/* 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. = PolynomialRing(QQ) g = P([1, -4, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([47, 47, w^2 + w - 4]) primes_array = [ [3, 3, w + 1],\ [3, 3, w - 1],\ [7, 7, w^2 - 2],\ [8, 2, 2],\ [11, 11, -w^2 + w + 1],\ [23, 23, -w - 3],\ [29, 29, -w^2 + 2*w + 4],\ [31, 31, 2*w - 3],\ [41, 41, -2*w^2 + 3*w + 6],\ [43, 43, w^2 - 3*w + 3],\ [47, 47, w^2 + w - 4],\ [49, 7, 2*w^2 - 3*w - 3],\ [53, 53, w^2 - 3*w - 2],\ [59, 59, 2*w^2 - w - 5],\ [59, 59, w^2 - w - 7],\ [59, 59, -w^2 - w + 7],\ [67, 67, 2*w^2 - 3*w - 7],\ [73, 73, -w^2 + 4*w - 5],\ [79, 79, w^2 - 8],\ [79, 79, w^2 - 5*w + 5],\ [79, 79, w^2 - 3*w - 3],\ [83, 83, -3*w^2 + w + 9],\ [89, 89, 2*w^2 - w - 2],\ [97, 97, w^2 - 3*w - 6],\ [101, 101, 3*w - 4],\ [103, 103, 3*w - 5],\ [107, 107, -3*w^2 + 10],\ [107, 107, w^2 - 3*w - 5],\ [109, 109, w^2 + 2*w - 4],\ [121, 11, 3*w^2 - 2*w - 9],\ [125, 5, -5],\ [127, 127, w^2 + w - 10],\ [137, 137, 3*w^2 - 3*w - 8],\ [139, 139, -5*w^2 + 3*w + 18],\ [149, 149, 3*w^2 - 4*w - 6],\ [157, 157, w - 6],\ [163, 163, -4*w^2 + 2*w + 13],\ [163, 163, -w^2 - 3],\ [163, 163, 2*w^2 - 4*w - 11],\ [181, 181, 3*w^2 - 11],\ [193, 193, 3*w^2 - 3*w - 7],\ [193, 193, -3*w^2 + 3*w + 16],\ [193, 193, w^2 + 2*w - 7],\ [197, 197, 2*w^2 + w - 8],\ [211, 211, 4*w^2 - 5*w - 10],\ [227, 227, -w - 6],\ [229, 229, w^2 - 4*w - 7],\ [233, 233, 3*w^2 - 5],\ [239, 239, 2*w^2 - 3*w - 13],\ [251, 251, 3*w^2 - 4*w - 3],\ [257, 257, 3*w^2 - w - 6],\ [257, 257, 3*w^2 - 5*w - 9],\ [257, 257, w^2 + 3*w - 5],\ [263, 263, 2*w^2 + w - 11],\ [277, 277, 3*w^2 - 2*w - 6],\ [281, 281, 3*w^2 - 3*w - 5],\ [281, 281, -w^2 - 4],\ [281, 281, 4*w^2 - 3*w - 12],\ [293, 293, 2*w^2 - 5*w - 5],\ [307, 307, 3*w^2 - 2*w - 3],\ [317, 317, 3*w^2 - w - 18],\ [317, 317, -w^2 + 2*w - 5],\ [317, 317, -4*w^2 + 7*w + 4],\ [349, 349, -w^2 + 3*w - 6],\ [353, 353, 3*w^2 - 6*w - 7],\ [353, 353, w^2 - w - 10],\ [353, 353, -5*w - 3],\ [367, 367, -4*w^2 - w + 7],\ [379, 379, 4*w^2 - 3*w - 11],\ [383, 383, 4*w^2 - w - 