/*
  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([41, 13, -12, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([19,19,-w + 2])

primes_array = [
[9, 3, -w^3 + 3*w^2 + 5*w - 15],\
[9, 3, -w^3 + 8*w + 8],\
[16, 2, 2],\
[19, 19, w + 1],\
[19, 19, -w^2 + 6],\
[19, 19, -w^2 + 2*w + 5],\
[19, 19, -w + 2],\
[25, 5, 2*w^2 - 2*w - 13],\
[29, 29, -w^2 + 9],\
[29, 29, -w^2 + 2*w + 6],\
[29, 29, w^2 - 7],\
[29, 29, -w^2 + 2*w + 8],\
[31, 31, -2*w^2 + w + 12],\
[31, 31, 2*w^2 - 3*w - 11],\
[41, 41, -w],\
[41, 41, -w + 1],\
[49, 7, w^3 + 2*w^2 - 10*w - 20],\
[49, 7, w^3 - 5*w^2 - 3*w + 27],\
[61, 61, 2*w^2 - 3*w - 14],\
[61, 61, 2*w^2 - w - 15],\
[71, 71, -w^3 + w^2 + 7*w - 5],\
[71, 71, w^3 - 2*w^2 - 6*w + 2],\
[79, 79, w^3 - 2*w^2 - 6*w + 4],\
[79, 79, 3*w^2 - 2*w - 18],\
[89, 89, 2*w^3 - 6*w^2 - 11*w + 33],\
[89, 89, -4*w^2 + 3*w + 25],\
[101, 101, w^3 + w^2 - 9*w - 12],\
[101, 101, w^3 - 4*w^2 - 4*w + 19],\
[109, 109, -w^3 + 3*w^2 + 6*w - 19],\
[109, 109, -2*w^2 + w + 18],\
[121, 11, -3*w^2 + 3*w + 19],\
[121, 11, 3*w^2 - 3*w - 20],\
[131, 131, 2*w^2 - 3*w - 15],\
[131, 131, 2*w^2 - w - 16],\
[139, 139, 3*w^2 - 4*w - 21],\
[139, 139, -w^3 - w^2 + 7*w + 13],\
[151, 151, 4*w^2 - 3*w - 27],\
[151, 151, 2*w^3 - w^2 - 13*w - 8],\
[151, 151, w^3 + 3*w^2 - 13*w - 27],\
[151, 151, 4*w^2 - 5*w - 26],\
[179, 179, w^3 - 3*w^2 - 5*w + 11],\
[179, 179, 3*w^3 - 11*w^2 - 14*w + 61],\
[179, 179, 2*w^3 - 2*w^2 - 12*w + 3],\
[179, 179, w^3 - 8*w - 4],\
[181, 181, -w - 4],\
[181, 181, w^3 - 5*w^2 - 3*w + 25],\
[181, 181, w^3 + 2*w^2 - 10*w - 18],\
[181, 181, w - 5],\
[229, 229, w^2 - 2*w - 11],\
[229, 229, w^2 - 12],\
[239, 239, 6*w^2 - 7*w - 42],\
[239, 239, 2*w^3 - 2*w^2 - 14*w - 3],\
[241, 241, w^3 - 4*w^2 - 4*w + 18],\
[241, 241, 3*w^2 - 2*w - 16],\
[269, 269, 3*w^2 - 4*w - 22],\
[269, 269, -w^3 + 6*w + 8],\
[281, 281, w^3 - w^2 - 9*w + 4],\
[281, 281, 2*w^3 - 9*w^2 - 8*w + 49],\
[311, 311, -2*w^3 - w^2 + 17*w + 19],\
[311, 311, 2*w^3 - 7*w^2 - 9*w + 33],\
[331, 331, w^3 + 2*w^2 - 9*w - 21],\
[331, 331, w^3 - 5*w^2 - 2*w + 27],\
[349, 349, 2*w^3 - w^2 - 15*w - 4],\
[349, 349, -2*w^3 + 5*w^2 + 11*w - 18],\
[359, 359, -w^3 + 6*w^2 - 31],\
[359, 359, -w^3 - 3*w^2 + 9*w + 26],\
[379, 379, 2*w^3 - 5*w^2 - 11*w + 20],\
[379, 379, 2*w^3 - 14*w - 11],\
