/* 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([36, 6, -13, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9]) primes_array = [ [4, 2, 1/3*w^3 - 4/3*w^2 - 4/3*w + 6],\ [4, 2, -1/3*w^3 - 2/3*w^2 + 10/3*w + 7],\ [9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9],\ [9, 3, 1/3*w^3 + 2/3*w^2 - 7/3*w - 5],\ [11, 11, -1/6*w^3 + 1/6*w^2 + 1/6*w],\ [19, 19, w + 1],\ [19, 19, 1/6*w^3 - 1/6*w^2 - 13/6*w + 2],\ [25, 5, -1/3*w^3 + 1/3*w^2 + 7/3*w - 1],\ [29, 29, -1/6*w^3 + 1/6*w^2 + 13/6*w],\ [29, 29, w - 1],\ [31, 31, 1/3*w^3 - 1/3*w^2 - 10/3*w + 3],\ [31, 31, 1/6*w^3 - 1/6*w^2 - 1/6*w + 2],\ [41, 41, -1/2*w^3 - 1/2*w^2 + 9/2*w + 5],\ [41, 41, -1/2*w^3 + 3/2*w^2 + 5/2*w - 8],\ [59, 59, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1],\ [59, 59, -1/3*w^3 + 4/3*w^2 + 7/3*w - 7],\ [59, 59, 1/2*w^3 - 1/2*w^2 - 5/2*w + 2],\ [79, 79, w^2 - 11],\ [79, 79, 1/6*w^3 - 7/6*w^2 - 7/6*w + 3],\ [89, 89, -1/6*w^3 + 1/6*w^2 + 19/6*w - 5],\ [89, 89, 1/6*w^3 - 1/6*w^2 - 19/6*w - 3],\ [109, 109, -1/6*w^3 + 7/6*w^2 + 1/6*w - 9],\ [109, 109, -7/6*w^3 + 19/6*w^2 + 49/6*w - 20],\ [109, 109, -5/6*w^3 + 17/6*w^2 + 23/6*w - 12],\ [109, 109, 1/6*w^3 + 5/6*w^2 - 13/6*w - 4],\ [121, 11, 1/6*w^3 - 1/6*w^2 - 7/6*w - 3],\ [139, 139, 1/3*w^3 - 4/3*w^2 + 5/3*w - 1],\ [139, 139, -5/3*w^3 - 7/3*w^2 + 50/3*w + 29],\ [169, 13, w^3 + w^2 - 10*w - 13],\ [169, 13, -5/6*w^3 + 17/6*w^2 + 17/6*w - 12],\ [179, 179, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7],\ [179, 179, -2/3*w^3 + 2/3*w^2 + 17/3*w - 5],\ [181, 181, -w^3 + 3*w^2 + 4*w - 13],\ [181, 181, -1/6*w^3 + 7/6*w^2 + 1/6*w - 11],\ [181, 181, 7/6*w^3 + 11/6*w^2 - 79/6*w - 25],\ [181, 181, 1/6*w^3 + 5/6*w^2 - 13/6*w - 2],\ [191, 191, -5/6*w^3 - 1/6*w^2 + 53/6*w + 7],\ [191, 191, 1/6*w^3 + 11/6*w^2 - 19/6*w - 16],\ [211, 211, -1/6*w^3 + 1/6*w^2 - 5/6*w - 2],\ [211, 211, -1/2*w^3 + 1/2*w^2 + 9/2*w + 2],\ [211, 211, 1/3*w^3 - 1/3*w^2 - 4/3*w - 3],\ [211, 211, -1/2*w^3 + 1/2*w^2 + 11/2*w - 4],\ [229, 229, 5/6*w^3 + 1/6*w^2 - 53/6*w - 9],\ [229, 229, 1/2*w^3 - 3/2*w^2 - 1/2*w + 2],\ [239, 239, 5/6*w^3 + 7/6*w^2 - 59/6*w - 19],\ [239, 239, 1/2*w^3 - 5/2*w^2 + 1/2*w + 5],\ [241, 241, 1/6*w^3 - 1/6*w^2 - 13/6*w - 4],\ [241, 241, w - 5],\ [269, 269, -1/6*w^3 + 7/6*w^2 + 1/6*w - 2],\ [269, 269, 1/3*w^3 - 7/3*w^2 - 1/3*w + 7],\ [271, 271, 5/3*w^3 + 7/3*w^2 - 47/3*w - 25],\ [271, 271, -5/3*w^3 + 17/3*w^2 + 23/3*w - 27],\ [281, 281, 1/6*w^3 + 5/6*w^2 - 1/6*w - 7],\ [281, 281, -1/2*w^3 + 3/2*w^2 + 9/2*w - 8],\ [311, 311, 11/6*w^3 + 7/6*w^2 - 113/6*w - 23],\ [311, 311, -4/3*w^3 + 13/3*w^2 + 10/3*w - 13],\ [311, 311, -2/3*w^3 + 5/3*w^2 + 20/3*w - 17],\ [311, 311, 1/6*w^3 + 5/6*w^2 + 5/6*w + 1],\ [349, 349, -1/2*w^3 + 1/2*w^2 + 11/2*w - 1],\ [349, 349, -5/6*w^3 + 17/6*w^2 + 29/6*w - 14],\ [349, 349, 1/6*w^3 - 1/6*w^2 + 5/6*w - 1],\ [349, 349, -2/3*w^3 - 4/3*w^2 + 17/3*w + 13],\ [359, 359, -1/6*w^3 + 13/6*w^2 + 7/6*w - 18],\ [359, 359, -1/6*w^3 - 11/6*w^2 + 13/6*w + 18],\ [361, 19, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1],\ [379, 379, 1/2*w^3 + 1/2*w^2 - 7/2*w - 7],\ [379, 379, -5/6*w^3 + 11/6*w^2 + 23/6*w - 7],\ [379, 379, w^3 - 9*w - 5],\ [379, 379, -2/3*w^3 + 5/3*w^2 + 14/3*w - 7],\ [401, 401, -1/3*w^3 + 7/3*w^2 + 4/3*w - 17],\ [401, 401, -4/3*w^3 - 8/3*w^2 + 43/3*w + 31],\ [419, 419, 1/6*w^3 - 1/6*w^2 + 5/6*w],\ [419, 419, 1/2*w^3 - 1/2*w^2 - 11/2*w + 2],\ [421, 421, -5/6*w^3 - 7/6*w^2 + 47/6*w + 11],\ [421, 421, 1/3*w^3 - 1/3*w^2 - 19/3*w - 7],\ [431, 431, 5/6*w^3 + 1/6*w^2 - 41/6*w - 6],\ [431, 431, 2/3*w^3 - 8/3*w^2 - 8/3*w + 15],\ [431, 431, 5/6*w^3 - 11/6*w^2 - 29/6*w + 7],\ [431, 431, 1/2*w^3 - 5/2*w^2 + 5/2*w + 2],\ [439, 439, 5/6*w^3 + 1/6*w^2 - 41/6*w - 4],\ [439, 439, 1/2*w^3 - 1/2*w^2 - 9/2*w + 8],\ [449, 449, 5/6*w^3 - 17/6*w^2 - 29/6*w + 18],\ [449, 449, 11/6*w^3 - 41/6*w^2 - 41/6*w + 29],\ [449, 449, -7/6*w^3 + 31/6*w^2 + 7/6*w - 16],\ [449, 449, 5/3*w^3 + 7/3*w^2 - 56/3*w - 33],\ [461, 461, -1/6*w^3 + 1/6*w^2 + 19/6*w - 3],\ [461, 461, 1/6*w^3 - 1/6*w^2 - 19/6*w - 1],\ [479, 479, -2*w - 1],\ [479, 479, 1/3*w^3 - 1/3*w^2 - 13/3*w + 3],\ [491, 491, 2/3*w^3 + 1/3*w^2 - 14/3*w - 7],\ [491, 491, 5/6*w^3 - 11/6*w^2 - 35/6*w + 7],\ [509, 509, 5/6*w^3 - 11/6*w^2 - 29/6*w + 8],\ [509, 509, 5/6*w^3 + 1/6*w^2 - 41/6*w - 5],\ [521, 521, -1/6*w^3 + 7/6*w^2 - 17/6*w + 1],\ [521, 521, -1/6*w^3 + 7/6*w^2 - 11/6*w - 3],\ [521, 521, -1/6*w^3 + 7/6*w^2 + 19/6*w - 5],\ [521, 521, 2/3*w^3 + 1/3*w^2 - 26/3*w - 11],\ [541, 541, 1/6*w^3 + 5/6*w^2 - 31/6*w - 17],\ [541, 541, 5/6*w^3 - 17/6*w^2 - 47/6*w + 23],\ [541, 541, 3*w^3 + 3*w^2 - 32*w - 47],\ [541, 541, 2/3*w^3 + 4/3*w^2 - 