/*
  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([2, 2, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 4, w^2 - w - 3])

primes_array = [
[2, 2, -w],\
[3, 3, w + 1],\
[4, 2, -w^2 - w + 1],\
[13, 13, -w^2 + 3],\
[17, 17, -w + 3],\
[27, 3, w^3 - 2*w^2 - 3*w + 5],\
[31, 31, -w^2 - 2*w + 1],\
[41, 41, -w^2 + 5],\
[43, 43, w^3 - w^2 - 5*w - 1],\
[43, 43, w^3 - w^2 - 3*w + 1],\
[59, 59, -w - 3],\
[59, 59, -2*w^3 + 2*w^2 + 9*w - 5],\
[59, 59, -w^3 - 3*w^2 - w + 3],\
[59, 59, w^3 - 7*w + 1],\
[61, 61, -w^3 + w^2 + 2*w + 5],\
[61, 61, -w^3 - w^2 + 4*w + 3],\
[67, 67, 4*w^3 - 4*w^2 - 18*w + 7],\
[73, 73, -2*w^3 + 6*w - 3],\
[73, 73, -2*w + 3],\
[97, 97, w^3 - 2*w^2 - 5*w + 3],\
[101, 101, w^3 + w^2 - 5*w - 7],\
[101, 101, -w^3 - w^2 + 4*w + 5],\
[103, 103, 2*w^3 - 8*w - 1],\
[103, 103, w^2 - 2*w - 7],\
[109, 109, -w^3 + 2*w^2 + 3*w - 7],\
[113, 113, -w^3 + w^2 + 6*w - 3],\
[127, 127, -w^3 + w^2 + 6*w - 1],\
[131, 131, -2*w^3 + 3*w^2 + 10*w - 11],\
[137, 137, w^3 + w^2 - 6*w - 5],\
[139, 139, -3*w^3 + 2*w^2 + 15*w - 1],\
[149, 149, w^3 - 3*w^2 - 4*w + 11],\
[149, 149, -w^3 + 5*w - 1],\
[157, 157, -2*w^3 + 3*w^2 + 6*w - 1],\
[163, 163, 2*w^2 - 3],\
[163, 163, -2*w^3 + 2*w^2 + 7*w - 5],\
[167, 167, -2*w^3 + 2*w^2 + 8*w - 3],\
[167, 167, -2*w^2 + 2*w + 9],\
[173, 173, 2*w^3 - w^2 - 8*w + 3],\
[173, 173, 2*w^3 - 3*w^2 - 6*w + 3],\
[181, 181, 2*w^3 - 3*w^2 - 8*w + 5],\
[191, 191, -2*w^3 + w^2 + 10*w - 1],\
[193, 193, -w^3 + 3*w^2 + 2*w - 7],\
[193, 193, w^3 - 3*w - 3],\
[193, 193, 2*w^2 - 2*w - 3],\
[193, 193, w^3 - 7*w - 1],\
[197, 197, w^2 - 2*w - 5],\
[211, 211, w^2 - 4*w - 1],\
[229, 229, -w^3 + w^2 + 6*w - 7],\
[229, 229, -4*w^3 + 6*w^2 + 16*w - 13],\
[233, 233, 3*w^2 + 2*w - 5],\
[233, 233, 2*w^3 - 2*w^2 - 11*w + 7],\
[239, 239, -w^3 + w^2 + 7*w + 1],\
[241, 241, w^3 - 3*w^2 - 2*w + 9],\
[241, 241, w^3 + w^2 - 9*w - 5],\
[251, 251, 2*w^3 - 6*w + 1],\
[271, 271, 2*w^3 - w^2 - 8*w - 1],\
[271, 271, -2*w^2 + w + 7],\
[281, 281, 2*w^3 + 2*w^2 - 5*w - 1],\
[293, 293, w^3 + w^2 - 5*w - 1],\
[293, 293, -3*w + 7],\
[307, 307, -w^3 - 2*w^2 + 3*w + 5],\
[311, 311, -w^3 + 3*w^2 + 4*w - 7],\
[313, 313, 2*w^2 - 2*w - 5],\
[317, 317, -2*w^3 + 4*w^2 + 7*w - 13],\
[317, 317, -2*w^3 + 3*w^2 + 8*w - 11],\
[337, 337, 3*w^3 + 2*w^2 - 7*w + 1],\
[347, 347, 2*w^3 - 2*w^2 - 11*w + 1],\
[349, 349, -5*w^3 + 6*w^2 + 23*w - 13],\
[359, 359, 2*w^3 - 2*w^2 - 12*w + 9],\
[359, 359, -2*w^3 + 8*w + 5],\
[367, 367, -4*w^3 + 4*w^2 + 19*w - 5],\
