/*
  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([1, -1, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 5, w^2 + w - 2])

primes_array = [
[3, 3, w + 1],\
[5, 5, -w^3 + 5*w + 2],\
[5, 5, w - 1],\
[11, 11, -w^3 + 5*w],\
[13, 13, -w^3 + w^2 + 6*w - 3],\
[16, 2, 2],\
[19, 19, 2*w^3 - w^2 - 11*w + 2],\
[25, 5, -w^2 + w + 3],\
[27, 3, w^3 - w^2 - 5*w + 4],\
[31, 31, -w - 3],\
[37, 37, -w^3 - w^2 + 6*w + 4],\
[41, 41, w^3 + w^2 - 6*w - 5],\
[43, 43, w^3 - 7*w - 2],\
[47, 47, -2*w^3 + 11*w + 2],\
[61, 61, w^2 - 3],\
[67, 67, w^2 + w - 4],\
[79, 79, -4*w^3 + 2*w^2 + 22*w - 9],\
[97, 97, -3*w^3 + 2*w^2 + 19*w - 6],\
[97, 97, -w^3 + 6*w - 3],\
[97, 97, -3*w^3 + 16*w],\
[97, 97, -w^3 + w^2 + 4*w - 3],\
[101, 101, -2*w^3 + w^2 + 11*w - 6],\
[103, 103, w^3 - w^2 - 7*w],\
[109, 109, -w^3 - w^2 + 6*w + 2],\
[121, 11, 2*w^3 - 11*w + 1],\
[127, 127, -2*w^3 + w^2 + 13*w - 1],\
[127, 127, w^3 - w^2 - 6*w - 2],\
[157, 157, -2*w^3 + 2*w^2 + 10*w - 7],\
[157, 157, w - 4],\
[163, 163, 2*w^3 - w^2 - 13*w + 3],\
[173, 173, -2*w^3 + w^2 + 13*w - 6],\
[173, 173, 2*w^3 - 12*w + 1],\
[173, 173, 2*w^3 - 11*w + 2],\
[173, 173, w^2 + w - 5],\
[179, 179, -2*w^3 + 10*w + 3],\
[181, 181, -w^3 - w^2 + 7*w + 8],\
[191, 191, w^3 - 5*w - 5],\
[191, 191, 2*w^3 - w^2 - 9*w - 1],\
[193, 193, -3*w^3 + 3*w^2 + 19*w - 7],\
[197, 197, -w^3 + w^2 + 6*w - 7],\
[223, 223, w^3 + w^2 - 6*w + 1],\
[227, 227, 6*w^3 - 3*w^2 - 34*w + 9],\
[227, 227, w^3 + w^2 - 8*w],\
[233, 233, 2*w^3 - 13*w - 3],\
[233, 233, -w^3 + 2*w^2 + 4*w - 6],\
[239, 239, -2*w^3 + 10*w + 1],\
[239, 239, w^3 - 8*w - 2],\
[251, 251, -3*w^3 + w^2 + 18*w],\
[251, 251, -5*w^3 + 2*w^2 + 30*w - 11],\
[263, 263, -2*w^3 + w^2 + 10*w + 2],\
[269, 269, 3*w^3 - 18*w - 8],\
[271, 271, 2*w^3 + w^2 - 10*w - 2],\
[271, 271, -3*w^3 + 19*w],\
[277, 277, -w^3 + w^2 + 4*w - 8],\
[277, 277, 2*w^3 + w^2 - 14*w - 8],\
[281, 281, w^3 - 8*w],\
[307, 307, 3*w^3 - w^2 - 16*w + 2],\
[307, 307, 2*w^3 - w^2 - 9*w + 1],\
[307, 307, -2*w^3 + 2*w^2 + 13*w - 7],\
[307, 307, -w^3 + w^2 + 7*w - 6],\
