/*
  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([2, 0, -6, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11, 11, w^3 - 2*w^2 - 5*w - 1])

primes_array = [
[2, 2, w],\
[5, 5, -w^3 + 3*w^2 + 2*w - 1],\
[5, 5, w - 1],\
[11, 11, w^3 - 2*w^2 - 5*w - 1],\
[13, 13, -w^3 + 3*w^2 + 3*w - 1],\
[17, 17, 2*w^3 - 5*w^2 - 9*w + 5],\
[23, 23, -w^3 + 3*w^2 + 4*w - 5],\
[25, 5, -w^2 + 3*w + 1],\
[29, 29, -2*w^3 + 6*w^2 + 5*w - 1],\
[31, 31, -w^2 + 2*w + 1],\
[43, 43, -w^3 + 3*w^2 + 2*w - 3],\
[43, 43, -w^3 + 2*w^2 + 6*w - 3],\
[59, 59, 2*w^3 - 6*w^2 - 7*w + 7],\
[73, 73, 3*w^3 - 6*w^2 - 16*w - 5],\
[79, 79, -5*w^3 + 14*w^2 + 20*w - 17],\
[81, 3, -3],\
[83, 83, -w - 3],\
[83, 83, w^2 - 3*w - 7],\
[89, 89, w^2 - 2*w - 7],\
[101, 101, -2*w^3 + 5*w^2 + 8*w - 3],\
[101, 101, 5*w^3 - 14*w^2 - 19*w + 17],\
[103, 103, -w^3 + w^2 + 8*w + 3],\
[103, 103, 2*w^3 - 5*w^2 - 7*w - 1],\
[109, 109, 3*w^3 - 7*w^2 - 14*w + 1],\
[109, 109, -w^2 + 4*w + 1],\
[127, 127, -3*w^3 + 8*w^2 + 11*w - 7],\
[127, 127, -w^3 + 2*w^2 + 7*w + 1],\
[137, 137, -2*w^3 + 5*w^2 + 9*w - 1],\
[139, 139, -w^3 + 3*w^2 + 2*w - 5],\
[149, 149, w^3 - 3*w^2 - w - 1],\
[149, 149, -2*w^3 + 4*w^2 + 10*w + 1],\
[163, 163, w^3 - 4*w^2 - w + 11],\
[163, 163, 2*w^3 - 4*w^2 - 10*w + 1],\
[173, 173, -4*w^3 + 11*w^2 + 15*w - 13],\
[179, 179, 2*w^2 - 6*w - 3],\
[179, 179, -w^3 + 2*w^2 + 7*w - 1],\
[181, 181, w^3 - 10*w - 9],\
[181, 181, -3*w^3 + 8*w^2 + 14*w - 7],\
[199, 199, w^3 - 8*w - 9],\
[211, 211, 2*w - 3],\
[223, 223, -w^3 + 4*w^2 + w - 5],\
[227, 227, w^3 - 2*w^2 - 5*w - 5],\
[227, 227, -3*w^3 + 7*w^2 + 14*w - 5],\
[227, 227, -4*w^3 + 10*w^2 + 19*w - 7],\
[227, 227, w^2 - 4*w - 5],\
[239, 239, -2*w^3 + 5*w^2 + 7*w - 3],\
[251, 251, -w^3 + 4*w^2 + 2*w - 11],\
[251, 251, 2*w^3 - 6*w^2 - 6*w + 1],\
[257, 257, -3*w^3 + 6*w^2 + 16*w + 3],\
[263, 263, -w^3 + 3*w^2 + 3*w - 7],\
[263, 263, w^3 - 4*w^2 + 7],\
[269, 269, -2*w^3 + 6*w^2 + 6*w - 11],\
[269, 269, -w^3 + 4*w^2 - w - 5],\
[271, 271, -3*w^3 + 9*w^2 + 11*w - 11],\
[271, 271, w^2 - 5*w - 3],\
[277, 277, w^3 - 4*w^2 - 2*w + 7],\
[277, 277, -2*w^3 + 7*w^2 + 8*w - 9],\
[281, 281, 2*w^2 - 4*w - 5],\
