/*
  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^3 + 2*w^2 + 5*w - 3])

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^7 - x^6 - 30*x^5 + 8*x^4 + 267*x^3 + 86*x^2 - 500*x - 24
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 29/458*e^6 + 15/229*e^5 - 501/458*e^4 - 366/229*e^3 + 663/458*e^2 + 1237/458*e + 827/229, -89/916*e^6 - 21/916*e^5 + 414/229*e^4 + 151/229*e^3 - 4151/916*e^2 + 877/229*e - 507/229, -25/458*e^6 + 61/458*e^5 + 212/229*e^4 - 561/229*e^3 - 919/458*e^2 + 2811/229*e - 784/229, -53/916*e^6 + 111/916*e^5 + 298/229*e^4 - 471/229*e^3 - 6455/916*e^2 + 1482/229*e + 488/229, -1, 49/458*e^6 + 27/458*e^5 - 443/229*e^4 - 421/229*e^3 + 2131/458*e^2 + 591/229*e + 126/229, 1/229*e^6 - 69/458*e^5 - 153/458*e^4 + 567/229*e^3 + 1310/229*e^2 - 807/458*e - 1467/229, -21/229*e^6 - 77/229*e^5 + 347/229*e^4 + 1604/229*e^3 - 30/229*e^2 - 4007/229*e + 350/229, -24/229*e^6 - 405/458*e^5 + 695/458*e^4 + 3796/229*e^3 + 1765/229*e^2 - 17043/458*e - 1203/229, -59/458*e^6 - 369/458*e^5 + 482/229*e^4 + 3540/229*e^3 + 1257/458*e^2 - 8077/229*e + 1026/229, 115/458*e^6 + 269/458*e^5 - 1021/229*e^4 - 2778/229*e^3 + 2945/458*e^2 + 5252/229*e - 424/229, 1/2*e^5 + 1/2*e^4 - 9*e^3 - 12*e^2 + 37/2*e + 11, 5/458*e^6 + 171/458*e^5 + 95/229*e^4 - 1674/229*e^3 - 5129/458*e^2 + 3972/229*e + 2172/229, -211/916*e^6 - 163/916*e^5 + 1087/229*e^4 + 1063/229*e^3 - 16953/916*e^2 - 2331/229*e + 2673/229, 127/458*e^6 + 313/458*e^5 - 1022/229*e^4 - 3269/229*e^3 - 113/458*e^2 + 5808/229*e + 1766/229, 81/229*e^6 + 68/229*e^5 - 1502/229*e^4 - 1705/229*e^3 + 3747/229*e^2 + 2010/229*e + 482/229, -101/916*e^6 - 65/916*e^5 + 529/229*e^4 + 511/229*e^3 - 8879/916*e^2 - 1920/229*e + 917/229, -50/229*e^6 - 107/229*e^5 + 848/229*e^4 + 2107/229*e^3 - 464/229*e^2 - 2038/229*e - 1304/229, 66/229*e^6 + 255/458*e^5 - 2541/458*e^4 - 2653/229*e^3 + 3333/229*e^2 + 10629/458*e - 1329/229, 57/458*e^6 + 667/458*e^5 - 291/229*e^4 - 6168/229*e^3 - 8915/458*e^2 + 12717/229*e + 1128/229, -22/229*e^6 - 85/458*e^5 + 847/458*e^4 + 808/229*e^3 - 1340/229*e^2 - 1253/458*e + 2733/229, -37/458*e^6 - 106/229*e^5 + 655/458*e^4 + 2220/229*e^3 - 609/458*e^2 - 13581/458*e + 1835/229, -22/229*e^6 + 72/229*e^5 + 538/229*e^4 - 1253/229*e^3 - 3630/229*e^2 + 3152/229*e + 2046/229, -18/229*e^6 - 66/229*e^5 + 232/229*e^4 + 1473/229*e^3 + 923/229*e^2 - 3729/229*e - 1990/229, -121/458*e^6 - 260/229*e^5 + 2043/458*e^4 + 5199/229*e^3 + 187/458*e^2 - 25029/458*e + 1161/229, -9/458*e^6 - 33/458*e^5 + 58/229*e^4 + 311/229*e^3 - 111/458*e^2 - 188/229*e + 2594/229, 58/229*e^6 + 60/229*e^5 - 1002/229*e^4 - 1464/229*e^3 + 1555/229*e^2 + 1329/229*e + 1934/229, 11/229*e^6 + 157/458*e^5 - 767/458*e^4 - 1549/229*e^3 + 2960/229*e^2 + 11733/458*e - 4687/229, 189/458*e^6 + 3/229*e^5 - 3581/458*e^4 - 577/229*e^3 + 11949/458*e^2 - 2867/458*e - 3865/229, 3/229*e^6 + 240/229*e^5 + 114/229*e^4 - 4482/229*e^3 - 4314/229*e^2 + 11499/229*e + 6362/229, 51/458*e^6 + 187/458*e^5 - 405/229*e^4 - 1686/229*e^3 - 1203/458*e^2 + 1447/229*e + 720/229, 123/458*e^6 + 451/458*e^5 - 1098/229*e^4 - 4403/229*e^3 + 1975/458*e^2 + 8447/229*e + 120/229, -74/229*e^6 - 195/229*e^5 + 1310/229*e^4 + 4071/229*e^3 - 1447/229*e^2 - 9987/229*e + 12/229, 281/916*e^6 + 725/916*e^5 - 1109/229*e^4 - 3392/229*e^3 - 4473/916*e^2 + 1510/229*e + 6119/229, 47/229*e^6 - 37/458*e^5 - 2153/458*e^4 + 85/229*e^3 + 5694/229*e^2 + 543/458*e - 4371/229, -26/229*e^6 - 19/229*e^5 + 615/229*e^4 + 601/229*e^3 - 3603/229*e^2 - 3478/229*e + 2876/229, -59/458*e^6 - 369/458*e^5 + 482/229*e^4 + 3769/229*e^3 + 1257/458*e^2 - 11512/229*e - 1264/229, 70/229*e^6 - 21/458*e^5 - 2695/458*e^4 - 156/229*e^3 + 3993/229*e^2 - 3591/458*e + 4253/229, -87/229*e^6 - 319/229*e^5 + 1274/229*e^4 + 6318/229*e^3 + 2820/229*e^2 - 10810/229*e - 4504/229, -119/458*e^6 + 327/458*e^5 + 1174/229*e^4 - 2936/229*e^3 - 10475/458*e^2 + 12272/229*e + 1526/229, 115/458*e^6 + 269/458*e^5 - 1021/229*e^4 - 2549/229*e^3 + 2945/458*e^2 + 1359/229*e - 2256/229, 83/229*e^6 + 228/229*e^5 - 1426/229*e^4 - 4464/229*e^3 + 871/229*e^2 + 6928/229*e + 1212/229, -16/229*e^6 + 417/458*e^5 + 845/458*e^4 - 3576/229*e^3 - 4701/229*e^2 + 16347/458*e + 4007/229, -33/916*e^6 - 121/916*e^5 + 30/229*e^4 + 761/229*e^3 + 6005/916*e^2 - 2711/229*e - 2725/229, -53/458*e^6 + 111/458*e^5 + 596/229*e^4 - 713/229*e^3 - 7829/458*e^2 - 13/229*e + 4182/229, -9/458*e^6 - 491/458*e^5 + 58/229*e^4 + 4433/229*e^3 + 3553/458*e^2 - 10722/229*e + 3510/229, 48/229*e^6 + 176/229*e^5 - 695/229*e^4 - 3470/229*e^3 - 1698/229*e^2 + 6051/229*e + 5612/229, 55/458*e^6 + 507/458*e^5 - 558/229*e^4 - 4674/229*e^3 + 831/458*e^2 + 11403/229*e - 2214/229, 139/458*e^6 + 357/458*e^5 - 1023/229*e^4 - 3531/229*e^3 - 3629/458*e^2 + 3845/229*e + 2582/229, -57/229*e^6 - 189/458*e^5 + 2309/458*e^4 + 2031/229*e^3 - 3451/229*e^2 - 9419/458*e - 2943/229, -107/458*e^6 - 87/458*e^5 + 1173/229*e^4 + 1382/229*e^3 - 11701/458*e^2 - 5492/229*e + 6464/229, 173/458*e^6 + 787/458*e^5 - 1522/229*e^4 - 7403/229*e^3 + 1065/458*e^2 + 14275/229*e - 4266/229, -15/458*e^6 + 87/229*e^5 + 575/458*e^4 - 1619/229*e^3 - 6597/458*e^2 + 11205/458*e + 