/*
  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![-1, -11, 10, 10, -6, -2, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {29,29,-w^4 + 5*w^2 + 2*w - 4}>;

primesArray := [
[7, 7, w^4 - 2*w^3 - 3*w^2 + 6*w - 1],
[7, 7, -w^4 + w^3 + 4*w^2 - w - 1],
[13, 13, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 3*w - 3],
[29, 29, -w^4 + w^3 + 4*w^2 - 3*w - 2],
[29, 29, w^4 - 5*w^2 - 2*w + 4],
[29, 29, -w^4 + w^3 + 3*w^2 - w + 2],
[29, 29, -w^2 + w + 1],
[41, 41, -w^5 + w^4 + 4*w^3 - w^2 - 3*w - 1],
[43, 43, 2*w^3 - 2*w^2 - 7*w + 3],
[43, 43, w^3 - w^2 - 2*w + 1],
[64, 2, -2],
[71, 71, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 3],
[71, 71, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 3*w - 1],
[83, 83, -2*w^4 + 3*w^3 + 6*w^2 - 7*w + 2],
[83, 83, w^4 - w^3 - 5*w^2 + 2*w + 3],
[83, 83, -w^5 + 3*w^4 + w^3 - 9*w^2 + 5*w + 3],
[83, 83, w^5 - 7*w^3 + 10*w - 1],
[97, 97, w^5 - 2*w^4 - 3*w^3 + 5*w^2 - w - 1],
[97, 97, w^5 - 5*w^3 - w^2 + 3*w - 3],
[113, 113, w^4 - w^3 - 4*w^2 + w + 4],
[113, 113, w^4 - 2*w^3 - 3*w^2 + 6*w + 2],
[127, 127, -w^4 + 2*w^3 + 4*w^2 - 5*w - 3],
[127, 127, w^5 - 9*w^3 + w^2 + 18*w - 1],
[127, 127, 2*w^4 - 4*w^3 - 5*w^2 + 10*w - 2],
[127, 127, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 2],
[127, 127, -3*w^4 + 5*w^3 + 9*w^2 - 11*w],
[127, 127, -w^5 + 3*w^4 + w^3 - 8*w^2 + 4*w - 1],
[139, 139, w^4 - 3*w^3 - 2*w^2 + 10*w - 3],
[139, 139, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 4*w - 3],
[167, 167, -w^4 + w^3 + 5*w^2 - 4*w - 3],
[167, 167, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 3],
[169, 13, w^4 - 3*w^3 - 2*w^2 + 8*w - 2],
[169, 13, 2*w^4 - 3*w^3 - 7*w^2 + 7*w + 3],
[181, 181, -w^5 + 4*w^3 + 3*w^2 - 2],
[181, 181, w^5 - 3*w^4 - 3*w^3 + 11*w^2 - 4],
[181, 181, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + 2*w - 4],
[181, 181, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 3*w - 2],
[197, 197, -3*w^4 + 5*w^3 + 10*w^2 - 11*w - 3],
[197, 197, -3*w^4 + 6*w^3 + 9*w^2 - 16*w - 1],
[197, 197, 2*w^3 - 3*w^2 - 5*w + 4],
[197, 197, -w^5 + 6*w^3 - 6*w + 1],
[223, 223, 2*w^4 - 2*w^3 - 9*w^2 + 3*w + 6],
[223, 223, -3*w^4 + 5*w^3 + 9*w^2 - 13*w + 1],
[223, 223, w^5 - w^4 - 6*w^3 + 4*w^2 + 10*w - 4],
[223, 223, w^4 - 4*w^3 - 2*w^2 + 12*w],
[239, 239, 2*w^4 - w^3 - 8*w^2 + 3],
[239, 239, -w^5 + 3*w^4 - 8*w^2 + 9*w + 3],
[239, 239, -w^5 + 2*w^4 + 2*w^3 - 6*w^2 + 3*w + 4],
[239, 239, w^4 - 6*w^2 + 6],
[239, 239, 3*w^4 - 4*w^3 - 11*w^2 + 10*w + 3],
[239, 239, -w^5 + 7*w^3 - 9*w - 1],
[251, 251, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 3*w - 2],
[251, 251, -w^5 + w^4 + 6*w^3 - 4*w^2 - 8*w + 2],
[281, 281, -3*w^4 + 4*w^3 + 11*w^2 - 10*w - 4],
[281, 281, 3*w^4 - 3*w^3 - 12*w^2 + 5*w + 6],
[293, 293, -w^5 + 8*w^3 - 15*w + 1],
[293, 293, w^5 - 4*w^4 + w^3 + 11*w^2 - 9*w + 1],
[293, 293, -2*w^4 + 5*w^3 + 5*w^2 - 14*w + 3],
[293, 293, -w^5 + 8*w^3 - 14*w + 2],
[293, 293, -2*w^4 + 4*w^3 + 6*w^2 - 9*w + 1],
[293, 293, w^5 - 4*w^4 + 12*w^2 - 5*w - 2],
[307, 307, 2*w^4 - 3*w^3 - 7*w^2 + 9*w + 2],
[307, 307, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 8*w + 6],
[307, 307, -w^3 + 6*w],
[307, 307, w^5 - w^4 - 7*w^3 + 5*w^2 + 12*w - 3],
[337, 337, -2*w^4 + 2*w^3 + 9*w^2 - 4*w - 8],
[337, 337, 3*w^4 - 4*w^3 - 10*w^2 + 9*w + 3],
[349, 349, 2*w^5 - 4*w^4 - 7*w^3 + 13*w^2 + 3*w - 6],
[349, 349, 2*w^5 - 2*w^4 - 9*w^3 + 5*w^2 + 7*w - 2],
[349, 349, w^5 - 3*w^4 + 8*w^2 - 7*w - 2],
[349, 349, w^5 - 9*w^3 + 2*w^2 + 17*w - 4],
[379, 379, w^5 - 3*w^4 + 6*w^2 - 8*w + 5],
[379, 379, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 3*w + 1],
[379, 379, w^5 - 4*w^4 + 12*w^2 - 8*w - 2],
[379, 379, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 5],
[419, 419, w^5 - 4*w^4 + w^3 + 10*w^2 - 10*w + 3],
[419, 419, 3*w^4 - 3*w^3 - 11*w^2 + 5*w + 4],
[421, 421, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 8*w - 4],
[421, 421, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 4],
[433, 433, -2*w^2 + w + 5],
[433, 433, -2*w^4 + 3*w^3 + 5*w^2 - 6*w + 3],
[461, 461, 2*w^3 - 2*w^2 - 5*w + 3],
[461, 461, -w^5 + 5*w^3 + 2*w^2 - 4*w + 1],
