/*
  This code can be loaded, or copied and pasted, into Magma.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
  At the *bottom* of the file, there is code to recreate the
  Hilbert modular form in Magma, by creating the HMF space
  and cutting out the corresponding Hecke irreducible subspace.
  From there, you can ask for more eigenvalues or modify as desired.
  It is commented out, as this computation may be lengthy.
*/

P<x> := PolynomialRing(Rationals());
g := P![20, 10, -11, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {19,19,w - 1}>;

primesArray := [
[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 := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^6 + 4*x^5 - 8*x^4 - 50*x^3 - 48*x^2 + 16*x + 17;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 1/4*e^5 + 1/2*e^4 - 11/4*e^3 - 25/4*e^2 - 2*e + 1/4, -1/2*e^5 - e^4 + 11/2*e^3 + 27/2*e^2 + 3*e - 9/2, -1/4*e^5 - 1/2*e^4 + 13/4*e^3 + 25/4*e^2 - 3*e - 7/4, -3/4*e^5 - e^4 + 37/4*e^3 + 55/4*e^2 - 15/2*e - 7/4, -1, -1/2*e^5 - e^4 + 13/2*e^3 + 27/2*e^2 - 6*e - 17/2, -1/2*e^4 - 1/2*e^3 + 6*e^2 + 15/2*e - 5/2, -e^5 - 9/4*e^4 + 47/4*e^3 + 57/2*e^2 + 3/4*e - 43/4, -7/4*e^5 - 17/4*e^4 + 20*e^3 + 217/4*e^2 + 25/4*e - 43/2, 3/2*e^5 + 7/2*e^4 - 17*e^3 - 91/2*e^2 - 15/2*e + 13, -5/4*e^5 - 3*e^4 + 55/4*e^3 + 157/4*e^2 + 17/2*e - 45/4, 1/4*e^5 + 1/2*e^4 - 9/4*e^3 - 25/4*e^2 - 6*e + 15/4, 5/4*e^5 + 7/4*e^4 - 15*e^3 - 103/4*e^2 + 33/4*e + 29/2, -1/2*e^5 - 3/2*e^4 + 5*e^3 + 37/2*e^2 + 21/2*e + 2, -1/4*e^5 - 3/4*e^4 + 2*e^3 + 39/4*e^2 + 43/4*e - 1/2, -1/2*e^5 - 7/4*e^4 + 23/4*e^3 + 20*e^2 + 13/4*e + 1/4, -e^5 - e^4 + 12*e^3 + 15*e^2 - 11*e - 2, 3/4*e^5 + 7/4*e^4 - 17/2*e^3 - 93/4*e^2 - 3/4*e + 9, e^3 - e^2 - 11*e + 5, 1/2*e^5 + 2*e^4 - 9/2*e^3 - 51/2*e^2 - 16*e + 19/2, -e^5 - 7/4*e^4 + 45/4*e^3 + 47/2*e^2 + 5/4*e - 17/4, 5/4*e^5 + 13/4*e^4 - 29/2*e^3 - 159/4*e^2 - 13/4*e + 12, 5/4*e^4 - 3/4*e^3 - 29/2*e^2 + 9/4*e + 75/4, 5/2*e^5 + 19/4*e^4 - 115/4*e^3 - 64*e^2 - 1/4*e + 115/4, 1/2*e^5 + 3/2*e^4 - 5*e^3 - 41/2*e^2 - 19/2*e + 17, 5/4*e^5 + 1/4*e^4 - 33/2*e^3 - 31/4*e^2 + 123/4*e - 3, -5/4*e^5 - 5/2*e^4 + 61/4*e^3 + 137/4*e^2 - 11*e - 91/4, 9/4*e^5 + 21/4*e^4 - 53/2*e^3 - 271/4*e^2 - 1/4*e + 32, 3/4*e^5 + 11/4*e^4 - 17/2*e^3 - 137/4*e^2 - 47/4*e + 14, e^5 + 7/4*e^4 - 49/4*e^3 - 45/2*e^2 + 35/4*e + 9/4, 3/4*e^5 + 5/4*e^4 - 9*e^3 - 65/4*e^2 + 15/4*e - 11/2, 