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

NN = ZF.ideal([17, 17, -w^3 + w^2 + 6*w - 1])

primes_array = [
[2, 2, w^3 - w^2 - 6*w - 2],\
[3, 3, -w^3 + 2*w^2 + 4*w - 2],\
[4, 2, w^3 - w^2 - 5*w - 2],\
[17, 17, -w^3 + w^2 + 6*w - 1],\
[17, 17, -w + 2],\
[29, 29, -w^3 + 2*w^2 + 4*w - 4],\
[29, 29, w^3 - 2*w^2 - 4*w],\
[31, 31, -w^2 + 2],\
[31, 31, -w^3 + 7*w + 5],\
[41, 41, -2*w^3 + 2*w^2 + 13*w - 2],\
[41, 41, 3*w^3 - 4*w^2 - 17*w + 5],\
[67, 67, 3*w^3 - 4*w^2 - 17*w + 1],\
[67, 67, -w^2 + 4*w + 2],\
[83, 83, 2*w^2 - 5*w - 2],\
[83, 83, -w^3 + 8*w + 6],\
[83, 83, w^3 - 2*w^2 - 2*w - 2],\
[83, 83, w^3 - 2*w^2 - 6*w],\
[97, 97, -3*w^3 + 2*w^2 + 17*w + 7],\
[97, 97, w^3 - 4*w^2 + 3*w + 1],\
[97, 97, -5*w^3 + 8*w^2 + 24*w - 8],\
[97, 97, 2*w^3 - 2*w^2 - 13*w - 4],\
[101, 101, -w^3 + 6*w + 6],\
[101, 101, -w^3 + 6*w + 2],\
[103, 103, -4*w^3 + 3*w^2 + 26*w + 12],\
[103, 103, -w^3 + 2*w^2 + 9*w + 3],\
[107, 107, 2*w^3 - 2*w^2 - 11*w],\
[107, 107, -w^3 + 2*w^2 + 3*w - 3],\
[107, 107, w^3 - w^2 - 4*w - 3],\
[107, 107, 2*w^3 - 3*w^2 - 10*w],\
[121, 11, -2*w^3 + 3*w^2 + 8*w + 2],\
[149, 149, -3*w^3 + 5*w^2 + 14*w - 3],\
[149, 149, -2*w^3 + 4*w^2 + 7*w - 4],\
[157, 157, 2*w^3 - 2*w^2 - 10*w - 1],\
[157, 157, 2*w^3 - 3*w^2 - 8*w + 2],\
[157, 157, 2*w^3 - 2*w^2 - 10*w - 3],\
[157, 157, -3*w^3 + 4*w^2 + 15*w + 1],\
[163, 163, -2*w^2 + 4*w + 5],\
[163, 163, 2*w^3 - 4*w^2 - 10*w + 5],\
[169, 13, 2*w^3 - 3*w^2 - 12*w + 2],\
[169, 13, -w^3 + 9*w + 3],\
[173, 173, 3*w^3 - 2*w^2 - 17*w - 9],\
[173, 173, -2*w^3 + 14*w + 7],\
[197, 197, 2*w^3 - 2*w^2 - 12*w + 1],\
[197, 197, 3*w^3 - 3*w^2 - 18*w - 1],\
[199, 199, 3*w^3 - 4*w^2 - 18*w + 8],\
[199, 199, 4*w^3 - 5*w^2 - 24*w + 6],\
[223, 223, w^3 - 2*w^2 - 3*w - 3],\
[223, 223, 2*w^3 - 3*w^2 - 10*w + 6],\
[227, 227, -w^3 + 2*w^2 + 6*w - 8],\
[227, 227, 3*w + 4],\
[227, 227, 3*w^3 - 3*w^2 - 18*w - 7],\
[227, 227, -2*w^3 + 3*w^2 + 12*w - 6],\
[229, 229, -w - 4],\
[229, 229, w^2 - 2*w + 2],\
[229, 229, -w^3 + w^2 + 6*w + 5],\
[229, 229, -w^3 + 2*w^2 + 5*w - 7],\
[233, 233, -2*w^3 + 3*w^2 + 8*w - 4],\
[233, 233, -3*w^3 + 4*w^2 + 15*w + 3],\
[281, 281, -2*w^3 + 3*w^2 + 10*w + 2],\
[281, 281, -w^3 + 2*w^2 + 3*w - 5],\
[289, 17, -2*w^3 + 2*w^2 + 14*w + 5],\
[293, 293, w^2 - 6],\
[293, 293, w^3 - 7*w - 1],\
[331, 331, -6*w^3 + 10*w^2 + 27*w - 6],\
[331, 331, 2*w^3 - 2*w^2 - 12*w - 7],\
[347, 347, 3*w^3 - 2*w^2 - 18*w - 6],\
[347, 347, -4*w^3 + 2*w^2 + 23*w + 10],\
