/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([-7, -14, 7, 13, -4, -3, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([43, 43, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - w + 3])

primes_array = [
[7, 7, w],\
[7, 7, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 + 5],\
[13, 13, w^2 - 3],\
[13, 13, -w^2 + 2*w + 2],\
[29, 29, w^4 - 2*w^3 - 4*w^2 + 4*w + 6],\
[29, 29, -w^4 + 2*w^3 + 4*w^2 - 6*w - 5],\
[41, 41, -w^2 + 4],\
[41, 41, -w^2 + 2*w + 3],\
[43, 43, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - w + 3],\
[43, 43, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w + 2],\
[64, 2, -2],\
[71, 71, w^5 - 3*w^4 - w^3 + 6*w^2 - 2*w + 2],\
[71, 71, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - w + 5],\
[71, 71, w^4 - 3*w^3 - 2*w^2 + 6*w + 2],\
[71, 71, 2*w^5 - 6*w^4 - 4*w^3 + 19*w^2 - w - 12],\
[83, 83, -w^4 + w^3 + 5*w^2 - w - 6],\
[83, 83, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 1],\
[97, 97, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 5*w + 4],\
[97, 97, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + 2*w - 2],\
[113, 113, -2*w^4 + 3*w^3 + 8*w^2 - 6*w - 6],\
[113, 113, -w^5 + 4*w^4 - w^3 - 12*w^2 + 9*w + 10],\
[113, 113, -w^5 + w^4 + 5*w^3 + w^2 - 7*w - 9],\
[113, 113, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 1],\
[125, 5, -w^5 + 4*w^4 - 12*w^2 + 4*w + 4],\
[125, 5, w^5 - w^4 - 6*w^3 + 2*w^2 + 9*w - 1],\
[139, 139, -w^4 + w^3 + 5*w^2 - 2*w - 8],\
[139, 139, w^5 - 4*w^4 + 13*w^2 - 4*w - 10],\
[167, 167, -w^5 + 3*w^4 + 2*w^3 - 11*w^2 + 2*w + 9],\
[167, 167, -w^5 + 7*w^3 + 2*w^2 - 9*w - 3],\
[167, 167, 2*w^5 - 6*w^4 - 3*w^3 + 15*w^2 - w - 5],\
[167, 167, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 8],\
[167, 167, -w^5 + 5*w^4 - 3*w^3 - 13*w^2 + 11*w + 4],\
[167, 167, 2*w^4 - 5*w^3 - 4*w^2 + 11*w + 2],\
[169, 13, -w^4 + 2*w^3 + 2*w^2 - 3*w + 1],\
[169, 13, 2*w^4 - 4*w^3 - 7*w^2 + 9*w + 8],\
[181, 181, -w^5 + 4*w^4 - 14*w^2 + 5*w + 12],\
[181, 181, -w^3 + 2*w^2 + 3*w - 2],\
[181, 181, -w^3 + w^2 + 4*w - 2],\
[181, 181, 3*w^4 - 7*w^3 - 9*w^2 + 15*w + 9],\
[197, 197, w^5 - 2*w^4 - 5*w^3 + 5*w^2 + 8*w + 3],\
[197, 197, -w^5 + 8*w^3 + w^2 - 14*w - 4],\
[197, 197, w^4 - w^3 - 6*w^2 + 5*w + 6],\
[197, 197, w^5 - 3*w^4 - 3*w^3 + 12*w^2 - 10],\
[211, 211, -w^5 + 4*w^4 + w^3 - 13*w^2 + 2*w + 8],\
[211, 211, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 3*w - 3],\
[211, 211, -w^5 + 3*w^4 + w^3 - 8*w^2 + 3*w + 5],\
[211, 211, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 3],\
