/*
  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, -5, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([37, 37, -2*w^3 + w^2 + 8*w - 1])

primes_array = [
[4, 2, -w^3 + 4*w + 1],\
[5, 5, w - 1],\
[7, 7, -w^2 + w + 2],\
[13, 13, -w^3 + w^2 + 4*w],\
[13, 13, -w^2 + 3],\
[17, 17, -w^2 + 2],\
[19, 19, -w^3 + 5*w],\
[31, 31, -w^2 + 2*w + 3],\
[37, 37, -2*w^3 + w^2 + 8*w - 1],\
[43, 43, -w - 3],\
[53, 53, -w^3 + 2*w^2 + 3*w - 2],\
[53, 53, w^3 - 6*w - 2],\
[59, 59, 2*w^3 - w^2 - 10*w - 2],\
[61, 61, 2*w^3 - w^2 - 10*w],\
[61, 61, 2*w^3 - w^2 - 8*w],\
[71, 71, 2*w^3 - 9*w - 2],\
[73, 73, -w^3 - w^2 + 6*w + 3],\
[81, 3, -3],\
[83, 83, -w^3 + 2*w^2 + 3*w - 3],\
[101, 101, 2*w^3 - 8*w - 3],\
[125, 5, w^3 + w^2 - 4*w - 6],\
[127, 127, 2*w^3 - w^2 - 7*w - 2],\
[127, 127, w^3 - 7*w - 7],\
[131, 131, w^3 - 3*w - 4],\
[131, 131, 3*w^3 - 13*w - 7],\
[137, 137, w^2 + w - 4],\
[137, 137, -w^3 + 2*w^2 + 4*w - 4],\
[149, 149, 3*w + 5],\
[157, 157, -2*w^3 - w^2 + 7*w + 2],\
[157, 157, -2*w^3 + 2*w^2 + 9*w - 1],\
[163, 163, -2*w^3 + w^2 + 7*w],\
[163, 163, -3*w^3 + w^2 + 15*w + 3],\
[163, 163, 2*w^3 - 7*w - 1],\
[163, 163, 2*w^3 - 11*w - 5],\
[167, 167, -2*w^3 + w^2 + 9*w - 4],\
[167, 167, w^3 - w^2 - 7*w + 1],\
[167, 167, w^3 - w^2 - 7*w - 1],\
[167, 167, w^2 - 2*w - 5],\
[169, 13, w^3 + w^2 - 6*w - 2],\
[173, 173, -3*w^3 + 13*w + 3],\
[181, 181, 2*w^2 + w - 4],\
[191, 191, 2*w^3 - 10*w - 1],\
[191, 191, -2*w^3 + 2*w^2 + 6*w - 3],\
[193, 193, 3*w^3 - 13*w - 6],\
[197, 197, -w^3 + w^2 + 2*w - 3],\
[197, 197, w^3 + w^2 - 7*w - 7],\
[199, 199, -w^2 + 2*w + 6],\
[223, 223, -2*w^3 + w^2 + 11*w + 2],\
[227, 227, -3*w^3 + 2*w^2 + 15*w - 1],\
[229, 229, -w^3 + w^2 + 6*w - 5],\
[233, 233, 2*w^3 - 11*w - 4],\
[239, 239, -2*w^3 + 11*w + 3],\
[251, 251, 2*w^3 - w^2 - 10*w - 4],\
[257, 257, -2*w^3 + w^2 + 6*w + 1],\
[257, 257, w^3 - 7*w - 2],\
[263, 263, 2*w^3 - 9*w],\
[269, 269, w^3 - 4*w - 6],\
[269, 269, -2*w^3 + 8*w - 3],\
[271, 271, 2*w^2 - w - 5],\
[277, 277, -3*w^3 + 2*w^2 + 11*w - 2],\
[277, 277, 3*w^3 - w^2 - 15*w - 5],\
[281, 281, 2*w^2 - 5],\
[283, 283, -3*w^3 + 2*w^2 + 12*w + 2],\
[283, 283, -2*w^3 + w^2 + 6*w + 6],\
[293, 293, -2*w^3 - w^2 + 12*w + 7],\
[293, 293, -2*w^3 + 9*w - 1],\
[311, 311, -3*w^3 + w^2 + 12*w + 4],\
[313, 313, -w^3 + w^2 + 2*w - 4],\
[313, 313, -4*w^3 + 2*w^2 + 16*w - 3],\
[331, 331, 3*w^3 - w^2 - 16*w - 5],\
[331, 331, 2*w^3 - 2*w^2 - 8*w - 1],\
[343, 7, 2*w^3 - 3*w^2 - 9*w + 6],\
[359, 359, -2*w^3 + 10*w - 1],\
