/* 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([3, -4, -8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, w^3 - 2*w^2 - 5*w + 1]) primes_array = [ [3, 3, w],\ [3, 3, w^3 - 2*w^2 - 6*w + 1],\ [9, 3, w^3 - 2*w^2 - 5*w + 1],\ [16, 2, 2],\ [17, 17, w^3 - w^2 - 8*w - 5],\ [17, 17, -2*w^3 + 4*w^2 + 11*w - 2],\ [17, 17, -w^3 + 3*w^2 + 2*w - 2],\ [17, 17, w^3 - 2*w^2 - 4*w + 1],\ [25, 5, w^3 - 3*w^2 - 3*w + 1],\ [25, 5, w^2 - 2*w - 7],\ [29, 29, w^3 - 2*w^2 - 6*w - 1],\ [29, 29, w - 2],\ [53, 53, w^3 - 3*w^2 - 4*w + 4],\ [53, 53, -w^3 + 3*w^2 + 4*w - 5],\ [61, 61, -w^3 + 2*w^2 + 7*w - 4],\ [61, 61, -4*w^3 + 11*w^2 + 14*w - 8],\ [101, 101, -w^3 + 2*w^2 + 7*w - 1],\ [103, 103, -w^3 + 3*w^2 + 2*w - 5],\ [103, 103, -w^3 + w^2 + 8*w + 2],\ [113, 113, w^3 - 3*w^2 - 3*w + 7],\ [113, 113, w^2 - 2*w - 1],\ [127, 127, w^3 - 2*w^2 - 4*w - 2],\ [127, 127, -2*w^3 + 4*w^2 + 11*w + 1],\ [131, 131, -3*w^3 + 7*w^2 + 14*w - 8],\ [131, 131, -w^2 + w + 8],\ [131, 131, 2*w^3 - 5*w^2 - 9*w + 1],\ [131, 131, -3*w^3 + 6*w^2 + 16*w + 1],\ [139, 139, -2*w^3 + 5*w^2 + 9*w - 2],\ [139, 139, -w^2 + w + 7],\ [157, 157, -2*w^3 + 5*w^2 + 7*w - 5],\ [157, 157, -2*w^3 + 3*w^2 + 13*w + 2],\ [157, 157, -2*w^3 + 5*w^2 + 6*w - 2],\ [157, 157, -3*w^3 + 5*w^2 + 19*w + 4],\ [169, 13, -2*w^3 + 4*w^2 + 10*w - 1],\ [173, 173, 3*w^3 - 8*w^2 - 10*w + 7],\ [173, 173, 2*w^3 - 2*w^2 - 15*w - 8],\ [179, 179, -3*w^2 + 6*w + 17],\ [179, 179, -2*w^3 + 3*w^2 + 12*w + 1],\ [179, 179, -3*w^3 + 7*w^2 + 13*w - 7],\ [179, 179, -2*w^3 + 3*w^2 + 14*w + 4],\ [191, 191, w^3 - 3*w^2 - w + 4],\ [191, 191, -2*w^3 + 3*w^2 + 14*w + 2],\ [199, 199, -w^3 + 8*w + 10],\ [199, 199, 5*w^3 - 15*w^2 - 14*w + 14],\ [211, 211, -w - 4],\ [211, 211, -w^3 + 2*w^2 + 6*w - 5],\ [211, 211, 2*w^3 - 3*w^2 - 12*w - 4],\ [211, 211, -3*w^3 + 7*w^2 + 13*w - 4],\ [257, 257, -3*w^3 + 8*w^2 + 10*w - 2],\ [257, 257, 2*w^3 - 2*w^2 - 16*w - 7],\ [263, 263, 3*w^3 - 6*w^2 - 17*w + 1],\ [263, 