[313, 313, -3*w^3 + w^2 + 15*w + 4],\
[317, 317, -4*w^3 + w^2 + 22*w - 3],\
[317, 317, 2*w^3 - w^2 - 10*w - 3],\
[337, 337, w^3 + w^2 - 4*w - 5],\
[349, 349, -2*w^3 - w^2 + 11*w + 3],\
[349, 349, -4*w^3 + 2*w^2 + 24*w - 11],\
[353, 353, 3*w^3 - w^2 - 17*w + 7],\
[353, 353, -3*w^3 - 2*w^2 + 17*w + 11],\
[367, 367, 2*w^3 - 11*w - 7],\
[373, 373, -w^3 + w^2 + 4*w - 5],\
[383, 383, -4*w^3 + 3*w^2 + 23*w - 9],\
[383, 383, 4*w^3 - w^2 - 22*w],\
[389, 389, w^2 - 2*w - 5],\
[401, 401, -3*w^3 + 2*w^2 + 16*w - 9],\
[401, 401, 2*w^3 - w^2 - 14*w - 1],\
[409, 409, 2*w^3 + 2*w^2 - 13*w - 9],\
[419, 419, -4*w^3 + 24*w + 7],\
[419, 419, 2*w^2 + 2*w - 7],\
[419, 419, -w^3 + 2*w^2 + 8*w - 6],\
[419, 419, 6*w^3 - 3*w^2 - 33*w + 13],\
[431, 431, 2*w^3 - w^2 - 12*w - 5],\
[439, 439, -3*w^3 + 2*w^2 + 18*w - 4],\
[439, 439, w^3 + 2*w^2 - 7*w - 3],\
[443, 443, 6*w^3 - 3*w^2 - 33*w + 7],\
[449, 449, -3*w^3 + w^2 + 14*w - 4],\
[457, 457, 2*w^3 - 9*w],\
[457, 457, 3*w^3 - w^2 - 16*w - 2],\
[479, 479, 3*w^3 - w^2 - 19*w + 4],\
[487, 487, -w^3 + w^2 + 4*w - 6],\
[491, 491, 3*w^3 + w^2 - 17*w - 5],\
[499, 499, 5*w^3 - 3*w^2 - 28*w + 8],\
[499, 499, 2*w^3 - w^2 - 12*w - 1],\
[503, 503, -2*w^3 - w^2 + 12*w + 3],\
[503, 503, w^3 - 3*w - 4],\
[509, 509, -3*w - 5],\
[509, 509, -4*w^3 + 3*w^2 + 25*w - 10],\
[523, 523, -2*w^3 + w^2 + 14*w - 6],\
[529, 23, 4*w^3 - 2*w^2 - 21*w + 5],\
[529, 23, -3*w^3 - w^2 + 15*w + 6],\
[557, 557, -2*w^3 + w^2 + 13*w + 2],\
[557, 557, 3*w^3 - 2*w^2 - 16*w + 3],\
[569, 569, 2*w^2 - w - 8],\
[587, 587, w^3 + 2*w^2 - 5*w - 16],\
[587, 587, -4*w^3 + w^2 + 25*w - 5],\
[599, 599, w^3 + 2*w^2 - 6*w - 5],\
[599, 599, -5*w^3 + 3*w^2 + 30*w - 15],\
[601, 601, w^3 - 6*w - 6],\
[607, 607, -w^3 + w^2 + 3*w - 4],\
[607, 607, -w^3 + 2*w - 3],\
[613, 613, 6*w^3 - 2*w^2 - 31*w + 11],\
[613, 613, w^3 + w^2 - 4*w - 6],\
[617, 617, 5*w^3 - w^2 - 30*w + 2],\
[617, 617, -2*w^3 + 2*w^2 + 9*w + 3],\
[619, 619, -w^3 + 2*w^2 + 6*w - 5],\
[619, 619, 2*w^3 - w^2 - 11*w - 3],\
[631, 631, -w^3 + 2*w^2 + 5*w - 5],\
[631, 631, -3*w^3 - w^2 + 18*w + 5],\