[367, 367, -w^3 + 2*w^2 + w - 4],\
[367, 367, 3*w^3 - 11*w - 1],\
[373, 373, -w^3 + w^2 + 2*w - 5],\
[373, 373, 2*w^3 - 2*w^2 - 11*w - 1],\
[389, 389, -2*w^3 + 3*w^2 + 8*w - 6],\
[409, 409, 3*w^3 - 2*w^2 - 13*w - 1],\
[419, 419, 3*w^3 - w^2 - 12*w - 1],\
[419, 419, w^3 - w^2 - 4*w - 4],\
[439, 439, w^2 + 2*w - 4],\
[439, 439, 3*w^3 + w^2 - 11*w - 5],\
[443, 443, 2*w^3 + 2*w^2 - 7*w - 8],\
[449, 449, 4*w^3 - w^2 - 16*w - 8],\
[457, 457, 2*w^3 + w^2 - 11*w - 4],\
[461, 461, -5*w^3 + 2*w^2 + 24*w + 2],\
[463, 463, -w^3 + 3*w^2 + 6*w - 5],\
[467, 467, w^3 - 3*w^2 - 6*w + 4],\
[467, 467, 3*w^3 - w^2 - 12*w - 2],\
[479, 479, -w^3 + w^2 + 4*w - 6],\
[479, 479, -w^3 + 2*w + 8],\
[491, 491, -w^3 + 2*w^2 + 2*w - 6],\
[491, 491, w - 5],\
[499, 499, 2*w^3 + w^2 - 10*w - 4],\
[509, 509, -4*w^3 + w^2 + 20*w + 5],\
[521, 521, w^3 - w + 6],\
[523, 523, -4*w^3 + 18*w + 5],\
[523, 523, -2*w^3 - 2*w^2 + 9*w + 12],\
[557, 557, w^2 - 3*w - 6],\
[571, 571, 3*w^3 - 11*w - 8],\
[577, 577, 2*w^3 + 2*w^2 - 11*w - 7],\
[577, 577, -3*w^3 + 4*w^2 + 11*w - 6],\
[587, 587, -w^3 - w^2 + 7*w + 11],\
[593, 593, w^3 + w^2 - 8*w - 8],\
[593, 593, -2*w^3 + 4*w^2 + 6*w - 9],\
[599, 599, 4*w^3 - 17*w - 9],\
[599, 599, w^3 + w^2 - 6*w - 10],\
[601, 601, 3*w^2 - 10],\
[607, 607, 4*w^3 - w^2 - 18*w - 8],\
[619, 619, w^2 - w - 8],\
[641, 641, -w^3 + 3*w^2 + 2*w - 10],\
[643, 643, 3*w^3 - w^2 - 16*w + 1],\
[653, 653, -2*w^3 + 2*w^2 + 9*w + 3],\
[677, 677, w^3 + w^2 - 8*w - 11],\
[677, 677, 2*w^3 - w^2 - 12*w - 3],\
[683, 683, 3*w^3 - 2*w^2 - 13*w - 2],\
[683, 683, 3*w^3 + 2*w^2 - 16*w - 10],\
[691, 691, -2*w^3 - 2*w^2 + 12*w + 15],\
[691, 691, 3*w^3 - 2*w^2 - 15*w - 2],\
[691, 691, w^3 - 2*w^2 - 6*w + 6],\
[691, 691, -4*w^3 + 3*w^2 + 15*w - 2],\
[719, 719, 2*w^3 - 7*w - 8],\
[719, 719, w^2 + 2*w - 5],\
[727, 727, -w^3 + 3*w^2 + 4*w - 8],\
[727, 727, 2*w^3 - 9*w - 9],\
[733, 733, w^3 - 8*w - 2],\
[739, 739, -w^3 - 2*w^2 + 4*w + 10],\
[743, 743, w^3 - w^2 - 2*w + 8],\
[743, 743, 4*w^3 - w^2 - 17*w - 4],\
[751, 751, -2*w^3 + 2*w^2 + 6*w - 5],\
[751, 751, w^3 - 5*w - 7],\
[769, 769, 3*w^3 - 2*w^2 - 10*w],\
[787, 787, -2*w^3 + 3*w^2 + 8*w],\
[787, 787, 3*w^3 - w^2 - 10*w - 4],\
[809, 809, 3*w^3 + w^2 - 16*w - 6],\
[811, 811, 3*w^3 - 14*w - 2],\
[811, 811, -w^3 + 3*w^2 + 5*w - 5],\
[811, 811, w^3 - 2*w - 6],\
[811, 811, 3*w^3 - w^2 - 11*w - 3],\
[823, 823, w^3 + 2*w^2 - 3*w - 8],\
[827, 827, -w^3 + 3*w^2 + 3*w - 7],\
[829, 829, w^3 + w^2 - 3*w - 7],\
