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

NN = ZF.ideal([37, 37, w^3 - 4*w + 1])

primes_array = [
[3, 3, w + 1],\
[5, 5, w^3 - w^2 - 3*w + 1],\
[9, 3, -w^2 + 2],\
[13, 13, -w^3 + w^2 + 4*w],\
[16, 2, 2],\
[23, 23, w^2 - 2*w - 2],\
[37, 37, w^3 - 4*w + 1],\
[37, 37, w^3 - w^2 - 5*w + 1],\
[41, 41, w^3 - 5*w + 1],\
[43, 43, 2*w^3 - w^2 - 7*w],\
[53, 53, 2*w - 3],\
[59, 59, -2*w^3 + w^2 + 9*w - 1],\
[67, 67, -w - 3],\
[67, 67, w^3 + w^2 - 5*w - 4],\
[71, 71, 2*w^3 - 3*w^2 - 7*w + 5],\
[73, 73, w^3 - 6*w],\
[73, 73, -w^3 - w^2 + 5*w + 3],\
[79, 79, w^3 - 3*w - 4],\
[83, 83, w^3 - 2*w^2 - 3*w + 1],\
[83, 83, -2*w^3 + 2*w^2 + 6*w - 3],\
[89, 89, 2*w^3 - w^2 - 7*w + 3],\
[89, 89, -2*w^3 + w^2 + 8*w - 2],\
[97, 97, 2*w^3 - 8*w - 1],\
[103, 103, -2*w^3 + 3*w^2 + 5*w - 2],\
[103, 103, w^2 + w - 4],\
[113, 113, 2*w^3 - w^2 - 7*w + 4],\
[125, 5, -2*w^3 + w^2 + 6*w - 1],\
[131, 131, -2*w^3 + 2*w^2 + 5*w - 3],\
[131, 131, -4*w^3 + 5*w^2 + 13*w - 9],\
[137, 137, w^3 - 2*w^2 - 4*w + 1],\
[137, 137, 2*w^2 - 2*w - 3],\
[137, 137, 3*w^3 - 2*w^2 - 10*w - 1],\
[137, 137, w - 4],\
[139, 139, w^2 - 2*w - 4],\
[149, 149, 2*w^3 - 7*w - 4],\
[151, 151, -2*w^3 + 4*w^2 + 7*w - 9],\
[157, 157, -w^3 + 3*w^2 + 2*w - 7],\
[173, 173, w^2 + w - 5],\
[173, 173, -w^3 + 3*w^2 + 3*w - 5],\
[179, 179, -w^3 + w^2 + 6*w - 3],\
[181, 181, 3*w^3 - 4*w^2 - 11*w + 7],\
[191, 191, -2*w^3 + 2*w^2 + 9*w - 3],\
[191, 191, 2*w^3 + w^2 - 9*w - 4],\
[193, 193, -2*w^3 + 3*w^2 + 9*w - 6],\
[197, 197, -w^3 + w^2 + 6*w - 1],\
[199, 199, 2*w^2 - w - 4],\
[211, 211, w^3 - 5*w - 5],\
[223, 223, w^3 + 2*w^2 - 4*w - 7],\
[223, 223, 2*w^3 - w^2 - 8*w - 4],\
[227, 227, -3*w^3 + 4*w^2 + 8*w - 6],\
[229, 229, w^3 - 3*w - 6],\
[229, 229, 2*w^3 - 2*w^2 - 9*w - 1],\
[233, 233, 2*w^3 - w^2 - 10*w + 6],\
[233, 233, -w^3 + 7*w - 2],\
[257, 257, 3*w^3 - 2*w^2 - 10*w + 3],\
[257, 257, 3*w^3 - 2*w^2 - 10*w],\
[263, 263, 3*w + 4],\
[269, 269, w^3 + w^2 - 3*w - 5],\
[281, 281, 2*w^3 - 9*w],\
[281, 281, -2*w^3 + w^2 + 9*w - 5],\
[283, 283, 3*w^3 - 3*w^2 - 9*w + 2],\
[283, 283, 3*w^3 - w^2 - 10*w - 1],\