[647, 647, 6*w^3 - w^2 - 36*w + 2],\
[659, 659, 4*w^3 + w^2 - 24*w - 14],\
[661, 661, 2*w^2 - w - 4],\
[673, 673, 2*w^3 + w^2 - 14*w - 12],\
[677, 677, 3*w^3 + 2*w^2 - 16*w - 7],\
[677, 677, -3*w^3 + w^2 + 15*w + 1],\
[683, 683, 2*w^2 - 2*w - 9],\
[683, 683, 2*w^3 - 14*w + 1],\
[691, 691, 5*w^3 - 2*w^2 - 30*w + 6],\
[701, 701, -2*w^3 + w^2 + 12*w + 2],\
[701, 701, -5*w^3 + 2*w^2 + 26*w],\
[719, 719, 3*w^3 - 18*w + 1],\
[719, 719, 3*w^3 - w^2 - 19*w + 1],\
[727, 727, -3*w^2 - 2*w + 11],\
[727, 727, 2*w^3 + w^2 - 13*w - 2],\
[733, 733, 2*w^3 - 3*w^2 - 8*w + 5],\
[739, 739, -3*w^3 + 16*w - 6],\
[743, 743, -4*w^3 - w^2 + 25*w + 8],\
[751, 751, w^2 - 2*w - 7],\
[751, 751, -3*w^3 + 15*w + 5],\
[757, 757, 3*w^3 - 19*w - 2],\
[761, 761, 2*w^2 + w - 5],\
[769, 769, -2*w^3 + w^2 + 14*w - 9],\
[769, 769, 2*w^2 - w - 7],\
[773, 773, w^3 - w^2 - 5*w - 4],\
[773, 773, w^3 - 3*w - 6],\
[787, 787, 3*w^3 - 19*w - 3],\
[797, 797, 8*w^3 - 3*w^2 - 47*w + 10],\
[809, 809, 4*w^3 - 25*w - 1],\
[811, 811, w^3 - 9*w - 1],\
[821, 821, 6*w^3 - 3*w^2 - 35*w + 8],\
[823, 823, 2*w^3 + w^2 - 10*w + 1],\
[823, 823, -2*w^3 + 2*w^2 + 7*w - 4],\
[829, 829, -5*w^3 + w^2 + 27*w - 4],\
[829, 829, 5*w^3 - 2*w^2 - 26*w + 10],\
[839, 839, w^3 + 2*w^2 - 5*w - 7],\
[839, 839, 3*w^3 - w^2 - 15*w + 2],\
[841, 29, 3*w^3 + w^2 - 14*w - 2],\
[841, 29, 4*w^3 - 2*w^2 - 21*w + 10],\
[857, 857, -8*w^3 + 4*w^2 + 44*w - 11],\
[857, 857, -3*w^3 + 3*w^2 + 20*w - 9],\
[859, 859, w^3 + 2*w^2 - 6*w - 6],\
[877, 877, w^3 - 3*w^2 - 4*w + 14],\
[883, 883, 2*w^3 + w^2 - 10*w - 11],\
[887, 887, 3*w^3 + w^2 - 20*w - 2],\
[919, 919, 7*w^3 - 3*w^2 - 39*w + 9],\
[929, 929, 3*w^3 - 17*w + 2],\
[929, 929, -6*w^3 + 2*w^2 + 35*w - 10],\
[937, 937, w^3 + w^2 - 3*w - 5],\
[937, 937, -2*w^3 + 3*w^2 + 12*w - 12],\
[937, 937, -3*w^3 - 2*w^2 + 19*w + 8],\
[937, 937, 3*w^3 - 2*w^2 - 13*w + 3],\
[941, 941, w^3 + 2*w^2 - 6*w - 8],\
[941, 941, 5*w^3 - w^2 - 28*w - 3],\
[947, 947, -4*w^3 + 2*w^2 + 25*w - 6],\
[953, 953, w^3 - 7*w - 7],\
[953, 953, -3*w^3 + 2*w^2 + 18*w - 3],\