1499/229, -3/229*e^6 - 11/229*e^5 - 114/229*e^4 + 589/229*e^3 + 2253/229*e^2 - 4400/229*e - 5446/229, 34/229*e^6 - 257/229*e^5 - 998/229*e^4 + 4622/229*e^3 + 9045/229*e^2 - 11429/229*e - 4536/229, 169/229*e^6 + 238/229*e^5 - 2967/229*e^4 - 5166/229*e^3 + 4756/229*e^2 + 4974/229*e + 542/229, 31/229*e^6 - 268/229*e^5 - 654/229*e^4 + 4753/229*e^3 + 4886/229*e^2 - 13768/229*e + 1926/229, -108/229*e^6 - 167/229*e^5 + 2079/229*e^4 + 3571/229*e^3 - 5912/229*e^2 - 6115/229*e + 2258/229, 80/229*e^6 + 205/458*e^5 - 2851/458*e^4 - 2501/229*e^3 + 3124/229*e^2 + 9407/458*e - 4921/229, -7/458*e^6 + 127/458*e^5 + 96/229*e^4 - 725/229*e^3 - 3445/458*e^2 - 1393/229*e + 3188/229, -168/229*e^6 - 545/458*e^5 + 6239/458*e^4 + 5962/229*e^3 - 7568/229*e^2 - 22663/458*e + 5319/229, 156/229*e^6 + 572/229*e^5 - 2774/229*e^4 - 11163/229*e^3 + 2611/229*e^2 + 22013/229*e - 3058/229, -41/458*e^6 - 303/458*e^5 + 366/229*e^4 + 2918/229*e^3 + 105/458*e^2 - 7472/229*e + 3624/229, -127/458*e^6 - 313/458*e^5 + 1022/229*e^4 + 3040/229*e^3 + 571/458*e^2 - 3518/229*e + 2814/229, 33/458*e^6 + 175/229*e^5 - 349/458*e^4 - 3354/229*e^3 - 3257/458*e^2 + 15653/458*e - 5313/229, 181/916*e^6 + 53/916*e^5 - 914/229*e^4 - 392/229*e^3 + 13835/916*e^2 - 1570/229*e - 945/229, 71/229*e^6 + 184/229*e^5 - 1424/229*e^4 - 3711/229*e^3 + 4387/229*e^2 + 8793/229*e - 7290/229, 142/229*e^6 + 139/229*e^5 - 2390/229*e^4 - 3071/229*e^3 + 2362/229*e^2 - 1192/229*e + 6488/229, -45/229*e^6 - 394/229*e^5 + 580/229*e^4 + 7461/229*e^3 + 4254/229*e^2 - 17681/229*e - 166/229, -489/458*e^6 - 877/458*e^5 + 4449/229*e^4 + 9188/229*e^3 - 17481/458*e^2 - 13497/229*e + 2930/229, -101/229*e^6 - 294/229*e^5 + 1658/229*e^4 + 5937/229*e^3 - 177/229*e^2 - 11573/229*e + 2294/229, 95/916*e^6 + 959/916*e^5 - 128/229*e^4 - 4453/229*e^3 - 23255/916*e^2 + 8880/229*e + 6207/229, -339/458*e^6 - 327/458*e^5 + 3177/229*e^4 + 3852/229*e^3 - 17005/458*e^2 - 4028/229*e + 1680/229, -331/916*e^6 - 603/916*e^5 + 1550/229*e^4 + 3289/229*e^3 - 15685/916*e^2 - 6027/229*e + 4089/229, 7/458*e^6 + 331/458*e^5 + 133/229*e^4 - 3168/229*e^3 - 7547/458*e^2 + 7576/229*e + 476/229, -40/229*e^6 - 217/458*e^5 + 1311/458*e^4 + 2052/229*e^3 + 41/229*e^2 - 3215/458*e - 2005/229, -285/916*e^6 - 1045/916*e^5 + 1071/229*e^4 + 5573/229*e^3 + 5645/916*e^2 - 13816/229*e + 615/229, 125/458*e^6 + 649/229*e^5 - 1891/458*e^4 - 12309/229*e^3 - 9603/458*e^2 + 63719/458*e + 4149/229, -269/458*e^6 + 3/229*e^5 + 5121/458*e^4 + 797/229*e^3 - 17363/458*e^2 + 1255/458*e + 5295/229, -87/458*e^6 + 1055/458*e^5 + 1095/229*e^4 - 9665/229*e^3 - 