - 14],\
[1019, 1019, -1/3*w^3 + 2*w^2 + 10/3*w - 19],\
[1021, 1021, 2/3*w^3 - 3*w^2 - 14/3*w + 19],\
[1021, 1021, 11/3*w^2 + 4/3*w - 27],\
[1021, 1021, 11/3*w^2 - 26/3*w - 22],\
[1021, 1021, -2/3*w^3 - w^2 + 26/3*w + 12],\
[1031, 1031, -2/3*w^3 + 5/3*w^2 + 4*w + 1],\
[1031, 1031, -2/3*w^3 + 1/3*w^2 + 16/3*w - 6],\
[1049, 1049, -1/3*w^3 - 2/3*w^2 + 4*w - 1],\
[1049, 1049, 1/3*w^3 + 5/3*w^2 - 6*w - 14],\
[1051, 1051, 1/3*w^3 - 16/3*w - 2],\
[1051, 1051, -1/3*w^3 + w^2 + 13/3*w - 7],\
[1061, 1061, 11/3*w^2 + 1/3*w - 27],\
[1061, 1061, 11/3*w^2 - 23/3*w - 23],\
[1069, 1069, w^2 + 2*w - 11],\
[1069, 1069, w^2 - 4*w - 8],\
[1109, 1109, w^3 - 5/3*w^2 - 19/3*w - 1],\
[1109, 1109, -w^3 - w^2 + 12*w + 16],\
[1129, 1129, -w^3 + 5/3*w^2 + 25/3*w - 11],\
[1129, 1129, -w^3 + 4/3*w^2 + 26/3*w + 2],\
[1151, 1151, 1/3*w^3 + w^2 - 16/3*w - 7],\
[1151, 1151, -1/3*w^3 + 2*w^2 + 7/3*w - 11],\
[1171, 1171, w^3 - 8/3*w^2 - 16/3*w + 1],\
[1171, 1171, -w^3 + 1/3*w^2 + 23/3*w - 6],\
[1201, 1201, -1/3*w^3 + 2/3*w^2 + 14/3*w - 4],\
[1201, 1201, -1/3*w^3 - 4/3*w^2 + 8/3*w + 13],\
[1201, 1201, 1/3*w^3 - 7/3*w^2 + w + 14],\
[1201, 1201, 1/3*w^3 - 1/3*w^2 - 5*w + 1],\
[1231, 1231, -1/3*w^3 + 5/3*w^2 + 8/3*w - 8],\
[1231, 1231, 1/3*w^3 + 2/3*w^2 - 5*w - 4],\
[1249, 1249, -4/3*w^3 + 7/3*w^2 + 9*w + 4],\
[1249, 1249, 4/3*w^2 - 13/3*w - 9],\
[1249, 1249, 4/3*w^2 + 5/3*w - 12],\
[1249, 1249, -4/3*w^3 + 5/3*w^2 + 29/3*w - 14],\
[1259, 1259, 2/3*w^3 - w^2 - 20/3*w + 11],\
[1259, 1259, -2/3*w^3 + w^2 + 20/3*w + 4],\
[1279, 1279, -2/3*w^3 - 1/3*w^2 + 5*w + 8],\
[1279, 1279, 1/3*w^3 - w^2 - 7/3*w + 12],\
[1279, 1279, -2*w^2 + 3*w + 13],\
[1279, 1279, -2/3*w^3 + 7/3*w^2 + 7/3*w - 12],\
[1289, 1289, w^3 + 1/3*w^2 - 28/3*w - 8],\
[1289, 1289, -2/3*w^3 + 3*w^2 + 8/3*w - 19],\
[1289, 1289, 2/3*w^3 + w^2 - 20/3*w - 14],\
[1289, 1289, 5/3*w^3 - 11/3*w^2 - 11*w - 1],\
[1291, 1291, -w^3 + 2/3*w^2 + 25/3*w - 7],\
[1291, 1291, w^3 - 7/3*w^2 - 20/3*w + 1],\
[1301, 1301, w^3 - 10/3*w^2 - 14/3*w + 16],\
