/*
  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([-8, -14, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([4, 4, -1/2*w^2 + 1/2*w + 6])

primes_array = [
[2, 2, -1/2*w^2 + 1/2*w + 8],\
[2, 2, 1/2*w^2 - 3/2*w - 1],\
[2, 2, w + 3],\
[11, 11, -w^2 + 3*w + 7],\
[11, 11, -2*w - 1],\
[11, 11, -w^2 + w + 11],\
[27, 3, 3],\
[41, 41, 2*w + 5],\
[41, 41, -w^2 + 3*w + 3],\
[41, 41, -w^2 + w + 15],\
[43, 43, -3*w^2 + 11*w + 11],\
[47, 47, -w^2 - w + 5],\
[47, 47, w^2 - 5*w - 3],\
[47, 47, -2*w^2 + 4*w + 23],\
[59, 59, -w^2 + w + 13],\
[59, 59, w^2 - 3*w - 5],\
[59, 59, -2*w - 3],\
[97, 97, 7*w^2 - 11*w - 91],\
[97, 97, -2*w^2 - 8*w - 5],\
[97, 97, 5*w^2 - 19*w - 15],\
[107, 107, w^2 + 3*w - 1],\
[107, 107, -3*w^2 + 5*w + 37],\
[107, 107, w^2 - 5*w - 23],\
[113, 113, w^2 - 3*w - 1],\
[113, 113, w^2 - w - 17],\
[113, 113, -2*w - 7],\
[125, 5, -5],\
[127, 127, -w^2 - w - 1],\
[127, 127, 2*w^2 - 4*w - 29],\
[127, 127, -w^2 + 5*w - 3],\
[131, 131, -w^2 + 5*w - 1],\
[131, 131, 2*w^2 - 4*w - 27],\
[131, 131, w^2 + w - 1],\
[137, 137, 2*w^2 - 6*w - 5],\
[137, 137, -4*w - 11],\
[137, 137, 2*w^2 - 2*w - 31],\
[151, 151, -2*w^2 + 8*w + 3],\
[151, 151, 3*w^2 - 5*w - 41],\
[151, 151, -w^2 - 3*w - 3],\
[173, 173, 2*w^2 - 4*w - 25],\
[173, 173, w^2 + w - 3],\
[173, 173, -w^2 + 5*w + 1],\
[193, 193, -6*w - 17],\
[193, 193, 3*w^2 - 9*w - 7],\
[193, 193, 3*w^2 - 3*w - 47],\
[199, 199, w^2 + w - 7],\
[199, 199, 2*w^2 - 4*w - 21],\
[199, 199, -w^2 + 5*w + 5],\
[211, 211, 2*w - 7],\
[211, 211, w^2 - w - 3],\
[211, 211, -w^2 + 3*w + 15],\
[223, 223, w^2 - w - 7],\
[223, 223, w^2 - 3*w - 11],\
[223, 223, 2*w - 3],\
[257, 257, -2*w^2 - 4*w - 1],\
[257, 257, -3*w^2 + 13*w + 3],\
[257, 257, 5*w^2 - 9*w - 67],\
[269, 269, 2*w - 5],\
[269, 269, w^2 - 3*w - 13],\
[269, 269, w^2 - w - 5],\
[293, 293, -13*w^2 + 51*w + 35],\
[293, 293, -19*w^2 + 31*w + 247],\
[293, 293, 6*w^2 + 20*w + 9],\
[317, 317, 5*w^2 - 19*w - 17],\
[317, 317, 7*w^2 - 11*w - 89],\
[317, 317, 2*w^2 + 8*w + 3],\
[343, 7, -7],\
[379, 379, 3*w^2 - 11*w - 13],\