[967, 967, w^3 - 2*w^2 - 5*w - 3],\
[971, 971, w^2 + 2*w - 6],\
[977, 977, 2*w^3 - 11*w - 8],\
[997, 997, -3*w^3 + w^2 + 17*w + 2],\
[997, 997, -2*w^3 + 2*w^2 + 14*w - 7]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 2*x^5 - 12*x^4 + 8*x^3 + 47*x^2 + 33*x + 5
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1, 1, -e^5 + 3*e^4 + 8*e^3 - 16*e^2 - 23*e, 2*e^3 - e^2 - 16*e - 8, -e^5 + 3*e^4 + 9*e^3 - 16*e^2 - 32*e - 10, e^5 - 3*e^4 - 9*e^3 + 16*e^2 + 32*e + 8, e^5 - 3*e^4 - 12*e^3 + 19*e^2 + 51*e + 17, -2*e^5 + 6*e^4 + 16*e^3 - 29*e^2 - 53*e - 16, -e^4 + 2*e^3 + 8*e^2 - 9*e - 10, e^4 - e^3 - 7*e^2 - 2*e + 5, e^5 - 3*e^4 - 6*e^3 + 14*e^2 + 11*e - 7, e^4 + 3*e^3 - 12*e^2 - 26*e - 4, -e^5 + e^4 + 15*e^3 - 5*e^2 - 56*e - 22, e^5 - 5*e^4 - 9*e^3 + 32*e^2 + 47*e + 12, e^5 - 4*e^4 - 10*e^3 + 24*e^2 + 49*e + 11, -e^5 + 3*e^4 + 11*e^3 - 17*e^2 - 45*e - 20, -2*e^4 + 4*e^3 + 10*e^2 - 8*e + 5, -2*e^5 + 5*e^4 + 12*e^3 - 16*e^2 - 19*e - 12, e^5 - 3*e^4 - 7*e^3 + 10*e^2 + 24*e + 21, -e^5 + 3*e^4 + 10*e^3 - 15*e^2 - 42*e - 8, -e^5 + 3*e^4 + 10*e^3 - 16*e^2 - 42*e - 14, 3*e^5 - 11*e^4 - 25*e^3 + 60*e^2 + 105*e + 29, 3*e^5 - 7*e^4 - 27*e^3 + 31*e^2 + 82*e + 33, e^5 - e^4 - 7*e^3 - e^2, 5*e^5 - 12*e^4 - 47*e^3 + 57*e^2 + 149*e + 48, 3*e^5 - 7*e^4 - 25*e^3 + 28*e^2 + 68*e + 27, e^5 - 4*e^4 - 6*e^3 + 22*e^2 + 17*e - 8, e^5 - 2*e^4 - 14*e^3 + 15*e^2 + 57*e + 9, -e^4 + 2*e^3 + 4*e^2 - 5*e + 1, -e^5 + 3*e^4 + 7*e^3 - 17*e^2 - 10*e + 8, -2*e^5 + 5*e^4 + 15*e^3 - 18*e^2 - 42*e - 17, 2*e^5 - 3*e^4 - 27*e^3 + 17*e^2 + 101*e + 37, e^5 - 5*e^4 - 8*e^3 + 32*e^2 + 39*e + 1, -e^5 + 4*e^4 + 5*e^3 - 20*e^2 - 15*e + 6, -2*e^5 + 8*e^4 + 11*e^3 - 38*e^2 - 42*e - 19, 2*e^4 - 12*e^3 - 6*e^2 + 62*e + 36, -e^5 + 5*e^4 + 14*e^3 - 40*e^2 - 75*e - 7, -e^5 + 5*e^4 + 8*e^3 - 31*e^2 - 43*e + 3, -4*e^5 + 15*e^4 + 30*e^3 - 79*e^2 - 120*e - 34, e^5 - 5*e^4 - 11*e^3 + 31*e^2 + 70*e + 18, -3*e^5 + 5*e^4 + 31*e^3 - 20*e^2 - 91*e - 21, -3*e^5 + 10*e^4 + 28*e^3 - 55*e^2 - 113*e - 32, e^4 - 5*e^3 - 4*e^2 + 22*e + 14, 2*e^3 - 3*e^2 - 15*e + 6, -e^4 - 5*e^3 + 13*e^2 + 38*e + 14, e^5 + e^4 - 18*e^3 - 12*e^2 + 71*e + 46, 2*e^4 - 15*e^2 - 23*e + 7, -2*e^5 + 2*e^4 + 22*e^3 - 9*e^2 - 49*e - 8, -5*e^5 + 13*e^4 + 44*e^3 - 65*e^2 - 136*e - 21, -4*e^5 + 11*e^4 + 38*e^3 - 60*e^2 - 127*e - 25, -4*e^5 + 9*e^4 + 45*e^3 - 53*e^2 - 154*e - 41, e^5 - 7*e^4 - 8*e^3 + 43*e^2 + 67*e + 24, -3*e^4 + 20*e^2 + 31*e + 17, -4*e^5 + 12*e^4 + 32*e^3 - 65*e^2 - 98*e - 3, -3*e^5 + 13*e^4 + 14*e^3 - 70*e^2 - 43*e + 19, 2*e^5 - 5*e^4 - 22*e^3 + 33*e^2 + 73*e + 11, 3*e^5 - 7*e^4 - 26*e^3 + 35*e^2 + 66*e + 11, -e^5 - 2*e^4 + 18*e^3 + 12*e^2 - 45*e - 22, -2*e^5 + 6*e^4 + 17*e^3 - 35*e^2 - 49*e + 7, 7*e^5 - 15*e^4 - 70*e^3 + 72*e^2 + 216*e + 74, 2*e^5 - 2*e^4 - 18*e^3 - 2*e^2 + 33*e + 29, -e^5 + 6*e^4 + 4*e^3 - 37*e^2 - 19*e + 10, 2*e^5 - 6*e^4 - 21*e^3 + 34*e^2 + 84*e + 17, 2*e^5 - 4*e^4 - 19*e^3 + 17*e^2 + 59*e + 21, -4*e^5 + 14*e^4 + 44*e^3 - 88*e^2 - 193*e - 60, -e^5 - e^4 + 15*e^3 + 10*e^2 - 41*e - 24, 2*e^4 - 6*e^3 - 10*e^2 + 27*e + 5, -2*e^5 + 4*e^4 + 22*e^3 - 16*e^2 - 79*e - 29, e^5 - 3*e^4 - 13*e^3 + 23*e^2 + 52*e + 10, 4*e^5 - 8*e^4 - 48*e^3 + 46*e^2 + 169*e + 61, e^5 - 3*e^4 - 15*e^3 + 18*e^2 + 75*e + 32, 4*e^5 - 8*e^4 - 46*e^3 + 39*e^2 + 168*e + 68, 5*e^5 - 11*e^4 - 51*e^3 + 58*e^2 + 160*e + 41, -6*e^5 + 12*e^4 + 61*e^3 - 52*e^2 - 198*e - 67, -5*e^5 + 7*e^4 + 62*e^3 - 32*e^2 - 212*e - 79, -2*e^5 + 5*e^4 + 15*e^3 - 15*e^2 - 44*e - 32, 2*e^5 - e^4 - 17*e^3 - 10*e^2 + 21*e + 13, -e^5 + 11*e^3 + 4*e^2 - 11*e - 8, 2*e^5 - 4*e^4 - 14*e^3 + 9*e^2 + 26*e + 5, -3*e^5 + 5*e^4 + 27*e^3 - 14*e^2 - 71*e - 36, -6*e^5 + 16*e^4 + 56*e^3 - 80*e^2 - 191*e - 53, 3*e^4 - 5*e^3 - 10*e^2 - 7*e - 28, -7*e^4 + 15*e^3 + 39*e^2 - 39*e - 24, e^5 + 2*e^4 - 19*e^3 - 9*e^2 + 55*e + 2, -4*e^5 + 15*e^4 + 33*e^3 - 82*e^2 - 135*e - 40, -4*e^5 + 13*e^4 + 38*e^3 - 76*e^2 - 141*e - 24, -e^5 - 3*e^4 + 19*e^3 + 21*e^2 - 40*e - 30, -2*e^5 + 3*e^4 + 20*e^3 - 15*e^2 - 49*e + 14, 5*e^5 - 14*e^4 - 49*e^3 + 77*e^2 + 169*e + 54, 4*e^5 - 9*e^4 - 44*e^3 + 41*e^2 + 163*e + 73, 6*e^5 - 19*e^4 - 60*e^3 + 