[853, 853, 3*w^3 + w^2 - 14*w - 6],\
[857, 857, 3*w^3 + w^2 - 13*w - 5],\
[857, 857, 3*w^3 - 3*w^2 - 11*w - 1],\
[859, 859, 4*w^3 - 2*w^2 - 18*w - 3],\
[859, 859, 3*w^3 - 11*w - 3],\
[863, 863, 3*w^3 + w^2 - 17*w - 9],\
[877, 877, -w^3 - 2*w^2 + 9*w + 1],\
[877, 877, 5*w^3 + w^2 - 23*w - 11],\
[911, 911, w^2 - 4*w - 6],\
[911, 911, -2*w^3 + 2*w^2 + 10*w + 3],\
[919, 919, -4*w^3 + 3*w^2 + 18*w - 1],\
[929, 929, 2*w^3 - 13*w - 12],\
[929, 929, -w^3 + 2*w^2 + 7*w - 5],\
[953, 953, -3*w^3 + 3*w^2 + 13*w - 1],\
[967, 967, -3*w^3 + 4*w^2 + 13*w - 7],\
[971, 971, 2*w^2 - 3*w - 12],\
[971, 971, 3*w^3 - w^2 - 16*w - 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 + 8*x^6 + 9*x^5 - 62*x^4 - 136*x^3 + 62*x^2 + 285*x + 139
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 21/103*e^6 + e^5 - 120/103*e^4 - 960/103*e^3 - 223/103*e^2 + 1953/103*e + 1073/103, -11/309*e^6 + 70/103*e^4 - 71/309*e^3 - 342/103*e^2 + 110/309*e + 929/309, -17/103*e^6 - e^5 + 53/103*e^4 + 1042/103*e^3 + 568/103*e^2 - 2405/103*e - 1673/103, -98/309*e^6 - 2*e^5 + 15/103*e^4 + 5407/309*e^3 + 1457/103*e^2 - 10144/309*e - 9196/309, -65/309*e^6 - e^5 + 114/103*e^4 + 2839/309*e^3 + 423/103*e^2 - 6148/309*e - 5494/309, 43/309*e^6 + e^5 + 26/103*e^4 - 2981/309*e^3 - 1004/103*e^2 + 6677/309*e + 6116/309, 43/309*e^6 + e^5 + 26/103*e^4 - 2672/309*e^3 - 798/103*e^2 + 4205/309*e + 3644/309, 1, -29/309*e^6 + 222/103*e^4 - 131/309*e^3 - 1426/103*e^2 + 599/309*e + 6101/309, 52/309*e^6 + e^5 + 53/103*e^4 - 2024/309*e^3 - 1183/103*e^2 + 2879/309*e + 4148/309, 217/309*e^6 + 4*e^5 - 173/103*e^4 - 10847/309*e^3 - 2439/103*e^2 + 20078/309*e + 18023/309, -8/103*e^6 + 134/103*e^4 - 61/103*e^3 - 381/103*e^2 + 389/103*e - 139/103, -16/309*e^6 - e^5 - 151/103*e^4 + 3071/309*e^3 + 982/103*e^2 - 6329/309*e - 2750/309, 169/309*e^6 + 3*e^5 - 214/103*e^4 - 8123/309*e^3 - 935/103*e^2 + 14996/309*e + 7301/309, -37/309*e^6 - e^5 - 8/103*e^4 + 3104/309*e^3 + 404/103*e^2 - 6737/309*e - 1763/309, -29/103*e^6 - e^5 + 254/103*e^4 + 796/103*e^3 - 364/103*e^2 - 1049/103*e - 1212/103, -5/309*e^6 - 15/103*e^4 - 566/309*e^3 - 15/103*e^2 + 2522/309*e + 2810/309, -64/309*e^6 - 2*e^5 - 192/103*e^4 + 5795/309*e^3 + 2486/103*e^2 - 12029/309*e - 14090/309, 59/103*e^6 + 3*e^5 - 293/103*e^4 - 2859/103*e^3 - 705/103*e^2 + 5796/103*e + 2480/103, 113/309*e^6 + e^5 - 485/103*e^4 - 2473/309*e^3 + 1987/103*e^2 + 2887/309*e - 6650/309, -41/103*e^6 - 2*e^5 + 249/103*e^4 + 1786/103*e^3 - 266/103*e^2 - 