[401, 401, w^3 - 3*w^2 - 4*w + 16],\
[401, 401, -2*w^3 + 4*w^2 + 11*w - 16],\
[401, 401, 2*w^3 - 2*w^2 - 13*w - 3],\
[401, 401, w^3 - 7*w - 10],\
[409, 409, w^3 - 4*w^2 - 4*w + 17],\
[409, 409, 2*w^3 - 6*w^2 - 9*w + 22],\
[409, 409, -2*w^3 + 15*w + 9],\
[409, 409, -w^3 + 3*w^2 + 6*w - 12],\
[419, 419, -w^3 + 5*w^2 + 3*w - 24],\
[419, 419, w^3 + 2*w^2 - 10*w - 17],\
[421, 421, w^3 + 3*w^2 - 12*w - 25],\
[421, 421, -w^3 - w^2 + 9*w + 7],\
[431, 431, -w^3 - 2*w^2 + 12*w + 20],\
[431, 431, w^3 + 3*w^2 - 10*w - 28],\
[431, 431, -w^3 + 6*w^2 + w - 34],\
[431, 431, -w^3 + 5*w^2 + 5*w - 29],\
[439, 439, w^3 - 7*w^2 - 2*w + 39],\
[439, 439, w^3 + 4*w^2 - 13*w - 31],\
[449, 449, -w^3 - 4*w^2 + 13*w + 34],\
[449, 449, 6*w^2 - 5*w - 36],\
[461, 461, -w^3 + 5*w^2 + w - 25],\
[461, 461, 2*w^3 - 15*w - 12],\
[461, 461, -2*w^3 + 6*w^2 + 9*w - 25],\
[461, 461, w^3 + 2*w^2 - 8*w - 20],\
[479, 479, -w^3 - 4*w^2 + 12*w + 31],\
[479, 479, 2*w^3 - 15*w - 16],\
[479, 479, -2*w^3 + 6*w^2 + 9*w - 29],\
[479, 479, w^3 - 7*w^2 - w + 38],\
[491, 491, w^2 - 3*w - 7],\
[491, 491, -2*w^3 + 3*w^2 + 11*w - 2],\
[491, 491, 4*w^2 - 2*w - 29],\
[491, 491, w^2 + w - 9],\
[499, 499, 5*w^2 - 6*w - 33],\
[499, 499, 5*w^2 - 4*w - 34],\
[509, 509, 2*w - 3],\
[509, 509, -2*w - 1],\
[541, 541, -w^3 - 4*w^2 + 12*w + 29],\
[541, 541, -w^3 + 7*w^2 + w - 36],\
[599, 599, -w^3 - w^2 + 8*w + 7],\
[599, 599, w^3 - 4*w^2 - 3*w + 13],\
[619, 619, w^2 - 3*w - 6],\
[619, 619, w^2 + w - 8],\
[641, 641, -2*w^3 + 16*w + 11],\
[641, 641, -2*w^3 + 6*w^2 + 10*w - 25],\
[659, 659, 2*w^3 + w^2 - 16*w - 16],\
[659, 659, 2*w^3 - 7*w^2 - 8*w + 29],\
[691, 691, -w^3 + 5*w^2 + 3*w - 23],\
[691, 691, -w^3 + 3*w^2 + 6*w - 11],\
[701, 701, w^3 - w^2 - 9*w + 3],\
[701, 701, 2*w^3 - w^2 - 14*w - 5],\
[709, 709, 2*w^3 - 3*w^2 - 11*w + 6],\
[719, 719, w^2 - 2*w - 12],\
[719, 719, -w^2 + 13],\
[739, 739, -2*w^3 + 8*w^2 + 7*w - 36],\
[739, 739, w^2 + 2*w - 13],\
[751, 751, -2*w^3 + 5*w^2 + 10*w - 20],\
[751, 751, 2*w^3 - w^2 - 14*w - 7],\
[761, 761, w^3 + 4*w^2 - 12*w - 32],\
[761, 761, -w^3 + 7*w^2 + w - 39],\
[769, 769, -2*w^3 - 4*w^2 + 23*w + 45],\
[769, 769, 2*w^3 - 5*w^2 - 9*w + 21],\
[769, 769, 2*w^3 + 2*w^2 - 18*w - 31],\
[769, 769, 2*w^3 - 10*w^2 - 9*w + 62],\
[811, 811, -w^3 + 10*w + 5],\
[811, 811, -5*w^2 + 8*w + 30],\