[379, 379, 4*w^2 - 6*w - 49],\
[379, 379, w^2 + 5*w + 1],\
[383, 383, -4*w - 5],\
[383, 383, -2*w^2 + 2*w + 25],\
[383, 383, 2*w^2 - 6*w - 11],\
[389, 389, 4*w^2 - 18*w - 13],\
[389, 389, -7*w^2 + 13*w + 83],\
[389, 389, 4*w^2 - 14*w - 11],\
[409, 409, 2*w - 11],\
[409, 409, w^2 - 3*w - 19],\
[409, 409, -w^2 + w - 1],\
[419, 419, 10*w^2 - 38*w - 31],\
[419, 419, -14*w^2 + 22*w + 181],\
[419, 419, 4*w^2 - 14*w - 17],\
[431, 431, -4*w^2 + 16*w + 13],\
[431, 431, 2*w^2 + 6*w - 1],\
[431, 431, -6*w^2 + 10*w + 75],\
[457, 457, -2*w^2 + 8*w + 9],\
[457, 457, 3*w^2 - 5*w - 35],\
[457, 457, w^2 + 3*w - 3],\
[557, 557, 5*w^2 - 9*w - 63],\
[557, 557, -3*w^2 + 13*w + 7],\
[557, 557, 2*w^2 + 4*w - 3],\
[563, 563, -9*w^2 + 35*w + 23],\
[563, 563, 13*w^2 - 21*w - 171],\
[563, 563, -4*w^2 - 14*w - 9],\
[601, 601, 5*w^2 - 17*w - 13],\
[601, 601, 6*w^2 - 8*w - 85],\
[601, 601, -w^2 - 9*w - 17],\
[613, 613, -2*w^2 + 15],\
[613, 613, 3*w^2 - 7*w - 31],\
[613, 613, 22*w^2 - 36*w - 285],\
[641, 641, 3*w^2 - 5*w - 43],\
[641, 641, -2*w^2 + 8*w + 1],\
[641, 641, -w^2 - 3*w - 5],\
[643, 643, 2*w^2 + 4*w - 1],\
[643, 643, 5*w^2 - 9*w - 65],\
[643, 643, -3*w^2 + 13*w + 5],\
[647, 647, 9*w^2 - 35*w - 27],\
[647, 647, 4*w^2 + 14*w + 5],\
[647, 647, 13*w^2 - 21*w - 167],\
[653, 653, -4*w^2 + 16*w + 7],\
[653, 653, 6*w^2 - 10*w - 81],\
[653, 653, -2*w^2 - 6*w - 5],\
[661, 661, -w^2 - 7*w - 13],\
[661, 661, -4*w^2 + 14*w + 9],\
[661, 661, 5*w^2 - 7*w - 71],\
[677, 677, -12*w^2 + 20*w + 155],\
[677, 677, -4*w^2 - 12*w - 3],\
[677, 677, -8*w^2 + 32*w + 21],\
[709, 709, -2*w^2 + 10*w - 3],\
[709, 709, 19*w^2 - 31*w - 249],\
[709, 709, 4*w^2 - 8*w - 55],\
[727, 727, -w^2 + 5*w + 21],\
[727, 727, -23*w^2 + 37*w + 301],\
[727, 727, -w^2 - w + 23],\
[733, 733, 2*w^2 + 2*w - 9],\
[733, 733, -2*w^2 + 10*w + 5],\
[733, 733, 4*w^2 - 8*w - 47],\
[739, 739, 2*w^2 - 6*w - 17],\
[739, 739, 2*w^2 - 2*w - 19],\
[739, 739, 4*w - 1],\
[773, 773, 8*w^2 - 12*w - 103],\
[773, 773, 6*w^2 - 22*w - 21],\
[773, 773, -2*w^2 - 10*w - 7],\
[809, 809, 4*w^2 + 16*w + 11],\