3/4*e^5 + 7/4*e^4 - 15/2*e^3 - 85/4*e^2 - 51/4*e - 4, -9/4*e^5 - 17/4*e^4 + 53/2*e^3 + 223/4*e^2 - 15/4*e - 19, 11/4*e^5 + 5*e^4 - 137/4*e^3 - 259/4*e^2 + 51/2*e + 119/4, -9/4*e^5 - 21/4*e^4 + 51/2*e^3 + 283/4*e^2 + 25/4*e - 40, -7/2*e^5 - 31/4*e^4 + 151/4*e^3 + 101*e^2 + 109/4*e - 127/4, 3/2*e^4 + 1/2*e^3 - 16*e^2 - 27/2*e - 1/2, 5/4*e^4 + 1/4*e^3 - 29/2*e^2 - 43/4*e + 75/4, -3*e^5 - 11/2*e^4 + 73/2*e^3 + 72*e^2 - 29/2*e - 31/2, 1/4*e^5 + 3/2*e^4 - 5/4*e^3 - 77/4*e^2 - 24*e + 35/4, -1/4*e^5 - 1/4*e^4 + 5/2*e^3 + 11/4*e^2 + 17/4*e + 18, -1/4*e^5 - e^4 + 7/4*e^3 + 45/4*e^2 + 21/2*e + 39/4, -9/4*e^5 - 7/2*e^4 + 105/4*e^3 + 189/4*e^2 - 4*e - 15/4, -9/4*e^5 - 17/4*e^4 + 51/2*e^3 + 227/4*e^2 + 9/4*e - 11, 13/4*e^5 + 23/4*e^4 - 39*e^3 - 307/4*e^2 + 69/4*e + 69/2, -15/4*e^5 - 25/4*e^4 + 45*e^3 + 333/4*e^2 - 99/4*e - 49/2, 9/4*e^5 + 15/4*e^4 - 27*e^3 - 203/4*e^2 + 29/4*e + 27/2, -e^5 - 11/4*e^4 + 45/4*e^3 + 71/2*e^2 + 13/4*e - 37/4, -e^5 - 3*e^4 + 12*e^3 + 40*e^2 - 7*e - 39, -9/4*e^5 - 15/4*e^4 + 26*e^3 + 199/4*e^2 - 9/4*e - 25/2, -1/4*e^5 + e^4 + 15/4*e^3 - 43/4*e^2 - 39/2*e + 39/4, 9/4*e^5 + 11/4*e^4 - 29*e^3 - 155/4*e^2 + 145/4*e + 19/2, -7/4*e^5 - 3*e^4 + 81/4*e^3 + 159/4*e^2 - 1/2*e + 21/4, 11/4*e^5 + 13/2*e^4 - 127/4*e^3 - 331/4*e^2 - 8*e + 109/4, 5*e^5 + 39/4*e^4 - 233/4*e^3 - 253/2*e^2 + 15/4*e + 125/4, 1/4*e^5 - 3/4*e^4 - 9/2*e^3 + 37/4*e^2 + 95/4*e - 1, 1/2*e^5 + 9/4*e^4 - 25/4*e^3 - 27*e^2 - 3/4*e + 33/4, 15/4*e^5 + 27/4*e^4 - 87/2*e^3 - 361/4*e^2 + 17/4*e + 14, -3/2*e^5 - 7/2*e^4 + 16*e^3 + 93/2*e^2 + 31/2*e - 25, -1/2*e^5 + 5/4*e^4 + 31/4*e^3 - 11*e^2 - 143/4*e - 27/4, -7/2*e^5 - 7*e^4 + 79/2*e^3 + 185/2*e^2 + 15*e - 37/2, -7/4*e^5 - 7/2*e^4 + 91/4*e^3 + 183/4*e^2 - 25*e - 137/4, 5/4*e^5 + 2*e^4 - 55/4*e^3 - 113/4*e^2 + 5/2*e + 65/4, 5/4*e^5 + 4*e^4 - 55/4*e^3 - 201/4*e^2 - 31/2*e + 121/4, 5/2*e^5 + 4*e^4 - 61/2*e^3 - 107/2*e^2 + 27*e + 37/2, e^5 + 1/2*e^4 - 21/2*e^3 - 10*e^2 - 1/2*e + 19/2, -1/4*e^5 + 1/4*e^4 + 5*e^3 + 3/4*e^2 - 101/4*e - 15/2, 9/4*e^5 + 19/4*e^4 - 29*e^3 - 239/4*e^2 + 117/4*e + 79/2, -e^5 - 15/4*e^4 + 49/4*e^3 + 93/2*e^2 - 7/4*e - 165/4, 7/4*e^5 + 7/2*e^4 - 91/4*e^3 - 183/4*e^2 + 20*e + 93/4, 1/2*e^5 + 17/4*e^4 - 21/4*e^3 - 50*e^2 - 83/4*e + 129/4, 3/2*e^5 + 13/2*e^4 - 16*e^3 - 159/2*e^2 - 67/2*e + 35, -1/4*e^5 - 5/2*e^4 + 9/4*e^3 + 109/4*e^2 + 11*e - 23/4, 7/2*e^5 + 29/4*e^4 - 161/4*e^3 - 