263, w^3 - 2*w^2 - 3*w - 1],\ [269, 269, 5*w^3 - 13*w^2 - 19*w + 7],\ [269, 269, -3*w^3 + 6*w^2 + 18*w - 1],\ [277, 277, w^3 - 4*w^2 - w + 5],\ [277, 277, -w^3 + 4*w^2 + w - 11],\ [283, 283, -w^3 + 5*w^2 - w - 14],\ [283, 283, 2*w^3 - 7*w^2 - 4*w + 10],\ [283, 283, -w^3 + w^2 + 9*w + 1],\ [283, 283, w^2 - 4*w - 5],\ [311, 311, -w^3 + w^2 + 9*w + 5],\ [311, 311, w^2 - 4*w - 1],\ [313, 313, -4*w^3 + 9*w^2 + 19*w - 10],\ [313, 313, -2*w^2 + 5*w + 11],\ [337, 337, -3*w^3 + 6*w^2 + 14*w + 2],\ [337, 337, -4*w^3 + 8*w^2 + 21*w + 1],\ [347, 347, -2*w^3 + 6*w^2 + 7*w - 10],\ [347, 347, -w^3 + 4*w^2 + 2*w - 7],\ [361, 19, -4*w^3 + 11*w^2 + 13*w - 10],\ [361, 19, -2*w^3 + 5*w^2 + 8*w - 10],\ [373, 373, 2*w^3 - 5*w^2 - 10*w + 2],\ [373, 373, -w^3 + 2*w^2 + 8*w - 2],\ [373, 373, -2*w^3 + 4*w^2 + 13*w - 1],\ [373, 373, -w^3 + 3*w^2 + 5*w - 8],\ [389, 389, -w^3 + 4*w^2 + 2*w - 10],\ [389, 389, -2*w^3 + 6*w^2 + 7*w - 7],\ [419, 419, -2*w^3 + 5*w^2 + 6*w - 1],\ [419, 419, -3*w^3 + 5*w^2 + 19*w + 5],\ [433, 433, w^2 - 4*w - 2],\ [433, 433, w^3 - w^2 - 9*w - 4],\ [439, 439, -w^3 + 4*w^2 + w - 2],\ [439, 439, w^3 - 4*w^2 - w + 14],\ [443, 443, -2*w^3 + 5*w^2 + 9*w + 1],\ [443, 443, -w^2 + w + 10],\ [467, 467, w^3 - w^2 - 8*w + 4],\ [467, 467, w^3 - 4*w^2 + 2],\ [491, 491, -4*w^3 + 12*w^2 + 10*w - 11],\ [491, 491, 2*w^3 - w^2 - 18*w - 11],\ [491, 491, 3*w^3 - 9*w^2 - 7*w + 11],\ [491, 491, 2*w^3 - 20*w - 19],\ [503, 503, w^3 - 3*w^2 - 4*w + 10],\ [503, 503, -w^3 + w^2 + 10*w - 2],\ [523, 523, -4*w^3 + 9*w^2 + 22*w - 7],\ [523, 523, w^3 - 3*w^2 - 7*w + 5],\ [529, 23, -2*w^3 + 4*w^2 + 10*w + 5],\ [529, 23, -2*w^3 + 4*w^2 + 10*w - 7],\ [547, 547, 2*w^3 - w^2 - 18*w - 14],\ [547, 547, 3*w^3 - 8*w^2 - 14*w + 8],\ [571, 571, 5*w^3 - 11*w^2 - 25*w + 5],\ [571, 571, -4*w^3 + 9*w^2 + 19*w - 11],\ [599, 599, -5*w^3 + 12*w^2 + 20*w - 4],\ [599, 599, 4*w^3 - 6*w^2 - 25*w - 11],\ [601, 601, -4*w^3 + 9*w^2 + 20*w - 5],\ [601, 601, w^3 - 9*w - 14],\ [601, 601, 3*w^3 - 8*w^2 - 11*w + 2],\ [601, 601, -2*w^3 + 3*w^2 + 14*w - 1],\ [641, 641, -2*w^3 + 3*w^2 + 15*w - 5],\ [641, 641, -4*w^3 + 8*w^2 + 23*w - 2],\ [647, 647, -3*w^3 + 8*w^2 + 13*w - 11],\ [647, 647, -w^3 + 4*w^2 + 3*w - 7],\ [659, 659, 3*w^3 - 7*w^2 - 14*w - 2],\ [659, 659, w^3 - w^2 - 6*w - 11],\ [673, 673, -3*w^3 + 7*w^2 + 11*w - 1],\ [673, 673, -4*w^3 + 7*w^2 + 24*w + 5],\ [677, 677, 5*w^3 - 12*w^2 - 21*w + 11],\ [677, 677, -2*w^3 + 6*w^2 + 5*w - 1],\ [677, 677, -2*w^3 + 6*w^2 + 8*w - 7],\ [677, 677, 2*w^3 - 6*w^2 - 8*w + 11],\ [719, 719, -2*w^3 + 6*w^2 + 10*w - 7],\ [719, 719, -4*w^3 + 10*w^2 + 20*w - 13],\ [727, 727, 3*w^3 - 10*w^2 - 8*w + 10],\ [727, 727, 3*w^3 - 8*w^2 - 13*w + 10],\ [727, 727, 2*w^3 - 8*w^2 - 3*w + 23],\ [727, 727, -w^3 + 4*w^2 + 3*w - 8],\ [751, 751, -7*w^3 + 18*w^2 + 25*w - 7],\ [751, 751, w^3 - 7*w^2 + 5*w + 26],\ [757, 757, -4*w^3 + 9*w^2 + 18*w - 7],\ [757, 757, -3*w^3 + 5*w^2 + 17*w + 1],\ [797, 797, 2*w^2 - 4*w - 5],\ [797, 797, 2*w^3 - 6*w^2 - 6*w + 11],\ [823, 823, -2*w^3 + 2*w^2 + 15*w + 14],\ [823, 823, -3*w^3 + 8*w^2 + 10*w - 1],\ [829, 829, -6*w^3 + 16*w^2 + 22*w - 7],\ [829, 829, 5*w^3 - 13*w^2 - 20*w + 8],\ [829, 829, -w^3 + 7*w + 4],\ [829, 829, -5*w^3 + 12*w^2 + 23*w - 14],\ [841, 29, -3*w^3 + 6*w^2 + 15*w - 2],\ [859, 859, -4*w^3 + 7*w^2 + 24*w - 1],\ [859, 859, -5*w^3 + 15*w^2 + 14*w - 13],\ [881, 881, 3*w^3 - 7*w^2 - 16*w + 4],\ [881, 881, -w^3 + 3*w^2 + 6*w - 7],\ [883, 883, -2*w^3 + 3*w^2 + 12*w + 10],\ [883, 883, -3*w^3 + 7*w^2 + 13*w + 2],\ [887, 887, 4*w^3 - 11*w^2 - 11*w + 11],\ [887, 887, 2*w^3 - 7*w^2 - 3*w + 7],\ [887, 887, 4*w^3 - 5*w^2 - 29*w - 10],\ [887, 887, 3*w^2 - 7*w - 16],\ [907, 907, -w^3 + 3*w^2 + 8*w - 5],\ [907, 907, -5*w^3 + 11*w^2 + 28*w - 8],\ [911, 911, -4*w^3 + 10*w^2 + 18*w - 17],\ [911, 911, 2*w^2 - 2*w - 1],\ [919, 919, 4*w^3 - 7*w^2 - 25*w - 4],\ [919, 919, 2*w^3 - 5*w^2 - 5*w + 1],\ [937, 937, -w^3 + 