/*
  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([20, 10, -11, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([20,10,1/2*w^3 + 3/2*w^2 - 7/2*w - 9])

primes_array = [
[4, 2, -w + 2],\
[4, 2, 1/2*w^3 + 1/2*w^2 - 9/2*w - 4],\
[5, 5, -1/2*w^3 - 3/2*w^2 + 7/2*w + 10],\
[5, 5, -1/2*w^3 - 1/2*w^2 + 5/2*w + 3],\
[19, 19, 1/2*w^3 + 1/2*w^2 - 9/2*w - 3],\
[19, 19, w - 1],\
[31, 31, 1/2*w^3 + 3/2*w^2 - 7/2*w - 6],\
[31, 31, -w^3 - 2*w^2 + 7*w + 13],\
[49, 7, -2*w^3 - 2*w^2 + 15*w + 9],\
[49, 7, 1/2*w^3 + 3/2*w^2 - 9/2*w - 4],\
[59, 59, -3/2*w^3 - 3/2*w^2 + 17/2*w + 8],\
[59, 59, -1/2*w^3 - 5/2*w^2 + 11/2*w + 9],\
[61, 61, -1/2*w^3 - 3/2*w^2 + 9/2*w + 9],\
[61, 61, -3/2*w^3 - 5/2*w^2 + 23/2*w + 12],\
[71, 71, -3/2*w^3 - 1/2*w^2 + 23/2*w - 1],\
[71, 71, 3/2*w^3 + 3/2*w^2 - 19/2*w - 9],\
[79, 79, -1/2*w^3 - 3/2*w^2 + 11/2*w + 4],\
[79, 79, -5/2*w^3 - 7/2*w^2 + 37/2*w + 18],\
[81, 3, -3],\
[89, 89, w^3 - 7*w + 1],\
[89, 89, -2*w^3 - 3*w^2 + 14*w + 17],\
[89, 89, 1/2*w^3 - 1/2*w^2 - 7/2*w + 2],\
[89, 89, -5/2*w^3 - 7/2*w^2 + 35/2*w + 18],\
[101, 101, -2*w^2 + 11],\
[101, 101, 3*w^3 + 5*w^2 - 21*w - 27],\
[121, 11, -3/2*w^3 - 3/2*w^2 + 21/2*w + 7],\
[121, 11, 3/2*w^3 + 3/2*w^2 - 21/2*w - 8],\
[131, 131, -3/2*w^3 - 5/2*w^2 + 21/2*w + 16],\
[131, 131, -3/2*w^3 - 5/2*w^2 + 19/2*w + 14],\
[139, 139, -2*w^3 - w^2 + 16*w + 1],\
[139, 139, 1/2*w^3 + 1/2*w^2 - 3/2*w - 8],\
[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 24],\
[149, 149, -w^3 + w^2 + 5*w - 3],\
[149, 149, -5*w^3 - 7*w^2 + 37*w + 39],\
[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 14],\
[181, 181, -5/2*w^3 - 9/2*w^2 + 37/2*w + 27],\
[181, 181, -5/2*w^3 - 7/2*w^2 + 33/2*w + 19],\
[181, 181, 3/2*w^3 + 1/2*w^2 - 23/2*w - 2],\
[181, 181, w^3 + 3*w^2 - 8*w - 13],\
[191, 191, 1/2*w^3 + 5/2*w^2 - 7/2*w - 14],\
[191, 191, -5/2*w^3 - 9/2*w^2 + 35/2*w + 24],\
[199, 199, -1/2*w^3 - 5/2*w^2 + 7/2*w + 16],\
[199, 199, 5/2*w^3 + 9/2*w^2 - 35/2*w - 22],\
[211, 211, -2*w^3 - 4*w^2 + 14*w + 19],\
[211, 211, -w^3 - 3*w^2 + 7*w + 19],\
[229, 229, 3/2*w^3 + 7/2*w^2 - 21/2*w - 17],\
[229, 229, -3/2*w^3 - 7/2*w^2 + 21/2*w + 21],\
