/*
  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, 10, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11, 11, -w^3 + 6*w - 4])

primes_array = [
[2, 2, -w + 1],\
[5, 5, w^3 + w^2 - 4*w + 1],\
[7, 7, -w^3 + 6*w - 2],\
[8, 2, w^3 - 7*w + 3],\
[11, 11, -w^3 + 6*w - 4],\
[17, 17, w^3 + w^2 - 6*w - 1],\
[17, 17, -w^2 - w + 3],\
[31, 31, 2*w^3 + w^2 - 13*w + 3],\
[37, 37, -3*w^3 - w^2 + 18*w - 3],\
[41, 41, w^2 + 2*w - 4],\
[47, 47, 2*w^3 + 2*w^2 - 11*w - 2],\
[47, 47, -3*w^3 - w^2 + 19*w - 6],\
[59, 59, -2*w^3 + 13*w - 6],\
[59, 59, -w^3 - w^2 + 5*w + 2],\
[59, 59, w^2 + w - 1],\
[59, 59, w^2 + 2*w - 6],\
[61, 61, -w^3 + w^2 + 8*w - 7],\
[67, 67, w^3 + 2*w^2 - 4*w - 4],\
[73, 73, -2*w^3 - w^2 + 12*w - 4],\
[81, 3, -3],\
[107, 107, 2*w^2 + 2*w - 11],\
[109, 109, 2*w^3 + w^2 - 11*w + 3],\
[113, 113, w^3 + w^2 - 7*w - 2],\
[113, 113, 2*w^3 - 12*w + 9],\
[125, 5, -4*w^3 - 3*w^2 + 24*w + 2],\
[131, 131, 5*w^3 + 3*w^2 - 31*w + 2],\
[151, 151, 4*w^3 + 2*w^2 - 26*w + 1],\
[151, 151, w^3 + 2*w^2 - 6*w - 10],\
[167, 167, w + 4],\
[167, 167, 4*w^3 + w^2 - 26*w + 10],\
[173, 173, -2*w^3 + w^2 + 13*w - 11],\
[179, 179, 4*w^3 + w^2 - 24*w + 4],\
[179, 179, 2*w^3 + 2*w^2 - 12*w - 3],\
[179, 179, -w^3 + 8*w - 4],\
[179, 179, w^3 + 2*w^2 - 4*w - 6],\
[181, 181, 6*w^3 + 3*w^2 - 39*w + 5],\
[197, 197, -w^3 + 4*w - 4],\
[199, 199, 2*w^3 - 12*w + 3],\
[199, 199, 3*w - 2],\
[223, 223, w^3 + w^2 - 7*w - 4],\
[223, 223, 2*w^3 + w^2 - 10*w + 4],\
[227, 227, 7*w^3 + 2*w^2 - 44*w + 12],\
[227, 227, -4*w^3 - w^2 + 25*w - 9],\
[229, 229, 8*w^3 + 4*w^2 - 51*w + 4],\
[229, 229, 3*w^3 + w^2 - 18*w + 5],\
[233, 233, -6*w^3 - 3*w^2 + 39*w - 7],\
[233, 233, -w^3 - 2*w^2 + 8*w + 2],\
[241, 241, 2*w^3 + w^2 - 10*w],\
[251, 251, w^3 + w^2 - 7*w - 6],\
[257, 257, -6*w^3 - w^2 + 39*w - 17],\
[263, 263, -2*w^3 + 13*w - 4],\
[263, 263, -w^3 + 6*w - 8],\
[269, 269, -8*w^3 - 4*w^2 + 50*w - 7],\
[269, 269, -w^3 + w^2 + 7*w - 6],\
[277, 277, 2*w^3 + 2*w^2 - 11*w + 4],\
[277, 277, w^3 + w^2 - 4*w - 3],\
[281, 281, -w^2 - 3*w + 5],\
[281, 281, 2*w^3 + 3*w^2 - 9*w - 3],\
[283, 283, -3*w^3 - 4*w^2 + 12*w + 2],\
[289, 17, -2*w^3 - w^2 + 13*w - 5],\
[293, 293, -w^3 - 2*w^2 + 6*w + 6],\
[293, 293, w^3 + w^2 - 8*w - 1],\
[307, 307, 2*w^3 - 11*w + 12],\
[317, 317, 2*w^3 - 14*w + 11],\
[317, 317, -2*w^3 - 2*w^2 + 8*w + 1],\
[337, 337, 2*w^2 + 4*w - 11],\
[343, 7, -5*w^3 - w^2 + 31*w - 10],\
[349, 349, 2*w^3 - 11*w + 8],\