[281, 281, 2*w^3 - 4*w^2 - 11*w + 1],\
[283, 283, -3*w^3 + 8*w^2 + 14*w - 11],\
[293, 293, w^3 - 2*w^2 - 6*w + 5],\
[307, 307, -2*w^3 + 5*w^2 + 7*w - 1],\
[313, 313, 2*w^3 - 4*w^2 - 9*w + 3],\
[313, 313, -2*w^3 + 5*w^2 + 6*w - 3],\
[317, 317, -2*w^3 + 5*w^2 + 9*w + 1],\
[347, 347, 4*w^3 - 9*w^2 - 21*w + 3],\
[347, 347, 4*w^3 - 10*w^2 - 18*w + 5],\
[349, 349, -2*w^3 + 6*w^2 + 7*w - 3],\
[353, 353, -w^3 + 12*w + 5],\
[353, 353, w^2 - w - 7],\
[359, 359, -2*w^3 + 5*w^2 + 6*w - 7],\
[359, 359, -w^3 + 4*w^2 - 11],\
[373, 373, -w^3 + 2*w^2 + 6*w + 5],\
[379, 379, -3*w^3 + 8*w^2 + 14*w - 5],\
[397, 397, 6*w^3 - 14*w^2 - 30*w + 7],\
[401, 401, 3*w^3 - 5*w^2 - 20*w - 7],\
[409, 409, 3*w^3 - 7*w^2 - 12*w - 3],\
[409, 409, 2*w^2 - 4*w - 7],\
[421, 421, w^3 - 11*w - 11],\
[421, 421, -w^3 + 3*w^2 + w - 7],\
[431, 431, 2*w^3 - 3*w^2 - 14*w - 3],\
[431, 431, -4*w^3 + 11*w^2 + 15*w - 15],\
[433, 433, 2*w^3 - 5*w^2 - 6*w + 1],\
[439, 439, -4*w^3 + 11*w^2 + 13*w - 9],\
[439, 439, -2*w^3 + 6*w^2 + 8*w - 11],\
[443, 443, 2*w - 5],\
[443, 443, -6*w^3 + 17*w^2 + 24*w - 21],\
[449, 449, w^3 - 2*w^2 - 8*w + 3],\
[449, 449, 4*w^3 - 12*w^2 - 15*w + 17],\
[457, 457, -2*w^3 + 4*w^2 + 9*w + 5],\
[461, 461, -3*w^3 + 6*w^2 + 15*w - 1],\
[461, 461, -3*w^3 + 7*w^2 + 17*w + 1],\
[463, 463, -4*w^3 + 10*w^2 + 17*w - 7],\
[463, 463, -3*w^3 + 10*w^2 + 9*w - 17],\
[467, 467, 4*w^3 - 8*w^2 - 21*w - 7],\
[467, 467, w^3 - 6*w^2 + 3*w + 19],\
[479, 479, -w^3 + w^2 + 8*w + 1],\
[487, 487, -4*w^3 + 11*w^2 + 14*w - 15],\
[487, 487, 3*w^3 - 6*w^2 - 15*w - 5],\
[491, 491, w^2 - 5],\
[503, 503, 2*w^3 - 5*w^2 - 11*w + 3],\
[523, 523, -3*w^3 + 7*w^2 + 13*w + 1],\
[547, 547, 2*w^3 - 3*w^2 - 12*w - 3],\
[547, 547, 2*w^3 - 3*w^2 - 12*w - 9],\
[557, 557, -3*w^3 + 9*w^2 + 9*w - 11],\
[557, 557, -6*w^3 + 15*w^2 + 27*w - 13],\
[563, 563, -3*w^3 + 7*w^2 + 14*w - 7],\
[571, 571, -5*w^3 + 11*w^2 + 26*w - 3],\
[593, 593, -6*w^3 + 15*w^2 + 26*w - 7],\
[599, 599, 7*w^3 - 18*w^2 - 29*w + 17],\
[599, 599, -2*w^3 + 6*w^2 + 8*w - 3],\
[601, 601, -7*w^3 + 20*w^2 + 28*w - 23],\
[601, 601, 3*w^3 - 7*w^2 - 12*w + 5],\
[607, 607, 5*w^3 - 12*w^2 - 24*w + 9],\
[607, 607, w^3 - 5*w^2 + 15],\