[229, 229, -1/2*w^3 - 3/2*w^2 + 13/2*w + 1],\
[229, 229, 5/2*w^3 + 7/2*w^2 - 41/2*w - 24],\
[241, 241, -1/2*w^3 - 5/2*w^2 + 7/2*w + 12],\
[241, 241, 3/2*w^3 + 3/2*w^2 - 23/2*w - 3],\
[241, 241, w^3 + w^2 - 6*w - 1],\
[241, 241, -5/2*w^3 - 9/2*w^2 + 35/2*w + 26],\
[251, 251, 2*w^3 + 2*w^2 - 13*w - 9],\
[251, 251, -5/2*w^3 - 5/2*w^2 + 37/2*w + 11],\
[269, 269, -2*w^3 - 3*w^2 + 12*w + 17],\
[269, 269, 5/2*w^3 + 11/2*w^2 - 37/2*w - 21],\
[271, 271, 3/2*w^3 + 5/2*w^2 - 23/2*w - 9],\
[271, 271, 1/2*w^3 + 3/2*w^2 - 9/2*w - 12],\
[281, 281, 5/2*w^3 + 9/2*w^2 - 39/2*w - 28],\
[281, 281, 3/2*w^3 + 7/2*w^2 - 25/2*w - 14],\
[311, 311, 1/2*w^3 + 7/2*w^2 - 5/2*w - 24],\
[311, 311, 3*w^3 + 5*w^2 - 22*w - 27],\
[311, 311, 3/2*w^3 + 5/2*w^2 - 17/2*w - 12],\
[311, 311, 1/2*w^3 + 5/2*w^2 - 9/2*w - 13],\
[349, 349, 3*w^3 + 4*w^2 - 21*w - 21],\
[349, 349, -3/2*w^3 - 1/2*w^2 + 21/2*w + 2],\
[359, 359, -w^3 - 3*w^2 + 7*w + 17],\
[359, 359, -2*w^3 - 4*w^2 + 14*w + 21],\
[361, 19, -2*w^3 - 2*w^2 + 14*w + 11],\
[389, 389, -2*w^3 - 2*w^2 + 13*w + 11],\
[389, 389, 5/2*w^3 + 5/2*w^2 - 37/2*w - 13],\
[401, 401, 3/2*w^3 + 7/2*w^2 - 21/2*w - 19],\
[401, 401, 5/2*w^3 + 9/2*w^2 - 37/2*w - 23],\
[401, 401, -w^3 - 3*w^2 + 8*w + 17],\
[431, 431, 5/2*w^3 + 5/2*w^2 - 29/2*w - 13],\
[431, 431, -15/2*w^3 - 23/2*w^2 + 107/2*w + 61],\
[439, 439, -3/2*w^3 + 1/2*w^2 + 21/2*w - 6],\
[439, 439, -9/2*w^3 - 13/2*w^2 + 63/2*w + 32],\
[449, 449, -w^2 - 2*w + 1],\
[449, 449, -1/2*w^3 - 3/2*w^2 + 3/2*w + 14],\
[461, 461, -2*w^3 - 2*w^2 + 12*w + 9],\
[461, 461, -3*w^3 - 3*w^2 + 23*w + 13],\
[479, 479, 7/2*w^3 + 9/2*w^2 - 47/2*w - 26],\
[479, 479, 3/2*w^3 + 5/2*w^2 - 27/2*w - 16],\
[479, 479, -7/2*w^3 - 9/2*w^2 + 51/2*w + 24],\
[479, 479, 3/2*w^3 + 1/2*w^2 - 19/2*w - 3],\
[491, 491, 2*w^3 + 4*w^2 - 15*w - 23],\
[491, 491, -7/2*w^3 - 7/2*w^2 + 53/2*w + 17],\
[491, 491, -1/2*w^3 - 5/2*w^2 + 11/2*w + 6],\
[491, 491, -3/2*w^3 - 7/2*w^2 + 23/2*w + 17],\
[499, 499, 3*w^2 - 19],\
[499, 499, 3/2*w^3 + 5/2*w^2 - 19/2*w - 16],\
[499, 499, -9/2*w^3 - 15/2*w^2 + 63/2*w + 38],\
[499, 499, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1],\