[461, 461, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + 3*w + 5],
[461, 461, -w^5 + 3*w^4 + 3*w^3 - 11*w^2 - w + 3],
[463, 463, -2*w^4 + 3*w^3 + 7*w^2 - 8*w - 4],
[463, 463, -w^5 + 4*w^4 + w^3 - 12*w^2 + 3*w - 1],
[491, 491, w^5 - 7*w^3 - w^2 + 10*w + 3],
[491, 491, -w^5 + 4*w^4 - w^3 - 11*w^2 + 10*w + 2],
[503, 503, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + w + 3],
[503, 503, 2*w^4 - w^3 - 8*w^2 + w + 1],
[503, 503, -2*w^5 + 3*w^4 + 7*w^3 - 7*w^2 - 3*w + 1],
[503, 503, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 11*w + 2],
[547, 547, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 10*w - 5],
[547, 547, -w^4 + 2*w^3 + 2*w^2 - 4*w + 5],
[547, 547, -2*w^5 + 4*w^4 + 7*w^3 - 12*w^2 - 3*w + 4],
[547, 547, -w^5 + w^4 + 3*w^3 - 2*w^2 + 3*w + 2],
[587, 587, -w^5 - w^4 + 8*w^3 + 4*w^2 - 13*w + 1],
[587, 587, w^5 - w^4 - 5*w^3 + 2*w^2 + 7*w - 2],
[617, 617, w^5 - w^4 - 4*w^3 + 3*w^2 - 1],
[617, 617, w^4 - 2*w^3 - 5*w^2 + 5*w + 6],
[617, 617, -w^5 + w^4 + 4*w^3 - 3*w^2 + 4],
[617, 617, -w^5 + 3*w^4 + 6*w^3 - 13*w^2 - 11*w + 8],
[631, 631, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 11*w + 1],
[631, 631, -w^5 + w^4 + 4*w^3 - 2*w - 4],
[631, 631, -2*w^4 + 5*w^3 + 4*w^2 - 12*w + 4],
[631, 631, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + w + 4],
[643, 643, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 6*w - 2],
[643, 643, -w^5 + 2*w^4 + w^3 - 3*w^2 + 6*w - 3],
[659, 659, -2*w^4 + 4*w^3 + 7*w^2 - 10*w - 2],
[659, 659, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],
[659, 659, w^5 - 4*w^4 + 13*w^2 - 6*w - 6],
[659, 659, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 7*w - 5],
[673, 673, 2*w^5 - 3*w^4 - 7*w^3 + 8*w^2 + 2*w - 3],
[673, 673, w^5 - 4*w^4 - w^3 + 12*w^2 - 3*w - 2],
[673, 673, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 8*w + 5],
[673, 673, w^5 - w^4 - 4*w^3 + 3*w + 6],
[701, 701, -2*w^4 + 4*w^3 + 6*w^2 - 11*w - 3],
[701, 701, 2*w^4 - 3*w^3 - 7*w^2 + 6*w + 5],
[727, 727, -w^5 + 2*w^4 + w^3 - 3*w^2 + 7*w - 2],
[727, 727, 2*w^5 - 3*w^4 - 7*w^3 + 8*w^2 + 3*w - 4],
[727, 727, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 2*w + 1],
[727, 727, w^5 + 2*w^4 - 9*w^3 - 8*w^2 + 16*w + 2],
[729, 3, -3],
[743, 743, w^5 - 4*w^4 + 13*w^2 - 8*w - 5],
[743, 743, -w^3 + w^2 + w - 2],
[743, 743, w^4 - 4*w^3 - w^2 + 10*w - 2],
[743, 743, 3*w^3 - 3*w^2 - 11*w + 6],
[757, 757, -w^5 + 4*w^4 - 11*w^2 + 5*w - 2],
[757, 757, -3*w^4 + 3*w^3 + 11*w^2 - 5*w - 2],
[757, 757, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 4],
[757, 757, w^5 - 8*w^3 + w^2 + 15*w - 4],
[769, 769, w^5 - 5*w^3 - 3*w^2 + 4*w + 6],
[769, 769, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 4*w + 3],
[769, 769, w^4 - 3*w^3 - w^2 + 9*w - 3],
[769, 769, w^5 - 4*w^4 - w^3 + 13*w^2 - 4*w - 5],
[797, 797, w^5 + w^4 - 8*w^3 - 4*w^2 + 11*w + 2],
[797, 797, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 9*w - 6],
[811, 811, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 4*w - 4],
[811, 811, 2*w^4 - 2*w^3 - 6*w^2 + 3*w - 4],
[811, 811, -2*w^5 + 3*w^4 + 9*w^3 - 8*w^2 - 9*w + 1],
[811, 811, -w^5 + w^4 + 2*w^3 + w^2 + 4*w - 5],
[827, 827, w^5 + w^4 - 9*w^3 - 2*w^2 + 14*w - 3],
[827, 827, w^5 - 3*w^4 + w^3 + 6*w^2 - 11*w + 4],
[827, 827, w^5 - 3*w^4 + 9*w^2 - 9*w - 4],
[827, 827, w^5 - w^4 - 4*w^3 + 4*w + 5],
[827, 827, -w^5 + 4*w^4 + 2*w^3 - 13*w^2 - w + 3],
[827, 827, -w^5 + w^4 + 7*w^3 - 4*w^2 - 11*w + 3],
[839, 839, -w^5 + w^4 + 7*w^3 - 4*w^2 - 13*w + 4],
[839, 839, -w^5 + 3*w^4 + w^3 - 8*w^2 + 3*w - 1],
[841, 29, -2*w^4 + 5*w^3 + 5*w^2 - 13*w + 1],
[853, 853, -2*w^4 + 10*w^2 + 3*w - 6],
[853, 853, 2*w^5 - 4*w^4 - 8*w^3 + 13*w^2 + 8*w - 6],
[853, 853, -2*w^4 + w^3 + 9*w^2 - 2*w - 4],
[853, 853, -2*w^5 + 3*w^4 + 8*w^3 - 8*w^2 - 7*w + 1],
[881, 881, w^5 - 5*w^3 - 2*w^2 + 5*w - 1],
[881, 881, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - 5*w + 5],
[883, 883, 3*w^4 - 4*w^3 - 11*w^2 + 10*w + 5],
[883, 883, -3*w^4 + 3*w^3 + 12*w^2 - 5*w - 7],
[883, 883, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 5*w - 2],
[883, 883, w^5 - w^4 - 6*w^3 + 4*w^2 + 10*w - 6],