94*e^2 - 43/4*e + 125/4, -3/2*e^5 - 9/2*e^4 + 17*e^3 + 119/2*e^2 + 15/2*e - 44, 2*e^5 + 13/4*e^4 - 95/4*e^3 - 93/2*e^2 + 21/4*e + 139/4, -2*e^5 - 23/4*e^4 + 93/4*e^3 + 145/2*e^2 + 17/4*e - 141/4, -11/4*e^5 - 21/4*e^4 + 32*e^3 + 285/4*e^2 + 13/4*e - 67/2, -3/4*e^5 - 4*e^4 + 17/4*e^3 + 203/4*e^2 + 117/2*e - 59/4, 1/4*e^5 + 5/4*e^4 - 7/2*e^3 - 67/4*e^2 + 3/4*e + 21, 7/4*e^5 + 3*e^4 - 77/4*e^3 - 159/4*e^2 - 17/2*e + 75/4, -1/2*e^5 + 5/4*e^4 + 39/4*e^3 - 14*e^2 - 175/4*e + 17/4, -e^5 - 4*e^4 + 10*e^3 + 48*e^2 + 25*e - 6, 5/4*e^5 + 1/2*e^4 - 61/4*e^3 - 41/4*e^2 + 15*e - 37/4, 5/4*e^5 + 7/4*e^4 - 19*e^3 - 83/4*e^2 + 185/4*e + 19/2, 7/2*e^5 + 13/2*e^4 - 42*e^3 - 181/2*e^2 + 21/2*e + 68, -5/4*e^5 - 3*e^4 + 67/4*e^3 + 153/4*e^2 - 33/2*e - 105/4, 2*e^5 + 25/4*e^4 - 91/4*e^3 - 155/2*e^2 - 71/4*e + 139/4, 1/2*e^5 - 3/2*e^4 - 9*e^3 + 33/2*e^2 + 107/2*e - 14, -13/4*e^5 - 23/4*e^4 + 36*e^3 + 303/4*e^2 + 47/4*e - 7/2, -5/4*e^5 - 3*e^4 + 63/4*e^3 + 145/4*e^2 - 33/2*e - 45/4, 7/4*e^5 + 19/4*e^4 - 45/2*e^3 - 253/4*e^2 + 49/4*e + 58, 3/2*e^5 + 6*e^4 - 33/2*e^3 - 149/2*e^2 - 20*e + 95/2, 27/4*e^5 + 25/2*e^4 - 307/4*e^3 - 663/4*e^2 - 5*e + 169/4, 7/4*e^5 + 9/4*e^4 - 21*e^3 - 137/4*e^2 + 83/4*e + 67/2, 15/4*e^5 + 25/4*e^4 - 45*e^3 - 345/4*e^2 + 119/4*e + 109/2, 7/4*e^5 + 4*e^4 - 81/4*e^3 - 203/4*e^2 + 3/2*e + 55/4, 9/4*e^5 + 21/4*e^4 - 49/2*e^3 - 271/4*e^2 - 69/4*e + 13, 25/4*e^5 + 47/4*e^4 - 70*e^3 - 619/4*e^2 - 63/4*e + 71/2, 4*e^5 + 43/4*e^4 - 177/4*e^3 - 273/2*e^2 - 161/4*e + 205/4, 23/4*e^5 + 12*e^4 - 265/4*e^3 - 627/4*e^2 - 17/2*e + 207/4, -e^5 - 3/4*e^4 + 41/4*e^3 + 17/2*e^2 + 33/4*e + 135/4, 1/2*e^5 - 7/4*e^4 - 29/4*e^3 + 15*e^2 + 149/4*e + 69/4, -7/4*e^5 - 13/4*e^4 + 22*e^3 + 161/4*e^2 - 47/4*e - 17/2, -3/4*e^5 - 5/2*e^4 + 31/4*e^3 + 139/4*e^2 + 10*e - 109/4, -27/4*e^5 - 31/2*e^4 + 307/4*e^3 + 803/4*e^2 + 29*e - 289/4, 7/4*e^5 + 7/2*e^4 - 75/4*e^3 - 187/4*e^2 - 14*e - 7/4, -19/4*e^5 - 35/4*e^4 + 115/2*e^3 + 461/4*e^2 - 117/4*e - 55, -2*e^5 - 4*e^4 + 23*e^3 + 52*e^2 + 5*e, 3/2*e^5 + 6*e^4 - 27/2*e^3 - 145/2*e^2 - 56*e + 25/2, -5*e^5 - 21/2*e^4 + 111/2*e^3 + 137*e^2 + 47/2*e - 69/2, 5/4*e^5 + 3/4*e^4 - 13*e^3 - 55/4*e^2 - 23/4*e - 29/2, -7/4*e^5 - 13/4*e^4 + 22*e^3 + 181/4*e^2 - 95/4*e - 59/2, 5/4*e^5 + 3/2*e^4 - 65/4*e^3 - 89/4*e^2 + 26*e + 55/4, -6*e^5 - 10*e^4 + 71*e^3 + 137*e^2 - 29*e - 47, 4*e^5 + 21/2*e^4 - 91/2*e^3 - 