[509, 509, 2*w^2 - w - 7],\
[509, 509, 7/2*w^3 + 11/2*w^2 - 51/2*w - 33],\
[521, 521, 4*w^3 + 5*w^2 - 32*w - 31],\
[521, 521, -1/2*w^3 + 1/2*w^2 - 1/2*w + 4],\
[541, 541, 1/2*w^3 - 7/2*w^2 - 3/2*w + 18],\
[541, 541, -15/2*w^3 - 23/2*w^2 + 109/2*w + 62],\
[541, 541, -w^3 - 3*w^2 + 7*w + 11],\
[541, 541, 2*w^3 + 4*w^2 - 14*w - 27],\
[569, 569, 1/2*w^3 + 5/2*w^2 - 7/2*w - 21],\
[569, 569, -5/2*w^3 - 5/2*w^2 + 31/2*w + 14],\
[571, 571, 2*w^2 + 2*w - 11],\
[571, 571, 2*w^3 + 4*w^2 - 12*w - 23],\
[601, 601, w^3 + 3*w^2 - 8*w - 9],\
[601, 601, 3*w^3 + 2*w^2 - 23*w - 7],\
[601, 601, -3/2*w^3 - 7/2*w^2 + 23/2*w + 19],\
[601, 601, -2*w^3 - 4*w^2 + 15*w + 21],\
[631, 631, -5/2*w^3 - 3/2*w^2 + 33/2*w + 3],\
[631, 631, -13/2*w^3 - 19/2*w^2 + 101/2*w + 58],\
[641, 641, 13/2*w^3 + 19/2*w^2 - 97/2*w - 52],\
[641, 641, -3/2*w^3 - 9/2*w^2 + 23/2*w + 16],\
[659, 659, 1/2*w^3 - 1/2*w^2 - 1/2*w + 2],\
[659, 659, 3/2*w^3 + 7/2*w^2 - 15/2*w - 11],\
[661, 661, -3/2*w^3 - 3/2*w^2 + 25/2*w + 3],\
[661, 661, -1/2*w^3 - 1/2*w^2 + 3/2*w - 1],\
[691, 691, -2*w^3 - 7*w^2 + 14*w + 49],\
[691, 691, -1/2*w^3 - 7/2*w^2 + 13/2*w + 14],\
[691, 691, -13/2*w^3 - 19/2*w^2 + 101/2*w + 59],\
[691, 691, -7/2*w^3 - 13/2*w^2 + 49/2*w + 36],\
[701, 701, 3/2*w^3 + 11/2*w^2 - 21/2*w - 38],\
[701, 701, -2*w^3 - 2*w^2 + 10*w + 11],\
[709, 709, 1/2*w^3 + 5/2*w^2 - 9/2*w - 17],\
[709, 709, -3*w^3 - 3*w^2 + 22*w + 13],\
[709, 709, -3*w^3 - 5*w^2 + 22*w + 23],\
[709, 709, -5/2*w^3 - 5/2*w^2 + 33/2*w + 11],\
[751, 751, -3/2*w^3 + 3/2*w^2 + 15/2*w - 4],\
[751, 751, 15/2*w^3 + 21/2*w^2 - 111/2*w - 59],\
[751, 751, 1/2*w^3 - 1/2*w^2 - 9/2*w - 2],\
[751, 751, -3/2*w^3 - 5/2*w^2 + 19/2*w + 19],\
[769, 769, -9/2*w^3 - 15/2*w^2 + 65/2*w + 38],\
[769, 769, -1/2*w^3 - 7/2*w^2 + 9/2*w + 21],\
[809, 809, -7/2*w^3 - 13/2*w^2 + 51/2*w + 42],\
[809, 809, -5/2*w^3 - 3/2*w^2 + 27/2*w + 14],\
[809, 809, -3*w^3 - 5*w^2 + 21*w + 29],\
[809, 809, 2*w^2 - 9],\
[811, 811, 3*w^3 + 5*w^2 - 20*w - 27],\
[811, 811, 1/2*w^3 - 7/2*w^2 - 9/2*w + 31],\
[811, 811, w^3 - w^2 - 2*w + 1],\
[811, 811, 3/2*w^3 + 5/2*w^2 - 19/2*w - 18],\