3092/103*e - 339/103, -1/309*e^6 - e^5 - 312/103*e^4 + 3224/309*e^3 + 2469/103*e^2 - 9569/309*e - 13652/309, 18/103*e^6 + e^5 - 44/103*e^4 - 970/103*e^3 - 765/103*e^2 + 2189/103*e + 1729/103, 49/309*e^6 + e^5 + 44/103*e^4 - 2858/309*e^3 - 1707/103*e^2 + 6308/309*e + 10469/309, -70/309*e^6 - 2*e^5 - 107/103*e^4 + 5981/309*e^3 + 1747/103*e^2 - 12896/309*e - 10718/309, -143/309*e^6 - 4*e^5 - 223/103*e^4 + 12364/309*e^3 + 4412/103*e^2 - 27616/309*e - 28093/309, 9/103*e^6 + e^5 + 81/103*e^4 - 1103/103*e^3 - 846/103*e^2 + 3206/103*e + 1946/103, 32/309*e^6 + e^5 - 7/103*e^4 - 3670/309*e^3 - 213/103*e^2 + 11113/309*e + 1792/309, 113/309*e^6 + 3*e^5 + 133/103*e^4 - 9271/309*e^3 - 3266/103*e^2 + 20191/309*e + 20542/309, 140/309*e^6 + 2*e^5 - 301/103*e^4 - 4855/309*e^3 + 420/103*e^2 + 7870/309*e + 424/309, 142/309*e^6 + 2*e^5 - 398/103*e^4 - 6050/309*e^3 + 323/103*e^2 + 12485/309*e + 8261/309, 1/3*e^6 + 2*e^5 - 50/3*e^3 - 15*e^2 + 98/3*e + 50/3, 1/103*e^6 + e^5 + 318/103*e^4 - 855/103*e^3 - 2154/103*e^2 + 1226/103*e + 2219/103, 15/103*e^6 - 380/103*e^4 - 53/103*e^3 + 2401/103*e^2 + 468/103*e - 2765/103, -47/309*e^6 + 374/103*e^4 - 191/309*e^3 - 2510/103*e^2 + 1397/309*e + 11582/309, -62/309*e^6 - 2*e^5 - 289/103*e^4 + 5527/309*e^3 + 3316/103*e^2 - 12667/309*e - 15523/309, -380/309*e^6 - 7*e^5 + 302/103*e^4 + 19093/309*e^3 + 4319/103*e^2 - 35443/309*e - 31786/309, -386/309*e^6 - 7*e^5 + 387/103*e^4 + 19897/309*e^3 + 4198/103*e^2 - 41254/309*e - 33667/309, 151/309*e^6 + 3*e^5 - 62/103*e^4 - 8801/309*e^3 - 2637/103*e^2 + 20738/309*e + 21743/309, -7/103*e^6 + 246/103*e^4 + 320/103*e^3 - 1505/103*e^2 - 1578/103*e + 1256/103, -64/103*e^6 - 4*e^5 + 42/103*e^4 + 3838/103*e^3 + 3132/103*e^2 - 8218/103*e - 6777/103, 281/309*e^6 + 6*e^5 + 19/103*e^4 - 16024/309*e^3 - 4307/103*e^2 + 29326/309*e + 24697/309, 12/103*e^6 + 2*e^5 + 417/103*e^4 - 1917/103*e^3 - 3703/103*e^2 + 3691/103*e + 4792/103, 188/309*e^6 + 4*e^5 + 49/103*e^4 - 10978/309*e^3 - 3659/103*e^2 + 22840/309*e + 21034/309, -19/309*e^6 + 46/103*e^4 - 1162/309*e^3 - 160/103*e^2 + 6370/309*e - 137/309, -167/309*e^6 - 4*e^5 - 192/103*e^4 + 10945/309*e^3 + 4134/103*e^2 - 21814/309*e - 23566/309, -25/103*e^6 - 2*e^5 - 122/103*e^4 + 1702/103*e^3 + 1526/103*e^2 - 2428/103*e - 1812/103, 59/309*e^6 + e^5 - 132/103*e^4 - 3271/309*e^3 + 74/103*e^2 + 7753/309*e + 2686/309, 13/309*e^6 - e^5 - 476/103*e^4 + 2584/309*e^3 + 3129/103*e^2 - 6619/309*e - 10396/309, 224/309*e^6 + 4*e^5 - 358/103*e^4 - 