[349, 349, w^2 + w - 9],\
[353, 353, 4*w^3 + 4*w^2 - 23*w - 8],\
[373, 373, -2*w - 3],\
[373, 373, -4*w^3 + 26*w - 13],\
[389, 389, 6*w^3 + 3*w^2 - 37*w + 1],\
[389, 389, -2*w^3 - w^2 + 14*w - 6],\
[401, 401, 2*w^3 - 12*w + 13],\
[421, 421, 2*w^2 + 2*w - 15],\
[421, 421, 3*w^3 + 2*w^2 - 20*w + 4],\
[431, 431, w^3 + 3*w^2 - 2*w - 9],\
[433, 433, 2*w^3 + 2*w^2 - 12*w + 3],\
[433, 433, -7*w^3 - 2*w^2 + 44*w - 16],\
[433, 433, -3*w^3 + 18*w - 14],\
[433, 433, -w^3 + w^2 + 9*w - 10],\
[439, 439, 5*w^3 + 3*w^2 - 31*w - 2],\
[443, 443, -w^3 - w^2 + 3*w - 4],\
[443, 443, -4*w^3 + 27*w - 14],\
[449, 449, w^3 + w^2 - 4*w - 5],\
[449, 449, w^3 + 3*w^2 - 3*w - 8],\
[449, 449, 2*w^3 - 11*w + 6],\
[449, 449, -3*w^3 - 2*w^2 + 18*w - 4],\
[461, 461, -3*w^3 + w^2 + 20*w - 15],\
[463, 463, 2*w^3 - 10*w + 7],\
[479, 479, -2*w^3 - 3*w^2 + 11*w + 9],\
[491, 491, w^3 + w^2 - 4*w + 5],\
[499, 499, -2*w^3 - 2*w^2 + 14*w - 3],\
[499, 499, -6*w^3 - 2*w^2 + 39*w - 10],\
[499, 499, 4*w^3 + w^2 - 24*w + 14],\
[499, 499, -5*w^3 - 3*w^2 + 30*w - 5],\
[503, 503, -2*w^3 + w^2 + 14*w - 18],\
[509, 509, 4*w^3 + 3*w^2 - 24*w],\
[509, 509, 4*w^3 + 2*w^2 - 23*w + 4],\
[547, 547, w^3 + 2*w^2 - 2*w - 6],\
[547, 547, 6*w^3 + 2*w^2 - 38*w + 7],\
[563, 563, -5*w^3 - w^2 + 33*w - 12],\
[569, 569, 2*w^3 - w^2 - 15*w + 13],\
[569, 569, -4*w^3 - 2*w^2 + 24*w - 7],\
[577, 577, -w^2 - 2],\
[577, 577, 3*w^3 - 20*w + 8],\
[587, 587, 6*w^3 + 4*w^2 - 36*w - 1],\
[587, 587, -w^3 + w^2 + 9*w - 8],\
[593, 593, 6*w^3 + 3*w^2 - 36*w + 2],\
[593, 593, -3*w^3 - w^2 + 21*w - 4],\
[599, 599, -2*w^3 - w^2 + 12*w - 10],\
[599, 599, -4*w^3 - 2*w^2 + 25*w - 6],\
[601, 601, -2*w^3 + 2*w^2 + 15*w - 16],\
[607, 607, w^3 - w^2 - 7*w + 4],\
[607, 607, -2*w^3 - 2*w^2 + 10*w + 3],\
[631, 631, 2*w^2 + 4*w - 7],\
[641, 641, -3*w^3 - 2*w^2 + 16*w],\
[643, 643, w^3 + w^2 - 3*w - 4],\
[643, 643, w^3 + 3*w^2 - 6*w - 13],\
[653, 653, -w^3 + 6*w + 2],\
[653, 653, -3*w^2 - 5*w + 11],\
[659, 659, -2*w^3 + 10*w - 5],\
[661, 661, w^3 - w^2 - 8*w + 3],\
[673, 673, 3*w^3 + 4*w^2 - 14*w - 2],\
[677, 677, 4*w^3 + 2*w^2 - 23*w + 6],\
[677, 677, 2*w^3 - 13*w + 14],\
[683, 683, 2*w^3 + w^2 - 13*w + 7],\
[701, 701, 8*w^3 + 4*w^2 - 51*w + 8],\
[701, 701, -4*w^3 - w^2 + 24*w - 12],\
[709, 709, -4*w^3 - w^2 + 27*w - 7],\
[709, 709, 3*w^3 + 3*w^2 - 18*w - 5],\
[709, 709, -3*w^3 + w^2 + 21*w - 14],\
[709, 709, w^2 - w - 7],\
[719, 719, -9*w^3 - 4*w^2 + 58*w - 8],\