[311, 311, -w^3 + 7*w - 1],\
[317, 317, -w^3 + w^2 + 4*w - 6],\
[317, 317, -w^3 - w^2 + 6*w - 1],\
[349, 349, 3*w^3 - w^2 - 13*w + 1],\
[353, 353, w^3 + w^2 - 2*w - 4],\
[359, 359, 3*w^2 - 10],\
[373, 373, -w^3 + 2*w^2 + 7*w - 1],\
[379, 379, -3*w^3 + 3*w^2 + 9*w - 5],\
[397, 397, -2*w^3 + w^2 + 10*w - 1],\
[409, 409, 4*w^3 - 5*w^2 - 12*w + 5],\
[419, 419, 2*w^3 - 5*w^2 - 3*w + 8],\
[419, 419, w^2 - w - 7],\
[421, 421, -2*w^3 + 8*w - 1],\
[431, 431, w^3 - 2*w - 5],\
[431, 431, w^3 + 2*w^2 - 4*w - 6],\
[433, 433, -3*w^3 + 3*w^2 + 8*w - 8],\
[433, 433, -3*w^3 + 4*w^2 + 11*w - 6],\
[439, 439, -3*w^3 + 3*w^2 + 9*w - 4],\
[439, 439, -3*w^3 + 3*w^2 + 11*w - 2],\
[449, 449, 2*w^2 - 3*w - 6],\
[449, 449, -w^2 + w - 3],\
[463, 463, -w^3 - w^2 + 9*w + 2],\
[491, 491, -3*w^2 + 3*w + 10],\
[491, 491, 5*w^3 - 7*w^2 - 16*w + 12],\
[499, 499, -2*w^3 + 9*w - 1],\
[503, 503, -w^3 + 2*w^2 - 4],\
[503, 503, -4*w^3 + 7*w^2 + 12*w - 15],\
[509, 509, 4*w^3 - w^2 - 14*w + 1],\
[541, 541, 3*w^3 - 2*w^2 - 9*w],\
[557, 557, 2*w^3 - 3*w^2 - 7*w + 2],\
[563, 563, 4*w^3 - 2*w^2 - 17*w + 3],\
[569, 569, 2*w^3 - w^2 - 9*w - 5],\
[577, 577, -3*w^3 + 3*w^2 + 7*w],\
[577, 577, 3*w^3 - 2*w^2 - 9*w + 3],\
[601, 601, -3*w^3 + 3*w^2 + 13*w - 1],\
[607, 607, w^2 + 2*w - 6],\
[613, 613, -2*w^3 - 2*w^2 + 9*w + 4],\
[613, 613, -3*w^3 + 4*w^2 + 13*w - 8],\
[619, 619, 4*w^3 - 4*w^2 - 13*w + 5],\
[619, 619, -2*w^3 + 2*w^2 + 10*w - 5],\
[631, 631, -w^3 + w^2 + 7*w - 2],\
[641, 641, -w - 5],\
[641, 641, -3*w^3 + 2*w^2 + 14*w - 5],\
[659, 659, -w^3 + 2*w^2 + w - 7],\
[661, 661, 3*w^2 - 5],\
[673, 673, -w^3 + 4*w^2 + 4*w - 8],\
[673, 673, -4*w^3 + w^2 + 15*w],\
[677, 677, -w^3 + 4*w^2 + 3*w - 6],\
[683, 683, -w^3 + 4*w^2 - 7],\
[701, 701, -4*w^3 + 4*w^2 + 13*w - 6],\
[701, 701, 2*w^3 - 2*w^2 - 8*w + 9],\
[701, 701, -w^3 + 2*w^2 + 7*w - 3],\
[701, 701, -3*w^3 + 4*w^2 + 9*w - 3],\
[709, 709, -w^2 + 2*w - 4],\
[709, 709, -4*w^3 + 5*w^2 + 15*w - 8],\
[727, 727, -2*w^3 + 3*w^2 + 10*w - 5],\
[727, 727, -w^3 + 2*w^2 + 6*w - 8],\
[727, 727, -4*w^3 + 3*w^2 + 17*w - 4],\
[727, 727, -3*w^3 + 14*w + 1],\