12094/309*e^3 - 1079/103*e^2 + 25879/309*e + 11308/309, -5/309*e^6 + e^5 + 294/103*e^4 - 3656/309*e^3 - 2075/103*e^2 + 9320/309*e + 5282/309, 319/309*e^6 + 6*e^5 - 176/103*e^4 - 16790/309*e^3 - 4708/103*e^2 + 36053/309*e + 36095/309, -5/309*e^6 + e^5 + 294/103*e^4 - 3347/309*e^3 - 1972/103*e^2 + 7157/309*e + 6518/309, -33/103*e^6 - 2*e^5 - 91/103*e^4 + 1538/103*e^3 + 2278/103*e^2 - 2554/103*e - 3599/103, -44/103*e^6 - e^5 + 428/103*e^4 + 334/103*e^3 - 1117/103*e^2 + 1058/103*e + 2068/103, 96/103*e^6 + 5*e^5 - 578/103*e^4 - 5242/103*e^3 - 578/103*e^2 + 11709/103*e + 4758/103, -316/309*e^6 - 6*e^5 + 185/103*e^4 + 16388/309*e^3 + 4099/103*e^2 - 31139/309*e - 26966/309, 43/103*e^6 + 2*e^5 - 128/103*e^4 - 1436/103*e^3 - 849/103*e^2 + 1939/103*e + 451/103, -81/103*e^6 - 3*e^5 + 713/103*e^4 + 2717/103*e^3 - 1141/103*e^2 - 5576/103*e - 2785/103, -151/309*e^6 - 4*e^5 - 144/103*e^4 + 13127/309*e^3 + 4388/103*e^2 - 31244/309*e - 30086/309, -118/309*e^6 - 2*e^5 + 58/103*e^4 + 4997/309*e^3 + 1809/103*e^2 - 10253/309*e - 14024/309, -53/103*e^6 - 4*e^5 - 168/103*e^4 + 4012/103*e^3 + 4364/103*e^2 - 9358/103*e - 9457/103, 4/103*e^6 + 36/103*e^4 + 82/103*e^3 - 1200/103*e^2 + 63/103*e + 2902/103, 2/3*e^6 + 4*e^5 - e^4 - 106/3*e^3 - 24*e^2 + 205/3*e + 121/3, 153/103*e^6 + 8*e^5 - 580/103*e^4 - 7627/103*e^3 - 4185/103*e^2 + 15465/103*e + 12688/103, 104/309*e^6 + e^5 - 409/103*e^4 - 2812/309*e^3 + 1136/103*e^2 + 4522/309*e - 4682/309, -358/309*e^6 - 6*e^5 + 471/103*e^4 + 15836/309*e^3 + 2531/103*e^2 - 26084/309*e - 21902/309, 218/309*e^6 + 4*e^5 - 376/103*e^4 - 13144/309*e^3 - 1303/103*e^2 + 31501/309*e + 17770/309, -1/309*e^6 - 3/103*e^4 - 175/309*e^3 + 512/103*e^2 + 4645/309*e - 6236/309, 115/309*e^6 + 3*e^5 + 139/103*e^4 - 8612/309*e^3 - 2848/103*e^2 + 18008/309*e + 17255/309, -559/309*e^6 - 10*e^5 + 589/103*e^4 + 27938/309*e^3 + 5636/103*e^2 - 56210/309*e - 49535/309, -217/309*e^6 - 4*e^5 + 276/103*e^4 + 11774/309*e^3 + 1306/103*e^2 - 25640/309*e - 9371/309, -52/103*e^6 - 4*e^5 - 262/103*e^4 + 3466/103*e^3 + 3858/103*e^2 - 6381/103*e - 5178/103, -185/309*e^6 - 4*e^5 + 63/103*e^4 + 11503/309*e^3 + 2020/103*e^2 - 23488/309*e - 12832/309, 182/309*e^6 + 2*e^5 - 587/103*e^4 - 5848/309*e^3 + 855/103*e^2 + 16411/309*e + 5866/309, 43/309*e^6 + e^5 + 26/103*e^4 - 3290/309*e^3 - 1416/103*e^2 + 7604/309*e + 7352/309, -50/103*e^6 - 2*e^5 + 477/103*e^4 + 2168/103*e^3 - 656/103*e^2 - 5062/103*e - 2697/103, 175/103*e^6 + 9*e^5 - 691/103*e^4 - 