/*
  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, 5, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([29, 29, 2*w^3 - w^2 - 9*w + 5])

primes_array = [
[5, 5, w^3 - 4*w],\
[7, 7, w + 1],\
[7, 7, -w^3 + 4*w - 1],\
[13, 13, -w^2 + 3],\
[16, 2, 2],\
[17, 17, w^3 + w^2 - 4*w - 2],\
[17, 17, -w^3 + 5*w - 2],\
[19, 19, -w^2 - w + 4],\
[19, 19, -w^2 - w + 1],\
[29, 29, 2*w^3 - w^2 - 9*w + 5],\
[41, 41, -w^3 + w^2 + 5*w - 3],\
[43, 43, w^3 - w^2 - 4*w + 2],\
[43, 43, w^3 - 6*w],\
[47, 47, -w^3 - w^2 + 5*w],\
[49, 7, w^2 + 2*w - 2],\
[59, 59, 2*w^3 - 8*w + 3],\
[67, 67, w^2 - w - 4],\
[79, 79, w^3 - w^2 - 4*w + 1],\
[81, 3, -3],\
[97, 97, w^3 + w^2 - 5*w + 1],\
[107, 107, -2*w^3 + 3*w^2 + 10*w - 12],\
[109, 109, 2*w^3 - w^2 - 9*w + 3],\
[125, 5, -3*w^3 - w^2 + 12*w + 1],\
[127, 127, -2*w^3 + w^2 + 10*w - 8],\
[137, 137, -w^3 + w^2 + 3*w - 5],\
[139, 139, w^3 - w^2 - 5*w + 1],\
[149, 149, 2*w^2 - w - 6],\
[149, 149, 2*w^3 + w^2 - 9*w],\
[163, 163, w^3 - 5*w - 3],\
[163, 163, 2*w^3 - 7*w],\
[173, 173, -2*w^3 + 11*w - 3],\
[173, 173, -w^3 + w^2 + 4*w - 8],\
[179, 179, 2*w^3 - w^2 - 8*w + 5],\
[181, 181, 2*w^3 - w^2 - 8*w],\
[181, 181, 2*w^3 - 9*w - 3],\
[191, 191, 2*w^2 - 5],\
[191, 191, -2*w^2 - w + 10],\
[193, 193, w^3 + w^2 - 3*w - 4],\
[193, 193, -w^3 + 2*w^2 + 3*w - 3],\
[197, 197, -2*w^3 + 9*w - 4],\
[197, 197, w^2 - 7],\
[199, 199, 3*w^3 - 13*w + 1],\
[199, 199, w^3 + 2*w^2 - 5*w - 7],\
[227, 227, -3*w^3 + w^2 + 13*w - 4],\
[227, 227, -w^3 + 2*w^2 + 7*w - 6],\
[241, 241, -2*w^3 + 7*w - 1],\
[257, 257, -2*w^3 + w^2 + 7*w - 5],\
[257, 257, 2*w^3 - w^2 - 7*w + 2],\
[263, 263, -w^3 + 7*w - 3],\
[269, 269, -2*w^3 + 2*w^2 + 11*w - 8],\
[271, 271, w^2 + 3*w - 2],\
[271, 271, w^2 + 2*w - 7],\
[277, 277, -2*w^3 + 11*w - 2],\
[281, 281, 2*w^3 - 11*w + 1],\
[283, 283, 2*w^3 - 9*w + 5],\
[283, 283, -2*w^3 + w^2 + 11*w - 7],\
[289, 17, -w^3 + 2*w^2 + 4*w - 4],\
[293, 293, -2*w^3 - w^2 + 7*w + 3],\
[307, 307, -3*w^3 + 2*w^2 + 13*w - 9],\
[311, 311, -w^3 + w^2 + 3*w - 7],\
[313, 313, -w^3 + 2*w^2 + 3*w - 2],\
[313, 313, w^2 - w - 8],\
[317, 317, -2*w^3 - w^2 + 9*w - 1],\
[331, 331, w^3 + 2*w^2 - 5*w - 3],\
[337, 337, w^3 + 2*w^2 - 6*w - 4],\
[337, 337, w^3 - 2*w^2 - 6*w + 5],\