[733, 733, 2*w^2 - 4*w - 5],\
[739, 739, 3*w^2 - 3*w - 5],\
[739, 739, -w^3 + 4*w^2 + w - 5],\
[739, 739, 2*w^3 - 6*w - 5],\
[739, 739, -2*w^3 + 5*w^2 - 5],\
[743, 743, w^3 - 3*w - 7],\
[743, 743, w^3 + w^2 - 3*w - 8],\
[751, 751, -w^3 + w^2 + 2*w - 7],\
[751, 751, w^2 + 2*w - 7],\
[757, 757, -3*w^3 + 3*w^2 + 8*w - 3],\
[769, 769, 3*w^3 - 5*w^2 - 11*w + 8],\
[787, 787, -2*w^3 + 4*w^2 + 3*w - 7],\
[787, 787, -3*w^3 + w^2 + 11*w - 3],\
[797, 797, -3*w^3 + 2*w^2 + 10*w - 9],\
[809, 809, 2*w^2 - 2*w - 11],\
[809, 809, 3*w^2 - w - 8],\
[809, 809, -3*w^3 + 3*w^2 + 7*w - 4],\
[809, 809, -2*w^3 + 4*w^2 + 8*w - 5],\
[821, 821, 3*w^3 - 11*w],\
[821, 821, -w^3 + 4*w^2 + 3*w - 10],\
[823, 823, -4*w^3 + 4*w^2 + 15*w - 4],\
[829, 829, 2*w^3 + w^2 - 8*w],\
[853, 853, -w^3 + 2*w^2 - 5],\
[857, 857, 6*w^3 - 6*w^2 - 25*w + 16],\
[857, 857, 3*w^2 - w - 5],\
[859, 859, 4*w + 5],\
[859, 859, w^3 - w^2 - 2*w - 5],\
[877, 877, 2*w^3 - 3*w^2 - 9*w + 1],\
[877, 877, -w^3 + 3*w^2 + w - 10],\
[883, 883, w^3 + 2*w^2 - 3*w - 8],\
[883, 883, -3*w^3 + 4*w^2 + 10*w - 4],\
[907, 907, -5*w^3 + 8*w^2 + 15*w - 18],\
[911, 911, -w^3 + 3*w - 5],\
[937, 937, -3*w^3 + w^2 + 16*w - 5],\
[937, 937, -2*w^3 + 9*w - 4],\
[941, 941, -4*w^3 + 5*w^2 + 10*w - 3],\
[947, 947, -w^3 + 4*w^2 + 3*w - 7],\
[947, 947, 3*w^2 - 2*w - 7],\
[947, 947, -2*w^3 + 4*w^2 + 11*w - 9],\
[947, 947, -4*w^3 + 3*w^2 + 13*w - 5],\
[967, 967, 3*w^2 - w - 6],\
[971, 971, 3*w^3 - 2*w^2 - 8*w + 2],\
[983, 983, -3*w^2 + 6*w + 5],\
[983, 983, -w^3 + 4*w^2 + w - 6],\
[983, 983, 4*w^3 - 3*w^2 - 13*w + 1],\
[983, 983, -2*w^3 + w^2 + 11*w],\
[997, 997, 3*w^3 - 3*w^2 - 7*w + 3],\
[997, 997, w^3 - w - 5]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^9 - 3*x^8 - 19*x^7 + 59*x^6 + 101*x^5 - 353*x^4 - 104*x^3 + 670*x^2 - 99*x - 297