[809, 809, w^2 - 9*w - 7],\
[809, 809, 3*w^2 - w - 29],\
[821, 821, 3*w^2 + w - 23],\
[821, 821, 2*w^2 - 12*w - 9],\
[821, 821, 5*w^2 - 11*w - 51],\
[839, 839, 2*w^2 + 4*w - 7],\
[839, 839, 5*w^2 - 9*w - 59],\
[839, 839, 3*w^2 - 13*w - 11],\
[859, 859, w^2 + w - 11],\
[859, 859, 2*w^2 - 4*w - 17],\
[859, 859, w^2 - 5*w - 9],\
[881, 881, 4*w^2 - 14*w - 15],\
[881, 881, 5*w^2 - 7*w - 65],\
[881, 881, -w^2 - 7*w - 7],\
[887, 887, 5*w^2 - 7*w - 67],\
[887, 887, 4*w^2 - 14*w - 13],\
[887, 887, -w^2 - 7*w - 9],\
[907, 907, -3*w^2 - 11*w - 9],\
[907, 907, 10*w^2 - 16*w - 133],\
[907, 907, -7*w^2 + 27*w + 17],\
[911, 911, w^2 - 7*w - 7],\
[911, 911, 3*w^2 - 7*w - 27],\
[911, 911, 2*w^2 - 19],\
[919, 919, -3*w^2 - 5*w - 1],\
[919, 919, -4*w^2 + 18*w + 1],\
[919, 919, 7*w^2 - 13*w - 95],\
[947, 947, 4*w^2 - 6*w - 57],\
[947, 947, -3*w^2 + 11*w + 5],\
[947, 947, -w^2 - 5*w - 9],\
[967, 967, 8*w^2 - 30*w - 25],\
[967, 967, -3*w^2 - 13*w - 9],\
[967, 967, 11*w^2 - 17*w - 143],\
[991, 991, 2*w^2 - 8*w - 11],\
[991, 991, w^2 + 3*w - 5],\
[991, 991, 3*w^2 - 5*w - 33],\
[997, 997, 4*w^2 + 2*w - 27],\
[997, 997, 7*w^2 - 15*w - 75],\
[997, 997, -3*w^2 + 17*w + 11]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 17*x^3 - 19*x^2 + 9*x + 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, -1/2*e^6 + 3/2*e^5 + 2*e^4 - 9*e^3 + 11/2*e^2 + 3*e - 5/2, -e^6 + 3*e^5 + 5*e^4 - 19*e^3 + 4*e^2 + 11*e + 1, e^6 - 2*e^5 - 7*e^4 + 12*e^3 + 7*e^2 - 5*e - 2, -e^5 + 2*e^4 + 6*e^3 - 12*e^2 + 5, -2*e^6 + 6*e^5 + 11*e^4 - 38*e^3 + 3*e^2 + 23*e + 1, -e^5 + 2*e^4 + 6*e^3 - 12*e^2 - 3*e + 6, e^5 - 4*e^4 - 4*e^3 + 24*e^2 - 9*e - 8, 3*e^6 - 8*e^5 - 16*e^4 + 48*e^3 - 7*e^2 - 19*e + 3, -e^6 + 4*e^5 + 3*e^4 - 25*e^3 + 17*e^2 + 12*e - 6, e^6 - e^5 - 10*e^4 + 7*e^3 + 26*e^2 - 8*e - 11, e^6 - 3*e^5 - 4*e^4 + 17*e^3 - 12*e^2 + 2*e + 7, e^6 - e^5 - 8*e^4 + 5*e^3 + 12*e^2 + 4*e + 3, 2*e^6 - 7*e^5 - 9*e^4 + 45*e^3 - 13*e^2 - 30*e + 4, -2*e^6 + 6*e^5 + 11*e^4 - 38*e^3 + 4*e^2 + 22*e - 3, -3*e^6 + 7*e^5 + 18*e^4 - 42*e^3 - 5*e^2 + 17*e + 4, e^6 - e^5 - 9*e^4 + 9*e^3 + 