[911, 911, -w^5 + w^4 + 6*w^3 - 5*w^2 - 7*w + 4],
[911, 911, 2*w^5 - 4*w^4 - 6*w^3 + 10*w^2 + 2*w + 1],
[911, 911, w^5 - w^4 - 3*w^3 + 2*w^2 - 2*w - 3],
[911, 911, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 5*w + 2],
[911, 911, w^5 - 2*w^4 - w^3 + 2*w^2 - 5*w + 6],
[911, 911, -2*w^5 + 4*w^4 + 8*w^3 - 12*w^2 - 8*w + 3],
[937, 937, w^4 - 2*w^3 - 5*w^2 + 7*w + 5],
[937, 937, w^5 + w^4 - 7*w^3 - 5*w^2 + 9*w + 4],
[937, 937, 3*w^4 - 4*w^3 - 9*w^2 + 7*w - 1],
[937, 937, -w^5 + 4*w^4 + w^3 - 14*w^2 + 4*w + 8],
[953, 953, w^5 - 3*w^4 - w^3 + 7*w^2 - 5*w + 4],
[953, 953, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + 2],
[967, 967, w^5 - 6*w^4 + 2*w^3 + 20*w^2 - 12*w - 6],
[967, 967, w^5 - 4*w^4 - 2*w^3 + 14*w^2 + w - 5],
[967, 967, -w^5 + 8*w^3 - 2*w^2 - 14*w + 10],
[967, 967, w^5 - 3*w^4 + 7*w^2 - 9*w],
[967, 967, -w^5 + 6*w^3 + 2*w^2 - 9*w - 2],
[967, 967, -w^5 + w^4 + 5*w^3 - 2*w^2 - 4*w - 3],
[1009, 1009, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 2*w - 4],
[1009, 1009, -2*w^5 + 4*w^4 + 6*w^3 - 11*w^2 - w + 2],
[1009, 1009, 2*w^5 - 3*w^4 - 9*w^3 + 9*w^2 + 9*w - 3],
[1009, 1009, -w^5 + w^4 + 4*w^3 - w^2 - 2*w - 5],
[1021, 1021, w^5 - w^4 - 5*w^3 + 5*w^2 + 6*w - 10],
[1021, 1021, w^5 - 8*w^3 + 3*w^2 + 14*w - 6],
[1021, 1021, 2*w^5 - 4*w^4 - 7*w^3 + 12*w^2 + 4*w - 4],
[1021, 1021, -2*w^5 + 3*w^4 + 8*w^3 - 8*w^2 - 6*w + 1],
[1051, 1051, w^5 - w^4 - 3*w^3 + w^2 - w - 2],
[1051, 1051, 3*w^4 - 6*w^3 - 8*w^2 + 16*w - 3],
[1091, 1091, -w^5 + 4*w^4 - 13*w^2 + 6*w + 5],
[1091, 1091, -w^5 - w^4 + 9*w^3 + 3*w^2 - 16*w + 1],
[1093, 1093, w^2 + w - 5],
[1093, 1093, w^4 - 3*w^3 - w^2 + 9*w - 2],
[1093, 1093, 2*w^5 - 5*w^4 - 5*w^3 + 14*w^2 - w - 2],
[1093, 1093, 2*w^5 - 3*w^4 - 8*w^3 + 7*w^2 + 6*w + 2],
[1163, 1163, -w^3 + 3*w^2 + 2*w - 5],
[1163, 1163, 2*w^4 - 2*w^3 - 6*w^2 + 3*w - 3],
[1217, 1217, w^5 + w^4 - 6*w^3 - 6*w^2 + 3*w + 5],
[1217, 1217, w^5 - w^4 - 5*w^3 + w^2 + 9*w],
[1231, 1231, -w^5 + 4*w^4 - w^3 - 10*w^2 + 10*w - 1],
[1231, 1231, -w^5 + w^4 + 5*w^3 - w^2 - 5*w - 5],
[1259, 1259, w^5 - w^4 - 5*w^3 + 4*w^2 + 6*w - 7],
[1259, 1259, w^5 - w^4 - 6*w^3 + 5*w^2 + 9*w - 4],
[1289, 1289, w^5 + w^4 - 11*w^3 + 23*w - 7],
[1289, 1289, -w^5 + w^4 + 5*w^3 - 2*w^2 - 8*w - 2],
[1289, 1289, 2*w^5 - 13*w^3 - w^2 + 19*w - 1],
[1289, 1289, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 14*w + 9],
[1301, 1301, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 6*w + 4],
[1301, 1301, -w^5 - w^4 + 11*w^3 + 2*w^2 - 23*w + 3],
[1301, 1301, -2*w^5 + w^4 + 11*w^3 - 2*w^2 - 12*w + 1],
[1301, 1301, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 9*w + 6],
[1303, 1303, w^5 - 4*w^4 - w^3 + 13*w^2 - 2*w - 2],
[1303, 1303, w^5 - 4*w^4 - w^3 + 14*w^2 - 3*w - 4],
[1331, 11, -w^4 + 4*w^3 - 2*w^2 - 10*w + 8],
[1331, 11, w^5 - 5*w^4 + w^3 + 16*w^2 - 10*w - 4],
[1399, 1399, -w^5 + 6*w^4 - w^3 - 21*w^2 + 8*w + 8],
[1399, 1399, 2*w^4 - 4*w^3 - 6*w^2 + 13*w - 4],
[1399, 1399, 2*w^5 - 4*w^4 - 9*w^3 + 15*w^2 + 9*w - 7],
[1399, 1399, w^5 - 7*w^3 + w^2 + 10*w],
[1427, 1427, 2*w^5 - 5*w^4 - 7*w^3 + 17*w^2 + 6*w - 6],
[1427, 1427, -w^5 + 3*w^4 + 2*w^3 - 12*w^2 + 3*w + 9],
[1471, 1471, w^5 - 5*w^3 - w^2 + 4*w - 3],
[1471, 1471, w^5 - w^4 - 6*w^3 + 3*w^2 + 7*w - 1],
[1471, 1471, -w^5 + 3*w^4 - w^3 - 6*w^2 + 12*w - 4],
[1471, 1471, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 6],
[1483, 1483, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 6],
[1483, 1483, -w^5 + 4*w^4 - 2*w^3 - 8*w^2 + 12*w - 7],
[1483, 1483, -w^5 + 5*w^4 + w^3 - 18*w^2 + w + 3],
[1483, 1483, w^5 - 4*w^4 - 4*w^3 + 17*w^2 + 7*w - 8],
[1499, 1499, -2*w^5 + 6*w^4 + 6*w^3 - 21*w^2 - 2*w + 8],
[1499, 1499, 2*w^5 - 5*w^4 - 7*w^3 + 17*w^2 + 5*w - 7],
[1567, 1567, 2*w^5 - 7*w^4 - w^3 + 19*w^2 - 11*w],
[1567, 1567, -w^5 + w^4 + 4*w^3 - 2*w^2 - w - 3],
[1567, 1567, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - w - 5],
[1567, 1567, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w - 2],
[1583, 1583, 2*w^4 - 6*w^3 - 4*w^2 + 17*w - 3],
[1583, 1583, -2*w^4 + 5*w^3 + 5*w^2 - 12*w + 1],
[1609, 1609, -4*w^4 + 5*w^3 + 13*w^2 - 11*w + 2],
[1609, 1609, 2*w^5 - 2*w^4 - 10*w^3 + 3*w^2 + 12*w + 5],