8515/103*e^3 - 4502/103*e^2 + 18026/103*e + 14538/103, 143/309*e^6 + 2*e^5 - 395/103*e^4 - 5875/309*e^3 + 944/103*e^2 + 13402/309*e - 3116/309, 49/309*e^6 + 2*e^5 + 250/103*e^4 - 6257/309*e^3 - 2840/103*e^2 + 12488/309*e + 16958/309, -83/309*e^6 + 369/103*e^4 - 1238/309*e^3 - 352/103*e^2 + 5774/309*e - 6811/309, 311/309*e^6 + 6*e^5 - 303/103*e^4 - 17263/309*e^3 - 2569/103*e^2 + 35206/309*e + 21742/309, 7/309*e^6 - e^5 - 494/103*e^4 + 1225/309*e^3 + 2802/103*e^2 + 2711/309*e - 7024/309, -256/309*e^6 - 4*e^5 + 365/103*e^4 + 9893/309*e^3 + 1395/103*e^2 - 16907/309*e - 9701/309, -413/309*e^6 - 7*e^5 + 615/103*e^4 + 19807/309*e^3 + 2778/103*e^2 - 39130/309*e - 33016/309, -135/103*e^6 - 7*e^5 + 330/103*e^4 + 6245/103*e^3 + 5274/103*e^2 - 12864/103*e - 13637/103, 295/309*e^6 + 5*e^5 - 248/103*e^4 - 12647/309*e^3 - 3544/103*e^2 + 22079/309*e + 29498/309, 176/309*e^6 + 4*e^5 + 219/103*e^4 - 10297/309*e^3 - 4519/103*e^2 + 18016/309*e + 20053/309, -154/309*e^6 - 3*e^5 + 156/103*e^4 + 9821/309*e^3 + 2113/103*e^2 - 24725/309*e - 17894/309, 151/309*e^6 + 4*e^5 + 350/103*e^4 - 10964/309*e^3 - 5933/103*e^2 + 19502/309*e + 29468/309, 54/103*e^6 + 4*e^5 + 74/103*e^4 - 4146/103*e^3 - 3737/103*e^2 + 8833/103*e + 8174/103, -557/309*e^6 - 10*e^5 + 698/103*e^4 + 29215/309*e^3 + 4612/103*e^2 - 63028/309*e - 43552/309, 2*e^5 + 4*e^4 - 24*e^3 - 24*e^2 + 52*e + 12, 48/103*e^6 + 4*e^5 + 226/103*e^4 - 4063/103*e^3 - 4512/103*e^2 + 9408/103*e + 11649/103, 40/309*e^6 - 189/103*e^4 + 511/309*e^3 + 326/103*e^2 + 527/309*e + 9965/309, -404/309*e^6 - 6*e^5 + 848/103*e^4 + 17674/309*e^3 + 1878/103*e^2 - 38602/309*e - 34057/309, 7/103*e^6 - 246/103*e^4 - 114/103*e^3 + 2020/103*e^2 + 1166/103*e - 2492/103, 8/103*e^6 - 134/103*e^4 + 164/103*e^3 + 896/103*e^2 - 389/103*e - 685/103, 17/309*e^6 + 2*e^5 + 566/103*e^4 - 5677/309*e^3 - 4584/103*e^2 + 12190/309*e + 21964/309, 14/103*e^6 + e^5 - 80/103*e^4 - 1155/103*e^3 + 23/103*e^2 + 2126/103*e - 1997/103, 148/309*e^6 + 2*e^5 - 380/103*e^4 - 5000/309*e^3 + 650/103*e^2 + 6245/309*e + 3344/309, 36/103*e^6 + 2*e^5 + 15/103*e^4 - 1631/103*e^3 - 2354/103*e^2 + 2730/103*e + 4694/103, 581/309*e^6 + 11*e^5 - 420/103*e^4 - 29959/309*e^3 - 6394/103*e^2 + 55063/309*e + 43969/309, 15/103*e^6 + e^5 - 174/103*e^4 - 1495/103*e^3 + 547/103*e^2 + 4073/103*e + 943/103, -644/309*e^6 - 11*e^5 + 746/103*e^4 + 28513/309*e^3 + 4660/103*e^2 - 50107/309*e - 40390/309, -122/103*e^6 - 7*e^5 + 138/103*e^4 + 6666/103*e^3 + 6730/103*e^2 - 