/*
  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, -2, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

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

primes_array = [
[5, 5, -w^3 + 2*w^2 + 3*w],\
[7, 7, w - 1],\
[11, 11, -w^3 + 2*w^2 + 4*w],\
[13, 13, -2*w^3 + 3*w^2 + 10*w - 2],\
[16, 2, 2],\
[17, 17, -w^3 + 2*w^2 + 5*w - 3],\
[17, 17, -w^3 + w^2 + 5*w],\
[17, 17, -w^2 + 2*w + 1],\
[19, 19, w^2 - w - 2],\
[29, 29, w^3 - 2*w^2 - 5*w],\
[29, 29, w^2 - w - 3],\
[31, 31, -w^3 + 2*w^2 + 3*w - 2],\
[43, 43, 2*w^3 - 3*w^2 - 11*w],\
[47, 47, w^3 - 7*w - 4],\
[53, 53, -2*w^3 + 3*w^2 + 9*w - 1],\
[61, 61, -w - 3],\
[73, 73, -w^3 + 2*w^2 + 3*w - 3],\
[73, 73, w^3 - w^2 - 7*w - 1],\
[81, 3, -3],\
[83, 83, -2*w^3 + 3*w^2 + 9*w + 1],\
[83, 83, -w^3 + 3*w^2 + 2*w - 3],\
[89, 89, w - 4],\
[103, 103, w^3 - 2*w^2 - 6*w + 3],\
[113, 113, 2*w^3 - w^2 - 14*w - 6],\
[121, 11, -w^2 + 2*w + 7],\
[125, 5, -3*w^3 + 4*w^2 + 15*w + 1],\
[139, 139, w^3 - 2*w^2 - 5*w - 3],\
[139, 139, w^3 - 5*w - 5],\
[151, 151, w^3 - 9*w - 7],\
[157, 157, -3*w^3 + 6*w^2 + 13*w - 6],\
[163, 163, w^3 - 3*w^2 - 2*w + 9],\
[167, 167, -w^3 + 7*w + 3],\
[167, 167, -3*w^3 + 4*w^2 + 15*w - 1],\
[173, 173, 2*w^3 - 3*w^2 - 7*w - 2],\
[181, 181, -w^3 + 3*w^2 + 4*w - 5],\
[191, 191, w^3 - w^2 - 4*w - 4],\
[193, 193, -w^3 + w^2 + 7*w + 6],\
[193, 193, 2*w^3 - 2*w^2 - 13*w - 5],\
[199, 199, -2*w^3 + 5*w^2 + 5*w - 5],\
[211, 211, w^3 - w^2 - 8*w - 3],\
[211, 211, -2*w^2 + 3*w + 8],\
[227, 227, -w^3 + 3*w^2 + 4*w - 4],\
[227, 227, w^2 - 3*w - 6],\
[229, 229, w^2 - 5],\
[229, 229, 3*w^3 - 4*w^2 - 17*w - 2],\
[233, 233, 3*w^3 - 6*w^2 - 13*w + 3],\
[233, 233, 3*w^3 - 4*w^2 - 16*w + 1],\
[241, 241, -2*w^3 + 4*w^2 + 8*w + 1],\
[251, 251, 2*w^3 - 2*w^2 - 9*w - 3],\
[277, 277, 3*w^3 - 4*w^2 - 17*w - 1],\
[281, 281, -2*w^2 + 5*w + 1],\
[283, 283, -4*w^3 + 6*w^2 + 19*w - 2],\
[293, 293, -3*w^3 + 6*w^2 + 12*w - 2],\
[307, 307, w^3 - w^2 - 4*w - 5],\
[307, 307, w^3 - w^2 - 8*w - 2],\
[311, 311, 2*w^2 - 3*w - 7],\
[313, 313, -2*w^3 + w^2 + 15*w + 3],\
[317, 317, -w^3 + 3*w^2 + w - 5],\
[331, 331, 2*w^3 - 3*w^2 - 12*w],\
[337, 337, w^3 - w^2 - 8*w - 1],\