132*e^2 - 59/2*e + 69/2, 17/4*e^5 + 25/4*e^4 - 105/2*e^3 - 351/4*e^2 + 191/4*e + 45, -1/4*e^5 + 3/4*e^4 + 9/2*e^3 - 41/4*e^2 - 67/4*e + 37, 1/4*e^5 + 5/4*e^4 - 7/2*e^3 - 75/4*e^2 + 43/4*e + 39, -1/2*e^5 - 3/4*e^4 + 19/4*e^3 + 13*e^2 + 45/4*e - 27/4, 17/4*e^5 + 31/4*e^4 - 51*e^3 - 407/4*e^2 + 61/4*e + 53/2, -1/2*e^5 - 11/4*e^4 + 15/4*e^3 + 35*e^2 + 69/4*e - 71/4, 15/4*e^5 + 7*e^4 - 185/4*e^3 - 375/4*e^2 + 83/2*e + 231/4, -11/4*e^5 - 15/2*e^4 + 123/4*e^3 + 375/4*e^2 + 27*e - 165/4, 7/4*e^5 + 17/4*e^4 - 22*e^3 - 217/4*e^2 + 39/4*e + 63/2, -3/4*e^5 - 3/2*e^4 + 31/4*e^3 + 59/4*e^2 + 16*e + 143/4, 1/2*e^5 - 7/4*e^4 - 29/4*e^3 + 17*e^2 + 145/4*e + 57/4, 11/4*e^5 + 7/2*e^4 - 131/4*e^3 - 211/4*e^2 + 21*e + 105/4, 13/2*e^5 + 15*e^4 - 147/2*e^3 - 387/2*e^2 - 31*e + 113/2, -29/4*e^5 - 27/2*e^4 + 341/4*e^3 + 741/4*e^2 - 16*e - 343/4, -3*e^5 - 21/4*e^4 + 143/4*e^3 + 137/2*e^2 - 33/4*e - 75/4, -17/4*e^5 - 43/4*e^4 + 48*e^3 + 547/4*e^2 + 119/4*e - 93/2, -1/2*e^5 + 15/2*e^3 - 7/2*e^2 - 21*e + 7/2, 1/4*e^5 + 1/4*e^4 - 3/2*e^3 - 31/4*e^2 - 81/4*e + 20, 3*e^5 + 11/4*e^4 - 153/4*e^3 - 73/2*e^2 + 203/4*e - 59/4, -3/4*e^5 - 7/2*e^4 + 27/4*e^3 + 167/4*e^2 + 26*e - 1/4, -1/2*e^5 - 11/2*e^4 + e^3 + 127/2*e^2 + 137/2*e - 7, -31/4*e^5 - 31/2*e^4 + 363/4*e^3 + 823/4*e^2 - 6*e - 301/4, -15/4*e^5 - 31/4*e^4 + 91/2*e^3 + 393/4*e^2 - 57/4*e - 37, -5/4*e^5 - 15/4*e^4 + 15*e^3 + 171/4*e^2 + 27/4*e - 9/2, e^5 + 3*e^4 - 8*e^3 - 43*e^2 - 43*e + 36, 9/4*e^5 + 13/2*e^4 - 81/4*e^3 - 341/4*e^2 - 65*e + 111/4, 3*e^5 + 15/2*e^4 - 59/2*e^3 - 98*e^2 - 111/2*e + 73/2, -2*e^5 - 19/4*e^4 + 85/4*e^3 + 125/2*e^2 + 57/4*e - 73/4, -3/4*e^5 - 7/4*e^4 + 19/2*e^3 + 93/4*e^2 - 29/4*e - 24, -27/4*e^5 - 13*e^4 + 309/4*e^3 + 675/4*e^2 + 7/2*e - 127/4, 3*e^5 + 31/4*e^4 - 121/4*e^3 - 189/2*e^2 - 233/4*e + 77/4, -1/4*e^5 - 1/2*e^4 + 29/4*e^3 + 29/4*e^2 - 42*e - 71/4, -e^5 - 13/4*e^4 + 51/4*e^3 + 83/2*e^2 + 3/4*e - 135/4, -7/2*e^5 - 25/4*e^4 + 149/4*e^3 + 84*e^2 + 75/4*e - 69/4, -1/4*e^5 + 11/4*e^4 + 9/2*e^3 - 125/4*e^2 - 159/4*e + 5, -7/4*e^5 + 1/2*e^4 + 99/4*e^3 + 23/4*e^2 - 67*e - 89/4, -15/2*e^5 - 11*e^4 + 185/2*e^3 + 311/2*e^2 - 74*e - 147/2, 15/4*e^5 + 41/4*e^4 - 40*e^3 - 509/4*e^2 - 169/4*e + 49/2, 25/4*e^5 + 10*e^4 - 311/4*e^3 - 545/4*e^2 + 143/2*e + 273/4, -3*e^5 - 19/4*e^4 + 145/4*e^3 + 129/2*e^2 - 91/4*e - 53/4, 7*e^5 + 25/2*e^4 - 167/2*e^3 - 165*e^2 + 55/2*e + 