[811, 811, w^3 - 8*w^2 + 2*w + 43],\
[811, 811, 2*w^3 - 2*w^2 - 13*w + 2],\
[829, 829, -2*w^3 - 2*w^2 + 18*w + 25],\
[829, 829, -2*w^3 + 8*w^2 + 8*w - 39],\
[859, 859, -w^3 - 4*w^2 + 12*w + 33],\
[859, 859, -w^3 + 7*w^2 + w - 40],\
[919, 919, w^3 - 4*w^2 - 3*w + 24],\
[919, 919, -w^3 + 5*w^2 + w - 26],\
[929, 929, 5*w^2 - 7*w - 28],\
[929, 929, -w^3 + 2*w^2 + 6*w - 13],\
[929, 929, w^3 - w^2 - 7*w - 6],\
[929, 929, -2*w^3 + 2*w^2 + 14*w - 5],\
[941, 941, -2*w^3 + 3*w^2 + 11*w - 1],\
[941, 941, 2*w^3 - 3*w^2 - 11*w + 11],\
[961, 31, 5*w^2 - 5*w - 33],\
[971, 971, -w^3 - 3*w^2 + 11*w + 22],\
[971, 971, 7*w^2 - 5*w - 45],\
[971, 971, 7*w^2 - 9*w - 43],\
[971, 971, w^3 - 6*w^2 - 2*w + 29],\
[991, 991, w^3 - 3*w^2 - 3*w + 15],\
[991, 991, -w^3 + 5*w^2 + 2*w - 29]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 15*x^5 + 79*x^4 - 151*x^3 - 46*x^2 + 453*x - 364
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 9/29*e^5 - 98/29*e^4 + 321/29*e^3 - 136/29*e^2 - 30*e + 858/29, -14/29*e^5 + 175/29*e^4 - 683/29*e^3 + 537/29*e^2 + 60*e - 2369/29, -11/29*e^5 + 123/29*e^4 - 402/29*e^3 + 134/29*e^2 + 36*e - 923/29, 5, -19/29*e^5 + 223/29*e^4 - 813/29*e^3 + 561/29*e^2 + 70*e - 2691/29, -1, 1/29*e^5 - 27/29*e^4 + 171/29*e^3 - 260/29*e^2 - 12*e + 685/29, 20/29*e^5 - 221/29*e^4 + 723/29*e^3 - 299/29*e^2 - 63*e + 1955/29, -2/29*e^5 + 25/29*e^4 - 81/29*e^3 - 2/29*e^2 + 7*e + 22/29, 24/29*e^5 - 300/29*e^4 + 1175/29*e^3 - 933/29*e^2 - 104*e + 4144/29, -25/29*e^5 + 298/29*e^4 - 1085/29*e^3 + 671/29*e^2 + 96*e - 3292/29, 11/29*e^5 - 181/29*e^4 + 895/29*e^3 - 1033/29*e^2 - 78*e + 3678/29, 9/29*e^5 - 98/29*e^4 + 350/29*e^3 - 310/29*e^2 - 27*e + 1235/29, -20/29*e^5 + 250/29*e^4 - 955/29*e^3 + 647/29*e^2 + 86*e - 2970/29, -2/29*e^5 + 54/29*e^4 - 342/29*e^3 + 491/29*e^2 + 33*e - 1631/29, -27/29*e^5 + 265/29*e^4 - 673/29*e^3 - 230/29*e^2 + 64*e - 834/29, 17/29*e^5 - 169/29*e^4 + 500/29*e^3 - 186/29*e^2 - 46*e + 1698/29, -4/29*e^5 + 50/29*e^4 - 191/29*e^3 + 112/29*e^2 + 18*e - 246/29, e^4 - 8*e^3 + 13*e^2 + 19*e - 42, 12/29*e^5 - 150/29*e^4 + 573/29*e^3 - 423/29*e^2 - 48*e + 2014/29, 5/29*e^5 - 135/29*e^4 + 855/29*e^3 - 1300/29*e^2 - 70*e + 4034/29, 42/29*e^5 - 467/29*e^4 + 1527/29*e^3 - 538/29*e^2 - 144*e + 4120/29, 14/29*e^5 - 204/29*e^4 + 944/29*e^3 - 1088/29*e^2 - 76*e + 3935/29, -21/29*e^5 + 248/29*e^4 - 952/29*e^3 + 878/29*e^2 + 78*e - 3684/29, -56/29*e^5 + 671/29*e^4 - 2500/29*e^3 + 1800/29*e^2 + 215*e - 8258/29, -7/29*e^5 + 131/29*e^4 - 733/29*e^3 + 1037/29*e^2 + 64*e - 3258/29, -10/29*e^5 + 96/29*e^4 - 231/29*e^3 - 126/29*e^2 + 25*e - 470/29, -28/29*e^5 + 321/29*e^4 - 1105/29*e^3 + 610/29*e^2 + 93*e - 3375/29, 26/29*e^5 - 296/29*e^4 + 995/29*e^3 - 467/29*e^2 - 84*e + 2817/29, 59/29*e^5 - 665/29*e^4 + 2259/29*e^3 - 1159/29*e^2 - 198*e + 6862/29, -14/29*e^5 + 117/29*e^4 - 248/29*e^3 - 72/29*e^2 + 24*e - 774/29, 60/29*e^5 - 721/29*e^4 + 2720/29*e^3 - 2057/29*e^2 - 236*e + 9316/29, -45/29*e^5 + 548/29*e^4 - 2098/29*e^3 + 1666/29*e^2 + 182*e - 7538/29, -44/29*e^5 + 550/29*e^4 - 2130/29*e^3 + 1609/29*e^2 + 182*e - 6911/29, 22/29*e^5 - 304/29*e^4 + 1384/29*e^3 - 1602/29*e^2 - 119*e + 5790/29, -75/29*e^5 + 894/29*e^4 - 3313/29*e^3 + 2332/29*e^2 + 284*e - 10514/29, 39/29*e^5 - 531/29*e^4 + 2261/29*e^3 - 2078/29*e^2 - 200*e + 8358/29, 23/29*e^5 - 244/29*e^4 + 743/29*e^3 - 151/29*e^2 - 67*e + 1487/29, 9/29*e^5 - 156/29*e^4 + 843/29*e^3 - 1209/29*e^2 - 63*e + 3584/29, 2*e^4 - 19*e^3 + 41*e^2 + 43*e - 117, 42/29*e^5 - 467/29*e^4 + 1527/29*e^3 - 567/29*e^2 - 140*e + 4207/29, -6/29*e^5 + 133/29*e^4 - 823/29*e^3 + 1299/29*e^2 + 67*e - 3704/29, -4/29*e^5 + 50/29*e^4 - 191/29*e^3 + 170/29*e^2 + 10*e - 333/29, -45/29*e^5 + 490/29*e^4 - 1663/29*e^3 + 1028/29*e^2 + 145*e - 5363/29, 20/29*e^5 - 105/29*e^4 - 292/29*e^3 + 1644/29*e^2 + 18*e - 3497/29, 7/29*e^5 - 102/29*e^4 + 501/29*e^3 - 689/29*e^2 - 36*e + 2098/29, 89/29*e^5 - 1069/29*e^4 + 3996/29*e^3 - 2927/29*e^2 - 340*e + 13318/29, 49/29*e^5 - 598/29*e^4 + 2231/29*e^3 - 1546/29*e^2 - 190*e + 7233/29, 69/29*e^5 - 819/29*e^4 + 3012/29*e^3 - 2019/29*e^2 - 268*e + 9768/29, -46/29*e^5 + 604/29*e^4 - 2588/29*e^3 + 2767/29*e^2 + 210*e - 10108/29, 23/29*e^5 - 360/29*e^4 + 1700/29*e^3 - 1862/29*e^2 - 144*e + 7084/29, -e^5 + 11*e^4 - 38*e^3 + 24*e^2 + 100*e - 126, 16/29*e^5 - 84/29*e^4 - 135/29*e^3 + 799/29*e^2 + 8*e - 814/29, -51/29*e^5 + 623/29*e^4 - 2399/29*e^3 + 1892/29*e^2 + 204*e - 7907/29, -7/29*e^5 - 43/29*e^4 + 746/29*e^3 - 1631/29*e^2 - 56*e + 3934/29, 20/29*e^5 - 250/29*e^4 + 955/29*e^3 - 589/29*e^2 - 93*e + 3144/29, 4/29*e^5 - 50/29*e^4 + 278/29*e^3 - 634/29*e^2 - 12*e + 1957/29, 26/29*e^5 - 238/29*e^4 + 560/29*e^3 + 229/29*e^2 - 54*e + 700/29, -49/29*e^5 + 656/29*e^4 - 2898/29*e^3 + 3315/29*e^2 + 232*e - 11757/29, -43/29*e^5 + 436/29*e^4 - 1234/29*e^3 + 102/29*e^2 + 105*e - 2282/29, -41/29*e^5 + 469/29*e^4 - 1588/29*e^3 + 771/29*e^2 + 132*e - 4450/29, -27/29*e^5 + 410/29*e^4 - 1978/29*e^3 + 2438/29*e^2 + 157*e - 8142/29, -56/29*e^5 + 729/29*e^4 - 2993/29*e^3 + 2670/29*e^2 + 259*e - 11129/29, -22/29*e^5 + 362/29*e^4 - 1819/29*e^3 + 2182/29*e^2 + 162*e - 7588/29, 111/29*e^5 - 1286/29*e^4 + 4539/29*e^3 - 2528/29*e^2 - 416*e + 13975/29, 35/29*e^5 - 394/29*e^4 + 1403/29*e^3 - 1096/29*e^2 - 110*e + 5299/29, 24/29*e^5 - 213/29*e^4 + 392/29*e^3 + 633/29*e^2 - 50*e - 32/29, -129/29*e^5 + 1598/29*e^4 - 6254/29*e^3 + 5207/29*e^2 + 535*e - 22042/29, -5/29*e^5 - 10/29*e^4 + 421/29*e^3 - 1165/29*e^2 - 32*e + 3216/29, 8/29*e^5 - 303/29*e^4 + 2180/29*e^3 - 3791/29*e^2 - 174*e + 11222/29, 123/29*e^5 - 1436/29*e^4 + 5141/29*e^3 - 3241/29*e^2 - 442*e + 15931/29, -5/29*e^5 + 77/29*e^4 - 362/29*e^3 + 343/29*e^2 + 31*e - 1250/29, 111/29*e^5 - 1315/29*e^4 + 4800/29*e^3 - 3224/29*e^2 - 412*e + 15193/29, -39/29*e^5 + 444/29*e^4 - 1594/29*e^3 + 1150/29*e^2 + 140*e - 5661/29, -81/29*e^5 + 969/29*e^4 - 3585/29*e^3 + 2413/29*e^2 + 313*e - 11173/29, 92/29*e^5 - 1005/29*e^4 + 3204/29*e^3 - 923/29*e^2 - 301*e + 8065/29, -17/29*e^5 + 53/29*e^4 + 573/29*e^3 - 2105/29*e^2 - 33*e + 5117/29, -15/29*e^5 + 202/29*e^4 - 883/29*e^3 + 971/29*e^2 + 73*e - 3054/29, -46/29*e^5 + 691/29*e^4 - 3284/29*e^3 + 3869/29*e^2 + 274*e - 13762/29, 45/29*e^5 - 374/29*e^4 + 590/29*e^3 + 1147/29*e^2 - 51*e - 640/29, -10/29*e^5 - 20/29*e^4 + 755/29*e^3 - 1953/29*e^2 - 50*e + 4518/29, -65/29*e^5 + 682/29*e^4 - 2038/29*e^3 + 399/29*e^2 + 174*e - 4418/29, 2/29*e^5 + 4/29*e^4 - 209/29*e^3 + 727/29*e^2 + 8*e - 1907/29, -77/29*e^5 + 977/29*e^4 - 3887/29*e^3 + 3345/29*e^2 + 321*e - 13885/29, 37/29*e^5 - 535/29*e^4 + 2441/29*e^3 - 2689/29*e^2 - 209*e + 10294/29, 17/29*e^5 - 169/29*e^4 + 384/29*e^3 + 452/29*e^2 - 35*e - 854/29, 30/29*e^5 - 491/29*e^4 + 2346/29*e^3 - 2348/29*e^2 - 213*e + 8747/29, -54/29*e^5 + 762/29*e^4 - 3347/29*e^3 + 3368/29*e^2 + 280*e - 13094/29, 2/29*e^5 + 33/29*e^4 - 441/29*e^3 + 1046/29*e^2 + 38*e - 3038/29, 45/29*e^5 - 548/29*e^4 + 