[613, 613, -w^3 + 5*w^2 - 2*w - 9],\
[617, 617, w^3 + w^2 - 13*w - 15],\
[617, 617, 2*w^3 - 4*w^2 - 8*w - 1],\
[619, 619, 5*w^3 - 10*w^2 - 27*w - 7],\
[619, 619, 2*w^3 - 4*w^2 - 10*w + 3],\
[643, 643, w^3 - 5*w^2 + 5*w + 5],\
[643, 643, 4*w^3 - 9*w^2 - 20*w - 1],\
[643, 643, 3*w^3 - 7*w^2 - 14*w - 3],\
[643, 643, -3*w^3 + 7*w^2 + 13*w - 3],\
[647, 647, -3*w^3 + 8*w^2 + 12*w - 3],\
[653, 653, -w^3 + 9*w + 13],\
[653, 653, -w^3 + 4*w^2 + 3*w - 9],\
[653, 653, -2*w^3 + 7*w^2 + 4*w - 7],\
[653, 653, w^2 - 4*w - 9],\
[673, 673, -w^3 + 5*w^2 + w - 13],\
[683, 683, w^3 - 3*w^2 - 3*w - 3],\
[701, 701, 5*w^3 - 13*w^2 - 23*w + 9],\
[709, 709, 2*w^3 - w^2 - 19*w - 15],\
[719, 719, -5*w^3 + 15*w^2 + 20*w - 19],\
[727, 727, -w - 5],\
[751, 751, -4*w^3 + 10*w^2 + 15*w - 9],\
[751, 751, 6*w^3 - 17*w^2 - 22*w + 21],\
[757, 757, 3*w^3 - 6*w^2 - 18*w - 1],\
[757, 757, -w^3 + 4*w^2 + 2*w + 1],\
[769, 769, w^2 - 2*w + 3],\
[773, 773, 5*w^3 - 12*w^2 - 23*w + 9],\
[787, 787, 2*w^3 - 4*w^2 - 5*w + 1],\
[797, 797, -3*w^3 + 8*w^2 + 10*w - 3],\
[809, 809, 2*w^2 - 5*w - 1],\
[809, 809, 4*w^3 - 6*w^2 - 28*w - 11],\
[827, 827, 4*w^3 - 8*w^2 - 22*w - 1],\
[827, 827, 2*w^2 - 6*w - 9],\
[829, 829, -w^3 + w^2 + 10*w + 1],\
[839, 839, -2*w^3 + 2*w^2 + 16*w + 7],\
[877, 877, 6*w^3 - 16*w^2 - 25*w + 13],\
[877, 877, w^3 - w^2 - 7*w + 1],\
[881, 881, 2*w^3 - 2*w^2 - 15*w - 7],\
[881, 881, -4*w^3 + 7*w^2 + 26*w + 9],\
[887, 887, 2*w^3 - 4*w^2 - 13*w - 1],\
[907, 907, 5*w^3 - 11*w^2 - 26*w - 1],\
[907, 907, 5*w^3 - 13*w^2 - 22*w + 9],\
[907, 907, w^3 - 5*w^2 + 2*w + 13],\
[907, 907, -2*w^3 + 7*w^2 + 5*w - 7],\
[911, 911, -3*w^3 + 8*w^2 + 9*w - 5],\
[919, 919, -2*w^3 + 7*w^2 + 6*w - 3],\
[919, 919, -3*w^3 + 8*w^2 + 15*w - 7],\
[947, 947, -2*w^3 + 5*w^2 + 12*w - 9],\
[947, 947, -w^2 + w - 3],\
[947, 947, 3*w^3 - 6*w^2 - 14*w - 7],\
[947, 947, -w^3 + 5*w^2 - w - 17],\
[953, 953, 3*w^3 - 9*w^2 - 9*w + 13],\
[953, 953, -4*w^3 + 13*w^2 + 11*w - 23],\