3*w^2 + w - 8],\ [937, 937, -2*w^3 + 3*w^2 + 14*w - 2],\ [953, 953, -2*w^3 + w^2 + 17*w + 19],\ [953, 953, 4*w^3 - 11*w^2 - 13*w + 4],\ [961, 31, 2*w^3 - 3*w^2 - 11*w - 8],\ [961, 31, w^3 - 4*w^2 + 2*w + 11],\ [971, 971, 2*w^2 - 5*w - 4],\ [971, 971, -w^3 + 4*w^2 - 11],\ [991, 991, -2*w^3 + 6*w^2 + 9*w - 8],\ [991, 991, -2*w^3 + 3*w^2 + 13*w - 1],\ [991, 991, 3*w^3 - 8*w^2 - 14*w + 11],\ [991, 991, -2*w^3 + 5*w^2 + 7*w - 8],\ [997, 997, -2*w^3 + 5*w^2 + 6*w + 1],\ [997, 997, -3*w^3 + 5*w^2 + 19*w + 7],\ [997, 997, -6*w^3 + 12*w^2 + 33*w - 4],\ [997, 997, 4*w^3 - 11*w^2 - 15*w + 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 + 4*x^5 - 4*x^4 - 30*x^3 - 16*x^2 + 40*x + 34 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e^4 + 8*e^2 - e - 12, 1, -e^4 + 8*e^2 - 11, 2*e^5 + 5*e^4 - 15*e^3 - 38*e^2 + 19*e + 50, e^5 - 8*e^3 + 10*e, -2*e^5 - 2*e^4 + 15*e^3 + 14*e^2 - 19*e - 20, e^5 + 2*e^4 - 8*e^3 - 14*e^2 + 14*e + 16, -5*e^5 - 9*e^4 + 38*e^3 + 64*e^2 - 52*e - 80, 3*e^5 + 7*e^4 - 22*e^3 - 50*e^2 + 28*e + 60, -3*e^5 - 4*e^4 + 22*e^3 + 28*e^2 - 26*e - 36, 5*e^5 + 10*e^4 - 38*e^3 - 74*e^2 + 50*e + 96, 2*e^5 + 4*e^4 - 14*e^3 - 27*e^2 + 16*e + 32, -6*e^5 - 12*e^4 + 46*e^3 + 87*e^2 - 64*e - 108, -9*e^5 - 15*e^4 + 70*e^3 + 110*e^2 - 100*e - 146, -e^5 + e^4 + 10*e^3 - 8*e^2 - 20*e + 10, 10*e^5 + 12*e^4 - 80*e^3 - 86*e^2 + 120*e + 114, -5*e^5 - 10*e^4 + 38*e^3 + 71*e^2 - 52*e - 82, 3*e^5 + 6*e^4 - 22*e^3 - 41*e^2 + 28*e + 50, 5*e^5 + 4*e^4 - 40*e^3 - 26*e^2 + 57*e + 24, 5*e^5 + 7*e^4 - 40*e^3 - 52*e^2 + 63*e + 68, -5*e^5 - 9*e^4 + 40*e^3 + 68*e^2 - 56*e - 98, -5*e^5 - 13*e^4 + 40*e^3 + 98*e^2 - 64*e - 138, 3*e^5 + 4*e^4 - 26*e^3 - 28*e^2 + 46*e + 30, -e^5 - e^4 + 6*e^3 + 6*e^2 - 4*e - 10, 7*e^5 + 15*e^4 - 54*e^3 - 112*e^2 + 76*e + 146, 11*e^5 + 18*e^4 - 86*e^3 - 134*e^2 + 122*e + 178, e^5 + 2*e^4 - 6*e^3 - 18*e^2 + 26, -7*e^5 - 10*e^4 + 54*e^3 + 76*e^2 - 72*e - 114, -4*e^5 - 8*e^4 + 32*e^3 + 62*e^2 - 48*e - 