/*
  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([6, 4, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([8, 2, w^3 - 2*w^2 - 4*w + 8])

primes_array = [
[2, 2, w - 2],\
[2, 2, w + 1],\
[3, 3, -w^2 + w + 3],\
[27, 3, -w^3 - 2*w^2 + 3*w + 5],\
[29, 29, w^3 + w^2 - 2*w - 1],\
[31, 31, -w^2 - w + 1],\
[31, 31, w^3 - 2*w^2 - 5*w + 7],\
[37, 37, -w^3 + 3*w + 1],\
[41, 41, -w^2 + w + 5],\
[41, 41, -w^3 + w^2 + 4*w - 1],\
[43, 43, -2*w - 1],\
[47, 47, w^2 + w - 5],\
[47, 47, 2*w^3 - 3*w^2 - 9*w + 11],\
[53, 53, w^3 + 2*w^2 - 5*w - 5],\
[59, 59, w^3 + w^2 - 4*w - 1],\
[59, 59, w^3 + w^2 - 4*w - 5],\
[71, 71, 2*w^3 - 4*w^2 - 10*w + 19],\
[71, 71, w^2 + 3*w + 1],\
[73, 73, w^3 - 5*w + 1],\
[89, 89, -4*w^3 + 7*w^2 + 19*w - 29],\
[97, 97, -w^3 + 2*w^2 + 3*w - 7],\
[101, 101, 2*w^3 - 12*w - 7],\
[103, 103, 2*w - 1],\
[103, 103, w^2 + w - 7],\
[107, 107, 2*w^3 - w^2 - 9*w + 1],\
[107, 107, 2*w^2 - 7],\
[109, 109, -w^3 + w^2 + 4*w + 1],\
[113, 113, -4*w^3 - 3*w^2 + 17*w + 13],\
[121, 11, -w^2 - w - 1],\
[121, 11, -w^3 + 2*w^2 + 5*w - 11],\
[139, 139, 2*w^3 - 10*w - 1],\
[139, 139, 2*w^3 - 10*w - 5],\
[149, 149, w^3 - w^2 - 6*w + 5],\
[157, 157, w^2 - 3*w - 1],\
[157, 157, 4*w^3 - 6*w^2 - 18*w + 25],\
[157, 157, 2*w^3 - w^2 - 9*w + 5],\
[157, 157, -w^3 - 2*w^2 + 3*w + 7],\
[163, 163, -w^3 + w^2 + 4*w - 7],\
[179, 179, w^3 - 3*w - 5],\
[181, 181, 3*w^3 - 4*w^2 - 13*w + 17],\
[191, 191, 2*w^3 - 8*w + 1],\
[191, 191, w^3 - 5*w - 5],\
[211, 211, 2*w + 5],\
[227, 227, w^3 + w^2 - 4*w - 7],\
[239, 239, 2*w^3 + 2*w^2 - 8*w - 5],\
[257, 257, 2*w^3 - 4*w^2 - 8*w + 19],\
[257, 257, w^3 + 2*w^2 - 5*w - 7],\
[263, 263, -2*w^3 - 2*w^2 + 6*w + 1],\
[269, 269, -2*w^3 + 4*w^2 + 8*w - 13],\
[277, 277, -3*w^2 + w + 13],\
[293, 293, -2*w^3 + 4*w^2 + 8*w - 17],\
[293, 293, -3*w^3 - 3*w^2 + 14*w + 11],\
[293, 293, 3*w^3 - 4*w^2 - 15*w + 19],\
[293, 293, 3*w^3 + w^2 - 14*w - 7],\
[307, 307, 2*w^3 - 3*w^2 - 5*w + 1],\
[307, 307, 2*w^3 - 4*w^2 - 4*w + 7],\
[311, 311, -3*w^3 + 3*w^2 + 14*w - 13],\
[313, 313, w^3 + 3*w^2 + 2*w + 1],\
[317, 317, -3*w^3 - 3*w^2 + 10*w + 5],\
[331, 331, -2*w^3 - 3*w^2 + 9*w + 13],\