[223, 223, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 6*w + 2],\
[223, 223, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - w + 4],\
[293, 293, w^5 - 8*w^3 - w^2 + 13*w + 4],\
[293, 293, -w^5 + 5*w^4 - 2*w^3 - 15*w^2 + 8*w + 9],\
[307, 307, -w^5 + 4*w^4 + w^3 - 13*w^2 + w + 10],\
[307, 307, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + w - 6],\
[307, 307, -w^5 + 3*w^4 + w^3 - 8*w^2 + 4*w + 6],\
[307, 307, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*w - 5],\
[307, 307, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 9*w + 4],\
[307, 307, 2*w^4 - 4*w^3 - 9*w^2 + 10*w + 11],\
[337, 337, w^5 - 4*w^4 - w^3 + 13*w^2 - 2*w - 5],\
[337, 337, -w^5 + w^4 + 5*w^3 + w^2 - 9*w - 5],\
[337, 337, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 6*w + 2],\
[337, 337, -2*w^4 + 4*w^3 + 9*w^2 - 12*w - 11],\
[337, 337, w^5 - w^4 - 7*w^3 + 5*w^2 + 9*w - 2],\
[337, 337, -w^5 + 5*w^4 - 2*w^3 - 14*w^2 + 7*w + 8],\
[349, 349, 2*w^4 - 4*w^3 - 9*w^2 + 10*w + 13],\
[349, 349, w^5 - 5*w^4 + 3*w^3 + 15*w^2 - 12*w - 11],\
[379, 379, -w^5 + 5*w^4 - 2*w^3 - 15*w^2 + 7*w + 11],\
[379, 379, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 1],\
[379, 379, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 8*w - 1],\
[379, 379, -w^5 + 3*w^4 + 3*w^3 - 10*w^2 - 4*w + 8],\
[379, 379, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w + 2],\
[379, 379, 2*w^4 - 3*w^3 - 8*w^2 + 5*w + 10],\
[419, 419, -w^5 + w^4 + 6*w^3 - 10*w - 9],\
[419, 419, w^4 - 2*w^3 - w^2 + w - 3],\
[419, 419, -2*w^5 + 5*w^4 + 6*w^3 - 14*w^2 - 5*w + 6],\
[419, 419, w^5 - 4*w^4 + 14*w^2 - 7*w - 13],\
[421, 421, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 8*w + 2],\
[421, 421, 3*w^4 - 6*w^3 - 11*w^2 + 15*w + 12],\
[421, 421, -3*w^4 + 6*w^3 + 11*w^2 - 13*w - 13],\
[421, 421, w^5 - 4*w^4 - w^3 + 15*w^2 - 4*w - 13],\
[433, 433, -2*w^3 + 3*w^2 + 6*w - 3],\
[433, 433, w^5 - 3*w^4 - w^3 + 5*w^2 + 3],\
[433, 433, -w^5 + 2*w^4 + 3*w^3 - 6*w^2 + 5],\
[433, 433, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 6*w - 3],\
[449, 449, w^5 - 5*w^4 + w^3 + 17*w^2 - 7*w - 11],\
[449, 449, 2*w^4 - 4*w^3 - 7*w^2 + 10*w + 9],\
[463, 463, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 3],\
[463, 463, w^5 - 9*w^3 + 16*w + 3],\
[463, 463, -w^5 + 5*w^4 - w^3 - 17*w^2 + 6*w + 11],\
[463, 463, -2*w^4 + 5*w^3 + 4*w^2 - 11*w - 1],\
[491, 491, 3*w^4 - 7*w^3 - 9*w^2 + 16*w + 10],\
[491, 491, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4],\
[491, 491, w^3 - w^2 - 3*w - 3],\
[491, 491, -w^3 + 2*w^2 + 2*w - 6],\
[491, 491, -w^5 + 4*w^4 + w^3 - 12*w^2 + 4],\
