/*
  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^2 - w - 1}>;

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^7 + 7*x^6 - 6*x^5 - 120*x^4 - 214*x^3 - 100*x^2 + 7*x + 9;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 5/4*e^6 + 49/6*e^5 - 34/3*e^4 - 434/3*e^3 - 399/2*e^2 - 199/6*e + 81/4, 1/3*e^6 + 2*e^5 - 4*e^4 - 109/3*e^3 - 107/3*e^2 + 8*e + 4, 35/6*e^6 + 227/6*e^5 - 109/2*e^4 - 4031/6*e^3 - 1803/2*e^2 - 733/6*e + 96, -9/4*e^6 - 29/2*e^5 + 65/3*e^4 + 775/3*e^3 + 2017/6*e^2 + 187/6*e - 165/4, -39/4*e^6 - 63*e^5 + 185/2*e^4 + 2241/2*e^3 + 1482*e^2 + 172*e - 669/4, 1, e^6 + 19/3*e^5 - 31/3*e^4 - 341/3*e^3 - 410/3*e^2 + 2*e + 18, 7/3*e^6 + 46/3*e^5 - 62/3*e^4 - 815/3*e^3 - 1145/3*e^2 - 184/3*e + 45, 43/12*e^6 + 137/6*e^5 - 107/3*e^4 - 1223/3*e^3 - 3091/6*e^2 - 203/6*e + 249/4, -25/6*e^6 - 27*e^5 + 116/3*e^4 + 479*e^3 + 649*e^2 + 278/3*e - 145/2, -29/2*e^6 - 563/6*e^5 + 821/6*e^4 + 10009/6*e^3 + 13303/6*e^2 + 539/2*e - 246, 40/3*e^6 + 517/6*e^5 - 253/2*e^4 - 9197/6*e^3 - 12161/6*e^2 - 1385/6*e + 459/2, -16/3*e^6 - 104/3*e^5 + 148/3*e^4 + 615*e^3 + 2498/3*e^2 + 371/3*e - 84, 9/2*e^6 + 29*e^5 - 130/3*e^4 - 1550/3*e^3 - 2017/3*e^2 - 193/3*e + 141/2, -29/2*e^6 - 281/3*e^5 + 412/3*e^4 + 4994/3*e^3 + 2208*e^2 + 830/3*e - 489/2, 13/3*e^6 + 167/6*e^5 - 251/6*e^4 - 989/2*e^3 - 3869/6*e^2 - 169/2*e + 117/2, -3/4*e^6 - 14/3*e^5 + 15/2*e^4 + 165/2*e^3 + 320/3*e^2 + 55/3*e - 9/4, 3/2*e^6 + 59/6*e^5 - 79/6*e^4 - 1043/6*e^3 - 493/2*e^2 - 269/6*e + 15, 29/12*e^6 + 47/3*e^5 - 133/6*e^4 - 555/2*e^3 - 1142/3*e^2 - 61*e + 117/4, 11/3*e^6 + 47/2*e^5 - 71/2*e^4 - 2509/6*e^3 - 3269/6*e^2 - 123/2*e + 123/2, -23/6*e^6 - 49/2*e^5 + 227/6*e^4 + 873/2*e^3 + 1113/2*e^2 + 329/6*e - 60, -37/4*e^6 - 179/3*e^5 + 175/2*e^4 + 2121/2*e^3 + 4235/3*e^2 + 514/3*e - 675/4, 151/12*e^6 + 245/3*e^5 - 235/2*e^4 - 8705/6*e^3 - 5836/3*e^2 - 754/3*e + 831/4, -29/6*e^6 - 63/2*e^5 + 89/2*e^4 + 3353/6*e^3 + 4549/6*e^2 + 223/2*e - 74, -85/6*e^6 - 275/3*e^5 + 134*e^4 + 4889/3*e^3 + 2160*e^2 + 793/3*e - 471/2, 25/4*e^6 + 122/3*e^5 - 349/6*e^4 - 4337/6*e^3 - 2911/3*e^2 - 122*e + 415/4, 59/12*e^6 + 193/6*e^5 - 133/3*e^4 - 1711/3*e^3 - 4733/6*e^2 - 715/6*e + 361/4, -95/12*e^6 - 307/6*e^5 + 227/3*e^4 + 912*e^3 + 7159/6*e^2 + 211/2*e - 569/4, 