/* 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, 5, -4, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([27, 27, w^3 - 2*w^2 - 2*w + 3]) primes_array = [ [3, 3, w - 1],\ [5, 5, w^2 - w - 2],\ [7, 7, w^4 - 2*w^3 - 3*w^2 + 4*w + 2],\ [13, 13, w^3 - 2*w^2 - 2*w + 2],\ [29, 29, -w^4 + 3*w^3 + 2*w^2 - 7*w - 1],\ [29, 29, -w^2 + 2*w + 3],\ [31, 31, w^4 - 2*w^3 - 3*w^2 + 5*w],\ [31, 31, w^3 - 2*w^2 - 3*w + 2],\ [32, 2, 2],\ [43, 43, -w^2 - w + 4],\ [53, 53, -w^4 + w^3 + 6*w^2 - 2*w - 5],\ [53, 53, -w^4 + 2*w^3 + 4*w^2 - 5*w - 2],\ [73, 73, w^4 - w^3 - 6*w^2 + 2*w + 6],\ [73, 73, w^3 - w^2 - 4*w + 2],\ [81, 3, 2*w^4 - 5*w^3 - 4*w^2 + 9*w + 2],\ [83, 83, w^3 - w^2 - 5*w],\ [89, 89, -w^4 + 2*w^3 + 4*w^2 - 4*w - 2],\ [97, 97, w^4 - 3*w^3 - 2*w^2 + 6*w + 2],\ [101, 101, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\ [103, 103, -w^4 + w^3 + 6*w^2 - w - 7],\ [103, 103, 2*w^4 - 4*w^3 - 6*w^2 + 8*w + 1],\ [103, 103, w^4 - w^3 - 6*w^2 + 3*w + 4],\ [107, 107, -w^4 + 2*w^3 + 3*w^2 - 5*w + 2],\ [109, 109, w^3 - 4*w - 1],\ [109, 109, -w^2 + 2*w + 4],\ [131, 131, w^4 - w^3 - 6*w^2 + w + 6],\ [137, 137, w^3 - w^2 - 5*w + 3],\ [149, 149, w^4 - 3*w^3 - 3*w^2 + 9*w + 6],\ [149, 149, -w^4 + 6*w^2 + 3*w],\ [163, 163, 2*w^2 - w - 5],\ [167, 167, -2*w^4 + 3*w^3 + 8*w^2 - 4*w - 3],\ [169, 13, w^4 - 3*w^3 + 6*w - 3],\ [169, 13, w^3 - 4*w - 4],\ [173, 173, w^4 - w^3 - 4*w^2 + 2*w + 1],\ [173, 173, -w^4 + 3*w^3 + 3*w^2 - 7*w - 5],\ [173, 173, w^4 - w^3 - 4*w^2 + w - 1],\ [179, 179, w^2 - 3*w - 2],\ [191, 191, -w^4 + 3*w^3 + w^2 - 6*w - 1],\ [193, 193, -w^3 + 2*w^2 + w - 4],\ [193, 193, -w^4 + 3*w^3 + 3*w^2 - 8*w - 1],\ [199, 199, w^4 - 3*w^3 - w^2 + 7*w],\ [199, 199, -2*w^4 + 5*w^3 + 5*w^2 - 10*w - 2],\ [199, 199, w^4 - 3*w^3 + 5*w - 4],\ [211, 211, 2*w^3 - 2*w^2 - 7*w - 1],\ [211, 211, -2*w^3 + 3*w^2 + 5*w - 2],\ [223, 223, -2*w^4 + 3*w^3 + 10*w^2 - 7*w - 9],\ [227, 227, w^3 - w^2 - 4*w + 3],\ [229, 