/*
  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([11, 0, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([41,41,-w^3 + 2*w^2 + 4*w - 6])

primes_array = [
[4, 2, -w^2 + w + 3],\
[5, 5, w + 1],\
[5, 5, -w^3 + w^2 + 4*w - 4],\
[11, 11, w],\
[29, 29, w^3 - 2*w^2 - 3*w + 7],\
[29, 29, -w^3 - 2*w^2 + 3*w + 7],\
[31, 31, -w^3 + w^2 + 4*w - 2],\
[31, 31, -w^3 - w^2 + 4*w + 2],\
[41, 41, w^3 + 2*w^2 - 4*w - 6],\
[41, 41, w^3 - 5*w + 2],\
[49, 7, -w^3 + w^2 + 4*w - 1],\
[49, 7, w^3 + w^2 - 4*w - 1],\
[59, 59, -3*w^2 - w + 10],\
[59, 59, -3*w^2 + w + 10],\
[61, 61, -2*w^3 + 2*w^2 + 7*w - 5],\
[61, 61, 2*w^3 + w^2 - 8*w - 6],\
[71, 71, 2*w^2 + w - 9],\
[71, 71, 2*w^2 - w - 9],\
[81, 3, -3],\
[101, 101, 2*w^2 - w - 10],\
[101, 101, 2*w^2 + w - 10],\
[109, 109, 2*w^3 + w^2 - 8*w - 3],\
[109, 109, -2*w^3 + w^2 + 8*w - 3],\
[121, 11, -w^2 + 7],\
[131, 131, 4*w^2 - 2*w - 15],\
[131, 131, 2*w^2 + 2*w - 3],\
[131, 131, 2*w^2 - 2*w - 3],\
[131, 131, -w^3 - w^2 + 3*w + 7],\
[139, 139, w^3 + 4*w^2 - 5*w - 16],\
[139, 139, w^3 + 3*w^2 - 6*w - 10],\
[139, 139, 2*w^3 - w^2 - 8*w + 1],\
[139, 139, -4*w^2 - w + 12],\
[149, 149, 2*w^3 - w^2 - 8*w + 4],\
[149, 149, 2*w^3 + w^2 - 8*w - 4],\
[151, 151, 3*w^2 - 3*w - 8],\
[151, 151, 2*w^3 - 4*w^2 - 8*w + 17],\
[151, 151, w^2 - 2*w - 7],\
[151, 151, w^3 + 2*w^2 - 6*w - 8],\
[179, 179, w^3 - w^2 - 5*w + 1],\
[179, 179, -w^3 - w^2 + 5*w + 1],\
[191, 191, 2*w^3 - w^2 - 7*w + 2],\
[191, 191, 3*w^3 - 2*w^2 - 10*w + 2],\
[199, 199, w^3 - 4*w^2 - 3*w + 13],\
[199, 199, -w^3 - 4*w^2 + 3*w + 13],\
[211, 211, -w^3 + w^2 + 6*w - 5],\
[211, 211, w^3 - 5*w - 5],\
[211, 211, -w^3 + 5*w - 5],\
[211, 211, w^3 + w^2 - 6*w - 5],\
[229, 229, w^3 - 4*w^2 - 2*w + 14],\
[229, 229, 2*w^3 + 3*w^2 - 7*w - 12],\
[229, 229, 2*w^3 - 3*w^2 - 7*w + 12],\
[229, 229, 2*w^3 + w^2 - 7*w - 8],\
[241, 241, w^3 + w^2 - 6*w - 4],\
[241, 241, -w^3 + w^2 + 6*w - 4],\
[251, 251, 2*w^2 - w - 2],\
[251, 251, 2*w^2 + w - 2],\
[271, 271, 2*w^3 - 2*w^2 - 8*w + 5],\
[271, 271, -4*w^2 - w + 14],\
[271, 271, -4*w^2 + w + 14],\
[271, 271, 2*w^3 + 2*w^2 - 8*w - 5],\
[281, 281, -2*w^3 - w^2 + 9*w + 2],\
[281, 281, 2*w^3 - w^2 - 9*w + 2],\
[311, 311, -w^3 + 3*w - 5],\
[311, 311, w^3 - 3*w - 5],\