[491, 491, 3*w^4 - 5*w^3 - 12*w^2 + 11*w + 13],\
[503, 503, -w^3 + 4*w^2 + w - 8],\
[503, 503, -w^5 + 4*w^4 - w^3 - 10*w^2 + 7*w + 6],\
[547, 547, w^5 - 3*w^4 - w^3 + 7*w^2 - 3*w - 4],\
[547, 547, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - w - 3],\
[587, 587, w^5 - 5*w^4 + 3*w^3 + 14*w^2 - 11*w - 11],\
[587, 587, w^5 - 7*w^3 - 3*w^2 + 11*w + 9],\
[601, 601, w^5 - 5*w^4 + 2*w^3 + 15*w^2 - 7*w - 9],\
[601, 601, w^5 - 8*w^3 - w^2 + 14*w + 3],\
[631, 631, w^5 - 2*w^4 - 4*w^3 + 4*w^2 + 6*w - 1],\
[631, 631, -w^5 + 3*w^4 + 2*w^3 - 6*w^2 - 3*w - 3],\
[631, 631, -w^5 + 2*w^4 + 4*w^3 - 8*w^2 - 2*w + 8],\
[631, 631, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + w + 4],\
[643, 643, w^5 - 4*w^4 + 12*w^2 - 4*w - 10],\
[643, 643, -3*w^4 + 6*w^3 + 10*w^2 - 14*w - 10],\
[643, 643, -3*w^4 + 6*w^3 + 10*w^2 - 12*w - 11],\
[643, 643, -w^5 + 3*w^4 + w^3 - 9*w^2 + 5*w + 6],\
[659, 659, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w + 1],\
[659, 659, 2*w^4 - 5*w^3 - 4*w^2 + 9*w + 1],\
[659, 659, -2*w^4 + 4*w^3 + 5*w^2 - 6*w - 2],\
[659, 659, 2*w^4 - 4*w^3 - 5*w^2 + 8*w + 1],\
[659, 659, -2*w^4 + 3*w^3 + 7*w^2 - 6*w - 3],\
[659, 659, -w^5 + 4*w^4 - 12*w^2 + 3*w + 5],\
[673, 673, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 10],\
[673, 673, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 8],\
[701, 701, -4*w^4 + 8*w^3 + 12*w^2 - 17*w - 8],\
[701, 701, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 2*w - 6],\
[701, 701, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 5*w - 5],\
[701, 701, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 3*w + 1],\
[701, 701, w^5 - w^4 - 7*w^3 + 6*w^2 + 7*w - 4],\
[727, 727, w^3 - w^2 - 2*w - 3],\
[727, 727, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - 3*w - 10],\
[727, 727, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 6],\
[727, 727, -w^3 + 2*w^2 + w - 5],\
[729, 3, -3],\
[743, 743, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 12*w - 5],\
[743, 743, 2*w^5 - 7*w^4 - w^3 + 20*w^2 - 7*w - 12],\
[757, 757, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 11],\
[757, 757, -w^5 + 4*w^4 + 2*w^3 - 15*w^2 - w + 10],\
[757, 757, -w^5 + w^4 + 8*w^3 - 5*w^2 - 14*w + 1],\
[757, 757, -2*w^4 + 3*w^3 + 10*w^2 - 9*w - 13],\
[769, 769, w^5 - 3*w^4 + 5*w^2 - 4*w - 1],\
[769, 769, -w^5 + 2*w^4 + 2*w^3 - 3*w^2 + w - 2],\
[797, 797, -w^5 + 5*w^4 - w^3 - 17*w^2 + 5*w + 12],\
[797, 797, w^5 - 9*w^3 + 17*w + 3],\
[811, 811, -w^4 + w^3 + 4*w^2 - 6],\
[811, 811, w^4 - 3*w^3 - w^2 + 7*w + 2],\
[827, 827, w^5 + w^4 - 9*w^3 - 5*w^2 + 16*w + 6],\