111/2, -1/2*e^5 - 5/2*e^4 + e^3 + 59/2*e^2 + 113/2*e - 8, -5/4*e^5 + 3/4*e^4 + 35/2*e^3 - 21/4*e^2 - 179/4*e + 20, 3*e^5 + 9/2*e^4 - 73/2*e^3 - 61*e^2 + 53/2*e + 47/2, 17/2*e^5 + 16*e^4 - 201/2*e^3 - 423/2*e^2 + 32*e + 183/2, -13/2*e^5 - 41/4*e^4 + 313/4*e^3 + 136*e^2 - 189/4*e - 141/4, 3/2*e^5 + 3*e^4 - 41/2*e^3 - 81/2*e^2 + 23*e + 59/2, -13/4*e^5 - 33/4*e^4 + 75/2*e^3 + 403/4*e^2 + 49/4*e - 24, 5/2*e^5 + 4*e^4 - 61/2*e^3 - 111/2*e^2 + 24*e + 79/2, -5/4*e^5 - 9/4*e^4 + 33/2*e^3 + 115/4*e^2 - 43/4*e - 4, -1/4*e^5 - e^4 + 7/4*e^3 + 41/4*e^2 + 13/2*e + 91/4, -5*e^5 - 43/4*e^4 + 237/4*e^3 + 281/2*e^2 - 23/4*e - 189/4, 5*e^5 + 39/4*e^4 - 225/4*e^3 - 267/2*e^2 - 21/4*e + 285/4, 5/4*e^5 + 17/4*e^4 - 23/2*e^3 - 219/4*e^2 - 121/4*e + 46, -17/4*e^5 - 25/4*e^4 + 103/2*e^3 + 367/4*e^2 - 127/4*e - 56, -3*e^5 - 15/2*e^4 + 73/2*e^3 + 98*e^2 - 9/2*e - 107/2, -2*e^5 - 3/2*e^4 + 43/2*e^3 + 31*e^2 - 13/2*e - 113/2, 19/4*e^5 + 21/2*e^4 - 227/4*e^3 - 547/4*e^2 + 5*e + 197/4, -1/2*e^5 - 9/4*e^4 + 21/4*e^3 + 28*e^2 + 23/4*e - 101/4, 1/4*e^5 - 2*e^4 - 27/4*e^3 + 95/4*e^2 + 97/2*e + 65/4, -25/4*e^5 - 11*e^4 + 295/4*e^3 + 605/4*e^2 - 29/2*e - 261/4, 6*e^5 + 17/2*e^4 - 143/2*e^3 - 119*e^2 + 69/2*e + 39/2, 3/2*e^5 + 5/4*e^4 - 81/4*e^3 - 22*e^2 + 177/4*e + 65/4, -3/4*e^5 + 2*e^4 + 61/4*e^3 - 81/4*e^2 - 149/2*e + 25/4, -19/4*e^5 - 53/4*e^4 + 51*e^3 + 693/4*e^2 + 225/4*e - 151/2, -2*e^5 - 17/4*e^4 + 99/4*e^3 + 119/2*e^2 - 57/4*e - 203/4, 19/4*e^5 + 19/4*e^4 - 121/2*e^3 - 285/4*e^2 + 345/4*e + 37, -5/4*e^5 + e^4 + 79/4*e^3 - 51/4*e^2 - 113/2*e + 159/4, -9/2*e^5 - 43/4*e^4 + 203/4*e^3 + 139*e^2 + 65/4*e - 167/4, -e^5 - 3*e^4 + 11*e^3 + 37*e^2 + 3*e + 3, -1/2*e^5 + 1/2*e^4 + 11*e^3 - 11/2*e^2 - 107/2*e - 22, -3*e^5 - 3*e^4 + 40*e^3 + 40*e^2 - 58*e + 16, 3/4*e^5 + 3/2*e^4 - 47/4*e^3 - 67/4*e^2 + 30*e - 55/4, -11/4*e^5 - 35/4*e^4 + 63/2*e^3 + 445/4*e^2 + 107/4*e - 75, -7/2*e^5 - 4*e^4 + 91/2*e^3 + 113/2*e^2 - 60*e - 17/2, 17/2*e^5 + 39/2*e^4 - 97*e^3 - 505/2*e^2 - 53/2*e + 90, 3*e^5 + 13/4*e^4 - 147/4*e^3 - 91/2*e^2 + 157/4*e + 7/4, -13/4*e^5 - 13/2*e^4 + 161/4*e^3 + 349/4*e^2 - 34*e - 183/4, e^5 + 3*e^4 - 12*e^3 - 43*e^2 - 3*e + 56, -e^5 + 1/4*e^4 + 61/4*e^3 - 7/2*e^2 - 155/4*e + 35/4, -5/4*e^5 - 13/4*e^4 + 25/2*e^3 + 159/4*e^2 + 61/4*e - 16, 13*e^5 + 105/4*e^4 - 587/4*e^3 - 697/2*e^2 - 159/4*e + 427/4, 3/2*e^5 + 3/2*e^4 - 16*e^3 - 59/2*e^2 + 3/2*e + 