[967, 967, 8*w^3 - 20*w^2 - 33*w + 19]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 4*x^7 - 2*x^6 + 22*x^5 - 14*x^4 - 19*x^3 + 16*x^2 - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e^7 + 3*e^6 + 5*e^5 - 17*e^4 - 3*e^3 + 16*e^2, -e^7 + 4*e^6 + 3*e^5 - 23*e^4 + 8*e^3 + 23*e^2 - 10*e - 2, -1, -e^7 + 5*e^6 + e^5 - 29*e^4 + 18*e^3 + 31*e^2 - 17*e - 4, 2*e^7 - 6*e^6 - 9*e^5 + 34*e^4 - e^3 - 34*e^2 + 9*e + 4, -2*e^7 + 8*e^6 + 4*e^5 - 44*e^4 + 27*e^3 + 40*e^2 - 28*e - 3, -e^5 + e^4 + 7*e^3 - 6*e^2 - 8*e + 6, e^7 - 4*e^6 - 5*e^5 + 25*e^4 + 4*e^3 - 30*e^2 - 2*e + 4, -4*e^7 + 14*e^6 + 15*e^5 - 79*e^4 + 15*e^3 + 75*e^2 - 21*e - 3, -3*e^7 + 11*e^6 + 9*e^5 - 63*e^4 + 26*e^3 + 64*e^2 - 31*e - 6, -3*e^7 + 9*e^6 + 15*e^5 - 52*e^4 - 8*e^3 + 56*e^2 - 4*e - 5, -3*e^7 + 12*e^6 + 7*e^5 - 65*e^4 + 31*e^3 + 53*e^2 - 23*e, -4*e^7 + 14*e^6 + 17*e^5 - 83*e^4 + 3*e^3 + 97*e^2 - 11*e - 17, -4*e^7 + 12*e^6 + 17*e^5 - 66*e^4 + 6*e^3 + 61*e^2 - 16*e - 8, -3*e^7 + 9*e^6 + 17*e^5 - 57*e^4 - 21*e^3 + 81*e^2 + 12*e - 19, -e^7 + 4*e^6 + e^5 - 18*e^4 + 18*e^3 - 3*e^2 - 15*e + 13, e^7 - 6*e^6 + 3*e^5 + 31*e^4 - 38*e^3 - 20*e^2 + 28*e + 1, -2*e^6 + 2*e^5 + 15*e^4 - 10*e^3 - 27*e^2 + 5*e + 8, -6*e^7 + 19*e^6 + 21*e^5 - 101*e^4 + 35*e^3 + 78*e^2 - 50*e + 3, e^7 - 4*e^6 - 5*e^5 + 25*e^4 + 7*e^3 - 33*e^2 - 11*e + 7, 6*e^7 - 23*e^6 - 17*e^5 + 127*e^4 - 50*e^3 - 110*e^2 + 47*e + 5, 4*e^7 - 13*e^6 - 10*e^5 + 66*e^4 - 46*e^3 - 42*e^2 + 51*e, -e^7 + e^6 + 9*e^5 - 8*e^4 - 23*e^3 + 21*e^2 + 17*e - 11, -2*e^7 + 7*e^6 + 3*e^5 - 35*e^4 + 32*e^3 + 21*e^2 - 27*e + 8, -3*e^7 + 12*e^6 + 7*e^5 - 64*e^4 + 33*e^3 + 46*e^2 - 32*e + 8, -2*e^7 + 7*e^6 + 7*e^5 - 42*e^4 + 12*e^3 + 49*e^2 - 14*e - 3, -10*e^7 + 37*e^6 + 31*e^5 - 209*e^4 + 75*e^3 + 202*e^2 - 85*e - 11, -e^7 + e^6 + 8*e^5 - 5*e^4 - 18*e^3 + 5*e^2 + 5*e + 2, 13*e^7 - 47*e^6 - 43*e^5 + 263*e^4 - 80*e^3 - 247*e^2 + 94*e + 18, 5*e^7 - 13*e^6 - 29*e^5 + 75*e^4 + 38*e^3 - 82*e^2 - 28*e + 14, -7*e^7 + 26*e^6 + 21*e^5 - 145*e^4 + 58*e^3 + 129*e^2 - 66*e - 1, 6*e^7 - 21*e^6 - 23*e^5 + 119*e^4 - 19*e^3 - 114*e^2 + 28*e + 10, -e^7 + 5*e^6 + 3*e^5 - 29*e^4 + 8*e^3 + 28*e^2 - 21*e, -3*e^7 + 11*e^6 + 5*e^5 - 59*e^4 + 52*e^3 + 47*e^2 - 64*e + 3, 2*e^7 - 4*e^6 - 14*e^5 + 22*e^4 + 30*e^3 - 17*e^2 - 37*e - 2, -2*e^7 + 3*e^6 + 13*e^5 - 18*e^4 - 15*e^3 + 23*e^2 - e, 8*e^7 - 27*e^6 - 34*e^5 + 156*e^4 - 7*e^3 - 164*e^2 + 17*e + 24, 