[1301, 1301, -w^3 + 14/3*w^2 + 25/3*w - 34],\
[1319, 1319, -5/3*w^3 + 6*w^2 + 17/3*w - 14],\
[1319, 1319, 1/3*w^3 - 2/3*w^2 - 8/3*w - 4],\
[1319, 1319, -1/3*w^3 + 1/3*w^2 + 3*w - 7],\
[1319, 1319, -5/3*w^3 - w^2 + 38/3*w + 4],\
[1361, 1361, w^3 - 4*w^2 - 6*w + 23],\
[1361, 1361, w^3 + w^2 - 11*w - 14],\
[1369, 37, -w^3 + 7*w - 4],\
[1369, 37, -1/3*w^3 - 2*w^2 + 10/3*w + 16],\
[1381, 1381, -2/3*w^3 + 20/3*w + 1],\
[1381, 1381, 2/3*w^3 - 2*w^2 - 14/3*w + 7],\
[1399, 1399, -w^3 + 4/3*w^2 + 20/3*w + 4],\
[1399, 1399, -w^3 + 5/3*w^2 + 19/3*w - 11],\
[1429, 1429, -2/3*w^3 + 2/3*w^2 + 4*w - 7],\
[1429, 1429, w^3 + 1/3*w^2 - 19/3*w + 1],\
[1451, 1451, w^3 - 4/3*w^2 - 23/3*w + 9],\
[1451, 1451, -1/3*w^3 + 2*w^2 - 2/3*w - 12],\
[1451, 1451, -1/3*w^3 - w^2 + 7/3*w + 11],\
[1451, 1451, 1/3*w^3 - 8/3*w^2 + 10/3*w + 12],\
[1459, 1459, -2/3*w^3 + 8/3*w^2 + 5*w - 16],\
[1459, 1459, -1/3*w^3 + 8/3*w^2 + 2/3*w - 16],\
[1459, 1459, -1/3*w^3 - 5/3*w^2 + 5*w + 13],\
[1459, 1459, 2/3*w^3 + 2/3*w^2 - 25/3*w - 9],\
[1471, 1471, -2/3*w^3 + 3*w^2 + 5/3*w - 16],\
[1471, 1471, -13/3*w^2 - 5/3*w + 33],\
[1471, 1471, -13/3*w^2 + 31/3*w + 27],\
[1471, 1471, 2/3*w^3 + w^2 - 17/3*w - 12],\
[1489, 1489, 1/3*w^3 - 7/3*w^2 - 4*w + 17],\
[1489, 1489, 1/3*w^3 + 4/3*w^2 - 23/3*w - 11],\
[1531, 1531, -w^3 + 3*w^2 + 7*w - 17],\
[1531, 1531, w^3 - 10*w - 8],\
[1549, 1549, w^3 + 2/3*w^2 - 35/3*w - 13],\
[1549, 1549, -2/3*w^3 + 5*w^2 + 17/3*w - 36],\
[1549, 1549, -2/3*w^3 - 3*w^2 + 41/3*w + 26],\
[1549, 1549, -w^3 + 11/3*w^2 + 22/3*w - 23],\
[1571, 1571, -w^3 + 3*w^2 + 7*w - 23],\
[1571, 1571, -1/3*w^3 - 2*w^2 + 4/3*w + 17],\
[1571, 1571, -1/3*w^3 + 1/3*w^2 + 6*w - 13],\
[1571, 1571, -2/3*w^3 + 4*w^2 + 8/3*w - 23],\
[1601, 1601, -w^3 + 4/3*w^2 + 26/3*w - 11],\
[1601, 1601, -w^3 + 8/3*w^2 + 25/3*w - 24],\
[1601, 1601, -1/3*w^3 - 7/3*w^2 + 23/3*w + 18],\
[1601, 1601, -w^3 + 5/3*w^2 + 25/3*w + 2],\
[1609, 1609, -5/3*w^3 + 2/3*w^2 + 12*w - 8],\