[719, 719, 11*w^3 + 5*w^2 - 68*w + 9],\
[727, 727, -w^3 + 4*w - 6],\
[733, 733, 2*w^3 + w^2 - 13*w + 9],\
[739, 739, -2*w^2 - 3*w + 4],\
[743, 743, 3*w^3 + 3*w^2 - 19*w - 4],\
[751, 751, 2*w^3 + 3*w^2 - 10*w - 2],\
[761, 761, -12*w^3 - 5*w^2 + 75*w - 9],\
[761, 761, -3*w^3 - 3*w^2 + 17*w],\
[769, 769, -6*w^3 - 4*w^2 + 37*w],\
[769, 769, -8*w^3 - 3*w^2 + 51*w - 7],\
[773, 773, -w^2 - 2*w - 2],\
[787, 787, -5*w^3 - 5*w^2 + 28*w + 7],\
[811, 811, 7*w^3 + 2*w^2 - 42*w + 6],\
[811, 811, -2*w^3 - w^2 + 9*w - 7],\
[823, 823, -3*w^3 - 2*w^2 + 14*w - 10],\
[829, 829, 4*w^3 + 3*w^2 - 20*w + 6],\
[829, 829, -7*w^3 - 2*w^2 + 44*w - 14],\
[841, 29, w^3 + 4*w^2 - 2*w - 14],\
[841, 29, -w^2 + 10],\
[857, 857, -3*w^3 - w^2 + 20*w - 9],\
[859, 859, -w^3 + 2*w^2 + 10*w - 18],\
[863, 863, 11*w^3 + 5*w^2 - 69*w + 6],\
[863, 863, w^3 - 2*w^2 - 10*w + 12],\
[877, 877, 3*w^3 - 18*w + 10],\
[883, 883, 4*w^3 + 3*w^2 - 22*w],\
[887, 887, 3*w^3 + 3*w^2 - 15*w - 2],\
[887, 887, w^2 + 4*w - 10],\
[887, 887, w^3 + w^2 - 3*w - 8],\
[887, 887, w - 6],\
[907, 907, 6*w^3 + w^2 - 38*w + 16],\
[919, 919, -2*w^3 - 3*w^2 + 11*w + 1],\
[919, 919, 5*w^3 - w^2 - 34*w + 27],\
[937, 937, -w^3 - w^2 + 8*w + 3],\
[941, 941, -4*w^3 + 25*w - 20],\
[947, 947, -2*w^3 + w^2 + 8*w - 6],\
[967, 967, -7*w^3 - w^2 + 44*w - 23],\
[971, 971, 2*w^2 + 2*w - 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^13 + 4*x^12 - 11*x^11 - 56*x^10 + 31*x^9 + 282*x^8 + 27*x^7 - 622*x^6 - 214*x^5 + 579*x^4 + 250*x^3 - 175*x^2 - 81*x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -503/3809*e^12 - 1516/3809*e^11 + 6725/3809*e^10 + 21423/3809*e^9 - 2380/293*e^8 - 109398/3809*e^7 + 55311/3809*e^6 + 247708/3809*e^5 - 24825/3809*e^4 - 244532/3809*e^3 - 12976/3809*e^2 + 81836/3809*e + 5663/3809, 154/3809*e^12 - 490/3809*e^11 - 3369/3809*e^10 + 7261/3809*e^9 + 1843/293*e^8 - 38264/3809*e^7 - 65232/3809*e^6 + 85290/3809*e^5 + 51900/3809*e^4 - 76153/3809*e^3 + 10258/3809*e^2 + 30270/3809*e - 6868/3809, -131/3809*e^12 - 622/3809*e^11 + 714/3809*e^10 + 7056/3809*e^9 + 371/293*e^8 - 23448/3809*e^7 - 41170/3809*e^6 + 12186/3809*e^5 + 94954/3809*e^4 + 43830/3809*e^3 - 75705/3809*e^2 - 35890/3809*e + 6238/3809, 1, -721/3809*e^12 - 2900/3809*e^11 + 9367/3809*e^10 + 43051/3809*e^9 - 3288/293*e^8 - 233612/3809*e^7 + 82751/3809*e^6 + 564711/3809*e^5 - 58423/3809*e^4 - 586193/3809*e^3 - 19978/3809*e^2 + 203169/3809*e + 28692/3809, 131/3809*e^12 + 622/3809*e^11 - 