/* 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([31, 0, -12, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 5, w^2 - 6]) primes_array = [ [4, 2, -1/2*w^3 - 1/2*w^2 + 7/2*w + 11/2],\ [5, 5, -1/2*w^3 + w^2 + 5/2*w - 4],\ [5, 5, -1/2*w^2 - w + 3/2],\ [9, 3, -1/2*w^3 + 1/2*w^2 + 7/2*w - 9/2],\ [9, 3, -1/2*w^3 - 1/2*w^2 + 7/2*w + 9/2],\ [19, 19, -1/2*w^2 + w + 5/2],\ [19, 19, 1/2*w^2 + w - 5/2],\ [29, 29, -3/2*w^2 - w + 17/2],\ [29, 29, -3/2*w^2 + w + 17/2],\ [31, 31, 1/2*w^3 - 7/2*w],\ [59, 59, 1/2*w^2 + w - 11/2],\ [59, 59, 1/2*w^2 - w - 11/2],\ [61, 61, -1/2*w^3 + w^2 + 7/2*w - 5],\ [61, 61, 1/2*w^3 + w^2 - 7/2*w - 5],\ [71, 71, -1/2*w^3 - 2*w^2 + 11/2*w + 13],\ [71, 71, 3/2*w^3 + 2*w^2 - 23/2*w - 18],\ [79, 79, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1/2],\ [79, 79, -2*w^2 + w + 10],\ [79, 79, 2*w^2 + w - 10],\ [79, 79, 1/2*w^3 - 1/2*w^2 - 7/2*w + 1/2],\ [89, 89, 1/2*w^3 - 2*w^2 - 5/2*w + 11],\ [89, 89, -1/2*w^2 + w + 15/2],\ [109, 109, -w^3 + 7*w + 3],\ [109, 109, 1/2*w^3 - 2*w^2 - 9/2*w + 12],\ [109, 109, w^3 + w^2 - 8*w - 11],\ [109, 109, w^3 - 7*w + 3],\ [121, 11, 3/2*w^2 - 19/2],\ [121, 11, -1/2*w^2 + 13/2],\ [131, 131, -1/2*w^3 + 3/2*w^2 + 7/2*w - 15/2],\ [131, 131, -1/2*w^3 + 9/2*w + 3],\ [179, 179, -w^3 - 5/2*w^2 + 9*w + 35/2],\ [179, 179, 1/2*w^3 + 2*w^2 - 7/2*w - 13],\ [179, 179, -1/2*w^3 + 2*w^2 + 7/2*w - 13],\ [179, 179, 3/2*w^3 + 4*w^2 - 27/2*w - 29],\ [181, 181, -1/2*w^3 + w^2 + 5/2*w - 7],\ [181, 181, 1/2*w^3 + w^2 - 5/2*w - 7],\ [191, 191, 2*w^2 + w - 12],\ [191, 191, 2*w^2 - w - 12],\ [211, 211, w^3 - w^2 - 7*w + 4],\ [211, 211, -w^3 - w^2 + 7*w + 4],\ [229, 229, 3/2*w^2 + w - 23/2],\ [229, 229, 3/2*w^2 - w - 23/2],\ [241, 241, 1/2*w^3 + 3/2*w^2 - 9/2*w - 17/2],\ [241, 241, -1/2*w^3 + 3/2*w^2 + 9/2*w - 17/2],\ [251, 251, w^3 - 5*w + 3],\ [251, 251, 3/2*w^3 - 23/2*w + 2],\ [251, 251, 5/2*w^2 + 3*w - 23/2],\ [251, 251, w^3 + 3*w^2 - 9*w - 24],\ [269, 269, 1/2*w^2 + 2*w - 9/2],\ [269, 269, 1/2*w^2 - 2*w - 9/2],\ [271, 271, 1/2*w^3 - 1/2*w^2 - 3/2*w - 3/2],\ [271, 271, w^3 + 3/2*w^2 - 6*w - 15/2],\ [271, 271, 1/2*w^3 + 3*w^2 - 9/2*w - 16],\ [271, 271, -1/2*w^3 - 2*w^2 + 5/2*w + 13],\ [281, 281, w^3 - 5/2*w^2 - 8*w + 33/2],\ [281, 281, w^2 + 2*w - 6],\ [281, 281, w^2 - 