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 19/10*e^8 - 29/10*e^7 - 202/5*e^6 + 264/5*e^5 + 270*e^4 - 1381/5*e^3 - 605*e^2 + 787/2*e + 3909/10, 37/15*e^8 - 19/5*e^7 - 787/15*e^6 + 1034/15*e^5 + 1051/3*e^4 - 5381/15*e^3 - 2341/3*e^2 + 1526/3*e + 2479/5, -1/5*e^8 + 1/5*e^7 + 21/5*e^6 - 17/5*e^5 - 27*e^4 + 78/5*e^3 + 53*e^2 - 17*e - 121/5, -23/6*e^8 + 6*e^7 + 244/3*e^6 - 655/6*e^5 - 3253/6*e^4 + 3421/6*e^3 + 3635/3*e^2 - 2425/3*e - 782, -14/15*e^8 + 8/5*e^7 + 299/15*e^6 - 881/30*e^5 - 404/3*e^4 + 2332/15*e^3 + 1861/6*e^2 - 1337/6*e - 2121/10, -1, -9/5*e^8 + 14/5*e^7 + 383/10*e^6 - 511/10*e^5 - 256*e^4 + 2679/10*e^3 + 572*e^2 - 381*e - 3643/10, -34/15*e^8 + 18/5*e^7 + 724/15*e^6 - 983/15*e^5 - 970/3*e^4 + 5147/15*e^3 + 2185/3*e^2 - 1478/3*e - 2373/5, 17/15*e^8 - 9/5*e^7 - 362/15*e^6 + 499/15*e^5 + 485/3*e^4 - 2671/15*e^3 - 1094/3*e^2 + 784/3*e + 1199/5, 17/15*e^8 - 9/5*e^7 - 362/15*e^6 + 983/30*e^5 + 485/3*e^4 - 2566/15*e^3 - 2191/6*e^2 + 1439/6*e + 2463/10, 21/5*e^8 - 31/5*e^7 - 446/5*e^6 + 562/5*e^5 + 595*e^4 - 2923/5*e^3 - 1328*e^2 + 831*e + 4236/5, -94/15*e^8 + 48/5*e^7 + 1999/15*e^6 - 2618/15*e^5 - 2671/3*e^4 + 13682/15*e^3 + 5968/3*e^2 - 3905/3*e - 6343/5, -7/15*e^8 + 4/5*e^7 + 299/30*e^6 - 433/30*e^5 - 202/3*e^4 + 2227/30*e^3 + 463/3*e^2 - 308/3*e - 1003/10, 71/15*e^8 - 37/5*e^7 - 1511/15*e^6 + 2017/15*e^5 + 2024/3*e^4 - 10528/15*e^3 - 4556/3*e^2 + 2998/3*e + 4932/5, 57/10*e^8 - 87/10*e^7 - 606/5*e^6 + 787/5*e^5 + 809*e^4 - 4078/5*e^3 - 1803*e^2 + 2299/2*e + 11527/10, -32/5*e^8 + 99/10*e^7 + 1359/10*e^6 - 1803/10*e^5 - 1815/2*e^4 + 4721/5*e^3 + 4073/2*e^2 - 1347*e - 13199/10, -82/15*e^8 + 83/10*e^7 + 3479/30*e^6 - 4513/30*e^5 - 4625/6*e^4 + 11726/15*e^3 + 10217/6*e^2 - 3320/3*e - 10723/10, -7/5*e^8 + 19/10*e^7 + 299/10*e^6 - 343/10*e^5 - 401/2*e^4 + 886/5*e^3 + 895/2*e^2 - 248*e - 2769/10, -91/15*e^8 + 47/5*e^7 + 1936/15*e^6 - 2567/15*e^5 - 2593/3*e^4 + 13433/15*e^3 + 5842/3*e^2 - 3836/3*e - 6327/5, -91/15*e^8 + 47/5*e^7 + 1936/15*e^6 - 2567/15*e^5 - 2590/3*e^4 + 13418/15*e^3 + 5809/3*e^2 - 3812/3*e - 6252/5, 19/15*e^8 - 21/10*e^7 - 803/30*e^6 + 1171/30*e^5 + 1073/6*e^4 - 3152/15*e^3 - 2459/6*e^2 + 914/3*e + 2811/10, -5*e^8 + 15/2*e^7 + 213/2*e^6 - 271/2*e^5 - 1425/2*e^4 + 701*e^3 + 3185/2*e^2 - 991*e - 2033/2, -64/15*e^8 + 33/5*e^7 + 1354/15*e^6 - 3601/30*e^5 - 1798/3*e^4 + 9407/15*e^3 + 7991/6*e^2 - 5347/6*e - 8531/10, -18/5*e^8 + 28/5*e^7 + 383/5*e^6 - 511/5*e^5 - 512*e^4 + 2684/5*e^3 + 1144*e^2 - 771*e - 3643/5, 20/3*e^8 - 10*e^7 - 425/3*e^6 + 544/3*e^5 + 2836/3*e^4 - 2833/3*e^3 - 6319/3*e^2 + 4037/3*e + 1338, 18/5*e^8 - 28/5*e^7 - 383/5*e^6 + 511/5*e^5 + 513*e^4 - 2684/5*e^3 - 1157*e^2 + 766*e + 3798/5, 25/3*e^8 - 13*e^7 - 1061/6*e^6 + 1417/6*e^5 + 3533/3*e^4 - 7387/6*e^3 - 7865/3*e^2 + 5233/3*e + 3363/2, -67/15*e^8 + 34/5*e^7 + 2849/30*e^6 - 3703/30*e^5 - 1900/3*e^4 + 19297/30*e^3 + 4219/3*e^2 - 2750/3*e - 8913/10, 74/15*e^8 - 38/5*e^7 - 1574/15*e^6 + 2068/15*e^5 + 2102/3*e^4 - 10762/15*e^3 - 4682/3*e^2 + 3058/3*e + 4938/5, 112/15*e^8 - 59/5*e^7 - 2377/15*e^6 + 3224/15*e^5 + 3169/3*e^4 - 16856/15*e^3 - 7072/3*e^2 + 4766/3*e + 7584/5, -68/15*e^8 + 36/5*e^7 + 1448/15*e^6 - 1966/15*e^5 - 1943/3*e^4 + 10279/15*e^3 + 4403/3*e^2 - 2920/3*e - 4851/5, -151/15*e^8 + 77/5*e^7 + 3211/15*e^6 - 4187/15*e^5 - 4291/3*e^4 + 21788/15*e^3 + 9595/3*e^2 - 6203/3*e - 10227/5, -158/15*e^8 + 81/5*e^7 + 3353/15*e^6 - 4411/15*e^5 - 4466/3*e^4 + 22969/15*e^3 + 9932/3*e^2 - 6508/3*e - 10586/5, 83/15*e^8 - 41/5*e^7 - 1763/15*e^6 + 2221/15*e^5 + 2348/3*e^4 - 11479/15*e^3 - 5198/3*e^2 + 3229/3*e + 5436/5, -37/15*e^8 + 19/5*e^7 + 1559/30*e^6 - 2083/30*e^5 - 1027/3*e^4 + 10957/30*e^3 + 2245/3*e^2 - 1571/3*e - 4733/10, 8/3*e^8 - 4*e^7 - 170/3*e^6 + 214/3*e^5 + 1132/3*e^4 - 1087/3*e^3 - 2503/3*e^2 + 1508/3*e + 533, 10/3*e^8 - 5*e^7 - 214/3*e^6 + 272/3*e^5 + 1439/3*e^4 - 1415/3*e^3 - 3227/3*e^2 + 2020/3*e + 684, -28/3*e^8 + 14*e^7 + 595/3*e^6 - 761/3*e^5 - 3968/3*e^4 + 3953/3*e^3 + 8828/3*e^2 - 5590/3*e - 1875, -124/15*e^8 + 63/5*e^7 + 2629/15*e^6 - 3428/15*e^5 - 3499/3*e^4 + 17837/15*e^3 + 7777/3*e^2 - 5057/3*e - 8223/5, 137/15*e^8 - 69/5*e^7 - 2912/15*e^6 + 3754/15*e^5 + 3890/3*e^4 - 19546/15*e^3 - 8702/3*e^2 + 5563/3*e + 9299/5, 91/15*e^8 - 47/5*e^7 - 1936/15*e^6 + 2552/15*e^5 + 2590/3*e^4 - 13238/15*e^3 - 5809/3*e^2 + 3743/3*e + 6267/5, 71/15*e^8 - 37/5*e^7 - 1511/15*e^6 + 2017/15*e^5 + 2021/3*e^4 - 10543/15*e^3 - 4520/3*e^2 + 3031/3*e + 4812/5, 9/5*e^8 - 14/5*e^7 - 189/5*e^6 + 253/5*e^5 + 247*e^4 - 1302/5*e^3 - 527*e^2 + 359*e + 1594/5, -9*e^8 + 27/2*e^7 + 383/2*e^6 - 489/2*e^5 - 2559/2*e^4 + 1271*e^3 + 5707/2*e^2 - 1807*e - 3621/2, -37/15*e^8 + 19/5*e^7 + 787/15*e^6 - 1034/15*e^5 - 1051/3*e^4 + 5396/15*e^3 + 2344/3*e^2 - 1550/3*e - 2524/5, -109/15*e^8 + 58/5*e^7 + 2314/15*e^6 - 3173/15*e^5 - 3088/3*e^4 + 16622/15*e^3 + 6919/3*e^2 - 4718/3*e - 7493/5, 23/3*e^8 - 12*e^7 - 488/3*e^6 + 655/3*e^5 + 3253/3*e^4 - 3421/3*e^3 - 7264/3*e^2 + 4850/3*e + 1562, 17/5*e^8 - 27/5*e^7 - 362/5*e^6 + 489/5*e^5 + 485*e^4 - 2541/5*e^3 - 1091*e^2 + 722*e + 3557/5, 199/30*e^8 - 103/10*e^7 - 2117/15*e^6 + 2809/15*e^5 + 2837/3*e^4 - 14671/15*e^3 - 6404/3*e^2 + 8363/6*e + 13863/10, -77/15*e^8 + 39/5*e^7 + 1637/15*e^6 - 4223/30*e^5 - 2183/3*e^4 + 10891/15*e^3 + 9685/6*e^2 - 6113/6*e - 10183/10, 47/15*e^8 - 24/5*e^7 - 992/15*e^6 + 1309/15*e^5 + 1313/3*e^4 - 6826/15*e^3 - 2906/3*e^2 + 1927/3*e + 3094/5, 7/5*e^8 - 12/5*e^7 - 147/5*e^6 + 219/5*e^5 + 193*e^4 - 1146/5*e^3 - 419*e^2 + 321*e + 1332/5, 16/3*e^8 - 8*e^7 - 340/3*e^6 + 437/3*e^5 + 2270/3*e^4 - 2288/3*e^3 - 5069/3*e^2 + 3265/3*e + 1071, 41/15*e^8 - 22/5*e^7 - 866/15*e^6 + 1207/15*e^5 + 1148/3*e^4 - 6358/15*e^3 - 2549/3*e^2 + 1804/3*e + 2757/5, 19/3*e^8 - 10*e^7 - 403/3*e^6 + 545/3*e^5 + 2687/3*e^4 - 2840/3*e^3 - 6023/3*e^2 + 4009/3*e + 1320, -4*e^8 + 6*e^7 + 85*e^6 - 109*e^5 - 569*e^4 + 570*e^3 + 1285*e^2 - 820*e - 828, -9*e^8 + 14*e^7 + 191*e^6 - 254*e^5 - 1273*e^4 + 1322*e^3 + 2836*e^2 - 1874*e - 1803, -19*e^8 + 29*e^7 + 404*e^6 - 526*e^5 - 2698*e^4 + 2737*e^3 + 6024*e^2 - 3882*e - 3867, -163/15*e^8 + 86/5*e^7 + 3463/15*e^6 - 4706/15*e^5 - 4630/3*e^4 + 24689/15*e^3 + 10411/3*e^2 - 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4258/15*e^5 - 4229/3*e^4 + 22267/15*e^3 + 9533/3*e^2 - 6319/3*e - 10543/5, 118/5*e^8 - 178/5*e^7 - 2508/5*e^6 + 3231/5*e^5 + 3348*e^4 - 16834/5*e^3 - 7469*e^2 + 4787*e + 23813/5, 224/15*e^8 - 118/5*e^7 - 4754/15*e^6 + 6463/15*e^5 + 6341/3*e^4 - 33937/15*e^3 - 14186/3*e^2 + 9655/3*e + 15358/5, 44/5*e^8 - 69/5*e^7 - 934/5*e^6 + 1258/5*e^5 + 1245*e^4 - 6577/5*e^3 - 2777*e^2 + 1847*e + 