10],\ [389, 389, w^2 - 5*w - 4],\ [389, 389, -5*w^2 + 7*w + 11],\ [389, 389, -7*w^2 + 4*w + 25],\ [397, 397, -w^2 + w - 5],\ [397, 397, 5*w^2 - 6*w - 22],\ [397, 397, -5*w^2 - w + 11],\ [401, 401, 2*w^2 - w - 14],\ [401, 401, 5*w^2 - 3*w - 16],\ [401, 401, w^2 + 3*w - 8],\ [409, 409, w^2 + 3*w - 9],\ [431, 431, 2*w - 9],\ [433, 433, w^2 - 3*w - 11],\ [439, 439, w^2 - 11],\ [439, 439, 5*w - 6],\ [439, 439, 3*w^2 + 2*w - 9],\ [443, 443, -6*w^2 + 3*w + 20],\ [443, 443, -w^2 - w - 5],\ [443, 443, 2*w^2 - 5*w - 11],\ [461, 461, 3*w^2 - 4*w - 18],\ [463, 463, 3*w^2 - 6*w - 17],\ [463, 463, -4*w^2 - 3*w + 9],\ [463, 463, 3*w^2 - 6*w - 8],\ [467, 467, 2*w^2 - 5*w - 8],\ [487, 487, 2*w^2 + 3*w - 7],\ [499, 499, 5*w^2 - 8*w - 8],\ [503, 503, 3*w^2 + w - 12],\ [509, 509, w^2 - 6*w - 11],\ [523, 523, 3*w^2 - 9*w - 2],\ [529, 23, -w^2 + 4*w - 8],\ [541, 541, 2*w^2 + 2*w - 11],\ [569, 569, 4*w^2 - 3*w - 9],\ [587, 587, -w^2 - 4*w + 13],\ [599, 599, 3*w - 11],\ [601, 601, -3*w^2 + 10*w - 9],\ [607, 607, 4*w^2 - 6*w - 15],\ [613, 613, w - 9],\ [619, 619, 5*w^2 - 2*w - 14],\ [631, 631, 4*w^2 - 5*w - 4],\ [647, 647, 4*w^2 - 4*w - 7],\ [647, 647, w^2 - 12],\ [647, 647, 4*w^2 - w - 7],\ [653, 653, 4*w^2 - 6*w - 17],\ [659, 659, 3*w^2 - 6*w - 10],\ [659, 659, 3*w^2 + w - 15],\ [659, 659, 4*w^2 - 17],\ [661, 661, 2*w^2 - 3*w - 15],\ [661, 661, -5*w^2 + 5*w + 26],\ [661, 661, 5*w^2 - 12*w - 4],\ [673, 673, w^2 + w - 13],\ [677, 677, w^2 - 3*w - 12],\ [683, 683, 5*w^2 - 4*w - 14],\ [709, 709, 4*w^2 - 2*w - 7],\ [733, 733, 3*w^2 - 6*w - 11],\ [739, 739, -2*w - 9],\ [743, 743, 6*w - 7],\ [751, 751, w^2 - 6*w - 9],\ [757, 757, 4*w^2 - 3*w - 5],\ [761, 761, -7*w^2 + 8*w + 31],\ [769, 769, w^2 - 6*w - 6],\ [773, 773, -w - 9],\ [773, 773, w^2 - 4*w - 13],\ [773, 773, 5*w^2 - 18],\ [787, 787, 3*w^2 - 6*w - 14],\ [797, 797, w^2 - 6*w - 8],\ [811, 811, 2*w^2 + 3*w - 10],\ [811, 811, -2*w^2 - 3*w + 16],\ [811, 811, -6*w^2 + 11*w + 6],\ [823, 823, w^2 + 5*w - 7],\ [829, 829, -5*w^2 - 2*w + 14],\ [839, 839, 2*w^2 - 6*w - 9],\ [841, 29, 2*w^2 - 7*w - 5],\ [853, 853, 5*w^2 - 28],\ [857, 857, 7*w^2 - 9*w - 23],\ [877, 877, -8*w^2 + 3*w + 31],\ [881, 881, 6*w^2 - 9*w - 11],\ [907, 907, 4*w^2 - 7*w - 13],\ [911, 911, 2*w^2 + 3*w - 15],\ [911, 911, -w^2 - 7],\ [911, 911, 3*w^2 + 3*w - 10],\ [919, 919, w^2 - 7*w - 4],\ [941, 941, 6*w^2 - 11*w - 12],\ [947, 947, 5*w^2 - w - 11],\ [947, 947, 3*w^2 - 8*w - 6],\ [947, 947, 2*w^2 + 3*w - 12],\ [953, 953, -5*w^2 - 4*w + 11],\ [953, 953, 4*w^2 - w - 25],\ [953, 953, 6*w^2 - 7*w - 15],\ [961, 31, 4*w^2 + 2*w - 13],\ [977, 977, -2*w^2 + 3*w - 6],\ [991, 991, 5*w^2 - 5*w - 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 - 2*x^8 - 15*x^7 + 24*x^6 + 81*x^5 - 86*x^4 - 181*x^3 + 84*x^2 + 122*x - 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/2*e^7 + 1/2*e^6 + 6*e^5 - 4*e^4 - 43/2*e^3 + 15/2*e^2 + 20*e - 4, 1/2*e^7 - 13/2*e^5 - 1/2*e^4 + 24*e^3 + 5/2*e^2 - 20*e + 2, e^2 - e - 3, 1/2*e^8 - 1/2*e^7 - 13/2*e^6 + 5*e^5 + 51/2*e^4 - 29/2*e^3 - 55/2*e^2 + 14*e + 4, 1/2*e^8 - 1/2*e^7 - 6*e^6 + 4*e^5 + 41/2*e^4 - 13/2*e^3 - 13*e^2 + e - 6, -1/2*e^8 + 13/2*e^6 + e^5 - 51/2*e^4 - 6*e^3 + 57/2*e^2 + 5*e - 6, e^3 - e^2 - 5*e + 4, -1/2*e^6 + 1/2*e^5 + 9/2*e^4 - 9/2*e^3 - 10*e^2 + 10*e + 6, 1/2*e^8 - 1/2*e^7 - 6*e^6 + 9/2*e^5 + 22*e^4 - 11*e^3 - 53/2*e^2 + 7*e + 12, 1, -1/2*e^7 + 1/2*e^6 + 15/2*e^5 - 11/2*e^4 - 33*e^3 + 15*e^2 + 36*e - 6, -1/2*e^8 + e^7 + 11/2*e^6 - 10*e^5 - 35/2*e^4 + 30*e^3 + 25/2*e^2 - 29*e + 2, e^8 - e^7 - 13*e^6 + 10*e^5 + 51*e^4 - 28*e^3 - 55*e^2 + 21*e + 8, -1/2*e^5 - 1/2*e^4 + 7/2*e^3 + 9/2*e^2 - e - 6, 1/2*e^8 + e^7 - 15/2*e^6 - 14*e^5 + 67/2*e^4 + 55*e^3 - 81/2*e^2 - 44*e + 10, -1/2*e^7 + 6*e^5 - 41/2*e^3 + 4*e^2 + 15*e - 8, -e^7 + 12*e^5 + 3*e^4 - 42*e^3 - 17*e^2 + 35*e + 12, e^8 + 1/2*e^7 - 27/2*e^6 - 9*e^5 + 53*e^4 + 83/2*e^3 - 101/2*e^2 - 33*e + 6, 2*e^3 - 12*e, e^7 - e^6 - 25/2*e^5 + 17/2*e^4 + 95/2*e^3 - 39/2*e^2 - 48*e + 20, 2*e^7 - e^6 - 25*e^5 + 6*e^4 + 89*e^3 - e^2 - 68*e + 4, -1/2*e^7 + 6*e^5 + 3*e^4 - 39/2*e^3 - 21*e^2 + 10*e + 16, -1/2*e^8 + 