[367, 367, 2*w^3 + w^2 - 10*w - 7],\
[383, 383, 2*w^3 - 2*w^2 - 7*w + 1],\
[389, 389, 2*w^2 - w - 5],\
[397, 397, 3*w^3 - 4*w^2 - 11*w + 9],\
[397, 397, 3*w^3 - 3*w^2 - 12*w + 7],\
[397, 397, 2*w^3 - 4*w^2 - 8*w + 15],\
[397, 397, -w^3 + 3*w^2 + w - 7],\
[409, 409, -w^3 - w^2 + 9*w - 1],\
[419, 419, 2*w^2 - 3*w - 7],\
[419, 419, 4*w^3 - 3*w^2 - 18*w + 3],\
[431, 431, -3*w^3 + w^2 + 17*w - 1],\
[431, 431, 3*w^3 - w^2 - 16*w - 1],\
[433, 433, -2*w^3 + 5*w^2 + 8*w - 19],\
[443, 443, 3*w - 5],\
[449, 449, -2*w^3 + 2*w^2 + 9*w - 9],\
[449, 449, -5*w^3 + 8*w^2 + 19*w - 17],\
[457, 457, -3*w^3 + 3*w^2 + 13*w - 9],\
[457, 457, -3*w^3 + 2*w^2 + 13*w + 1],\
[457, 457, -2*w^3 + w^2 + 8*w + 7],\
[457, 457, 3*w^3 - 3*w^2 - 15*w + 7],\
[461, 461, -2*w^3 + 2*w^2 + 9*w + 1],\
[479, 479, -w^3 + w^2 + 7*w - 9],\
[487, 487, -w^3 - w^2 + w - 3],\
[499, 499, -2*w^3 + 7*w - 3],\
[499, 499, -5*w^3 + 7*w^2 + 20*w - 15],\
[541, 541, -3*w^3 + 4*w^2 + 13*w - 7],\
[547, 547, -w^3 - w^2 + 3*w + 5],\
[557, 557, 4*w - 1],\
[563, 563, 2*w^3 - w^2 - 6*w - 1],\
[571, 571, w^3 - w^2 - w - 3],\
[587, 587, -2*w^3 + 2*w^2 + 10*w + 1],\
[593, 593, 2*w^3 - 2*w^2 - 6*w + 3],\
[613, 613, -5*w^3 + 5*w^2 + 23*w - 7],\
[613, 613, -w^3 + w^2 + 5*w - 7],\
[617, 617, -w - 5],\
[619, 619, -3*w^3 + 4*w^2 + 11*w - 7],\
[625, 5, -5],\
[643, 643, -3*w^3 + 3*w^2 + 14*w - 9],\
[643, 643, -3*w^2 - 4*w + 1],\
[653, 653, -w^3 + w^2 + 9*w + 3],\
[653, 653, -4*w^2 + 6*w + 11],\
[659, 659, -w^2 - 4*w + 1],\
[661, 661, -3*w^3 + 3*w^2 + 15*w - 5],\
[661, 661, w^3 + w^2 - 7*w - 11],\
[673, 673, 2*w^3 - 3*w^2 - 12*w + 1],\
[673, 673, -2*w^3 + w^2 + 10*w - 3],\
[683, 683, -w^3 - 2*w^2 + 5*w + 11],\
[691, 691, 4*w^3 - 3*w^2 - 18*w + 5],\
[709, 709, w^3 - 3*w - 7],\
[719, 719, 2*w^3 - 8*w + 1],\
[727, 727, -3*w^3 + 6*w^2 + 13*w - 19],\
[733, 733, w^3 - w^2 + 3],\
[739, 739, -w^3 + w^2 + 3*w - 7],\
[751, 751, -w^2 - 3],\
[773, 773, 2*w^3 - 2*w^2 - 11*w + 3],\
[787, 787, w^3 - w^2 - 3*w - 5],\
[797, 797, -2*w^3 + 2*w^2 + 5*w - 1],\
[797, 797, -7*w^3 + 8*w^2 + 31*w - 15],\
[809, 809, 4*w^3 - 6*w^2 - 17*w + 13],\
[809, 809, 3*w^2 - 4*w - 5],\
[811, 811, 2*w^2 + 4*w + 3],\
[811, 811, -3*w^3 + 3*w^2 + 12*w - 5],\
[821, 821, 2*w^3 - 10*w - 1],\
[821, 821, 6*w^3 - 10*w^2 - 24*w + 29],\
[823, 823, -5*w^3 + 3*w^2 + 24*w - 1],\
[823, 823, w^3 + w^2 + w + 3],\
[827, 827, -4*w^3 + 3*w^2 + 16*w - 7],\
[829, 829, 2*w^3 - 4*w^2 - 6*w + 11],\
[841, 29, w^3 - 3*w^2 - 5*w + 3],\