112*e^2 + 234*e + 59, -8*e^5 + 22*e^4 + 72*e^3 - 107*e^2 - 240*e - 81, 6*e^5 - 15*e^4 - 54*e^3 + 73*e^2 + 165*e + 49, -e^5 + 8*e^3 + 5*e^2 + 9*e + 9, -2*e^5 + 6*e^4 + 29*e^3 - 39*e^2 - 139*e - 57, 3*e^5 - 5*e^4 - 35*e^3 + 25*e^2 + 115*e + 47, 3*e^5 - 4*e^4 - 36*e^3 + 18*e^2 + 112*e + 50, 8*e^5 - 25*e^4 - 77*e^3 + 140*e^2 + 296*e + 86, 2*e^5 - 4*e^4 - 13*e^3 + 13*e^2 + 11*e - 3, -e^5 + 6*e^4 + 15*e^3 - 45*e^2 - 98*e - 23, 4*e^5 - 11*e^4 - 46*e^3 + 63*e^2 + 193*e + 77, 4*e^5 - 12*e^4 - 18*e^3 + 49*e^2 + 2*e - 37, -11*e^3 + 4*e^2 + 87*e + 48, e^5 - 5*e^4 - 13*e^3 + 46*e^2 + 58*e - 21, -6*e^5 + 15*e^4 + 67*e^3 - 86*e^2 - 251*e - 83, -5*e^5 + 16*e^4 + 50*e^3 - 95*e^2 - 203*e - 35, 6*e^5 - 11*e^4 - 60*e^3 + 45*e^2 + 181*e + 53, 4*e^5 - 11*e^4 - 35*e^3 + 57*e^2 + 111*e + 4, 4*e^5 - 14*e^4 - 24*e^3 + 61*e^2 + 70*e + 18, 4*e^5 - 8*e^4 - 28*e^3 + 27*e^2 + 40*e, 6*e^5 - 20*e^4 - 53*e^3 + 117*e^2 + 188*e + 24, -5*e^5 + 14*e^4 + 42*e^3 - 70*e^2 - 125*e - 32, 6*e^5 - 13*e^4 - 69*e^3 + 71*e^2 + 242*e + 90, -3*e^5 + 13*e^4 + 21*e^3 - 76*e^2 - 83*e + 9, 11*e^5 - 30*e^4 - 94*e^3 + 148*e^2 + 289*e + 60, 2*e^5 - 6*e^4 - 15*e^3 + 27*e^2 + 38*e + 28, -4*e^5 + 16*e^4 + 22*e^3 - 84*e^2 - 69*e + 2, -5*e^5 + 12*e^4 + 42*e^3 - 56*e^2 - 121*e - 4, -5*e^5 + 10*e^4 + 54*e^3 - 50*e^2 - 179*e - 44, 2*e^5 - 4*e^4 - 16*e^3 + 6*e^2 + 51*e + 36, 6*e^5 - 15*e^4 - 52*e^3 + 67*e^2 + 148*e + 64, -3*e^5 + 13*e^4 + 20*e^3 - 71*e^2 - 85*e - 32, 3*e^5 - 6*e^4 - 42*e^3 + 41*e^2 + 164*e + 56, -5*e^5 + 7*e^4 + 64*e^3 - 33*e^2 - 217*e - 92, 5*e^5 - 17*e^4 - 50*e^3 + 105*e^2 + 203*e + 47, -4*e^5 + 13*e^4 + 41*e^3 - 75*e^2 - 167*e - 53, -3*e^5 + 4*e^4 + 51*e^3 - 31*e^2 - 208*e - 70, e^4 - 5*e^3 - e^2 + 9*e - 3, 2*e^5 - 5*e^4 - 21*e^3 + 17*e^2 + 88*e + 48, 7*e^5 - 17*e^4 - 66*e^3 + 92*e^2 + 195*e + 40, -3*e^4 - 2*e^3 + 24*e^2 + 36*e + 17, 2*e^5 - 8*e^4 - 27*e^3 + 52*e^2 + 151*e + 51, -3*e^5 + 13*e^4 + 24*e^3 - 77*e^2 - 116*e - 6, -6*e^5 + 21*e^4 + 59*e^3 - 123*e^2 - 252*e - 68, -8*e^5 + 25*e^4 + 70*e^3 - 130*e^2 - 265*e - 96, -2*e^5 + 2*e^4 + 16*e^3 - 