/*
  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, 10, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([8, 2, w^3 - 7*w + 3])

primes_array = [
[2, 2, -w + 1],\
[5, 5, w^3 + w^2 - 4*w + 1],\
[7, 7, -w^3 + 6*w - 2],\
[8, 2, w^3 - 7*w + 3],\
[11, 11, -w^3 + 6*w - 4],\
[17, 17, w^3 + w^2 - 6*w - 1],\
[17, 17, -w^2 - w + 3],\
[31, 31, 2*w^3 + w^2 - 13*w + 3],\
[37, 37, -3*w^3 - w^2 + 18*w - 3],\
[41, 41, w^2 + 2*w - 4],\
[47, 47, 2*w^3 + 2*w^2 - 11*w - 2],\
[47, 47, -3*w^3 - w^2 + 19*w - 6],\
[59, 59, -2*w^3 + 13*w - 6],\
[59, 59, -w^3 - w^2 + 5*w + 2],\
[59, 59, w^2 + w - 1],\
[59, 59, w^2 + 2*w - 6],\
[61, 61, -w^3 + w^2 + 8*w - 7],\
[67, 67, w^3 + 2*w^2 - 4*w - 4],\
[73, 73, -2*w^3 - w^2 + 12*w - 4],\
[81, 3, -3],\
[107, 107, 2*w^2 + 2*w - 11],\
[109, 109, 2*w^3 + w^2 - 11*w + 3],\
[113, 113, w^3 + w^2 - 7*w - 2],\
[113, 113, 2*w^3 - 12*w + 9],\
[125, 5, -4*w^3 - 3*w^2 + 24*w + 2],\
[131, 131, 5*w^3 + 3*w^2 - 31*w + 2],\
[151, 151, 4*w^3 + 2*w^2 - 26*w + 1],\
[151, 151, w^3 + 2*w^2 - 6*w - 10],\
[167, 167, w + 4],\
[167, 167, 4*w^3 + w^2 - 26*w + 10],\
[173, 173, -2*w^3 + w^2 + 13*w - 11],\
[179, 179, 4*w^3 + w^2 - 24*w + 4],\
[179, 179, 2*w^3 + 2*w^2 - 12*w - 3],\
[179, 179, -w^3 + 8*w - 4],\
[179, 179, w^3 + 2*w^2 - 4*w - 6],\
[181, 181, 6*w^3 + 3*w^2 - 39*w + 5],\
[197, 197, -w^3 + 4*w - 4],\
[199, 199, 2*w^3 - 12*w + 3],\
[199, 199, 3*w - 2],\
[223, 223, w^3 + w^2 - 7*w - 4],\
[223, 223, 2*w^3 + w^2 - 10*w + 4],\
[227, 227, 7*w^3 + 2*w^2 - 44*w + 12],\
[227, 227, -4*w^3 - w^2 + 25*w - 9],\
[229, 229, 8*w^3 + 4*w^2 - 51*w + 4],\
[229, 229, 3*w^3 + w^2 - 18*w + 5],\
[233, 233, -6*w^3 - 3*w^2 + 39*w - 7],\
[233, 233, -w^3 - 2*w^2 + 8*w + 2],\
[241, 241, 2*w^3 + w^2 - 10*w],\
[251, 251, w^3 + w^2 - 7*w - 6],\
[257, 257, -6*w^3 - w^2 + 39*w - 17],\
[263, 263, -2*w^3 + 13*w - 4],\
[263, 263, -w^3 + 6*w - 8],\
[269, 269, -8*w^3 - 4*w^2 + 50*w - 7],\
[269, 269, -w^3 + w^2 + 7*w - 6],\
[277, 277, 2*w^3 + 2*w^2 - 11*w + 4],\