43, -2*e^5 - 7*e^4 + 19*e^3 + 96*e^2 + 51*e - 69, -5/4*e^5 - 17/4*e^4 + 29/2*e^3 + 183/4*e^2 + 29/4*e + 11, e^4 - 2*e^3 - 19*e^2 + 18*e + 44, -e^5 - 7/4*e^4 + 41/4*e^3 + 53/2*e^2 - 15/4*e - 93/4, 17/4*e^5 + e^4 - 231/4*e^3 - 105/4*e^2 + 251/2*e + 45/4, -1/4*e^5 - 1/2*e^4 + 1/4*e^3 + 41/4*e^2 + 33*e + 21/4, -9/4*e^5 - 6*e^4 + 99/4*e^3 + 297/4*e^2 + 35/2*e - 9/4, 39/4*e^5 + 95/4*e^4 - 221/2*e^3 - 1209/4*e^2 - 207/4*e + 94, -11/4*e^5 - 11/2*e^4 + 131/4*e^3 + 295/4*e^2 - 7*e - 29/4, 11/2*e^5 + 23/4*e^4 - 267/4*e^3 - 83*e^2 + 255/4*e - 1/4, 23/4*e^5 + 55/4*e^4 - 121/2*e^3 - 725/4*e^2 - 323/4*e + 70, 8*e^5 + 71/4*e^4 - 349/4*e^3 - 473/2*e^2 - 229/4*e + 337/4, 6*e^5 + 49/4*e^4 - 275/4*e^3 - 323/2*e^2 + 21/4*e + 191/4, -1/4*e^5 + 3/4*e^4 + 9/2*e^3 - 21/4*e^2 - 95/4*e - 33, 33/4*e^5 + 61/4*e^4 - 195/2*e^3 - 823/4*e^2 + 123/4*e + 98, 15/4*e^5 + 10*e^4 - 177/4*e^3 - 515/4*e^2 - 19/2*e + 147/4, 1/2*e^5 + 5/2*e^4 - e^3 - 67/2*e^2 - 83/2*e + 43, 39/4*e^5 + 75/4*e^4 - 235/2*e^3 - 1005/4*e^2 + 201/4*e + 125, 9/4*e^5 + 9/4*e^4 - 53/2*e^3 - 123/4*e^2 + 91/4*e - 23, 4*e^5 + 9*e^4 - 47*e^3 - 124*e^2 + 14*e + 86, -15/4*e^5 - 8*e^4 + 169/4*e^3 + 431/4*e^2 + 31/2*e - 247/4, -9/2*e^5 - 11/2*e^4 + 53*e^3 + 147/2*e^2 - 51/2*e + 31, 5/2*e^5 + 3*e^4 - 71/2*e^3 - 75/2*e^2 + 73*e + 49/2, -10*e^5 - 31/2*e^4 + 239/2*e^3 + 216*e^2 - 121/2*e - 163/2, 1/4*e^5 + 2*e^4 - 31/4*e^3 - 81/4*e^2 + 73/2*e + 5/4, -4*e^5 - 17/4*e^4 + 203/4*e^3 + 113/2*e^2 - 289/4*e + 57/4, -e^5 - 15/4*e^4 + 45/4*e^3 + 101/2*e^2 + 49/4*e - 57/4, -27/4*e^5 - 53/4*e^4 + 78*e^3 + 709/4*e^2 - 67/4*e - 183/2, -13/4*e^5 - 25/4*e^4 + 79/2*e^3 + 323/4*e^2 - 79/4*e - 56, 17/4*e^5 + 17/4*e^4 - 109/2*e^3 - 251/4*e^2 + 327/4*e + 28, 17/4*e^5 + 10*e^4 - 195/4*e^3 - 517/4*e^2 - 35/2*e + 213/4, 13/4*e^5 + e^4 - 167/4*e^3 - 85/4*e^2 + 135/2*e - 19/4, 13/4*e^5 + 6*e^4 - 155/4*e^3 - 333/4*e^2 + 25/2*e + 185/4, -19/4*e^5 - 27/4*e^4 + 117/2*e^3 + 377/4*e^2 - 229/4*e - 41, -15/4*e^5 - 29/4*e^4 + 41*e^3 + 397/4*e^2 + 89/4*e - 1/2, 4*e^5 + 11/4*e^4 - 205/4*e^3 - 91/2*e^2 + 319/4*e + 125/4, 1/4*e^5 - 7/2*e^4 - 37/4*e^3 + 151/4*e^2 + 76*e - 109/4, 13/4*e^5 + 21/4*e^4 - 81/2*e^3 - 247/4*e^2 + 111/4*e - 13, -5/4*e^5 - 5/2*e^4 + 65/4*e^3 + 117/4*e^2 - 26*e + 113/4, 3/2*e^5 + 27/4*e^4 - 39/4*e^3 - 87*e^2 - 317/4*e + 227/4, 1/2*e^5 - 7/4*e^4 - 29/4*e^3 + 20*e^2 + 129/4*e - 11/4, 3/4*e^5 - 3/2*e^4 - 