[841, 29, -3*w^3 + 3*w^2 + 13*w - 1],\
[857, 857, -4*w^3 + 6*w^2 + 13*w - 7],\
[857, 857, -3*w^3 + w^2 + 15*w + 1],\
[859, 859, -4*w^2 + 3*w + 17],\
[863, 863, -4*w^3 + 8*w^2 + 14*w - 21],\
[877, 877, -w^3 - w^2 + 6*w - 1],\
[881, 881, -5*w - 1],\
[883, 883, -4*w^3 + 4*w^2 + 21*w - 13],\
[883, 883, 2*w^3 - 11*w - 1],\
[887, 887, -3*w^3 - w^2 + 8*w - 5],\
[907, 907, w^3 - w^2 - w + 5],\
[911, 911, 2*w^2 - 5*w - 5],\
[919, 919, -w^3 + 3*w^2 + 6*w - 3],\
[919, 919, 5*w^2 + 4*w - 9],\
[929, 929, w^3 + 3*w^2 - 8*w - 17],\
[937, 937, -4*w^3 + 4*w^2 + 17*w - 7],\
[953, 953, -2*w^3 + 2*w^2 + 7*w + 5],\
[953, 953, 3*w^3 - 4*w^2 - 11*w + 3],\
[967, 967, 4*w^3 - 2*w^2 - 17*w + 3],\
[971, 971, w^3 - 3*w^2 - 8*w + 1],\
[983, 983, -2*w^3 - 2*w^2 + 12*w + 13],\
[991, 991, -2*w^3 - 2*w^2 + 8*w + 7],\
[991, 991, w^3 + w^2 - 10*w + 1]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^11 - x^10 - 15*x^9 + 15*x^8 + 74*x^7 - 69*x^6 - 141*x^5 + 114*x^4 + 89*x^3 - 60*x^2 - 12*x + 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -61/163*e^10 + 8/163*e^9 + 946/163*e^8 - 61/163*e^7 - 4893/163*e^6 - 387/163*e^5 + 9689/163*e^4 + 2453/163*e^3 - 5561/163*e^2 - 1650/163*e + 410/163, 0, 92/163*e^10 + 20/163*e^9 - 1384/163*e^8 - 234/163*e^7 + 6920/163*e^6 + 1233/163*e^5 - 13186/163*e^4 - 2914/163*e^3 + 7369/163*e^2 + 1417/163*e - 442/163, -117/163*e^10 + 10/163*e^9 + 1753/163*e^8 - 117/163*e^7 - 8602/163*e^6 - 280/163*e^5 + 15575/163*e^4 + 2944/163*e^3 - 7155/163*e^2 - 2307/163*e - 58/163, 223/163*e^10 - 72/163*e^9 - 3298/163*e^8 + 1201/163*e^7 + 16001/163*e^6 - 5482/163*e^5 - 29336/163*e^4 + 8078/163*e^3 + 15982/163*e^2 - 3406/163*e - 756/163, 32/163*e^10 - 71/163*e^9 - 531/163*e^8 + 1010/163*e^7 + 2981/163*e^6 - 4532/163*e^5 - 6670/163*e^4 + 7427/163*e^3 + 4753/163*e^2 - 3816/163*e - 338/163, -275/163*e^10 + 4/163*e^9 + 4222/163*e^8 - 112/163*e^7 - 21762/163*e^6 - 438/163*e^5 + 43883/163*e^4 + 3753/163*e^3 - 28290/163*e^2 - 1803/163*e + 2976/163, 274/163*e^10 - 68/163*e^9 - 4129/163*e^8 + 926/163*e^7 + 20482/163*e^6 - 2497/163*e^5 - 38265/163*e^4 - 1209/163*e^3 + 20292/163*e^2 + 2778/163*e - 1040/163, -345/163*e^10 + 88/163*e^9 + 5190/163*e^8 - 1323/163*e^7 - 25787/163*e^6 + 4708/163*e^5 + 48877/163*e^4 - 3335/163*e^3 - 28082/163*e^2 + 1410/163*e + 2228/163, -27/163*e^10 - 98/163*e^9 + 392/163*e^8 + 1440/163*e^7 - 1797/163*e^6 - 7036/163*e^5 + 2215/163*e^4 + 12942/163*e^3 + 1659/163*e^2 - 6438/163*e - 866/163, -177/163*e^10 - 81/163*e^9 + 2769/163*e^8 + 1290/163*e^7 - 14660/163*e^6 - 7675/163*e^5 + 30241/163*e^4 + 17360/163*e^3 - 18410/163*e^2 - 8518/163*e + 1024/163, -142/163*e^10 + 40/163*e^9 + 2122/163*e^8 - 631/163*e^7 - 10447/163*e^6 + 2466/163*e^5 + 19594/163*e^4 - 1916/163*e^3 - 11342/163*e^2 - 752/163*e + 1072/163, -172/163*e^10 + 76/163*e^9 + 2630/163*e^8 - 1150/163*e^7 - 13313/163*e^6 + 5044/163*e^5 + 25623/163*e^4 - 7911/163*e^3 - 14606/163*e^2 + 5026/163*e + 1776/163, 218/163*e^10 - 66/163*e^9 - 3159/163*e^8 + 1033/163*e^7 + 14817/163*e^6 - 4020/163*e^5 - 25696/163*e^4 + 3683/163*e^3 + 12667/163*e^2 + 2/163*e - 530/163, 81/163*e^10 - 32/163*e^9 - 1176/163*e^8 + 407/163*e^7 + 5554/163*e^6 - 1060/163*e^5 - 9905/163*e^4 - 195/163*e^3 + 5292/163*e^2 - 83/163*e - 336/163, 135/163*e^10 + 1/163*e^9 - 2123/163*e^8 - 28/163*e^7 + 11267/163*e^6 + 950/163*e^5 - 23300/163*e^4 - 4400/163*e^3 + 14688/163*e^2 + 3176/163*e - 560/163, -264/163*e^10 + 219/163*e^9 + 3851/163*e^8 - 3198/163*e^7 - 18114/163*e^6 + 13591/163*e^5 + 31474/163*e^4 - 18852/163*e^3 - 15618/163*e^2 + 7684/163*e + 1566/163, 157/163*e^10 - 58/163*e^9 - 2376/163*e^8 + 809/163*e^7 + 11880/163*e^6 - 2777/163*e^5 - 22527/163*e^4 + 1898/163*e^3 + 11996/163*e^2 - 833/163*e - 120/163, -175/163*e^10 + 47/163*e^9 + 2583/163*e^8 - 827/163*e^7 - 12589/163*e^6 + 3900/163*e^5 + 23895/163*e^4 - 5984/163*e^3 - 15291/163*e^2 + 2898/163*e + 1390/163, -182/163*e^10 + 88/163*e^9 + 2745/163*e^8 - 1160/163*e^7 - 13399/163*e^6 + 3567/163*e^5 + 23123/163*e^4 - 401/163*e^3 - 7381/163*e^2 - 2502/163*e - 1358/163, 483/163*e^10 - 221/163*e^9 - 7266/163*e^8 + 3254/163*e^7 + 36004/163*e^6 - 13046/163*e^5 - 67841/163*e^4 + 15101/163*e^3 + 38728/163*e^2 - 5071/163*e - 3380/163, -400/163*e^10 - 9/163*e^9 + 6067/163*e^8 + 89/163*e^7 - 30661/163*e^6 - 2030/163*e^5 + 59740/163*e^4 + 7978/163*e^3 - 35696/163*e^2 - 3482/163*e + 3084/163, 196/163*e^10 + 156/163*e^9 - 2906/163*e^8 - 2086/163*e^7 + 14367/163*e^6 + 9650/163*e^5 - 27121/163*e^4 - 16633/163*e^3 + 14544/163*e^2 + 6130/163*e + 8/163, 245/163*e^10 - 131/163*e^9 - 3714/163*e^8 + 1875/163*e^7 + 18570/163*e^6 - 7416/163*e^5 - 35083/163*e^4 + 8997/163*e^3 + 18506/163*e^2 - 4481/163*e - 968/163, -360/163*e^10 + 269/163*e^9 + 5281/163*e^8 - 3946/163*e^7 - 25101/163*e^6 + 16592/163*e^5 + 44149/163*e^4 - 21573/163*e^3 - 21238/163*e^2 + 5929/163*e - 28/163, 157/163*e^10 + 105/163*e^9 - 2376/163*e^8 - 1473/163*e^7 + 11880/163*e^6 + 7329/163*e^5 - 21712/163*e^4 - 14076/163*e^3 + 