14951/103*e - 16514/103, -169/309*e^6 - 3*e^5 + 214/103*e^4 + 8741/309*e^3 + 1553/103*e^2 - 16850/309*e - 19043/309, 139/309*e^6 + 2*e^5 - 98/103*e^4 - 4103/309*e^3 - 2055/103*e^2 + 8189/309*e + 17054/309, 31/309*e^6 + 3*e^5 + 917/103*e^4 - 7553/309*e^3 - 7323/103*e^2 + 14213/309*e + 29855/309, 152/309*e^6 + 3*e^5 - 59/103*e^4 - 8317/309*e^3 - 2222/103*e^2 + 17020/309*e + 15001/309, -211/309*e^6 - 4*e^5 + 191/103*e^4 + 11897/309*e^3 + 2354/103*e^2 - 26936/309*e - 14597/309, 310/309*e^6 + 4*e^5 - 924/103*e^4 - 12494/309*e^3 + 827/103*e^2 + 30272/309*e + 11180/309, -140/103*e^6 - 8*e^5 + 491/103*e^4 + 8048/103*e^3 + 3684/103*e^2 - 17243/103*e - 10209/103, -87/103*e^6 - 5*e^5 + 453/103*e^4 + 5066/103*e^3 - 268/103*e^2 - 11078/103*e - 958/103, 79/309*e^6 + 3*e^5 + 443/103*e^4 - 8423/309*e^3 - 4501/103*e^2 + 18677/309*e + 24509/309, -211/309*e^6 - 5*e^5 - 15/103*e^4 + 15605/309*e^3 + 3693/103*e^2 - 34352/309*e - 20159/309, -160/309*e^6 - 4*e^5 - 274/103*e^4 + 10007/309*e^3 + 3949/103*e^2 - 14777/309*e - 15758/309, 679/309*e^6 + 12*e^5 - 847/103*e^4 - 33203/309*e^3 - 4761/103*e^2 + 63662/309*e + 36170/309, 416/309*e^6 + 5*e^5 - 1224/103*e^4 - 12484/309*e^3 + 2690/103*e^2 + 21178/309*e + 4756/309, 329/309*e^6 + 6*e^5 - 249/103*e^4 - 16894/309*e^3 - 4163/103*e^2 + 37189/309*e + 25840/309, -358/309*e^6 - 6*e^5 + 471/103*e^4 + 16454/309*e^3 + 2840/103*e^2 - 32573/309*e - 23447/309, -445/309*e^6 - 6*e^5 + 1137/103*e^4 + 15752/309*e^3 - 1335/103*e^2 - 23978/309*e - 2363/309, -874/309*e^6 - 16*e^5 + 983/103*e^4 + 46664/309*e^3 + 8605/103*e^2 - 98174/309*e - 79844/309, 87/103*e^6 + 4*e^5 - 453/103*e^4 - 3315/103*e^3 - 1277/103*e^2 + 3559/103*e + 5387/103, -184/103*e^6 - 12*e^5 - 8/103*e^4 + 10957/103*e^3 + 7820/103*e^2 - 20923/103*e - 14630/103, 29/103*e^6 + 3*e^5 + 261/103*e^4 - 3577/103*e^3 - 4271/103*e^2 + 9495/103*e + 7804/103, -245/309*e^6 - 5*e^5 + 89/103*e^4 + 14908/309*e^3 + 3694/103*e^2 - 34012/309*e - 19900/309, 18/103*e^6 - 44/103*e^4 + 987/103*e^3 - 662/103*e^2 - 4506/103*e + 184/103, 62/309*e^6 - e^5 - 844/103*e^4 + 3125/309*e^3 + 5954/103*e^2 - 6491/309*e - 22175/309, 401/309*e^6 + 9*e^5 + 173/103*e^4 - 24070/309*e^3 - 7037/103*e^2 + 43576/309*e + 32962/309, -746/309*e^6 - 15*e^5 + 337/103*e^4 + 43108/309*e^3 + 10740/103*e^2 - 90493/309*e - 78238/309, 214/309*e^6 + 4*e^5 - 285/103*e^4 - 11681/309*e^3 - 1521/103*e^2 + 23507/309*e + 19709/309, -337/309*e^6 - 6*e^5 + 328/103*e^4 + 15803/309*e^3 + 3109/103*e^2 - 29693/309*e - 31850/309, 30/103*e^6 + 2*e^5 + 167/103*e^4 - 1239/103*e^3 - 1790/103*e^2 + 1245/103*e - 895/103, 275/309*e^6 + 5*e^5 - 308/103*e^4 - 13675/309*e^3 - 2471/103*e^2 + 21970/309*e + 15400/309, -42/103*e^6 - 2*e^5 + 240/103*e^4 + 1920/103*e^3 + 549/103*e^2 - 3803/103*e - 2970/103, -145/103*e^6 - 8*e^5 + 240/103*e^4 + 6967/103*e^3 + 5905/103*e^2 - 11631/103*e - 13785/103, -114/103*e^6 - 5*e^5 + 725/103*e^4 + 4873/103*e^3 + 931/103*e^2 - 11426/103*e - 4221/103, -544/309*e^6 - 8*e^5 + 943/103*e^4 + 20984/309*e^3 + 2900/103*e^2 - 40910/309*e - 26447/309, -152/103*e^6 - 7*e^5 + 898/103*e^4 + 6463/103*e^3 + 1104/103*e^2 - 13003/103*e - 6967/103, 98/309*e^6 - 530/103*e^4 + 773/309*e^3 + 1942/103*e^2 + 1492/309*e - 2546/309, 179/309*e^6 + 6*e^5 + 434/103*e^4 - 19351/309*e^3 - 5746/103*e^2 + 47341/309*e + 35671/309, 169/103*e^6 + 10*e^5 - 230/103*e^4 - 9256/103*e^3 - 7028/103*e^2 + 17571/103*e + 12966/103, -295/309*e^6 - 9*e^5 - 988/103*e^4 + 23771/309*e^3 + 11269/103*e^2 - 42473/309*e - 52673/309, -340/309*e^6 - 5*e^5 + 937/103*e^4 + 14351/309*e^3 - 2462/103*e^2 - 30281/309*e + 2590/309, 6/103*e^6 - 255/103*e^4 - 495/103*e^3 + 981/103*e^2 + 2927/103*e + 645/103, 533/309*e^6 + 9*e^5 - 564/103*e^4 - 23218/309*e^3 - 4993/103*e^2 + 41020/309*e + 36337/309, -51/103*e^6 - 4*e^5 - 356/103*e^4 + 3744/103*e^3 + 5721/103*e^2 - 8760/103*e - 9963/103, 179/103*e^6 + 11*e^5 - 243/103*e^4 - 10596/103*e^3 - 7968/103*e^2 + 20767/103*e + 19706/103, 46/309*e^6 - 171/103*e^4 + 1561/309*e^3 - 171/103*e^2 - 11584/309*e + 2267/309, 182/309*e^6 + 3*e^5 + 31/103*e^4 - 5848/309*e^3 - 3471/103*e^2 + 6214/309*e + 17608/309, 36/103*e^6 - 1118/103*e^4 - 807/103*e^3 + 6401/103*e^2 + 3039/103*e - 5297/103, 55/309*e^6 - 247/103*e^4 + 1282/309*e^3 + 989/103*e^2 - 3022/309*e - 8971/309, -116/103*e^6 - 7*e^5 + 295/103*e^4 + 6892/103*e^3 + 3488/103*e^2 - 14084/103*e - 9174/103, 166/309*e^6 + 2*e^5 - 429/103*e^4 - 4631/309*e^3 + 910/103*e^2 + 7610/309*e - 13570/309, 254/309*e^6 + 4*e^5 - 268/103*e^4 - 8698/309*e^3 - 1916/103*e^2 + 6730/309*e + 13297/309, 181/309*e^6 + 3*e^5 - 281/103*e^4 - 8495/309*e^3 - 796/103*e^2 + 17657/309*e + 4265/309, 191/309*e^6 + 5*e^5 + 470/103*e^4 - 13234/309*e^3 - 6946/103*e^2 + 27445/309*e + 33871/309, -380/309*e^6 - 8*e^5 - 213/103*e^4 + 20329/309*e^3 + 8233/103*e^2 - 36061/309*e - 42910/309]
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, -2*w^3 + w^2 + 8*w - 1])] = -1

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