2040/29*e^3 - 1289/29*e^2 - 180*e + 6030/29, 65/29*e^5 - 711/29*e^4 + 2299/29*e^3 - 805/29*e^2 - 218*e + 5897/29, 89/29*e^5 - 1127/29*e^4 + 4518/29*e^3 - 3913/29*e^2 - 393*e + 16856/29, -122/29*e^5 + 1380/29*e^4 - 4709/29*e^3 + 2488/29*e^2 + 408*e - 14144/29, -40/29*e^5 + 355/29*e^4 - 634/29*e^3 - 1171/29*e^2 + 74*e + 962/29, -90/29*e^5 + 980/29*e^4 - 3297/29*e^3 + 1940/29*e^2 + 289*e - 10958/29, -14/29*e^5 + 146/29*e^4 - 422/29*e^3 + 189/29*e^2 + 17*e - 1325/29, 44/29*e^5 - 550/29*e^4 + 2130/29*e^3 - 1522/29*e^2 - 194*e + 6795/29, -7/29*e^5 + 15/29*e^4 + 282/29*e^3 - 906/29*e^2 - 14*e + 1759/29, -14/29*e^5 + 146/29*e^4 - 509/29*e^3 + 363/29*e^2 + 52*e - 1528/29, 4/29*e^5 - 137/29*e^4 + 974/29*e^3 - 1649/29*e^2 - 79*e + 4973/29, -1/29*e^5 + 114/29*e^4 - 954/29*e^3 + 1855/29*e^2 + 76*e - 5354/29, -26/29*e^5 + 267/29*e^4 - 734/29*e^3 - 84/29*e^2 + 73*e - 1396/29, -59/29*e^5 + 810/29*e^4 - 3506/29*e^3 + 3421/29*e^2 + 298*e - 12894/29, 13/29*e^5 - 206/29*e^4 + 1063/29*e^3 - 1466/29*e^2 - 87*e + 4990/29, -164/29*e^5 + 1992/29*e^4 - 7657/29*e^3 + 6216/29*e^2 + 654*e - 26674/29, 56/29*e^5 - 613/29*e^4 + 1891/29*e^3 - 263/29*e^2 - 173*e + 3589/29, -70/29*e^5 + 730/29*e^4 - 2081/29*e^3 - 99/29*e^2 + 206*e - 4276/29, 59/29*e^5 - 607/29*e^4 + 1824/29*e^3 - 405/29*e^2 - 183*e + 4919/29, 31/29*e^5 - 402/29*e^4 + 1734/29*e^3 - 1970/29*e^2 - 141*e + 6880/29, -9/29*e^5 + 127/29*e^4 - 553/29*e^3 + 658/29*e^2 + 33*e - 2482/29, -84/29*e^5 + 760/29*e^4 - 1604/29*e^3 - 1389/29*e^2 + 152*e - 700/29, -57/29*e^5 + 814/29*e^4 - 3686/29*e^3 + 4061/29*e^2 + 306*e - 14540/29, -1/29*e^5 - 31/29*e^4 + 380/29*e^3 - 813/29*e^2 - 39*e + 1664/29, 82/29*e^5 - 967/29*e^4 + 3640/29*e^3 - 2905/29*e^2 - 310*e + 11974/29, 69/29*e^5 - 761/29*e^4 + 2519/29*e^3 - 1149/29*e^2 - 229*e + 8231/29, 142/29*e^5 - 1775/29*e^4 + 6969/29*e^3 - 5629/29*e^2 - 608*e + 24393/29, -46/29*e^5 + 633/29*e^4 - 2617/29*e^3 + 1984/29*e^2 + 247*e - 9006/29, 65/29*e^5 - 769/29*e^4 + 2821/29*e^3 - 1994/29*e^2 - 244*e + 10189/29, -32/29*e^5 + 342/29*e^4 - 1035/29*e^3 + 287/29*e^2 + 86*e - 3360/29, 82/29*e^5 - 1170/29*e^4 + 5351/29*e^3 - 6095/29*e^2 - 438*e + 21312/29, -187/29*e^5 + 2323/29*e^4 - 9096/29*e^3 + 7440/29*e^2 + 792*e - 32366/29, 38/29*e^5 - 388/29*e^4 + 1104/29*e^3 - 223/29*e^2 - 88*e + 3468/29, -38/29*e^5 + 475/29*e^4 - 1945/29*e^3 + 2050/29*e^2 + 152*e - 7673/29, 42/29*e^5 - 612/29*e^4 + 2861/29*e^3 - 3293/29*e^2 - 247*e + 12095/29, -54/29*e^5 + 762/29*e^4 - 3347/29*e^3 + 3194/29*e^2 + 300*e - 12282/29, -50/29*e^5 + 770/29*e^4 - 3707/29*e^3 + 4242/29*e^2 + 329*e - 15371/29, 180/29*e^5 - 2250/29*e^4 + 8798/29*e^3 - 7070/29*e^2 - 764*e + 30732/29, -155/29*e^5 + 1865/29*e^4 - 6988/29*e^3 + 5152/29*e^2 + 604*e - 23844/29, 104/29*e^5 - 1300/29*e^4 + 5111/29*e^3 - 4159/29*e^2 - 453*e + 18837/29, 13/29*e^5 - 61/29*e^4 - 329/29*e^3 + 1463/29*e^2 + 32*e - 3449/29, 44/29*e^5 - 637/29*e^4 + 2942/29*e^3 - 3291/29*e^2 - 256*e + 12218/29, 10/29*e^5 - 415/29*e^4 + 3015/29*e^3 - 5181/29*e^2 - 251*e + 16072/29, 84/29*e^5 - 963/29*e^4 + 3460/29*e^3 - 2352/29*e^2 - 314*e + 12068/29, -68/29*e^5 + 879/29*e^4 - 3537/29*e^3 + 2977/29*e^2 + 309*e - 12650/29, 18/29*e^5 - 283/29*e^4 + 1338/29*e^3 - 1316/29*e^2 - 130*e + 5370/29, 6/29*e^5 - 220/29*e^4 + 1606/29*e^3 - 2865/29*e^2 - 117*e + 7474/29, -72/29*e^5 + 784/29*e^4 - 2597/29*e^3 + 1262/29*e^2 + 241*e - 7850/29, 140/29*e^5 - 1692/29*e^4 + 6279/29*e^3 - 4297/29*e^2 - 536*e + 19746/29, -20/29*e^5 + 250/29*e^4 - 1129/29*e^3 + 1546/29*e^2 + 99*e - 6102/29, -117/29*e^5 + 1245/29*e^4 - 3825/29*e^3 + 840/29*e^2 + 362*e - 8776/29, -45/29*e^5 + 519/29*e^4 - 1924/29*e^3 + 1695/29*e^2 + 155*e - 7538/29, 49/29*e^5 - 598/29*e^4 + 2376/29*e^3 - 2300/29*e^2 - 195*e + 9176/29, 131/29*e^5 - 1797/29*e^4 + 7785/29*e^3 - 7757/29*e^2 - 651*e + 29154/29, e^5 - 14*e^4 + 62*e^3 - 66*e^2 - 156*e + 266, 17/29*e^5 - 24/29*e^4 - 834/29*e^3 + 2540/29*e^2 + 64*e - 6074/29, 10/29*e^5 + 20/29*e^4 - 813/29*e^3 + 2156/29*e^2 + 68*e - 5736/29, -66/29*e^5 + 767/29*e^4 - 2789/29*e^3 + 1935/29*e^2 + 245*e - 9163/29, 43/29*e^5 - 581/29*e^4 + 2510/29*e^3 - 2567/29*e^2 - 222*e + 10895/29, -14/29*e^5 + 175/29*e^4 - 654/29*e^3 + 537/29*e^2 + 33*e - 1818/29, 21/29*e^5 - 74/29*e^4 - 672/29*e^3 + 2544/29*e^2 + 51*e - 5944/29, -19/29*e^5 + 223/29*e^4 - 668/29*e^3 - 135/29*e^2 + 57*e + 354/29, 11/29*e^5 - 239/29*e^4 + 1243/29*e^3 - 1149/29*e^2 - 113*e + 3359/29, 122/29*e^5 - 1177/29*e^4 + 2998/29*e^3 + 557/29*e^2 - 268*e + 6024/29]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([19,19,-w + 2])] = 1

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