[827, 827, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 10*w + 2],\
[827, 827, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + 2*w - 9],\
[827, 827, -2*w^5 + 6*w^4 + 5*w^3 - 17*w^2 - 7*w + 6],\
[839, 839, -2*w^5 + 6*w^4 + 4*w^3 - 18*w^2 - w + 10],\
[839, 839, -w^5 + 4*w^4 - w^3 - 12*w^2 + 7*w + 12],\
[839, 839, -w^5 + w^4 + 5*w^3 + w^2 - 9*w - 9],\
[839, 839, -2*w^5 + 4*w^4 + 8*w^3 - 10*w^2 - 11*w + 1],\
[841, 29, -3*w^4 + 6*w^3 + 11*w^2 - 14*w - 12],\
[841, 29, -2*w^4 + 4*w^3 + 9*w^2 - 11*w - 11],\
[853, 853, -w^4 + 6*w^2 + w - 4],\
[853, 853, -w^5 + 5*w^4 - 2*w^3 - 17*w^2 + 9*w + 15],\
[853, 853, -w^5 + 8*w^3 + 3*w^2 - 16*w - 9],\
[853, 853, w^4 - 4*w^3 + 9*w - 2],\
[881, 881, -w - 3],\
[881, 881, w - 4],\
[883, 883, w^2 + w - 5],\
[883, 883, w^5 - 7*w^3 - 5*w^2 + 13*w + 11],\
[883, 883, w^5 - 5*w^4 + 3*w^3 + 16*w^2 - 13*w - 13],\
[883, 883, w^2 - 3*w - 3],\
[911, 911, -w^5 + 2*w^4 + 4*w^3 - 4*w^2 - 4*w - 3],\
[911, 911, -w^4 + 3*w^3 + 2*w^2 - 5*w - 5],\
[937, 937, -2*w^5 + 4*w^4 + 6*w^3 - 10*w^2 - 2*w + 3],\
[937, 937, -w^5 + 4*w^4 - 10*w^2 + 2*w + 1],\
[937, 937, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 4],\
[937, 937, -2*w^4 + 5*w^3 + 4*w^2 - 7*w - 2],\
[953, 953, w^5 - 4*w^4 + 2*w^3 + 9*w^2 - 9*w - 4],\
[953, 953, w^5 - w^4 - 4*w^3 - w^2 + 4*w + 5],\
[967, 967, -2*w^5 + 5*w^4 + 6*w^3 - 13*w^2 - 7*w + 2],\
[967, 967, w^4 - 3*w^3 - 3*w^2 + 10*w + 3],\
[967, 967, -w^4 + w^3 + 6*w^2 - w - 8],\
[967, 967, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 5*w + 9],\
[1021, 1021, w^5 - 3*w^4 - 2*w^3 + 11*w^2 - 3*w - 8],\
[1021, 1021, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 4],\
[1049, 1049, -w^5 + w^4 + 5*w^3 - 2*w^2 - 4*w - 2],\
[1049, 1049, 2*w^5 - 6*w^4 - 4*w^3 + 17*w^2 + 2*w - 8],\
[1049, 1049, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 10*w - 3],\
[1049, 1049, w^5 - 4*w^4 + w^3 + 9*w^2 - 6*w - 3],\
[1051, 1051, -w^5 + 7*w^3 + 3*w^2 - 10*w - 9],\
[1051, 1051, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 3],\
[1051, 1051, -w^5 + 4*w^4 + w^3 - 12*w^2 - w + 6],\
[1051, 1051, w^5 - 5*w^4 + 3*w^3 + 14*w^2 - 12*w - 10],\
[1063, 1063, 2*w^5 - 5*w^4 - 6*w^3 + 16*w^2 + 3*w - 9],\
[1063, 1063, -2*w^5 + 5*w^4 + 6*w^3 - 12*w^2 - 7*w + 1],\
[1091, 1091, -w^4 + 2*w^3 + 4*w^2 - 3*w - 8],\
[1091, 1091, -w^4 + 2*w^3 + 4*w^2 - 7*w - 6],\
[1093, 1093, 3*w^5 - 10*w^4 - 4*w^3 + 30*w^2 - 5*w - 16],\
[1093, 1093, 3*w^4 - 5*w^3 - 11*w^2 + 10*w + 9],\
[1093, 1093, 3*w^4 - 7*w^3 - 8*w^2 + 15*w + 6],\
[1093, 1093, 2*w^5 - 2*w^4 - 11*w^3 + 4*w^2 + 14*w + 4],\