43/4*e^3 + 37/4*e^2 + 33*e + 29/4, -4*e^5 - 6*e^4 + 47*e^3 + 88*e^2 - 6*e - 53, -1/2*e^5 - 13/4*e^4 - 11/4*e^3 + 39*e^2 + 375/4*e + 43/4, 6*e^5 + 39/4*e^4 - 305/4*e^3 - 263/2*e^2 + 299/4*e + 177/4, 7*e^5 + 7*e^4 - 89*e^3 - 100*e^2 + 124*e + 19, -11/2*e^5 - 17/4*e^4 + 289/4*e^3 + 67*e^2 - 481/4*e - 129/4, -8*e^5 - 43/4*e^4 + 393/4*e^3 + 297/2*e^2 - 339/4*e - 113/4, 29/4*e^5 + 63/4*e^4 - 85*e^3 - 803/4*e^2 + 1/4*e + 151/2, -7/4*e^5 - 31/4*e^4 + 43/2*e^3 + 377/4*e^2 + 71/4*e - 47, 10*e^5 + 77/4*e^4 - 483/4*e^3 - 509/2*e^2 + 221/4*e + 479/4, -19/2*e^5 - 81/4*e^4 + 437/4*e^3 + 264*e^2 + 67/4*e - 413/4, -9*e^5 - 63/4*e^4 + 433/4*e^3 + 413/2*e^2 - 143/4*e - 117/4, -15/4*e^5 - 35/4*e^4 + 75/2*e^3 + 449/4*e^2 + 295/4*e - 36, -9/2*e^5 - 7*e^4 + 109/2*e^3 + 197/2*e^2 - 22*e - 91/2, e^5 + 4*e^4 - 6*e^3 - 54*e^2 - 67*e + 36, 31/4*e^5 + 67/4*e^4 - 183/2*e^3 - 845/4*e^2 + 49/4*e + 71, 5*e^5 + 11*e^4 - 53*e^3 - 148*e^2 - 41*e + 84, -5/4*e^5 - 27/4*e^4 + 12*e^3 + 307/4*e^2 + 179/4*e - 21/2, 6*e^5 + 47/4*e^4 - 261/4*e^3 - 309/2*e^2 - 145/4*e + 93/4, 3*e^5 + 7/2*e^4 - 77/2*e^3 - 49*e^2 + 97/2*e - 19/2, 3/2*e^5 + 13/4*e^4 - 93/4*e^3 - 42*e^2 + 205/4*e + 89/4, 1/4*e^5 - 13/4*e^4 - 6*e^3 + 153/4*e^2 + 153/4*e - 21/2, -9/2*e^5 - 11/2*e^4 + 61*e^3 + 139/2*e^2 - 207/2*e - 33, 13/2*e^5 + 43/4*e^4 - 295/4*e^3 - 140*e^2 - 17/4*e + 23/4, 1/2*e^5 - 2*e^4 - 19/2*e^3 + 29/2*e^2 + 48*e + 85/2, 3*e^5 + 9/2*e^4 - 71/2*e^3 - 55*e^2 - 17/2*e - 81/2, 3/2*e^5 - e^4 - 53/2*e^3 + 23/2*e^2 + 97*e - 33/2, -9/4*e^5 - 4*e^4 + 95/4*e^3 + 217/4*e^2 + 25/2*e - 201/4, 9*e^5 + 19*e^4 - 105*e^3 - 256*e^2 + 2*e + 131, 25/4*e^5 + 23/2*e^4 - 285/4*e^3 - 601/4*e^2 - 10*e + 39/4, -7*e^5 - 33/2*e^4 + 159/2*e^3 + 222*e^2 + 49/2*e - 209/2, -11/2*e^5 - 5*e^4 + 137/2*e^3 + 157/2*e^2 - 85*e - 79/2, 5*e^5 + 73/4*e^4 - 211/4*e^3 - 445/2*e^2 - 335/4*e + 379/4, 5/2*e^5 + 21/4*e^4 - 141/4*e^3 - 66*e^2 + 241/4*e + 273/4, -17/4*e^5 - 11*e^4 + 191/4*e^3 + 557/4*e^2 + 97/2*e - 129/4, -3*e^5 - 27/4*e^4 + 145/4*e^3 + 169/2*e^2 + 17/4*e + 63/4, 1/4*e^5 - 5/4*e^4 - 2*e^3 + 61/4*e^2 + 33/4*e - 55/2, -3/4*e^5 + 11/4*e^4 + 8*e^3 - 119/4*e^2 - 23/4*e + 141/2, -5/2*e^5 - 25/4*e^4 + 93/4*e^3 + 87*e^2 + 255/4*e - 153/4, -19/4*e^5 - 17/4*e^4 + 54*e^3 + 269/4*e^2 - 115/4*e - 45/2, 43/4*e^5 + 17*e^4 - 533/4*e^3 - 915/4*e^2 + 209/2*e + 335/4, -1/2*e^5 + 3/4*e^4 + 33/4*e^3 - 16*e^2 - 109/4*e + 199/4, 