2*w - 6],\ [281, 281, w^3 + 5/2*w^2 - 8*w - 33/2],\ [311, 311, -5/2*w^3 - 3*w^2 + 37/2*w + 30],\ [311, 311, 2*w^2 - 2*w - 13],\ [331, 331, -1/2*w^3 + 7/2*w - 5],\ [331, 331, -w^3 + 5/2*w^2 + 7*w - 29/2],\ [331, 331, w^3 + 5/2*w^2 - 7*w - 29/2],\ [331, 331, 1/2*w^3 - 7/2*w - 5],\ [349, 349, 1/2*w^3 - 2*w^2 - 11/2*w + 16],\ [349, 349, w^3 + 3*w^2 - 6*w - 19],\ [349, 349, 1/2*w^3 - w^2 - 1/2*w - 1],\ [349, 349, 1/2*w^3 + 2*w^2 - 11/2*w - 16],\ [359, 359, 1/2*w^3 + 3/2*w^2 - 11/2*w - 15/2],\ [359, 359, w^3 - 4*w^2 - 2*w + 16],\ [361, 19, -1/2*w^2 + 15/2],\ [379, 379, 1/2*w^3 + 5/2*w^2 - 11/2*w - 37/2],\ [379, 379, -w^3 + 1/2*w^2 + 6*w - 15/2],\ [389, 389, w^3 - 1/2*w^2 - 7*w + 5/2],\ [389, 389, w^3 + 1/2*w^2 - 7*w - 5/2],\ [401, 401, 1/2*w^3 + 3/2*w^2 - 5/2*w - 21/2],\ [401, 401, -1/2*w^3 + 3/2*w^2 + 5/2*w - 21/2],\ [409, 409, -2*w^3 - 5*w^2 + 18*w + 38],\ [409, 409, 1/2*w^3 - w^2 - 13/2*w + 1],\ [419, 419, -1/2*w^3 + 1/2*w^2 + 5/2*w - 19/2],\ [419, 419, 1/2*w^3 + 1/2*w^2 - 5/2*w - 19/2],\ [431, 431, 1/2*w^3 - 3/2*w^2 - 7/2*w + 11/2],\ [431, 431, 1/2*w^3 + 3/2*w^2 - 7/2*w - 11/2],\ [439, 439, -1/2*w^3 + 5/2*w^2 + 5/2*w - 27/2],\ [439, 439, -1/2*w^3 - 5/2*w^2 + 5/2*w + 27/2],\ [449, 449, w^3 - 1/2*w^2 - 7*w + 7/2],\ [449, 449, w^3 + 1/2*w^2 - 7*w - 7/2],\ [461, 461, w^3 - 7/2*w^2 - 5*w + 37/2],\ [461, 461, -1/2*w^2 + 2*w + 21/2],\ [479, 479, -w^3 + 4*w^2 + 4*w - 20],\ [479, 479, 1/2*w^3 - 3/2*w + 8],\ [491, 491, 1/2*w^3 - 5/2*w^2 - 3/2*w + 29/2],\ [491, 491, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7/2],\ [491, 491, 1/2*w^3 + w^2 - 11/2*w - 8],\ [491, 491, -1/2*w^3 + w^2 + 5/2*w - 12],\ [499, 499, 3*w^2 - w - 21],\ [499, 499, 1/2*w^3 + 5/2*w^2 - 11/2*w - 29/2],\ [499, 499, w^3 + 5*w^2 - 11*w - 32],\ [499, 499, 3*w^2 + w - 21],\ [509, 509, -w^3 + 3/2*w^2 + 4*w - 3/2],\ [509, 509, 1/2*w^3 + 3*w^2 - 3/2*w - 18],\ [529, 23, 1/2*w^3 - 2*w^2 - 11/2*w + 11],\ [529, 23, 1/2*w^3 + 2*w^2 - 11/2*w - 11],\ [569, 569, 1/2*w^3 + w^2 - 11/2*w - 3],\ [569, 569, -1/2*w^3 + w^2 + 11/2*w - 3],\ [571, 571, 5/2*w^2 + 2*w - 33/2],\ [571, 571, 2*w^3 - 5/2*w^2 - 16*w + 49/2],\ [571, 571, 2*w^3 + 5/2*w^2 - 16*w - 49/2],\ [571, 571, 5/2*w^2 - 2*w - 33/2],\ [599, 599, 1/2*w^3 - 1/2*w^2 - 11/2*w - 3/2],\ [599, 599, -1/2*w^3 - 1/2*w^2 + 11/2*w - 3/2],\ [601, 601, 2*w^3 + 3/2*w^2 - 15*w - 35/2],\ [601, 601, 5/2*w^3 + 3*w^2 - 39/2*w - 29],\ [619, 619, 5/2*w^3 + 5/2*w^2 - 37/2*w - 51/2],\ [619, 619, w^3 - 1/2*w^2 - 5*w + 11/2],\ [619, 619, 3/2*w^2 - 2*w - 23/2],\ [619, 619, w^3 + 3*w^2 - 10*w - 21],\ [631, 631, -5/2*w^3 + 33/2*w + 13],\ [631, 631, 3/2*w^3 - 5*w^2 - 13/2*w + 22],\ [631, 631, -2*w^3 - 2*w^2 + 14*w + 23],\ [631, 631, -5/2*w^2 - 5*w + 13/2],\ [641, 641, -1/2*w^3 + 1/2*w^2 + 11/2*w - 5/2],\ [641, 641, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5/2],\ [659, 659, -3/2*w^3 - w^2 + 23/2*w + 14],\ [659, 659, 3/2*w^3 + 5/2*w^2 - 19/2*w - 27/2],\ [661, 661, -1/2*w^3 + 1/2*w^2 + 11/2*w - 9/2],\ [661, 661, w^3 + w^2 - 8*w - 5],\ [661, 661, -1/2*w^3 + 2*w^2 + 7/2*w - 8],\ [661, 661, -1/2*w^3 - 1/2*w^2 + 11/2*w + 9/2],\ [691, 691, 1/2*w^3 - 3/2*w^2 - 3/2*w + 19/2],\ [691, 691, 1/2*w^3 + 3/2*w^2 - 3/2*w - 19/2],\ [709, 709, 1/2*w^3 - 2*w^2 - 3/2*w + 12],\ [709, 709, 1/2*w^3 + 2*w^2 - 3/2*w - 12],\ [751, 751, 3/2*w^3 - w^2 - 21/2*w + 11],\ [751, 751, 3/2*w^3 + w^2 - 21/2*w - 11],\ [761, 761, 2*w^3 + 11/2*w^2 - 17*w - 85/2],\ [761, 761, -3/2*w^3 - 4*w^2 + 17/2*w + 23],\ [769, 769, w^3 - 7/2*w^2 - 8*w + 45/2],\ [769, 769, -1/2*w^3 - 5/2*w^2 + 5/2*w + 35/2],\ [769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 35/2],\ [769, 769, w^3 + 7/2*w^2 - 8*w - 45/2],\ [809, 809, w^3 - 7/2*w^2 - 7*w + 41/2],\ [809, 809, w^3 + 7/2*w^2 - 7*w - 41/2],\ [811, 811, -1/2*w^3 - 9/2*w^2 + 13/2*w + 59/2],\ [811, 811, 3*w^3 + 5*w^2 - 24*w - 45],\ [821, 821, -2*w^3 - 7/2*w^2 + 12*w + 33/2],\ [821, 821, w^3 - 4*w^2 - w + 13],\ [829, 829, -w^3 + 1/2*w^2 + 8*w - 1/2],\ [829, 829, w^3 + 1/2*w^2 - 8*w - 1/2],\ [839, 839, w^3 - 3/2*w^2 - 7*w + 13/2],\ [839, 839, w^3 + 3/2*w^2 - 7*w - 13/2],\ [841, 29, 5/2*w^2 - 27/2],\ [859, 859, 1/2*w^3 - 7/2*w - 6],\ [859, 859, -3/2*w^3 + 2*w^2 + 21/2*w - 15],\ [859, 859, 3/2*w^3 + 2*w^2 - 21/2*w - 15],\ [859, 859, 1/2*w^3 - 7/2*w + 6],\ [881, 881, -3/2*w^3 + 21/2*w + 8],\ [881, 881, -2*w^3 + 1/2*w^2 + 13*w + 15/2],\ [919, 919, -3/2*w^3 + 5/2*w^2 + 15/2*w - 19/2],\ [919, 919, 3/2*w^3 + w^2 - 21/2*w - 4],\ [929, 929, 1/2*w^3 + w^2 - 9/2*w - 1],\ [929, 929, 1/2*w^3 - w^2 - 9/2*w + 1],\ [941, 941, 2*w^3 + 7*w^2 - 19*w - 51],\ [941, 941, 5/2*w^2 - 3*w - 33/2],\ [961, 31, -w^2 + 12],\ [971, 971, 3/2*w^2 - 3*w - 25/2],\ [971, 971, w^3 + 7/2*w^2 - 6*w - 39/2],\ [991, 991, 1/2*w^3 - 3/2*w^2 - 13/2*w + 13/2],\ [991, 991, w^3 + 5/2*w^2 - 5*w - 29/2],\ [991, 991, w^3 - 5/2*w^2 - 5*w + 29/2],\ [991, 991, -3/2*w^3 + 2*w^2 + 17/2*w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 + 2*x^3 - 24*x^2 - 62*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [-2, -1, 1, e, 1/6*e^3 + 1/6*e^2 - 25/6*e - 31/6, -1/12*e^3 + 5/12*e^2 + 7/12*e - 83/12, -1/4*e^3 + 1/4*e^2 + 23/4*e + 17/4, 1/3*e^3 - 1/6*e^2 - 22/3*e - 41/6, -1/6*e^3 + 1/3*e^2 + 13/6*e - 13/3, 1/6*e^3 - 5/6*e^2 - 19/6*e + 47/6, 1/4*e^3 + 1/4*e^2 - 19/4*e - 43/4, -1/4*e^3 - 1/4*e^2 + 19/4*e + 19/4, -1/4*e^3 + 1/4*e^2 + 11/4*e + 5/4, -7/12*e^3 - 1/12*e^2 + 157/12*e + 139/12, -1/4*e^3 - 3/4*e^2 + 19/4*e + 57/4, -1/4*e^3 - 3/4*e^2 + 19/4*e + 57/4, 1/3*e^3 + 1/3*e^2 - 16/3*e - 31/3, -7/12*e^3 - 1/12*e^2 + 145/12*e + 115/12, 5/12*e^3 - 1/12*e^2 - 83/12*e - 101/12, 1/2*e^3 + 1/2*e^2 - 21/2*e - 31/2, -5/12*e^3 + 7/12*e^2 + 119/12*e + 35/12, 1/12*e^3 - 11/12*e^2 + 5/12*e + 161/12, e^3 - e^2 - 20*e - 11, -2/3*e^3 + 1/3*e^2 + 38/3*e + 23/3, -2/3*e^3 + 1/3*e^2 + 38/3*e + 23/3, 5/6*e^3 - 7/6*e^2 - 89/6*e + 37/6, 1/12*e^3 + 1/12*e^2 - 31/12*e - 91/12, 1/6*e^3 + 1/6*e^2 - 31/6*e - 97/6, 2/3*e^3 - 5/6*e^2 - 44/3*e - 43/6, 1/3*e^3 - 7/6*e^2 - 13/3*e + 91/6, 1/12*e^3 - 17/12*e^2 + 5/12*e + 239/12, -1/6*e^3 + 5/6*e^2 + 31/6*e - 83/6, -1/6*e^3 - 7/6*e^2 + 31/6*e + 73/6, 5/12*e^3 - 13/12*e^2 - 119/12*e + 43/12, 7/12*e^3 - 17/12*e^2 - 145/12*e - 1/12, -5/12*e^3 + 19/12*e^2 + 83/12*e - 253/12, -1/6*e^3 + 5/6*e^2 + 31/6*e - 101/6, -1/6*e^3 - 7/6*e^2 + 31/6*e + 55/6, -1/2*e^3 + e^2 + 23/2*e + 8, -1/6*e^3 + 4/3*e^2 + 7/6*e - 79/3, 2/3*e^3 - 11/6*e^2 - 35/3*e + 41/6, -5/6*e^3 + 5/3*e^2 + 101/6*e - 35/3, -11/6*e^3 + 7/6*e^2 + 221/6*e + 143/6, -3/2*e^3 + 3/2*e^2 + 53/2*e + 3/2, -4/3*e^3 + 2/3*e^2 + 70/3*e + 46/3, -1/12*e^3 - 7/12*e^2 + 67/12*e + 109/12, 7/12*e^3 + 1/12*e^2 - 181/12*e - 139/12, 5/3*e^3 - 1/3*e^2 - 101/3*e - 77/3, -3/4*e^3 - 5/4*e^2 + 69/4*e + 59/4, -1/4*e^3 - 3/4*e^2 + 7/4*e + 117/4, -1/12*e^3 + 23/12*e^2 + 31/12*e - 305/12, 3/2*e^3 - 61/2*e - 21, 7/6*e^3 - 1/3*e^2 - 121/6*e - 68/3, -1/12*e^3 - 