[331, 331, -3*w^3 + 3*w^2 + 12*w - 13],\
[331, 331, 3*w^3 + 3*w^2 - 12*w - 13],\
[349, 349, 2*w^3 + 2*w^2 - 7*w - 10],\
[349, 349, -2*w^3 + 2*w^2 + 7*w - 10],\
[361, 19, 4*w^2 - 15],\
[361, 19, -4*w^2 + 13],\
[379, 379, -w^3 + 3*w^2 + 3*w - 13],\
[379, 379, w^3 + 3*w^2 - 3*w - 13],\
[409, 409, 3*w^3 - 2*w^2 - 11*w + 2],\
[409, 409, w^3 + 3*w^2 - 6*w - 9],\
[419, 419, -w^3 + w^2 + 6*w + 2],\
[419, 419, -3*w^3 + 5*w^2 + 13*w - 19],\
[421, 421, -w^3 + 3*w^2 + 7*w - 13],\
[421, 421, 2*w^3 - 2*w^2 - 9*w + 6],\
[421, 421, -2*w^3 - 2*w^2 + 9*w + 6],\
[421, 421, w^3 + 3*w^2 - 7*w - 13],\
[439, 439, 3*w^2 + 2*w - 13],\
[439, 439, 3*w^3 + 2*w^2 - 12*w - 10],\
[439, 439, -3*w^3 + 2*w^2 + 12*w - 10],\
[439, 439, 3*w^2 - 2*w - 13],\
[449, 449, 2*w^3 - 4*w^2 - 9*w + 14],\
[449, 449, -3*w^3 + 3*w^2 + 11*w - 9],\
[449, 449, 3*w^3 + 3*w^2 - 11*w - 9],\
[449, 449, w^3 - 2*w^2 - 5*w + 2],\
[461, 461, -w - 5],\
[461, 461, w - 5],\
[499, 499, w^3 - 5*w^2 - w + 17],\
[499, 499, -w^3 - 5*w^2 + w + 17],\
[509, 509, w^3 + 5*w^2 - 4*w - 16],\
[509, 509, w^2 - 2*w - 10],\
[509, 509, w^2 + 2*w - 10],\
[509, 509, w^3 - w^2 - 5*w + 9],\
[541, 541, 3*w^3 - 10*w - 6],\
[541, 541, -2*w^3 + 5*w^2 + 5*w - 16],\
[569, 569, 3*w^3 + 2*w^2 - 13*w - 6],\
[569, 569, -2*w^3 + 4*w^2 + 7*w - 10],\
[599, 599, w^3 + 2*w^2 - 7*w - 10],\
[599, 599, -w^3 + 2*w^2 + 7*w - 10],\
[601, 601, -3*w^3 - w^2 + 12*w + 6],\
[601, 601, 3*w^3 - w^2 - 12*w + 6],\
[619, 619, 3*w^3 - 12*w + 2],\
[619, 619, -3*w^3 + 12*w + 2],\
[631, 631, -w^3 + w^2 + 2*w - 8],\
[631, 631, w^3 + w^2 - 2*w - 8],\
[641, 641, w^3 + w^2 - 7*w - 1],\
[641, 641, -3*w^3 - 2*w^2 + 12*w + 4],\
[641, 641, 3*w^3 - 2*w^2 - 12*w + 4],\
[641, 641, w^3 - w^2 - 7*w + 1],\
[659, 659, -2*w^3 + w^2 + 10*w - 1],\
[659, 659, -w^3 + 5*w^2 + 4*w - 19],\
[659, 659, w^3 + 5*w^2 - 4*w - 19],\
[659, 659, 2*w^3 + w^2 - 10*w - 1],\
[691, 691, 3*w^2 - 2*w - 14],\
[691, 691, 3*w^2 + 2*w - 14],\
[701, 701, w^3 + 4*w^2 - 7*w - 12],\
[701, 701, 3*w^3 - w^2 - 12*w - 1],\
[719, 719, -w^3 + 7*w - 3],\
[719, 719, w^3 - 7*w - 3],\
[739, 739, 3*w^3 + w^2 - 12*w - 3],\
[739, 739, w^3 + 2*w^2 - 3*w - 1],\
[739, 739, -w^3 + 2*w^2 + 3*w - 1],\
[739, 739, -3*w^3 + w^2 + 12*w - 3],\
[751, 751, -2*w^3 + 6*w^2 + 7*w - 20],\