21225/458*e^2 + 28716/229*e + 6450/229, 109/458*e^6 + 705/458*e^5 - 906/229*e^4 - 6769/229*e^3 - 3083/458*e^2 + 16653/229*e + 5580/229, 49/458*e^6 + 485/458*e^5 - 214/229*e^4 - 4772/229*e^3 - 7487/458*e^2 + 12270/229*e + 584/229, -217/916*e^6 - 185/916*e^5 + 1030/229*e^4 + 1243/229*e^3 - 12447/916*e^2 - 1554/229*e + 1553/229, 31/458*e^6 + 324/229*e^5 - 425/458*e^4 - 6211/229*e^3 - 4503/458*e^2 + 38215/458*e - 4075/229, 509/458*e^6 + 1103/458*e^5 - 4756/229*e^4 - 11533/229*e^3 + 20781/458*e^2 + 24118/229*e - 6150/229, 323/458*e^6 + 879/458*e^5 - 3023/229*e^4 - 8846/229*e^3 + 11159/458*e^2 + 18706/229*e + 438/229, -279/458*e^6 - 1023/458*e^5 + 2256/229*e^4 + 9870/229*e^3 + 4345/458*e^2 - 17965/229*e - 7522/229, 275/458*e^6 + 8/229*e^5 - 5351/458*e^4 - 928/229*e^3 + 16979/458*e^2 + 217/458*e + 2441/229, -199/458*e^6 - 403/229*e^5 + 3201/458*e^4 + 7589/229*e^3 + 4721/458*e^2 - 26303/458*e - 9639/229, 25/458*e^6 - 145/229*e^5 - 653/458*e^4 + 2851/229*e^3 + 5499/458*e^2 - 19591/458*e - 3567/229, 103/458*e^6 + 225/458*e^5 - 1020/229*e^4 - 2287/229*e^3 + 5087/458*e^2 + 5154/229*e + 1508/229, 865/916*e^6 + 1645/916*e^5 - 3805/229*e^4 - 8775/229*e^3 + 24103/916*e^2 + 15421/229*e - 6085/229, -177/916*e^6 + 267/916*e^5 + 723/229*e^4 - 1102/229*e^3 - 4015/916*e^2 + 6090/229*e - 2125/229, -54/229*e^6 - 198/229*e^5 + 925/229*e^4 + 3732/229*e^3 + 21/229*e^2 - 5004/229*e - 3222/229, -171/229*e^6 - 398/229*e^5 + 3120/229*e^4 + 7696/229*e^3 - 5315/229*e^2 - 9892/229*e + 6972/229, -87/458*e^6 + 597/458*e^5 + 1095/229*e^4 - 5543/229*e^3 - 16645/458*e^2 + 16808/229*e + 1412/229, 191/458*e^6 + 83/229*e^5 - 3047/458*e^4 - 2071/229*e^3 + 1287/458*e^2 - 239/458*e + 3599/229, 99/458*e^6 + 363/458*e^5 - 867/229*e^4 - 3421/229*e^3 - 611/458*e^2 + 6419/229*e + 9938/229, -254/229*e^6 - 626/229*e^5 + 4317/229*e^4 + 12847/229*e^3 - 2980/229*e^2 - 23461/229*e - 3858/229, 31/458*e^6 + 419/458*e^5 - 327/229*e^4 - 4150/229*e^3 + 993/458*e^2 + 14184/229*e - 2472/229, 823/916*e^6 + 1491/916*e^5 - 3746/229*e^4 - 7973/229*e^3 + 29997/916*e^2 + 14448/229*e - 3391/229, 33/458*e^6 - 795/458*e^5 - 747/229*e^4 + 7180/229*e^3 + 21475/458*e^2 - 17478/229*e - 9664/229, -193/458*e^6 - 163/229*e^5 + 3887/458*e^4 + 3565/229*e^3 - 13525/458*e^2 - 15671/458*e + 6341/229, -221/458*e^6 - 47/458*e^5 + 1984/229*e^4 + 1123/229*e^3 - 8527/458*e^2 + 676/229*e - 6784/229, 60/229*e^6 - 238/229*e^5 - 1155/229*e^4 + 3792/229*e^3 + 5091/229*e^2 - 9554/229*e + 5870/229, -355/916*e^6 - 1607/916*e^5 + 1551/229*e^4 + 7444/229*e^3 - 2241/916*e^2 - 12079/229*e + 6479/229, 