[1637, 1637, -w^5 - 2*w^4 + 10*w^3 + 6*w^2 - 18*w],
[1637, 1637, -w^4 + 6*w^2 - 10],
[1637, 1637, -2*w^4 + w^3 + 8*w^2 - 7],
[1637, 1637, -w^5 + 4*w^4 - 3*w^3 - 11*w^2 + 17*w + 2],
[1667, 1667, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],
[1667, 1667, 3*w^4 - 2*w^3 - 12*w^2 + 2*w + 4],
[1667, 1667, w^5 - 7*w^3 + w^2 + 9*w - 2],
[1667, 1667, w^5 - 2*w^4 - 2*w^3 + 6*w^2 - 4*w - 5],
[1681, 41, -w^4 + 4*w^3 + w^2 - 11*w + 4],
[1681, 41, -3*w^4 + 6*w^3 + 9*w^2 - 15*w + 1],
[1693, 1693, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - w - 7],
[1693, 1693, -w^4 - 3*w^3 + 7*w^2 + 12*w - 7],
[1693, 1693, -w^4 + 5*w^2 - w + 1],
[1693, 1693, -w^5 - w^4 + 9*w^3 + 2*w^2 - 16*w + 4],
[1709, 1709, -w^5 + 7*w^3 - 12*w + 3],
[1709, 1709, -w^5 + 3*w^4 + 3*w^3 - 11*w^2 - 3*w + 5],
[1723, 1723, 2*w^5 - w^4 - 10*w^3 + 11*w + 2],
[1723, 1723, 2*w^5 - 6*w^4 - 6*w^3 + 21*w^2 + 4*w - 9],
[1723, 1723, -w^5 + 2*w^4 + 6*w^3 - 11*w^2 - 8*w + 10],
[1723, 1723, -w^5 - w^4 + 5*w^3 + 5*w^2 - 2*w + 2],
[1777, 1777, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 8*w - 2],
[1777, 1777, w^5 - 5*w^4 + 17*w^2 - 5*w - 4],
[1777, 1777, -2*w^5 + 6*w^4 + 5*w^3 - 20*w^2 + 9],
[1777, 1777, -w^5 + 6*w^4 - 3*w^3 - 17*w^2 + 11*w],
[1847, 1847, 3*w^5 - 4*w^4 - 14*w^3 + 11*w^2 + 14*w - 3],
[1847, 1847, 2*w^3 - 3*w^2 - 8*w + 3],
[1849, 43, 2*w^4 - 5*w^3 - 5*w^2 + 13*w - 2],
[1849, 43, -w^4 - w^3 + 6*w^2 + 4*w - 3],
[1861, 1861, 3*w^4 - 5*w^3 - 8*w^2 + 13*w - 6],
[1861, 1861, 3*w^4 - w^3 - 12*w^2 - w + 2],
[1861, 1861, -w^5 + w^4 + 6*w^3 - 4*w^2 - 11*w + 6],
[1861, 1861, -w^5 + 4*w^4 + 3*w^3 - 13*w^2 - 4*w + 2],
[1933, 1933, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 4*w + 2],
[1933, 1933, -2*w^5 + 4*w^4 + 6*w^3 - 10*w^2 - w - 2],
[1933, 1933, 2*w^4 - 3*w^3 - 7*w^2 + 8*w + 6],
[1933, 1933, -2*w^4 + 2*w^3 + 8*w^2 - 3*w - 8],
[1973, 1973, w^4 - 4*w^3 + 12*w - 4],
[1973, 1973, w^3 - 2*w - 3],
[1987, 1987, -3*w^5 + 6*w^4 + 10*w^3 - 19*w^2 - 3*w + 9],
[1987, 1987, -w^4 + 4*w^3 + w^2 - 14*w + 1]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^9 - 10*x^8 + 15*x^7 + 115*x^6 - 281*x^5 - 515*x^4 + 1326*x^3 + 1268*x^2 - 2069*x - 1697;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 2089/29705*e^8 - 17168/29705*e^7 + 682/2285*e^6 + 184023/29705*e^5 - 36182/5941*e^4 - 143937/5941*e^3 + 393164/29705*e^2 + 1055944/29705*e + 313211/29705, 5223/29705*e^8 - 45441/29705*e^7 + 2974/2285*e^6 + 472686/29705*e^5 - 124682/5941*e^4 - 371102/5941*e^3 + 1421583/29705*e^2 + 3062083/29705*e + 924802/29705, -2064/5941*e^8 + 15879/5941*e^7 + 159/457*e^6 - 200167/5941*e^5 + 78203/5941*e^4 + 952543/5941*e^3 - 13462/5941*e^2 - 1730441/5941*e - 965609/5941, -1, 4388/29705*e^8 - 53481/29705*e^7 + 13364/2285*e^6 + 206296/29705*e^5 - 355652/5941*e^4 + 175570/5941*e^3 + 5135508/29705*e^2 - 3299612/29705*e - 4644598/29705, 4772/29705*e^8 - 29079/29705*e^7 - 6019/2285*e^6 + 577614/29705*e^5 + 92512/5941*e^4 - 724662/5941*e^3 - 2096053/29705*e^2 + 7609607/29705*e + 5825553/29705, 12084/29705*e^8 - 91688/29705*e^7 - 2363/2285*e^6 + 1234323/29705*e^5 - 68352/5941*e^4 - 1239701/5941*e^3 - 281306/29705*e^2 + 11757339/29705*e + 6974451/29705, 10887/29705*e^8 - 86529/29705*e^7 + 986/2285*e^6 + 1033449/29705*e^5 - 126596/5941*e^4 - 941725/5941*e^3 + 795482/29705*e^2 + 8400552/29705*e + 4361588/29705, -589/5941*e^8 + 5179/5941*e^7 - 492/457*e^6 - 41696/5941*e^5 + 72369/5941*e^4 + 117892/5941*e^3 - 151198/5941*e^2 - 146699/5941*e + 14913/5941, -7187/29705*e^8 + 56164/29705*e^7 + 549/2285*e^6 - 737429/29705*e^5 + 58157/5941*e^4 + 753838/5941*e^3 - 64762/29705*e^2 - 7460807/29705*e - 4292068/29705, 24/5941*e^8 - 2188/5941*e^7 + 1502/457*e^6 - 29519/5941*e^5 - 170366/5941*e^4 + 375158/5941*e^3 + 547972/5941*e^2 - 918902/5941*e - 864655/5941, -277/5941*e^8 + 499/5941*e^7 + 1211/457*e^6 - 51160/5941*e^5 - 116508/5941*e^4 + 414435/5941*e^3 + 366046/5941*e^2 - 923345/5941*e - 650622/5941, 4152/29705*e^8 - 51769/29705*e^7 + 13066/2285*e^6 + 216349/29705*e^5 - 354087/5941*e^4 + 143154/5941*e^3 + 5125702/29705*e^2 - 2822743/29705*e - 4280337/29705, 11003/29705*e^8 - 