8984/5, -13/3*e^8 + 7*e^7 + 557/6*e^6 - 769/6*e^5 - 1889/3*e^4 + 4063/6*e^3 + 4379/3*e^2 - 2959/3*e - 2003/2, -331/30*e^8 + 167/10*e^7 + 3503/15*e^6 - 4546/15*e^5 - 4649/3*e^4 + 23689/15*e^3 + 10295/3*e^2 - 13457/6*e - 22037/10, 191/15*e^8 - 97/5*e^7 - 4061/15*e^6 + 5257/15*e^5 + 5420/3*e^4 - 27223/15*e^3 - 12056/3*e^2 + 7711/3*e + 12762/5, 2/5*e^8 + 1/10*e^7 - 79/10*e^6 - 27/10*e^5 + 93/2*e^4 + 104/5*e^3 - 149/2*e^2 - 38*e - 101/10, 67/15*e^8 - 34/5*e^7 - 1432/15*e^6 + 1859/15*e^5 + 1927/3*e^4 - 9701/15*e^3 - 4354/3*e^2 + 2732/3*e + 4774/5, 11/5*e^8 - 16/5*e^7 - 231/5*e^6 + 282/5*e^5 + 301*e^4 - 1418/5*e^3 - 634*e^2 + 400*e + 1851/5, -329/15*e^8 + 168/5*e^7 + 6989/15*e^6 - 9133/15*e^5 - 9320/3*e^4 + 47467/15*e^3 + 20744/3*e^2 - 13453/3*e - 22053/5, -367/15*e^8 + 189/5*e^7 + 15599/30*e^6 - 20623/30*e^5 - 10417/3*e^4 + 107677/30*e^3 + 23323/3*e^2 - 15269/3*e - 50253/10, 49/15*e^8 - 28/5*e^7 - 1039/15*e^6 + 1553/15*e^5 + 1387/3*e^4 - 8282/15*e^3 - 3139/3*e^2 + 2363/3*e + 3558/5, -37/15*e^8 + 14/5*e^7 + 787/15*e^6 - 719/15*e^5 - 1039/3*e^4 + 3386/15*e^3 + 2191/3*e^2 - 863/3*e - 1944/5, -26*e^8 + 40*e^7 + 552*e^6 - 1453/2*e^5 - 3680*e^4 + 3789*e^3 + 16419/2*e^2 - 10775/2*e - 10535/2, 67/15*e^8 - 34/5*e^7 - 1432/15*e^6 + 1844/15*e^5 + 1927/3*e^4 - 9551/15*e^3 - 4351/3*e^2 + 2699/3*e + 4629/5, 184/15*e^8 - 93/5*e^7 - 3904/15*e^6 + 5063/15*e^5 + 5197/3*e^4 - 26327/15*e^3 - 11536/3*e^2 + 7442/3*e + 12213/5, -39/5*e^8 + 59/5*e^7 + 829/5*e^6 - 1073/5*e^5 - 1107*e^4 + 5622/5*e^3 + 2465*e^2 - 1623*e - 7719/5, 289/15*e^8 - 148/5*e^7 - 6139/15*e^6 + 8078/15*e^5 + 8194/3*e^4 - 42197/15*e^3 - 18313/3*e^2 + 11993/3*e + 19488/5, 217/15*e^8 - 109/5*e^7 - 4612/15*e^6 + 5939/15*e^5 + 6166/3*e^4 - 30986/15*e^3 - 13855/3*e^2 + 8846/3*e + 14964/5, 41/5*e^8 - 66/5*e^7 - 871/5*e^6 + 1207/5*e^5 + 1165*e^4 - 6348/5*e^3 - 2623*e^2 + 1801*e + 8606/5, 54/5*e^8 - 84/5*e^7 - 1149/5*e^6 + 1523/5*e^5 + 1535*e^4 - 7917/5*e^3 - 3416*e^2 + 2238*e + 10699/5]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([37, 37, w^3 - 4*w + 1])] = 1

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