17*e^2 - 17*e, -2*e^6 + 2*e^5 + 19*e^4 - 13*e^3 - 44*e^2 + 11*e + 21, 2*e^6 - 2*e^5 - 17*e^4 + 11*e^3 + 30*e^2 + e - 5, 2*e^6 - 3*e^5 - 18*e^4 + 23*e^3 + 39*e^2 - 36*e - 15, 3*e^6 - 5*e^5 - 23*e^4 + 32*e^3 + 33*e^2 - 25*e - 7, -e^6 + 4*e^5 + 5*e^4 - 29*e^3 + 6*e^2 + 31*e - 8, 4*e^6 - 10*e^5 - 25*e^4 + 64*e^3 + 11*e^2 - 47*e + 3, 3*e^6 - 7*e^5 - 17*e^4 + 42*e^3 - 4*e^2 - 13*e + 10, 3*e^6 - 7*e^5 - 19*e^4 + 44*e^3 + 12*e^2 - 31*e - 6, 2*e^6 - 4*e^5 - 15*e^4 + 25*e^3 + 18*e^2 - 15*e + 3, -5*e^6 + 14*e^5 + 25*e^4 - 87*e^3 + 24*e^2 + 45*e - 12, -3*e^5 + 6*e^4 + 19*e^3 - 33*e^2 - 14*e + 5, -e^6 + 5*e^5 + e^4 - 32*e^3 + 27*e^2 + 17*e - 5, -e^6 + 4*e^5 + 5*e^4 - 24*e^3 + e^2 + 8*e + 7, -4*e^5 + 10*e^4 + 23*e^3 - 63*e^2 + 3*e + 27, 3*e^6 - 3*e^5 - 29*e^4 + 21*e^3 + 70*e^2 - 26*e - 24, e^5 - 3*e^4 - 6*e^3 + 19*e^2 + 5*e - 2, 2*e^5 - 8*e^4 - 9*e^3 + 48*e^2 - 12*e - 21, e^6 - 12*e^4 + 2*e^3 + 40*e^2 - 10*e - 25, -2*e^6 + 4*e^5 + 15*e^4 - 25*e^3 - 23*e^2 + 15*e + 20, 3*e^6 - 10*e^5 - 14*e^4 + 64*e^3 - 17*e^2 - 42*e + 4, -e^5 + 5*e^4 + 4*e^3 - 30*e^2 + 7*e + 19, -2*e^6 - e^5 + 24*e^4 + 8*e^3 - 72*e^2 - 11*e + 24, e^5 - 12*e^3 + 29*e + 6, -e^6 + 4*e^5 + 2*e^4 - 28*e^3 + 21*e^2 + 33*e - 3, -3*e^6 + 7*e^5 + 16*e^4 - 42*e^3 + 8*e^2 + 13*e + 3, -3*e^6 + 8*e^5 + 18*e^4 - 55*e^3 - 5*e^2 + 59*e - 2, -3*e^6 + 7*e^5 + 21*e^4 - 46*e^3 - 24*e^2 + 36*e + 17, -2*e^6 + e^5 + 19*e^4 - e^3 - 46*e^2 - 20*e + 21, 2*e^6 - 3*e^5 - 13*e^4 + 15*e^3 + 6*e^2 + 6*e + 11, 2*e^6 - 11*e^5 - 3*e^4 + 71*e^3 - 50*e^2 - 44*e + 19, -2*e^6 + 2*e^5 + 18*e^4 - 9*e^3 - 40*e^2 - 10*e + 17, 2*e^6 - 7*e^5 - 10*e^4 + 48*e^3 - 5*e^2 - 46*e - 2, e^6 - 6*e^5 + e^4 + 42*e^3 - 40*e^2 - 43*e + 13, 3*e^6 - 5*e^5 - 21*e^4 + 25*e^3 + 25*e^2 + 15*e - 18, e^6 - 5*e^5 - e^4 + 35*e^3 - 31*e^2 - 33*e + 14, -3*e^6 + 11*e^5 + 9*e^4 - 65*e^3 + 53*e^2 + 17*e - 26, e^6 - 4*e^5 + 23*e^3 - 39*e^2 - 2*e + 21, -4*e^4 + 4*e^3 + 31*e^2 - 20*e - 29, 3*e^6 - 12*e^5 - 9*e^4 + 73*e^3 - 53*e^2 - 25*e + 27, -2*e^5 + 4*e^4 + 11*e^3 - 22*e^2 - 7*e + 2, 4*e^6 - 15*e^5 - 14*e^4 + 94*e^3 - 51*e^2 - 41*e + 5, -e^6 - 3*e^5 + 17*e^4 + 19*e^3 - 63*e^2 - 10*e + 7, 4*e^6 - 14*e^5 - 16*e^4 + 88*e^3 - 41*e^2 - 54*e + 11, 3*e^6 - 10*e^5 - 13*e^4 + 65*e^3 - 29*e^2 - 51*e + 15, -e^6 + 8*e^5 - 8*e^4 - 49*e^3 + 83*e^2 + 20*e - 29, -7*e^6 + 17*e^5 + 40*e^4 - 101*e^3 + 7*e^2 + 26*e - 16, 4*e^6 - 9*e^5 - 25*e^4 + 58*e^3 + 9*e^2 - 39*e + 12, 3*e^6 - 8*e^5 - 16*e^4 + 48*e^3 - 14*e^2 - 18*e + 23, -e^6 + 3*e^5 + 2*e^4 - 16*e^3 + 25*e^2 - 12*e - 5, -7*e^6 + 18*e^5 + 39*e^4 - 110*e^3 + 3*e^2 + 50*e + 15, -6*e^6 + 20*e^5 + 26*e^4 - 121*e^3 + 49*e^2 + 49*e - 13, -5*e^6 + 21*e^5 + 15*e^4 - 133*e^3 + 78*e^2 + 76*e - 20, -7*e^6 + 17*e^5 + 45*e^4 - 109*e^3 - 24*e^2 + 80*e - 6, 2*e^6 - 8*e^5 - 4*e^4 + 45*e^3 - 45*e^2 + 7*e + 19, -3*e^6 + 4*e^5 + 25*e^4 - 28*e^3 - 45*e^2 + 34*e + 9, 2*e^5 - 2*e^4 - 13*e^3 + 5*e^2 + 17*e + 17, e^6 - 5*e^5 + e^4 + 29*e^3 - 40*e^2 - 12*e + 18, 2*e^6 - 9*e^5 - 3*e^4 + 54*e^3 - 54*e^2 - 14*e + 12, -e^5 + 4*e^4 + 10*e^3 - 23*e^2 - 29*e + 19, -2*e^6 + 4*e^5 + 13*e^4 - 21*e^3 - 12*e^2 - 14*e + 8, -4*e^6 + 14*e^5 + 14*e^4 - 91*e^3 + 56*e^2 + 63*e - 18, 4*e^6 - 6*e^5 - 29*e^4 + 34*e^3 + 37*e^2 - 12*e - 16, -5*e^6 + 7*e^5 + 44*e^4 - 50*e^3 - 90*e^2 + 63*e + 35, -3*e^6 + 8*e^5 + 10*e^4 - 43*e^3 + 47*e^2 - 11*e - 28, -e^6 - 4*e^5 + 20*e^4 + 29*e^3 - 82*e^2 - 29*e + 19, -3*e^6 + 14*e^5 + 6*e^4 - 87*e^3 + 68*e^2 + 37*e - 19, e^6 - 12*e^5 + 14*e^4 + 75*e^3 - 112*e^2 - 39*e + 21, 7*e^6 - 18*e^5 - 44*e^4 + 116*e^3 + 24*e^2 - 88*e - 7, e^6 - 3*e^5 - 6*e^4 + 17*e^3 + e^2 - 4*e - 10, 3*e^6 - 8*e^5 - 13*e^4 + 44*e^3 - 22*e^2 - e - 3, -e^6 - 3*e^5 + 23*e^4 + 14*e^3 - 102*e^2 + 13*e + 36, 3*e^6 - 7*e^5 - 17*e^4 + 40*e^3 - 6*e^2 - 3*e + 36, -6*e^6 + 22*e^5 + 21*e^4 - 136*e^3 + 77*e^2 + 61*e - 15, e^6 + 4*e^5 - 21*e^4 - 19*e^3 + 95*e^2 - 27*e - 33, 5*e^5 - 12*e^4 - 27*e^3 + 70*e^2 - 20, 2*e^6 + 2*e^5 - 28*e^4 - 18*e^3 + 93*e^2 + 38*e - 33, 4*e^6 - 11*e^5 - 18*e^4 + 57*e^3 - 35*e^2 + 26*e + 19, 9*e^6 - 28*e^5 - 43*e^4 + 175*e^3 - 56*e^2 - 95*e + 28, -9*e^6 + 27*e^5 + 45*e^4 - 172*e^3 + 39*e^2 + 105*e - 5, -e^6 - e^5 + 12*e^4 + 