25/12*e^2 + 31/12*e + 319/12, 2/3*e^3 + 1/6*e^2 - 44/3*e - 157/6, 5/12*e^3 - 31/12*e^2 - 47/12*e + 385/12, 13/12*e^3 - 23/12*e^2 - 295/12*e - 7/12, 1/3*e^3 - 1/6*e^2 - 13/3*e + 49/6, -3/2*e^3 + 1/2*e^2 + 69/2*e + 59/2, 1/2*e^3 - 3/2*e^2 - 7/2*e + 39/2, -1/2*e^3 + 1/2*e^2 + 19/2*e - 17/2, -2/3*e^3 + 1/3*e^2 + 50/3*e + 59/3, e^2 - 4*e - 25, 1/2*e^3 - 1/2*e^2 - 19/2*e - 27/2, -5/4*e^3 + 3/4*e^2 + 119/4*e + 95/4, 17/12*e^3 - 1/12*e^2 - 383/12*e - 389/12, -7/12*e^3 + 11/12*e^2 + 73/12*e - 113/12, 1/4*e^3 - 7/4*e^2 + 5/4*e + 117/4, -7/12*e^3 - 13/12*e^2 + 109/12*e + 331/12, -11/12*e^3 - 17/12*e^2 + 233/12*e + 383/12, -1/2*e^3 - 1/2*e^2 + 31/2*e + 17/2, -1/4*e^3 + 3/4*e^2 + 19/4*e + 31/4, 1/4*e^3 - 3/4*e^2 - 19/4*e + 73/4, -1/12*e^3 + 17/12*e^2 - 5/12*e - 383/12, -5/12*e^3 + 13/12*e^2 + 119/12*e + 101/12, 1/6*e^3 + 1/6*e^2 - 31/6*e + 23/6, 1/6*e^3 + 1/6*e^2 - 31/6*e + 23/6, -13/12*e^3 + 5/12*e^2 + 343/12*e + 205/12, 1/4*e^3 + 7/4*e^2 - 51/4*e - 121/4, -11/12*e^3 + 7/12*e^2 + 197/12*e - 37/12, 13/12*e^3 - 5/12*e^2 - 259/12*e - 313/12, 1/6*e^3 - 5/6*e^2 - 31/6*e + 11/6, -1/6*e^3 - 7/6*e^2 + 31/6*e + 145/6, 4/3*e^3 - 7/6*e^2 - 79/3*e - 131/6, -7/6*e^3 + 4/3*e^2 + 127/6*e - 28/3, 1/12*e^3 + 31/12*e^2 - 31/12*e - 313/12, -1/12*e^3 + 29/12*e^2 + 31/12*e - 467/12, -1/6*e^3 - 7/6*e^2 - 5/6*e + 163/6, 5/6*e^3 + 11/6*e^2 - 119/6*e - 179/6, 2/3*e^3 + 1/6*e^2 - 53/3*e - 139/6, 1/6*e^3 + 2/3*e^2 - 49/6*e - 62/3, e^3 - 25*e - 18, -5/6*e^3 + 2/3*e^2 + 119/6*e - 17/3, -1/6*e^3 + 4/3*e^2 - 5/6*e - 7/3, e^2 - 6*e - 13, -1/3*e^3 - 5/6*e^2 + 22/3*e + 95/6, -5/6*e^3 + 13/6*e^2 + 77/6*e - 151/6, -4/3*e^3 + 5/3*e^2 + 85/3*e + 43/3, 1/6*e^3 + 2/3*e^2 - 13/6*e - 38/3, -1/6*e^3 - 7/6*e^2 + 31/6*e + 37/6, -1/6*e^3 + 5/6*e^2 + 31/6*e - 119/6, 1/6*e^3 - 5/6*e^2 - 43/6*e - 25/6, -1/2*e^3 - 3/2*e^2 + 27/2*e + 81/2, 2*e^3 - 44*e - 42, e^3 - e^2 - 13*e + 1, 17/12*e^3 - 31/12*e^2 - 311/12*e + 193/12, 7/12*e^3 + 1/12*e^2 - 157/12*e + 149/12, 1/4*e^3 - 1/4*e^2 - 11/4*e - 101/4, -19/12*e^3 + 29/12*e^2 + 373/12*e + 61/12, -17/12*e^3 + 13/12*e^2 + 383/12*e + 389/12, -7/12*e^3 + 23/12*e^2 + 73/12*e - 425/12, 3/4*e^3 - 9/4*e^2 - 49/4*e + 39/4, 13/12*e^3 - 23/12*e^2 - 271/12*e + 137/12, 1/2*e^3 + 3/2*e^2 - 23/2*e - 93/2, -3/2*e^3 + 2*e^2 + 51/2*e - 6, 2*e^3 - 3/2*e^2 - 41*e - 47/2, 1/6*e^3 + 7/6*e^2 - 7/6*e - 1/6, -1/3*e^3 + 7/6*e^2 + 7/3*e - 55/6, -1/6*e^3 + 5/6*e^2 - 5/6*e + 13/6, 5/6*e^3 - 1/6*e^2 - 119/6*e - 17/6, -e^3 + 1/2*e^2 + 23*e + 23/2, 5/6*e^3 + 1/3*e^2 - 119/6*e - 22/3, 1/6*e^3 - 1/3*e^2 + 5/6*e - 32/3, 3*e - 12, 1/2*e^3 + 1/2*e^2 - 25/2*e - 7/2, -2/3*e^3 + 17/6*e^2 + 32/3*e - 77/6, 1/12*e^3 + 1/12*e^2 - 43/12*e - 175/12, -1/4*e^3 - 1/4*e^2 + 27/4*e + 79/4, -e^3 + 5/2*e^2 + 21*e - 53/2, -5/12*e^3 + 7/12*e^2 + 155/12*e + 47/12, -5/12*e^3 - 17/12*e^2 + 155/12*e + 359/12, 1/6*e^3 - 29/6*e^2 + 5/6*e + 299/6, -5/6*e^3 + 25/6*e^2 + 119/6*e - 295/6, 5/6*e^3 - 7/6*e^2 - 59/6*e - 35/6, 11/6*e^3 - 1/6*e^2 - 245/6*e - 149/6, -1/12*e^3 - 1/12*e^2 - 41/12*e + 175/12, 11/12*e^3 + 11/12*e^2 - 269/12*e - 197/12, 17/12*e^3 - 1/12*e^2 - 311/12*e - 341/12, 1/3*e^3 - 13/6*e^2 - 4/3*e + 103/6, -7/6*e^3 + 4/3*e^2 + 163/6*e - 4/3, -19/12*e^3 - 1/12*e^2 + 373/12*e + 307/12, -4/3*e^3 - 5/6*e^2 + 97/3*e + 155/6, 1/6*e^3 - 1/3*e^2 + 23/6*e - 23/3, 3/2*e^3 + 3/2*e^2 - 81/2*e - 113/2, 1/2*e^3 + 1/2*e^2 - 43/2*e - 51/2, -1/3*e^3 + 13/6*e^2 + 31/3*e - 169/6, 1/3*e^3 + 17/6*e^2 - 31/3*e - 221/6, 3/4*e^3 - 3/4*e^2 - 73/4*e - 27/4, 1/12*e^3 - 17/12*e^2 + 29/12*e + 239/12, 1/2*e^3 - 3/2*e^2 - 1/2*e + 21/2, 2*e^3 - 47*e - 36, 11/12*e^3 + 11/12*e^2 - 341/12*e - 689/12, 5/3*e^3 - 5/6*e^2 - 110/3*e - 157/6, -19/12*e^3 - 1/12*e^2 + 361/12*e + 319/12, -19/12*e^3 - 1/12*e^2 + 361/12*e + 391/12, -5/6*e^3 + 5/3*e^2 + 65/6*e - 41/3, -5/12*e^3 + 13/12*e^2 + 119/12*e + 209/12, -1/12*e^3 + 17/12*e^2 - 5/12*e - 491/12, -7/3*e^3 - 1/3*e^2 + 148/3*e + 157/3, -3/2*e^3 + 1/2*e^2 + 47/2*e + 29/2, 4/3*e^3 - 5/3*e^2 - 79/3*e - 61/3, 7/6*e^3 - 11/6*e^2 - 127/6*e + 125/6, 5/4*e^3 - 11/4*e^2 - 59/4*e + 89/4, -11/4*e^3 + 5/4*e^2 + 245/4*e + 169/4, -1/12*e^3 - 1/12*e^2 + 31/12*e - 269/12, -25/12*e^3 - 1/12*e^2 + 487/12*e + 607/12, 23/12*e^3 - 1/12*e^2 - 425/12*e - 257/12, -19/12*e^3 + 53/12*e^2 + 361/12*e - 203/12, 5/3*e^3 - 7/3*e^2 - 119/3*e - 11/3, -1/3*e^3 + 11/3*e^2 - 5/3*e - 137/3, -19/12*e^3 + 53/12*e^2 + 361/12*e - 491/12] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5,5,-1/2*w^3+w^2+5/2*w-4])] = 1 AL_eigenvalues[ZF.ideal([5,5,-1/2*w^2-w+3/2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]