[1609, 1609, 2/3*w^3 + 4/3*w^2 - 7*w - 17],\
[1619, 1619, w^3 - 4/3*w^2 - 23/3*w - 3],\
[1619, 1619, -w^3 + 5/3*w^2 + 22/3*w - 11],\
[1621, 1621, 7/3*w^2 - 13/3*w - 11],\
[1621, 1621, -2/3*w^3 + 8/3*w^2 + 6*w - 17],\
[1669, 1669, 5/3*w^2 + 1/3*w - 16],\
[1669, 1669, 5/3*w^2 - 11/3*w - 14],\
[1681, 41, 2*w^2 - 2*w - 17],\
[1681, 41, 2*w^2 - 2*w - 13],\
[1699, 1699, 1/3*w^3 - 2*w^2 + 5/3*w + 11],\
[1699, 1699, -1/3*w^3 - w^2 + 4/3*w + 11],\
[1721, 1721, 1/3*w^2 + 8/3*w - 11],\
[1721, 1721, 1/3*w^2 - 10/3*w - 8],\
[1789, 1789, -2/3*w^2 - 7/3*w - 4],\
[1789, 1789, -w^3 + 2*w^2 + 8*w - 13],\
[1789, 1789, 4/3*w^2 - 13/3*w - 8],\
[1789, 1789, 2/3*w^2 - 11/3*w + 7],\
[1811, 1811, 2/3*w^2 - 11/3*w - 9],\
[1811, 1811, 2/3*w^2 + 7/3*w - 12],\
[1831, 1831, 4/3*w^2 + 5/3*w - 9],\
[1831, 1831, -w^3 + 5/3*w^2 + 25/3*w - 2],\
[1861, 1861, 14/3*w^2 + 1/3*w - 33],\
[1861, 1861, 14/3*w^2 - 29/3*w - 28],\
[1871, 1871, -w^3 + 2/3*w^2 + 28/3*w - 3],\
[1871, 1871, 1/3*w^3 + w^2 - 22/3*w - 7],\
[1871, 1871, -1/3*w^3 + 2*w^2 + 13/3*w - 13],\
[1871, 1871, -w^3 + 7/3*w^2 + 23/3*w - 6],\
[1879, 1879, -w^3 + 8/3*w^2 + 22/3*w - 13],\
[1879, 1879, -w^3 + 1/3*w^2 + 29/3*w + 4],\
[1889, 1889, -5/3*w^3 + 2*w^2 + 38/3*w - 16],\
[1889, 1889, 5/3*w^3 - 3*w^2 - 35/3*w - 3],\
[1901, 1901, w^2 - 3*w - 11],\
[1901, 1901, w^2 + w - 13],\
[1931, 1931, 2/3*w^3 + 2*w^2 - 38/3*w - 21],\
[1931, 1931, w^3 - 2/3*w^2 - 25/3*w - 9],\
[1931, 1931, -w^3 + 7/3*w^2 + 20/3*w - 17],\
[1931, 1931, -2/3*w^3 + 4*w^2 + 20/3*w - 31],\
[1949, 1949, 2/3*w^3 + 5/3*w^2 - 28/3*w - 21],\
[1949, 1949, -1/3*w^3 + 3*w^2 + 1/3*w - 17],\
[1951, 1951, -1/3*w^3 + 8/3*w^2 + 2/3*w - 19],\
[1951, 1951, 1/3*w^3 + 5/3*w^2 - 5*w - 16],\
[1999, 1999, -5/3*w^3 + 3*w^2 + 38/3*w - 23],\
[1999, 1999, -1/3*w^3 - 5/3*w^2 + 4*w + 19],\
[1999, 1999, 1/3*w^3 - 8/3*w^2 + 1/3*w + 21],\