[821, 821, 9/2*w^3 + 13/2*w^2 - 67/2*w - 34],\
[821, 821, 3/2*w^3 + 3/2*w^2 - 25/2*w - 1],\
[829, 829, 1/2*w^3 + 5/2*w^2 - 1/2*w - 21],\
[829, 829, 4*w^3 + 2*w^2 - 32*w - 3],\
[839, 839, -1/2*w^3 - 1/2*w^2 + 3/2*w - 2],\
[839, 839, -3/2*w^3 - 3/2*w^2 + 25/2*w + 2],\
[841, 29, -5/2*w^3 - 5/2*w^2 + 35/2*w + 11],\
[841, 29, 5/2*w^3 + 5/2*w^2 - 35/2*w - 14],\
[881, 881, -9/2*w^3 - 13/2*w^2 + 63/2*w + 36],\
[881, 881, 1/2*w^3 + 5/2*w^2 - 3/2*w - 21],\
[911, 911, -1/2*w^3 + 3/2*w^2 + 7/2*w - 7],\
[911, 911, 7/2*w^3 + 13/2*w^2 - 49/2*w - 38],\
[911, 911, 7*w^3 + 11*w^2 - 51*w - 61],\
[911, 911, -7/2*w^3 - 11/2*w^2 + 49/2*w + 31],\
[919, 919, -1/2*w^3 + 7/2*w^2 + 3/2*w - 16],\
[919, 919, 15/2*w^3 + 23/2*w^2 - 109/2*w - 64],\
[929, 929, -3/2*w^3 - 7/2*w^2 + 19/2*w + 23],\
[929, 929, -5/2*w^3 - 7/2*w^2 + 33/2*w + 21],\
[941, 941, -1/2*w^3 - 7/2*w^2 + 11/2*w + 18],\
[941, 941, -5*w^3 - 8*w^2 + 37*w + 43],\
[961, 31, 5/2*w^3 + 5/2*w^2 - 35/2*w - 13],\
[971, 971, 2*w^3 + w^2 - 14*w - 3],\
[971, 971, -5/2*w^3 - 9/2*w^2 + 35/2*w + 31],\
[971, 971, 7/2*w^3 + 9/2*w^2 - 49/2*w - 22],\
[971, 971, 3/2*w^3 + 1/2*w^2 - 27/2*w + 6],\
[991, 991, 5/2*w^3 + 7/2*w^2 - 39/2*w - 16],\
[991, 991, 5/2*w^3 + 7/2*w^2 - 37/2*w - 14],\
[1009, 1009, 1/2*w^3 + 7/2*w^2 - 9/2*w - 18],\
[1009, 1009, 9/2*w^3 + 15/2*w^2 - 65/2*w - 41],\
[1019, 1019, 2*w^3 + 5*w^2 - 14*w - 21],\
[1019, 1019, 5/2*w^3 + 11/2*w^2 - 35/2*w - 36],\
[1021, 1021, 1/2*w^3 + 3/2*w^2 - 7/2*w - 2],\
[1021, 1021, w^3 + 2*w^2 - 7*w - 17],\
[1039, 1039, -3/2*w^3 - 5/2*w^2 + 27/2*w + 8],\
[1039, 1039, -7/2*w^3 - 13/2*w^2 + 51/2*w + 31],\
[1039, 1039, -3*w^3 - 4*w^2 + 25*w + 19],\
[1039, 1039, -4*w^3 - 6*w^2 + 29*w + 29],\
[1051, 1051, 3/2*w^3 + 7/2*w^2 - 27/2*w - 13],\
[1051, 1051, -7/2*w^3 - 9/2*w^2 + 53/2*w + 22],\
[1061, 1061, 1/2*w^3 + 3/2*w^2 - 1/2*w - 17],\
[1061, 1061, -3*w^3 - w^2 + 24*w - 3],\
[1069, 1069, -7/2*w^3 - 9/2*w^2 + 47/2*w + 23],\
[1069, 1069, 2*w^3 + 3*w^2 - 14*w - 23],\
[1129, 1129, 3*w^3 + 4*w^2 - 23*w - 19],\
[1129, 1129, 5/2*w^3 + 7/2*w^2 - 37/2*w - 13],\
[1151, 1151, w^3 + w^2 - 4*w - 13],\
[1151, 1151, -5*w^3 - 8*w^2 + 35*w + 43],\