[337, 337, -w^3 + 2*w^2 + 3*w - 11],\
[337, 337, w^3 + 2*w^2 - w - 5],\
[337, 337, -w^3 + 2*w^2 + 3*w - 1],\
[337, 337, w^3 - 3*w - 7],\
[347, 347, 3*w^3 - 4*w^2 - 15*w + 17],\
[347, 347, -w^3 + 2*w^2 + 5*w - 5],\
[349, 349, -2*w^3 + 2*w^2 + 8*w - 5],\
[353, 353, -2*w^3 + 3*w^2 + 3*w + 1],\
[361, 19, -5*w^3 - 4*w^2 + 21*w + 17],\
[361, 19, 3*w^3 + w^2 - 10*w + 1],\
[373, 373, -2*w^3 + w^2 + 11*w - 1],\
[379, 379, w^3 - w^2 - 6*w - 1],\
[379, 379, -w^3 + 7*w - 5],\
[389, 389, 2*w^3 - 2*w^2 - 8*w + 7],\
[397, 397, 2*w^3 + 5*w^2 - 5*w - 13],\
[409, 409, w^3 + w^2 - 6*w - 1],\
[421, 421, -2*w^3 + 2*w^2 + 10*w - 5],\
[433, 433, -w^3 - 3*w^2 + 6*w + 7],\
[439, 439, 3*w^2 - 3*w - 7],\
[443, 443, 3*w^3 + w^2 - 14*w - 5],\
[449, 449, -4*w^3 - 3*w^2 + 19*w + 17],\
[449, 449, -w^3 + 3*w^2 + 6*w - 17],\
[457, 457, w^3 + 2*w^2 + w + 1],\
[457, 457, -2*w^3 + w^2 + 9*w - 7],\
[461, 461, -w^3 + 7*w + 7],\
[461, 461, -4*w^2 + 17],\
[467, 467, -2*w^3 + w^2 + 11*w + 1],\
[479, 479, 5*w^3 - 8*w^2 - 25*w + 37],\
[487, 487, w^3 + w^2 - 8*w + 1],\
[487, 487, 7*w^3 - 12*w^2 - 31*w + 49],\
[487, 487, 2*w^3 + w^2 - 13*w - 11],\
[487, 487, 4*w^3 + 3*w^2 - 17*w - 11],\
[491, 491, -2*w^2 - 2*w + 1],\
[499, 499, 2*w^3 - 8*w - 1],\
[503, 503, -2*w^3 - w^2 + 11*w + 11],\
[503, 503, 3*w^3 - w^2 - 14*w + 1],\
[509, 509, -4*w^3 + 9*w^2 + 17*w - 37],\
[523, 523, -w^3 - 3*w^2 + 5],\
[541, 541, 6*w^3 + 6*w^2 - 20*w - 13],\
[541, 541, w^3 - 7*w + 1],\
[547, 547, w^2 - 3*w - 5],\
[547, 547, w^2 + 3*w - 1],\
[557, 557, -7*w^3 - 4*w^2 + 35*w + 25],\
[557, 557, -3*w^3 - 2*w^2 + 13*w + 7],\
[569, 569, -2*w^3 + 5*w^2 + 5*w - 11],\
[569, 569, w^3 + w^2 - 8*w - 5],\
[571, 571, -w^3 - 3*w^2 + 4*w + 11],\
[571, 571, -2*w^3 - 2*w^2 + 12*w + 13],\
[593, 593, -4*w^2 + 4*w + 7],\
[593, 593, 3*w^2 + w - 13],\
[599, 599, -2*w^3 + 2*w^2 + 6*w - 1],\
[601, 601, -w^3 + 3*w - 5],\
[607, 607, 2*w^3 - 12*w - 5],\
[607, 607, w^3 + w^2 + 1],\
[613, 613, -2*w^3 - 2*w^2 + 6*w + 7],\
[617, 617, w^3 - 7*w - 1],\
[619, 619, -2*w^3 + 12*w - 1],\
[625, 5, -5],\
[631, 631, -w^3 + w^2 + 2*w - 5],\
[641, 641, 2*w^3 - w^2 - 7*w - 1],\
[641, 641, 4*w^3 + 2*w^2 - 22*w - 19],\