[277, 277, w^3 + w^2 - 4*w - 3],\
[281, 281, -w^2 - 3*w + 5],\
[281, 281, 2*w^3 + 3*w^2 - 9*w - 3],\
[283, 283, -3*w^3 - 4*w^2 + 12*w + 2],\
[289, 17, -2*w^3 - w^2 + 13*w - 5],\
[293, 293, -w^3 - 2*w^2 + 6*w + 6],\
[293, 293, w^3 + w^2 - 8*w - 1],\
[307, 307, 2*w^3 - 11*w + 12],\
[317, 317, 2*w^3 - 14*w + 11],\
[317, 317, -2*w^3 - 2*w^2 + 8*w + 1],\
[337, 337, 2*w^2 + 4*w - 11],\
[343, 7, -5*w^3 - w^2 + 31*w - 10],\
[349, 349, 2*w^3 - 11*w + 8],\
[349, 349, w^2 + w - 9],\
[353, 353, 4*w^3 + 4*w^2 - 23*w - 8],\
[373, 373, -2*w - 3],\
[373, 373, -4*w^3 + 26*w - 13],\
[389, 389, 6*w^3 + 3*w^2 - 37*w + 1],\
[389, 389, -2*w^3 - w^2 + 14*w - 6],\
[401, 401, 2*w^3 - 12*w + 13],\
[421, 421, 2*w^2 + 2*w - 15],\
[421, 421, 3*w^3 + 2*w^2 - 20*w + 4],\
[431, 431, w^3 + 3*w^2 - 2*w - 9],\
[433, 433, 2*w^3 + 2*w^2 - 12*w + 3],\
[433, 433, -7*w^3 - 2*w^2 + 44*w - 16],\
[433, 433, -3*w^3 + 18*w - 14],\
[433, 433, -w^3 + w^2 + 9*w - 10],\
[439, 439, 5*w^3 + 3*w^2 - 31*w - 2],\
[443, 443, -w^3 - w^2 + 3*w - 4],\
[443, 443, -4*w^3 + 27*w - 14],\
[449, 449, w^3 + w^2 - 4*w - 5],\
[449, 449, w^3 + 3*w^2 - 3*w - 8],\
[449, 449, 2*w^3 - 11*w + 6],\
[449, 449, -3*w^3 - 2*w^2 + 18*w - 4],\
[461, 461, -3*w^3 + w^2 + 20*w - 15],\
[463, 463, 2*w^3 - 10*w + 7],\
[479, 479, -2*w^3 - 3*w^2 + 11*w + 9],\
[491, 491, w^3 + w^2 - 4*w + 5],\
[499, 499, -2*w^3 - 2*w^2 + 14*w - 3],\
[499, 499, -6*w^3 - 2*w^2 + 39*w - 10],\
[499, 499, 4*w^3 + w^2 - 24*w + 14],\
[499, 499, -5*w^3 - 3*w^2 + 30*w - 5],\
[503, 503, -2*w^3 + w^2 + 14*w - 18],\
[509, 509, 4*w^3 + 3*w^2 - 24*w],\
[509, 509, 4*w^3 + 2*w^2 - 23*w + 4],\
[547, 547, w^3 + 2*w^2 - 2*w - 6],\
[547, 547, 6*w^3 + 2*w^2 - 38*w + 7],\
[563, 563, -5*w^3 - w^2 + 33*w - 12],\
[569, 569, 2*w^3 - w^2 - 15*w + 13],\
[569, 569, -4*w^3 - 2*w^2 + 24*w - 7],\
[577, 577, -w^2 - 2],\
[577, 577, 3*w^3 - 20*w + 8],\
[587, 587, 6*w^3 + 4*w^2 - 36*w - 1],\
[587, 587, -w^3 + w^2 + 9*w - 8],\
[593, 593, 6*w^3 + 3*w^2 - 36*w + 2],\
[593, 593, -3*w^3 - w^2 + 21*w - 4],\