[1217, 1217, -w^5 + 4*w^4 + w^3 - 12*w^2 - w + 5],\
[1217, 1217, -w^5 + 6*w^4 - 4*w^3 - 19*w^2 + 13*w + 15],\
[1217, 1217, -w^5 - w^4 + 10*w^3 + 5*w^2 - 18*w - 10],\
[1217, 1217, w^5 - w^4 - 7*w^3 + 5*w^2 + 11*w - 4],\
[1231, 1231, -w^4 + w^3 + 7*w^2 - 3*w - 8],\
[1231, 1231, w^4 - 3*w^3 - 4*w^2 + 10*w + 4],\
[1259, 1259, -w^5 - w^4 + 9*w^3 + 9*w^2 - 17*w - 19],\
[1259, 1259, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 4*w - 10],\
[1259, 1259, -w^5 + 7*w^4 - 6*w^3 - 22*w^2 + 17*w + 16],\
[1259, 1259, 2*w^5 - 6*w^4 - 3*w^3 + 17*w^2 - w - 13],\
[1289, 1289, -w^5 + 3*w^4 + 2*w^3 - 11*w^2 + 3*w + 9],\
[1289, 1289, w^5 - 8*w^3 - w^2 + 14*w + 2],\
[1289, 1289, w^5 - 5*w^4 + 2*w^3 + 15*w^2 - 7*w - 8],\
[1289, 1289, w^5 - 2*w^4 - 4*w^3 + 3*w^2 + 6*w + 5],\
[1301, 1301, w^5 - w^4 - 7*w^3 + 2*w^2 + 14*w + 2],\
[1301, 1301, w^5 - 4*w^4 - 2*w^3 + 13*w^2 + w - 4],\
[1301, 1301, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 - w + 9],\
[1301, 1301, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 9*w - 1],\
[1301, 1301, 2*w^5 - w^4 - 15*w^3 + 26*w + 10],\
[1301, 1301, w^5 - 8*w^3 + 13*w + 2],\
[1303, 1303, -w^5 + 3*w^4 + w^3 - 5*w^2 + w - 2],\
[1303, 1303, w^5 + w^4 - 8*w^3 - 7*w^2 + 13*w + 9],\
[1303, 1303, -2*w^5 + 2*w^4 + 13*w^3 - 5*w^2 - 21*w - 6],\
[1303, 1303, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - w - 3],\
[1373, 1373, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 3*w - 4],\
[1373, 1373, -2*w^5 + 7*w^4 + 3*w^3 - 21*w^2 - 2*w + 12],\
[1373, 1373, -w^5 + w^4 + 6*w^3 - 2*w^2 - 11*w - 1],\
[1373, 1373, w^5 - 4*w^4 + 12*w^2 - 2*w - 8],\
[1373, 1373, -2*w^5 + 3*w^4 + 11*w^3 - 10*w^2 - 17*w + 3],\
[1373, 1373, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 5],\
[1399, 1399, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 5*w + 8],\
[1399, 1399, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 8*w + 1],\
[1399, 1399, -2*w^5 + 6*w^4 + 4*w^3 - 17*w^2 + 8],\
[1399, 1399, w^5 - 3*w^4 + 6*w^2 - 6*w - 2],\
[1427, 1427, -2*w^4 + 3*w^3 + 10*w^2 - 9*w - 11],\
[1427, 1427, -2*w^4 + 5*w^3 + 7*w^2 - 12*w - 9],\
[1429, 1429, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 2],\
[1429, 1429, -w^4 + 7*w^2 - 2*w - 3],\
[1429, 1429, -w^5 + 2*w^4 + 4*w^3 - 2*w^2 - 7*w - 4],\
[1429, 1429, -3*w^5 + 8*w^4 + 8*w^3 - 23*w^2 - 5*w + 13],\
[1471, 1471, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 8*w + 3],\
[1471, 1471, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 5],\
[1483, 1483, w^4 - 3*w^3 + 4*w - 4],\
[1483, 1483, w^4 - w^3 - 3*w^2 + w - 2],\