714/3809*e^10 - 7056/3809*e^9 - 371/293*e^8 + 23448/3809*e^7 + 41170/3809*e^6 - 12186/3809*e^5 - 94954/3809*e^4 - 43830/3809*e^3 + 75705/3809*e^2 + 35890/3809*e - 17665/3809, 503/3809*e^12 + 1516/3809*e^11 - 6725/3809*e^10 - 21423/3809*e^9 + 2380/293*e^8 + 109398/3809*e^7 - 55311/3809*e^6 - 251517/3809*e^5 + 21016/3809*e^4 + 271195/3809*e^3 + 32021/3809*e^2 - 116117/3809*e - 24708/3809, 912/3809*e^12 + 1946/3809*e^11 - 11542/3809*e^10 - 22198/3809*e^9 + 3597/293*e^8 + 73715/3809*e^7 - 55668/3809*e^6 - 37268/3809*e^5 - 30359/3809*e^4 - 134837/3809*e^3 + 37400/3809*e^2 + 116487/3809*e + 3007/3809, -1210/3809*e^12 - 3768/3809*e^11 + 16132/3809*e^10 + 52322/3809*e^9 - 5900/293*e^8 - 258189/3809*e^7 + 161565/3809*e^6 + 540038/3809*e^5 - 161289/3809*e^4 - 433894/3809*e^3 + 92983/3809*e^2 + 84841/3809*e - 36909/3809, -1821/3809*e^12 - 3209/3809*e^11 + 28534/3809*e^10 + 45601/3809*e^9 - 12727/293*e^8 - 239443/3809*e^7 + 434968/3809*e^6 + 581261/3809*e^5 - 504229/3809*e^4 - 647874/3809*e^3 + 194058/3809*e^2 + 231819/3809*e + 12452/3809, 882/3809*e^12 + 2734/3809*e^11 - 8907/3809*e^10 - 34248/3809*e^9 + 1206/293*e^8 + 148247/3809*e^7 + 82786/3809*e^6 - 270897/3809*e^5 - 300075/3809*e^4 + 218999/3809*e^3 + 258896/3809*e^2 - 78722/3809*e - 52147/3809, 2378/3809*e^12 + 5592/3809*e^11 - 36193/3809*e^10 - 79615/3809*e^9 + 16012/293*e^8 + 410466/3809*e^7 - 568853/3809*e^6 - 937126/3809*e^5 + 743342/3809*e^4 + 922838/3809*e^3 - 373327/3809*e^2 - 308136/3809*e + 20980/3809, 972/3809*e^12 + 370/3809*e^11 - 16812/3809*e^10 - 1907/3809*e^9 + 8379/293*e^8 - 10596/3809*e^7 - 321149/3809*e^6 + 71944/3809*e^5 + 406230/3809*e^4 - 103563/3809*e^3 - 158007/3809*e^2 + 38398/3809*e + 14281/3809, -48/293*e^12 - 87/293*e^11 + 700/293*e^10 + 1230/293*e^9 - 3556/293*e^8 - 6563/293*e^7 + 6816/293*e^6 + 16704/293*e^5 - 777/293*e^4 - 19628/293*e^3 - 9571/293*e^2 + 7270/293*e + 3990/293, -1822/3809*e^12 - 2167/3809*e^11 + 31796/3809*e^10 + 31233/3809*e^9 - 16059/293*e^8 - 163064/3809*e^7 + 634350/3809*e^6 + 376802/3809*e^5 - 877106/3809*e^4 - 375036/3809*e^3 + 453597/3809*e^2 + 126405/3809*e - 33063/3809, -2438/3809*e^12 - 7825/3809*e^11 + 30036/3809*e^10 + 105032/3809*e^9 - 9367/293*e^8 - 493751/3809*e^7 + 179186/3809*e^6 + 965038/3809*e^5 - 75321/3809*e^4 - 706527/3809*e^3 + 35474/3809*e^2 + 108168/3809*e - 13209/3809, -242/3809*e^12 - 3039/3809*e^11 + 941/3809*e^10 + 46269/3809*e^9 + 871/293*e^8 - 252753/3809*e^7 - 