107006/29705*e^7 + 14339/2285*e^6 + 844236/29705*e^5 - 439016/5941*e^4 - 428963/5941*e^3 + 5759023/29705*e^2 + 2388788/29705*e - 2076148/29705, -4902/29705*e^8 + 60734/29705*e^7 - 15446/2285*e^6 - 237014/29705*e^5 + 417816/5941*e^4 - 209518/5941*e^3 - 6090307/29705*e^2 + 3897928/29705*e + 5494587/29705, 928/5941*e^8 - 9350/5941*e^7 + 1257/457*e^6 + 84425/5941*e^5 - 216753/5941*e^4 - 259256/5941*e^3 + 604666/5941*e^2 + 378507/5941*e - 141943/5941, 14043/29705*e^8 - 77201/29705*e^7 - 23146/2285*e^6 + 1758946/29705*e^5 + 405794/5941*e^4 - 2317818/5941*e^3 - 8015092/29705*e^2 + 24261408/29705*e + 18221637/29705, 718/2285*e^8 - 7571/2285*e^7 + 17092/2285*e^6 + 51036/2285*e^5 - 38010/457*e^4 - 14606/457*e^3 + 510613/2285*e^2 - 1097/2285*e - 256668/2285, 1578/29705*e^8 + 4664/29705*e^7 - 12066/2285*e^6 + 347896/29705*e^5 + 289959/5941*e^4 - 708840/5941*e^3 - 5207322/29705*e^2 + 8643348/29705*e + 8489537/29705, -380/5941*e^8 + 2958/5941*e^7 - 170/457*e^6 - 20768/5941*e^5 + 20051/5941*e^4 + 34664/5941*e^3 - 18206/5941*e^2 + 25517/5941*e + 56766/5941, -11744/29705*e^8 + 100298/29705*e^7 - 5302/2285*e^6 - 1083163/29705*e^5 + 237178/5941*e^4 + 908494/5941*e^3 - 2213884/29705*e^2 - 8090809/29705*e - 3603851/29705, -8939/29705*e^8 + 67363/29705*e^7 + 2868/2285*e^6 - 994588/29705*e^5 + 46716/5941*e^4 + 1055936/5941*e^3 + 118206/29705*e^2 - 10383764/29705*e - 5679631/29705, -6232/29705*e^8 + 53264/29705*e^7 - 2331/2285*e^6 - 618634/29705*e^5 + 118761/5941*e^4 + 588265/5941*e^3 - 1157647/29705*e^2 - 5901557/29705*e - 2392433/29705, -9013/29705*e^8 + 113716/29705*e^7 - 29564/2285*e^6 - 427796/29705*e^5 + 787264/5941*e^4 - 378860/5941*e^3 - 11603743/29705*e^2 + 6885157/29705*e + 10884863/29705, -13794/29705*e^8 + 128763/29705*e^7 - 14397/2285*e^6 - 1113903/29705*e^5 + 485039/5941*e^4 + 613824/5941*e^3 - 6205019/29705*e^2 - 3215204/29705*e + 1497399/29705, -3709/29705*e^8 + 16333/29705*e^7 + 9898/2285*e^6 - 582743/29705*e^5 - 200684/5941*e^4 + 919307/5941*e^3 + 3819561/29705*e^2 - 10767634/29705*e - 8295116/29705, 8002/29705*e^8 - 66104/29705*e^7 + 2281/2285*e^6 + 736319/29705*e^5 - 115646/5941*e^4 - 660018/5941*e^3 + 696502/29705*e^2 + 6201542/29705*e + 3121108/29705, -3893/5941*e^8 + 35088/5941*e^7 - 3293/457*e^6 - 316824/5941*e^5 + 562143/5941*e^4 + 997502/5941*e^3 - 1292511/5941*e^2 - 1312653/5941*e - 149159/5941, 9273/29705*e^8 - 87911/29705*e^7 + 10799/2285*e^6 + 697156/29705*e^5 - 316729/5941*e^4 - 378702/5941*e^3 + 3648068/29705*e^2 + 2359403/29705*e - 522888/29705, 696/29705*e^8 + 25663/29705*e^7 - 22707/2285*e^6 + 498497/29705*e^5 + 531585/5941*e^4 - 1195007/5941*e^3 - 9013484/29705*e^2 + 15170541/29705*e + 14694059/29705, -23371/29705*e^8 + 175077/29705*e^7 + 5287/2285*e^6 - 2330282/29705*e^5 + 93482/5941*e^4 + 2307231/5941*e^3 + 1442824/29705*e^2 - 21408346/29705*e - 13718349/29705, -489/2285*e^8 + 23/2285*e^7 + 34594/2285*e^6 - 91648/2285*e^5 - 56998/457*e^4 + 158955/457*e^3 + 955396/2285*e^2 - 1780334/2285*e - 1557746/2285, 1591/5941*e^8 - 1472/5941*e^7 - 7863/457*e^6 + 296013/5941*e^5 + 838171/5941*e^4 - 2548361/5941*e^3 - 2903436/5941*e^2 + 5838026/5941*e + 5105884/5941, -14882/29705*e^8 + 148739/29705*e^7 - 22316/2285*e^6 - 1086689/29705*e^5 + 664845/5941*e^4 + 423700/5941*e^3 - 8920152/29705*e^2 - 1206567/29705*e + 4839177/29705, -1358/5941*e^8 + 8945/5941*e^7 + 1461/457*e^6 - 173902/5941*e^5 - 98413/5941*e^4 + 1129283/5941*e^3 + 483198/5941*e^2 - 2485422/5941*e - 1615520/5941, -30898/29705*e^8 + 282041/29705*e^7 - 27629/2285*e^6 - 2565361/29705*e^5 + 939314/5941*e^4 + 1705032/5941*e^3 - 11276298/29705*e^2 - 12722448/29705*e - 1033092/29705, 933/29705*e^8 - 10796/29705*e^7 + 2979/2285*e^6 - 20989/29705*e^5 - 31537/5941*e^4 + 74382/5941*e^3 - 224802/29705*e^2 - 502582/29705*e + 711407/29705, -16569/29705*e^8 + 129258/29705*e^7 + 1018/2285*e^6 - 1662673/29705*e^5 + 130895/5941*e^4 + 1656286/5941*e^3 + 79091/29705*e^2 - 16047079/29705*e - 9456476/29705, -4294/29705*e^8 + 84518/29705*e^7 - 35282/2285*e^6 + 147922/29705*e^5 + 866005/5941*e^4 - 1098215/5941*e^3 - 12997889/29705*e^2 + 14266921/29705*e + 14633699/29705, -8587/29705*e^8 + 104584/29705*e^7 - 26896/2285*e^6 - 332409/29705*e^5 + 701114/5941*e^4 - 484177/5941*e^3 - 10265932/29705*e^2 + 8406558/29705*e + 11074437/29705, 19423/29705*e^8 - 141906/29705*e^7 - 7871/2285*e^6 + 2097691/29705*e^5 - 57534/5941*e^4 - 2184523/5941*e^3 - 710682/29705*e^2 + 20674178/29705*e + 11798702/29705, 12874/29705*e^8 - 124103/29705*e^7 + 16992/2285*e^6 + 898838/29705*e^5 - 481959/5941*e^4 - 369030/5941*e^3 + 5685974/29705*e^2 + 1358039/29705*e - 1671399/29705, -1804/29705*e^8 + 35743/29705*e^7 - 15407/2285*e^6 + 92957/29705*e^5 + 381614/5941*e^4 - 529031/5941*e^3 - 6139309/29705*e^2 + 7110131/29705*e + 8136874/29705, 4566/29705*e^8 - 59807/29705*e^7 + 17268/2285*e^6 + 127472/29705*e^5 - 438647/5941*e^4 + 367475/5941*e^3 + 6391521/29705*e^2 - 5553104/29705*e - 6810136/29705, 12637/29705*e^8 - 117349/29705*e^7 + 11871/2285*e^6 + 1091569/29705*e^5 - 400058/5941*e^4 - 782915/5941*e^3 + 4739412/29705*e^2 + 6634412/29705*e + 1231288/29705, -3808/29705*e^8 + 40211/29705*e^7 - 6009/2285*e^6 - 350326/29705*e^5 + 183746/5941*e^4 + 249480/5941*e^3 - 2240093/29705*e^2 - 2401108/29705*e - 809582/29705, -26107/29705*e^8 + 216574/29705*e^7 - 8276/2285*e^6 - 2399014/29705*e^5 + 426297/5941*e^4 + 2079346/5941*e^3 - 3267582/29705*e^2 - 18773367/29705*e - 10019508/29705, -1198/5941*e^8 + 10201/5941*e^7 - 560/457*e^6 - 107311/5941*e^5 + 116401/5941*e^4 + 455862/5941*e^3 - 222369/5941*e^2 - 826745/5941*e - 359605/5941, -10012/29705*e^8 + 71119/29705*e^7 + 5599/2285*e^6 - 1123209/29705*e^5 + 7688/5941*e^4 + 1199360/5941*e^3 + 493268/29705*e^2 - 11303562/29705*e - 6104968/29705, 11722/29705*e^8 - 108194/29705*e^7 + 11161/2285*e^6 + 973084/29705*e^5 - 376847/5941*e^4 - 626952/5941*e^3 + 4686037/29705*e^2 + 4454612/29705*e - 346942/29705, 200/5941*e^8 - 4371/5941*e^7 + 2158/457*e^6 - 28155/5941*e^5 - 263202/5941*e^4 + 514257/5941*e^3 + 875092/5941*e^2 - 1451152/5941*e - 1428826/5941, -4081/5941*e^8 + 32424/5941*e^7 - 130/457*e^6 - 407396/5941*e^5 + 223295/5941*e^4 + 1971903/5941*e^3 - 253901/5941*e^2 - 3754850/5941*e - 1936019/5941, 1947/29705*e^8 - 14124/29705*e^7 - 969/2285*e^6 + 191834/29705*e^5 + 42043/5941*e^4 - 279140/5941*e^3 - 1597433/29705*e^2 + 3766852/29705*e + 4161178/29705, 14392/29705*e^8 - 143674/29705*e^7 + 21736/2285*e^6 + 1038334/29705*e^5 - 653389/5941*e^4 - 362417/5941*e^3 + 8673732/29705*e^2 + 535462/29705*e - 3867637/29705, 696/29705*e^8 - 4042/29705*e^7 - 2142/2285*e^6 + 201447/29705*e^5 + 2836/5941*e^4 - 291975/5941*e^3 + 165361/29705*e^2 + 3377656/29705*e + 1683269/29705, -23783/29705*e^8 + 202736/29705*e^7 - 12119/2285*e^6 - 2072071/29705*e^5 + 516414/5941*e^4 + 1550710/5941*e^3 - 5613373/29705*e^2 - 11879833/29705*e - 3492252/29705, 12266/29705*e^8 - 147887/29705*e^7 + 36828/2285*e^6 + 543607/29705*e^5 - 971735/5941*e^4 + 531549/5941*e^3 + 14049101/29705*e^2 - 9694169/29705*e - 13573076/29705, -17502/29705*e^8 + 169759/29705*e^7 - 22526/2285*e^6 - 1344634/29705*e^5 + 691181/5941*e^4 + 678872/5941*e^3 - 8934362/29705*e^2 - 3484267/29705*e + 3021137/29705, 384/2285*e^8 - 733/2285*e^7 - 21194/2285*e^6 + 67413/2285*e^5 + 33208/457*e^4 - 110079/457*e^3 - 557076/2285*e^2 + 1209394/2285*e + 980546/2285, -6713/29705*e^8 + 42656/29705*e^7 + 6221/2285*e^6 - 707021/29705*e^5 - 81881/5941*e^4 + 755809/5941*e^3 + 2155117/29705*e^2 - 6666243/29705*e - 5463462/29705, 3612/29705*e^8 - 61949/29705*e^7 + 22686/2285*e^6 + 33934/29705*e^5 - 579587/5941*e^4 + 563998/5941*e^3 + 8866737/29705*e^2 - 7931388/29705*e - 9673832/29705, -1589/29705*e^8 - 8612/29705*e^7 + 13853/2285*e^6 - 298968/29705*e^5 - 356823/5941*e^4 + 671381/5941*e^3 + 6309726/29705*e^2 - 8248424/29705*e - 8727191/29705, -7708/29705*e^8 + 9596/29705*e^7 + 35541/2285*e^6 - 1331111/29705*e^5 - 760990/5941*e^4 + 2226130/5941*e^3 + 13038417/29705*e^2 - 24536793/29705*e - 21556737/29705, -19348/29705*e^8 + 120216/29705*e^7 + 22276/2285*e^6 - 2282766/29705*e^5 - 311834/5941*e^4 + 2753178/5941*e^3 + 7101632/29705*e^2 - 27682168/29705*e - 20148412/29705, 6273/29705*e^8 + 7359/29705*e^7 - 39851/2285*e^6 + 1268006/29705*e^5 + 900629/5941*e^4 - 2361107/5941*e^3 - 