[1229, 1229, -3*w^3 - 4*w^2 + 19*w + 23],\
[1229, 1229, -3/2*w^3 - 9/2*w^2 + 19/2*w + 31],\
[1249, 1249, 3*w^3 + 6*w^2 - 21*w - 23],\
[1249, 1249, 7/2*w^3 + 1/2*w^2 - 55/2*w + 7],\
[1279, 1279, 2*w^3 + 2*w^2 - 17*w - 9],\
[1279, 1279, -3*w^3 - 6*w^2 + 21*w + 29],\
[1319, 1319, 3/2*w^3 + 9/2*w^2 - 19/2*w - 22],\
[1319, 1319, -w^3 + w^2 + 9],\
[1319, 1319, 5/2*w^3 + 11/2*w^2 - 33/2*w - 33],\
[1319, 1319, 9*w^3 + 14*w^2 - 65*w - 77],\
[1321, 1321, 3*w^3 + 3*w^2 - 16*w - 19],\
[1321, 1321, -3*w^3 - 8*w^2 + 21*w + 53],\
[1361, 1361, -11*w^3 - 17*w^2 + 79*w + 89],\
[1361, 1361, -9/2*w^3 - 11/2*w^2 + 59/2*w + 24],\
[1409, 1409, -3/2*w^3 - 1/2*w^2 + 15/2*w + 3],\
[1409, 1409, -5*w^3 - 6*w^2 + 39*w + 31],\
[1409, 1409, 7/2*w^3 + 13/2*w^2 - 51/2*w - 27],\
[1409, 1409, 1/2*w^3 + 5/2*w^2 - 9/2*w - 21],\
[1429, 1429, -1/2*w^3 - 1/2*w^2 + 13/2*w - 1],\
[1429, 1429, 7/2*w^3 + 13/2*w^2 - 49/2*w - 34],\
[1429, 1429, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17],\
[1429, 1429, 11/2*w^3 + 17/2*w^2 - 79/2*w - 42],\
[1439, 1439, -17/2*w^3 - 25/2*w^2 + 125/2*w + 71],\
[1439, 1439, 9/2*w^3 + 17/2*w^2 - 65/2*w - 51],\
[1451, 1451, 3/2*w^3 - 3/2*w^2 - 15/2*w + 7],\
[1451, 1451, -7/2*w^3 - 5/2*w^2 + 47/2*w + 7],\
[1459, 1459, 3/2*w^3 + 11/2*w^2 - 25/2*w - 18],\
[1459, 1459, -7/2*w^3 - 9/2*w^2 + 55/2*w + 22],\
[1459, 1459, 3*w^3 + 5*w^2 - 22*w - 21],\
[1459, 1459, w^3 + 7*w^2 - 5*w - 53],\
[1471, 1471, -1/2*w^3 - 9/2*w^2 + 7/2*w + 37],\
[1471, 1471, -21/2*w^3 - 31/2*w^2 + 151/2*w + 82],\
[1481, 1481, -11/2*w^3 - 15/2*w^2 + 81/2*w + 38],\
[1481, 1481, 3/2*w^3 - 1/2*w^2 - 17/2*w + 4],\
[1489, 1489, -7/2*w^3 - 7/2*w^2 + 45/2*w + 22],\
[1489, 1489, 9/2*w^3 + 9/2*w^2 - 67/2*w - 26],\
[1499, 1499, 7/2*w^3 + 9/2*w^2 - 45/2*w - 26],\
[1499, 1499, 7*w^3 + 11*w^2 - 49*w - 53],\
[1511, 1511, -7/2*w^3 - 9/2*w^2 + 51/2*w + 19],\
[1511, 1511, -3/2*w^3 - 1/2*w^2 + 19/2*w - 2],\
[1511, 1511, -5*w^3 - 3*w^2 + 39*w + 9],\
[1511, 1511, 1/2*w^3 - 9/2*w^2 - 5/2*w + 26],\
[1559, 1559, -9/2*w^3 - 13/2*w^2 + 65/2*w + 31],\
[1559, 1559, -3/2*w^3 - 5/2*w^2 + 27/2*w + 4],\
