/*
  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 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 2])

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^2 - 7*x + 11
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-2, -2, e - 4, e, -e + 9, 3*e - 11, -5*e + 15, -e + 7, 4*e - 12, 1, 6*e - 19, -2*e, 2*e - 8, -10*e + 40, -2*e + 4, -6*e + 16, -6*e + 16, -11*e + 32, e - 4, 9*e - 33, -3*e + 14, 9*e - 26, e - 5, 13*e - 45, 9*e - 41, -6*e + 22, 6*e - 26, 12*e - 34, 12*e - 42, -4*e + 26, 4*e - 18, -16*e + 58, -14, -4*e + 14, 4*e - 26, -3*e + 30, -e - 12, -9*e + 20, e + 14, 11*e - 37, -e - 2, -5*e + 2, -17*e + 63, -12*e + 42, -2*e - 2, -2*e - 10, 20*e - 70, -6*e + 22, 10*e - 46, 21*e - 67, -15*e + 49, -20*e + 62, -12*e + 36, -18, -20*e + 70, 12*e - 32, -12*e + 34, -7*e + 33, -17*e + 58, -9*e + 40, -13*e + 64, -e + 14, 9*e - 51, -9*e + 11, -e - 1, -10*e + 38, 6*e + 8, -6*e - 2, 10*e - 30, 2*e - 32, -6*e + 6, -14*e + 48, 12*e - 48, -12, 2*e - 8, 3*e - 30, e + 11, e - 9, 23*e - 66, 27*e - 91, -11*e + 37, e - 11, -13*e + 33, 3*e - 46, -13*e + 54, -8*e + 34, 12*e - 58, -24*e + 82, -4*e + 14, -20*e + 52, 10*e - 42, 16*e - 72, 24*e - 92, 14*e - 46, -4*e + 36, -14*e + 34, 6*e - 2, 20*e - 54, -8*e + 50, 10*e - 38, -22*e + 86, 9*e - 59, -19*e + 65, 20*e - 70, 24*e - 84, -16*e + 56, 20*e - 90, 0, 24*e - 96, -4*e + 36, 4*e - 28, -18*e + 58, -12*e + 38, -6*e - 12, -30*e + 100, -12*e + 66, -22*e + 82, 19*e - 56, 3*e + 24, e - 25, -15*e + 54, 28*e - 90, -11*e + 54, -35*e + 115, 10*e - 14, -10*e + 50, -10*e + 10, -6*e + 54, -5*e + 6, 36*e - 120, -4*e + 24, -5*e + 44, 19*e - 63, 31*e - 119, 7*e - 40, 15*e - 64, -29*e + 88, -7*e, 5*e + 8, -4*e, -12*e + 48, -4*e + 36, -10*e + 48, -22*e + 104, -24*e + 92, 10*e + 8, -10, 36*e - 114, 30*e - 124, -20*e + 50, 46, -5*e - 3, -25*e + 114, -e + 42, 15*e - 19, 9*e - 28, e - 12, -10*e + 14, 16*e - 80, -36*e + 128, 10*e - 30, 30*e - 82, -2*e - 30, 39*e - 131, -7*e - 16, -31*e + 120, 19*e - 103, -e + 25, 7*e - 51, -6*e, -6*e, -34*e + 112, 18*e - 76, -7*e - 5, -11*e + 27, -26, -32*e + 102, -8*e + 38, 40*e - 146, -44, -4*e - 18, 16*e - 18, -4*e - 8, -4*e - 30, 32*e - 94, -18*e + 56, -14*e + 56, 25*e - 117, -19*e + 49, -23*e + 69, -11*e + 47, -39*e + 153, 32*e - 86, 8*e + 10, 25*e - 55, 12*e - 6, 20*e - 74, 26*e - 94, 18*e - 78, 14*e - 70, 18*e - 54, -e + 42, -29*e + 74, 35*e - 110, 3*e - 22, -5*e + 37, -3*e + 6, 49*e - 176, -39*e + 136, -39*e + 130, 3*e - 31, 2*e + 46, 28*e - 126, -8*e + 70, 2*e - 34, 39*e - 140, -25*e + 68, -e - 36, -33*e + 92, 11*e - 12, -29*e + 108, -20*e + 68, -38*e + 108, 6*e - 72, 32*e - 132, -26*e + 50, 10*e - 98, 11*e + 7, -e - 28, -61*e + 208, -13*e + 51, 6*e - 70, -30*e + 110, 46*e - 148, 2*e - 56, -2*e + 26, 22*e - 86, 28*e - 74, 4*e + 8, -44*e + 176, 32*e - 122, 19*e - 102, 23*e - 54, 24*e - 70, 32*e - 122, -16*e + 74, -44*e + 138, -12*e + 70, -6, 11*e - 66, -16*e + 110, -32*e + 94, -37*e + 150, 5*e - 9, 28*e - 70, 68*e - 238, 13*e - 37, 18*e - 28, 68*e - 236, 32*e - 136, 30*e - 72, -4*e - 6, -44*e + 146, -40*e + 162, -31*e + 110, -3*e - 46, -8*e - 6, -45*e + 182, e - 37, -9*e + 11, 3*e - 5, 17*e - 57, 27*e - 106, -20*e + 26, -8*e - 18, -44, -12*e - 8, -21*e + 65, 35*e - 139, 24*e - 50, 21*e - 55, -35*e + 157, 24*e - 98, 41*e - 115, -17*e + 66, -52*e + 166, -12*e + 54, 23*e - 110, -19*e + 93, -43*e + 118, -3*e + 46, 22*e - 32, 22*e - 24, 49*e - 150, 35*e - 79, -45*e + 129, -15*e + 6, -44*e + 178, -12*e + 34]
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 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 2])] = -1

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