8899/163*e^2 + 6176/163*e + 858/163, 188/163*e^10 - 30/163*e^9 - 2977/163*e^8 + 351/163*e^7 + 15863/163*e^6 - 301/163*e^5 - 32707/163*e^4 - 2801/163*e^3 + 19998/163*e^2 + 890/163*e - 152/163, 18/163*e^10 + 11/163*e^9 - 207/163*e^8 + 18/163*e^7 + 546/163*e^6 - 1286/163*e^5 + 425/163*e^4 + 5716/163*e^3 - 943/163*e^2 - 6303/163*e - 618/163, -508/163*e^10 + 88/163*e^9 + 7798/163*e^8 - 1323/163*e^7 - 39968/163*e^6 + 4056/163*e^5 + 79032/163*e^4 - 564/163*e^3 - 46990/163*e^2 + 758/163*e + 2880/163, 153/163*e^10 + 12/163*e^9 - 2330/163*e^8 - 10/163*e^7 + 11813/163*e^6 - 336/163*e^5 - 22549/163*e^4 + 1153/163*e^3 + 11137/163*e^2 - 2475/163*e + 778/163, 108/163*e^10 - 260/163*e^9 - 1568/163*e^8 + 3694/163*e^7 + 7025/163*e^6 - 16192/163*e^5 - 10164/163*e^4 + 24679/163*e^3 + 1025/163*e^2 - 10597/163*e + 530/163, 5/163*e^10 - 169/163*e^9 + 24/163*e^8 + 2287/163*e^7 - 1098/163*e^6 - 9449/163*e^5 + 5162/163*e^4 + 13034/163*e^3 - 6139/163*e^2 - 4549/163*e - 226/163, 67/163*e^10 - 113/163*e^9 - 1015/163*e^8 + 1534/163*e^7 + 5075/163*e^6 - 6290/163*e^5 - 10145/163*e^4 + 9504/163*e^3 + 7094/163*e^2 - 6482/163*e - 616/163, 604/163*e^10 - 138/163*e^9 - 9065/163*e^8 + 2071/163*e^7 + 44999/163*e^6 - 7057/163*e^5 - 85676/163*e^4 + 3937/163*e^3 + 50165/163*e^2 + 182/163*e - 3894/163, 473/163*e^10 - 209/163*e^9 - 7151/163*e^8 + 3081/163*e^7 + 35755/163*e^6 - 12241/163*e^5 - 68222/163*e^4 + 13483/163*e^3 + 38618/163*e^2 - 2656/163*e - 2276/163, 734/163*e^10 - 294/163*e^9 - 10886/163*e^8 + 4320/163*e^7 + 52800/163*e^6 - 16544/163*e^5 - 96208/163*e^4 + 16332/163*e^3 + 51758/163*e^2 - 3666/163*e - 4228/163, -698/163*e^10 + 153/163*e^9 + 10472/163*e^8 - 2002/163*e^7 - 51708/163*e^6 + 4192/163*e^5 + 96569/163*e^4 + 7651/163*e^3 - 52829/163*e^2 - 8288/163*e + 3970/163, -127/163*e^10 + 22/163*e^9 + 1705/163*e^8 - 453/163*e^7 - 6895/163*e^6 + 2155/163*e^5 + 8022/163*e^4 - 3075/163*e^3 + 2026/163*e^2 + 1412/163*e - 1562/163, 123/163*e^10 + 48/163*e^9 - 1822/163*e^8 - 692/163*e^7 + 8784/163*e^6 + 3872/163*e^5 - 15053/163*e^4 - 8591/163*e^3 + 4776/163*e^2 + 3955/163*e + 504/163, 92/163*e^10 - 143/163*e^9 - 1384/163*e^8 + 2211/163*e^7 + 6920/163*e^6 - 10992/163*e^5 - 14164/163*e^4 + 20884/163*e^3 + 11770/163*e^2 - 12764/163*e - 2072/163, -160/163*e^10 + 29/163*e^9 + 2492/163*e^8 - 323/163*e^7 - 12786/163*e^6 + 492/163*e^5 + 23896/163*e^4 + 518/163*e^3 - 8932/163*e^2 + 1965/163*e - 2548/163, 327/163*e^10 - 99/163*e^9 - 4983/163*e^8 + 1468/163*e^7 + 