[347, 347, 2*w^3 - 6*w^2 - w + 4],\
[347, 347, -4*w^3 + 3*w^2 + 24*w + 8],\
[359, 359, -3*w^3 + 4*w^2 + 17*w + 1],\
[359, 359, w^2 - 4*w - 4],\
[359, 359, w^3 - 8*w],\
[359, 359, -w^3 + 2*w^2 + 6*w - 6],\
[367, 367, 2*w^2 - 3*w - 4],\
[367, 367, -w^3 + 3*w^2 + 4*w - 7],\
[379, 379, 3*w^3 - 3*w^2 - 16*w - 3],\
[379, 379, 2*w^3 - 2*w^2 - 9*w - 2],\
[461, 461, -2*w^3 + 5*w^2 + 2*w + 2],\
[461, 461, 4*w^3 - 4*w^2 - 26*w - 11],\
[463, 463, -2*w^3 + 13*w + 8],\
[463, 463, -w^3 - w^2 + 6*w + 7],\
[487, 487, 2*w^3 - 17*w - 8],\
[487, 487, -w^3 + 10*w + 4],\
[491, 491, -5*w^3 + 3*w^2 + 30*w + 13],\
[491, 491, -5*w^3 + 4*w^2 + 28*w + 14],\
[491, 491, 3*w^3 - 8*w^2 - 4*w + 4],\
[491, 491, 7*w^3 - 12*w^2 - 33*w + 15],\
[499, 499, -2*w^3 + 2*w^2 + 12*w - 5],\
[499, 499, 2*w^2 - 7*w],\
[529, 23, -w^3 + 3*w^2 + 4*w - 5],\
[529, 23, 2*w^2 - 3*w - 6],\
[557, 557, -2*w^3 + 3*w^2 + 12*w + 4],\
[557, 557, w^3 - 9*w - 9],\
[569, 569, 4*w^3 - 5*w^2 - 22*w + 4],\
[569, 569, -3*w^3 + 2*w^2 + 20*w + 4],\
[577, 577, 3*w^3 - 3*w^2 - 20*w + 3],\
[577, 577, -4*w^3 + 8*w^2 + 16*w - 9],\
[577, 577, 7*w^3 - 11*w^2 - 34*w + 9],\
[577, 577, -4*w^3 + 6*w^2 + 22*w - 11],\
[593, 593, -6*w^3 + 10*w^2 + 29*w - 14],\
[593, 593, -w^3 + 4*w^2 - w - 7],\
[619, 619, -3*w^3 + 5*w^2 + 12*w - 1],\
[619, 619, -4*w^3 + 8*w^2 + 18*w - 15],\
[625, 5, -5],\
[631, 631, -3*w^3 + 8*w^2 + 6*w - 4],\
[631, 631, -2*w^3 + 8*w^2 - 3*w - 8],\
[643, 643, 3*w^3 - 4*w^2 - 14*w + 2],\
[643, 643, -3*w^3 + 4*w^2 + 14*w + 2],\
[661, 661, w^3 - 8*w - 10],\
[661, 661, -3*w^3 + 2*w^2 + 21*w + 3],\
[661, 661, w^3 - 2*w^2 - 6*w - 4],\
[661, 661, 2*w^3 - 3*w^2 - 14*w + 4],\
[677, 677, -9*w^3 + 12*w^2 + 50*w - 10],\
[677, 677, 3*w^3 - 4*w^2 - 17*w - 7],\
[691, 691, 3*w^3 - 2*w^2 - 21*w - 9],\
[691, 691, 2*w^3 - 3*w^2 - 14*w - 2],\
[701, 701, -9*w^3 + 13*w^2 + 48*w - 15],\
[701, 701, 2*w^3 - 6*w^2 + w - 2],\
[709, 709, 2*w^2 - 2*w - 5],\
[709, 709, 2*w^2 - 2*w - 7],\
[709, 709, 4*w^3 - 5*w^2 - 20*w - 4],\
[709, 709, -3*w^3 + 6*w^2 + 14*w - 10],\
[727, 727, 7*w^3 - 10*w^2 - 36*w + 8],\
[727, 727, 3*w^2 - 6*w - 8],\
[743, 743, 9*w^3 - 12*w^2 - 51*w + 13],\
[743, 743, w^3 - 2*w^2 - w - 5],\
[743, 743, -4*w^3 + 4*w^2 + 27*w - 8],\
[743, 743, -3*w^3 + 4*w^2 + 21*w + 9],\
[751, 751, -w^3 + 10*w + 2],\
[751, 751, 3*w^3 - 4*w^2 - 18*w + 2],\
[761, 761, 4*w^3 - 4*w^2 - 23*w - 2],\
[761, 761, -3*w^3 + 2*w^2 + 19*w + 5],\