14/3*w - 11],\ [571, 571, -1/3*w^3 + 1/3*w^2 + 13/3*w - 1],\ [571, 571, 2*w - 1],\ [571, 571, -1/3*w^3 + 4/3*w^2 + 7/3*w - 1],\ [571, 571, 1/6*w^3 + 5/6*w^2 - 7/6*w - 13],\ [599, 599, 1/2*w^3 + 1/2*w^2 - 9/2*w - 2],\ [599, 599, -1/6*w^3 + 1/6*w^2 + 19/6*w - 2],\ [599, 599, 1/6*w^3 - 1/6*w^2 - 19/6*w],\ [599, 599, 1/2*w^3 - 3/2*w^2 - 5/2*w + 11],\ [601, 601, 1/6*w^3 + 11/6*w^2 - 7/6*w - 15],\ [601, 601, -1/3*w^3 + 7/3*w^2 - 5/3*w - 5],\ [601, 601, 2/3*w^3 + 4/3*w^2 - 26/3*w - 19],\ [601, 601, 1/2*w^3 - 5/2*w^2 - 7/2*w + 13],\ [659, 659, w^2 - 13],\ [659, 659, -5/6*w^3 + 11/6*w^2 + 29/6*w - 12],\ [659, 659, -1/6*w^3 + 7/6*w^2 + 7/6*w - 1],\ [659, 659, 5/6*w^3 + 1/6*w^2 - 41/6*w - 1],\ [691, 691, 1/2*w^3 - 1/2*w^2 - 11/2*w + 10],\ [691, 691, -1/6*w^3 + 1/6*w^2 - 5/6*w - 8],\ [701, 701, -2*w^2 + w + 11],\ [701, 701, -1/6*w^3 + 13/6*w^2 + 7/6*w - 9],\ [701, 701, -1/6*w^3 + 13/6*w^2 + 1/6*w - 16],\ [701, 701, -w^3 + w^2 + 9*w - 1],\ [709, 709, -2/3*w^3 + 11/3*w^2 + 14/3*w - 21],\ [709, 709, 1/3*w^3 + 5/3*w^2 + 2/3*w - 5],\ [709, 709, 7/6*w^3 - 25/6*w^2 - 43/6*w + 25],\ [709, 709, 2/3*w^3 - 2/3*w^2 - 23/3*w - 1],\ [719, 719, 2*w^2 - 2*w - 19],\ [719, 719, -2*w^2 + 2*w + 7],\ [739, 739, 5/6*w^3 - 5/6*w^2 - 29/6*w + 4],\ [739, 739, -5/6*w^3 + 11/6*w^2 + 53/6*w - 17],\ [739, 739, -1/6*w^3 - 5/6*w^2 - 11/6*w],\ [739, 739, -w^3 + w^2 + 8*w - 5],\ [751, 751, -1/6*w^3 + 1/6*w^2 + 25/6*w + 8],\ [751, 751, -1/3*w^3 + 1/3*w^2 + 16/3*w - 11],\ [761, 761, -2/3*w^3 + 5/3*w^2 + 8/3*w - 9],\ [761, 761, 5/6*w^3 + 1/6*w^2 - 47/6*w - 3],\ [769, 769, 1/3*w^3 - 7/3*w^2 - 7/3*w + 11],\ [769, 769, -4/3*w^3 - 8/3*w^2 + 46/3*w + 33],\ [769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 20],\ [769, 769, 2*w^2 - 17],\ [809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 15],\ [809, 809, -5/6*w^3 - 1/6*w^2 + 35/6*w + 3],\ [809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 9],\ [809, 809, w^3 - 2*w^2 - 7*w + 11],\ [811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w + 7],\ [811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 15],\ [811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w - 4],\ [811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 4],\ [821, 821, -1/2*w^3 - 5/2*w^2 + 13/2*w + 16],\ [821, 821, 1/6*w^3 - 13/6*w^2 - 7/6*w + 21],\ [821, 821, 