[1499, 1499, -w^5 + 3*w^4 + 2*w^3 - 9*w^2 - 2*w + 4],\
[1499, 1499, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w + 3],\
[1511, 1511, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 4*w + 5],\
[1511, 1511, -2*w^5 + 5*w^4 + 5*w^3 - 15*w^2 + 8],\
[1511, 1511, 3*w^5 - 10*w^4 - 4*w^3 + 31*w^2 - 5*w - 20],\
[1511, 1511, 2*w^5 - 5*w^4 - 6*w^3 + 13*w^2 + 6*w - 5],\
[1553, 1553, w^5 - 3*w^4 - 2*w^3 + 7*w^2 + 3*w + 2],\
[1553, 1553, -w^5 + 2*w^4 + 4*w^3 - 7*w^2 - 4*w + 8],\
[1567, 1567, -3*w^4 + 7*w^3 + 7*w^2 - 15*w - 1],\
[1567, 1567, -2*w^5 + 6*w^4 + 4*w^3 - 19*w^2 - w + 13],\
[1583, 1583, -3*w^5 + 6*w^4 + 13*w^3 - 18*w^2 - 15*w + 6],\
[1583, 1583, 2*w^5 - 3*w^4 - 10*w^3 + 9*w^2 + 10*w - 3],\
[1583, 1583, 2*w^5 - 4*w^4 - 7*w^3 + 12*w^2 + 5*w - 9],\
[1583, 1583, -w^5 + w^4 + 5*w^3 + 2*w^2 - 10*w - 9],\
[1597, 1597, 2*w^5 - 5*w^4 - 7*w^3 + 15*w^2 + 7*w - 4],\
[1597, 1597, w^5 - 4*w^4 + 12*w^2 - 5*w - 9],\
[1597, 1597, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w - 5],\
[1597, 1597, 2*w^5 - 5*w^4 - 7*w^3 + 16*w^2 + 6*w - 8],\
[1609, 1609, w^5 - 7*w^3 - 4*w^2 + 13*w + 10],\
[1609, 1609, w^4 - 4*w^3 + 8*w - 1],\
[1609, 1609, -w^4 + 6*w^2 - 4],\
[1609, 1609, w^5 - 5*w^4 + 3*w^3 + 15*w^2 - 11*w - 13],\
[1667, 1667, -w^5 + 9*w^3 - 17*w - 4],\
[1667, 1667, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 4*w - 8],\
[1667, 1667, 2*w^5 - 5*w^4 - 5*w^3 + 12*w^2 + 4*w - 3],\
[1667, 1667, w^5 - 5*w^4 + w^3 + 17*w^2 - 5*w - 13],\
[1681, 41, 3*w^2 - 3*w - 5],\
[1681, 41, -3*w^4 + 6*w^3 + 12*w^2 - 15*w - 16],\
[1693, 1693, w^5 - w^4 - 6*w^3 + w^2 + 8*w + 6],\
[1693, 1693, -w^5 + 4*w^4 - 12*w^2 + 7*w + 3],\
[1693, 1693, w^5 - 6*w^4 + 4*w^3 + 22*w^2 - 17*w - 20],\
[1693, 1693, w^5 - 4*w^4 + w^3 + 13*w^2 - 9*w - 13],\
[1709, 1709, -w^5 - w^4 + 10*w^3 + 6*w^2 - 20*w - 13],\
[1709, 1709, -w^5 + 4*w^4 - w^3 - 11*w^2 + 7*w + 10],\
[1709, 1709, 2*w^4 - 4*w^3 - 6*w^2 + 5*w + 8],\
[1709, 1709, 3*w^5 - 7*w^4 - 10*w^3 + 19*w^2 + 10*w - 3],\
[1709, 1709, -w^5 + w^4 + 5*w^3 - 7*w - 8],\
[1709, 1709, w^4 - 3*w^3 - w^2 + 3*w - 1],\
[1723, 1723, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w + 2],\
[1723, 1723, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + w - 4],\
[1847, 1847, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\
[1847, 1847, -2*w^5 + 6*w^4 + 5*w^3 - 19*w^2 - 2*w + 13],\
[1849, 43, w^4 - 2*w^3 - 6*w^2 + 7*w + 8],\
[1849, 43, -3*w^4 + 6*w^3 + 11*w^2 - 14*w - 13],\
[1861, 1861, -w^5 + 9*w^3 - 2*w^2 - 14*w + 2],\
[1861, 1861, -w^5 + 4*w^4 - w^3 - 10*w^2 + 3*w + 4],\