[343, 7, -w^3 + 6*w + 8],\
[347, 347, 2*w^3 - 4*w^2 - 7*w + 5],\
[349, 349, 2*w^3 - 4*w^2 - 9*w],\
[353, 353, -3*w^3 + 4*w^2 + 16*w + 5],\
[353, 353, -3*w^3 + 4*w^2 + 14*w],\
[353, 353, -w^3 + 3*w^2 + 4*w - 8],\
[353, 353, -w^3 + 2*w^2 + 8*w - 3],\
[359, 359, -4*w^3 + 7*w^2 + 19*w - 3],\
[367, 367, -w^3 + 2*w^2 + 6*w - 5],\
[373, 373, 5*w^3 - 8*w^2 - 26*w + 3],\
[379, 379, -3*w^3 + 5*w^2 + 17*w - 4],\
[379, 379, -w^3 + 2*w^2 + 4*w - 6],\
[383, 383, w^2 - 6],\
[389, 389, w^3 - 2*w^2 - 3*w - 4],\
[389, 389, w^2 + w - 4],\
[397, 397, -4*w^3 + 5*w^2 + 23*w + 5],\
[397, 397, -3*w^3 + 5*w^2 + 12*w - 2],\
[419, 419, -3*w^3 + 4*w^2 + 17*w + 5],\
[419, 419, -3*w^3 + 5*w^2 + 15*w],\
[419, 419, 3*w^3 - 5*w^2 - 14*w - 1],\
[419, 419, 2*w^3 - 3*w^2 - 10*w - 6],\
[431, 431, 2*w^3 - 2*w^2 - 11*w],\
[433, 433, w^3 - 8*w - 1],\
[433, 433, 2*w^2 - 2*w - 5],\
[439, 439, 2*w^3 - 2*w^2 - 9*w - 6],\
[443, 443, 2*w^3 - 5*w^2 - 7*w],\
[443, 443, 2*w^3 - 5*w^2 - 9*w + 4],\
[457, 457, -2*w^3 + 5*w^2 + 7*w - 4],\
[457, 457, -w^3 + 2*w^2 - 3],\
[461, 461, -4*w^3 + 7*w^2 + 17*w - 7],\
[479, 479, 3*w^3 - 5*w^2 - 12*w + 6],\
[487, 487, -2*w^3 + 5*w^2 + 9*w - 9],\
[487, 487, w^3 - 10*w - 8],\
[499, 499, 2*w^3 - 2*w^2 - 12*w + 1],\
[503, 503, w^2 - 7],\
[503, 503, w^3 + w^2 - 7*w - 8],\
[529, 23, -3*w^3 + 5*w^2 + 12*w + 1],\
[529, 23, 3*w^3 - 4*w^2 - 14*w - 1],\
[541, 541, w^3 - 4*w^2 - 2*w + 11],\
[563, 563, -2*w^3 + w^2 + 15*w + 6],\
[569, 569, w^3 - 2*w^2 - 4*w - 4],\
[601, 601, 3*w^3 - 5*w^2 - 17*w + 1],\
[607, 607, -2*w^3 + 5*w^2 + 7*w - 5],\
[607, 607, -w^3 + 3*w^2 + 6*w - 5],\
[613, 613, -4*w^3 + 5*w^2 + 21*w + 1],\
[613, 613, -5*w^3 + 8*w^2 + 23*w - 4],\
[619, 619, w^3 + w^2 - 9*w - 5],\
[619, 619, -3*w^3 + 4*w^2 + 14*w + 2],\
[641, 641, -6*w^3 + 8*w^2 + 31*w + 3],\
[643, 643, 3*w^3 - 4*w^2 - 17*w - 6],\
[643, 643, -2*w^3 + 5*w^2 + 7*w - 6],\
[647, 647, 3*w^3 - 4*w^2 - 13*w - 10],\
[653, 653, -3*w^3 + 5*w^2 + 14*w + 2],\
[653, 653, w^3 - 2*w^2 - w - 3],\
[661, 661, 5*w^3 - 9*w^2 - 24*w + 5],\
[683, 683, 2*w^3 - 3*w^2 - 13*w - 2],\
[683, 683, 4*w^3 - 7*w^2 - 18*w + 1],\
[719, 719, -w^3 + 2*w^2 + 3*w - 7],\
[719, 719, 3*w^3 - 5*w^2 - 16*w - 1],\