157/12*e^6 + 169/2*e^5 - 124*e^4 - 4507/3*e^3 - 11947/6*e^2 - 471/2*e + 891/4, 2/3*e^6 + 14/3*e^5 - 14/3*e^4 - 82*e^3 - 389/3*e^2 - 32*e + 6, 41/6*e^6 + 263/6*e^5 - 397/6*e^4 - 4681/6*e^3 - 6097/6*e^2 - 659/6*e + 122, 25/4*e^6 + 81/2*e^5 - 176/3*e^4 - 2158/3*e^3 - 5767/6*e^2 - 775/6*e + 413/4, 49/3*e^6 + 211/2*e^5 - 311/2*e^4 - 11255/6*e^3 - 14833/6*e^2 - 601/2*e + 531/2, -89/6*e^6 - 575/6*e^5 + 279/2*e^4 + 10205/6*e^3 + 4553/2*e^2 + 1927/6*e - 240, -61/3*e^6 - 395/3*e^5 + 574/3*e^4 + 2341*e^3 + 9356/3*e^2 + 1115/3*e - 351, -5/6*e^6 - 5*e^5 + 32/3*e^4 + 275/3*e^3 + 232/3*e^2 - 100/3*e - 45/2, -31/6*e^6 - 67/2*e^5 + 289/6*e^4 + 1191/2*e^3 + 1603/2*e^2 + 577/6*e - 90, 55/6*e^6 + 178/3*e^5 - 259/3*e^4 - 3166/3*e^3 - 1406*e^2 - 163*e + 339/2, -18*e^6 - 233/2*e^5 + 1013/6*e^4 + 12415/6*e^3 + 16625/6*e^2 + 2201/6*e - 579/2, 28/3*e^6 + 121/2*e^5 - 523/6*e^4 - 6451/6*e^3 - 8663/6*e^2 - 1057/6*e + 333/2, -4*e^6 - 157/6*e^5 + 217/6*e^4 + 2783/6*e^3 + 3839/6*e^2 + 203/2*e - 135/2, -20/3*e^6 - 87/2*e^5 + 365/6*e^4 + 4631/6*e^3 + 6337/6*e^2 + 911/6*e - 213/2, 47/6*e^6 + 151/3*e^5 - 226/3*e^4 - 894*e^3 - 3514/3*e^2 - 158*e + 209/2, 103/4*e^6 + 500/3*e^5 - 1457/6*e^4 - 17779/6*e^3 - 3940*e^2 - 1430/3*e + 1753/4, 11/4*e^6 + 35/2*e^5 - 82/3*e^4 - 935/3*e^3 - 2375/6*e^2 - 221/6*e + 147/4, 151/12*e^6 + 244/3*e^5 - 719/6*e^4 - 2895/2*e^3 - 5710/3*e^2 - 204*e + 831/4, 52/3*e^6 + 112*e^5 - 164*e^4 - 5968/3*e^3 - 7922/3*e^2 - 354*e + 270, -61/3*e^6 - 395/3*e^5 + 572/3*e^4 + 7016/3*e^3 + 3131*e^2 + 413*e - 336, -13/6*e^6 - 83/6*e^5 + 125/6*e^4 + 1481/6*e^3 + 653/2*e^2 + 43/2*e - 60, 193/12*e^6 + 623/6*e^5 - 153*e^4 - 5539/3*e^3 - 4875/2*e^2 - 1747/6*e + 1035/4, -343/12*e^6 - 1111/6*e^5 + 806/3*e^4 + 9872/3*e^3 + 8779/2*e^2 + 1111/2*e - 1929/4, -95/12*e^6 - 154/3*e^5 + 449/6*e^4 + 5483/6*e^3 + 1207*e^2 + 127*e - 519/4, -23/2*e^6 - 224/3*e^5 + 106*e^4 + 1325*e^3 + 5414/3*e^2 + 754/3*e - 399/2, -19/2*e^6 - 123/2*e^5 + 179/2*e^4 + 2185/2*e^3 + 2909/2*e^2 + 385/2*e - 162, -119/12*e^6 - 383/6*e^5 + 95*e^4 + 3407/3*e^3 + 8947/6*e^2 + 1009/6*e - 669/4, -21/2*e^6 - 409/6*e^5 + 195/2*e^4 + 2421/2*e^3 + 9805/6*e^2 + 1307/6*e - 174, -25/12*e^6 - 83/6*e^5 + 52/3*e^4 + 245*e^3 + 2171/6*e^2 + 107/2*e - 231/4, -27/4*e^6 - 43*e^5 + 403/6*e^4 + 