229, w^4 - 4*w^3 + 10*w - 5],\ [229, 229, -2*w^4 + 4*w^3 + 7*w^2 - 9*w - 8],\ [239, 239, -2*w^4 + 3*w^3 + 7*w^2 - 3*w - 3],\ [241, 241, w^3 - w^2 - 2*w - 2],\ [257, 257, -w^4 + w^3 + 6*w^2 - 4*w - 4],\ [263, 263, 2*w^3 - 4*w^2 - 5*w + 6],\ [269, 269, w^3 - 2*w^2 - 4*w + 4],\ [269, 269, -2*w^4 + 2*w^3 + 11*w^2 - 3*w - 10],\ [271, 271, w^3 - 5*w],\ [281, 281, w^4 - w^3 - 5*w^2 + 3*w + 3],\ [281, 281, -2*w^4 + 4*w^3 + 6*w^2 - 6*w - 3],\ [281, 281, w^3 - 5*w - 1],\ [283, 283, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\ [289, 17, -2*w^4 + 3*w^3 + 8*w^2 - 5*w - 2],\ [293, 293, 2*w^4 - 5*w^3 - 7*w^2 + 14*w + 9],\ [311, 311, -w^4 + 2*w^3 + 2*w^2 - 4*w + 3],\ [313, 313, w^3 - 6*w],\ [331, 331, w^4 - 2*w^3 - 2*w^2 + w - 2],\ [359, 359, w^4 - w^3 - 5*w^2 + 2*w - 1],\ [373, 373, -w^4 + 3*w^3 + 2*w^2 - 8*w - 3],\ [373, 373, 2*w^3 - 4*w^2 - 3*w + 3],\ [379, 379, -w^4 + 4*w^3 - w^2 - 9*w + 3],\ [379, 379, -w^4 + 3*w^3 + w^2 - 6*w - 2],\ [379, 379, w^4 + w^3 - 7*w^2 - 6*w + 3],\ [383, 383, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\ [383, 383, w^4 - 5*w^2 - 3*w + 3],\ [383, 383, 2*w^4 - 5*w^3 - 3*w^2 + 8*w],\ [389, 389, 3*w^4 - 7*w^3 - 8*w^2 + 16*w + 1],\ [397, 397, -2*w^4 + 3*w^3 + 8*w^2 - 3*w - 7],\ [397, 397, -w^4 + 2*w^3 + 3*w^2 - 4*w - 5],\ [397, 397, -2*w^4 + 3*w^3 + 7*w^2 - 4*w - 3],\ [409, 409, -w^4 + w^3 + 7*w^2 - 5*w - 9],\ [419, 419, w^4 - 2*w^3 - w^2 + 2*w - 2],\ [419, 419, 2*w^4 - 3*w^3 - 7*w^2 + 5*w + 2],\ [419, 419, -w^4 + 4*w^3 - 9*w - 2],\ [433, 433, -w^4 + 3*w^3 - 8*w + 4],\ [433, 433, w^4 - 7*w^2 - w + 6],\ [439, 439, 3*w^4 - 6*w^3 - 10*w^2 + 11*w + 7],\ [449, 449, -2*w^4 + 5*w^3 + 5*w^2 - 11*w - 4],\ [457, 457, -2*w^4 + 5*w^3 + 4*w^2 - 10*w - 2],\ [463, 463, 2*w^4 - 5*w^3 - 4*w^2 + 8*w + 1],\ [467, 467, 2*w^4 - 4*w^3 - 6*w^2 + 6*w + 1],\ [479, 479, 3*w^4 - 4*w^3 - 12*w^2 + 4*w + 7],\ [479, 479, 2*w^4 - 6*w^3 - 4*w^2 + 14*w + 1],\ [491, 491, w^4 - 6*w^2 - w + 4],\ [503, 503, 2*w^4 - w^3 - 11*w^2 - 3*w + 8],\ [503, 503, 2*w^3 - 5*w^2 - 2*w + 6],\ [509, 509, w^4 - 5*w^2 - 6*w],\ [509, 509, w^4 - 3*w^3 - 3*w^2 + 9*w + 1],\ [523, 523, 3*w^4 - 7*w^3 - 7*w^2 + 12*w + 3],\ [523, 523, 3*w^4 - 8*w^3 - 7*w^2 + 17*w + 3],\ [523, 523, w^4 - 7*w^2 - 2*w + 4],\ [529, 23, -w^4 + w^3 + 7*w^2 - 2*w - 9],\ [541, 541, w^4 - 3*w^3 - 3*w^2 + 5*w + 2],\ [547, 547, -w^3 + 3*w^2 + 3*w - 4],\ [557, 557, 2*w^3 - 4*w^2 - 6*w + 9],\ [577, 577, 2*w^4 - 2*w^3 - 11*w^2 + 5*w + 10],\ [577, 577, w^4 - 4*w^3 - w^2 + 9*w],\ [577, 577, 2*w^4 - 3*w^3 - 9*w^2 + 4*w + 8],\ [577, 577, w^4 - 7*w^2 - 3*w + 7],\ [577, 577, -3*w^4 + 3*w^3 + 13*w^2 - w - 4],\ [593, 593, 3*w - 2],\ [601, 601, 2*w^4 - 4*w^3 - 7*w^2 + 5*w + 6],\ [601, 601, -w^4 + 3*w^3 + w^2 - 7*w - 1],\ [607, 607, w^3 - w^2 - 2*w - 3],\ [625, 5, 2*w^4 - 5*w^3 - 8*w^2 + 14*w + 11],\ [631, 631, -w^2 + w - 2],\ [631, 631, w^4 - 7*w^2 - w + 8],\ [643, 643, -2*w^4 + 4*w^3 + 9*w^2 - 10*w - 8],\ [647, 647, 3*w^4 - 6*w^3 - 10*w^2 + 12*w + 8],\ [653, 653, -3*w^4 + 6*w^3 + 11*w^2 - 12*w - 9],\ [653, 653, w^4 - w^3 - 2*w^2 - 3*w - 3],\ [653, 653, -2*w^4 + 4*w^3 + 7*w^2 - 6*w - 8],\ [701, 701, w^4 - w^3 - 2*w^2 - w - 5],\ [719, 719, 2*w^4 - 5*w^3 - 6*w^2 + 14*w + 2],\ [727, 727, 2*w^4 - 5*w^3 - 5*w^2 + 9*w + 3],\ [733, 733, 2*w^4 - 5*w^3 - 5*w^2 + 13*w + 3],\ [739, 739, -2*w^3 + 4*w^2 + 4*w - 5],\ [743, 743, w^4 - 2*w^3 - 3*w^2 + 6*w - 3],\ [743, 743, 2*w^4 - 2*w^3 - 11*w^2 + 2*w + 10],\ [757, 757, -w^4 + 2*w^3 + 5*w^2 - 6*w - 10],\ [757, 757, 2*w^4 - 6*w^3 - 2*w^2 + 11*w - 4],\ [761, 761, 3*w^3 - 4*w^2 - 9*w + 3],\ [769, 769, 3*w^3 - 5*w^2 - 9*w + 7],\ [769, 769, -2*w^4 + 4*w^3 + 7*w^2 - 11*w - 2],\ [773, 773, 2*w^4 - 5*w^3 - 6*w^2 + 12*w + 1],\ [773, 773, 3*w^4 - 4*w^3 - 12*w^2 + 3*w + 5],\ [773, 773, 2*w^3 - w^2 - 10*w - 4],\ [797, 797, -w^4 + 4*w^3 + 2*w^2 - 12*w - 3],\ [811, 811, w^4 - 2*w^3 - 6*w^2 + 8*w + 4],\ [823, 823, w^4 - 