[1999, 1999, 5/3*w^3 - 2*w^2 - 41/3*w - 9]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^3 - 3*x^2 + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [1, -1, -e - 2, e, -2*e^2 + 4*e, -e^2 + 4*e - 2, 2*e^2 - 5*e + 2, -2*e^2 + 5*e + 4, -3*e^2 + 7*e + 7, e^2 - 3*e - 1, -e^2 + e - 1, 3*e^2 - 3*e - 9, 6*e^2 - 15*e + 3, 4*e^2 - 7*e - 5, 2*e - 1, 6*e^2 - 20*e + 1, -e^2 - 2*e + 6, 2*e^2 - 7*e + 6, -6*e^2 + 13*e - 2, -e^2 + 10*e - 6, -6*e + 6, -2*e^2 + 2*e - 5, 4*e^2 - 4*e - 11, 6*e^2 - 21*e, -6*e^2 + 15*e, 4*e^2 - 10*e - 10, 4*e^2 - 10*e - 10, -3*e^2 + 3*e + 4, -e^2 + 2*e - 9, -13*e^2 + 30*e + 7, -7*e^2 + 14*e, 5*e^2 - 22*e, -e^2 + 11*e - 6, e^2 + 3*e - 4, e^2 + 7*e - 12, 5*e^2 - 9*e - 8, -e^2 - 5*e + 5, 11*e^2 - 21*e - 17, -9*e^2 + 23*e - 1, 7*e^2 - 25*e + 1, -3*e^2 + 9*e - 11, 11*e^2 - 26*e - 6, -7*e^2 + 28*e - 6, -3*e^2 + 3*e + 1, -14*e^2 + 33*e + 5, 4*e^2 - 11*e - 3, -e^2 - 5*e + 3, 11*e^2 - 41*e + 3, 8*e^2 - 24*e - 11, e^2 - 14*e + 12, e^2 - 2*e + 12, 8*e^2 - 16*e - 3, 7*e^2 - 20*e - 9, 3*e^2 - 4*e + 5, -7*e^2 + 7*e + 20, e^2 - e - 8, -8*e^2 + 19*e - 3, 10*e^2 - 21*e - 19, 15*e^2 - 48*e - 7, e^2 - 13*e - 5, e^2 + 5*e - 17, 10*e - 8, 4*e^2 - 6*e - 4, 14*e^2 - 48*e + 7, -8*e^2 + 22*e + 21, e^2 - e - 11, -7*e^2 + 31*e - 7, 13*e^2 - 38*e - 12, -11*e^2 + 30*e + 8, 6*e^2 - 17*e + 10, 10*e^2 - 15*e - 4, 5*e^2 - 19*e - 9, -9*e^2 + 25*e + 7, -5*e^2 + 9*e - 13, -7*e^2 + 21*e + 19, -2*e^2 + 3*e - 25, -7*e^2 + 5*e + 18, 11*e^2 - 19*e - 24, 16*e^2 - 29*e - 9, e^2 + 10*e - 21, -12*e^2 + 38*e - 1, -12*e^2 + 22*e + 19, e^2 + 10*e - 33, 25*e^2 - 64*e - 12, -18*e^2 + 42*e + 14, 18*e^2 - 42*e - 10, 19*e^2 - 34*e - 24, 6*e^2 - 15*e + 6, -3*e^2 + 19*e - 17, 9*e^2 - 31*e + 11, -18*e^2 + 39*e + 12, -5*e^2 + 8*e - 2, -11*e^2 + 19*e + 21, 13*e^2 - 29*e + 9, -13*e^2 + 28*e + 14, 4*e^2 - 15*e - 10, 2*e^2 + 4*e - 9, 2*e^2 - 8*e - 9, -8*e^2 + 33*e - 10, -8*e^2 + 41*e - 8, -16*e^2 + 31*e + 14, 13*e^2 - 40*e + 4, -11*e^2 + 32*e - 20, 18*e^2 - 42*e - 12, -6*e^2 + 6*e + 12, e^2 + 2*e + 12, 14*e^2 - 35*e - 25, 14*e^2 - 35*e - 13, -11*e^2 + 38*e - 12, 4*e^2 - 19*e + 25, 2*e^2 - 11*e - 19, -29*e^2 + 71*e - 4, -5*e^2 + 23*e - 16, -13*e^2 + 26*e + 21, -13*e^2 + 38*e + 27, -5*e^2 + 14*e + 9, 19*e^2 - 34*e - 27, 11*e^2 - 29*e - 30, -25*e^2 + 79*e + 6, 12*e^2 - 13*e - 28, -e^2 + 7*e - 25, -5*e^2 + 11*e - 5, -12*e^2 + 43*e + 4, -3*e^2 + 19*e - 32, -5*e^2 - 9*e + 26, 17*e^2 - 49*e + 15, 6*e^2 - 9*e + 15, 12*e^2 - 57*e + 15, 17*e^2 - 43*e - 9, -9*e^2 + 15*e + 38, 9*e^2 - 21*e - 28, 10*e^2 - 43*e + 12, -14*e^2 + 29*e + 36, -10*e^2 + 43*e + 5, 2*e^2 - 5*e + 11, -22*e^2 + 55*e - 1, -2*e^2 - e + 37, -8*e^2 + 12*e + 26, e^2 - 13*e + 18, -17*e^2 + 47*e - 12, 16*e - 38, -22*e^2 + 34*e + 33, 2*e^2 + 10*e - 27, -8*e^2 + 37*e - 12, 16*e^2 - 23*e - 24, 11*e^2 - 24*e + 22, 2*e^2 - 3*e + 1, 20*e^2 - 43*e - 3, 17*e^2 - 46*e - 18, -12*e^2 + 42*e - 25, -13*e^2 + 28*e + 26, -7*e^2 + 10*e + 50, -9*e^2 + 17*e + 8, 11*e^2 - 39*e + 16, -19*e^2 + 49*e + 13, -4*e^2 + 15*e + 28, -7*e + 2, -19*e^2 + 55*e + 13, -9*e^2 + 19*e - 29, 19*e^2 - 33*e - 25, 16*e^2 - 31*e - 39, 2*e^2 + 3*e - 8, -7*e^2 + 12*e + 7, -3*e^2 + 20*e + 11, 6*e^2 - 37*e + 8, -10*e^2 + 33*e + 28, 2*e^2 - 27*e + 40, -7*e^2 + 40*e - 15, -19*e^2 + 52*e - 9, 7*e^2 + 4*e - 21, -29*e^2 + 84*e + 17, -9*e^2 + 14*e + 29, 6*e^2 - 19*e - 7, 10*e^2 - 47*e + 33, -13*e^2 + 42*e - 11, -26*e^2 + 59*e + 31, -14*e^2 + 47*e + 7, 11*e^2 - 18*e - 44, -7*e^2 - 4*e + 24, -25*e^2 + 72*e + 13, -e^2 + 12*e - 23, 23*e^2 - 63*e + 10, -25*e^2 + 53*e + 30, -8*e^2 + 10*e + 15, -6*e^2 + 32*e + 17, -3*e^2 + e - 8, -5*e^2 - 15*e + 38, 15*e^2 - 38*e + 10, 5*e^2 - 28*e + 18, 10*e^2 - 25*e - 26, -10*e^2 + 31*e + 38, 16*e^2 - 10*e - 52, 4*e^2 - 34*e + 32, 9*e^2 - 14*e + 10, 8*e^2 - 41*e + 15, 8*e^2 + 7*e - 33, -15*e^2 + 34*e + 34, e^2 + 9*e + 2, 9*e^2 + e - 14, 5*e^2 - 26*e + 4, 4*e^2 - 12*e + 5, -26*e^2 + 66*e + 11, -13*e^2 + 4*e + 40, -20*e^2 + 61*e + 24, -32*e^2 + 91*e + 6, -18*e^2 + 51*e - 22, 14*e^2 - 29*e - 42, 14*e^2 - 23*e - 24, 18*e^2 - 39*e + 8, -31*e^2 + 78*e + 34, 5*e^2 - 33*e + 19, 5*e^2 - 19*e + 51, 15*e^2 - 52*e + 2, -22*e^2 + 50*e, 