3/2*w^3 + 1/2*w^2 - 35/2*w - 20],\ [821, 821, -1/6*w^3 + 13/6*w^2 + 7/6*w - 7],\ [829, 829, -1/6*w^3 + 19/6*w^2 - 11/6*w - 23],\ [829, 829, 5/6*w^3 - 17/6*w^2 - 5/6*w + 8],\ [829, 829, -4/3*w^3 - 2/3*w^2 + 43/3*w + 15],\ [829, 829, -1/6*w^3 - 17/6*w^2 + 25/6*w + 16],\ [839, 839, 1/3*w^3 - 7/3*w^2 + 2/3*w + 5],\ [839, 839, 1/2*w^3 + 3/2*w^2 - 13/2*w - 20],\ [841, 29, -5/6*w^3 + 5/6*w^2 + 35/6*w - 4],\ [859, 859, 1/6*w^3 + 5/6*w^2 - 37/6*w + 7],\ [859, 859, 13/6*w^3 + 17/6*w^2 - 127/6*w - 33],\ [881, 881, -2/3*w^3 + 2/3*w^2 + 20/3*w + 5],\ [881, 881, 17/6*w^3 + 19/6*w^2 - 167/6*w - 42],\ [911, 911, -1/6*w^3 + 13/6*w^2 - 11/6*w - 6],\ [911, 911, 3/2*w^3 + 1/2*w^2 - 33/2*w - 17],\ [911, 911, 5/6*w^3 - 17/6*w^2 + 1/6*w + 5],\ [911, 911, 7/6*w^3 - 1/6*w^2 - 61/6*w - 1],\ [929, 929, -7/6*w^3 - 11/6*w^2 + 67/6*w + 22],\ [929, 929, -1/6*w^3 + 1/6*w^2 - 11/6*w + 6],\ [941, 941, 11/6*w^3 + 19/6*w^2 - 107/6*w - 34],\ [941, 941, 4/3*w^3 - 10/3*w^2 - 25/3*w + 19],\ [941, 941, -11/6*w^3 + 41/6*w^2 + 47/6*w - 31],\ [941, 941, 1/2*w^3 + 1/2*w^2 - 13/2*w - 13],\ [961, 31, -1/3*w^3 + 1/3*w^2 + 7/3*w + 5],\ [991, 991, -1/6*w^3 - 5/6*w^2 + 25/6*w + 6],\ [991, 991, 1/6*w^3 + 5/6*w^2 - 25/6*w - 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 25*x^8 + 182*x^6 - 510*x^4 + 505*x^2 - 121 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 9/176*e^9 - 12/11*e^7 + 467/88*e^5 - 71/11*e^3 - 207/176*e, -1, -1/16*e^8 + 11/8*e^6 - 15/2*e^4 + 117/8*e^2 - 135/16, 1/44*e^9 - 39/88*e^7 + 133/88*e^5 + 47/88*e^3 - 255/88*e, 1/16*e^9 - 11/8*e^7 + 29/4*e^5 - 81/8*e^3 - 13/16*e, -7/176*e^9 + 93/88*e^7 - 92/11*e^5 + 2027/88*e^3 - 2985/176*e, -1/4*e^8 + 11/2*e^6 - 59/2*e^4 + 97/2*e^2 - 65/4, 5/176*e^9 - 23/44*e^7 + 103/88*e^5 + 237/44*e^3 - 2491/176*e, 7/88*e^9 - 41/22*e^7 + 505/44*e^5 - 469/22*e^3 + 367/88*e, -3/176*e^9 + 4/11*e^7 - 163/88*e^5 + 73/22*e^3 + 113/176*e, -1/8*e^9 + 11/4*e^7 - 15*e^5 + 117/4*e^3 - 183/8*e, 3/22*e^9 - 75/22*e^7 + 535/22*e^5 - 1321/22*e^3 + 389/11*e, 1/176*e^9 + 15/88*e^7 - 56/11*e^5 + 1725/88*e^3 - 1321/176*e, -3/8*e^8 + 67/8*e^6 - 375/8*e^4 + 685/8*e^2 - 155/4, -1/16*e^8 + 11/8*e^6 - 15/2*e^4 + 109/8*e^2 - 55/16, -1/16*e^8 + 5/4*e^6 - 39/8*e^4 + 13/4*e^2 - 41/16, 1/16*e^8 - 11/8*e^6 + 29/4*e^4 - 73/8*e^2 + 3/16, 1/16*e^8 - 11/8*e^6 + 8*e^4 - 181/8*e^2 + 