[1559, 1559, -6*w^3 - 8*w^2 + 43*w + 37],\
[1559, 1559, w^3 - w^2 - 6*w + 9],\
[1571, 1571, 9/2*w^3 + 17/2*w^2 - 65/2*w - 39],\
[1571, 1571, -2*w^3 - 6*w^2 + 15*w + 39],\
[1601, 1601, -3*w^3 - 5*w^2 + 24*w + 33],\
[1601, 1601, -7/2*w^3 - 9/2*w^2 + 51/2*w + 14],\
[1609, 1609, 4*w^3 + 5*w^2 - 28*w - 23],\
[1609, 1609, -3/2*w^3 - 3/2*w^2 + 13/2*w + 8],\
[1609, 1609, -13/2*w^3 - 19/2*w^2 + 91/2*w + 48],\
[1609, 1609, -5/2*w^3 - 3/2*w^2 + 35/2*w + 4],\
[1619, 1619, 5/2*w^3 + 7/2*w^2 - 29/2*w - 14],\
[1619, 1619, -11/2*w^3 - 17/2*w^2 + 75/2*w + 44],\
[1621, 1621, 2*w^3 + 2*w^2 - 16*w - 3],\
[1621, 1621, w^3 + w^2 - 5*w + 1],\
[1669, 1669, -6*w^3 - 6*w^2 + 46*w + 31],\
[1669, 1669, -1/2*w^3 - 9/2*w^2 + 15/2*w + 11],\
[1681, 41, 3*w^3 + 3*w^2 - 21*w - 13],\
[1681, 41, 3*w^3 + 3*w^2 - 21*w - 17],\
[1699, 1699, 7/2*w^3 + 7/2*w^2 - 39/2*w - 23],\
[1699, 1699, -7/2*w^3 - 17/2*w^2 + 49/2*w + 56],\
[1709, 1709, -1/2*w^3 + 1/2*w^2 + 13/2*w - 1],\
[1709, 1709, 1/2*w^3 + 3/2*w^2 - 1/2*w - 12],\
[1721, 1721, 5/2*w^3 + 9/2*w^2 - 39/2*w - 19],\
[1721, 1721, -3*w^3 - 3*w^2 + 23*w + 11],\
[1741, 1741, 5/2*w^3 + 9/2*w^2 - 31/2*w - 26],\
[1741, 1741, -3*w^3 - 5*w^2 + 21*w + 31],\
[1759, 1759, w^3 + 5*w^2 - 6*w - 33],\
[1759, 1759, 9/2*w^3 + 17/2*w^2 - 61/2*w - 41],\
[1789, 1789, 5/2*w^3 + 11/2*w^2 - 35/2*w - 28],\
[1789, 1789, 2*w^3 + 5*w^2 - 14*w - 29],\
[1801, 1801, w^3 + 3*w^2 - 4*w - 23],\
[1801, 1801, 3/2*w^3 + 9/2*w^2 - 21/2*w - 26],\
[1801, 1801, 3*w^3 + 6*w^2 - 21*w - 31],\
[1801, 1801, 11/2*w^3 + 17/2*w^2 - 79/2*w - 48],\
[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 1],\
[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 16],\
[1831, 1831, -9/2*w^3 - 13/2*w^2 + 63/2*w + 37],\
[1831, 1831, -w^3 - 3*w^2 + 5*w + 23],\
[1849, 43, 6*w^3 + 8*w^2 - 44*w - 43],\
[1849, 43, 1/2*w^3 - 3/2*w^2 + 1/2*w - 3],\
[1861, 1861, 5/2*w^3 + 7/2*w^2 - 33/2*w - 23],\
[1861, 1861, 5/2*w^3 + 9/2*w^2 - 33/2*w - 27],\
[1861, 1861, -2*w^3 + 13*w - 1],\
[1861, 1861, 2*w^3 + 3*w^2 - 12*w - 7],\
[1871, 1871, 3/2*w^3 + 5/2*w^2 - 15/2*w - 14],\
[1871, 1871, 3/2*w^3 + 1/2*w^2 - 27/2*w - 1],\
[1901, 1901, -4*w^3 - 5*w^2 + 28*w + 27],\