[641, 641, -w^3 - 2*w^2 + 7*w + 11],\
[641, 641, 3*w^2 - 3*w - 11],\
[661, 661, -w^3 - w^2 + 6*w - 1],\
[661, 661, 3*w^3 + 2*w^2 - 11*w - 7],\
[673, 673, 3*w^3 - 2*w^2 - 13*w + 11],\
[673, 673, 2*w^3 - 6*w - 1],\
[683, 683, w^2 + 3*w - 5],\
[709, 709, 3*w^2 - w - 11],\
[719, 719, -2*w^3 + 6*w + 5],\
[719, 719, 2*w^3 + 5*w^2 - w - 5],\
[727, 727, 2*w^2 - 2*w - 11],\
[733, 733, 4*w^2 - 2*w - 19],\
[739, 739, -2*w^3 + 4*w^2 + 6*w - 13],\
[739, 739, w^3 - 9*w + 7],\
[739, 739, -2*w^3 + 10*w - 1],\
[739, 739, -2*w^3 - 2*w^2 + 12*w + 7],\
[751, 751, -4*w^3 - 3*w^2 + 15*w + 11],\
[751, 751, -2*w^3 - w^2 + 5*w - 1],\
[821, 821, 3*w^3 + 5*w^2 - 10*w - 11],\
[823, 823, -w^3 - w^2 + 8*w + 11],\
[839, 839, w^3 + 2*w^2 + w - 1],\
[853, 853, 2*w^3 + w^2 - 7*w - 7],\
[857, 857, w^3 + 4*w^2 - w - 13],\
[859, 859, 2*w - 7],\
[859, 859, -5*w^3 + 11*w^2 + 20*w - 43],\
[863, 863, 2*w^3 + 2*w^2 - 8*w - 1],\
[863, 863, -w^3 + 3*w^2 + 4*w - 7],\
[877, 877, -4*w^3 + 7*w^2 + 17*w - 31],\
[883, 883, 5*w^3 - 7*w^2 - 24*w + 31],\
[907, 907, 4*w^3 - 6*w^2 - 16*w + 19],\
[919, 919, 2*w^3 + 3*w^2 - 9*w - 11],\
[929, 929, w^3 - w^2 - 2*w - 5],\
[937, 937, -w^3 + 3*w^2 + 2*w - 11],\
[937, 937, -3*w^3 + 7*w^2 + 12*w - 29],\
[947, 947, 2*w^3 - 3*w^2 - 11*w + 13],\
[947, 947, 2*w^3 - w^2 - 11*w + 7],\
[961, 31, 2*w^3 - 4*w^2 - 2*w - 1],\
[967, 967, 3*w^3 + 4*w^2 - 9*w - 11],\
[971, 971, -4*w^3 - 4*w^2 + 18*w + 17],\
[991, 991, -w^3 + w^2 + 2*w - 7]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 4*x^5 - x^4 + 17*x^3 - 11*x^2 - 6*x + 2
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, e^5 - 3*e^4 - 3*e^3 + 12*e^2 - 3*e - 2, -e^5 + 3*e^4 + 4*e^3 - 13*e^2 - 2*e + 7, -e^5 + 3*e^4 + 2*e^3 - 11*e^2 + 9*e, -2*e^5 + 5*e^4 + 8*e^3 - 20*e^2 - e + 4, -e^5 + 2*e^4 + 6*e^3 - 8*e^2 - 8*e + 3, e^5 - 9*e^3 - e^2 + 17*e, -e^5 + 3*e^4 + 6*e^3 - 15*e^2 - 9*e + 10, e^5 - 6*e^4 + 2*e^3 + 27*e^2 - 22*e - 6, -2*e^3 + e^2 + 12*e - 3, e^5 - 4*e^4 - 4*e^3 + 19*e^2 + 3*e - 7, 2*e^5 - 6*e^4 - 8*e^3 + 28*e^2 + e - 11, -e^4 - e^3 + 8*e^2 + 5*e - 5, -e^5 + 7*e^4 - 4*e^3 - 30*e^2 + 27*e + 9, e^5 - 3*e^4 - 4*e^3 + 12*e^2 + 