205/229*e^6 + 370/229*e^5 - 3660/229*e^4 - 8112/229*e^3 + 6345/229*e^2 + 14951/229*e + 2690/229, -307/458*e^6 - 372/229*e^5 + 5509/458*e^4 + 7428/229*e^3 - 8519/458*e^2 - 22571/458*e + 7749/229, 685/916*e^6 + 1901/916*e^5 - 2996/229*e^4 - 10016/229*e^3 + 15471/916*e^2 + 23846/229*e - 2587/229, -134/229*e^6 - 873/229*e^5 + 2007/229*e^4 + 16538/229*e^3 + 6286/229*e^2 - 35699/229*e + 554/229, 23/229*e^6 - 221/229*e^5 - 729/229*e^4 + 3881/229*e^3 + 7688/229*e^2 - 10311/229*e - 6948/229, -261/916*e^6 - 957/916*e^5 + 1070/229*e^4 + 5082/229*e^3 + 2277/916*e^2 - 15321/229*e - 1317/229, -149/458*e^6 + 675/458*e^5 + 1749/229*e^4 - 6403/229*e^3 - 24127/458*e^2 + 22561/229*e + 11394/229, 92/229*e^6 + 293/458*e^5 - 3313/458*e^4 - 3254/229*e^3 + 3959/229*e^2 + 10715/458*e - 10159/229, 257/458*e^6 - 279/458*e^5 - 2445/229*e^4 + 2213/229*e^3 + 17673/458*e^2 - 13206/229*e - 4050/229, 202/229*e^6 + 359/229*e^5 - 3316/229*e^4 - 7981/229*e^3 + 1957/229*e^2 + 13757/229*e + 5946/229, 29/458*e^6 - 199/458*e^5 - 365/229*e^4 + 2153/229*e^3 + 7075/458*e^2 - 10488/229*e - 5814/229, -455/916*e^6 + 469/916*e^5 + 1975/229*e^4 - 1693/229*e^3 - 19657/916*e^2 + 12092/229*e + 789/229, -219/458*e^6 + 113/458*e^5 + 2022/229*e^4 + 87/229*e^3 - 13235/458*e^2 - 987/229*e + 2054/229, -115/458*e^6 - 727/458*e^5 + 563/229*e^4 + 6900/229*e^3 + 14459/458*e^2 - 12122/229*e - 5530/229, -213/229*e^6 - 875/458*e^5 + 7857/458*e^4 + 9530/229*e^3 - 8581/229*e^2 - 45201/458*e + 7901/229, -66/229*e^6 + 445/229*e^5 + 1614/229*e^4 - 7652/229*e^3 - 12264/229*e^2 + 18158/229*e - 274/229, -367/916*e^6 - 735/916*e^5 + 1666/229*e^4 + 3453/229*e^3 - 12465/916*e^2 - 1823/229*e + 3323/229, -27/458*e^6 - 99/458*e^5 + 403/229*e^4 + 1162/229*e^3 - 5829/458*e^2 - 5831/229*e - 1378/229, 83/229*e^6 + 457/229*e^5 - 1426/229*e^4 - 9273/229*e^3 + 642/229*e^2 + 26393/229*e - 6574/229, -181/458*e^6 - 511/458*e^5 + 1599/229*e^4 + 5364/229*e^3 - 5591/458*e^2 - 11974/229*e + 5096/229, -155/229*e^6 - 263/229*e^5 + 2812/229*e^4 + 5776/229*e^3 - 4965/229*e^2 - 10394/229*e - 5050/229, 85/229*e^6 + 617/229*e^5 - 1350/229*e^4 - 11345/229*e^3 - 3608/229*e^2 + 22380/229*e - 2638/229, 277/458*e^6 - 53/458*e^5 - 2752/229*e^4 - 132/229*e^3 + 20973/458*e^2 - 4188/229*e - 3148/229, 553/458*e^6 + 1875/458*e^5 - 4836/229*e^4 - 18982/229*e^3 + 8805/458*e^2 + 42950/229*e - 6364/229, 135/458*e^6 - 96/229*e^5 - 2885/458*e^4 + 1060/229*e^3 + 13573/458*e^2 - 543/458*e + 2081/229, -125/229*e^6 - 535/458*e^5 + 4469/458*e^4 + 5840/229*e^3 - 3908/229*e^2 - 25991/458*e - 2115/229, 60/229*e^6 - 238/229*e^5 - 1384/229*e^4 + 4250/229*e^3 + 8984/229*e^2 - 13218/229*e - 5122/229, 273/458*e^6 + 543/458*e^5 - 2370/229*e^4 - 6075/229*e^3 + 7031/458*e^2 + 13794/229*e + 3908/229, -599/916*e^6 - 3723/916*e^5 + 2210/229*e^4 + 17741/229*e^3 + 28947/916*e^2 - 36815/229*e - 5023/229, 125/458*e^6 + 153/458*e^5 - 1060/229*e^4 - 1546/229*e^3 + 2305/458*e^2 - 1689/229*e + 5294/229, -67/458*e^6 + 68/229*e^5 + 1347/458*e^4 - 789/229*e^3 - 5101/458*e^2 + 585/458*e - 4327/229, -549/458*e^6 - 2013/458*e^5 + 4912/229*e^4 + 20345/229*e^3 - 11809/458*e^2 - 48795/229*e + 10758/229, -773/916*e^6 + 219/916*e^5 + 3763/229*e^4 - 168/229*e^3 - 52891/916*e^2 + 7015/229*e + 5091/229, -18/229*e^6 - 295/229*e^5 + 232/229*e^4 + 5366/229*e^3 + 2297/229*e^2 - 10141/229*e + 3506/229, -22/229*e^6 + 301/229*e^5 + 538/229*e^4 - 5833/229*e^3 - 4775/229*e^2 + 19411/229*e + 1130/229, -27/229*e^6 - 328/229*e^5 + 348/229*e^4 + 6217/229*e^3 + 2644/229*e^2 - 14410/229*e + 1824/229, -215/916*e^6 + 1349/916*e^5 + 1278/229*e^4 - 5458/229*e^3 - 40513/916*e^2 + 11240/229*e + 6659/229, -197/458*e^6 + 593/229*e^5 + 4193/458*e^4 - 10393/229*e^3 - 26551/458*e^2 + 60139/458*e - 4465/229, 167/458*e^6 - 151/458*e^5 - 1407/229*e^4 + 1201/229*e^3 + 5571/458*e^2 - 11651/229*e + 822/229, -208/229*e^6 - 839/229*e^5 + 3317/229*e^4 + 16258/229*e^3 + 3236/229*e^2 - 29427/229*e - 5388/229, -345/458*e^6 - 349/458*e^5 + 3063/229*e^4 + 3983/229*e^3 - 11125/458*e^2 - 871/229*e - 1476/229, 159/458*e^6 + 583/458*e^5 - 1559/229*e^4 - 5647/229*e^3 + 4709/458*e^2 + 13550/229*e + 5774/229, -17/458*e^6 + 7/229*e^5 + 499/458*e^4 + 333/229*e^3 - 4637/458*e^2 - 14323/458*e + 447/229, -25/458*e^6 - 397/458*e^5 - 246/229*e^4 + 3561/229*e^3 + 18317/458*e^2 - 3830/229*e - 12234/229, -177/458*e^6 - 649/458*e^5 + 1446/229*e^4 + 6727/229*e^3 + 1023/458*e^2 - 15987/229*e - 7914/229, 713/916*e^6 + 477/916*e^5 - 3417/229*e^4 - 3070/229*e^3 + 42991/916*e^2 + 984/229*e - 8505/229, 611/916*e^6 + 1935/916*e^5 - 2554/229*e^4 - 9170/229*e^3 - 1319/916*e^2 + 13048/229*e + 1767/229, -267/458*e^6 - 604/229*e^5 + 4739/458*e^4 + 11669/229*e^3 - 3293/458*e^2 - 51535/458*e + 5889/229, -146/229*e^6 - 688/229*e^5 + 2238/229*e^4 + 12940/229*e^3 + 4535/229*e^2 - 20781/229*e - 2910/229, 233/916*e^6 + 549/916*e^5 - 1336/229*e^4 - 2868/229*e^3 + 25163/916*e^2 + 10703/229*e - 5131/229, -407/458*e^6 - 729/458*e^5 + 3717/229*e^4 + 7932/229*e^3 - 14485/458*e^2 - 15728/229*e + 2552/229]
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^3 + 2*w^2 + 5*w - 3])] = 1

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