4*w^3 - w^2 + 10*w + 1],\ [823, 823, 2*w^4 - 4*w^3 - 4*w^2 + 4*w - 3],\ [827, 827, -w^4 + 2*w^3 + 2*w^2 - w + 3],\ [827, 827, 2*w^4 - 4*w^3 - 5*w^2 + 7*w + 2],\ [829, 829, -w^4 + 4*w^3 + 2*w^2 - 10*w - 2],\ [829, 829, 3*w^3 - 3*w^2 - 11*w - 2],\ [829, 829, w^4 - 2*w^3 - 3*w^2 + 2*w - 3],\ [839, 839, -w^4 + 5*w^3 - 3*w^2 - 10*w + 5],\ [839, 839, -w^4 + w^3 + 5*w^2 - 9],\ [853, 853, 2*w^4 - 6*w^3 - 5*w^2 + 15*w + 4],\ [859, 859, -3*w^4 + 8*w^3 + 6*w^2 - 18*w + 5],\ [863, 863, w^4 - w^3 - 6*w^2 + 5*w + 2],\ [877, 877, 3*w^3 - 4*w^2 - 8*w + 1],\ [881, 881, 3*w^4 - 7*w^3 - 9*w^2 + 15*w + 3],\ [881, 881, -w^3 + 7*w + 1],\ [883, 883, -2*w^4 + 6*w^3 + 3*w^2 - 15*w],\ [887, 887, w^4 - w^3 - 5*w^2 + w - 1],\ [907, 907, 3*w^4 - 5*w^3 - 11*w^2 + 9*w + 5],\ [919, 919, w^4 - 2*w^3 - 6*w^2 + 8*w + 7],\ [937, 937, 2*w^4 - 2*w^3 - 9*w^2 + 2*w + 3],\ [937, 937, -3*w^4 + 8*w^3 + 6*w^2 - 16*w + 1],\ [937, 937, 3*w^4 - 5*w^3 - 11*w^2 + 7*w + 4],\ [947, 947, w^3 - w^2 - 7*w + 2],\ [947, 947, -w^4 + 2*w^3 + 4*w^2 - 7*w - 3],\ [967, 967, -w^4 + 4*w^3 - 11*w],\ [971, 971, 3*w^4 - 6*w^3 - 8*w^2 + 10*w],\ [971, 971, w^4 - 8*w^2 + 2*w + 9],\ [971, 971, w^4 - 4*w^3 + 2*w^2 + 7*w - 4],\ [977, 977, -w^4 + 4*w^3 - 12*w + 5],\ [983, 983, -w^4 + w^3 + 4*w^2 + 3*w - 2],\ [983, 983, -2*w^4 + 3*w^3 + 8*w^2 - 6*w - 4],\ [997, 997, 2*w^4 - 4*w^3 - 5*w^2 + 5*w - 3],\ [997, 997, w^4 + w^3 - 5*w^2 - 9*w - 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - x^4 - 12*x^3 + 9*x^2 + 33*x - 9 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, 1/3*e^4 + 2/3*e^3 - 2*e^2 - 5*e, 1/3*e^4 - 1/3*e^3 - 3*e^2 + 2*e + 6, -e^4 - e^3 + 8*e^2 + 6*e - 6, -e^4 - 2*e^3 + 8*e^2 + 13*e - 3, 1/3*e^4 + 2/3*e^3 - e^2 - 4*e - 6, -2/3*e^4 - 4/3*e^3 + 4*e^2 + 9*e + 4, -e^4 - e^3 + 6*e^2 + 7*e + 6, 4/3*e^4 + 5/3*e^3 - 10*e^2 - 12*e + 6, e^4 + 2*e^3 - 9*e^2 - 13*e + 12, e^4 - e^3 - 9*e^2 + 5*e + 12, -2/3*e^4 - 7/3*e^3 + 4*e^2 + 18*e + 9, -5/3*e^4 - 4/3*e^3 + 14*e^2 + 10*e - 9, -10/3*e^4 - 14/3*e^3 + 27*e^2 + 31*e - 22, -e^3 + 6*e + 3, -2*e^4 - 2*e^3 + 15*e^2 + 16*e - 3, 10/3*e^4 + 8/3*e^3 - 25*e^2 - 18*e + 12, -e^4 + e^3 + 8*e^2 - 6*e - 9, 10/3*e^4 + 14/3*e^3 - 27*e^2 - 31*e + 19, 4/3*e^4 + 5/3*e^3 - 11*e^2 - 8*e + 6, -8/3*e^4 - 16/3*e^3 + 23*e^2 + 36*e - 21, e^4 + 3*e^3 - 6*e^2 - 17*e - 6, 10/3*e^4 + 20/3*e^3 - 28*e^2 - 47*e + 28, -5/3*e^4 - 13/3*e^3 + 13*e^2 + 30*e - 11, -3*e^4 - 4*e^3 + 23*e^2 + 24*e - 6, 2*e^3 - 2*e^2 - 14*e + 9, e^4 + 2*e^3 - 10*e^2 - 17*e + 18, -e^4 - 4*e^3 + 6*e^2 + 33*e + 9, 4/3*e^4 + 2/3*e^3 - 12*e^2 + 12, 2*e^4 + e^3 - 17*e^2 - 7*e + 27, 4/3*e^4 + 5/3*e^3 - 10*e^2 - 12*e + 9, -3*e^3 + 23*e + 5, 3*e^4 + 6*e^3 - 23*e^2 - 40*e, 2*e^4 + 6*e^3 - 17*e^2 - 41*e + 18, 3*e^4 + 5*e^3 - 20*e^2 - 38*e, e^4 + 2*e^3 - 5*e^2 - 16*e - 6, 2*e^4 + 5*e^3 - 14*e^2 - 32*e + 6, 7/3*e^4 + 14/3*e^3 - 18*e^2 - 34*e + 1, -2*e^4 - 2*e^3 + 14*e^2 + 11*e + 2, -8/3*e^4 - 22/3*e^3 + 19*e^2 + 52*e - 3, -5/3*e^4 + 2/3*e^3 + 13*e^2 - 3*e - 11, 1/3*e^4 + 8/3*e^3 - 2*e^2 - 16*e - 6, -6*e^4 - 10*e^3 + 50*e^2 + 64*e - 37, 16/3*e^4 + 29/3*e^3 - 41*e^2 - 69*e + 27, -2/3*e^4 - 10/3*e^3 + 7*e^2 + 27*e - 8, -2*e^4 - e^3 + 16*e^2 + 11*e - 9, 1/3*e^4 - 4/3*e^3 - 4*e^2 + 15*e + 15, 7/3*e^4 + 17/3*e^3 - 17*e^2 - 39*e + 4, -3*e^3 + e^2 + 20*e - 9, -8/3*e^4 - 13/3*e^3 + 22*e^2 + 28*e - 23, -e^3 + 4*e^2 + e - 21, -e^4 - e^3 + 8*e^2 + 9*e - 3, -6*e^4 - 8*e^3 + 43*e^2 + 57*e - 3, -e^4 + 3*e^3 + 10*e^2 - 18*e - 9, -3*e^4 - 2*e^3 + 26*e^2 + 11*e - 28, 2*e^4 + 6*e^3 - 14*e^2 - 47*e, -2*e^3 + e^2 + 12*e + 3, 6*e^4 + 7*e^3 - 47*e^2 - 44*e + 30, 5*e^4 + 9*e^3 - 36*e^2 - 63*e + 5, -5/3*e^4 - 4/3*e^3 + 7*e^2 + 6*e + 24, -e^4 - 5*e^3 + 13*e^2 + 37*e - 21, -2*e^4 + 15*e^2 - e - 3, -17/3*e^4 - 22/3*e^3 + 47*e^2 + 51*e - 33, 7/3*e^4 + 14/3*e^3 - 21*e^2 - 30*e + 21, 2*e^3 + 4*e^2 - 18*e - 18, 7/3*e^4 + 5/3*e^3 - 18*e^2 - 7*e + 6, -5*e^4 - 12*e^3 + 37*e^2 + 78*e - 4, -14/3*e^4 - 31/3*e^3 + 36*e^2 + 65*e - 9, -17/3*e^4 - 22/3*e^3 + 43*e^2 + 49*e - 17, -5*e^4 - 9*e^3 + 36*e^2 + 59*e + 8, 4*e^4 + 8*e^3 - 27*e^2 - 53*e - 6, 3*e^3 + 3*e^2 - 30*e - 18, 2*e^4 + 8*e^3 - 15*e^2 - 49*e - 3, 5*e^4 + 11*e^3 - 35*e^2 - 77*e, 22/3*e^4 + 32/3*e^3 - 58*e^2 - 75*e + 36, -8/3*e^4 - 7/3*e^3 + 18*e^2 + 23*e, 4/3*e^4 - 1/3*e^3 - 15*e^2 + e + 27, -11/3*e^4 - 13/3*e^3 + 32*e^2 + 33*e - 33, -5*e^2 + 4*e + 18, 2*e^4 + 9*e^3 - 16*e^2 - 61*e + 6, -4*e^4 - 10*e^3 + 36*e^2 + 66*e - 36, 19/3*e^4 + 26/3*e^3 - 46*e^2 - 60*e + 6, 4/3*e^4 + 2/3*e^3 - 4*e^2 - 6*e - 36, 19/3*e^4 + 35/3*e^3 - 55*e^2 - 78*e + 51, 3*e^4 + 5*e^3 - 22*e^2 - 34*e, e^4 - 2*e^3 - 13*e^2 + 16*e + 20, -14/3*e^4 - 13/3*e^3 + 37*e^2 + 30*e - 18, -5*e^4 - 7*e^3 + 35*e^2 + 44*e + 12, e^4 + 2*e^3 - 7*e^2 - 6*e - 12, 3*e^4 + 7*e^3 - 18*e^2 - 50*e - 6, 11*e^4 + 13*e^3 - 87*e^2 - 89*e + 57, -3*e^4 - 7*e^3 + 18*e^2 + 47*e + 6, 8*e^4 + 10*e^3 - 66*e^2 - 62*e + 54, 4*e^4 + 7*e^3 - 32*e^2 - 48*e + 21, -5*e^4 - 6*e^3 + 43*e^2 + 43*e - 36, 2*e^4 + 4*e^3 - 23*e^2 - 36*e + 47, -2/3*e^4 + 17/3*e^3 + 9*e^2 - 39*e - 29, -8/3*e^4 - 10/3*e^3 + 17*e^2 + 21*e + 24, 2*e^4 + 9*e^3 - 19*e^2 - 55*e + 32, 13/3*e^4 + 32/3*e^3 - 34*e^2 - 66*e + 15, 4/3*e^4 + 14/3*e^3 - 9*e^2 - 25*e, -7*e^4 - 12*e^3 + 56*e^2 + 86*e - 42, 8*e^4 + 14*e^3 - 62*e^2 - 100*e + 53, -5/3*e^4 - 31/3*e^3 + 9*e^2 + 69*e + 25, 4/3*e^4 + 17/3*e^3 - 8*e^2 - 44*e + 1, -20/3*e^4 - 28/3*e^3 + 57*e^2 + 54*e - 48, -20/3*e^4 - 46/3*e^3 + 54*e^2 + 99*e - 33, 2*e^4 + 2*e^3 - 14*e^2 - 11*e - 3, -e^4 - 6*e^3 + 3*e^2 + 39*e + 17, -14/3*e^4 - 13/3*e^3 + 32*e^2 + 27*e + 10, -23/3*e^4 - 28/3*e^3 + 61*e^2 + 63*e - 27, -20/3*e^4 - 46/3*e^3 + 51*e^2 + 101*e - 18, -14/3*e^4 - 19/3*e^3 + 42*e^2 + 43*e - 48, 25/3*e^4 + 20/3*e^3 - 60*e^2 - 48*e + 16, -11/3*e^4 - 28/3*e^3 + 21*e^2 + 70*e + 9, -6*e^3 - e^2 + 37*e + 15, -e^4 - 3*e^3 + 3*e^2 + 19*e + 21, 5*e^4 + 6*e^3 - 43*e^2 - 36*e + 45, -3*e^4 - 7*e^3 + 21*e^2 + 58*e, -5*e^4 - 2*e^3 + 34*e^2 + 13*e - 12, -3*e^4 - 3*e^3 + 19*e^2 + 20*e - 3, -e^4 - 6*e^3 + 4*e^2 + 40*e + 11, 31/3*e^4 + 29/3*e^3 - 82*e^2 - 64*e + 57, -29/3*e^4 - 31/3*e^3 + 69*e^2 + 71*e - 6, 5*e^4 + 4*e^3 - 32*e^2 - 29*e - 21, e^4 - 3*e^3 - 12*e^2 + 14*e + 36, 13/3*e^4 + 26/3*e^3 - 41*e^2 - 58*e + 40, -11/3*e^4 - 4/3*e^3 + 34*e^2 + 9*e - 20, 3*e^4 - e^3 - 22*e^2 - e + 18, -5/3*e^4 + 2/3*e^3 + 9*e^2 - 6*e + 3, 1/3*e^4 + 2/3*e^3 - 5*e^2 - 9*e + 54, -e^4 - 4*e^3 + 10*e^2 + 39*e - 3, 4*e^4 + 9*e^3 - 28*e^2 - 61*e - 15, -5*e^4 - 10*e^3 + 43*e^2 + 68*e - 54, -3*e^4 - 5*e^3 + 30*e^2 + 26*e - 36, -8/3*e^4 + 14/3*e^3 + 25*e^2 - 36*e - 48, -8/3*e^4 - 16/3*e^3 + 10*e^2 + 37*e + 39, -e^3 - 3*e^2 + e + 26, -8*e^4 - 19*e^3 + 67*e^2 + 129*e - 57, -4*e^4 - 2*e^3 + 36*e^2 + 10*e - 39, 7/3*e^4 + 35/3*e^3 - 17*e^2 - 78*e - 3, -11/3*e^4 - 31/3*e^3 + 33*e^2 + 58*e - 45, 4/3*e^4 + 17/3*e^3 - 9*e^2 - 37*e + 3, 6*e^4 + 3*e^3 - 46*e^2 - 27*e + 24, e^4 + 2*e^3 - 14*e^2 - 16*e + 33, -2/3*e^4 - 4/3*e^3 + 11*e^2 + 9*e - 6, -2/3*e^4 - 19/3*e^3 + e^2 + 51*e + 40, 4*e^4 + 9*e^3 - 28*e^2 - 71*e, 2*e^4 + e^3 - 25*e^2 - 6*e + 41, -8*e^4 - 12*e^3 + 62*e^2 + 93*e - 48, -3*e^4 - 13*e^3 + 25*e^2 + 90*e - 9, 13/3*e^4 + 14/3*e^3 - 38*e^2 - 27*e + 43, 4*e^4 + 8*e^3 - 34*e^2 - 56*e + 30, 10/3*e^4 + 14/3*e^3 - 25*e^2 - 35*e - 9, -26/3*e^4 - 31/3*e^3 + 71*e^2 + 67*e - 39, -10*e^4 - 11*e^3 + 78*e^2 + 66*e - 43, 6*e^4 + 11*e^3 - 40*e^2 - 83*e - 13, -e^4 + 3*e^3 + 10*e^2 - 21*e - 25, -4*e^4 - e^3 + 35*e^2 + 7*e - 15, -e^4 - 6*e^3 + 11*e^2 + 28*e - 33, 31/3*e^4 + 47/3*e^3 - 75*e^2 - 108*e + 22, -3*e^4 - 5*e^3 + 20*e^2 + 39*e, -5*e^4 - 3*e^3 + 46*e^2 + 13*e - 63, 8*e^4 + 9*e^3 - 67*e^2 - 56*e + 42, -e^4 - e^3 + 6*e^2 + 20*e + 24, 7*e^4 + 8*e^3 - 47*e^2 - 62*e + 3, e^4 + 7*e^3 - 5*e^2 - 51*e - 39, -6*e^4 - e^3 + 43*e^2 - 19, 22/3*e^4 + 35/3*e^3 - 66*e^2 - 75*e + 69] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]