[347, 347, 2*w^3 + 2*w^2 - 9*w - 3],\
[347, 347, -2*w^3 + w^2 + 7*w - 4],\
[349, 349, w^2 - 2*w - 4],\
[353, 353, -w^3 + 2*w^2 + 2*w - 6],\
[359, 359, -w^3 + w^2 + 7*w - 6],\
[359, 359, -w^2 - w - 2],\
[361, 19, 2*w^3 - w^2 - 11*w],\
[367, 367, -2*w^3 + 2*w^2 + 8*w - 5],\
[373, 373, w^3 + w^2 - 2*w - 4],\
[379, 379, 2*w^3 - w^2 - 11*w + 4],\
[389, 389, 3*w^2 + w - 11],\
[397, 397, 3*w^3 - 13*w + 5],\
[401, 401, w - 5],\
[409, 409, 3*w^3 - 12*w + 4],\
[409, 409, 3*w^3 + 2*w^2 - 14*w - 4],\
[421, 421, 2*w^3 - w^2 - 10*w + 1],\
[421, 421, w^3 + 2*w^2 - 5*w - 4],\
[439, 439, -2*w^3 + 10*w - 5],\
[443, 443, -2*w^3 + 12*w - 5],\
[443, 443, -4*w^3 + w^2 + 18*w - 9],\
[443, 443, -2*w^3 + w^2 + 7*w - 9],\
[443, 443, 3*w^3 + 2*w^2 - 14*w - 5],\
[449, 449, w^3 + 2*w^2 - 2*w - 6],\
[449, 449, -2*w^3 + w^2 + 11*w - 5],\
[461, 461, 2*w^3 + 2*w^2 - 9*w - 4],\
[467, 467, -w^3 + w^2 + 7*w - 5],\
[487, 487, 2*w^2 + 4*w - 7],\
[491, 491, -w^3 + w^2 + 7*w - 4],\
[503, 503, 2*w^3 + w^2 - 9*w + 2],\
[521, 521, w^2 - 3*w - 3],\
[523, 523, -w^3 + 2*w^2 + 5*w - 4],\
[523, 523, -w^3 + 8*w - 5],\
[563, 563, w^3 + 3*w^2 - w - 8],\
[563, 563, w^3 - 2*w^2 - 8*w + 4],\
[563, 563, -w^3 + w^2 + 2*w - 5],\
[563, 563, -3*w^3 - w^2 + 10*w - 2],\
[577, 577, 3*w^3 - 16*w],\
[587, 587, w^3 + 2*w^2 - 6],\
[587, 587, -w^3 + 4*w - 6],\
[601, 601, -w - 5],\
[607, 607, w^3 - 2*w^2 - 4*w + 1],\
[613, 613, 4*w^3 - 17*w],\
[617, 617, -3*w^3 + w^2 + 14*w - 2],\
[617, 617, -4*w^3 + 17*w - 4],\
[619, 619, -3*w^3 + 12*w - 2],\
[643, 643, 3*w^3 - w^2 - 12*w + 3],\
[643, 643, -2*w^3 - w^2 + 11*w - 2],\
[647, 647, 2*w^3 + w^2 - 9*w + 3],\
[653, 653, w^3 + w^2 - 7*w - 4],\
[661, 661, -w^3 + 4*w^2 + 6*w - 15],\
[661, 661, 3*w^3 - 2*w^2 - 12*w + 10],\
[677, 677, -3*w^2 - 2*w + 12],\
[691, 691, -2*w^3 + 3*w^2 + 11*w - 10],\
[691, 691, -3*w^3 + 16*w - 3],\
[701, 701, 3*w^3 - 13*w + 6],\
[719, 719, -3*w^2 + w + 10],\
[727, 727, w^3 - 3*w^2 - 4*w + 6],\
[743, 743, -w^3 + 2*w^2 + 5*w - 3],\
[761, 761, -w^3 + 3*w^2 + 3*w - 12],\
[761, 761, 3*w^3 - 2*w^2 - 14*w + 7],\
[769, 769, -3*w^3 + 3*w^2 + 16*w - 13],\
[769, 769, w^3 + 2*w^2 - 7*w - 6],\
[773, 773, w^3 - 8*w + 4],\
[773, 773, 4*w^2 + w - 16],\
[787, 787, w^2 + 4*w - 2],\