70530/3809*e^6 + 582609/3809*e^5 + 124673/3809*e^4 - 485962/3809*e^3 - 81961/3809*e^2 + 59629/3809*e + 12425/3809, 834/3809*e^12 + 3233/3809*e^11 - 12309/3809*e^10 - 49719/3809*e^9 + 5350/293*e^8 + 279687/3809*e^7 - 189334/3809*e^6 - 695744/3809*e^5 + 237389/3809*e^4 + 726478/3809*e^3 - 66236/3809*e^2 - 247838/3809*e - 58119/3809, 120/293*e^12 + 364/293*e^11 - 1750/293*e^10 - 5126/293*e^9 + 10062/293*e^8 + 25930/293*e^7 - 30225/293*e^6 - 56996/293*e^5 + 49555/293*e^4 + 51707/293*e^3 - 35405/293*e^2 - 15538/293*e + 4382/293, -894/3809*e^12 - 5466/3809*e^11 + 6152/3809*e^10 + 75136/3809*e^9 + 1295/293*e^8 - 362972/3809*e^7 - 200333/3809*e^6 + 731274/3809*e^5 + 442059/3809*e^4 - 555875/3809*e^3 - 313516/3809*e^2 + 93578/3809*e + 58272/3809, 3043/3809*e^12 + 13518/3809*e^11 - 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557827/3809*e - 180130/3809, 5340/3809*e^12 + 8287/3809*e^11 - 84321/3809*e^10 - 110028/3809*e^9 + 38545/293*e^8 + 525693/3809*e^7 - 1394676/3809*e^6 - 1143400/3809*e^5 + 1832941/3809*e^4 + 1206460/3809*e^3 - 1020141/3809*e^2 - 524138/3809*e + 173024/3809, -16570/3809*e^12 - 45965/3809*e^11 + 230170/3809*e^10 + 639888/3809*e^9 - 88857/293*e^8 - 3193106/3809*e^7 + 2571811/3809*e^6 + 6935137/3809*e^5 - 2461222/3809*e^4 - 6253672/3809*e^3 + 699209/3809*e^2 + 1689582/3809*e + 63203/3809, 10233/3809*e^12 + 25268/3809*e^11 - 142712/3809*e^10 - 346275/3809*e^9 + 54444/293*e^8 + 1696453/3809*e^7 - 1489711/3809*e^6 - 3612359/3809*e^5 + 1188235/3809*e^4 + 3199598/3809*e^3 - 136371/3809*e^2 - 891026/3809*e - 154267/3809, -12046/3809*e^12 - 36813/3809*e^11 + 156577/3809*e^10 + 506820/3809*e^9 - 53993/293*e^8 - 2493602/3809*e^7 + 1274255/3809*e^6 + 5334122/3809*e^5 - 796780/3809*e^4 - 4799869/3809*e^3 - 66114/3809*e^2 + 1387189/3809*e + 184220/3809, 5059/3809*e^12 + 19223/3809*e^11 - 70432/3809*e^10 - 285110/3809*e^9 + 28719/293*e^8 + 1541480/3809*e^7 - 994970/3809*e^6 - 3697262/3809*e^5 + 1409677/3809*e^4 + 3769843/3809*e^3 - 780638/3809*e^2 - 1193263/3809*e + 2526/3809, 1114/293*e^12 + 3008/293*e^11 - 14732/293*e^10 - 40486/293*e^9 + 67244/293*e^8 + 193788/293*e^7 - 121563/293*e^6 - 403494/293*e^5 + 61580/293*e^4 + 360064/293*e^3 + 26464/293*e^2 - 107512/293*e - 14883/293, -7519/3809*e^12 - 19360/3809*e^11 + 107479/3809*e^10 + 268305/3809*e^9 - 43707/293*e^8 - 1333806/3809*e^7 + 1393514/3809*e^6 + 2887637/3809*e^5 - 1590358/3809*e^4 - 2587654/3809*e^3 + 637256/3809*e^2 + 