[599, 599, -2*w^3 - w^2 + 12*w - 10],\
[599, 599, -4*w^3 - 2*w^2 + 25*w - 6],\
[601, 601, -2*w^3 + 2*w^2 + 15*w - 16],\
[607, 607, w^3 - w^2 - 7*w + 4],\
[607, 607, -2*w^3 - 2*w^2 + 10*w + 3],\
[631, 631, 2*w^2 + 4*w - 7],\
[641, 641, -3*w^3 - 2*w^2 + 16*w],\
[643, 643, w^3 + w^2 - 3*w - 4],\
[643, 643, w^3 + 3*w^2 - 6*w - 13],\
[653, 653, -w^3 + 6*w + 2],\
[653, 653, -3*w^2 - 5*w + 11],\
[659, 659, -2*w^3 + 10*w - 5],\
[661, 661, w^3 - w^2 - 8*w + 3],\
[673, 673, 3*w^3 + 4*w^2 - 14*w - 2],\
[677, 677, 4*w^3 + 2*w^2 - 23*w + 6],\
[677, 677, 2*w^3 - 13*w + 14],\
[683, 683, 2*w^3 + w^2 - 13*w + 7],\
[701, 701, 8*w^3 + 4*w^2 - 51*w + 8],\
[701, 701, -4*w^3 - w^2 + 24*w - 12],\
[709, 709, -4*w^3 - w^2 + 27*w - 7],\
[709, 709, 3*w^3 + 3*w^2 - 18*w - 5],\
[709, 709, -3*w^3 + w^2 + 21*w - 14],\
[709, 709, w^2 - w - 7],\
[719, 719, -9*w^3 - 4*w^2 + 58*w - 8],\
[719, 719, 11*w^3 + 5*w^2 - 68*w + 9],\
[727, 727, -w^3 + 4*w - 6],\
[733, 733, 2*w^3 + w^2 - 13*w + 9],\
[739, 739, -2*w^2 - 3*w + 4],\
[743, 743, 3*w^3 + 3*w^2 - 19*w - 4],\
[751, 751, 2*w^3 + 3*w^2 - 10*w - 2],\
[761, 761, -12*w^3 - 5*w^2 + 75*w - 9],\
[761, 761, -3*w^3 - 3*w^2 + 17*w],\
[769, 769, -6*w^3 - 4*w^2 + 37*w],\
[769, 769, -8*w^3 - 3*w^2 + 51*w - 7],\
[773, 773, -w^2 - 2*w - 2],\
[787, 787, -5*w^3 - 5*w^2 + 28*w + 7],\
[811, 811, 7*w^3 + 2*w^2 - 42*w + 6],\
[811, 811, -2*w^3 - w^2 + 9*w - 7],\
[823, 823, -3*w^3 - 2*w^2 + 14*w - 10],\
[829, 829, 4*w^3 + 3*w^2 - 20*w + 6],\
[829, 829, -7*w^3 - 2*w^2 + 44*w - 14],\
[841, 29, w^3 + 4*w^2 - 2*w - 14],\
[841, 29, -w^2 + 10],\
[857, 857, -3*w^3 - w^2 + 20*w - 9],\
[859, 859, -w^3 + 2*w^2 + 10*w - 18],\
[863, 863, 11*w^3 + 5*w^2 - 69*w + 6],\
[863, 863, w^3 - 2*w^2 - 10*w + 12],\
[877, 877, 3*w^3 - 18*w + 10],\
[883, 883, 4*w^3 + 3*w^2 - 22*w],\
[887, 887, 3*w^3 + 3*w^2 - 15*w - 2],\
[887, 887, w^2 + 4*w - 10],\
[887, 887, w^3 + w^2 - 3*w - 8],\
[887, 887, w - 6],\
[907, 907, 6*w^3 + w^2 - 38*w + 16],\
[919, 919, -2*w^3 - 3*w^2 + 11*w + 1],\