[809, 809, -3*w^3 + 5*w^2 + 10*w + 5],\
[809, 809, -w^3 - w^2 + 10*w + 3],\
[821, 821, -w^3 + 3*w^2 + 2*w - 9],\
[821, 821, 2*w^2 - 4*w - 9],\
[823, 823, w^3 - 6*w^2 + 9*w + 1],\
[823, 823, -3*w^3 + 2*w^2 + 15*w + 5],\
[827, 827, 3*w^3 - 3*w^2 - 18*w + 1],\
[827, 827, 2*w^3 - 16*w - 11],\
[827, 827, 3*w^3 - 24*w - 14],\
[827, 827, 3*w - 4],\
[829, 829, w^2 - 6*w - 2],\
[829, 829, 2*w^3 - 2*w^2 - 10*w - 9],\
[829, 829, 5*w^3 - 6*w^2 - 29*w - 1],\
[829, 829, w^3 + 2*w^2 - 14*w - 6],\
[841, 29, -2*w^3 + 2*w^2 + 14*w + 3],\
[857, 857, -3*w^3 + 6*w^2 + 11*w - 7],\
[857, 857, -4*w^3 + 7*w^2 + 18*w - 4],\
[859, 859, -w^3 + w^2 + 6*w - 5],\
[859, 859, w - 6],\
[883, 883, 5*w^3 - 5*w^2 - 26*w - 11],\
[883, 883, -3*w^3 + 3*w^2 + 14*w + 5],\
[887, 887, 5*w^3 - 2*w^2 - 34*w - 16],\
[887, 887, -w^3 + 4*w^2 - 10],\
[887, 887, 4*w^3 - 2*w^2 - 26*w - 11],\
[887, 887, 2*w^3 - 8*w^2 + 4*w + 7],\
[907, 907, 6*w^3 - 8*w^2 - 34*w + 7],\
[907, 907, -w^3 + w^2 + 8*w - 7],\
[941, 941, 2*w^3 - 2*w^2 - 8*w - 5],\
[941, 941, -3*w^3 + 23*w + 11],\
[953, 953, 2*w^3 - 10*w - 3],\
[953, 953, -4*w^3 + 2*w^2 + 24*w + 15],\
[961, 31, -2*w^3 + 2*w^2 + 14*w - 7],\
[991, 991, -3*w^3 + 4*w^2 + 13*w + 3],\
[991, 991, 4*w^3 - 5*w^2 - 20*w + 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^9 - 6*x^8 + 5*x^7 + 31*x^6 - 61*x^5 - 9*x^4 + 79*x^3 - 26*x^2 - 21*x + 9
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -1/3*e^8 + e^7 + 7/3*e^6 - 22/3*e^5 - 14/3*e^4 + 14*e^3 + 14/3*e^2 - 22/3*e - 1, 5/3*e^8 - 7*e^7 - 11/3*e^6 + 131/3*e^5 - 83/3*e^4 - 55*e^3 + 128/3*e^2 + 50/3*e - 11, -1, 2*e^8 - 10*e^7 + 2*e^6 + 57*e^5 - 72*e^4 - 50*e^3 + 95*e^2 + 7*e - 21, e^8 - 5*e^7 + 33*e^5 - 34*e^4 - 50*e^3 + 60*e^2 + 23*e - 18, -2*e^7 + 5*e^6 + 12*e^5 - 29*e^4 - 14*e^3 + 27*e^2 + 7*e, 8/3*e^8 - 13*e^7 + 1/3*e^6 + 233/3*e^5 - 248/3*e^4 - 84*e^3 + 341/3*e^2 + 71/3*e - 29, 8/3*e^8 - 15*e^7 + 19/3*e^6 + 263/3*e^5 - 356/3*e^4 - 86*e^3 + 458/3*e^2 + 44/3*e - 35, 5*e^8 - 24*e^7 - e^6 + 146*e^5 - 147*e^4 - 170*e^3 + 214*e^2 + 48*e - 57, e^8 - 3*e^7 - 5*e^6 + 17*e^5 + 2*e^4 - 13*e^3 - 2*e^2 - e, -7/3*e^8 + 7*e^7 + 37/3*e^6 - 124/3*e^5 - 35/3*e^4 + 41*e^3 + 74/3*e^2 - 1/3*e - 14, -10/3*e^8 + 13*e^7 + 37/3*e^6 - 259/3*e^5 + 76/3*e^4 + 130*e^3 - 157/3*e^2 - 148/3*e + 16, -7*e^7 + 23*e^6 + 34*e^5 - 146*e^4 - 3*e^3 + 187*e^2 - 13*e - 39, -e^8 + 6*e^7 - 3*e^6 - 37*e^5 + 49*e^4 + 46*e^3 - 62*e^2 - 18*e + 12, -2*e^6 + 3*e^5 + 13*e^4 - 15*e^3 - 14*e^2 + 4*e - 3, -2*e^8 + 13*e^7 - 10*e^6 - 78*e^5 + 129*e^4 + 87*e^3 - 193*e^2 - 29*e + 57, 2/3*e^8 + 3*e^7 - 53/3*e^6 - 52/3*e^5 + 271/3*e^4 + 19*e^3 - 322/3*e^2 - 46/3*e + 22, 14/3*e^8 - 22*e^7 - 14/3*e^6 + 419/3*e^5 - 347/3*e^4 - 186*e^3 + 539/3*e^2 + 197/3*e - 56, -1/3*e^8 + e^7 + 4/3*e^6 - 16/3*e^5 + 7/3*e^4 + 3*e^3 - 16/3*e^2 + 5/3*e - 5, 5/3*e^8 - 13*e^7 + 46/3*e^6 + 224/3*e^5 - 437/3*e^4 - 73*e^3 + 560/3*e^2 + 80/3*e - 44, e^8 - 4*e^7 - 4*e^6 + 27*e^5 - 6*e^4 - 41*e^3 + 19*e^2 + 9*e - 9, 5*e^8 - 24*e^7 + 2*e^6 + 138*e^5 - 164*e^4 - 125*e^3 + 227*e^2 + 13*e - 54, -19/3*e^8 + 34*e^7 - 29/3*e^6 - 604/3*e^5 + 754/3*e^4 + 208*e^3 - 1018/3*e^2 - 118/3*e + 82, 17/3*e^8 - 28*e^7 + 4/3*e^6 + 503/3*e^5 - 539/3*e^4 - 183*e^3 + 746/3*e^2 + 146/3*e - 62, 4*e^8 - 17*e^7 - 8*e^6 + 104*e^5 - 70*e^4 - 118*e^3 + 101*e^2 + 18*e - 24, e^8 - 5*e^7 + 34*e^5 - 37*e^4 - 56*e^3 + 75*e^2 + 30*e - 24, -7*e^8 + 35*e^7 - 5*e^6 - 206*e^5 + 242*e^4 + 212*e^3 - 329*e^2 - 53*e + 87, -7*e^8 + 33*e^7 + 3*e^6 - 199*e^5 + 196*e^4 + 222*e^3 - 289*e^2 - 56*e + 81, -1/3*e^8 + 3*e^7 - 11/3*e^6 - 52/3*e^5 + 94/3*e^4 + 17*e^3 - 100/3*e^2 - 16/3*e + 4, 5*e^8 - 30*e^7 + 19*e^6 + 173*e^5 - 272*e^4 - 161*e^3 + 370*e^2 + 33*e - 93, -e^8 + 4*e^7 + 3*e^6 - 21*e^5 + 2*e^4 + 10*e^3 + 30*e^2 + 3*e - 24, -10/3*e^8 + 13*e^7 + 31/3*e^6 - 247/3*e^5 + 118/3*e^4 + 105*e^3 - 235/3*e^2 - 49/3*e + 28, -2*e^8 + 15*e^7 - 16*e^6 - 85*e^5 + 157*e^4 + 73*e^3 - 194*e^2 - 6*e + 50, -1/3*e^8 + 16/3*e^6 - 4/3*e^5 - 86/3*e^4 + 9*e^3 + 170/3*e^2 - 25/3*e - 23, -4*e^8 + 20*e^7 - 2*e^6 - 120*e^5 + 137*e^4 + 133*e^3 - 200*e^2 - 42*e + 50, -22/3*e^8 + 33*e^7 + 19/3*e^6 - 592/3*e^5 + 559/3*e^4 + 213*e^3 - 853/3*e^2 - 145/3*e + 82, 8/3*e^8 - 14*e^7 + 10/3*e^6 + 239/3*e^5 - 290/3*e^4 - 66*e^3 + 338/3*e^2 + 2/3*e - 17, 8/3*e^8 - 22*e^7 + 82/3*e^6 + 386/3*e^5 - 770/3*e^4 - 131*e^3 + 1061/3*e^2 + 104/3*e - 92, -10/3*e^8 + 21*e^7 - 50/3*e^6 - 358/3*e^5 + 613/3*e^4 + 108*e^3 - 805/3*e^2 - 91/3*e + 76, -e^8 - 2*e^7 + 21*e^6 + 6*e^5 - 100*e^4 + 16*e^3 + 120*e^2 - 8*e - 30, 2*e^8 - 4*e^7 - 18*e^6 + 31*e^5 + 50*e^4 - 65*e^3 - 47*e^2 + 34*e + 21, 7*e^8 - 25*e^7 - 28*e^6 + 154*e^5 - 28*e^4 - 181*e^3 + 31*e^2 + 29*e + 9, -7*e^8 + 34*e^7 - 209*e^5 + 221*e^4 + 256*e^3 - 341*e^2 - 95*e + 99, e^8 - 14*e^6 + e^5 + 57*e^4 - 2*e^3 - 65*e^2 - 12*e + 20, 3*e^8 - 20*e^7 + 19*e^6 + 109*e^5 - 208*e^4 - 75*e^3 + 270*e^2 + 7*e - 67, -4/3*e^8 + 3*e^7 + 31/3*e^6 - 58/3*e^5 - 77/3*e^4 + 27*e^3 + 80/3*e^2 - 25/3*e + 7, -4/3*e^8 + 15*e^7 - 83/3*e^6 - 238/3*e^5 + 625/3*e^4 + 44*e^3 - 739/3*e^2 + 17/3*e + 55, -e^7 + 6*e^6 + 2*e^5 - 45*e^4 + 13*e^3 + 89*e^2 - 11*e - 39, -3*e^8 + 11*e^7 + 9*e^6 - 67*e^5 + 35*e^4 + 82*e^3 - 57*e^2 - 35*e + 15, 3*e^8 - 13*e^7 - 6*e^6 + 80*e^5 - 47*e^4 - 98*e^3 + 49*e^2 + 31*e - 3, 6*e^8 - 28*e^7 - 4*e^6 + 172*e^5 - 161*e^4 - 210*e^3 + 250*e^2 + 79*e - 78, -10/3*e^8 + 24*e^7 - 74/3*e^6 - 412/3*e^5 + 766/3*e^4 + 121*e^3 - 985/3*e^2 - 46/3*e + 70, -22/3*e^8 + 32*e^7 + 31/3*e^6 - 586/3*e^5 + 472/3*e^4 + 229*e^3 - 664/3*e^2 - 196/3*e + 46, 5/3*e^8 - 4*e^7 - 38/3*e^6 + 83/3*e^5 + 79/3*e^4 - 40*e^3 - 43/3*e^2 - 19/3*e - 11, 20/3*e^8 - 30*e^7 - 20/3*e^6 + 530/3*e^5 - 452/3*e^4 - 181*e^3 + 539/3*e^2 + 128/3*e - 26, -2*e^8 + 10*e^7 - 63*e^5 + 65*e^4 + 80*e^3 - 110*e^2 - 17*e + 45, 2*e^8 - 7*e^7 - 6*e^6 + 38*e^5 - 19*e^4 - 23*e^3 + 15*e^2 - 14*e + 6, e^8 - 3*e^7 - 4*e^6 + 13*e^5 + e^4 + 9*e^3 - 17*e^2 - 22*e - 6, -3*e^8 + 10*e^7 + 13*e^6 - 58*e^5 + 6*e^4 + 49*e^3 - 11*e^2 + 13*e + 15, -28/3*e^8 + 45*e^7 + 16/3*e^6 - 844/3*e^5 + 751/3*e^4 + 360*e^3 - 1078/3*e^2 - 382/3*e + 94, 2*e^8 - 13*e^7 + 10*e^6 + 76*e^5 - 125*e^4 - 79*e^3 + 177*e^2 + 31*e - 39, 3*e^8 - 15*e^7 + 4*e^6 + 86*e^5 - 121*e^4 - 75*e^3 + 179*e^2 - 2*e - 33, -e^8 + 7*e^7 - 5*e^6 - 48*e^5 + 73*e^4 + 80*e^3 - 136*e^2 - 44*e + 38, -12*e^8 + 54*e^7 + 12*e^6 - 324*e^5 + 287*e^4 + 354*e^3 - 408*e^2 - 92*e + 119, -5*e^7 + 18*e^6 + 18*e^5 - 106*e^4 + 30*e^3 + 101*e^2 - 19*e - 9, 2*e^8 - 5*e^7 - 14*e^6 + 29*e^5 + 33*e^4 - 24*e^3 - 58*e^2 - 5*e + 36, 11*e^8 - 48*e^7 - 16*e^6 + 292*e^5 - 235*e^4 - 330*e^3 + 350*e^2 + 56*e - 96, 2*e^8 - 18*e^7 + 26*e^6 + 100*e^5 - 224*e^4 - 76*e^3 + 290*e^2 + 10*e - 66, -17*e^8 + 78*e^7 + 11*e^6 - 459*e^5 + 432*e^4 + 460*e^3 - 562*e^2 - 75*e + 132, -6*e^8 + 33*e^7 - 14*e^6 - 189*e^5 + 265*e^4 + 171*e^3 - 340*e^2 - 32*e + 90, 7*e^8 - 29*e^7 - 17*e^6 + 178*e^5 - 103*e^4 - 202*e^3 + 148*e^2 + 22*e - 30, -6*e^8 + 24*e^7 + 14*e^6 - 142*e^5 + 93*e^4 + 139*e^3 - 142*e^2 - e + 51, -28/3*e^8 + 47*e^7 - 17/3*e^6 - 859/3*e^5 + 985/3*e^4 + 337*e^3 - 1468/3*e^2 - 310/3*e + 145, 20/3*e^8 - 36*e^7 + 34/3*e^6 + 635/3*e^5 - 812/3*e^4 - 210*e^3 + 1058/3*e^2 + 89/3*e - 74, -34/3*e^8 + 46*e^7 + 97/3*e^6 - 877/3*e^5 + 427/3*e^4 + 388*e^3 - 703/3*e^2 - 394/3*e + 76, -1/3*e^8 + 6*e^7 - 35/3*e^6 - 103/3*e^5 + 241/3*e^4 + 30*e^3 - 289/3*e^2 - 16/3*e + 31, -11*e^8 + 52*e^7 + 