[797, 797, -2*w^3 + 3*w^2 + 10*w - 10],\
[797, 797, -w^3 - w^2 + 4*w - 4],\
[797, 797, w^3 + 2*w^2 - 3*w - 9],\
[797, 797, -3*w^3 + 3*w^2 + 11*w - 10],\
[821, 821, w^2 + w - 9],\
[827, 827, w^3 - 8*w + 1],\
[827, 827, -2*w^3 + w^2 + 9*w - 11],\
[827, 827, 3*w^3 - 14*w + 5],\
[827, 827, 2*w^3 + w^2 - 7*w - 5],\
[829, 829, -2*w^3 - 2*w^2 + 9*w - 1],\
[839, 839, -3*w^3 + 15*w - 5],\
[853, 853, -4*w^3 + 15*w - 8],\
[853, 853, -w^3 + 2*w^2 + 6*w - 3],\
[859, 859, -w^3 + w^2 + w - 4],\
[859, 859, w^3 + w^2 - w - 5],\
[881, 881, -w^3 + w^2 + 2*w - 6],\
[881, 881, w^3 + w^2 - 2*w - 6],\
[883, 883, w^3 + 3*w^2 - 3*w - 6],\
[887, 887, w^3 + 3*w^2 - 3*w - 8],\
[919, 919, 2*w^3 - w^2 - 13*w],\
[929, 929, -w^3 - 3*w^2 + 2*w + 10],\
[929, 929, w^3 + w^2 - 5*w - 8],\
[941, 941, w^3 + 2*w^2 - 3*w - 10],\
[953, 953, -w^3 + 5*w - 7],\
[953, 953, -2*w^3 + 3*w^2 + 9*w - 9],\
[953, 953, -2*w^3 - w^2 + 10*w - 3],\
[953, 953, -3*w^3 + 11*w - 1],\
[961, 31, -w^3 + 3*w^2 + 2*w - 10],\
[961, 31, -3*w^2 + 2*w + 7],\
[967, 967, w^3 + 3*w^2 - 3*w - 7],\
[967, 967, 4*w^3 + w^2 - 20*w + 1],\
[983, 983, 2*w^3 - w^2 - 12*w + 8],\
[983, 983, 2*w^3 + w^2 - 6*w - 4],\
[991, 991, 2*w^3 - 12*w + 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 11*x^5 + 40*x^4 - 40*x^3 - 62*x^2 + 133*x - 51
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, e^5 - 8*e^4 + 17*e^3 + 5*e^2 - 41*e + 24, e^4 - 5*e^3 + 2*e^2 + 11*e - 6, -e^5 + 8*e^4 - 16*e^3 - 9*e^2 + 39*e - 12, -e^5 + 7*e^4 - 12*e^3 - 8*e^2 + 32*e - 11, e^5 - 9*e^4 + 22*e^3 + 4*e^2 - 55*e + 30, e^2 - 3*e, e^3 - 4*e^2 - 2*e + 10, -e^5 + 8*e^4 - 17*e^3 - 6*e^2 + 44*e - 18, -1, -3*e^5 + 24*e^4 - 51*e^3 - 16*e^2 + 123*e - 60, e^5 - 9*e^4 + 20*e^3 + 12*e^2 - 52*e + 12, e^4 - 5*e^3 + 17*e - 4, -e^5 + 11*e^4 - 33*e^3 + 5*e^2 + 74*e - 48, -e^5 + 11*e^4 - 34*e^3 + 7*e^2 + 80*e - 53, 2*e^5 - 16*e^4 + 32*e^3 + 18*e^2 - 77*e + 21, -4*e^5 + 33*e^4 - 73*e^3 - 20*e^2 + 176*e - 84, -e^5 + 5*e^4 - e^3 - 14*e^2 + 3*e + 3, 3*e^5 - 24*e^4 + 50*e^3 + 18*e^2 - 119*e + 64, -e^4 + 7*e^3 - 8*e^2 - 15*e + 10, -4*e^5 + 32*e^4 - 67*e^3 - 26*e^2 + 165*e - 72, 2*e^5 - 12*e^4 + 10*e^3 + 34*e^2 - 32*e - 12, e^5 - 8*e^4 + 19*e^3 - 3*e^2 - 41*e + 33, -6*e^4 + 29*e^3 - 6*e^2 - 68*e + 19, -e^3 + 