[919, 919, 5*w^3 - w^2 - 34*w + 27],\
[937, 937, -w^3 - w^2 + 8*w + 3],\
[941, 941, -4*w^3 + 25*w - 20],\
[947, 947, -2*w^3 + w^2 + 8*w - 6],\
[967, 967, -7*w^3 - w^2 + 44*w - 23],\
[971, 971, 2*w^2 + 2*w - 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - 3*x^6 - 6*x^5 + 16*x^4 + 15*x^3 - 17*x^2 - 16*x - 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e^4 + 2*e^3 + 4*e^2 - 5*e - 3, e^6 - 3*e^5 - 5*e^4 + 15*e^3 + 9*e^2 - 16*e - 7, -1, -2*e^6 + 7*e^5 + 9*e^4 - 36*e^3 - 16*e^2 + 39*e + 18, 4*e^6 - 14*e^5 - 17*e^4 + 72*e^3 + 26*e^2 - 78*e - 30, e^6 - 4*e^5 - 5*e^4 + 23*e^3 + 10*e^2 - 25*e - 9, -e^4 + e^3 + 5*e^2 - 2*e - 1, 2*e^6 - 8*e^5 - 9*e^4 + 46*e^3 + 17*e^2 - 59*e - 22, -2*e^4 + 3*e^3 + 11*e^2 - 9*e - 9, -2*e^6 + 9*e^5 + 4*e^4 - 46*e^3 + 4*e^2 + 51*e + 9, -e^6 + 3*e^5 + 4*e^4 - 16*e^3 + 20*e + 3, -e^6 + 6*e^5 - 32*e^3 + 9*e^2 + 33*e + 6, -e^6 + 5*e^5 + 3*e^4 - 29*e^3 - 7*e^2 + 42*e + 15, 3*e^6 - 9*e^5 - 16*e^4 + 48*e^3 + 30*e^2 - 57*e - 27, 2*e^6 - 8*e^5 - 8*e^4 + 42*e^3 + 14*e^2 - 45*e - 15, 4*e^6 - 13*e^5 - 20*e^4 + 69*e^3 + 35*e^2 - 80*e - 28, -4*e^6 + 12*e^5 + 20*e^4 - 61*e^3 - 33*e^2 + 66*e + 23, 2*e^6 - 8*e^5 - 6*e^4 + 41*e^3 + 3*e^2 - 48*e - 10, -2*e^6 + 6*e^5 + 6*e^4 - 23*e^3 + 15*e + 4, 2*e^5 - 5*e^4 - 10*e^3 + 21*e^2 + 9*e - 9, 6*e^6 - 21*e^5 - 24*e^4 + 105*e^3 + 30*e^2 - 111*e - 34, 6*e^6 - 20*e^5 - 28*e^4 + 104*e^3 + 47*e^2 - 115*e - 51, e^6 - 2*e^5 - 7*e^4 + 11*e^3 + 14*e^2 - 15*e - 3, 5*e^6 - 18*e^5 - 17*e^4 + 84*e^3 + 16*e^2 - 79*e - 21, -2*e^6 + 8*e^5 + 7*e^4 - 43*e^3 - 7*e^2 + 47*e + 18, 8*e^6 - 26*e^5 - 38*e^4 + 136*e^3 + 59*e^2 - 153*e - 55, -7*e^6 + 21*e^5 + 34*e^4 - 104*e^3 - 56*e^2 + 110*e + 44, 3*e^6 - 7*e^5 - 15*e^4 + 29*e^3 + 14*e^2 - 14*e + 3, -5*e^6 + 17*e^5 + 23*e^4 - 88*e^3 - 39*e^2 + 97*e + 36, -e^6 + 3*e^5 - 6*e^3 + 21*e^2 - 14*e - 27, 12*e^6 - 42*e^5 - 53*e^4 + 218*e^3 + 86*e^2 - 235*e - 93, -11*e^6 + 34*e^5 + 60*e^4 - 184*e^3 - 116*e^2 + 217*e + 96, -9*e^6 + 34*e^5 + 36*e^4 - 177*e^3 - 55*e^2 + 196*e + 69, 2*e^6 - 8*e^5 - 6*e^4 + 42*e^3 - 43*e - 6, -13*e^6 + 40*e^5 + 68*e^4 - 213*e^3 - 121*e^2 + 245*e + 104, 6*e^6 - 21*e^5 - 27*e^4 + 115*e^3 + 39*e^2 - 143*e - 48, -8*e^6 + 26*e^5 + 41*e^4 - 139*e^3 - 75*e^2 + 154*e + 62, 4*e^6 - 14*e^5 - 12*e^4 + 60*e^3 + 4*e^2 - 44*e - 4, 3*e^6 - 11*e^5 - 8*e^4 + 51*e^3 - 2*e^2 - 56*e - 10, 4*e^6 - 17*e^5 - 12*e^4 + 88*e^3 + 12*e^2 - 102*e - 19, 5*e^6 - 14*e^5 - 24*e^4 + 68*e^3 + 28*e^2 - 68*e - 6, 6*e^6 - 20*e^5 - 25*e^4 + 102*e^3 + 25*e^2 - 113*e - 27, -18*e^6 + 61*e^5 + 79*e^4 - 309*e^3 - 120*e^2 + 324*e + 125, 5*e^6 - 12*e^5 - 31*e^4 + 60*e^3 + 59*e^2 - 60*e - 25, 4*e^6 - 12*e^5 - 14*e^4 + 51*e^3 + e^2 - 36*e + 3, 4*e^6 - 14*e^5 - 14*e^4 + 69*e^3 + 5*e^2 - 70*e - 9, -9*e^6 + 31*e^5 + 37*e^4 - 158*e^3 - 49*e^2 + 175*e + 68, 5*e^6 - 16*e^5 - 24*e^4 + 81*e^3 + 41*e^2 - 90*e - 39, -6*e^6 + 17*e^5 + 35*e^4 - 92*e^3 - 67*e^2 + 103*e + 48, 11*e^6 - 39*e^5 - 49*e^4 + 209*e^3 + 78*e^2 - 242*e - 84, -e^6 + e^5 + 11*e^4 - 7*e^3 - 30*e^2 + 11*e + 15, -9*e^6 + 33*e^5 + 32*e^4 - 166*e^3 - 29*e^2 + 171*e + 51, -8*e^6 + 30*e^5 + 32*e^4 - 155*e^3 - 53*e^2 + 175*e + 75, -4*e^5 + 10*e^4 + 17*e^3 - 44*e^2 - 5*e + 29, 6*e^6 - 21*e^5 - 28*e^4 + 114*e^3 + 52*e^2 - 135*e - 64, 7*e^6 - 22*e^5 - 33*e^4 + 115*e^3 + 44*e^2 - 124*e - 36, e^6 - 8*e^4 - 8*e^3 + 18*e^2 + 24*e + 3, 8*e^6 - 26*e^5 - 40*e^4 + 136*e^3 + 72*e^2 - 139*e - 70, 10*e^6 - 33*e^5 - 49*e^4 + 178*e^3 + 81*e^2 - 210*e - 73, -4*e^6 + 17*e^5 + 12*e^4 - 85*e^3 - 15*e^2 + 84*e + 21, -e^6 + 5*e^5 - 23*e^3 + 7*e^2 + 18*e + 3, 2*e^6 - 9*e^5 - e^4 + 38*e^3 - 13*e^2 - 37*e - 4, -2*e^5 + 7*e^4 + 4*e^3 - 28*e^2 + 9*e + 18, 3*e^6 - 13*e^5 - 2*e^4 + 55*e^3 - 26*e^2 - 35*e + 12, 13*e^6 - 48*e^5 - 50*e^4 + 245*e^3 + 68*e^2 - 267*e - 85, -3*e^6 + 15*e^5 + 9*e^4 - 83*e^3 - 15*e^2 + 95*e + 32, -8*e^6 + 27*e^5 + 38*e^4 - 144*e^3 - 68*e^2 + 177*e + 80, -e^6 + 4*e^5 + 7*e^4 - 26*e^3 - 22*e^2 + 46*e + 5, -2*e^6 + 8*e^5 - 4*e^4 - 25*e^3 + 44*e^2 + 15*e - 21, -3*e^6 + 14*e^5 + 