10*e^6 - 323*e^5 + 269*e^4 + 401*e^3 - 383*e^2 - 124*e + 105, 17*e^8 - 85*e^7 + 8*e^6 + 507*e^5 - 568*e^4 - 541*e^3 + 798*e^2 + 128*e - 210, -10*e^8 + 41*e^7 + 23*e^6 - 253*e^5 + 159*e^4 + 317*e^3 - 251*e^2 - 128*e + 80, e^8 + 9*e^7 - 48*e^6 - 36*e^5 + 275*e^4 - 32*e^3 - 354*e^2 + 31*e + 80, 47/3*e^8 - 79*e^7 + 34/3*e^6 + 1412/3*e^5 - 1646/3*e^4 - 511*e^3 + 2324/3*e^2 + 437/3*e - 212, -37/3*e^8 + 51*e^7 + 79/3*e^6 - 925/3*e^5 + 610/3*e^4 + 348*e^3 - 877/3*e^2 - 265/3*e + 76, -6*e^8 + 33*e^7 - 17*e^6 - 185*e^5 + 286*e^4 + 149*e^3 - 377*e^2 + e + 96, -8*e^8 + 39*e^7 + 4*e^6 - 244*e^5 + 221*e^4 + 309*e^3 - 324*e^2 - 93*e + 78, -16*e^7 + 48*e^6 + 90*e^5 - 306*e^4 - 80*e^3 + 402*e^2 + 28*e - 102, -14*e^8 + 73*e^7 - 16*e^6 - 436*e^5 + 523*e^4 + 479*e^3 - 715*e^2 - 143*e + 195, -46/3*e^8 + 64*e^7 + 94/3*e^6 - 1168/3*e^5 + 796/3*e^4 + 448*e^3 - 1183/3*e^2 - 328/3*e + 103, 5/3*e^8 - 4*e^7 - 23/3*e^6 + 38/3*e^5 + 7/3*e^4 + 41*e^3 - 40/3*e^2 - 175/3*e - 5, 3*e^8 - 15*e^7 + 3*e^6 + 92*e^5 - 122*e^4 - 116*e^3 + 212*e^2 + 61*e - 70, -2*e^7 + 9*e^6 + 9*e^5 - 66*e^4 + 2*e^3 + 119*e^2 - 4*e - 49, 5*e^7 - 20*e^6 - 14*e^5 + 120*e^4 - 56*e^3 - 129*e^2 + 66*e + 18, -8*e^8 + 45*e^7 - 17*e^6 - 277*e^5 + 358*e^4 + 344*e^3 - 523*e^2 - 131*e + 153, 6*e^8 - 30*e^7 + 4*e^6 + 176*e^5 - 206*e^4 - 177*e^3 + 279*e^2 + 43*e - 69, -2*e^8 + 18*e^7 - 24*e^6 - 107*e^5 + 218*e^4 + 111*e^3 - 310*e^2 - 24*e + 90, 6*e^8 - 42*e^7 + 36*e^6 + 252*e^5 - 416*e^4 - 277*e^3 + 587*e^2 + 66*e - 160, -16/3*e^8 + 33*e^7 - 68/3*e^6 - 607/3*e^5 + 976/3*e^4 + 251*e^3 - 1555/3*e^2 - 304/3*e + 160, -40/3*e^8 + 54*e^7 + 112/3*e^6 - 1030/3*e^5 + 529/3*e^4 + 455*e^3 - 913/3*e^2 - 412/3*e + 91, e^8 + 5*e^7 - 33*e^6 - 16*e^5 + 177*e^4 - 44*e^3 - 227*e^2 + 50*e + 71, -12*e^7 + 33*e^6 + 70*e^5 - 204*e^4 - 74*e^3 + 249*e^2 + 34*e - 66, -e^8 + 8*e^7 - 10*e^6 - 48*e^5 + 100*e^4 + 53*e^3 - 155*e^2 - 13*e + 60, -43/3*e^8 + 76*e^7 - 65/3*e^6 - 1348/3*e^5 + 1723/3*e^4 + 469*e^3 - 2422/3*e^2 - 346/3*e + 220, 11/3*e^8 - 24*e^7 + 43/3*e^6 + 482/3*e^5 - 656/3*e^4 - 253*e^3 + 1061/3*e^2 + 353/3*e - 113, 2*e^8 - 17*e^7 + 23*e^6 + 103*e^5 - 217*e^4 - 129*e^3 + 329*e^2 + 75*e - 103, -4*e^8 + 21*e^7 - 7*e^6 - 122*e^5 + 167*e^4 + 119*e^3 - 233*e^2 - 39*e + 56, -2*e^8 + 16*e^7 - 20*e^6 - 93*e^5 + 198*e^4 + 91*e^3 - 308*e^2 - 24*e + 92, -4*e^8 + 15*e^7 + 13*e^6 - 96*e^5 + 47*e^4 + 132*e^3 - 104*e^2 - 36*e + 23, 5*e^8 - 14*e^7 - 35*e^6 + 99*e^5 + 70*e^4 - 