[751, 751, 2*w^3 + 6*w^2 - 7*w - 20],\
[761, 761, 2*w^3 + 6*w^2 - 8*w - 21],\
[761, 761, -2*w^3 + 6*w^2 + 8*w - 21],\
[769, 769, -2*w^3 + 6*w^2 + 8*w - 23],\
[769, 769, w^2 + 2*w + 3],\
[809, 809, 2*w^3 + 3*w^2 - 7*w - 14],\
[809, 809, -2*w^3 + 3*w^2 + 7*w - 14],\
[821, 821, -3*w^3 - w^2 + 11*w + 1],\
[821, 821, 3*w^3 - w^2 - 11*w + 1],\
[829, 829, 3*w^3 - w^2 - 12*w + 4],\
[829, 829, w^3 - 4*w^2 - 6*w + 12],\
[829, 829, -w^3 - 4*w^2 + 6*w + 12],\
[829, 829, -3*w^3 - w^2 + 12*w + 4],\
[839, 839, -w^3 + 3*w - 6],\
[839, 839, w^3 - 3*w - 6],\
[841, 29, 5*w^2 - 19],\
[859, 859, w^3 + 2*w^2 - 7*w - 9],\
[859, 859, -w^3 + 2*w^2 + 7*w - 9],\
[911, 911, -2*w^3 + 4*w^2 + 9*w - 13],\
[911, 911, 2*w^3 + 4*w^2 - 9*w - 13],\
[919, 919, 2*w^3 + 4*w^2 - 7*w - 17],\
[919, 919, 3*w^3 + 2*w^2 - 11*w - 6],\
[919, 919, 3*w^3 - 2*w^2 - 11*w + 6],\
[919, 919, 2*w^3 - 4*w^2 - 7*w + 17],\
[941, 941, -2*w^3 + 2*w^2 + 7*w - 15],\
[941, 941, 2*w^3 + 2*w^2 - 7*w - 15],\
[961, 31, -2*w^2 + 13],\
[971, 971, w^3 + 2*w^2 - 7*w - 7],\
[971, 971, -w^3 + 2*w^2 + 7*w - 7],\
[991, 991, 3*w^3 + 2*w^2 - 11*w - 7],\
[991, 991, -3*w^3 + 2*w^2 + 11*w - 7]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 + 4*x^5 - 5*x^4 - 24*x^3 + 5*x^2 + 34*x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e^5 - 2*e^4 + 9*e^3 + 5*e^2 - 19*e + 4, 2*e^5 + 4*e^4 - 19*e^3 - 13*e^2 + 41*e - 5, -3*e^5 - 6*e^4 + 29*e^3 + 22*e^2 - 62*e - 2, 2*e^5 + 4*e^4 - 19*e^3 - 14*e^2 + 38*e - 1, -6*e^5 - 13*e^4 + 54*e^3 + 47*e^2 - 111*e - 3, -4*e^5 - 9*e^4 + 34*e^3 + 30*e^2 - 69*e, 7*e^5 + 16*e^4 - 59*e^3 - 54*e^2 + 118*e - 4, 5*e^5 + 10*e^4 - 47*e^3 - 34*e^2 + 98*e - 4, 1, -e^5 - 2*e^4 + 10*e^3 + 8*e^2 - 25*e - 6, -e^4 - 3*e^3 + 5*e^2 + 8*e - 11, 16*e^5 + 35*e^4 - 141*e^3 - 119*e^2 + 293*e - 8, 2*e^5 + 2*e^4 - 25*e^3 - 4*e^2 + 58*e - 13, -15*e^5 - 34*e^4 + 129*e^3 + 118*e^2 - 264*e, 13*e^5 + 28*e^4 - 117*e^3 - 99*e^2 + 241*e - 6, 2*e^4 + 6*e^3 - 11*e^2 - 20*e + 13, -14*e^5 - 31*e^4 + 122*e^3 + 104*e^2 - 248*e + 15, 13*e^5 + 28*e^4 - 116*e^3 - 97*e^2 + 236*e - 8, -12*e^5 - 25*e^4 + 111*e^3 + 85*e^2 - 239*e + 10, 4*e^5 + 7*e^4 - 42*e^3 - 27*e^2 + 94*e + 6, 11*e^5 + 24*e^4 - 97*e^3 - 82*e^2 + 198*e - 12, 8*e^5 + 16*e^4 - 76*e^3 - 54*e^2 + 166*e - 4, -e^5 - e^4 + 13*e^3 + 2*e^2 - 33*e - 2, 7*e^5 + 14*e^4 - 67*e^3 - 47*e^2 + 144*e - 13, -18*e^5 - 38*e^4 + 165*e^3 + 132*e^2 - 351*e + 4, 20*e^5 + 44*e^4 - 177*e^3 - 156*e^2 + 359*e, -7*e^5 - 15*e^4 + 65*e^3 + 58*e^2 - 135*e - 12, e^4 + 2*e^3 - 8*e^2 - 2*e + 11, -16*e^5 - 33*e^4 + 149*e^3 + 115*e^2 - 314*e + 9, -5*e^5 - 8*e^4 + 54*e^3 + 28*e^2 - 118*e + 1, -8*e^5 - 17*e^4 + 74*e^3 + 60*e^2 - 164*e + 3, -4*e^5 - 10*e^4 + 32*e^3 + 36*e^2 - 62*e + 2, -14*e^5 - 32*e^4 + 119*e^3 + 114*e^2 - 237*e - 12, -e^4 - 4*e^3 + 2*e^2 + 11*e + 6, 14*e^5 + 28*e^4 - 132*e^3 - 92*e^2 + 286*e - 18, -7*e^5 - 16*e^4 + 57*e^3 + 51*e^2 - 106*e + 9, -16*e^5 - 33*e^4 + 147*e^3 + 111*e^2 - 306*e + 13, -18*e^5 - 41*e^4 + 154*e^3 + 144*e^2 - 309*e + 2, -7*e^5 - 14*e^4 + 65*e^3 + 42*e^2 - 140*e + 14, 5*e^5 + 8*e^4 - 53*e^3 - 23*e^2 + 119*e - 20, 8*e^5 + 18*e^4 - 67*e^3 - 54*e^2 + 137*e - 20, 22*e^5 + 47*e^4 - 200*e^3 - 169*e^2 + 416*e + 6, -13*e^5 - 30*e^4 + 110*e^3 + 107*e^2 - 216*e - 4, -3*e^5 - 4*e^4 + 34*e^3 + 6*e^2 - 89*e + 26, 4*e^5 + 10*e^4 - 30*e^3 - 32*e^2 + 54*e - 12, 9*e^5 + 20*e^4 - 82*e^3 - 77*e^2 + 178*e + 16, 15*e^5 + 35*e^4 - 126*e^3 - 126*e^2 + 249*e + 7, 2*e^5 + 5*e^4 - 14*e^3 - 12*e^2 + 26*e - 23, 9*e^5 + 20*e^4 - 79*e^3 - 67*e^2 + 168*e - 3, 4*e^5 + 6*e^4 - 46*e^3 - 20*e^2 + 112*e - 8, -11*e^5 - 23*e^4 + 102*e^3 + 82*e^2 - 217*e - 19, 4*e^5 + 13*e^4 - 22*e^3 - 50*e^2 + 31*e + 16, -12*e^5 - 24*e^4 + 113*e^3 + 81*e^2 - 235*e + 13, 8*e^5 + 16*e^4 - 74*e^3 - 45*e^2 + 164*e - 33, -14*e^5 - 30*e^4 + 127*e^3 + 108*e^2 - 260*e - 7, 6*e^5 + 14*e^4 - 51*e^3 - 51*e^2 + 101*e - 5, 6*e^5 + 11*e^4 - 58*e^3 - 25*e^2 + 129*e - 35, -4*e^5 - 7*e^4 + 41*e^3 + 23*e^2 - 93*e - 2, 29*e^5 + 61*e^4 - 265*e^3 - 207*e^2 + 558*e - 22, 13*e^5 + 28*e^4 - 114*e^3 - 92*e^2 + 224*e - 27, -9*e^5 - 20*e^4 + 81*e^3 + 76*e^2 - 166*e - 14, -14*e^5 - 28*e^4 + 135*e^3 + 100*e^2 - 296*e + 5, -24*e^5 - 55*e^4 + 202*e^3 + 187*e^2 - 402*e + 8, 6*e^5 + 12*e^4 - 57*e^3 - 41*e^2 + 123*e + 1, -6*e^5 - 16*e^4 + 46*e^3 + 62*e^2 - 94*e - 18, 18*e^5 + 40*e^4 - 158*e^3 - 142*e^2 + 322*e, -17*e^5 - 32*e^4 + 168*e^3 + 105*e^2 - 368*e + 42, -34*e^5 - 75*e^4 + 299*e^3 + 263*e^2 - 615*e + 2, 4*e^5 + 12*e^4 - 24*e^3 - 44*e^2 + 34*e + 20, -17*e^5 - 36*e^4 + 150*e^3 + 109*e^2 - 308*e + 46, -8*e^5 - 18*e^4 + 74*e^3 + 74*e^2 - 164*e - 28, -16*e^5 - 34*e^4 + 142*e^3 + 106*e^2 - 302*e + 40, 9*e^5 + 16*e^4 - 95*e^3 - 60*e^2 + 218*e - 12, 27*e^5 + 59*e^4 - 237*e^3 - 193*e^2 + 496*e - 48, -11*e^5 - 20*e^4 + 108*e^3 + 60*e^2 - 231*e + 30, -25*e^5 - 58*e^4 + 209*e^3 + 200*e^2 - 414*e - 2, -12*e^5 - 26*e^4 + 106*e^3 + 88*e^2 - 212*e - 6, 31*e^5 + 66*e^4 - 281*e^3 - 224*e^2 + 594*e - 24, 26*e^5 + 57*e^4 - 230*e^3 - 196*e^2 + 485*e - 8, 12*e^5 + 23*e^4 - 119*e^3 - 81*e^2 + 261*e - 6, 11*e^5 + 24*e^4 - 95*e^3 - 72*e^2 + 192*e - 36, 23*e^5 + 46*e^4 - 217*e^3 - 149*e^2 + 477*e - 44, -21*e^5 - 43*e^4 + 195*e^3 + 140*e^2 - 419*e + 28, -35*e^5 - 79*e^4 + 303*e^3 + 281*e^2 - 622*e - 20, 13*e^5 + 29*e^4 - 113*e^3 - 101*e^2 + 226*e + 2, 16*e^5 + 36*e^4 - 137*e^3 - 118*e^2 + 289*e - 30, 30*e^5 + 64*e^4 - 273*e^3 - 226*e^2 + 575*e + 8, -40*e^5 - 86*e^4 + 360*e^3 + 299*e^2 - 740*e + 25, -29*e^5 - 62*e^4 + 261*e^3 + 211*e^2 - 540*e + 19, 4*e^5 + 8*e^4 - 39*e^3 - 30*e^2 + 84*e - 3, -16*e^5 - 35*e^4 + 146*e^3 + 134*e^2 - 312*e - 19, 8*e^5 + 18*e^4 - 70*e^3 - 68*e^2 + 132*e + 16, -2*e^5 - e^4 + 26*e^3 - 6*e^2 - 52*e + 27, -10*e^5 - 24*e^4 + 84*e^3 + 94*e^2 - 172*e - 22, -15*e^5 - 37*e^4 + 116*e^3 + 128*e^2 - 213*e - 13, 36*e^5 + 78*e^4 - 324*e^3 - 280*e^2 + 680*e + 18, 16*e^5 + 36*e^4 - 142*e^3 - 136*e^2 + 294*e + 14, e^5 + 3*e^4 - 10*e^3 - 20*e^2 + 37*e + 31, 26*e^5 + 59*e^4 - 227*e^3 - 221*e^2 + 460*e + 29, 15*e^5 + 32*e^4 - 131*e^3 - 97*e^2 + 271*e - 26, -37*e^5 - 78*e^4 + 339*e^3 + 271*e^2 - 721*e + 10, -9*e^5 - 19*e^4 + 81*e^3 + 65*e^2 - 156*e + 10, 2*e^4 + 7*e^3 - 10*e^2 - 21*e + 22, -11*e^5 - 20*e^4 + 113*e^3 + 70*e^2 - 254*e + 20, 31*e^5 + 66*e^4 - 283*e^3 - 233*e^2 + 597*e - 8, -20*e^5 - 43*e^4 + 180*e^3 + 147*e^2 - 377*e + 21, -22*e^5 - 53*e^4 + 180*e^3 + 196*e^2 - 340*e - 39, -13*e^5 - 32*e^4 + 105*e^3 + 122*e^2 - 210*e - 34, -21*e^5 - 42*e^4 + 197*e^3 + 136*e^2 - 410*e + 46, 21*e^5 + 44*e^4 - 191*e^3 - 141*e^2 + 405*e - 36, 12*e^5 + 28*e^4 - 101*e^3 - 100*e^2 + 209*e + 2, -21*e^5 - 42*e^4 + 197*e^3 + 133*e^2 - 425*e + 28, 18*e^5 + 37*e^4 - 166*e^3 - 116*e^2 + 358*e - 55, 11*e^5 + 27*e^4 - 90*e^3 - 106*e^2 + 177*e + 29, -6*e^5 - 13*e^4 + 50*e^3 + 34*e^2 - 83*e + 