4601/6*e^3 + 2909/3*e^2 + 245/3*e - 429/4, 193/12*e^6 + 314/3*e^5 - 297/2*e^4 - 11147/6*e^3 - 7552/3*e^2 - 1063/3*e + 1101/4, 83/6*e^6 + 268/3*e^5 - 391/3*e^4 - 1586*e^3 - 6355/3*e^2 - 288*e + 447/2, 9/4*e^6 + 85/6*e^5 - 23*e^4 - 252*e^3 - 1873/6*e^2 - 233/6*e + 93/4, -41/2*e^6 - 397/3*e^5 + 195*e^4 + 2354*e^3 + 9328/3*e^2 + 1067/3*e - 739/2, 13/2*e^6 + 43*e^5 - 57*e^4 - 762*e^3 - 1072*e^2 - 173*e + 239/2, 8*e^6 + 154/3*e^5 - 230/3*e^4 - 2737/3*e^3 - 1203*e^2 - 454/3*e + 114, -175/12*e^6 - 283/3*e^5 + 829/6*e^4 + 10063/6*e^3 + 6656/3*e^2 + 796/3*e - 971/4, 77/12*e^6 + 83/2*e^5 - 179/3*e^4 - 736*e^3 - 1995/2*e^2 - 883/6*e + 451/4, -119/6*e^6 - 257/2*e^5 + 1121/6*e^4 + 4569/2*e^3 + 6075/2*e^2 + 2189/6*e - 340, 17/4*e^6 + 167/6*e^5 - 39*e^4 - 496*e^3 - 4019/6*e^2 - 361/6*e + 377/4, 155/12*e^6 + 251/3*e^5 - 733/6*e^4 - 2979/2*e^3 - 5909/3*e^2 - 201*e + 927/4, 61/4*e^6 + 197/2*e^5 - 434/3*e^4 - 5257/3*e^3 - 13921/6*e^2 - 1561/6*e + 1089/4, -1/4*e^6 - 11/6*e^5 + 4/3*e^4 + 98/3*e^3 + 355/6*e^2 + 9/2*e - 109/4, -271/12*e^6 - 146*e^5 + 1285/6*e^4 + 15583/6*e^3 + 10303/3*e^2 + 1163/3*e - 1543/4, 77/12*e^6 + 83/2*e^5 - 181/3*e^4 - 2212/3*e^3 - 5905/6*e^2 - 785/6*e + 315/4, -31*e^6 - 1201/6*e^5 + 589/2*e^4 + 7117/2*e^3 + 28225/6*e^2 + 3407/6*e - 1041/2, 59/2*e^6 + 381/2*e^5 - 559/2*e^4 - 6771/2*e^3 - 8981/2*e^2 - 1119/2*e + 495, 11/4*e^6 + 53/3*e^5 - 163/6*e^4 - 1901/6*e^3 - 1198/3*e^2 + e + 201/4, 23/6*e^6 + 73/3*e^5 - 116/3*e^4 - 1307/3*e^3 - 1628/3*e^2 - 25/3*e + 153/2, -41/12*e^6 - 131/6*e^5 + 101/3*e^4 + 389*e^3 + 2993/6*e^2 + 257/6*e - 363/4, 97/12*e^6 + 157/3*e^5 - 449/6*e^4 - 1853/2*e^3 - 3787/3*e^2 - 214*e + 525/4, -287/12*e^6 - 154*e^5 + 1373/6*e^4 + 16433/6*e^3 + 10805/3*e^2 + 1270/3*e - 1635/4, -25/12*e^6 - 27/2*e^5 + 20*e^4 + 721/3*e^3 + 1873/6*e^2 + 71/2*e - 123/4, 67/2*e^6 + 649/3*e^5 - 956/3*e^4 - 11545/3*e^3 - 5078*e^2 - 1747/3*e + 1167/2, 22/3*e^6 + 47*e^5 - 215/3*e^4 - 2510/3*e^3 - 3232/3*e^2 - 353/3*e + 111, -43*e^6 - 835/3*e^5 + 405*e^4 + 4948*e^3 + 19768/3*e^2 + 2390/3*e - 741, 3/2*e^6 + 19/2*e^5 - 29/2*e^4 - 335/2*e^3 - 445/2*e^2 - 107/2*e - 6, -26/3*e^6 - 169/3*e^5 + 80*e^4 + 3002/3*e^3 + 4076/3*e^2 + 533/3*e - 168, 55/6*e^6 + 179/3*e^5 - 84*e^4 - 3182/3*e^3 - 1449*e^2 - 499/3*e + 393/2, 67/3*e^6 + 