180*e^3 - 73*e^2 + 112*e + 26, -4/3*e^8 + 4*e^7 + 40/3*e^6 - 112/3*e^5 - 116/3*e^4 + 99*e^3 + 53/3*e^2 - 199/3*e + 19, -25/3*e^8 + 34*e^7 + 67/3*e^6 - 652/3*e^5 + 361/3*e^4 + 300*e^3 - 646/3*e^2 - 400/3*e + 49, -1/3*e^8 - 4*e^7 + 46/3*e^6 + 65/3*e^5 - 236/3*e^4 - 20*e^3 + 212/3*e^2 + 68/3*e - 8, 41/3*e^8 - 60*e^7 - 47/3*e^6 + 1067/3*e^5 - 941/3*e^4 - 374*e^3 + 1349/3*e^2 + 257/3*e - 122, e^8 + 3*e^7 - 26*e^6 - 7*e^5 + 129*e^4 - 39*e^3 - 142*e^2 + 30*e + 51, -11*e^8 + 58*e^7 - 14*e^6 - 352*e^5 + 442*e^4 + 404*e^3 - 682*e^2 - 120*e + 201, -12*e^8 + 52*e^7 + 16*e^6 - 311*e^5 + 270*e^4 + 325*e^3 - 412*e^2 - 33*e + 107, -3*e^8 + 11*e^7 + 6*e^6 - 55*e^5 + 38*e^4 + 18*e^3 + 6*e^2 - 37, e^8 - 15*e^7 + 35*e^6 + 74*e^5 - 244*e^4 - 17*e^3 + 283*e^2 - 15*e - 48, -20*e^8 + 82*e^7 + 49*e^6 - 506*e^5 + 294*e^4 + 606*e^3 - 435*e^2 - 146*e + 108, -7/3*e^8 - 5*e^7 + 157/3*e^6 + 44/3*e^5 - 794/3*e^4 + 47*e^3 + 1076/3*e^2 - 112/3*e - 104, 5/3*e^8 - 13*e^7 + 31/3*e^6 + 260/3*e^5 - 368/3*e^4 - 129*e^3 + 584/3*e^2 + 80/3*e - 68, 11/3*e^8 - 16*e^7 - 8/3*e^6 + 257/3*e^5 - 239/3*e^4 - 48*e^3 + 176/3*e^2 - 52/3*e + 1, -1/3*e^8 - e^7 + 16/3*e^6 + 44/3*e^5 - 116/3*e^4 - 49*e^3 + 332/3*e^2 + 47/3*e - 62, -3*e^8 + 29*e^7 - 48*e^6 - 154*e^5 + 389*e^4 + 89*e^3 - 491*e^2 + 6*e + 107, 25*e^8 - 110*e^7 - 34*e^6 + 664*e^5 - 542*e^4 - 740*e^3 + 786*e^2 + 168*e - 217, -7*e^8 + 32*e^7 + 7*e^6 - 198*e^5 + 173*e^4 + 243*e^3 - 254*e^2 - 79*e + 45, -10*e^8 + 41*e^7 + 21*e^6 - 249*e^5 + 169*e^4 + 295*e^3 - 246*e^2 - 110*e + 63, -25*e^8 + 118*e^7 + 9*e^6 - 705*e^5 + 697*e^4 + 753*e^3 - 969*e^2 - 147*e + 243, -3*e^8 + 24*e^7 - 27*e^6 - 142*e^5 + 265*e^4 + 154*e^3 - 378*e^2 - 57*e + 126, 7*e^8 - 27*e^7 - 26*e^6 + 180*e^5 - 64*e^4 - 268*e^3 + 173*e^2 + 81*e - 76, 6*e^8 - 14*e^7 - 50*e^6 + 103*e^5 + 133*e^4 - 192*e^3 - 145*e^2 + 75*e + 32, -8*e^8 + 40*e^7 - 3*e^6 - 239*e^5 + 256*e^4 + 256*e^3 - 330*e^2 - 54*e + 78, 14*e^8 - 49*e^7 - 60*e^6 + 318*e^5 - 62*e^4 - 445*e^3 + 196*e^2 + 138*e - 84, e^8 + 8*e^7 - 41*e^6 - 49*e^5 + 251*e^4 + 70*e^3 - 410*e^2 - 57*e + 147, -2*e^8 - 3*e^7 + 40*e^6 - e^5 - 181*e^4 + 86*e^3 + 190*e^2 - 72*e - 39, -5*e^8 + 13*e^7 + 39*e^6 - 87*e^5 - 105*e^4 + 126*e^3 + 150*e^2 - 21*e - 42, -11*e^8 + 60*e^7 - 25*e^6 - 347*e^5 + 491*e^4 + 327*e^3 - 668*e^2 - 60*e + 183, -1/3*e^8 + 7*e^7 - 47/3*e^6 - 127/3*e^5 + 334/3*e^4 + 58*e^3 - 448/3*e^2 - 190/3*e + 40, 8/3*e^8 - 18*e^7 + 25/3*e^6 + 362/3*e^5 - 