13*e^7 - 42*e^6 - 58*e^5 + 243*e^4 - 4*e^3 - 256*e^2 + 46*e + 36, -e^7 + 4*e^6 + 10*e^5 - 31*e^4 - 36*e^3 + 57*e^2 + 38*e - 15, 7*e^7 - 25*e^6 - 23*e^5 + 142*e^4 - 52*e^3 - 140*e^2 + 88*e + 12, e^7 - 7*e^6 + 5*e^5 + 38*e^4 - 54*e^3 - 31*e^2 + 63*e - 3, 7*e^7 - 23*e^6 - 27*e^5 + 129*e^4 - 25*e^3 - 119*e^2 + 39*e - 1, -2*e^7 + 4*e^6 + 12*e^5 - 21*e^4 - 13*e^3 + 15*e^2 - 4*e + 6, -e^7 + 6*e^6 - 7*e^5 - 33*e^4 + 67*e^3 + 34*e^2 - 63*e - 5, -10*e^7 + 33*e^6 + 40*e^5 - 189*e^4 + 30*e^3 + 194*e^2 - 63*e - 10, -7*e^7 + 20*e^6 + 35*e^5 - 115*e^4 - 16*e^3 + 121*e^2 - 16*e - 16, e^7 - 4*e^6 - 3*e^5 + 20*e^4 - 4*e^3 - 6*e^2 - 5*e - 7, -9*e^7 + 26*e^6 + 47*e^5 - 155*e^4 - 32*e^3 + 185*e^2 - 5*e - 30, -7*e^6 + 14*e^5 + 42*e^4 - 74*e^3 - 48*e^2 + 56*e + 11, 3*e^7 - 12*e^6 - 6*e^5 + 64*e^4 - 39*e^3 - 45*e^2 + 28*e - 7, -7*e^7 + 20*e^6 + 35*e^5 - 117*e^4 - 15*e^3 + 129*e^2 - 13*e - 13, 7*e^7 - 23*e^6 - 30*e^5 + 129*e^4 - 5*e^3 - 120*e^2 + 21*e + 7, -4*e^6 + 12*e^5 + 14*e^4 - 61*e^3 + 21*e^2 + 44*e - 18, 15*e^7 - 48*e^6 - 67*e^5 + 279*e^4 - 2*e^3 - 303*e^2 + 36*e + 51, 5*e^7 - 18*e^6 - 10*e^5 + 97*e^4 - 71*e^3 - 86*e^2 + 75*e + 5, 7*e^7 - 20*e^6 - 33*e^5 + 114*e^4 + 3*e^3 - 117*e^2 + 27*e + 8, 5*e^7 - 13*e^6 - 30*e^5 + 82*e^4 + 35*e^3 - 115*e^2 - 2*e + 32, -5*e^7 + 23*e^6 + 11*e^5 - 135*e^4 + 53*e^3 + 150*e^2 - 36*e - 24, 8*e^7 - 22*e^6 - 43*e^5 + 129*e^4 + 37*e^3 - 147*e^2 - 18*e + 27, -7*e^7 + 19*e^6 + 38*e^5 - 108*e^4 - 32*e^3 + 107*e^2 + 2*e - 18, 3*e^7 - 19*e^6 + 4*e^5 + 107*e^4 - 88*e^3 - 100*e^2 + 78*e + 16, -2*e^7 + 2*e^6 + 14*e^5 - 11*e^4 - 24*e^3 + 22*e^2 + 10*e - 17, 5*e^7 - 15*e^6 - 28*e^5 + 87*e^4 + 35*e^3 - 93*e^2 - 17*e + 23, -5*e^7 + 17*e^6 + 19*e^5 - 102*e^4 + 21*e^3 + 129*e^2 - 36*e - 30, -4*e^7 + 12*e^6 + 25*e^5 - 74*e^4 - 42*e^3 + 87*e^2 + 33*e - 11, -7*e^7 + 24*e^6 + 23*e^5 - 135*e^4 + 48*e^3 + 132*e^2 - 57*e - 3, -11*e^7 + 36*e^6 + 42*e^5 - 196*e^4 + 43*e^3 + 160*e^2 - 66*e - 7, 9*e^7 - 38*e^6 - 19*e^5 + 215*e^4 - 116*e^3 - 208*e^2 + 124*e + 20, 5*e^7 - 18*e^6 - 18*e^5 + 103*e^4 - 24*e^3 - 99*e^2 + 34*e - 1, -18*e^7 + 60*e^6 + 67*e^5 - 339*e^4 + 82*e^3 + 334*e^2 - 124*e - 31, -10*e^7 + 38*e^6 + 30*e^5 - 