25078/163*e^6 - 5541/163*e^5 - 47509/163*e^4 + 5280/163*e^3 + 24950/163*e^2 - 2116/163*e + 998/163, 92/163*e^10 + 20/163*e^9 - 1547/163*e^8 - 397/163*e^7 + 9039/163*e^6 + 2700/163*e^5 - 21825/163*e^4 - 6011/163*e^3 + 18779/163*e^2 + 2395/163*e - 1746/163, -29/163*e^10 - 63/163*e^9 + 415/163*e^8 + 786/163*e^7 - 1912/163*e^6 - 2800/163*e^5 + 2530/163*e^4 + 1893/163*e^3 + 2289/163*e^2 + 2684/163*e - 2862/163, 219/163*e^10 + 161/163*e^9 - 3252/163*e^8 - 2226/163*e^7 + 15934/163*e^6 + 11140/163*e^5 - 28543/163*e^4 - 22333/163*e^3 + 11211/163*e^2 + 11252/163*e + 1446/163, -32/163*e^10 - 92/163*e^9 + 368/163*e^8 + 1109/163*e^7 - 1351/163*e^6 - 4107/163*e^5 + 3084/163*e^4 + 5287/163*e^3 - 7361/163*e^2 - 2378/163*e + 2946/163, 206/163*e^10 - 182/163*e^9 - 3347/163*e^8 + 2488/163*e^7 + 18528/163*e^6 - 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60247/163*e^4 + 15166/163*e^3 + 24576/163*e^2 - 2218/163*e + 3904/163, -589/163*e^10 + 446/163*e^9 + 9137/163*e^8 - 6294/163*e^7 - 47315/163*e^6 + 25654/163*e^5 + 95294/163*e^4 - 33295/163*e^3 - 58150/163*e^2 + 12414/163*e + 2564/163, 1077/163*e^10 - 347/163*e^9 - 16216/163*e^8 + 4989/163*e^7 + 80428/163*e^6 - 17505/163*e^5 - 151290/163*e^4 + 12367/163*e^3 + 84708/163*e^2 - 2800/163*e - 5518/163, -806/163*e^10 + 576/163*e^9 + 12040/163*e^8 - 8141/163*e^7 - 58896/163*e^6 + 32283/163*e^5 + 109667/163*e^4 - 37403/163*e^3 - 65101/163*e^2 + 8014/163*e + 9634/163, 419/163*e^10 - 405/163*e^9 - 6367/163*e^8 + 5635/163*e^7 + 31672/163*e^6 - 22890/163*e^5 - 58739/163*e^4 + 29587/163*e^3 + 27755/163*e^2 - 7545/163*e + 2838/163, -879/163*e^10 + 468/163*e^9 + 13287/163*e^8 - 7073/163*e^7 - 66272/163*e^6 + 30906/163*e^5 + 126299/163*e^4 - 45172/163*e^3 - 74380/163*e^2 + 18716/163*e + 8174/163, -179/163*e^10 + 606/163*e^9 + 2792/163*e^8 - 8818/163*e^7 - 14123/163*e^6 + 40734/163*e^5 + 27296/163*e^4 - 66876/163*e^3 - 17617/163*e^2 + 26684/163*e + 2614/163, -571/163*e^10 + 131/163*e^9 + 8604/163*e^8 - 1386/163*e^7 - 42694/163*e^6 - 245/163*e^5 + 79745/163*e^4 + 18876/163*e^3 - 41978/163*e^2 - 15405/163*e + 4880/163, -588/163*e^10 + 184/163*e^9 + 8555/163*e^8 - 2870/163*e^7 - 39841/163*e^6 + 11311/163*e^5 + 64737/163*e^4 - 10248/163*e^3 - 18204/163*e^2 - 1764/163*e - 5892/163, 58/163*e^10 - 37/163*e^9 - 1319/163*e^8 + 221/163*e^7 + 10018/163*e^6 + 1036/163*e^5 - 29347/163*e^4 - 6557/163*e^3 + 27044/163*e^2 + 4738/163*e - 4708/163, -557/163*e^10 + 538/163*e^9 + 8280/163*e^8 - 7729/163*e^7 - 