15538132/29705*e^2 + 27453643/29705*e + 24979087/29705, -21621/29705*e^8 + 114552/29705*e^7 + 39022/2285*e^6 - 2806852/29705*e^5 - 679024/5941*e^4 + 3767120/5941*e^3 + 12991234/29705*e^2 - 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11806666/29705*e - 13453189/29705, -14608/5941*e^8 + 127720/5941*e^7 - 9205/457*e^6 - 1271707/5941*e^5 + 1776270/5941*e^4 + 4774710/5941*e^3 - 4022647/5941*e^2 - 7557478/5941*e - 1854361/5941, -1379/29705*e^8 - 57462/29705*e^7 + 46418/2285*e^6 - 787473/29705*e^5 - 1115391/5941*e^4 + 1966565/5941*e^3 + 18085156/29705*e^2 - 23284344/29705*e - 23147351/29705, -7119/29705*e^8 + 40063/29705*e^7 + 10898/2285*e^6 - 891368/29705*e^5 - 152847/5941*e^4 + 1129607/5941*e^3 + 1967066/29705*e^2 - 10963434/29705*e - 4972496/29705, -47114/29705*e^8 + 384068/29705*e^7 - 10422/2285*e^6 - 4372338/29705*e^5 + 646183/5941*e^4 + 3907741/5941*e^3 - 4158314/29705*e^2 - 35512799/29705*e - 18166511/29705, 1678/29705*e^8 - 53961/29705*e^7 + 24659/2285*e^6 + 51621/29705*e^5 - 685733/5941*e^4 + 485040/5941*e^3 + 10581768/29705*e^2 - 5918817/29705*e - 7445718/29705, 15377/29705*e^8 + 28921/29705*e^7 - 103799/2285*e^6 + 3162449/29705*e^5 + 2296507/5941*e^4 - 5867245/5941*e^3 - 37925463/29705*e^2 + 66608987/29705*e + 57839003/29705, -11867/29705*e^8 + 126364/29705*e^7 - 22711/2285*e^6 - 833109/29705*e^5 + 690139/5941*e^4 + 66203/5941*e^3 - 9843362/29705*e^2 + 4040358/29705*e + 6938567/29705, 46744/29705*e^8 - 211713/29705*e^7 - 108323/2285*e^6 + 6344853/29705*e^5 + 2082233/5941*e^4 - 8966725/5941*e^3 - 39034536/29705*e^2 + 95865529/29705*e + 78829051/29705, -8518/5941*e^8 + 83441/5941*e^7 - 11267/457*e^6 - 674967/5941*e^5 + 1799348/5941*e^4 + 1656414/5941*e^3 - 4849656/5941*e^2 - 1636286/5941*e + 2074990/5941, 21774/29705*e^8 - 291878/29705*e^7 + 84232/2285*e^6 + 759878/29705*e^5 - 2166194/5941*e^4 + 1502920/5941*e^3 + 31652424/29705*e^2 - 23003596/29705*e - 30784474/29705, 3118/5941*e^8 - 36716/5941*e^7 + 8755/457*e^6 + 145955/5941*e^5 - 1156702/5941*e^4 + 576580/5941*e^3 + 3239518/5941*e^2 - 2189509/5941*e - 2933046/5941, 4936/5941*e^8 - 24227/5941*e^7 - 10684/457*e^6 + 697705/5941*e^5 + 959892/5941*e^4 - 4913459/5941*e^3 - 3623225/5941*e^2 + 10691479/5941*e + 8209723/5941, -40229/29705*e^8 + 276223/29705*e^7 + 26873/2285*e^6 - 4341258/29705*e^5 - 215581/5941*e^4 + 4732502/5941*e^3 + 7798556/29705*e^2 - 45375274/29705*e - 29640081/29705, -43022/29705*e^8 + 308064/29705*e^7 + 24024/2285*e^6 - 4869374/29705*e^5 - 56414/5941*e^4 + 5455504/5941*e^3 + 5241408/29705*e^2 - 54722732/29705*e - 33697018/29705, -62657/29705*e^8 + 508904/29705*e^7 - 10316/2285*e^6 - 6083499/29705*e^5 + 884714/5941*e^4 + 5593787/5941*e^3 - 7310687/29705*e^2 - 51148147/29705*e - 24038178/29705, -44678/29705*e^8 + 399626/29705*e^7 - 33914/2285*e^6 - 3830651/29705*e^5 + 1220504/5941*e^4 + 2758097/5941*e^3 - 13961448/29705*e^2 - 22027523/29705*e - 4804262/29705, 4345/5941*e^8 - 8964/5941*e^7 - 17623/457*e^6 + 712433/5941*e^5 + 1889090/5941*e^4 - 5871456/5941*e^3 - 6545026/5941*e^2 + 13062116/5941*e + 11085495/5941, -20141/29705*e^8 + 197462/29705*e^7 - 25258/2285*e^6 - 1666592/29705*e^5 + 740828/5941*e^4 + 1171793/5941*e^3 - 8567476/29705*e^2 - 11112641/29705*e - 2104984/29705, 109/29705*e^8 - 74298/29705*e^7 + 50427/2285*e^6 - 722472/29705*e^5 - 1235318/5941*e^4 + 2042766/5941*e^3 + 20239424/29705*e^2 - 24636626/29705*e - 25651479/29705, -12245/5941*e^8 + 101415/5941*e^7 - 3638/457*e^6 - 1136059/5941*e^5 + 974201/5941*e^4 + 4970522/5941*e^3 - 1458897/5941*e^2 - 8895739/5941*e - 4818613/5941, 9563/5941*e^8 - 58900/5941*e^7 - 11344/457*e^6 + 1130126/5941*e^5 + 832329/5941*e^4 - 6920410/5941*e^3 - 3693934/5941*e^2 + 14112021/5941*e + 10313325/5941, -27704/29705*e^8 + 278003/29705*e^7 - 42147/2285*e^6 - 2038593/29705*e^5 + 1252793/5941*e^4 + 887175/5941*e^3 - 17195349/29705*e^2 - 4399114/29705*e + 8779024/29705, -12042/5941*e^8 + 99741/5941*e^7 - 3920/457*e^6 - 1088443/5941*e^5 + 961504/5941*e^4 + 4701419/5941*e^3 - 1451016/5941*e^2 - 8568060/5941*e - 4458114/5941, -131/2285*e^8 + 4707/2285*e^7 - 30984/2285*e^6 + 13723/2285*e^5 + 60087/457*e^4 - 