213*e^4 + 80*e^3 + 192*e^2 - 99*e, -11*e^7 + 42*e^6 + 35*e^5 - 241*e^4 + 72*e^3 + 250*e^2 - 81*e - 38, 5*e^7 - 22*e^6 - 8*e^5 + 129*e^4 - 81*e^3 - 144*e^2 + 88*e + 16, 4*e^7 - 20*e^6 + e^5 + 109*e^4 - 107*e^3 - 87*e^2 + 107*e - 2, -2*e^7 + 9*e^6 - 2*e^5 - 45*e^4 + 59*e^3 + 28*e^2 - 46*e - 9, -10*e^7 + 29*e^6 + 55*e^5 - 170*e^4 - 54*e^3 + 183*e^2 + 15*e - 29, -9*e^7 + 26*e^6 + 44*e^5 - 148*e^4 - 19*e^3 + 148*e^2 + 6*e - 17, 3*e^7 - 8*e^6 - 18*e^5 + 50*e^4 + 25*e^3 - 76*e^2 - 12*e + 27, -5*e^6 + 16*e^5 + 23*e^4 - 86*e^3 - 7*e^2 + 67*e - 10, 2*e^7 - 4*e^6 - 17*e^5 + 27*e^4 + 44*e^3 - 37*e^2 - 30*e + 6, -15*e^7 + 54*e^6 + 58*e^5 - 310*e^4 + 46*e^3 + 311*e^2 - 78*e - 34, 12*e^7 - 36*e^6 - 55*e^5 + 211*e^4 - e^3 - 242*e^2 + 36*e + 46, 8*e^7 - 30*e^6 - 21*e^5 + 162*e^4 - 81*e^3 - 131*e^2 + 89*e + 19, 10*e^7 - 28*e^6 - 46*e^5 + 149*e^4 + 8*e^3 - 114*e^2 + e - 1, 7*e^6 - 18*e^5 - 36*e^4 + 94*e^3 + 22*e^2 - 67*e + 5, 6*e^7 - 24*e^6 - 9*e^5 + 128*e^4 - 98*e^3 - 91*e^2 + 88*e - 7, e^7 - e^6 - 7*e^5 + 3*e^4 + 14*e^3 + 10*e^2 - 18*e - 18, 5*e^7 - 19*e^6 - 13*e^5 + 103*e^4 - 46*e^3 - 84*e^2 + 34*e + 5, 3*e^7 - 14*e^6 - 8*e^5 + 84*e^4 - 23*e^3 - 100*e^2 + 13*e + 15, -2*e^7 + 9*e^6 + 5*e^5 - 55*e^4 + 28*e^3 + 63*e^2 - 49*e + 5, -21*e^7 + 72*e^6 + 77*e^5 - 408*e^4 + 99*e^3 + 397*e^2 - 149*e - 25, 6*e^7 - 14*e^6 - 39*e^5 + 88*e^4 + 61*e^3 - 124*e^2 - 23*e + 37, 14*e^7 - 44*e^6 - 68*e^5 + 255*e^4 + 31*e^3 - 267*e^2 + 20*e + 26, -6*e^7 + 19*e^6 + 32*e^5 - 110*e^4 - 36*e^3 + 111*e^2 + 41*e - 13, -12*e^7 + 42*e^6 + 40*e^5 - 236*e^4 + 74*e^3 + 225*e^2 - 72*e - 20, 3*e^7 - 15*e^6 - 2*e^5 + 89*e^4 - 69*e^3 - 96*e^2 + 87*e + 18, 20*e^7 - 65*e^6 - 80*e^5 + 363*e^4 - 49*e^3 - 340*e^2 + 73*e + 31, 10*e^7 - 34*e^6 - 38*e^5 + 198*e^4 - 44*e^3 - 214*e^2 + 72*e + 22, -8*e^7 + 26*e^6 + 33*e^5 - 149*e^4 + 21*e^3 + 151*e^2 - 44*e - 20, 14*e^7 - 44*e^6 - 58*e^5 + 247*e^4 - 32*e^3 - 240*e^2 + 77*e + 29, -19*e^7 + 69*e^6 + 60*e^5 - 387*e^4 + 131*e^3 + 370*e^2 - 130*e - 34, 19*e^7 - 68*e^6 - 61*e^5 + 378*e^4 - 131*e^3 - 343*e^2 + 143*e + 24, 14*e^7 - 54*e^6 - 42*e^5 + 305*e^4 - 113*e^3 - 291*e^2 + 145*e + 30, 9*e^7 - 24*e^6 - 45*e^5 + 144*e^4 + 7*e^3 - 182*e^2 + 57*e + 44, 6*e^7 - 24*e^6 - 13*e^5 + 140*e^4 - 82*e^3 - 158*e^2 + 101*e + 25, -9*e^7 + 36*e^6 + 23*e^5 - 197*e^4 + 83*e^3 + 161*e^2 - 68*e + 22, -16*e^7 + 51*e^6 + 65*e^5 - 283*e^4 + 39*e^3 + 251*e^2 - 62*e, -7*e^7 + 27*e^6 + 20*e^5 - 152*e^4 + 59*e^3 + 150*e^2 - 58*e - 23, 4*e^7 - 15*e^6 - 16*e^5 + 86*e^4 - 7*e^3 - 90*e^2 + 21*e + 25, e^7 + 5*e^6 - 17*e^5 - 37*e^4 + 66*e^3 + 64*e^2 - 49*e - 11, -9*e^7 + 32*e^6 + 18*e^5 - 171*e^4 + 124*e^3 + 149*e^2 - 113*e - 20, -2*e^7 + 7*e^6 + 16*e^5 - 45*e^4 - 42*e^3 + 50*e^2 + 21*e + 15, 3*e^7 - 17*e^6 + 11*e^5 + 85*e^4 - 134*e^3 - 49*e^2 + 118*e - 4, -8*e^7 + 26*e^6 + 31*e^5 - 150*e^4 + 34*e^3 + 167*e^2 - 76*e - 35, 2*e^7 - 11*e^6 + 10*e^5 + 56*e^4 - 113*e^3 - 30*e^2 + 119*e - 9, -2*e^7 + 4*e^6 + 14*e^5 - 22*e^4 - 28*e^3 + 24*e^2 + 14*e - 16, -2*e^7 + 2*e^6 + 13*e^5 - 6*e^4 - 14*e^3 - 13*e^2 - 13*e + 17, 10*e^7 - 24*e^6 - 58*e^5 + 137*e^4 + 66*e^3 - 143*e^2 - 14*e + 9, 3*e^7 - 17*e^6 + 3*e^5 + 88*e^4 - 80*e^3 - 46*e^2 + 62*e - 19, 19*e^7 - 68*e^6 - 70*e^5 + 385*e^4 - 75*e^3 - 368*e^2 + 93*e + 41, -19*e^7 + 72*e^6 + 57*e^5 - 411*e^4 + 159*e^3 + 411*e^2 - 206*e - 27, 5*e^7 - 11*e^6 - 35*e^5 + 64*e^4 + 73*e^3 - 72*e^2 - 59*e + 5, -11*e^7 + 40*e^6 + 43*e^5 - 233*e^4 + 34*e^3 + 234*e^2 - 62*e + 4, -18*e^7 + 61*e^6 + 80*e^5 - 362*e^4 + 8*e^3 + 409*e^2 - 65*e - 63, -11*e^7 + 41*e^6 + 49*e^5 - 249*e^4 - e^3 + 298*e^2 - 45*e - 59, 3*e^7 - 13*e^6 - 3*e^5 + 71*e^4 - 53*e^3 - 73*e^2 + 37*e + 25, -4*e^7 + 18*e^6 + 5*e^5 - 102*e^4 + 67*e^3 + 101*e^2 - 47*e - 10, -23*e^7 + 81*e^6 + 76*e^5 - 457*e^4 + 151*e^3 + 447*e^2 - 186*e - 26, -9*e^7 + 17*e^6 + 61*e^5 - 94*e^4 - 105*e^3 + 91*e^2 + 49*e - 13, 8*e^7 - 20*e^6 - 46*e^5 + 109*e^4 + 55*e^3 - 94*e^2 - 32*e + 8, 17*e^7 - 60*e^6 - 62*e^5 + 339*e^4 - 75*e^3 - 334*e^2 + 108*e + 37, -9*e^7 + 23*e^6 + 55*e^5 - 133*e^4 - 84*e^3 + 145*e^2 + 59*e - 14, -3*e^7 + 17*e^6 - 2*e^5 - 92*e^4 + 76*e^3 + 77*e^2 - 62*e - 16, e^7 - e^6 - 4*e^5 + 2*e^4 - 13*e^3 + 9*e^2 + 39*e + 6, -17*e^7 + 59*e^6 + 52*e^5 - 323*e^4 + 140*e^3 + 278*e^2 - 163*e - 8, 7*e^7 - 18*e^6 - 28*e^5 + 94*e^4 - 22*e^3 - 75*e^2 + 17*e + 2, 4*e^7 - 15*e^6 - 12*e^5 + 79*e^4 - 