[727, 727, -2*w^3 + 5*w^2 + 8*w - 7],\
[727, 727, 2*w^3 - 5*w^2 - 7*w + 13],\
[733, 733, -2*w^2 + 7],\
[733, 733, -3*w^3 + 5*w^2 + 11*w + 2],\
[739, 739, -6*w^3 + 9*w^2 + 29*w - 3],\
[739, 739, -2*w^3 + 3*w^2 + 7*w + 5],\
[751, 751, 4*w^3 - 5*w^2 - 23*w - 3],\
[757, 757, -w^3 + 10*w + 4],\
[757, 757, 2*w^3 - w^2 - 14*w - 4],\
[769, 769, -w^3 + 4*w^2 + 4*w - 8],\
[769, 769, 4*w^3 - 6*w^2 - 21*w - 2],\
[787, 787, 3*w^3 - 3*w^2 - 19*w - 6],\
[787, 787, -2*w^2 + 6*w + 7],\
[839, 839, -3*w^3 + 3*w^2 + 19*w + 5],\
[841, 29, 3*w^3 - 4*w^2 - 13*w - 4],\
[853, 853, -3*w^3 + 5*w^2 + 14*w + 3],\
[853, 853, 2*w^2 - w - 9],\
[853, 853, 3*w^3 - 5*w^2 - 11*w + 1],\
[853, 853, w - 6],\
[857, 857, 2*w^3 - 2*w^2 - 9*w - 7],\
[857, 857, -4*w^3 + 8*w^2 + 13*w - 1],\
[859, 859, 2*w^3 - 4*w^2 - 13*w + 2],\
[859, 859, w^3 - w^2 - 9*w - 2],\
[863, 863, -2*w^3 - w^2 + 17*w + 11],\
[877, 877, 5*w^3 - 6*w^2 - 28*w - 9],\
[877, 877, -4*w^3 + 5*w^2 + 20*w + 6],\
[881, 881, 4*w^3 - 5*w^2 - 18*w - 8],\
[911, 911, -w^3 + 4*w^2 - w - 8],\
[911, 911, 2*w^3 - 3*w^2 - 13*w - 1],\
[919, 919, w^3 - w^2 - 7*w + 5],\
[929, 929, 2*w^3 - 3*w^2 - 13*w + 1],\
[929, 929, -2*w^3 + 5*w^2 + 6*w - 11],\
[941, 941, -3*w^3 + 7*w^2 + 12*w - 5],\
[953, 953, -2*w^3 + 5*w^2 + 5*w - 7],\
[971, 971, w^3 - w^2 - 3*w - 5],\
[971, 971, 3*w^3 - 7*w^2 - 12*w + 11],\
[977, 977, 3*w^3 - 5*w^2 - 11*w],\
[997, 997, -2*w^3 + 3*w^2 + 6*w - 5],\
[997, 997, -4*w^3 + 7*w^2 + 16*w - 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 4*x^4 - 14*x^3 + 72*x^2 - 56*x - 24
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/10*e^4 - 3/10*e^3 - 17/10*e^2 + 5*e - 8/5, 1/5*e^4 - 3/5*e^3 - 17/5*e^2 + 10*e - 6/5, -1/10*e^4 + 3/10*e^3 + 11/5*e^2 - 4*e - 32/5, e - 1, -7/20*e^4 + 3/10*e^3 + 31/5*e^2 - 7*e - 42/5, 3/20*e^4 - 1/5*e^3 - 23/10*e^2 + 4*e - 12/5, -1, 1/4*e^4 - 1/2*e^3 - 9/2*e^2 + 10*e + 2, 1/20*e^4 - 2/5*e^3 - 3/5*e^2 + 7*e - 24/5, 1/2*e^3 - 8*e + 6, -1/10*e^4 + 3/10*e^3 + 6/5*e^2 - 4*e + 28/5, -9/20*e^4 + 3/5*e^3 + 37/5*e^2 - 11*e - 14/5, -1/2*e^3 + 8*e, -1/2*e^4 + 1/2*e^3 + 8*e^2 - 12*e, 13/20*e^4 - 7/10*e^3 - 59/5*e^2 + 15*e + 88/5, -13/20*e^4 + 6/5*e^3 + 54/5*e^2 - 23*e - 8/5, 3/5*e^4 - 13/10*e^3 - 46/5*e^2 + 25*e - 38/5, 7/20*e^4 - 13/10*e^3 - 31/5*e^2 + 23*e - 28/5, 1/20*e^4 - 2/5*e^3 - 3/5*e^2 + 7*e - 24/5, 3/20*e^4 - 1/5*e^3 - 14/5*e^2 + 3*e + 78/5, 21/20*e^4 - 19/10*e^3 - 171/10*e^2 + 34*e + 6/5, -6/5*e^4 + 21/10*e^3 + 102/5*e^2 - 40*e - 14/5, -3/20*e^4 + 7/10*e^3 + 14/5*e^2 - 13*e + 42/5, 3/4*e^4 - 3/2*e^3 - 12*e^2 + 31*e - 4, 29/20*e^4 - 13/5*e^3 - 122/5*e^2 + 49*e + 24/5, 17/20*e^4 - 3/10*e^3 - 76/5*e^2 + 11*e + 112/5, -1/20*e^4 - 3/5*e^3 - 7/5*e^2 + 9*e + 64/5, -11/20*e^4 + 7/5*e^3 + 48/5*e^2 - 27*e + 34/5, 3/20*e^4 - 6/5*e^3 - 14/5*e^2 + 17*e - 32/5, 1/4*e^4 + 1/2*e^3 - 4*e^2 - 7*e + 8, -3/10*e^4 + 2/5*e^3 + 33/5*e^2 - 6*e - 96/5, -1/2*e^4 + e^3 + 17/2*e^2 - 19*e - 6, 7/20*e^4 - 3/10*e^3 - 31/5*e^2 + 3*e + 42/5, -11/20*e^4 - 1/10*e^3 + 53/5*e^2 - 5*e - 116/5, -3/4*e^4 + 3/2*e^3 + 27/2*e^2 - 28*e, -7/10*e^4 + 8/5*e^3 + 57/5*e^2 - 29*e + 16/5, -1/2*e^4 + 7*e^2 - 4*e + 8, 9/10*e^4 - 17/10*e^3 - 84/5*e^2 + 28*e + 118/5, -3/10*e^4 + 9/10*e^3 + 28/5*e^2 - 12*e - 26/5, 4/5*e^4 - 19/10*e^3 - 58/5*e^2 + 34*e - 74/5, -11/10*e^4 + 23/10*e^3 + 91/5*e^2 - 44*e - 42/5, 1/4*e^4 - 7/2*e^2 - 2*e + 6, 1/2*e^4 - 3/2*e^3 - 9*e^2 + 26*e + 2, -11/20*e^4 + 2/5*e^3 + 121/10*e^2 - 8*e - 146/5, -11/10*e^4 + 13/10*e^3 + 197/10*e^2 - 29*e - 102/5, -27/20*e^4 + 23/10*e^3 + 121/5*e^2 - 45*e - 72/5, 1/4*e^4 + 1/2*e^3 - 9/2*e^2 - 6*e + 8, 1/10*e^4 + 1/5*e^3 - 6/5*e^2 - 4*e + 12/5, 5/4*e^4 - e^3 - 43/2*e^2 + 24*e + 32, -13/10*e^4 + 19/10*e^3 + 103/5*e^2 - 44*e + 84/5, 1/2*e^4 - 3/2*e^3 - 9*e^2 + 29*e + 8, 3/5*e^4 - 4/5*e^3 - 66/5*e^2 + 16*e + 162/5, -1/10*e^4 + 3/10*e^3 + 6/5*e^2 - 10*e - 2/5, -e^4 + 5/2*e^3 + 18*e^2 - 40*e - 4, 4/5*e^4 - 2/5*e^3 - 73/5*e^2 + 12*e + 156/5, 3/10*e^4 - 9/10*e^3 - 41/10*e^2 + 19*e - 14/5, 3/10*e^4 - 2/5*e^3 - 31/10*e^2 + 11*e - 54/5, -11/20*e^4 - 1/10*e^3 + 48/5*e^2 - e - 116/5, 3/10*e^4 - 7/5*e^3 - 33/5*e^2 + 18*e + 136/5, 13/20*e^4 - 6/5*e^3 - 44/5*e^2 + 27*e - 122/5, 13/20*e^4 - 7/10*e^3 - 59/5*e^2 + 14*e + 78/5, -9/20*e^4 + 11/10*e^3 + 89/10*e^2 - 16*e - 164/5, 21/20*e^4 - 12/5*e^3 - 181/10*e^2 + 44*e + 36/5, -11/10*e^4 + 4/5*e^3 + 187/10*e^2 - 19*e - 72/5, 7/10*e^4 - 3/5*e^3 - 67/5*e^2 + 14*e + 144/5, -7/20*e^4 - 7/10*e^3 + 26/5*e^2 + 11*e - 72/5, -9/5*e^4 + 29/10*e^3 + 153/5*e^2 - 52*e - 96/5, -21/20*e^4 + 7/5*e^3 + 78/5*e^2 - 29*e + 94/5, -3/10*e^4 + 2/5*e^3 + 23/5*e^2 - 9*e + 124/5, -5/4*e^4 + 3/2*e^3 + 22*e^2 - 35*e - 16, -19/10*e^4 + 47/10*e^3 + 164/5*e^2 - 84*e + 22/5, 7/5*e^4 - 17/10*e^3 - 119/5*e^2 + 40*e + 18/5, 1/4*e^4 - 5*e^2 - 3*e + 12, 23/20*e^4 - 27/10*e^3 - 89/5*e^2 + 49*e - 42/5, 7/20*e^4 + 6/5*e^3 - 57/10*e^2 - 16*e + 52/5, 9/10*e^4 - 7/10*e^3 - 84/5*e^2 + 12*e + 148/5, -6/5*e^4 + 3/5*e^3 + 117/5*e^2 - 17*e - 234/5, -17/20*e^4 + 4/5*e^3 + 137/10*e^2 - 20*e + 18/5, -1/2*e^3 + e^2 + 9*e - 12, 1/5*e^4 + 2/5*e^3 - 17/5*e^2 - 6*e + 84/5, -23/20*e^4 + 27/10*e^3 + 94/5*e^2 - 47*e - 48/5, 11/20*e^4 + 11/10*e^3 - 38/5*e^2 - 15*e + 46/5, 11/10*e^4 - 4/5*e^3 - 177/10*e^2 + 19*e - 8/5, 9/10*e^4 - 27/10*e^3 - 79/5*e^2 + 50*e - 2/5, 1/20*e^4 - 9/10*e^3 - 11/10*e^2 + 10*e - 24/5, 2/5*e^4 - 1/5*e^3 - 34/5*e^2 + 3*e + 78/5, 21/20*e^4 - 19/10*e^3 - 211/10*e^2 + 30*e + 166/5, -e^3 + 2*e^2 + 20*e - 22, 7/10*e^4 - 8/5*e^3 - 47/5*e^2 + 30*e - 66/5, -9/5*e^4 + 12/5*e^3 + 148/5*e^2 - 52*e - 36/5, 1/5*e^4 - 8/5*e^3 - 27/5*e^2 + 22*e + 64/5, -11/20*e^4 - 1/10*e^3 + 111/10*e^2 - 6*e - 176/5, -4/5*e^4 + 2/5*e^3 + 73/5*e^2 - 12*e - 116/5, 29/20*e^4 - 13/5*e^3 - 127/5*e^2 + 46*e + 24/5, -17/20*e^4 + 3/10*e^3 + 147/10*e^2 - 8*e - 102/5, -3/20*e^4 + 7/10*e^3 + 23/10*e^2 - 16*e + 82/5, 1/5*e^4 + 19/10*e^3 - 7/5*e^2 - 26*e + 4/5, -1/2*e^4 + 5/2*e^3 + 10*e^2 - 44*e + 20, 13/10*e^4 - 7/5*e^3 - 118/5*e^2 + 26*e + 186/5, -1/4*e^4 - 1/2*e^3 + 3*e^2 + 4*e - 12, e^4 - 18*e^2 + 10*e + 26, -7/20*e^4 - 7/10*e^3 + 47/10*e^2 + 6*e - 92/5, 17/20*e^4 - 14/5*e^3 - 137/10*e^2 + 44*e - 68/5, 3/20*e^4 + 3/10*e^3 - 9/5*e^2 + e - 2/5, -17/10*e^4 + 13/5*e^3 + 137/5*e^2 - 52*e - 14/5, 7/10*e^4 - 8/5*e^3 - 52/5*e^2 + 28*e - 86/5, 7/5*e^4 - 6/5*e^3 - 119/5*e^2 + 24*e + 178/5, -2/5*e^4 + 11/5*e^3 + 34/5*e^2 - 36*e + 42/5, -21/10*e^4 + 43/10*e^3 + 176/5*e^2 - 80*e - 2/5, -9/5*e^4 + 39/10*e^3 + 321/10*e^2 - 65*e - 86/5, -3/5*e^4 + 4/5*e^3 + 41/5*e^2 - 12*e + 108/5, -13/10*e^4 + 2/5*e^3 + 108/5*e^2 - 14*e - 126/5, 1/4*e^4 - e^3 - 11/2*e^2 + 16*e + 18, -43/20*e^4 + 47/10*e^3 + 169/5*e^2 - 86*e + 52/5, -9/10*e^4 - 3/10*e^3 + 64/5*e^2 - 2*e + 42/5, 3/10*e^4 - 7/5*e^3 - 28/5*e^2 + 27*e - 54/5, 1/20*e^4 + 8/5*e^3 - 11/10*e^2 - 22*e + 66/5, -79/20*e^4 + 71/10*e^3 + 337/5*e^2 - 139*e - 24/5, 5/4*e^4 - 3/2*e^3 - 18*e^2 + 37*e - 28, 29/20*e^4 - 11/10*e^3 - 279/10*e^2 + 30*e + 214/5, -31/20*e^4 + 17/5*e^3 + 281/10*e^2 - 64*e - 86/5, -8/5*e^4 + 23/10*e^3 + 297/10*e^2 - 45*e - 242/5, 29/20*e^4 - 18/5*e^3 - 117/5*e^2 + 66*e - 116/5, -13/20*e^4 + 17/10*e^3 + 59/5*e^2 - 21*e - 68/5, 2/5*e^4 - 16/5*e^3 - 29/5*e^2 + 50*e - 32/5, -19/20*e^4 + 13/5*e^3 + 77/5*e^2 - 53*e + 136/5, 1/20*e^4 - 7/5*e^3 - 3/5*e^2 + 15*e - 104/5, -11/10*e^4 + 3/10*e^3 + 76/5*e^2 - 12*e + 28/5, -6/5*e^4 + 13/5*e^3 + 102/5*e^2 - 40*e + 46/5, 23/20*e^4 - 7/10*e^3 - 109/5*e^2 + 19*e + 148/5, -2*e^3 - e^2 + 30*e - 4, 13/10*e^4 - 2/5*e^3 - 118/5*e^2 + 22*e + 156/5, -1/20*e^4 - 1/10*e^3 + 8/5*e^2 + e + 34/5, 7/2*e^4 - 6*e^3 - 59*e^2 + 116*e + 2, -7/10*e^4 + 8/5*e^3 + 62/5*e^2 - 34*e + 106/5, -3/4*e^4 + 1/2*e^3 + 11*e^2 - 15*e + 14, 3/5*e^4 + 17/10*e^3 - 56/5*e^2 - 23*e + 202/5, 3/10*e^4 - 2/5*e^3 - 23/5*e^2 + 12*e + 6/5, 9/20*e^4 - 1/10*e^3 - 47/5*e^2 - e + 54/5, -3/4*e^4 + 3/2*e^3 + 12*e^2 - 35*e - 4, 12/5*e^4 - 21/5*e^3 - 403/10*e^2 + 81*e - 2/5, 11/5*e^4 - 23/5*e^3 - 202/5*e^2 + 86*e + 84/5, -4/5*e^4 + 2/5*e^3 + 141/10*e^2 - 5*e - 176/5, 1/4*e^4 - 3/2*e^3 - 5*e^2 + 26*e + 20, -1/10*e^4 + 4/5*e^3 + 1/5*e^2 - 11*e - 12/5, -1/5*e^4 - 2/5*e^3 + 22/5*e^2 + 4*e - 24/5, -1/2*e^4 + 13*e^2 - 3*e - 42, -13/20*e^4 + 7/10*e^3 + 143/10*e^2 - 14*e - 218/5, 13/5*e^4 - 19/5*e^3 - 216/5*e^2 + 80*e - 18/5, 9/5*e^4 - 7/5*e^3 - 148/5*e^2 + 36*e + 6/5, 5/2*e^4 - 11/2*e^3 - 87/2*e^2 + 93*e + 6, -9/10*e^4 + 11/5*e^3 + 94/5*e^2 - 38*e - 48/5, 9/10*e^4 - 16/5*e^3 - 74/5*e^2 + 54*e - 72/5, -3*e^4 + 5*e^3 + 52*e^2 - 104*e - 24, -7/10*e^4 + 8/5*e^3 + 42/5*e^2 - 30*e + 66/5, -2*e^3 + 3*e^2 + 32*e - 34, 1/10*e^4 - 9/5*e^3 - 11/5*e^2 + 22*e + 22/5]
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^2 + 2*w + 1])] = 1

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