13/2*e^6 + e^5 - 51/2*e^4 - 4*e^3 + 55/2*e^2 - 7*e - 2, 3/2*e^7 - 1/2*e^6 - 37/2*e^5 + 1/2*e^4 + 67*e^3 + 12*e^2 - 56*e, -1/2*e^8 + 1/2*e^7 + 11/2*e^6 - 7/2*e^5 - 13*e^4 + 3*e^3 - 16*e^2 + 20, -e^8 - 3/2*e^7 + 29/2*e^6 + 20*e^5 - 60*e^4 - 151/2*e^3 + 117/2*e^2 + 55*e - 10, -1/2*e^8 + e^7 + 11/2*e^6 - 10*e^5 - 33/2*e^4 + 28*e^3 + 11/2*e^2 - 21*e + 8, 1/2*e^8 - 13/2*e^6 - 2*e^5 + 49/2*e^4 + 14*e^3 - 41/2*e^2 - 16*e + 2, 1/2*e^8 - 2*e^7 - 9/2*e^6 + 22*e^5 + 23/2*e^4 - 69*e^3 - 23/2*e^2 + 43*e - 6, -e^7 + 15*e^5 - 63*e^3 + 57*e - 14, e^8 - e^7 - 12*e^6 + 8*e^5 + 42*e^4 - 14*e^3 - 36*e^2 + 9*e + 8, 1/2*e^8 - 5/2*e^7 - 5*e^6 + 30*e^5 + 27/2*e^4 - 215/2*e^3 - 9*e^2 + 104*e, -e^7 + 12*e^5 + 6*e^4 - 42*e^3 - 34*e^2 + 31*e + 12, -1/2*e^8 + 15/2*e^6 + 5/2*e^5 - 36*e^4 - 37/2*e^3 + 53*e^2 + 22*e - 6, -e^8 - e^7 + 13*e^6 + 17*e^5 - 48*e^4 - 76*e^3 + 36*e^2 + 66*e - 4, -1/2*e^8 - 3/2*e^7 + 17/2*e^6 + 20*e^5 - 87/2*e^4 - 155/2*e^3 + 135/2*e^2 + 69*e - 22, e^8 + e^7 - 14*e^6 - 15*e^5 + 57*e^4 + 61*e^3 - 54*e^2 - 47*e, -2*e^8 + e^7 + 26*e^6 - 6*e^5 - 102*e^4 - 2*e^3 + 110*e^2 + 20*e - 16, -e^7 + e^6 + 12*e^5 - 11*e^4 - 41*e^3 + 34*e^2 + 34*e - 26, -1/2*e^7 - 1/2*e^6 + 15/2*e^5 + 9/2*e^4 - 33*e^3 - 12*e^2 + 40*e + 20, -2*e^5 + 3*e^4 + 16*e^3 - 17*e^2 - 30*e + 14, -1/2*e^8 + 13/2*e^6 + 2*e^5 - 45/2*e^4 - 14*e^3 + 17/2*e^2 + 9*e + 10, -e^8 + 5/2*e^7 + 12*e^6 - 27*e^5 - 46*e^4 + 163/2*e^3 + 59*e^2 - 53*e - 10, -1/2*e^7 + e^6 + 6*e^5 - 8*e^4 - 37/2*e^3 + 9*e^2 + 3*e - 2, -1/2*e^8 - 2*e^7 + 17/2*e^6 + 26*e^5 - 81/2*e^4 - 97*e^3 + 89/2*e^2 + 79*e, 5/2*e^7 - e^6 - 31*e^5 + 3*e^4 + 231/2*e^3 + 16*e^2 - 115*e - 12, -e^8 + 1/2*e^7 + 13*e^6 - 4*e^5 - 50*e^4 + 23/2*e^3 + 46*e^2 - 30*e + 2, -e^8 + 3/2*e^7 + 13*e^6 - 37/2*e^5 - 101/2*e^4 + 68*e^3 + 105/2*e^2 - 67*e - 4, e^8 + 3*e^7 - 14*e^6 - 41*e^5 + 55*e^4 + 159*e^3 - 48*e^2 - 132*e + 20, -3/2*e^8 + 7/2*e^7 + 35/2*e^6 - 79/2*e^5 - 60*e^4 + 132*e^3 + 48*e^2 - 112*e + 18, -e^8 + 4*e^7 + 9*e^6 - 45*e^5 - 17*e^4 + 151*e^3 - 19*e^2 - 136*e + 42, -1/2*e^8 - 2*e^7 + 15/2*e^6 + 