9*e^3 - 33*e^2 - 21*e - 5, -5*e^6 + 23*e^5 + 7*e^4 - 143*e^3 + 129*e^2 + 76*e - 35, -2*e^6 + 7*e^5 + 10*e^4 - 52*e^3 + 13*e^2 + 61*e - 11, 4*e^6 - 8*e^5 - 28*e^4 + 50*e^3 + 31*e^2 - 27*e - 30, 4*e^6 - 8*e^5 - 27*e^4 + 46*e^3 + 17*e^2 - 8*e + 28, 5*e^6 - 2*e^5 - 52*e^4 + 15*e^3 + 137*e^2 - 33*e - 28, e^6 - e^5 - 9*e^4 + 12*e^3 + 10*e^2 - 29*e + 20, 13*e^6 - 39*e^5 - 61*e^4 + 238*e^3 - 80*e^2 - 101*e + 22, 5*e^6 - 13*e^5 - 25*e^4 + 72*e^3 - 24*e^2 - 3*e + 4, 3*e^6 - 8*e^5 - 16*e^4 + 52*e^3 - 10*e^2 - 45*e + 20, -5*e^6 + 7*e^5 + 42*e^4 - 43*e^3 - 75*e^2 + 25*e + 21, -6*e^6 + 10*e^5 + 47*e^4 - 63*e^3 - 72*e^2 + 46*e + 6, -e^6 - e^5 + 7*e^4 + 13*e^3 + 2*e^2 - 40*e - 22, -9*e^6 + 26*e^5 + 49*e^4 - 172*e^3 + 21*e^2 + 130*e - 11, 6*e^6 - 6*e^5 - 52*e^4 + 29*e^3 + 101*e^2 + 13*e - 21, 5*e^6 - 12*e^5 - 26*e^4 + 64*e^3 - 17*e^2 + 10*e + 22, -2*e^6 + e^5 + 19*e^4 - 2*e^3 - 40*e^2 - 21*e - 3, 3*e^6 - 11*e^5 - 13*e^4 + 67*e^3 - 18*e^2 - 15*e - 17, -5*e^6 + 7*e^5 + 42*e^4 - 39*e^3 - 68*e^2 + e - 6, 3*e^6 - 3*e^5 - 25*e^4 + 13*e^3 + 42*e^2 + 8*e + 16, -3*e^6 + 12*e^5 + 11*e^4 - 78*e^3 + 39*e^2 + 48*e - 21, -2*e^6 + 6*e^5 + 8*e^4 - 33*e^3 + 25*e^2 - 9*e - 19, -3*e^6 + 2*e^5 + 33*e^4 - 18*e^3 - 97*e^2 + 44*e + 29, -4*e^6 + 6*e^5 + 31*e^4 - 39*e^3 - 45*e^2 + 24*e + 7, -3*e^6 + 10*e^5 + 15*e^4 - 65*e^3 + 21*e^2 + 39*e - 33, -10*e^6 + 33*e^5 + 40*e^4 - 203*e^3 + 104*e^2 + 88*e - 24, -4*e^6 + 6*e^5 + 38*e^4 - 48*e^3 - 93*e^2 + 80*e + 33, -e^5 + 15*e^3 - e^2 - 58*e + 7, e^6 - 17*e^4 + 3*e^3 + 66*e^2 - 13*e - 16, e^4 - 6*e^3 - 12*e^2 + 31*e + 22, -5*e^6 + 9*e^5 + 40*e^4 - 62*e^3 - 64*e^2 + 71*e + 7, 7*e^6 - 14*e^5 - 50*e^4 + 87*e^3 + 49*e^2 - 45*e - 2, 4*e^6 - 14*e^5 - 17*e^4 + 98*e^3 - 35*e^2 - 102*e + 18, -7*e^6 + 14*e^5 + 52*e^4 - 88*e^3 - 72*e^2 + 48*e + 41, 2*e^6 - 5*e^5 - 19*e^4 + 42*e^3 + 47*e^2 - 77*e - 16, 8*e^6 - 26*e^5 - 38*e^4 + 163*e^3 - 42*e^2 - 96*e + 7, -6*e^6 + 22*e^5 + 25*e^4 - 144*e^3 + 51*e^2 + 107*e - 15, 11*e^6 - 35*e^5 - 51*e^4 + 218*e^3 - 68*e^2 - 123*e + 12, 3*e^6 - e^5 - 33*e^4 + 2*e^3 + 94*e^2 + 7*e - 18, 2*e^5 - 16*e^3 + 6*e^2 + 21*e - 25, 2*e^6 - 8*e^5 - 5*e^4 + 44*e^3 - 38*e^2 + 19, 2*e^6 - 13*e^5 + e^4 + 85*e^3 - 63*e^2 - 60*e - 8, -4*e^6 + 14*e^5 + 13*e^4 - 80*e^3 + 52*e^2 + 3*e - 10, -4*e^6 + 9*e^5 + 27*e^4 - 55*e^3 - 17*e^2 + 33*e - 33, 5*e^6 - 10*e^5 - 36*e^4 + 65*e^3 + 32*e^2 - 46*e + 30, -2*e^6 + 11*e^5 + 2*e^4 - 73*e^3 + 57*e^2 + 72*e - 39, -3*e^6 + 19*e^5 - 7*e^4 - 114*e^3 + 145*e^2 + 27*e - 43, -9*e^6 + 22*e^5 + 57*e^4 - 141*e^3 - 36*e^2 + 95*e + 32, 3*e^6 - 9*e^5 - 12*e^4 + 63*e^3 - 40*e^2 - 61*e + 28, 5*e^6 - 9*e^5 - 43*e^4 + 63*e^3 + 76*e^2 - 62*e + 4, -e^6 + 10*e^5 - 11*e^4 - 60*e^3 + 93*e^2 + 10*e - 17, 6*e^6 - 18*e^5 - 20*e^4 + 105*e^3 - 93*e^2 - 17*e + 41, -5*e^6 + 18*e^5 + 21*e^4 - 116*e^3 + 43*e^2 + 58*e + 9, -5*e^6 + 9*e^5 + 39*e^4 - 61*e^3 - 62*e^2 + 64*e + 8, 2*e^6 - 6*e^5 - 9*e^4 + 41*e^3 - 24*e^2 - 45*e + 33, -2*e^6 + 4*e^5 + 5*e^4 - 17*e^3 + 42*e^2 - 15*e - 37, -10*e^6 + 26*e^5 + 53*e^4 - 157*e^3 + 32*e^2 + 53*e - 1, -9*e^6 + 15*e^5 + 68*e^4 - 93*e^3 - 99*e^2 + 59*e + 35, -7*e^6 + 14*e^5 + 50*e^4 - 82*e^3 - 68*e^2 + 33*e + 48, -8*e^6 + 12*e^5 + 61*e^4 - 73*e^3 - 82*e^2 + 28*e + 10, e^6 - 13*e^5 + 16*e^4 + 84*e^3 - 124*e^2 - 44*e + 8, -6*e^6 + 11*e^5 + 51*e^4 - 75*e^3 - 100*e^2 + 79*e + 40, 7*e^6 - 16*e^5 - 38*e^4 + 89*e^3 - 11*e^2 - 6*e + 7, 5*e^6 - 12*e^5 - 26*e^4 + 65*e^3 - 19*e^2 + 13*e + 6, 3*e^6 - 7*e^5 - 22*e^4 + 50*e^3 + 18*e^2 - 57*e + 31, -10*e^6 + 28*e^5 + 51*e^4 - 176*e^3 + 37*e^2 + 98*e + 4, -2*e^6 + 18*e^5 - 12*e^4 - 117*e^3 + 140*e^2 + 65*e - 32, 7*e^6 - 15*e^5 - 49*e^4 + 101*e^3 + 55*e^2 - 96*e - 23, 5*e^5 - 10*e^4 - 30*e^3 + 65*e^2 + 7*e - 41, 8*e^6 - 22*e^5 - 39*e^4 + 128*e^3 - 47*e^2 - 26*e + 6, 9*e^6 - 16*e^5 - 64*e^4 + 91*e^3 + 79*e^2 - 17*e - 26, -7*e^6 + 9*e^5 + 62*e^4 - 56*e^3 - 128*e^2 + 29*e + 55, 4*e^6 - 12*e^5 - 23*e^4 + 77*e^3 - 4*e^2 - 46*e + 20, -6*e^6 + 5*e^5 + 54*e^4 - 22*e^3 - 117*e^2 - 11*e + 37, 8*e^6 - 20*e^5 - 56*e^4 + 131*e^3 + 62*e^2 - 115*e - 24]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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