35*e^3 - 43*e^2 + 44*e - 35, 4*e^7 - 7*e^6 - 35*e^5 + 38*e^4 + 101*e^3 - 31*e^2 - 92*e + 9, 13*e^7 - 50*e^6 - 43*e^5 + 275*e^4 - 73*e^3 - 220*e^2 + 87*e - 15, 8*e^7 - 31*e^6 - 28*e^5 + 185*e^4 - 40*e^3 - 213*e^2 + 40*e + 34, 8*e^7 - 24*e^6 - 36*e^5 + 142*e^4 - 8*e^3 - 174*e^2 + 40*e + 58, 19*e^7 - 56*e^6 - 91*e^5 + 323*e^4 + 25*e^3 - 346*e^2 + 35*e + 50, 9*e^7 - 33*e^6 - 16*e^5 + 172*e^4 - 136*e^3 - 126*e^2 + 137*e - 1, 17*e^7 - 58*e^6 - 61*e^5 + 322*e^4 - 83*e^3 - 291*e^2 + 116*e, 5*e^7 - 21*e^6 - 9*e^5 + 117*e^4 - 79*e^3 - 93*e^2 + 96*e - 18, 18*e^7 - 56*e^6 - 76*e^5 + 323*e^4 - 42*e^3 - 339*e^2 + 109*e + 19, -2*e^7 - 2*e^6 + 31*e^5 + 2*e^4 - 118*e^3 + 34*e^2 + 86*e - 7, 19*e^7 - 55*e^6 - 95*e^5 + 324*e^4 + 43*e^3 - 371*e^2 + 27*e + 72, 9*e^7 - 23*e^6 - 54*e^5 + 141*e^4 + 66*e^3 - 183*e^2 - 6*e + 38, 3*e^7 - 9*e^6 - 18*e^5 + 58*e^4 + 28*e^3 - 83*e^2 - 28*e + 4, 17*e^7 - 66*e^6 - 55*e^5 + 370*e^4 - 103*e^3 - 327*e^2 + 106*e + 18, 23*e^7 - 86*e^6 - 66*e^5 + 478*e^4 - 196*e^3 - 431*e^2 + 181*e + 12, 8*e^7 - 33*e^6 - 14*e^5 + 187*e^4 - 127*e^3 - 183*e^2 + 164*e - 2, -22*e^7 + 75*e^6 + 76*e^5 - 416*e^4 + 127*e^3 + 384*e^2 - 169*e - 13, 14*e^7 - 54*e^6 - 33*e^5 + 293*e^4 - 167*e^3 - 233*e^2 + 180*e + 11, 10*e^7 - 31*e^6 - 45*e^5 + 175*e^4 + 2*e^3 - 168*e^2 + 23*e - 7, -18*e^7 + 62*e^6 + 60*e^5 - 344*e^4 + 109*e^3 + 323*e^2 - 111*e - 23, -11*e^7 + 46*e^6 + 23*e^5 - 260*e^4 + 139*e^3 + 247*e^2 - 140*e + 17, 2*e^7 - 10*e^6 + 5*e^5 + 53*e^4 - 81*e^3 - 45*e^2 + 91*e + 4, 8*e^7 - 29*e^6 - 32*e^5 + 170*e^4 - 32*e^3 - 171*e^2 + 90*e + 8, -15*e^7 + 50*e^6 + 64*e^5 - 292*e^4 + 28*e^3 + 307*e^2 - 90*e - 15, 9*e^7 - 33*e^6 - 36*e^5 + 202*e^4 - 21*e^3 - 251*e^2 + 21*e + 43, 15*e^7 - 49*e^6 - 55*e^5 + 267*e^4 - 75*e^3 - 229*e^2 + 121*e + 24, 2*e^7 - 9*e^6 - 4*e^5 + 52*e^4 - 17*e^3 - 68*e^2 - 21*e + 43, 4*e^6 - 13*e^5 - 17*e^4 + 69*e^3 + 4*e^2 - 63*e - 17, 11*e^7 - 40*e^6 - 50*e^5 + 235*e^4 + 16*e^3 - 249*e^2 - 9*e + 28, -10*e^7 + 51*e^6 + 5*e^5 - 297*e^4 + 216*e^3 + 314*e^2 - 208*e - 29]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([11, 11, w^3 - 2*w^2 - 5*w - 1])] = 1

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