42, -26*e^5 - 56*e^4 + 232*e^3 + 186*e^2 - 486*e + 36, 14*e^5 + 27*e^4 - 136*e^3 - 89*e^2 + 304*e - 24, -21*e^5 - 46*e^4 + 185*e^3 + 154*e^2 - 382*e + 18, e^5 - 2*e^4 - 21*e^3 + 14*e^2 + 54*e - 12, 14*e^5 + 26*e^4 - 137*e^3 - 76*e^2 + 303*e - 34, -27*e^5 - 54*e^4 + 253*e^3 + 178*e^2 - 522*e + 44, 7*e^5 + 15*e^4 - 62*e^3 - 52*e^2 + 127*e - 5, 36*e^5 + 75*e^4 - 328*e^3 - 245*e^2 + 698*e - 48, 24*e^5 + 53*e^4 - 212*e^3 - 191*e^2 + 433*e + 11, -9*e^5 - 26*e^4 + 57*e^3 + 96*e^2 - 88*e - 28, 50*e^5 + 114*e^4 - 429*e^3 - 406*e^2 + 862*e + 23, 37*e^5 + 79*e^4 - 332*e^3 - 260*e^2 + 701*e - 39, 16*e^5 + 35*e^4 - 136*e^3 - 105*e^2 + 260*e - 50, -22*e^5 - 47*e^4 + 196*e^3 + 154*e^2 - 412*e + 11, 20*e^5 + 46*e^4 - 173*e^3 - 178*e^2 + 342*e + 43, -20*e^5 - 35*e^4 + 204*e^3 + 104*e^2 - 450*e + 59, -10*e^5 - 20*e^4 + 90*e^3 + 52*e^2 - 192*e + 38, 8*e^5 + 20*e^4 - 67*e^3 - 84*e^2 + 136*e + 15, -35*e^5 - 78*e^4 + 308*e^3 + 282*e^2 - 627*e - 22, -32*e^5 - 73*e^4 + 270*e^3 + 240*e^2 - 543*e + 36, 14*e^5 + 34*e^4 - 114*e^3 - 126*e^2 + 234*e + 22, e^5 + 8*e^4 + 7*e^3 - 50*e^2 - 38*e + 56, 14*e^5 + 29*e^4 - 125*e^3 - 91*e^2 + 256*e - 15, -26*e^5 - 56*e^4 + 235*e^3 + 194*e^2 - 495*e + 30, -38*e^5 - 83*e^4 + 334*e^3 + 280*e^2 - 688*e + 37, 24*e^5 + 55*e^4 - 203*e^3 - 187*e^2 + 403*e - 26, 44*e^5 + 91*e^4 - 405*e^3 - 303*e^2 + 851*e - 70, 18*e^5 + 38*e^4 - 164*e^3 - 132*e^2 + 348*e - 4, 24*e^5 + 52*e^4 - 216*e^3 - 186*e^2 + 450*e + 8, 15*e^5 + 33*e^4 - 137*e^3 - 125*e^2 + 296*e + 8, -28*e^5 - 60*e^4 + 251*e^3 + 211*e^2 - 511*e + 3, -8*e^5 - 20*e^4 + 62*e^3 + 66*e^2 - 124*e + 4, -10*e^5 - 22*e^4 + 91*e^3 + 83*e^2 - 207*e - 33, -33*e^5 - 70*e^4 + 297*e^3 + 232*e^2 - 628*e + 48, 58*e^5 + 127*e^4 - 510*e^3 - 430*e^2 + 1054*e - 53, -36*e^5 - 75*e^4 + 332*e^3 + 258*e^2 - 702*e + 23, 28*e^5 + 57*e^4 - 260*e^3 - 187*e^2 + 554*e - 28, -19*e^5 - 45*e^4 + 155*e^3 + 152*e^2 - 297*e, -43*e^5 - 96*e^4 + 377*e^3 + 336*e^2 - 782*e + 12, -25*e^5 - 51*e^4 + 233*e^3 + 177*e^2 - 488*e + 14, 51*e^5 + 108*e^4 - 465*e^3 - 372*e^2 + 982*e - 2, 43*e^5 + 93*e^4 - 388*e^3 - 336*e^2 + 801*e + 19]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([41,41,-w^3 + 2*w^2 + 4*w - 6])] = -1

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