[1901, 1901, 5/2*w^3 + 3/2*w^2 - 35/2*w - 8],\
[1931, 1931, -2*w^3 + w^2 + 10*w + 1],\
[1931, 1931, 17/2*w^3 + 23/2*w^2 - 127/2*w - 66],\
[1949, 1949, -w^3 - 2*w^2 + 3*w + 17],\
[1949, 1949, -4*w^2 + 2*w + 17],\
[1949, 1949, -w^3 - 5*w^2 + 7*w + 27],\
[1949, 1949, -5*w^3 - 9*w^2 + 35*w + 49],\
[1951, 1951, -13/2*w^3 - 17/2*w^2 + 103/2*w + 52],\
[1951, 1951, 11/2*w^3 + 13/2*w^2 - 87/2*w - 41],\
[1979, 1979, -15/2*w^3 - 19/2*w^2 + 119/2*w + 59],\
[1979, 1979, 9/2*w^3 + 17/2*w^2 - 61/2*w - 47],\
[1999, 1999, 3*w^3 + 3*w^2 - 20*w - 17],\
[1999, 1999, 7/2*w^3 + 7/2*w^2 - 51/2*w - 19]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-3, -1, 0, 1, -8, -2, -4, 8, 10, -2, 4, 0, -10, -6, 0, 10, 16, 6, -8, 2, -2, 18, -10, -4, -10, -18, 10, -16, -6, 12, -2, 6, 8, 2, 10, 16, -22, 16, 18, -6, -18, -18, -2, -12, 0, -26, -6, 30, -24, 2, 2, -26, 4, -16, -28, 24, 10, -22, -14, 6, 2, 4, 4, 24, -12, 20, -14, 4, 0, 14, -10, -26, -30, 16, -20, -36, -24, -22, -8, 22, -12, -30, 32, 38, 24, -16, 16, -30, -28, 30, -36, -4, 40, -28, 34, 10, -26, 30, -6, 22, -34, 10, -22, -8, -6, -10, 12, 12, 6, -8, -2, 16, -40, 6, 6, -36, -20, 26, -24, 40, 20, -12, 48, 30, -24, -12, 6, 18, -6, 24, -32, 12, -4, -42, -18, -6, 30, 26, 10, 20, 12, -8, 0, -22, -10, 6, -44, -36, -12, -10, -54, 0, -6, 40, 40, -8, 10, -24, -32, -36, 6, -10, -28, 52, 56, 0, -54, 12, 28, -52, -14, -2, -52, 46, -40, 2, -24, -56, -20, 10, -60, 2, 42, -42, 6, 28, 38, -8, -18, 50, -46, -28, -4, -52, -56, 8, 8, -36, -40, -32, -10, 22, -30, 10, -36, -6, -66, -24, 0, 66, -42, -58, 18, -38, -60, -52, 30, -28, 0, 8, -62, 40, 6, 66, 54, 2, -4, -6, -16, -42, 8, 12, 32, -32, 76, -72, 18, 20, 22, -46, -4, 14, -14, -54, 60, 52, -38, 20, 8, 50, -60, -52, 70, 4, 22, -24, 42, 30, 80, -22, -30, -16, 26, -12, -58, -30, -80, -10, 28, 28, 20, -68, -10, -30, 32, 10, 26, 26, -40, 32, -54, 70, 12, -4, -78, 30, -6, -78, -58, 8, -30, 0, 24, 4]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([4,2,-1/2*w^3 - 1/2*w^2 + 9/2*w + 4])] = 1
AL_eigenvalues[ZF.ideal([5,5,w^3 + 2*w^2 - 7*w - 9])] = -1

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