29*e^5 - 67/2*e^4 - 124*e^3 + 85/2*e^2 + 131*e - 14, 2*e^7 - e^6 - 23*e^5 + 4*e^4 + 79*e^3 + 9*e^2 - 75*e - 16, 1/2*e^8 - e^7 - 13/2*e^6 + 12*e^5 + 57/2*e^4 - 41*e^3 - 93/2*e^2 + 21*e + 14, -1/2*e^8 + 7/2*e^7 + 3*e^6 - 39*e^5 + 5/2*e^4 + 253/2*e^3 - 29*e^2 - 101*e + 40, -1/2*e^8 + 3*e^7 + 9/2*e^6 - 39*e^5 - 13/2*e^4 + 149*e^3 - 39/2*e^2 - 136*e + 42, -1/2*e^8 + e^7 + 9/2*e^6 - 11*e^5 - 13/2*e^4 + 40*e^3 - 43/2*e^2 - 49*e + 34, -e^8 + 2*e^7 + 23/2*e^6 - 43/2*e^5 - 71/2*e^4 + 133/2*e^3 + 13*e^2 - 61*e + 8, -1/2*e^8 - 5/2*e^7 + 8*e^6 + 33*e^5 - 71/2*e^4 - 251/2*e^3 + 36*e^2 + 109*e - 14, -e^7 + e^6 + 13*e^5 - 11*e^4 - 50*e^3 + 38*e^2 + 46*e - 36, 1/2*e^8 + 1/2*e^7 - 8*e^6 - 6*e^5 + 83/2*e^4 + 43/2*e^3 - 78*e^2 - 24*e + 34, -1/2*e^8 + 3/2*e^7 + 6*e^6 - 18*e^5 - 43/2*e^4 + 125/2*e^3 + 22*e^2 - 50*e - 8, 1/2*e^8 + 3/2*e^7 - 7*e^6 - 21*e^5 + 57/2*e^4 + 163/2*e^3 - 26*e^2 - 70*e - 4, 1/2*e^8 - e^7 - 11/2*e^6 + 10*e^5 + 39/2*e^4 - 28*e^3 - 49/2*e^2 + 19*e - 2, -2*e^7 + 3/2*e^6 + 51/2*e^5 - 13/2*e^4 - 199/2*e^3 - 13*e^2 + 100*e + 12, -1/2*e^7 + 1/2*e^6 + 9/2*e^5 + 3/2*e^4 - 6*e^3 - 32*e^2 - 28*e + 30, -e^8 - 5/2*e^7 + 29/2*e^6 + 36*e^5 - 65*e^4 - 299/2*e^3 + 187/2*e^2 + 148*e - 48, -e^8 + e^7 + 14*e^6 - 9*e^5 - 63*e^4 + 18*e^3 + 94*e^2 - 2*e - 20, -e^8 + 2*e^7 + 12*e^6 - 26*e^5 - 38*e^4 + 102*e^3 + 9*e^2 - 108*e + 36, -1/2*e^8 + 2*e^7 + 11/2*e^6 - 22*e^5 - 41/2*e^4 + 71*e^3 + 67/2*e^2 - 62*e - 22, -3*e^8 + 2*e^7 + 37*e^6 - 15*e^5 - 132*e^4 + 21*e^3 + 108*e^2 - 10*e + 10, -1/2*e^8 - 3*e^7 + 19/2*e^6 + 77/2*e^5 - 53*e^4 - 293/2*e^3 + 96*e^2 + 149*e - 54, -1/2*e^8 + 5*e^7 + 5/2*e^6 - 59*e^5 + 15/2*e^4 + 208*e^3 - 79/2*e^2 - 198*e + 34, 1/2*e^8 + 2*e^7 - 15/2*e^6 - 27*e^5 + 63/2*e^4 + 105*e^3 - 61/2*e^2 - 96*e + 18, 7/2*e^8 - 3*e^7 - 89/2*e^6 + 28*e^5 + 333/2*e^4 - 71*e^3 - 307/2*e^2 + 62*e + 2, -1/2*e^8 + 5/2*e^7 + 6*e^6 - 32*e^5 - 53/2*e^4 + 237/2*e^3 + 51*e^2 - 95*e - 6, -e^8 + 7/2*e^7 + 11*e^6 - 40*e^5 - 38*e^4 + 269/2*e^3 + 40*e^2 - 106*e + 20, 3/2*e^8 - 41/2*e^6 - 3*e^5 + 159/2*e^4 + 20*e^3 - 125/2*e^2 - 5*e - 10, 1/2*e^8 - 3*e^7 - 11/2*e^6 + 38*e^5 + 31/2*e^4 - 142*e^3 + 7/2*e^2 + 135*e - 34, -e^8 + e^7 + 12*e^6 - 10*e^5 - 43*e^4 + 32*e^3 + 47*e^2 - 33*e - 32, 1/2*e^8 + 5*e^7 - 17/2*e^6 - 65*e^5 + 69/2*e^4 + 247*e^3 - 27/2*e^2 - 215*e - 10, e^8 + 2*e^7 - 15*e^6 - 29*e^5 + 67*e^4 + 119*e^3 - 82*e^2 - 102*e + 32, 5/2*e^8 - e^7 - 65/2*e^6 + 3*e^5 + 265/2*e^4 + 16*e^3 - 333/2*e^2 - 6*e + 42, -1/2*e^8 - 2*e^7 + 13/2*e^6 + 29*e^5 - 43/2*e^4 - 118*e^3 - 9/2*e^2 + 103*e + 16, 1/2*e^8 - 2*e^7 - 9/2*e^6 + 25*e^5 + 13/2*e^4 - 97*e^3 + 43/2*e^2 + 100*e - 26, 2*e^8 - e^7 - 26*e^6 + 8*e^5 + 98*e^4 - 12*e^3 - 82*e^2 - 3*e - 20, e^7 - 11*e^5 - 6*e^4 + 34*e^3 + 36*e^2 - 19*e - 20, 2*e^8 - 28*e^6 - 3*e^5 + 118*e^4 + 23*e^3 - 138*e^2 - 26*e + 10, -e^8 + 4*e^7 + 19/2*e^6 - 87/2*e^5 - 47/2*e^4 + 273/2*e^3 + e^2 - 101*e + 38, 6*e^7 - 4*e^6 - 73*e^5 + 27*e^4 + 262*e^3 - 33*e^2 - 227*e + 32, e^8 + e^7 - 14*e^6 - 13*e^5 + 57*e^4 + 46*e^3 - 58*e^2 - 21*e, -e^8 + 2*e^7 + 11*e^6 - 20*e^5 - 37*e^4 + 55*e^3 + 42*e^2 - 31*e - 12, -2*e^8 + 6*e^7 + 21*e^6 - 67*e^5 - 60*e^4 + 223*e^3 + 19*e^2 - 200*e + 44, -2*e^8 + 3*e^7 + 25*e^6 - 29*e^5 - 97*e^4 + 76*e^3 + 108*e^2 - 48*e - 4, -3/2*e^8 - 2*e^7 + 19*e^6 + 59/2*e^5 - 61*e^4 - 243/2*e^3 + 19/2*e^2 + 102*e + 8, 1/2*e^8 - 3*e^7 - 11/2*e^6 + 35*e^5 + 41/2*e^4 - 114*e^3 - 59/2*e^2 + 78*e - 6, -e^8 + 2*e^7 + 13*e^6 - 24*e^5 - 56*e^4 + 85*e^3 + 90*e^2 - 81*e - 20, 3/2*e^8 - 33/2*e^6 - 8*e^5 + 95/2*e^4 + 56*e^3 - 23/2*e^2 - 70*e - 18, -3*e^8 + 4*e^7 + 75/2*e^6 - 85/2*e^5 - 279/2*e^4 + 261/2*e^3 + 131*e^2 - 102*e + 10, 5/2*e^8 - e^7 - 61/2*e^6 + e^5 + 217/2*e^4 + 35*e^3 - 185/2*e^2 - 49*e + 14, 2*e^8 - 3*e^7 - 24*e^6 + 28*e^5 + 87*e^4 - 75*e^3 - 81*e^2 + 70*e - 4, -e^8 + e^7 + 11*e^6 - 6*e^5 - 33*e^4 + 2*e^3 + 7*e^2 - 5*e + 24, 4*e^8 - 5/2*e^7 - 48*e^6 + 15*e^5 + 163*e^4 - 11/2*e^3 - 101*e^2 + 3*e - 32, e^8 - 3*e^7 - 11*e^6 + 33*e^5 + 41*e^4 - 107*e^3 - 67*e^2 + 85*e + 24, -1/2*e^8 + 1/2*e^7 + 4*e^6 - 3*e^5 + 1/2*e^4 - 5/2*e^3 - 40*e^2 + 25*e + 30, -e^8 + 7/2*e^7 + 17/2*e^6 - 