410/3*e^4 - 190*e^3 + 605/3*e^2 + 263/3*e - 77, -3*e^8 + 14*e^7 + 2*e^6 - 87*e^5 + 79*e^4 + 117*e^3 - 123*e^2 - 71*e + 60, 4*e^8 - 17*e^7 - e^6 + 88*e^5 - 101*e^4 - 39*e^3 + 82*e^2 - 19*e + 9, -10*e^7 + 36*e^6 + 42*e^5 - 227*e^4 + 33*e^3 + 278*e^2 - 57*e - 45, 2*e^8 - 17*e^7 + 22*e^6 + 101*e^5 - 203*e^4 - 122*e^3 + 282*e^2 + 94*e - 87, -4*e^8 + 15*e^7 + 16*e^6 - 101*e^5 + 26*e^4 + 162*e^3 - 72*e^2 - 77*e + 41, 2/3*e^8 - 6*e^7 + 7/3*e^6 + 155/3*e^5 - 146/3*e^4 - 123*e^3 + 371/3*e^2 + 197/3*e - 65, -20*e^8 + 94*e^7 + 9*e^6 - 566*e^5 + 553*e^4 + 629*e^3 - 800*e^2 - 154*e + 215, 20/3*e^8 - 24*e^7 - 74/3*e^6 + 458/3*e^5 - 161/3*e^4 - 196*e^3 + 341/3*e^2 + 89/3*e - 47, -14*e^8 + 48*e^7 + 62*e^6 - 306*e^5 + 41*e^4 + 407*e^3 - 140*e^2 - 111*e + 59, 2*e^8 - 3*e^7 - 13*e^6 + 6*e^5 + 25*e^4 + 45*e^3 - 36*e^2 - 43*e + 3, -4*e^8 + 17*e^7 + 8*e^6 - 105*e^5 + 70*e^4 + 131*e^3 - 98*e^2 - 69*e + 12, 10*e^8 - 37*e^7 - 31*e^6 + 219*e^5 - 103*e^4 - 229*e^3 + 153*e^2 + 59*e - 25, -e^8 - 7*e^7 + 35*e^6 + 39*e^5 - 190*e^4 - 37*e^3 + 225*e^2 + 24*e - 22, -37/3*e^8 + 68*e^7 - 89/3*e^6 - 1186/3*e^5 + 1699/3*e^4 + 379*e^3 - 2347/3*e^2 - 217/3*e + 196, -52/3*e^8 + 68*e^7 + 139/3*e^6 - 1225/3*e^5 + 661/3*e^4 + 445*e^3 - 871/3*e^2 - 292/3*e + 55, 7*e^7 - 25*e^6 - 35*e^5 + 169*e^4 + 17*e^3 - 270*e^2 - 13*e + 102, 2*e^8 - 22*e^7 + 31*e^6 + 144*e^5 - 269*e^4 - 215*e^3 + 402*e^2 + 110*e - 129, 10*e^8 - 47*e^7 - 5*e^6 + 282*e^5 - 267*e^4 - 310*e^3 + 365*e^2 + 74*e - 108, -8*e^8 + 44*e^7 - 15*e^6 - 259*e^5 + 330*e^4 + 268*e^3 - 425*e^2 - 87*e + 96, 11/3*e^8 - 34*e^7 + 154/3*e^6 + 593/3*e^5 - 1346/3*e^4 - 202*e^3 + 1931/3*e^2 + 233/3*e - 176, 17/3*e^8 - 30*e^7 + 31/3*e^6 + 527/3*e^5 - 713/3*e^4 - 172*e^3 + 974/3*e^2 + 44/3*e - 104, -17*e^8 + 77*e^7 + 13*e^6 - 451*e^5 + 420*e^4 + 451*e^3 - 551*e^2 - 102*e + 108, -8*e^8 + 40*e^7 - 4*e^6 - 234*e^5 + 256*e^4 + 235*e^3 - 307*e^2 - 67*e + 63, -5*e^8 + 26*e^7 - 3*e^6 - 156*e^5 + 162*e^4 + 173*e^3 - 188*e^2 - 50*e + 33, -23*e^8 + 117*e^7 - 14*e^6 - 707*e^5 + 793*e^4 + 806*e^3 - 1140*e^2 - 236*e + 324, -7*e^8 + 39*e^7 - 16*e^6 - 233*e^5 + 313*e^4 + 255*e^3 - 409*e^2 - 75*e + 71, -6*e^8 + 23*e^7 + 13*e^6 - 135*e^5 + 113*e^4 + 132*e^3 - 231*e^2 - e + 98, 8*e^8 - 61*e^7 + 61*e^6 + 369*e^5 - 633*e^4 - 432*e^3 + 873*e^2 + 159*e - 250]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([17, 17, -w^3 + w^2 + 6*w - 1])] = 1

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