40259/163*e^6 + 32695/163*e^5 + 74769/163*e^4 - 45754/163*e^3 - 44269/163*e^2 + 17726/163*e + 6138/163, 774/163*e^10 - 16/163*e^9 - 11672/163*e^8 + 285/163*e^7 + 58523/163*e^6 + 2241/163*e^5 - 112777/163*e^4 - 14523/163*e^3 + 64423/163*e^2 + 7212/163*e - 2450/163, -920/163*e^10 + 289/163*e^9 + 14003/163*e^8 - 3854/163*e^7 - 70830/163*e^6 + 11305/163*e^5 + 138217/163*e^4 - 2156/163*e^3 - 83144/163*e^2 + 826/163*e + 6376/163, -208/163*e^10 - 109/163*e^9 + 3370/163*e^8 + 1585/163*e^7 - 18806/163*e^6 - 7869/163*e^5 + 42377/163*e^4 + 13094/163*e^3 - 33095/163*e^2 - 1276/163*e + 4642/163, -777/163*e^10 + 150/163*e^9 + 11625/163*e^8 - 2244/163*e^7 - 57473/163*e^6 + 6558/163*e^5 + 107952/163*e^4 + 1780/163*e^3 - 58262/163*e^2 - 5102/163*e + 4672/163, 325/163*e^10 + 425/163*e^9 - 4960/163*e^8 - 6358/163*e^7 + 25452/163*e^6 + 32762/163*e^5 - 49476/163*e^4 - 64123/163*e^3 + 24439/163*e^2 + 32108/163*e + 958/163, 143/163*e^10 + 24/163*e^9 - 1726/163*e^8 - 20/163*e^7 + 5533/163*e^6 - 998/163*e^5 - 1740/163*e^4 + 4588/163*e^3 - 9511/163*e^2 - 6580/163*e + 6446/163, -7/163*e^10 - 122/163*e^9 + 162/163*e^8 + 1460/163*e^7 - 1788/163*e^6 - 4734/163*e^5 + 8682/163*e^4 + 3464/163*e^3 - 14747/163*e^2 + 468/163*e + 186/163, 1198/163*e^10 - 427/163*e^9 - 17689/163*e^8 + 6414/163*e^7 + 85185/163*e^6 - 24882/163*e^5 - 152662/163*e^4 + 25979/163*e^3 + 76911/163*e^2 - 9283/163*e - 4402/163, 79/163*e^10 - 486/163*e^9 - 1153/163*e^8 + 6925/163*e^7 + 4787/163*e^6 - 31380/163*e^5 - 5026/163*e^4 + 51837/163*e^3 - 3043/163*e^2 - 24865/163*e + 1906/163, 1211/163*e^10 - 410/163*e^9 - 17920/163*e^8 + 6590/163*e^7 + 87318/163*e^6 - 28781/163*e^5 - 162941/163*e^4 + 40829/163*e^3 + 94006/163*e^2 - 20328/163*e - 5120/163, -452/163*e^10 - 77/163*e^9 + 6665/163*e^8 + 1015/163*e^7 - 31858/163*e^6 - 6646/163*e^5 + 54075/163*e^4 + 18668/163*e^3 - 18664/163*e^2 - 13092/163*e + 740/163, -90/163*e^10 - 218/163*e^9 + 1361/163*e^8 + 2844/163*e^7 - 7457/163*e^6 - 11500/163*e^5 + 18576/163*e^4 + 16082/163*e^3 - 21039/163*e^2 - 9724/163*e + 7654/163, 1535/163*e^10 - 375/163*e^9 - 23113/163*e^8 + 5610/163*e^7 + 114913/163*e^6 - 19655/163*e^5 - 217394/163*e^4 + 12828/163*e^3 + 123161/163*e^2 - 1426/163*e - 10050/163, 429/163*e^10 - 91/163*e^9 - 6482/163*e^8 + 1244/163*e^7 + 32736/163*e^6 - 3320/163*e^5 - 65041/163*e^4 + 235/163*e^3 + 41394/163*e^2 - 3114/163*e - 1200/163, 913/163*e^10 - 85/163*e^9 - 13678/163*e^8 + 1076/163*e^7 + 67738/163*e^6 + 1402/163*e^5 - 128068/163*e^4 - 22416/163*e^3 + 73124/163*e^2 + 16594/163*e - 7168/163, -180/163*e^10 + 379/163*e^9 + 2722/163*e^8 - 5396/163*e^7 - 13610/163*e^6 + 23781/163*e^5 + 27698/163*e^4 - 36622/163*e^3 - 21866/163*e^2 + 12500/163*e + 2268/163, 727/163*e^10 - 579/163*e^9 - 11376/163*e^8 + 8225/163*e^7 + 59651/163*e^6 - 34155/163*e^5 - 122408/163*e^4 + 46202/163*e^3 + 79391/163*e^2 - 16890/163*e - 7302/163, -399/163*e^10 - 271/163*e^9 + 5974/163*e^8 + 3676/163*e^7 - 29707/163*e^6 - 17677/163*e^5 + 55752/163*e^4 + 34448/163*e^3 - 29980/163*e^2 - 21572/163*e + 5060/163, -838/163*e^10 + 321/163*e^9 + 12734/163*e^8 - 4261/163*e^7 - 63996/163*e^6 + 13343/163*e^5 + 122857/163*e^4 - 6199/163*e^3 - 70832/163*e^2 + 1072/163*e + 8016/163, 1320/163*e^10 - 443/163*e^9 - 19581/163*e^8 + 6699/163*e^7 + 95297/163*e^6 - 25575/163*e^5 - 175789/163*e^4 + 22866/163*e^3 + 99443/163*e^2 - 2560/163*e - 9134/163, -1150/163*e^10 + 239/163*e^9 + 17463/163*e^8 - 3432/163*e^7 - 87641/163*e^6 + 10260/163*e^5 + 165640/163*e^4 - 413/163*e^3 - 84696/163*e^2 - 3124/163*e - 506/163, 604/163*e^10 - 301/163*e^9 - 8576/163*e^8 + 4679/163*e^7 + 38642/163*e^6 - 20260/163*e^5 - 61878/163*e^4 + 27083/163*e^3 + 24574/163*e^2 - 7153/163*e + 2300/163, -185/163*e^10 - 104/163*e^9 + 3024/163*e^8 + 2097/163*e^7 - 16750/163*e^6 - 14692/163*e^5 + 35413/163*e^4 + 36245/163*e^3 - 19802/163*e^2 - 15877/163*e + 864/163, -287/163*e^10 + 51/163*e^9 + 4686/163*e^8 - 613/163*e^7 - 26201/163*e^6 + 1180/163*e^5 + 58976/163*e^4 + 1029/163*e^3 - 44396/163*e^2 + 2888/163*e + 6974/163, -645/163*e^10 + 285/163*e^9 + 9292/163*e^8 - 4068/163*e^7 - 42548/163*e^6 + 14840/163*e^5 + 67928/163*e^4 - 13244/163*e^3 - 21602/163*e^2 + 3444/163*e - 1816/163, 690/163*e^10 - 176/163*e^9 - 10543/163*e^8 + 2320/163*e^7 + 53204/163*e^6 - 5504/163*e^5 - 100036/163*e^4 - 7022/163*e^3 + 46873/163*e^2 + 11198/163*e + 1738/163, -1323/163*e^10 - 75/163*e^9 + 19697/163*e^8 + 1122/163*e^7 - 96529/163*e^6 - 12896/163*e^5 + 177647/163*e^4 + 46380/163*e^3 - 90674/163*e^2 - 30864/163*e + 4184/163, -793/163*e^10 + 593/163*e^9 + 11809/163*e^8 - 8780/163*e^7 - 58067/163*e^6 + 38164/163*e^5 + 111450/163*e^4 - 56131/163*e^3 - 70337/163*e^2 + 25168/163*e + 3374/163, 903/163*e^10 - 399/163*e^9 - 13400/163*e^8 + 5630/163*e^7 + 64881/163*e^6 - 20287/163*e^5 - 116876/163*e^4 + 17042/163*e^3 + 58018/163*e^2 - 4300/163*e - 848/163]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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