688755/3809*e - 53388/3809, 599/3809*e^12 + 8136/3809*e^11 + 7697/3809*e^10 - 116178/3809*e^9 - 13233/293*e^8 + 608318/3809*e^7 + 888874/3809*e^6 - 1458683/3809*e^5 - 1720487/3809*e^4 + 1636862/3809*e^3 + 1146983/3809*e^2 - 714899/3809*e - 168933/3809, -16013/3809*e^12 - 39773/3809*e^11 + 222511/3809*e^10 + 533503/3809*e^9 - 85572/293*e^8 - 2515486/3809*e^7 + 2456971/3809*e^6 + 4994728/3809*e^5 - 2393514/3809*e^4 - 3898994/3809*e^3 + 942739/3809*e^2 + 851465/3809*e - 131905/3809, -102/293*e^12 - 75/293*e^11 + 2220/293*e^10 + 2101/293*e^9 - 17079/293*e^8 - 18085/293*e^7 + 57848/293*e^6 + 63624/293*e^5 - 84973/293*e^4 - 92545/293*e^3 + 42620/293*e^2 + 47752/293*e - 3168/293, 84/3809*e^12 + 79/3809*e^11 + 240/3809*e^10 + 3268/3809*e^9 - 806/293*e^8 - 54806/3809*e^7 + 30557/3809*e^6 + 281641/3809*e^5 + 80250/3809*e^4 - 578607/3809*e^3 - 288044/3809*e^2 + 375942/3809*e + 82822/3809, 3817/3809*e^12 + 18327/3809*e^11 - 41332/3809*e^10 - 262147/3809*e^9 + 9369/293*e^8 + 1342985/3809*e^7 + 915/3809*e^6 - 2954173/3809*e^5 - 361286/3809*e^4 + 2582355/3809*e^3 + 350021/3809*e^2 - 646007/3809*e - 161522/3809, -4969/3809*e^12 - 6351/3809*e^11 + 81572/3809*e^10 + 88911/3809*e^9 - 37661/293*e^8 - 454780/3809*e^7 + 1272846/3809*e^6 + 1042420/3809*e^5 - 1232823/3809*e^4 - 1022351/3809*e^3 + 78060/3809*e^2 + 342897/3809*e + 113419/3809, -206/3809*e^12 + 5157/3809*e^11 + 16824/3809*e^10 - 64968/3809*e^9 - 14250/293*e^8 + 280961/3809*e^7 + 735382/3809*e^6 - 493802/3809*e^5 - 1158304/3809*e^4 + 303744/3809*e^3 + 626586/3809*e^2 + 11252/3809*e - 135456/3809, -1026/3809*e^12 + 2572/3809*e^11 + 25364/3809*e^10 - 38828/3809*e^9 - 16609/293*e^8 + 211792/3809*e^7 + 807286/3809*e^6 - 489429/3809*e^5 - 1344228/3809*e^4 + 381660/3809*e^3 + 872085/3809*e^2 + 62735/3809*e - 198118/3809, -750/3809*e^12 - 3154/3809*e^11 + 16358/3809*e^10 + 56796/3809*e^9 - 11137/293*e^8 - 384010/3809*e^7 + 619836/3809*e^6 + 1194498/3809*e^5 - 1212232/3809*e^4 - 1647895/3809*e^3 + 825667/3809*e^2 + 699960/3809*e - 57127/3809, -2538/3809*e^12 - 10277/3809*e^11 + 28662/3809*e^10 + 146124/3809*e^9 - 6789/293*e^8 - 744290/3809*e^7 - 13179/3809*e^6 + 1620998/3809*e^5 + 327034/3809*e^4 - 1350315/3809*e^3 - 174647/3809*e^2 + 220541/3809*e - 58662/3809, -4539/3809*e^12 - 8758/3809*e^11 + 65388/3809*e^10 + 111807/3809*e^9 - 25951/293*e^8 - 498451/3809*e^7 + 726871/3809*e^6 + 971890/3809*e^5 - 496622/3809*e^4 - 922648/3809*e^3 - 114269/3809*e^2 + 389525/3809*e - 43/3809, -5387/3809*e^12 - 20257/3809*e^11 + 66230/3809*e^10 + 291757/3809*e^9 - 20228/293*e^8 - 1525725/3809*e^7 + 336588/3809*e^6 + 3528368/3809*e^5 + 52504/3809*e^4 - 3466714/3809*e^3 - 234914/3809*e^2 + 1153674/3809*e + 144576/3809, -9614/3809*e^12 - 22736/3809*e^11 + 130877/3809*e^10 + 296535/3809*e^9 - 48210/293*e^8 - 1332082/3809*e^7 + 1270549/3809*e^6 + 2407193/3809*e^5 - 1088502/3809*e^4 - 1496446/3809*e^3 + 514823/3809*e^2 + 136131/3809*e - 170886/3809, 10266/3809*e^12 + 25163/3809*e^11 - 143706/3809*e^10 - 344447/3809*e^9 + 55111/293*e^8 + 1682268/3809*e^7 - 1521646/3809*e^6 - 3557625/3809*e^5 + 1266286/3809*e^4 + 3112813/3809*e^3 - 294695/3809*e^2 - 809992/3809*e - 31130/3809, -51/293*e^12 + 109/293*e^11 + 1989/293*e^10 - 268/293*e^9 - 20699/293*e^8 - 6845/293*e^7 + 87817/293*e^6 + 36207/293*e^5 - 160419/293*e^4 - 49935/293*e^3 + 106573/293*e^2 + 14207/293*e - 8909/293, 13305/3809*e^12 + 35231/3809*e^11 - 180187/3809*e^10 - 472168/3809*e^9 + 66992/293*e^8 + 2220207/3809*e^7 - 1858252/3809*e^6 - 4372593/3809*e^5 + 1791440/3809*e^4 + 3325982/3809*e^3 - 643087/3809*e^2 - 690903/3809*e - 15835/3809, -5105/3809*e^12 - 16999/3809*e^11 + 68124/3809*e^10 + 241240/3809*e^9 - 25236/293*e^8 - 1235224/3809*e^7 + 724031/3809*e^6 + 2774791/3809*e^5 - 785416/3809*e^4 - 2642486/3809*e^3 + 332564/3809*e^2 + 911210/3809*e + 74914/3809, 5446/3809*e^12 + 19723/3809*e^11 - 68238/3809*e^10 - 274407/3809*e^9 + 22850/293*e^8 + 1361624/3809*e^7 - 555047/3809*e^6 - 2892287/3809*e^5 + 434007/3809*e^4 + 2430058/3809*e^3 + 28607/3809*e^2 - 556332/3809*e - 121682/3809, -5221/3809*e^12 - 21824/3809*e^11 + 61807/3809*e^10 + 315265/3809*e^9 - 17370/293*e^8 - 1646366/3809*e^7 + 194644/3809*e^6 + 3758912/3809*e^5 + 339511/3809*e^4 - 3537374/3809*e^3 - 505228/3809*e^2 + 993874/3809*e + 143010/3809, -816/3809*e^12 - 6753/3809*e^11 - 699/3809*e^10 + 83612/3809*e^9 + 6867/293*e^8 - 340404/3809*e^7 - 462803/3809*e^6 + 475590/3809*e^5 + 734234/3809*e^4 - 11669/3809*e^3 - 141318/3809*e^2 - 227717/3809*e - 170086/3809, 505/3809*e^12 - 568/3809*e^11 - 5631/3809*e^10 + 14931/3809*e^9 - 39/293*e^8 - 127158/3809*e^7 + 197264/3809*e^6 + 431649/3809*e^5 - 718740/3809*e^4 - 503021/3809*e^3 + 712778/3809*e^2 + 79475/3809*e - 112701/3809, -1961/3809*e^12 - 17307/3809*e^11 + 5280/3809*e^10 + 239492/3809*e^9 + 9810/293*e^8 - 1167642/3809*e^7 - 737076/3809*e^6 + 2371866/3809*e^5 + 1201768/3809*e^4 - 1770861/3809*e^3 - 486344/3809*e^2 + 290869/3809*e - 6236/3809, 1786/3809*e^12 + 13016/3809*e^11 - 13398/3809*e^10 - 194244/3809*e^9 - 1343/293*e^8 + 1061534/3809*e^7 + 315687/3809*e^6 - 2595176/3809*e^5 - 696667/3809*e^4 + 2735373/3809*e^3 + 468108/3809*e^2 - 938862/3809*e - 123776/3809, 1034/293*e^12 + 3156/293*e^11 - 12784/293*e^10 - 42245/293*e^9 + 51160/293*e^8 + 198867/293*e^7 - 65667/293*e^6 - 394992/293*e^5 - 14430/293*e^4 + 309966/293*e^3 + 47528/293*e^2 - 70295/293*e - 7940/293, -2375/3809*e^12 - 1100/3809*e^11 + 49261/3809*e^10 + 23685/3809*e^9 - 28870/293*e^8 - 174905/3809*e^7 + 1296239/3809*e^6 + 563972/3809*e^5 - 1993909/3809*e^4 - 827192/3809*e^3 + 1118310/3809*e^2 + 475827/3809*e - 105357/3809, -5316/3809*e^12 - 10441/3809*e^11 + 70786/3809*e^10 + 123477/3809*e^9 - 24209/293*e^8 - 461907/3809*e^7 + 479452/3809*e^6 + 546411/3809*e^5 + 19940/3809*e^4 - 3257/3809*e^3 - 264713/3809*e^2 - 103587/3809*e - 86240/3809, 2559/3809*e^12 + 11249/3809*e^11 - 28602/3809*e^10 - 160543/3809*e^9 + 7613/293*e^8 + 839145/3809*e^7 - 105831/3809*e^6 - 1966721/3809*e^5 - 23201/3809*e^4 + 1962702/3809*e^3 + 201670/3809*e^2 - 581731/3809*e - 189167/3809, 5469/3809*e^12 + 7184/3809*e^11 - 86129/3809*e^10 - 88685/3809*e^9 + 38542/293*e^8 + 370516/3809*e^7 - 1305170/3809*e^6 - 623681/3809*e^5 + 1445504/3809*e^4 + 436100/3809*e^3 - 528201/3809*e^2 - 139153/3809*e - 15660/3809, 4582/3809*e^12 + 17278/3809*e^11 - 53294/3809*e^10 - 232929/3809*e^9 + 15695/293*e^8 + 1114570/3809*e^7 - 326293/3809*e^6 - 2304475/3809*e^5 + 380173/3809*e^4 + 1981236/3809*e^3 - 487360/3809*e^2 - 473231/3809*e + 128868/3809, -2152/3809*e^12 - 1117/3809*e^11 + 34118/3809*e^10 + 5335/3809*e^9 - 15404/293*e^8 + 39730/3809*e^7 + 538519/3809*e^6 - 277190/3809*e^5 - 690130/3809*e^4 + 511859/3809*e^3 + 456102/3809*e^2 - 333507/3809*e - 83643/3809, -66/3809*e^12 - 3599/3809*e^11 - 9439/3809*e^10 + 38243/3809*e^9 + 9214/293*e^8 - 112563/3809*e^7 - 496053/3809*e^6 + 42892/3809*e^5 + 826620/3809*e^4 + 70727/3809*e^3 - 532759/3809*e^2 + 127416/3809*e + 92727/3809, -5517/3809*e^12 - 14303/3809*e^11 + 71300/3809*e^10 + 187484/3809*e^9 - 23264/293*e^8 - 848516/3809*e^7 + 412183/3809*e^6 + 1554838/3809*e^5 + 150862/3809*e^4 - 1037040/3809*e^3 - 478742/3809*e^2 + 236667/3809*e + 70632/3809]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([11, 11, -w^3 + 6*w - 4])] = -1

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