4*e^4 - 64*e^3 + 3*e^2 + 53*e + 23, 10*e^6 - 33*e^5 - 50*e^4 + 178*e^3 + 91*e^2 - 201*e - 94, -11*e^6 + 35*e^5 + 50*e^4 - 179*e^3 - 66*e^2 + 195*e + 72, 9*e^6 - 35*e^5 - 29*e^4 + 172*e^3 + 19*e^2 - 159*e - 27, -6*e^6 + 18*e^5 + 30*e^4 - 91*e^3 - 48*e^2 + 94*e + 42, 20*e^6 - 65*e^5 - 92*e^4 + 331*e^3 + 141*e^2 - 355*e - 139, -11*e^6 + 33*e^5 + 59*e^4 - 170*e^3 - 114*e^2 + 184*e + 101, -10*e^6 + 34*e^5 + 36*e^4 - 159*e^3 - 32*e^2 + 150*e + 33, 9*e^6 - 33*e^5 - 34*e^4 + 162*e^3 + 47*e^2 - 164*e - 46, 9*e^6 - 33*e^5 - 36*e^4 + 170*e^3 + 51*e^2 - 176*e - 58, -e^6 + 6*e^5 - 2*e^4 - 22*e^3 + 2*e^2 + 14*e + 29, 6*e^6 - 22*e^5 - 31*e^4 + 123*e^3 + 62*e^2 - 137*e - 40, 8*e^6 - 25*e^5 - 36*e^4 + 131*e^3 + 38*e^2 - 158*e - 34, 11*e^6 - 41*e^5 - 45*e^4 + 218*e^3 + 71*e^2 - 264*e - 90, -7*e^6 + 21*e^5 + 32*e^4 - 105*e^3 - 39*e^2 + 114*e + 36, -9*e^6 + 31*e^5 + 44*e^4 - 172*e^3 - 78*e^2 + 211*e + 75, 12*e^6 - 44*e^5 - 45*e^4 + 219*e^3 + 57*e^2 - 230*e - 72, 4*e^5 - 11*e^4 - 12*e^3 + 34*e^2 - 4*e - 6, 11*e^6 - 42*e^5 - 37*e^4 + 205*e^3 + 37*e^2 - 204*e - 54, 8*e^6 - 28*e^5 - 30*e^4 + 133*e^3 + 46*e^2 - 128*e - 69, 12*e^6 - 40*e^5 - 54*e^4 + 209*e^3 + 81*e^2 - 243*e - 79, -19*e^6 + 60*e^5 + 93*e^4 - 308*e^3 - 157*e^2 + 328*e + 132, -3*e^6 + 15*e^5 + 12*e^4 - 93*e^3 - 23*e^2 + 124*e + 45, e^6 - 3*e^5 - 14*e^4 + 31*e^3 + 45*e^2 - 48*e - 19, 3*e^6 - 10*e^5 - 14*e^4 + 44*e^3 + 30*e^2 - 24*e - 25, -11*e^6 + 36*e^5 + 46*e^4 - 174*e^3 - 58*e^2 + 170*e + 68, -5*e^6 + 16*e^5 + 20*e^4 - 83*e^3 - 8*e^2 + 97*e + 5, -e^6 - 2*e^5 + 12*e^4 + 20*e^3 - 42*e^2 - 34*e + 24, 14*e^6 - 50*e^5 - 59*e^4 + 256*e^3 + 89*e^2 - 265*e - 93, -14*e^6 + 51*e^5 + 56*e^4 - 264*e^3 - 84*e^2 + 302*e + 105, -21*e^6 + 74*e^5 + 86*e^4 - 373*e^3 - 123*e^2 + 395*e + 134, e^6 - 4*e^5 - 4*e^4 + 25*e^3 - 3*e^2 - 31*e + 11, -10*e^6 + 33*e^5 + 50*e^4 - 182*e^3 - 87*e^2 + 220*e + 87, -17*e^6 + 56*e^5 + 81*e^4 - 296*e^3 - 134*e^2 + 342*e + 150, e^6 - 7*e^5 - 3*e^4 + 44*e^3 + 7*e^2 - 47*e - 21, 10*e^6 - 31*e^5 - 52*e^4 + 160*e^3 + 95*e^2 - 158*e - 79, -19*e^6 + 72*e^5 + 71*e^4 - 366*e^3 - 99*e^2 + 390*e + 146, 9*e^6 - 34*e^5 - 33*e^4 + 171*e^3 + 39*e^2 - 170*e - 48, -8*e^6 + 31*e^5 + 36*e^4 - 169*e^3 - 75*e^2 + 196*e + 84, -15*e^6 + 55*e^5 + 62*e^4 - 291*e^3 - 89*e^2 + 322*e + 114, -13*e^6 + 43*e^5 + 64*e^4 - 230*e^3 - 112*e^2 + 261*e + 108, -7*e^6 + 28*e^5 + 17*e^4 - 137*e^3 + 5*e^2 + 148*e + 36, -3*e^6 + 13*e^5 + 11*e^4 - 71*e^3 - 12*e^2 + 72*e + 24, -10*e^6 + 36*e^5 + 42*e^4 - 189*e^3 - 71*e^2 + 222*e + 98, -2*e^6 + e^5 + 21*e^4 - 8*e^3 - 50*e^2 + 8*e + 14, -23*e^6 + 80*e^5 + 99*e^4 - 411*e^3 - 149*e^2 + 450*e + 170, 14*e^6 - 48*e^5 - 62*e^4 + 252*e^3 + 97*e^2 - 295*e - 118, 14*e^6 - 44*e^5 - 66*e^4 + 220*e^3 + 98*e^2 - 218*e - 63, 7*e^6 - 25*e^5 - 25*e^4 + 122*e^3 + 19*e^2 - 119*e - 10, 12*e^6 - 40*e^5 - 56*e^4 + 215*e^3 + 94*e^2 - 271*e - 103, 17*e^6 - 55*e^5 - 82*e^4 + 287*e^3 + 131*e^2 - 303*e - 105, -16*e^6 + 53*e^5 + 74*e^4 - 272*e^3 - 118*e^2 + 288*e + 105, 7*e^6 - 28*e^5 - 16*e^4 + 140*e^3 - 23*e^2 - 146*e, -20*e^6 + 66*e^5 + 92*e^4 - 343*e^3 - 141*e^2 + 378*e + 149, e^6 - e^5 - 17*e^4 + 17*e^3 + 63*e^2 - 34*e - 52, -20*e^6 + 59*e^5 + 112*e^4 - 322*e^3 - 212*e^2 + 384*e + 174, 4*e^6 - 15*e^5 - 19*e^4 + 89*e^3 + 36*e^2 - 129*e - 48, e^6 - e^5 + 2*e^4 - 17*e^3 - 27*e^2 + 57*e + 42, 5*e^6 - 24*e^5 - 5*e^4 + 120*e^3 - 30*e^2 - 124*e - 9, 8*e^6 - 26*e^5 - 43*e^4 + 146*e^3 + 86*e^2 - 195*e - 78, -16*e^6 + 55*e^5 + 70*e^4 - 286*e^3 - 93*e^2 + 310*e + 101, -9*e^6 + 25*e^5 + 55*e^4 - 137*e^3 - 117*e^2 + 154*e + 83, 13*e^6 - 44*e^5 - 46*e^4 + 203*e^3 + 31*e^2 - 172*e - 31, 19*e^6 - 67*e^5 - 71*e^4 + 326*e^3 + 81*e^2 - 332*e - 103, 22*e^6 - 79*e^5 - 95*e^4 + 411*e^3 + 161*e^2 - 458*e - 177, 12*e^6 - 45*e^5 - 34*e^4 + 214*e^3 + 2*e^2 - 214*e - 27, 23*e^6 - 75*e^5 - 110*e^4 + 392*e^3 + 178*e^2 - 433*e - 172, 21*e^6 - 69*e^5 - 89*e^4 + 338*e^3 + 115*e^2 - 331*e - 118, -5*e^5 - e^4 + 41*e^3 + 25*e^2 - 65*e - 55, -12*e^6 + 40*e^5 + 55*e^4 - 205*e^3 - 90*e^2 + 213*e + 90, 9*e^6 - 28*e^5 - 51*e^4 + 155*e^3 + 109*e^2 - 194*e - 91, 6*e^6 - 21*e^5 - 29*e^4 + 113*e^3 + 52*e^2 - 137*e - 39, -10*e^6 + 25*e^5 + 55*e^4 - 114*e^3 - 97*e^2 + 94*e + 57, -11*e^6 + 41*e^5 + 49*e^4 - 221*e^3 - 96*e^2 + 263*e + 125, -13*e^6 + 51*e^5 + 39*e^4 - 254*e^3 - 10*e^2 + 261*e + 59, 2*e^6 - 6*e^5 - 12*e^4 + 37*e^3 + 30*e^2 - 81*e - 30, 8*e^6 - 23*e^5 - 40*e^4 + 109*e^3 + 73*e^2 - 114*e - 55, -18*e^6 + 62*e^5 + 75*e^4 - 307*e^3 - 113*e^2 + 318*e + 119, 12*e^6 - 33*e^5 - 64*e^4 + 159*e^3 + 111*e^2 - 139*e - 88, 20*e^6 - 69*e^5 - 100*e^4 + 384*e^3 + 184*e^2 - 467*e - 196, -6*e^6 + 20*e^5 + 31*e^4 - 110*e^3 - 60*e^2 + 129*e + 83, -7*e^6 + 17*e^5 + 54*e^4 - 108*e^3 - 132*e^2 + 136*e + 86, e^6 - 2*e^5 - 6*e^4 + 5*e^3 + 20*e^2 + 13*e - 34, e^6 + 4*e^5 - 19*e^4 - 30*e^3 + 71*e^2 + 52*e - 31, e^6 - 10*e^5 + 16*e^4 + 40*e^3 - 76*e^2 - 36*e + 36, 11*e^6 - 37*e^5 - 62*e^4 + 213*e^3 + 128*e^2 - 259*e - 115, 15*e^6 - 49*e^5 - 77*e^4 + 269*e^3 + 139*e^2 - 334*e - 120, -15*e^6 + 55*e^5 + 61*e^4 - 280*e^3 - 95*e^2 + 288*e + 93, 10*e^6 - 35*e^5 - 40*e^4 + 181*e^3 + 42*e^2 - 201*e - 37, 2*e^6 - 9*e^5 + 3*e^4 + 34*e^3 - 48*e^2 - 6*e + 50, -7*e^6 + 17*e^5 + 42*e^4 - 89*e^3 - 72*e^2 + 115*e + 18, -6*e^6 + 23*e^5 + 12*e^4 - 106*e^3 + 34*e^2 + 92*e - 9, -3*e^6 + 5*e^5 + 14*e^4 - 14*e^3 + 5*e^2 - 2*e - 54, -5*e^6 + 7*e^5 + 43*e^4 - 49*e^3 - 99*e^2 + 93*e + 81, -5*e^6 + 23*e^5 + 8*e^4 - 117*e^3 + 23*e^2 + 115*e + 11, 2*e^6 - 4*e^5 - 21*e^4 + 36*e^3 + 71*e^2 - 82*e - 64, -16*e^6 + 63*e^5 + 60*e^4 - 329*e^3 - 89*e^2 + 361*e + 131, -18*e^6 + 53*e^5 + 103*e^4 - 289*e^3 - 209*e^2 + 355*e + 170, -25*e^6 + 82*e^5 + 107*e^4 - 406*e^3 - 143*e^2 + 411*e + 138, 34*e^6 - 120*e^5 - 145*e^4 + 618*e^3 + 233*e^2 - 680*e - 267, -e^6 + 4*e^4 + 7*e^3 + 25*e^2 - 27*e - 49, -18*e^6 + 65*e^5 + 80*e^4 - 348*e^3 - 138*e^2 + 401*e + 168]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([8, 2, w^3 - 7*w + 3])] = 1

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