2*e + 2, 2*e^5 - 4*e^4 - 8*e^3 + 11*e^2 - e + 10, e^5 - 5*e^4 + 3*e^3 + 19*e^2 - 23*e - 9, e^5 - 3*e^4 - 4*e^3 + 14*e^2 - 2*e - 6, 3*e^5 - 11*e^4 - 6*e^3 + 43*e^2 - 16*e - 9, e^5 + e^4 - 9*e^3 - 7*e^2 + 13*e + 13, -2*e^5 + 5*e^4 + 9*e^3 - 21*e^2 - 8*e + 5, -2*e^5 + 7*e^4 + 6*e^3 - 34*e^2 + 10*e + 17, 2*e^4 - 7*e^3 - 7*e^2 + 28*e + 2, 3*e^5 - 11*e^4 - 4*e^3 + 45*e^2 - 33*e - 8, -e^5 + 10*e^3 - e^2 - 22*e, -e^5 + 3*e^4 + 4*e^3 - 13*e^2 - 3*e + 8, -6*e^5 + 16*e^4 + 23*e^3 - 65*e^2 - e + 19, -2*e^5 + 2*e^4 + 15*e^3 - 10*e^2 - 23*e + 8, e^5 - 5*e^4 - e^3 + 21*e^2 - 12*e + 6, 2*e^5 - 7*e^4 - 4*e^3 + 23*e^2 - 9*e + 9, 4*e^5 - 10*e^4 - 17*e^3 + 42*e^2 + 5*e - 12, e^4 - 2*e^3 - 9*e^2 + 10*e + 22, -4*e^5 + 10*e^4 + 16*e^3 - 43*e^2 + 6*e + 17, -e^5 + 4*e^4 - 4*e^3 - 13*e^2 + 30*e, -e^5 - e^4 + 10*e^3 + 5*e^2 - 19*e, -2*e^5 + 9*e^4 + 5*e^3 - 41*e^2 + 7*e + 16, 3*e^4 - 5*e^3 - 10*e^2 + 13*e - 13, e^5 - 3*e^4 - e^3 + 9*e^2 - 18*e + 4, 3*e^5 - 4*e^4 - 22*e^3 + 20*e^2 + 33*e - 12, -4*e^5 + 12*e^4 + 13*e^3 - 46*e^2 + 9*e - 4, -2*e^5 + 6*e^4 + 5*e^3 - 17*e^2 + 12*e - 14, -3*e^3 + 4*e^2 + 17*e - 18, 2*e^5 - 11*e^4 + 5*e^3 + 43*e^2 - 36*e - 9, -4*e^5 + 7*e^4 + 25*e^3 - 31*e^2 - 34*e + 19, 3*e^5 - 7*e^4 - 11*e^3 + 28*e^2 - 3*e - 14, 5*e^5 - 19*e^4 - 10*e^3 + 83*e^2 - 38*e - 25, 2*e^5 - 8*e^4 - 2*e^3 + 36*e^2 - 24*e - 12, -3*e^5 + 5*e^4 + 17*e^3 - 12*e^2 - 23*e - 4, 4*e^5 - 11*e^4 - 14*e^3 + 49*e^2 - 7*e - 25, -2*e^3 - e^2 + 20*e + 9, 5*e^5 - 10*e^4 - 27*e^3 + 42*e^2 + 32*e - 16, e^5 - 8*e^4 + 2*e^3 + 35*e^2 - 17*e - 3, -2*e^5 + 5*e^4 + 7*e^3 - 19*e^2 - e + 16, -7*e^5 + 26*e^4 + 12*e^3 - 105*e^2 + 42*e + 18, e^5 - 5*e^4 + 5*e^3 + 21*e^2 - 30*e - 20, 3*e^5 - 5*e^4 - 16*e^3 + 20*e^2 + 6*e - 6, 2*e^5 - 5*e^4 - 10*e^3 + 18*e^2 + 11*e, -e^5 + 6*e^4 + e^3 - 29*e^2 + 6*e + 19, 7*e^5 - 21*e^4 - 24*e^3 + 87*e^2 - 9*e - 32, -e^5 + 8*e^4 - 7*e^3 - 39*e^2 + 35*e + 28, 3*e^5 - 9*e^4 - 10*e^3 + 34*e^2 - 6*e + 12, -2*e^5 + 5*e^4 + e^3 - 17*e^2 + 37*e + 2, -3*e^4 + 10*e^3 + 9*e^2 - 43*e + 3, 6*e^5 - 21*e^4 - 14*e^3 + 90*e^2 - 39*e - 24, -e^5 + 3*e^4 - 12*e^2 + 13*e + 1, -7*e^5 + 14*e^4 + 39*e^3 - 60*e^2 - 46*e + 30, -5*e^5 + 16*e^4 + 11*e^3 - 58*e^2 + 31*e + 1, -6*e^5 + 20*e^4 + 17*e^3 - 81*e^2 + 8*e + 26, -5*e^5 + 16*e^4 + 12*e^3 - 60*e^2 + 19*e + 8, 3*e^5 - 6*e^4 - 19*e^3 + 22*e^2 + 35*e - 7, -7*e^5 + 24*e^4 + 14*e^3 - 93*e^2 + 44*e + 12, 2*e^5 - 16*e^4 + 16*e^3 + 67*e^2 - 80*e - 21, -2*e^5 - e^4 + 20*e^3 + 8*e^2 - 42*e - 17, -12*e^5 + 31*e^4 + 46*e^3 - 126*e^2 + 5*e + 28, 2*e^4 - 8*e^3 - 6*e^2 + 24*e - 10, -e^5 - 6*e^4 + 22*e^3 + 23*e^2 - 59*e - 1, 6*e^5 - 17*e^4 - 14*e^3 + 62*e^2 - 33*e - 20, 6*e^5 - 22*e^4 - 10*e^3 + 94*e^2 - 56*e - 20, 5*e^5 - 11*e^4 - 23*e^3 + 36*e^2 + 9*e + 26, -6*e^5 + 23*e^4 + 15*e^3 - 96*e^2 + 20*e + 24, -6*e^5 + 21*e^4 + 9*e^3 - 82*e^2 + 48*e + 18, -e^5 + e^4 + 5*e^3 - 3*e^2 + 6*e + 14, e^5 + e^4 - 9*e^3 - 8*e^2 + 19*e + 12, -3*e^5 + 5*e^4 + 20*e^3 - 16*e^2 - 34*e, -7*e^5 + 27*e^4 + 14*e^3 - 120*e^2 + 49*e + 35, -10*e^5 + 24*e^4 + 38*e^3 - 92*e^2 + 9*e + 13, 6*e^5 - 17*e^4 - 20*e^3 + 64*e^2 - 7*e - 4, 7*e^4 - 3*e^3 - 36*e^2 - 8*e + 18, -e^5 + 8*e^4 - 5*e^3 - 42*e^2 + 30*e + 34, -7*e^5 + 17*e^4 + 30*e^3 - 65*e^2 + e - 8, -e^5 + 9*e^4 + 2*e^3 - 48*e^2 - 3*e + 29, -6*e^5 + 16*e^4 + 22*e^3 - 68*e^2 + 11*e + 35, e^5 - 3*e^4 - 2*e^3 + 13*e^2 - 11*e - 2, -3*e^5 + 9*e^4 + 12*e^3 - 39*e^2 + 3*e + 2, 6*e^5 - 22*e^4 - 12*e^3 + 88*e^2 - 31*e + 1, 2*e^5 - 9*e^4 - 5*e^3 + 39*e^2 + 3*e - 8, 5*e^5 - 7*e^4 - 27*e^3 + 26*e^2 + 15*e - 6, e^5 - 5*e^4 + 2*e^3 + 24*e^2 - 20*e - 14, 3*e^5 - 6*e^4 - 14*e^3 + 29*e^2 + 8*e - 28, 5*e^5 - 6*e^4 - 35*e^3 + 24*e^2 + 62*e - 14, -2*e^5 - e^4 + 28*e^3 - e^2 - 72*e + 8, 8*e^5 - 16*e^4 - 41*e^3 + 64*e^2 + 37*e - 30, e^5 + 4*e^4 - 19*e^3 - 25*e^2 + 68*e + 21, -9*e^5 + 28*e^4 + 23*e^3 - 103*e^2 + 34*e + 5, -3*e^5 + 5*e^4 + 9*e^3 - 20*e^2 + 32*e + 7, 3*e^5 - 16*e^4 + 3*e^3 + 75*e^2 - 57*e - 18, -4*e^4 + 16*e^3 + 6*e^2 - 59*e + 15, 5*e^5 - 18*e^4 - 5*e^3 + 62*e^2 - 53*e + 1, -2*e^5 + 6*e^4 + e^3 - 26*e^2 + 42*e + 15, 7*e^5 - 15*e^4 - 38*e^3 + 61*e^2 + 34*e - 11, -7*e^5 + 22*e^4 + 16*e^3 - 83*e^2 + 28*e + 12, 9*e^3 - 7*e^2 - 32*e + 8, -2*e^5 + 8*e^4 - 2*e^3 - 34*e^2 + 41*e + 31, 3*e^5 - 9*e^4 - 6*e^3 + 26*e^2 - 20*e + 14, -11*e^5 + 32*e^4 + 35*e^3 - 128*e^2 + 