3*e^2 + 7*e - 6, -4*e^4 + 19*e^3 - 2*e^2 - 48*e + 15, -4*e^4 + 19*e^3 - 4*e^2 - 45*e + 24, 3*e^5 - 24*e^4 + 49*e^3 + 24*e^2 - 118*e + 36, 2*e^5 - 18*e^4 + 45*e^3 + 3*e^2 - 107*e + 59, e^5 - 8*e^4 + 17*e^3 + 6*e^2 - 41*e + 24, -5*e^5 + 41*e^4 - 88*e^3 - 34*e^2 + 222*e - 102, -e^5 + 6*e^4 - 3*e^3 - 26*e^2 + 14*e + 24, -3*e^5 + 20*e^4 - 31*e^3 - 20*e^2 + 69*e - 45, 6*e^5 - 47*e^4 + 98*e^3 + 29*e^2 - 236*e + 132, 9*e^5 - 74*e^4 + 162*e^3 + 51*e^2 - 401*e + 190, -e^5 + 3*e^4 + 10*e^3 - 20*e^2 - 29*e + 24, -e^5 + 8*e^4 - 15*e^3 - 14*e^2 + 38*e - 9, -e^5 + 5*e^4 - 4*e^3 - 2*e^2 + e - 10, -5*e^5 + 40*e^4 - 84*e^3 - 30*e^2 + 202*e - 99, 7*e^5 - 51*e^4 + 89*e^3 + 66*e^2 - 219*e + 66, -5*e^5 + 37*e^4 - 68*e^3 - 39*e^2 + 168*e - 75, 4*e^5 - 33*e^4 + 71*e^3 + 28*e^2 - 179*e + 84, -2*e^5 + 15*e^4 - 29*e^3 - 16*e^2 + 79*e - 27, 2*e^5 - 10*e^4 + 40*e^2 - 14*e - 30, 2*e^5 - 15*e^4 + 29*e^3 + 14*e^2 - 75*e + 33, 5*e^5 - 40*e^4 + 82*e^3 + 38*e^2 - 205*e + 87, 7*e^5 - 56*e^4 + 116*e^3 + 49*e^2 - 279*e + 111, 9*e^5 - 69*e^4 + 138*e^3 + 54*e^2 - 340*e + 171, -4*e^5 + 36*e^4 - 89*e^3 - 7*e^2 + 212*e - 129, -5*e^5 + 44*e^4 - 102*e^3 - 35*e^2 + 258*e - 90, -e^5 - e^4 + 31*e^3 - 31*e^2 - 81*e + 65, 4*e^5 - 33*e^4 + 72*e^3 + 29*e^2 - 186*e + 61, 3*e^5 - 21*e^4 + 31*e^3 + 38*e^2 - 69*e + 1, -4*e^5 + 29*e^4 - 51*e^3 - 35*e^2 + 130*e - 57, 6*e^5 - 41*e^4 + 61*e^3 + 71*e^2 - 166*e + 38, -e^5 + 9*e^4 - 24*e^3 + 4*e^2 + 56*e - 35, 2*e^5 - 17*e^4 + 38*e^3 + 12*e^2 - 94*e + 39, 6*e^5 - 53*e^4 + 125*e^3 + 32*e^2 - 307*e + 141, -e^5 + 11*e^4 - 33*e^3 + 2*e^2 + 80*e - 21, 3*e^5 - 29*e^4 + 77*e^3 + 4*e^2 - 182*e + 99, -3*e^5 + 23*e^4 - 41*e^3 - 36*e^2 + 97*e - 6, 5*e^5 - 36*e^4 + 65*e^3 + 39*e^2 - 177*e + 73, 7*e^4 - 32*e^3 - e^2 + 81*e - 12, e^5 - 12*e^4 + 38*e^3 - 6*e^2 - 87*e + 48, -e^5 + 15*e^4 - 55*e^3 + 18*e^2 + 126*e - 75, -e^5 + 8*e^4 - 16*e^3 - 9*e^2 + 40*e - 9, 3*e^5 - 28*e^4 + 73*e^3 + e^2 - 170*e + 99, e^5 - 7*e^4 + 10*e^3 + 17*e^2 - 37*e + 9, -3*e^5 + 30*e^4 - 80*e^3 - 11*e^2 + 206*e - 102, -7*e^4 + 37*e^3 - 19*e^2 - 93*e + 66, -5*e^5 + 36*e^4 - 63*e^3 - 42*e^2 + 151*e - 42, 10*e^5 - 78*e^4 + 158*e^3 + 63*e^2 - 382*e + 189, e^5 - 7*e^4 + 12*e^3 + 4*e^2 - 33*e + 45, -6*e^5 + 51*e^4 - 118*e^3 - 21*e^2 + 281*e - 159, 3*e^4 - 16*e^3 + 15*e^2 + 19*e - 37, -11*e^5 + 89*e^4 - 193*e^3 - 52*e^2 + 461*e - 244, -7*e^5 + 55*e^4 - 109*e^3 - 63*e^2 + 278*e - 84, -3*e^5 + 14*e^4 - 36*e^2 - 2*e + 10, -4*e^5 + 36*e^4 - 93*e^3 + 5*e^2 + 222*e - 144, -3*e^5 + 29*e^4 - 74*e^3 - 18*e^2 + 191*e - 90, -5*e^5 + 40*e^4 - 87*e^3 - 20*e^2 + 218*e - 126, -2*e^5 + 14*e^4 - 17*e^3 - 41*e^2 + 47*e + 21, 9*e^5 - 77*e^4 + 179*e^3 + 35*e^2 - 424*e + 210, -e^5 + 5*e^4 + e^3 - 20*e^2 - 3*e + 8, -e^5 + 14*e^4 - 42*e^3 - 14*e^2 + 105*e - 18, -5*e^5 + 41*e^4 - 88*e^3 - 30*e^2 + 212*e - 111, 2*e^5 - 16*e^4 + 30*e^3 + 32*e^2 - 90*e + 6, -7*e^5 + 63*e^4 - 155*e^3 - 19*e^2 + 370*e - 198, 6*e^5 - 51*e^4 + 116*e^3 + 30*e^2 - 291*e + 150, -2*e^5 + 20*e^4 - 53*e^3 - 10*e^2 + 134*e - 54, 2*e^5 - 11*e^4 + 11*e^3 + 6*e^2 - 12*e + 36, 7*e^5 - 52*e^4 + 101*e^3 + 37*e^2 - 245*e + 120, e^5 - 6*e^4 + e^3 + 28*e^2 + 3*e - 29, e^5 - 9*e^4 + 22*e^3 + 5*e^2 - 57*e + 30, 11*e^5 - 80*e^4 + 141*e^3 + 95*e^2 - 341*e + 123, -3*e^5 + 12*e^4 + 13*e^3 - 58*e^2 - 4*e + 42, -13*e^5 + 104*e^4 - 220*e^3 - 77*e^2 + 547*e - 252, 5*e^5 - 41*e^4 + 90*e^3 + 24*e^2 - 214*e + 130, -7*e^5 + 53*e^4 - 103*e^3 - 46*e^2 + 262*e - 150, -6*e^5 + 52*e^4 - 123*e^3 - 24*e^2 + 303*e - 168, 3*e^5 - 24*e^4 + 53*e^3 + 6*e^2 - 132*e + 108, -4*e^5 + 33*e^4 - 73*e^3 - 19*e^2 + 182*e - 90, 2*e^5 - 13*e^4 + 21*e^3 + 9*e^2 - 54*e + 43, -5*e^5 + 42*e^4 - 91*e^3 - 45*e^2 + 238*e - 81, -6*e^5 + 43*e^4 - 81*e^3 - 23*e^2 + 187*e - 117, -3*e^5 + 25*e^4 - 52*e^3 - 27*e^2 + 119*e - 40, 3*e^5 - 17*e^4 + 20*e^3 + 12*e^2 - 49*e + 69, e^5 - 6*e^4 + 5*e^3 + 12*e^2 - 6*e + 18, -6*e^4 + 29*e^3 - 4*e^2 - 72*e + 6, -9*e^5 + 68*e^4 - 129*e^3 - 72*e^2 + 321*e - 141, 8*e^5 - 59*e^4 + 105*e^3 + 70*e^2 - 244*e + 90, 4*e^5 - 32*e^4 + 69*e^3 + 23*e^2 - 189*e + 84, -8*e^5 + 70*e^4 - 167*e^3 - 28*e^2 + 397*e - 200, -3*e^5 + 20*e^4 - 30*e^3 - 30*e^2 + 83*e - 42, -e^5 - e^4 + 29*e^3 - 24*e^2 - 73*e + 54, 4*e^5 - 36*e^4 + 84*e^3 + 25*e^2 - 193*e + 78, -2*e^5 + 4*e^4 + 30*e^3 - 46*e^2 - 76*e + 87, -e^5 + 6*e^4 - 6*e^3 - 9*e^2 - 4*e + 12, 12*e^5 - 98*e^4 + 215*e^3 + 58*e^2 - 530*e + 285, 5*e^5 - 41*e^4 + 86*e^3 + 44*e^2 - 225*e + 53, e^5 - 8*e^4 + 22*e^3 - 15*e^2 - 39*e + 51, e^5 - 4*e^4 - 6*e^2 + 19*e + 45, 6*e^5 - 39*e^4 + 51*e^3 + 67*e^2 - 118*e + 36, 8*e^5 - 64*e^4 + 134*e^3 + 48*e^2 - 327*e + 165, -7*e^5 + 61*e^4 - 143*e^3 - 35*e^2 + 353*e - 162, 10*e^5 - 73*e^4 + 126*e^3 + 106*e^2 - 330*e + 93, 4*e^4 - 20*e^3 + e^2 + 62*e - 17, 22*e^5 - 178*e^4 + 386*e^3 + 103*e^2 - 920*e + 477, 17*e^5 - 138*e^4 + 293*e^3 + 115*e^2 - 734*e + 321, -9*e^5 + 74*e^4 - 158*e^3 - 59*e^2 + 380*e - 174, 4*e^4 - 22*e^3 + 15*e^2 + 40*e - 29, 5*e^5 - 42*e^4 + 97*e^3 + 25*e^2 - 258*e + 111, e^5 - 3*e^4 - 3*e^3 - 10*e^2 + 30*e + 33, 6*e^5 - 43*e^4 + 68*e^3 + 78*e^2 - 179*e + 18, -9*e^5 + 61*e^4 - 87*e^3 - 111*e^2 + 230*e - 51, -2*e^5 + 18*e^4 - 38*e^3 - 32*e^2 + 89*e + 12, -2*e^5 + 13*e^4 - 17*e^3 - 24*e^2 + 53*e - 30, -e^5 - 6*e^4 + 62*e^3 - 62*e^2 - 149*e + 144, -6*e^5 + 52*e^4 - 118*e^3 - 43*e^2 + 294*e - 96, 7*e^5 - 65*e^4 + 165*e^3 + 18*e^2 - 395*e + 198, 2*e^5 - 9*e^4 - 9*e^3 + 50*e^2 + 22*e - 71, 11*e^5 - 101*e^4 + 254*e^3 + 29*e^2 - 623*e + 345, 5*e^5 - 34*e^4 + 55*e^3 + 39*e^2 - 134*e + 33, -7*e^5 + 56*e^4 - 119*e^3 - 38*e^2 + 304*e - 162, -3*e^5 + 21*e^4 - 34*e^3 - 28*e^2 + 78*e - 39, 5*e^5 - 31*e^4 + 38*e^3 + 49*e^2 - 84*e + 23, 12*e^5 - 106*e^4 + 252*e^3 + 51*e^2 - 604*e + 297, -16*e^5 + 127*e^4 - 269*e^3 - 83*e^2 + 667*e - 354, -12*e^5 + 94*e^4 - 191*e^3 - 83*e^2 + 488*e - 237, 7*e^5 - 57*e^4 + 125*e^3 + 28*e^2 - 304*e + 189, 3*e^5 - 26*e^4 + 62*e^3 + 7*e^2 - 142*e + 71, -2*e^5 + 22*e^4 - 68*e^3 + 13*e^2 + 150*e - 75, -12*e^5 + 95*e^4 - 204*e^3 - 45*e^2 + 483*e - 267, 10*e^5 - 82*e^4 + 176*e^3 + 70*e^2 - 441*e + 174, -7*e^5 + 54*e^4 - 105*e^3 - 59*e^2 + 269*e - 93, 7*e^5 - 55*e^4 + 118*e^3 + 23*e^2 - 279*e + 150, -3*e^5 + 34*e^4 - 97*e^3 - 19*e^2 + 253*e - 99, 9*e^5 - 69*e^4 + 141*e^3 + 36*e^2 - 319*e + 201, -e^5 + 21*e^4 - 87*e^3 + 29*e^2 + 231*e - 141, e^5 - 11*e^4 + 36*e^3 - 16*e^2 - 89*e + 96, 11*e^5 - 83*e^4 + 150*e^3 + 118*e^2 - 385*e + 102, -6*e^5 + 44*e^4 - 77*e^3 - 57*e^2 + 184*e - 55, 12*e^5 - 88*e^4 + 160*e^3 + 87*e^2 - 368*e + 171, 10*e^5 - 81*e^4 + 174*e^3 + 52*e^2 - 426*e + 240, 4*e^4 - 22*e^3 + 15*e^2 + 62*e - 77]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([29, 29, 2*w^3 - w^2 - 9*w + 5])] = 1

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