9/4*e^5 + 29/4*e^4 - 55/2*e^3 - 355/4*e^2 - 25/4*e + 44, 29/4*e^5 + 18*e^4 - 335/4*e^3 - 913/4*e^2 - 19/2*e + 393/4, -7/2*e^5 - 11/4*e^4 + 175/4*e^3 + 39*e^2 - 227/4*e + 61/4, 15/4*e^5 + 23/2*e^4 - 155/4*e^3 - 611/4*e^2 - 62*e + 217/4, -3/4*e^5 + e^4 + 45/4*e^3 - 57/4*e^2 - 43/2*e + 57/4, -9/2*e^5 - 7*e^4 + 107/2*e^3 + 185/2*e^2 - 29*e - 51/2, 9/4*e^5 + 2*e^4 - 139/4*e^3 - 109/4*e^2 + 179/2*e - 71/4, -5*e^5 - 19/2*e^4 + 107/2*e^3 + 133*e^2 + 89/2*e - 69/2, -25/4*e^5 - 45/4*e^4 + 153/2*e^3 + 619/4*e^2 - 215/4*e - 81, 35/4*e^5 + 18*e^4 - 393/4*e^3 - 963/4*e^2 - 73/2*e + 275/4, 13/2*e^5 + 67/4*e^4 - 275/4*e^3 - 218*e^2 - 369/4*e + 259/4];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {19,19,w - 1}>] := 1;

// EXAMPLE:
// pp := Factorization(2*ZF)[1][1];
// heckeEigenvalues[pp];

print "To reconstruct the Hilbert newform f, type
  f, iso := Explode(make_newform());";

function make_newform();
 M := HilbertCuspForms(F, NN);
 S := NewSubspace(M);
 // SetVerbose("ModFrmHil", 1);
 NFD := NewformDecomposition(S);
 newforms := [* Eigenform(U) : U in NFD *];

 if #newforms eq 0 then;
  print "No Hilbert newforms at this level";
  return 0;
 end if;

 print "Testing ", #newforms, " possible newforms";
 newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *];
 print #newforms, " newforms have the correct Hecke field";

 if #newforms eq 0 then;
  print "No Hilbert newform found with the correct Hecke field";
  return 0;
 end if;

 autos := Automorphisms(K);
 xnewforms := [* *];
 for f in newforms do;
  if K eq RationalField() then;
   Append(~xnewforms, [* f, autos[1] *]);
  else;
   flag, iso := IsIsomorphic(K,BaseField(f));
   for a in autos do;
    Append(~xnewforms, [* f, a*iso *]);
   end for;
  end if;
 end for;
 newforms := xnewforms;

 for P in primes do;
  xnewforms := [* *];
  for f_iso in newforms do;
   f, iso := Explode(f_iso);
   if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then;
    Append(~xnewforms, f_iso);
   end if;
  end for;
  newforms := xnewforms;
  if #newforms eq 0 then;
   print "No Hilbert newform found which matches the Hecke eigenvalues";
   return 0;
  else if #newforms eq 1 then;
   print "success: unique match";
   return newforms[1];
  end if;
  end if;
 end for;
 print #newforms, "Hilbert newforms found which match the Hecke eigenvalues";
 return newforms[1];

end function;