72609/457*e^3 - 910826/2285*e^2 + 917564/2285*e + 914041/2285, 67196/29705*e^8 - 432577/29705*e^7 - 68362/2285*e^6 + 7875727/29705*e^5 + 881357/5941*e^4 - 9466155/5941*e^3 - 21541379/29705*e^2 + 97057501/29705*e + 68180184/29705, -12122/5941*e^8 + 87231/5941*e^7 + 6002/457*e^6 - 1314821/5941*e^5 - 120227/5941*e^4 + 7334326/5941*e^3 + 1893061/5941*e^2 - 14961145/5941*e - 9627966/5941, 8510/5941*e^8 - 78751/5941*e^7 + 8329/457*e^6 + 692728/5941*e^5 - 1360355/5941*e^4 - 2181494/5941*e^3 + 3278785/5941*e^2 + 3079298/5941*e - 125272/5941, 14384/29705*e^8 - 14223/29705*e^7 - 69403/2285*e^6 + 2588873/29705*e^5 + 1486431/5941*e^4 - 4489490/5941*e^3 - 25049831/29705*e^2 + 51407594/29705*e + 43174271/29705, -1016/2285*e^8 - 2583/2285*e^7 + 97301/2285*e^6 - 229062/2285*e^5 - 165629/457*e^4 + 433749/457*e^3 + 2766669/2285*e^2 - 5012336/2285*e - 4407604/2285, -508/2285*e^8 + 6706/2285*e^7 - 21042/2285*e^6 - 41411/2285*e^5 + 44917/457*e^4 + 15109/457*e^3 - 651458/2285*e^2 - 166328/2285*e + 295988/2285, 40762/29705*e^8 - 468389/29705*e^7 + 103406/2285*e^6 + 2326934/29705*e^5 - 2840394/5941*e^4 + 612591/5941*e^3 + 40837837/29705*e^2 - 18164163/29705*e - 33906337/29705, -55709/29705*e^8 + 439873/29705*e^7 - 497/2285*e^6 - 5560313/29705*e^5 + 617614/5941*e^4 + 5255314/5941*e^3 - 3798244/29705*e^2 - 48239029/29705*e - 25609101/29705, -12384/29705*e^8 + 178448/29705*e^7 - 59827/2285*e^6 + 40667/29705*e^5 + 1397299/5941*e^4 - 1741898/5941*e^3 - 19935594/29705*e^2 + 23760281/29705*e + 24463859/29705, 49037/29705*e^8 - 425709/29705*e^7 + 28516/2285*e^6 + 4314464/29705*e^5 - 1117827/5941*e^4 - 3373139/5941*e^3 + 11625447/29705*e^2 + 28875007/29705*e + 11334108/29705, 59672/29705*e^8 - 400149/29705*e^7 - 47964/2285*e^6 + 6706449/29705*e^5 + 452447/5941*e^4 - 7599104/5941*e^3 - 12973723/29705*e^2 + 74977432/29705*e + 49278228/29705, 21277/29705*e^8 - 73289/29705*e^7 - 62074/2285*e^6 + 2851714/29705*e^5 + 1324645/5941*e^4 - 4314220/5941*e^3 - 23392208/29705*e^2 + 46429272/29705*e + 38424843/29705, 5895/5941*e^8 - 47295/5941*e^7 + 244/457*e^6 + 602655/5941*e^5 - 325985/5941*e^4 - 3001387/5941*e^3 + 314170/5941*e^2 + 5861509/5941*e + 3264791/5941, -24491/29705*e^8 + 356397/29705*e^7 - 113553/2285*e^6 - 616072/29705*e^5 + 2921273/5941*e^4 - 2455716/5941*e^3 - 44081061/29705*e^2 + 35623229/29705*e + 45811746/29705, 40244/29705*e^8 - 322148/29705*e^7 + 8912/2285*e^6 + 3442798/29705*e^5 - 490415/5941*e^4 - 2812707/5941*e^3 + 2539659/29705*e^2 + 22425669/29705*e + 12624536/29705, 123408/29705*e^8 - 1061881/29705*e^7 + 63964/2285*e^6 + 11139286/29705*e^5 - 2758552/5941*e^4 - 8867154/5941*e^3 + 30475638/29705*e^2 + 74009073/29705*e + 24201912/29705, 1572/29705*e^8 - 54199/29705*e^7 + 29831/2285*e^6 - 368041/29705*e^5 - 731098/5941*e^4 + 1279866/5941*e^3 + 11569712/29705*e^2 - 16385088/29705*e - 15460802/29705, 7463/5941*e^8 - 81326/5941*e^7 + 15810/457*e^6 + 478164/5941*e^5 - 2238112/5941*e^4 - 78678/5941*e^3 + 6217915/5941*e^2 - 1716372/5941*e - 4258300/5941, 1949/29705*e^8 - 113323/29705*e^7 + 70372/2285*e^6 - 1124082/29705*e^5 - 1603879/5941*e^4 + 3085956/5941*e^3 + 24515359/29705*e^2 - 37616506/29705*e - 34185274/29705, 27098/29705*e^8 - 252461/29705*e^7 + 28214/2285*e^6 + 2149746/29705*e^5 - 911094/5941*e^4 - 1255480/5941*e^3 + 11747748/29705*e^2 + 7482193/29705*e - 3270868/29705, -7121/29705*e^8 + 20442/29705*e^7 + 28672/2285*e^6 - 1446867/29705*e^5 - 526865/5941*e^4 + 2315317/5941*e^3 + 9212989/29705*e^2 - 25989871/29705*e - 21075309/29705, -1991/2285*e^8 + 12042/2285*e^7 + 34686/2285*e^6 - 249757/2285*e^5 - 42154/457*e^4 + 325814/457*e^3 + 900074/2285*e^2 - 3494176/2285*e - 2456624/2285, 2461/29705*e^8 - 80787/29705*e^7 + 44528/2285*e^6 - 579483/29705*e^5 - 1089501/5941*e^4 + 1988624/5941*e^3 + 17328891/29705*e^2 - 26625579/29705*e - 24136231/29705, -17041/29705*e^8 + 162387/29705*e^7 - 20143/2285*e^6 - 1286107/29705*e^5 + 567718/5941*e^4 + 789419/5941*e^3 - 6119161/29705*e^2 - 7191811/29705*e - 1420524/29705];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {29,29,-w^4 + 5*w^2 + 2*w - 4}>] := 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;