383/16, -47/176*e^9 + 549/88*e^7 - 1715/44*e^5 + 7431/88*e^3 - 8973/176*e, 23/176*e^9 - 271/88*e^7 + 865/44*e^5 - 3841/88*e^3 + 3013/176*e, -3/22*e^9 + 139/44*e^7 - 425/22*e^5 + 1751/44*e^3 - 327/22*e, -1/16*e^8 + 7/8*e^6 + 9/4*e^4 - 171/8*e^2 + 181/16, -1/4*e^6 + 21/4*e^4 - 95/4*e^2 + 99/4, -9/176*e^9 + 107/88*e^7 - 169/22*e^5 + 1261/88*e^3 - 607/176*e, -1/8*e^8 + 19/8*e^6 - 59/8*e^4 - 11/8*e^2 - 7/2, -1/8*e^8 + 2*e^6 + 1/4*e^4 - 34*e^2 + 223/8, -3/16*e^8 + 4*e^6 - 159/8*e^4 + 63/2*e^2 - 199/16, -17/88*e^9 + 109/22*e^7 - 1635/44*e^5 + 2173/22*e^3 - 6209/88*e, -3/22*e^9 + 75/22*e^7 - 535/22*e^5 + 1299/22*e^3 - 268/11*e, 7/176*e^9 - 49/88*e^7 - 18/11*e^5 + 1449/88*e^3 - 1591/176*e, 1/44*e^9 - 25/44*e^7 + 193/44*e^5 - 719/44*e^3 + 599/22*e, -9/176*e^9 + 85/88*e^7 - 35/11*e^5 + 271/88*e^3 - 1311/176*e, -29/176*e^9 + 173/44*e^7 - 2287/88*e^5 + 2801/44*e^3 - 6989/176*e, -45/176*e^9 + 513/88*e^7 - 757/22*e^5 + 6107/88*e^3 - 6995/176*e, 3/44*e^9 - 53/44*e^7 + 117/44*e^5 + 21/44*e^3 + 178/11*e, -3/176*e^9 + 21/88*e^7 + 23/44*e^5 - 401/88*e^3 + 399/176*e, 1/44*e^9 - 25/44*e^7 + 193/44*e^5 - 719/44*e^3 + 511/22*e, -3/16*e^9 + 37/8*e^7 - 32*e^5 + 587/8*e^3 - 541/16*e, -1/4*e^8 + 23/4*e^6 - 137/4*e^4 + 261/4*e^2 - 53/2, 1/8*e^8 - 5/2*e^6 + 10*e^4 - 11*e^2 + 51/8, -13/88*e^9 + 42/11*e^7 - 1271/44*e^5 + 826/11*e^3 - 3221/88*e, 1/8*e^8 - 2*e^6 + 1/4*e^4 + 28*e^2 - 211/8, 1/8*e^8 - 5/2*e^6 + 41/4*e^4 - 25/2*e^2 + 117/8, 3/8*e^8 - 31/4*e^6 + 69/2*e^4 - 157/4*e^2 + 161/8, -1/16*e^8 + 7/4*e^6 - 123/8*e^4 + 199/4*e^2 - 433/16, -1/8*e^8 + 11/4*e^6 - 14*e^4 + 53/4*e^2 + 65/8, -1/16*e^8 + 7/8*e^6 + 11/4*e^4 - 227/8*e^2 + 381/16, -7/16*e^8 + 41/4*e^6 - 509/8*e^4 + 501/4*e^2 - 743/16, 5/16*e^8 - 57/8*e^6 + 42*e^4 - 643/8*e^2 + 515/16, 13/44*e^9 - 157/22*e^7 + 2091/44*e^5 - 1168/11*e^3 + 1099/22*e, -39/88*e^9 + 471/44*e^7 - 791/11*e^5 + 7525/44*e^3 - 8937/88*e, -1/16*e^8 + 13/8*e^6 - 23/2*e^4 + 135/8*e^2 + 193/16, 5/16*e^8 - 53/8*e^6 + 125/4*e^4 - 259/8*e^2 - 41/16, 1/4*e^6 - 21/4*e^4 + 91/4*e^2 - 95/4, 1/4*e^8 - 6*e^6 + 79/2*e^4 - 86*e^2 + 145/4, -3/16*e^8 + 31/8*e^6 - 67/4*e^4 + 65/8*e^2 + 367/16, -3/16*e^8 + 3*e^6 - 3/8*e^4 - 83/2*e^2 + 417/16, -61/176*e^9 + 669/88*e^7 - 1769/44*e^5 + 5435/88*e^3 - 2799/176*e, -5/16*e^8 + 55/8*e^6 - 145/4*e^4 + 413/8*e^2 + 177/16, -39/176*e^9 + 241/44*e^7 - 3417/88*e^5 + 4505/44*e^3 - 12831/176*e, 5/8*e^8 - 111/8*e^6 + 611/8*e^4 - 1089/8*e^2 + 61, 1/16*e^8 - 3/8*e^6 - 12*e^4 + 459/8*e^2 - 337/16, -5/16*e^8 + 53/8*e^6 - 129/4*e^4 + 387/8*e^2 - 359/16, -1/2*e^8 + 43/4*e^6 - 217/4*e^4 + 333/4*e^2 - 181/4, -7/16*e^8 + 71/8*e^6 - 36*e^4 + 141/8*e^2 + 335/16, 3/8*e^8 - 15/2*e^6 + 30*e^4 - 25*e^2 + 57/8, 1/4*e^8 - 25/4*e^6 + 177/4*e^4 - 407/4*e^2 + 87/2, 1/16*e^8 - 3/2*e^6 + 77/8*e^4 - 18*e^2 - 51/16, -69/176*e^9 + 791/88*e^7 - 2375/44*e^5 + 10005/88*e^3 - 13351/176*e, 13/176*e^9 - 9/22*e^7 - 1391/88*e^5 + 940/11*e^3 - 13015/176*e, 137/176*e^9 - 1531/88*e^7 + 1073/11*e^5 - 15685/88*e^3 + 13415/176*e, -9/44*e^9 + 203/44*e^7 - 1143/44*e^5 + 1829/44*e^3 - 6/11*e, -7/44*e^9 + 383/88*e^7 - 3109/88*e^5 + 7921/88*e^3 - 3165/88*e, -65/176*e^9 + 83/11*e^7 - 2813/88*e^5 + 555/22*e^3 + 2243/176*e, -5/16*e^8 + 61/8*e^6 - 52*e^4 + 959/8*e^2 - 739/16, -5/176*e^9 + 35/88*e^7 + 16/11*e^5 - 1651/88*e^3 + 7397/176*e, -3/16*e^8 + 33/8*e^6 - 93/4*e^4 + 451/8*e^2 - 865/16, 37/176*e^9 - 179/44*e^7 + 1167/88*e^5 + 469/44*e^3 - 6747/176*e, -1/2*e^8 + 21/2*e^6 - 195/4*e^4 + 54*e^2 + 31/4, 1/2*e^8 - 23/2*e^6 + 68*e^4 - 239/2*e^2 + 49/2, -13/88*e^9 + 42/11*e^7 - 1249/44*e^5 + 727/11*e^3 - 1769/88*e, -3/44*e^9 + 119/44*e^7 - 1437/44*e^5 + 5193/44*e^3 - 1124/11*e, -1/88*e^9 - 1/11*e^7 + 261/44*e^5 - 357/11*e^3 + 2311/88*e, -31/88*e^9 + 349/44*e^7 - 2007/44*e^5 + 3945/44*e^3 - 3511/88*e, -3/8*e^9 + 9*e^7 - 239/4*e^5 + 141*e^3 - 719/8*e, 79/176*e^9 - 883/88*e^7 + 2489/44*e^5 - 9541/88*e^3 + 11581/176*e, 43/176*e^9 - 61/11*e^7 + 2791/88*e^5 - 1127/22*e^3 - 417/176*e, -29/176*e^9 + 335/88*e^7 - 257/11*e^5 + 4513/88*e^3 - 4723/176*e, -11/16*e^8 + 109/8*e^6 - 205/4*e^4 + 159/8*e^2 + 439/16, -5/16*e^8 + 63/8*e^6 - 225/4*e^4 + 1045/8*e^2 - 879/16, e^8 - 87/4*e^6 + 227/2*e^4 - 727/4*e^2 + 68, 5/8*e^8 - 59/4*e^6 + 93*e^4 - 761/4*e^2 + 683/8, 1/16*e^9 - 3/2*e^7 + 81/8*e^5 - 28*e^3 + 613/16*e, -5/16*e^9 + 29/4*e^7 - 355/8*e^5 + 365/4*e^3 - 749/16*e, -111/176*e^9 + 1283/88*e^7 - 978/11*e^5 + 16425/88*e^3 - 19513/176*e, 9/176*e^9 - 195/88*e^7 + 1251/44*e^5 - 9401/88*e^3 + 15699/176*e, 65/176*e^9 - 763/88*e^7 + 1201/22*e^5 - 10261/88*e^3 + 10583/176*e, 3/4*e^8 - 125/8*e^6 + 571/8*e^4 - 707/8*e^2 + 383/8, 75/176*e^9 - 211/22*e^7 + 4823/88*e^5 - 1160/11*e^3 + 11343/176*e, -3/8*e^8 + 71/8*e^6 - 455/8*e^4 + 985/8*e^2 - 235/4, 17/88*e^9 - 185/44*e^7 + 241/11*e^5 - 1519/44*e^3 + 1127/88*e, -3/44*e^9 + 16/11*e^7 - 185/22*e^5 + 355/11*e^3 - 2791/44*e, -3/8*e^8 + 33/4*e^6 - 45*e^4 + 339/4*e^2 - 237/8, 3/8*e^8 - 31/4*e^6 + 35*e^4 - 197/4*e^2 + 285/8, 7/176*e^9 - 115/88*e^7 + 305/22*e^5 - 4601/88*e^3 + 9145/176*e, 25/88*e^9 - 137/22*e^7 + 368/11*e^5 - 678/11*e^3 + 4419/88*e, 25/88*e^9 - 63/11*e^7 + 258/11*e^5 - 465/22*e^3 + 811/88*e, 2/11*e^9 - 233/44*e^7 + 2083/44*e^5 - 6027/44*e^3 + 3193/44*e, 7/16*e^8 - 71/8*e^6 + 75/2*e^4 - 317/8*e^2 + 505/16, -3/44*e^9 + 21/22*e^7 + 34/11*e^5 - 731/22*e^3 + 1455/44*e, 1/44*e^9 - 7/22*e^7 - 4/11*e^5 - 13/22*e^3 + 439/44*e, -1/8*e^8 + 11/4*e^6 - 14*e^4 + 45/4*e^2 - 47/8, -1/2*e^8 + 43/4*e^6 - 213/4*e^4 + 273/4*e^2 - 61/4, -23/88*e^9 + 119/22*e^7 - 1059/44*e^5 + 573/22*e^3 - 1539/88*e, -1/16*e^8 + 19/8*e^6 - 115/4*e^4 + 897/8*e^2 - 1355/16, 51/88*e^9 - 621/44*e^7 + 2117/22*e^5 - 10167/44*e^3 + 12577/88*e, -9/8*e^8 + 197/8*e^6 - 1041/8*e^4 + 1643/8*e^2 - 251/4, 1/4*e^8 - 27/4*e^6 + 217/4*e^4 - 577/4*e^2 + 173/2, 1/22*e^9 - 7/11*e^7 - 30/11*e^5 + 394/11*e^3 - 1607/22*e, 1/8*e^8 - 17/4*e^6 + 87/2*e^4 - 483/4*e^2 + 331/8, 1/176*e^9 - 95/88*e^7 + 449/22*e^5 - 7801/88*e^3 + 16103/176*e, 21/16*e^8 - 223/8*e^6 + 269/2*e^4 - 1377/8*e^2 + 259/16, 57/176*e^9 - 685/88*e^7 + 570/11*e^5 - 10839/88*e^3 + 15871/176*e, 25/176*e^9 - 115/44*e^7 + 603/88*e^5 + 217/44*e^3 + 2153/176*e, -13/176*e^9 + 73/44*e^7 - 831/88*e^5 + 717/44*e^3 + 1091/176*e, 65/176*e^9 - 741/88*e^7 + 1113/22*e^5 - 10327/88*e^3 + 20703/176*e, 13/88*e^9 - 95/22*e^7 + 1733/44*e^5 - 2763/22*e^3 + 10833/88*e, -95/176*e^9 + 995/88*e^7 - 576/11*e^5 + 5393/88*e^3 - 345/176*e, -3/4*e^6 + 59/4*e^4 - 225/4*e^2 + 209/4, 63/88*e^9 - 749/44*e^7 + 1205/11*e^5 - 10323/44*e^3 + 9881/88*e, -17/44*e^9 + 707/88*e^7 - 3185/88*e^5 + 3205/88*e^3 + 1211/88*e, -11/16*e^8 + 63/4*e^6 - 741/8*e^4 + 667/4*e^2 - 835/16, 13/16*e^8 - 133/8*e^6 + 285/4*e^4 - 539/8*e^2 + 287/16, 7/8*e^8 - 20*e^6 + 475/4*e^4 - 237*e^2 + 859/8, 85/176*e^9 - 991/88*e^7 + 773/11*e^5 - 13513/88*e^3 + 15051/176*e, -131/176*e^9 + 1555/88*e^7 - 2499/22*e^5 + 21657/88*e^3 - 22573/176*e, -1/2*e^8 + 43/4*e^6 - 217/4*e^4 + 341/4*e^2 - 125/4, -25/176*e^9 + 285/88*e^7 - 857/44*e^5 + 4131/88*e^3 - 12163/176*e, -5/44*e^9 + 34/11*e^7 - 277/11*e^5 + 731/11*e^3 - 699/44*e, -3/8*e^8 + 9*e^6 - 235/4*e^4 + 124*e^2 - 591/8, -1/4*e^9 + 23/4*e^7 - 137/4*e^5 + 253/4*e^3 - 25/2*e, 7/16*e^8 - 9*e^6 + 307/8*e^4 - 49/2*e^2 - 357/16, 107/176*e^9 - 1233/88*e^7 + 1865/22*e^5 - 15295/88*e^3 + 13709/176*e, -5/8*e^8 + 15*e^6 - 393/4*e^4 + 214*e^2 - 785/8, 53/176*e^9 - 301/44*e^7 + 3503/88*e^5 - 3309/44*e^3 + 4325/176*e, 5/16*e^8 - 61/8*e^6 + 105/2*e^4 - 1047/8*e^2 + 1451/16, -9/16*e^8 + 51/4*e^6 - 591/8*e^4 + 551/4*e^2 - 465/16, -4/11*e^9 + 389/44*e^7 - 2659/44*e^5 + 6675/44*e^3 - 5693/44*e, 29/88*e^9 - 659/88*e^7 + 3859/88*e^5 - 7629/88*e^3 + 578/11*e, 1/8*e^8 - 7/2*e^6 + 119/4*e^4 - 167/2*e^2 + 233/8, -13/22*e^9 + 595/44*e^7 - 3511/44*e^5 + 6561/44*e^3 - 2075/44*e, 9/16*e^8 - 47/4*e^6 + 431/8*e^4 - 239/4*e^2 + 257/16, -5/22*e^9 + 125/22*e^7 - 455/11*e^5 + 2517/22*e^3 - 1755/22*e, 21/88*e^9 - 279/44*e^7 + 2241/44*e^5 - 6587/44*e^3 + 10517/88*e, -157/176*e^9 + 224/11*e^7 - 10613/88*e^5 + 5353/22*e^3 - 22833/176*e, -5/22*e^9 + 46/11*e^7 - 239/22*e^5 - 144/11*e^3 + 140/11*e, 7/16*e^8 - 73/8*e^6 + 163/4*e^4 - 267/8*e^2 - 475/16, -9/16*e^8 + 101/8*e^6 - 70*e^4 + 847/8*e^2 - 335/16, 11/8*e^8 - 30*e^6 + 629/4*e^4 - 248*e^2 + 555/8, -5/11*e^9 + 423/44*e^7 - 2067/44*e^5 + 3413/44*e^3 - 2917/44*e, 17/44*e^9 - 98/11*e^7 + 1195/22*e^5 - 1315/11*e^3 + 3965/44*e, -13/16*e^8 + 35/2*e^6 - 709/8*e^4 + 136*e^2 - 1201/16, -7/8*e^8 + 19*e^6 - 387/4*e^4 + 126*e^2 + 69/8, -5/16*e^9 + 7*e^7 - 325/8*e^5 + 189/2*e^3 - 1529/16*e, 13/176*e^9 - 289/88*e^7 + 1851/44*e^5 - 12951/88*e^3 + 16663/176*e, 75/176*e^9 - 433/44*e^7 + 5329/88*e^5 - 6037/44*e^3 + 18075/176*e, -83/176*e^9 + 439/44*e^7 - 4253/88*e^5 + 3207/44*e^3 - 9179/176*e, -5/16*e^8 + 53/8*e^6 - 63/2*e^4 + 231/8*e^2 + 597/16, 17/16*e^8 - 95/4*e^6 + 1063/8*e^4 - 959/4*e^2 + 1673/16, 39/88*e^9 - 449/44*e^7 + 670/11*e^5 - 4995/44*e^3 + 2337/88*e, -5/8*e^8 + 49/4*e^6 - 44*e^4 + 43/4*e^2 + 173/8, -31/176*e^9 + 393/88*e^7 - 719/22*e^5 + 7135/88*e^3 - 4281/176*e, 7/16*e^8 - 39/4*e^6 + 433/8*e^4 - 379/4*e^2 + 751/16, 1/4*e^8 - 19/4*e^6 + 57/4*e^4 + 67/4*e^2 - 133/2, 21/44*e^9 - 112/11*e^7 + 1075/22*e^5 - 538/11*e^3 - 1803/44*e, -13/176*e^9 + 73/44*e^7 - 963/88*e^5 + 1993/44*e^3 - 16773/176*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]