6*e^2 - 26*e - 8, 8*e^2 - 29*e - 28, -32*e^2 + 71*e + 4, 6*e^2 - 13*e - 25, -13*e^2 + 51*e - 23, 23*e^2 - 31*e - 51, -4*e^2 + 3*e - 5, 7*e^2 - 49, -21*e^2 + 64*e + 31, 6*e^2 - 6*e - 55, -24*e + 35, -30*e^2 + 72*e - 9, -22*e^2 + 40*e + 11, 7*e^2 - 28*e - 15, 7*e^2 + 8*e - 21, 12*e^2 - 48*e - 20, 12*e^2 - 60*e + 28, -28*e^2 + 95*e + 24, -12*e^2 + 46*e - 29, 24*e^2 - 82*e - 13, 20*e^2 - 49*e - 12, 24*e^2 - 84*e - 9, -3*e^2 - 21*e + 31, -15*e^2 + 57*e - 41, 18*e^2 - 54*e - 27, 28*e^2 - 67*e + 24, 13*e^2 - 32*e - 12, -3*e^2 - 28*e + 44, -20*e^2 + 41*e + 12, 33*e^2 - 105*e - 15, 21*e^2 - 39*e - 15, -43*e^2 + 107*e - 3, 5*e^2 - 25*e - 39, 33*e^2 - 98*e - 2, -17*e^2 + 54*e - 28, 21*e^2 - 68*e + 4, -13*e^2 + 56*e - 42, -26*e^2 + 53*e + 31, -e^2 + 17*e + 27, 23*e^2 - 39*e - 29, 22*e^2 - 43*e - 41, -27*e^2 + 82*e + 28, -23*e^2 + 76*e + 24, -11*e^2 + 12*e + 56, -35*e^2 + 78*e - 4, -10*e^2 - 17*e + 64, -22*e^2 + 49*e - 14, 35*e^2 - 79*e + 6, 17*e^2 - 43*e + 24, -2*e^2 - 2*e + 27, -2*e^2 - 2*e + 3, -30*e^2 + 108*e + 4, -42*e^2 + 96*e + 16, -6*e^2 + 24*e - 19, -12*e^2 + 27*e - 32, 11*e^2 - 62*e + 42, 17*e^2 - 44*e - 6, -17*e^2 + 31*e + 30, 19*e^2 - 69*e + 14, -e^2 - 26*e + 30, -8*e^2 + 7*e + 48, -4*e^2 - 15*e + 34, 17*e^2 - 44*e - 30, 24*e^2 - 42*e - 3, -12*e^2 + 42*e + 9, 24*e^2 - 100*e + 8, 20*e^2 - 60*e - 44, -26*e^2 + 98*e - 12, -26*e^2 + 38*e + 60, -7*e^2 + 46*e - 19, 7*e^2 - 19*e + 28, -37*e^2 + 73*e + 44, e^2 - 10*e - 11, 30*e^2 - 61*e - 1, 16*e^2 - 41*e - 21, 17*e^2 - 35*e - 19, -11*e^2 - e + 49, 31*e^2 - 68*e - 48, -5*e^2 - 16, 17*e^2 - 61*e + 3, -35*e^2 + 76*e + 6, 13*e^2 - 36*e + 26, -19*e^2 + 71*e + 15, -e^2 + 19*e - 22, 29*e^2 - 41*e - 52, -5*e^2 + 5*e - 34, 7*e^2 + 5*e - 58, 35*e^2 - 66*e - 20, 3*e - 13, 18*e^2 - 69*e - 1, 5*e^2 - 24*e - 8]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, 2/3*w^2 + 1/3*w - 5])] = -1
AL_eigenvalues[ZF.ideal([5, 5, 2/3*w^2 - 5/3*w - 4])] = 1

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