5*e^2 - 7*e + 46, 2*e^5 - 6*e^4 - 19*e^3 + 38*e^2 + 70*e + 2, -2*e^4 + 7*e^3 + 11*e^2 - 41*e - 5, -3*e^5 + 8*e^4 + 42*e^3 - 52*e^2 - 188*e - 77, -6*e^5 + 16*e^4 + 58*e^3 - 83*e^2 - 194*e - 77, 3*e^5 - 7*e^4 - 25*e^3 + 35*e^2 + 67*e - 7, 8*e^5 - 25*e^4 - 62*e^3 + 129*e^2 + 190*e + 9, 7*e^5 - 20*e^4 - 52*e^3 + 91*e^2 + 151*e + 47, 2*e^4 - 9*e^3 - 4*e^2 + 28*e - 5, -4*e^5 + 13*e^4 + 28*e^3 - 68*e^2 - 82*e - 7, -4*e^5 + 14*e^4 + 24*e^3 - 69*e^2 - 63*e, -10*e^5 + 32*e^4 + 88*e^3 - 173*e^2 - 317*e - 78, -3*e^4 - 3*e^3 + 28*e^2 + 50*e + 5, -9*e^5 + 29*e^4 + 73*e^3 - 149*e^2 - 253*e - 64, -7*e^5 + 23*e^4 + 55*e^3 - 123*e^2 - 189*e - 25, -10*e^5 + 25*e^4 + 98*e^3 - 125*e^2 - 338*e - 96, -e^5 + 8*e^4 - 5*e^3 - 36*e^2 + 13*e - 3, 6*e^5 - 16*e^4 - 46*e^3 + 78*e^2 + 110*e + 9, -3*e^5 + 5*e^4 + 28*e^3 - 26*e^2 - 60*e + 29, -8*e^4 + 14*e^3 + 42*e^2 - 20*e + 11, -3*e^5 + 16*e^4 + 10*e^3 - 84*e^2 - 43*e + 8, -3*e^5 + 10*e^4 + 26*e^3 - 48*e^2 - 97*e - 61, e^5 - 8*e^4 + 5*e^3 + 36*e^2 - 10*e + 1, -e^5 + 7*e^4 + 9*e^3 - 52*e^2 - 52*e + 15, 8*e^5 - 31*e^4 - 68*e^3 + 179*e^2 + 290*e + 46, 5*e^5 - 8*e^4 - 55*e^3 + 41*e^2 + 158*e + 35, 7*e^5 - 24*e^4 - 59*e^3 + 133*e^2 + 225*e + 33, -8*e^5 + 27*e^4 + 65*e^3 - 146*e^2 - 229*e - 50, -e^5 - 3*e^4 + 22*e^3 + 28*e^2 - 85*e - 55, 6*e^5 - 16*e^4 - 74*e^3 + 102*e^2 + 304*e + 89, 5*e^5 - 13*e^4 - 46*e^3 + 65*e^2 + 151*e + 56, 8*e^5 - 13*e^4 - 88*e^3 + 53*e^2 + 280*e + 102, -5*e^5 + 15*e^4 + 40*e^3 - 80*e^2 - 119*e + 10, -8*e^5 + 20*e^4 + 68*e^3 - 90*e^2 - 199*e - 52, -e^5 - 3*e^4 + 12*e^3 + 36*e^2 - 14*e - 49, 13*e^5 - 31*e^4 - 131*e^3 + 162*e^2 + 428*e + 133, -6*e^5 + 13*e^4 + 56*e^3 - 54*e^2 - 168*e - 59, 8*e^5 - 21*e^4 - 92*e^3 + 119*e^2 + 372*e + 127, 2*e^5 - 6*e^4 - 26*e^3 + 33*e^2 + 128*e + 27, 6*e^5 - 23*e^4 - 53*e^3 + 145*e^2 + 209*e + 16, 6*e^5 - 17*e^4 - 54*e^3 + 90*e^2 + 165*e + 35, 3*e^5 - 6*e^4 - 29*e^3 + 33*e^2 + 66*e + 19, 4*e^5 - 14*e^4 - 29*e^3 + 78*e^2 + 99*e - 17]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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