434/3*e^5 - 209*e^4 - 7702/3*e^3 - 10333/3*e^2 - 1471/3*e + 360, 421/12*e^6 + 1363/6*e^5 - 329*e^4 - 12106/3*e^3 - 32405/6*e^2 - 4235/6*e + 2283/4, 67/12*e^6 + 73/2*e^5 - 149/3*e^4 - 1934/3*e^3 - 5453/6*e^2 - 1051/6*e + 393/4, 149/12*e^6 + 481/6*e^5 - 117*e^4 - 4271/3*e^3 - 3803/2*e^2 - 1553/6*e + 723/4, 14*e^6 + 91*e^5 - 389/3*e^4 - 4849/3*e^3 - 6560/3*e^2 - 857/3*e + 258, -74/3*e^6 - 478/3*e^5 + 700/3*e^4 + 8494/3*e^3 + 3762*e^2 + 478*e - 426, 5*e^6 + 197/6*e^5 - 89/2*e^4 - 1165/2*e^3 - 4883/6*e^2 - 709/6*e + 179/2, 26/3*e^6 + 56*e^5 - 244/3*e^4 - 2983/3*e^3 - 4001/3*e^2 - 541/3*e + 135, 9*e^6 + 117/2*e^5 - 165/2*e^4 - 2069/2*e^3 - 2837/2*e^2 - 515/2*e + 263/2, 337/12*e^6 + 545/3*e^5 - 1589/6*e^4 - 6461/2*e^3 - 12896/3*e^2 - 1505/3*e + 2001/4, -47/3*e^6 - 101*e^5 + 449/3*e^4 + 1798*e^3 + 2365*e^2 + 734/3*e - 294, 25/6*e^6 + 27*e^5 - 39*e^4 - 1436/3*e^3 - 1927/3*e^2 - 101*e + 123/2, 14*e^6 + 541/6*e^5 - 267/2*e^4 - 3203/2*e^3 - 12685/6*e^2 - 1649/6*e + 411/2, -263/12*e^6 - 845/6*e^5 + 635/3*e^4 + 2507*e^3 + 19589/6*e^2 + 2045/6*e - 1485/4, 175/6*e^6 + 1127/6*e^5 - 1675/6*e^4 - 6681/2*e^3 - 26327/6*e^2 - 3077/6*e + 474, -3/2*e^6 - 59/6*e^5 + 77/6*e^4 + 1045/6*e^3 + 1531/6*e^2 + 79/2*e - 25, -1/4*e^6 - 11/6*e^5 + e^4 + 32*e^3 + 371/6*e^2 + 61/6*e + 7/4, -47/12*e^6 - 74/3*e^5 + 241/6*e^4 + 883/2*e^3 + 1628/3*e^2 + 12*e - 287/4, 5/3*e^6 + 11*e^5 - 15*e^4 - 587/3*e^3 - 802/3*e^2 - 25*e + 38, -85/2*e^6 - 827/3*e^5 + 1189/3*e^4 + 14687/3*e^3 + 6583*e^2 + 2642/3*e - 1413/2, -35/3*e^6 - 229/3*e^5 + 319/3*e^4 + 4069/3*e^3 + 1853*e^2 + 229*e - 246, 415/12*e^6 + 1345/6*e^5 - 970/3*e^4 - 3983*e^3 - 32053/6*e^2 - 4081/6*e + 2349/4, -31/6*e^6 - 199/6*e^5 + 293/6*e^4 + 3527/6*e^3 + 4733/6*e^2 + 721/6*e - 72, -73/12*e^6 - 79/2*e^5 + 169/3*e^4 + 700*e^3 + 1899/2*e^2 + 923/6*e - 363/4, 53/2*e^6 + 511/3*e^5 - 769/3*e^4 - 9101/3*e^3 - 11822/3*e^2 - 392*e + 921/2, -23/3*e^6 - 101/2*e^5 + 133/2*e^4 + 5359/6*e^3 + 7667/6*e^2 + 443/2*e - 277/2, 28/3*e^6 + 181/3*e^5 - 89*e^4 - 3220/3*e^3 - 1408*e^2 - 488/3*e + 150, -169/6*e^6 - 1093/6*e^5 + 531/2*e^4 + 19423/6*e^3 + 8625/2*e^2 + 3311/6*e - 464, -18*e^6 - 701/6*e^5 + 335/2*e^4 + 4145/2*e^3 + 16751/6*e^2 + 2485/6*e - 555/2, -283/12*e^6 - 917/6*e^5 + 662/3*e^4 + 8141/3*e^3 + 21841/6*e^2 + 2963/6*e - 1653/4, 385/12*e^6 + 1247/6*e^5 - 303*e^4 - 11095/3*e^3 - 9803/2*e^2 - 3229/6*e + 2259/4, -37/2*e^6 - 356/3*e^5 + 539/3*e^4 + 6337/3*e^3 + 8209/3*e^2 + 286*e - 605/2, -41/12*e^6 - 131/6*e^5 + 104/3*e^4 + 389*e^3 + 2861/6*e^2 + 299/6*e - 199/4, 559/12*e^6 + 904/3*e^5 - 2641/6*e^4 - 32161/6*e^3 - 21341/3*e^2 - 2398/3*e + 3287/4, -49/6*e^6 - 161/3*e^5 + 220/3*e^4 + 2860/3*e^3 + 3952/3*e^2 + 533/3*e - 341/2, -45/2*e^6 - 436/3*e^5 + 641/3*e^4 + 7753/3*e^3 + 3415*e^2 + 1201/3*e - 763/2, -343/12*e^6 - 1109/6*e^5 + 809/3*e^4 + 9857/3*e^3 + 26227/6*e^2 + 3191/6*e - 1893/4, -53/12*e^6 - 57/2*e^5 + 42*e^4 + 1511/3*e^3 + 4007/6*e^2 + 271/2*e - 195/4, 143/12*e^6 + 229/3*e^5 - 235/2*e^4 - 8167/6*e^3 - 5189/3*e^2 - 437/3*e + 747/4, 107/3*e^6 + 1379/6*e^5 - 2051/6*e^4 - 24539/6*e^3 - 10721/2*e^2 - 1177/2*e + 1203/2, -17/6*e^6 - 55/3*e^5 + 76/3*e^4 + 324*e^3 + 1378/3*e^2 + 85*e - 67/2, 13/3*e^6 + 27*e^5 - 142/3*e^4 - 487*e^3 - 548*e^2 + 131/3*e + 76, -419/12*e^6 - 679/3*e^5 + 1957/6*e^4 + 8043/2*e^3 + 16204/3*e^2 + 2053/3*e - 2463/4, 43/12*e^6 + 139/6*e^5 - 97/3*e^4 - 410*e^3 - 3463/6*e^2 - 559/6*e + 333/4, -199/4*e^6 - 964/3*e^5 + 943/2*e^4 + 11427/2*e^3 + 22723/3*e^2 + 2711/3*e - 3417/4, -31/12*e^6 - 49/3*e^5 + 57/2*e^4 + 1775/6*e^3 + 320*e^2 - 133/3*e - 163/4, -71/6*e^6 - 153/2*e^5 + 677/6*e^4 + 2727/2*e^3 + 3577/2*e^2 + 977/6*e - 217, -64/3*e^6 - 415/3*e^5 + 200*e^4 + 7372/3*e^3 + 3282*e^2 + 1295/3*e - 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61/3*e^5 + 92/3*e^4 + 362*e^3 + 1411/3*e^2 + 103/3*e - 93/2, 287/12*e^6 + 467/3*e^5 - 1327/6*e^4 - 5523/2*e^3 - 11210/3*e^2 - 566*e + 1443/4, 9*e^6 + 59*e^5 - 79*e^4 - 1043*e^3 - 1484*e^2 - 269*e + 141, 45/2*e^6 + 877/6*e^5 - 1255/6*e^4 - 15575/6*e^3 - 20975/6*e^2 - 931/2*e + 372, 113/2*e^6 + 2189/6*e^5 - 3227/6*e^4 - 38935/6*e^3 - 51319/6*e^2 - 1965/2*e + 957, 377/12*e^6 + 1213/6*e^5 - 902/3*e^4 - 3598*e^3 - 28381/6*e^2 - 987/2*e + 2191/4, -48*e^6 - 310*e^5 + 1367/3*e^4 + 16540/3*e^3 + 21887/3*e^2 + 2564/3*e - 850, -142/3*e^6 - 920/3*e^5 + 1333/3*e^4 + 5451*e^3 + 21839/3*e^2 + 2660/3*e - 819, 44*e^6 + 285*e^5 - 1238/3*e^4 - 15187/3*e^3 - 20318/3*e^2 - 2648/3*e + 714, -41/12*e^6 - 139/6*e^5 + 82/3*e^4 + 1225/3*e^3 + 3659/6*e^2 + 817/6*e - 231/4, -161/3*e^6 - 1042/3*e^5 + 506*e^4 + 18524/3*e^3 + 24644/3*e^2 + 3014/3*e - 891, -10*e^6 - 65*e^5 + 284/3*e^4 + 3466/3*e^3 + 4568/3*e^2 + 578/3*e - 210, 43/12*e^6 + 73/3*e^5 - 57/2*e^4 - 2591/6*e^3 - 646*e^2 - 275/3*e + 411/4, 581/12*e^6 + 940/3*e^5 - 2725/6*e^4 - 11137/2*e^3 - 22369/3*e^2 - 2767/3*e + 3365/4, -85/3*e^6 - 183*e^5 + 809/3*e^4 + 9773/3*e^3 + 12883/3*e^2 + 1367/3*e - 502, -44/3*e^6 - 569/6*e^5 + 835/6*e^4 + 3379/2*e^3 + 13379/6*e^2 + 1199/6*e - 567/2, -149/12*e^6 - 242/3*e^5 + 235/2*e^4 + 8629/6*e^3 + 1892*e^2 + 511/3*e - 813/4, -167/3*e^6 - 721/2*e^5 + 3127/6*e^4 + 12805/2*e^3 + 17173/2*e^2 + 6865/6*e - 1841/2, -113/12*e^6 - 176/3*e^5 + 605/6*e^4 + 6323/6*e^3 + 3682/3*e^2 - 70/3*e - 649/4, -225/4*e^6 - 729/2*e^5 + 529*e^4 + 6481*e^3 + 17265/2*e^2 + 2059/2*e - 3873/4, 139/6*e^6 + 899/6*e^5 - 1315/6*e^4 - 5327/2*e^3 - 21185/6*e^2 - 2561/6*e + 354, 409/12*e^6 + 441/2*e^5 - 967/3*e^4 - 3919*e^3 - 10399/2*e^2 - 3917/6*e + 2391/4, 139/2*e^6 + 1351/3*e^5 - 1958/3*e^4 - 24004/3*e^3 - 10681*e^2 - 4129/3*e + 2295/2, -587/12*e^6 - 950/3*e^5 + 917/2*e^4 + 33739/6*e^3 + 7536*e^2 + 3043/3*e - 3271/4, 89/2*e^6 + 862/3*e^5 - 1267/3*e^4 - 15326/3*e^3 - 20279/3*e^2 - 806*e + 1477/2, 53/3*e^6 + 233/2*e^5 - 313/2*e^4 - 12397/6*e^3 - 17315/6*e^2 - 857/2*e + 705/2, 61/6*e^6 + 389/6*e^5 - 203/2*e^4 - 6943/6*e^3 - 8737/6*e^2 - 631/6*e + 182, 155/6*e^6 + 1001/6*e^5 - 487/2*e^4 - 17783/6*e^3 - 7919/2*e^2 - 3091/6*e + 452, -172/3*e^6 - 2221/6*e^5 + 3259/6*e^4 + 39475/6*e^3 + 17457/2*e^2 + 2143/2*e - 1959/2, 41/2*e^6 + 398/3*e^5 - 193*e^4 - 2360*e^3 - 9431/3*e^2 - 1066/3*e + 663/2, 205/3*e^6 + 883/2*e^5 - 1293/2*e^4 - 47099/6*e^3 - 62521/6*e^2 - 2489/2*e + 2325/2, 44*e^6 + 283*e^5 - 425*e^4 - 5036*e^3 - 6550*e^2 - 720*e + 708, -559/12*e^6 - 1799/6*e^5 + 1340/3*e^4 + 16010/3*e^3 + 41989/6*e^2 + 4463/6*e - 3165/4, 104/3*e^6 + 1343/6*e^5 - 659/2*e^4 - 23905/6*e^3 - 31579/6*e^2 - 3325/6*e + 1263/2, -19/6*e^6 - 20*e^5 + 33*e^4 + 1073/3*e^3 + 1285/3*e^2 + 13*e - 123/2, 5/2*e^6 + 17*e^5 - 58/3*e^4 - 890/3*e^3 - 1375/3*e^2 - 439/3*e + 73/2, -67/6*e^6 - 215/3*e^5 + 331/3*e^4 + 3844/3*e^3 + 4852/3*e^2 + 227/3*e - 377/2];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {29,29,w^2 - 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;