30*e + 32, 6*e^5 - 13*e^4 - 25*e^3 + 47*e^2 + 7*e - 18, 3*e^5 - 9*e^4 - 15*e^3 + 46*e^2 + 13*e - 34, 5*e^5 - 15*e^4 - 17*e^3 + 67*e^2 - 18*e - 42, -e^5 + 7*e^4 - 6*e^3 - 28*e^2 + 30*e - 2, 2*e^5 + e^4 - 8*e^3 - 15*e^2 - 17*e + 25, -4*e^5 + 12*e^4 + 5*e^3 - 40*e^2 + 46*e - 3, 4*e^5 - 13*e^4 - 10*e^3 + 55*e^2 - 20*e - 18, -3*e^5 + 5*e^4 + 12*e^3 - 9*e^2 - 9*e - 22, -7*e^5 + 21*e^4 + 19*e^3 - 91*e^2 + 34*e + 42, -2*e^5 + 8*e^4 + 4*e^3 - 32*e^2 + 9*e + 21, 5*e^5 - 14*e^4 - 25*e^3 + 71*e^2 + 23*e - 28, -2*e^5 + 8*e^4 + 3*e^3 - 33*e^2 + 25*e - 1, 4*e^5 - 13*e^4 - 11*e^3 + 47*e^2 - 3*e + 10, -4*e^5 + 11*e^4 + 20*e^3 - 53*e^2 - 34*e + 40, -e^5 + 8*e^4 - 8*e^3 - 39*e^2 + 47*e + 21, e^5 - 3*e^4 - 2*e^3 + 16*e^2 - 10*e - 32, -3*e^5 + 12*e^4 + 5*e^3 - 49*e^2 + 20*e + 25, 8*e^5 - 30*e^4 - 14*e^3 + 127*e^2 - 57*e - 28, 4*e^5 - 17*e^4 - 5*e^3 + 70*e^2 - 46*e, -5*e^5 + 3*e^4 + 32*e^3 - 48*e - 4, -e^5 - 3*e^4 + 18*e^3 + 17*e^2 - 59*e - 20, 2*e^5 - 12*e^4 + 9*e^3 + 48*e^2 - 50*e - 11, e^5 - 6*e^4 + 4*e^3 + 29*e^2 - 21*e - 7, -5*e^5 + 11*e^4 + 24*e^3 - 44*e^2 + 2*e - 4, -7*e^5 + 28*e^4 + 11*e^3 - 110*e^2 + 46*e + 12, 8*e^5 - 22*e^4 - 34*e^3 + 106*e^2 + 8*e - 62, 2*e^5 - 3*e^4 - 6*e^3 + 3*e^2 + 10, 3*e^5 - 15*e^4 + 12*e^3 + 62*e^2 - 94*e - 20, -3*e^5 + 4*e^4 + 17*e^3 - 10*e^2 - 26*e - 26, -5*e^5 + 21*e^4 + 4*e^3 - 95*e^2 + 63*e + 36, -11*e^5 + 27*e^4 + 42*e^3 - 117*e^2 + 19*e + 52, 3*e^5 - 3*e^4 - 19*e^3 + 7*e^2 + 22*e + 26, -3*e^5 + 10*e^4 + 7*e^3 - 24*e^2 + 5*e - 27, -4*e^4 + 2*e^3 + 20*e^2 + 13*e - 13, -3*e^5 + 12*e^4 - 3*e^3 - 54*e^2 + 54*e + 38, 6*e^4 - 7*e^3 - 33*e^2 + 23*e + 43, -12*e^4 + 20*e^3 + 60*e^2 - 68*e - 14, 9*e^5 - 30*e^4 - 18*e^3 + 115*e^2 - 68*e - 8, -13*e^5 + 35*e^4 + 46*e^3 - 130*e^2 + e + 11, -6*e^5 + 10*e^4 + 25*e^3 - 14*e^2 - 15*e - 52, e^5 + 12*e^4 - 26*e^3 - 59*e^2 + 70*e + 16, -6*e^5 + 25*e^4 + 9*e^3 - 111*e^2 + 33*e + 60, -3*e^5 + 19*e^4 - 8*e^3 - 81*e^2 + 67*e + 14, 2*e^5 - 13*e^4 - 5*e^3 + 70*e^2 - 14*e - 30, -11*e^5 + 21*e^4 + 54*e^3 - 82*e^2 - 40*e + 32]
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, w - 2])] = 1

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