[1861, 1861, -w^5 + w^4 + 5*w^3 - w^2 - 9*w + 1],\
[1861, 1861, -w^5 + 5*w^4 - w^3 - 15*w^2 + 4*w + 6],\
[1877, 1877, -2*w^5 + 7*w^4 + 2*w^3 - 21*w^2 + 4*w + 15],\
[1877, 1877, 2*w^5 - 6*w^4 - 3*w^3 + 17*w^2 - 3*w - 10],\
[1877, 1877, w^5 - w^4 - 6*w^3 + w^2 + 12*w + 3],\
[1877, 1877, -w^5 + 4*w^4 - 13*w^2 + 3*w + 10],\
[1877, 1877, -2*w^5 + 4*w^4 + 7*w^3 - 8*w^2 - 8*w - 3],\
[1877, 1877, 2*w^5 - 3*w^4 - 10*w^3 + 7*w^2 + 14*w + 5],\
[1889, 1889, -w^5 + 5*w^4 - w^3 - 15*w^2 + 4*w + 4],\
[1889, 1889, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 10*w - 3],\
[1931, 1931, -2*w^5 + 5*w^4 + 7*w^3 - 17*w^2 - 4*w + 10],\
[1931, 1931, -2*w^5 + 6*w^4 + 3*w^3 - 19*w^2 + 5*w + 12],\
[1933, 1933, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 4*w - 4],\
[1933, 1933, w^5 - 6*w^4 + 3*w^3 + 22*w^2 - 13*w - 16],\
[1933, 1933, -2*w^5 + 8*w^4 - 23*w^2 + 7*w + 13],\
[1933, 1933, -w^5 + 3*w^4 - 3*w^2 + 3*w - 6],\
[1987, 1987, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 5*w - 1],\
[1987, 1987, 2*w^5 - 5*w^4 - 4*w^3 + 10*w^2 + 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-3, 3, -1, 5, 4, 4, 10, -2, -1, 4, 5, 8, 8, -10, 8, 5, -7, -2, 10, -15, 16, 16, 9, -9, -3, 9, -21, 0, 1, -23, 13, 25, 0, 15, 9, -7, 15, 3, 23, -2, 6, -6, -8, -4, 2, -28, -10, 8, 2, -33, 9, -11, -12, -10, 20, 6, -5, 23, -18, -10, 32, 12, -25, 9, -15, 1, 36, 9, -15, 12, -5, -6, -21, -27, -24, 17, 20, 2, 5, -2, -2, 10, -20, -20, 22, -28, 35, 29, 32, -12, -15, 27, 3, 33, 12, -13, 35, -35, 19, 12, 42, -8, -26, 8, -40, -34, -40, 47, -18, -42, -19, 29, -24, -38, -26, 0, 23, -2, 4, 38, 46, 30, -38, 2, -2, 14, 2, 28, 10, 15, 9, 16, -1, 17, -50, -14, -14, -56, 4, 2, 50, -33, -40, -22, -9, -22, 32, -16, -40, -22, 17, 42, 40, 40, 6, 30, 30, -33, 30, 18, 27, -36, 42, -9, 6, 6, -39, 12, 30, -51, 4, -14, -15, -4, -58, -12, -54, 6, 12, -27, -29, -11, 9, -9, 63, 36, -36, -14, -26, -50, -26, -42, -63, -27, -54, -8, -8, -66, 33, 63, -42, 9, -15, -51, 3, -66, -34, 16, 4, -40, -42, -71, 34, -14, -11, 67, -3, 35, -1, -57, 13, 52, 57, 15, -32, -53, 19, 59, 12, -60, -37, 20, -10, -16, -58, -64, 2, -36, -40, -64, 0, 9, -33, -26, -26, -11, 0, 36, -41, 76, 18, 18, -38, 67, 46, 16, -29, 78, -40, 32, 12, -46, -34, -48, 36, -66, -42, -6, -34, -18, -30, 50, -6, 14, 20, -74, -62, 42, 78, 10, 2, -22, -62, -8, 26, -3, 9, 62, -32, 44, 14, 87, -33, -8, 28, 34, -26, -76, -28]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([43, 43, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 - w + 3])] = 1

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