40*e^5 - 11*e^4 + 277/2*e^3 - 69/2*e^2 - 130*e + 44, 2*e^8 - e^7 - 28*e^6 + 11*e^5 + 124*e^4 - 38*e^3 - 180*e^2 + 37*e + 48, -2*e^8 + e^7 + 26*e^6 - 8*e^5 - 104*e^4 + 18*e^3 + 128*e^2 - 23*e - 24, -e^8 + 2*e^7 + 13*e^6 - 22*e^5 - 59*e^4 + 66*e^3 + 109*e^2 - 32*e - 46, 3/2*e^7 + e^6 - 43/2*e^5 - 17/2*e^4 + 83*e^3 + 27/2*e^2 - 67*e + 16, 3/2*e^8 - 4*e^7 - 35/2*e^6 + 45*e^5 + 123/2*e^4 - 148*e^3 - 103/2*e^2 + 121*e - 26, -4*e^8 + 2*e^7 + 50*e^6 - 12*e^5 - 181*e^4 + 7*e^3 + 148*e^2 - 25*e, e^8 - 5*e^7 - 7*e^6 + 56*e^5 - e^4 - 189*e^3 + 57*e^2 + 171*e - 44, 3*e^8 - 2*e^7 - 38*e^6 + 18*e^5 + 140*e^4 - 47*e^3 - 114*e^2 + 45*e - 20, 1/2*e^8 + e^7 - 13/2*e^6 - 13*e^5 + 53/2*e^4 + 42*e^3 - 81/2*e^2 - 9*e + 46, -1/2*e^8 - 5/2*e^7 + 13/2*e^6 + 67/2*e^5 - 17*e^4 - 130*e^3 - 25*e^2 + 109*e + 16, -7/2*e^7 + 2*e^6 + 41*e^5 - 11*e^4 - 273/2*e^3 - 3*e^2 + 93*e + 14, e^8 + e^7 - 12*e^6 - 19*e^5 + 42*e^4 + 88*e^3 - 39*e^2 - 70*e + 34, -3*e^8 - 2*e^7 + 40*e^6 + 38*e^5 - 164*e^4 - 179*e^3 + 197*e^2 + 161*e - 58, e^8 + 9/2*e^7 - 33/2*e^6 - 119/2*e^5 + 149/2*e^4 + 227*e^3 - 67*e^2 - 194*e - 6, e^8 - 11/2*e^7 - 8*e^6 + 64*e^5 + 14*e^4 - 445/2*e^3 - 5*e^2 + 196*e - 14, -1/2*e^8 + 9/2*e^6 + 3*e^5 - 11/2*e^4 - 20*e^3 - 45/2*e^2 + 31*e + 18, -4*e^7 + 3*e^6 + 54*e^5 - 26*e^4 - 214*e^3 + 53*e^2 + 213*e - 44, -2*e^8 + 24*e^6 + 7*e^5 - 82*e^4 - 39*e^3 + 59*e^2 + 4*e + 20, 2*e^8 - 3*e^7 - 25*e^6 + 34*e^5 + 94*e^4 - 118*e^3 - 102*e^2 + 121*e + 32, -11/2*e^7 + 2*e^6 + 72*e^5 - 11*e^4 - 553/2*e^3 - 9*e^2 + 256*e + 16, -1/2*e^8 + 9/2*e^6 + 4*e^5 - 17/2*e^4 - 29*e^3 - 11/2*e^2 + 50*e + 18, -5/2*e^8 + 61/2*e^6 + 12*e^5 - 215/2*e^4 - 90*e^3 + 173/2*e^2 + 124*e + 6, -1/2*e^8 - e^7 + 9/2*e^6 + 18*e^5 - 13/2*e^4 - 81*e^3 - 35/2*e^2 + 78*e + 6, -e^7 + 3*e^6 + 6*e^5 - 30*e^4 + 3*e^3 + 87*e^2 - 26*e - 42, -e^8 + 13*e^6 + 2*e^5 - 51*e^4 - 14*e^3 + 55*e^2 + 20*e - 6, e^8 - 14*e^6 + 57*e^4 + 2*e^3 - 66*e^2 - 2*e + 54, e^8 + 4*e^7 - 15*e^6 - 51*e^5 + 61*e^4 + 182*e^3 - 43*e^2 - 133*e - 12, e^8 + e^7 - 13*e^6 - 16*e^5 + 47*e^4 + 74*e^3 - 36*e^2 - 85*e - 4, 1/2*e^8 + 1/2*e^7 - 9*e^6 - 13/2*e^5 + 44*e^4 + 26*e^3 - 103/2*e^2 - 12*e + 10, 1/2*e^8 + 9/2*e^7 - 17/2*e^6 - 59*e^5 + 87/2*e^4 + 445/2*e^3 - 143/2*e^2 - 196*e + 48, -2*e^8 + 11/2*e^7 + 49/2*e^6 - 64*e^5 - 95*e^4 + 435/2*e^3 + 245/2*e^2 - 181*e - 14, 5/2*e^7 - e^6 - 28*e^5 + 3*e^4 + 171/2*e^3 + 14*e^2 - 38*e - 12, -1/2*e^8 - 1/2*e^7 + 7*e^6 + 4*e^5 - 65/2*e^4 - 1/2*e^3 + 60*e^2 - 25*e - 36, 1/2*e^8 + 13/2*e^7 - 9*e^6 - 81*e^5 + 69/2*e^4 + 581/2*e^3 - 226*e - 8, -5/2*e^8 + 9/2*e^7 + 30*e^6 - 49*e^5 - 223/2*e^4 + 315/2*e^3 + 134*e^2 - 143*e - 36, -2*e^8 - 3*e^7 + 29*e^6 + 43*e^5 - 125*e^4 - 181*e^3 + 146*e^2 + 186*e - 18, 1/2*e^8 - 3*e^7 - 13/2*e^6 + 79/2*e^5 + 29*e^4 - 315/2*e^3 - 51*e^2 + 169*e + 24, -e^8 - 2*e^7 + 16*e^6 + 28*e^5 - 81*e^4 - 120*e^3 + 140*e^2 + 148*e - 74, -e^7 - e^6 + 17*e^5 + 10*e^4 - 79*e^3 - 29*e^2 + 79*e, 5/2*e^8 - 4*e^7 - 29*e^6 + 85/2*e^5 + 99*e^4 - 283/2*e^3 - 173/2*e^2 + 157*e + 14, 5/2*e^8 - 1/2*e^7 - 65/2*e^6 + 4*e^5 + 243/2*e^4 - 37/2*e^3 - 207/2*e^2 + 65*e - 2, -e^8 - 3*e^7 + 15*e^6 + 37*e^5 - 62*e^4 - 124*e^3 + 57*e^2 + 70*e - 28, -e^8 + 15*e^6 + 4*e^5 - 70*e^4 - 30*e^3 + 100*e^2 + 38*e - 36, 7/2*e^8 - 3*e^7 - 87/2*e^6 + 27*e^5 + 327/2*e^4 - 69*e^3 - 333/2*e^2 + 57*e - 2, -1/2*e^8 - 6*e^7 + 25/2*e^6 + 73*e^5 - 159/2*e^4 - 262*e^3 + 323/2*e^2 + 237*e - 88, e^8 + 7*e^7 - 20*e^6 - 88*e^5 + 108*e^4 + 328*e^3 - 161*e^2 - 301*e + 60, -3*e^7 + 5/2*e^6 + 67/2*e^5 - 35/2*e^4 - 211/2*e^3 + 23*e^2 + 69*e - 2, -3*e^8 + 2*e^7 + 36*e^6 - 15*e^5 - 118*e^4 + 27*e^3 + 57*e^2 - 52*e + 30, 5/2*e^8 + 4*e^7 - 67/2*e^6 - 61*e^5 + 265/2*e^4 + 259*e^3 - 259/2*e^2 - 250*e + 10, 7/2*e^8 + e^7 - 89/2*e^6 - 26*e^5 + 337/2*e^4 + 133*e^3 - 339/2*e^2 - 106*e + 34, -e^8 + 11*e^6 + 9*e^5 - 37*e^4 - 64*e^3 + 43*e^2 + 77*e - 42, -3*e^7 + e^6 + 34*e^5 - 107*e^3 - 25*e^2 + 64*e - 6, -e^8 + 6*e^7 + 11*e^6 - 75*e^5 - 43*e^4 + 269*e^3 + 77*e^2 - 208*e - 16] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([47, 47, w^2 + w - 4])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]