82, -4*e^5 - 8*e^4 + 32*e^3 + 58*e^2 - 48*e - 66, 2*e^5 + 4*e^4 - 16*e^3 - 30*e^2 + 26*e + 30, 2*e^5 + 2*e^4 - 16*e^3 - 14*e^2 + 22*e + 6, 2*e^5 - 4*e^4 - 16*e^3 + 34*e^2 + 24*e - 42, 8*e^5 + 15*e^4 - 64*e^3 - 110*e^2 + 94*e + 142, 8*e^5 + 17*e^4 - 64*e^3 - 130*e^2 + 98*e + 182, 7*e^5 + 16*e^4 - 54*e^3 - 118*e^2 + 84*e + 162, -11*e^5 - 19*e^4 + 80*e^3 + 136*e^2 - 94*e - 178, 21*e^5 + 39*e^4 - 160*e^3 - 286*e^2 + 214*e + 366, -e^5 - 8*e^4 + 6*e^3 + 60*e^2 - 12*e - 74, -10*e^5 - 13*e^4 + 76*e^3 + 88*e^2 - 96*e - 96, 6*e^5 + 11*e^4 - 44*e^3 - 76*e^2 + 48*e + 88, -7*e^5 - 15*e^4 + 53*e^3 + 110*e^2 - 69*e - 146, 5*e^5 + 6*e^4 - 37*e^3 - 40*e^2 + 45*e + 40, -e^5 - 11*e^4 + 4*e^3 + 80*e^2 + 2*e - 94, 15*e^5 + 23*e^4 - 116*e^3 - 162*e^2 + 166*e + 202, -6*e^5 - 9*e^4 + 47*e^3 + 68*e^2 - 61*e - 98, -2*e^5 - 8*e^4 + 17*e^3 + 60*e^2 - 35*e - 84, 8*e^5 + 18*e^4 - 62*e^3 - 136*e^2 + 96*e + 184, -6*e^4 - 2*e^3 + 48*e^2 - 76, -6*e^5 - 8*e^4 + 44*e^3 + 50*e^2 - 52*e - 40, 10*e^5 + 20*e^4 - 76*e^3 - 142*e^2 + 100*e + 176, -13*e^5 - 17*e^4 + 101*e^3 + 116*e^2 - 137*e - 126, -e^5 + 11*e^3 + 6*e^2 - 31*e - 20, -4*e^5 - 9*e^4 + 28*e^3 + 62*e^2 - 34*e - 66, 12*e^5 + 25*e^4 - 92*e^3 - 182*e^2 + 130*e + 238, 3*e^5 + 10*e^4 - 19*e^3 - 72*e^2 + 13*e + 80, -17*e^5 - 27*e^4 + 131*e^3 + 194*e^2 - 181*e - 254, 20*e^5 + 36*e^4 - 154*e^3 - 264*e^2 + 210*e + 334, -4*e^5 - 6*e^4 + 26*e^3 + 40*e^2 - 18*e - 54, -8*e^5 - 5*e^4 + 64*e^3 + 30*e^2 - 100*e - 40, -8*e^5 - e^4 + 64*e^3 + 2*e^2 - 92*e - 8, -8*e^5 - 12*e^4 + 61*e^3 + 86*e^2 - 85*e - 112, 4*e^5 + 13*e^4 - 29*e^3 - 98*e^2 + 37*e + 130, 12*e^5 + 18*e^4 - 90*e^3 - 126*e^2 + 115*e + 152, -12*e^5 - 25*e^4 + 90*e^3 + 182*e^2 - 115*e - 232, -19*e^5 - 38*e^4 + 145*e^3 + 276*e^2 - 203*e - 364, 9*e^5 + 21*e^4 - 65*e^3 - 150*e^2 + 83*e + 174, 27*e^5 + 50*e^4 - 204*e^3 - 360*e^2 + 266*e + 448, -21*e^5 - 36*e^4 + 156*e^3 + 254*e^2 - 194*e - 312, -6*e^5 - 8*e^4 + 44*e^3 + 50*e^2 - 53*e - 40, 13*e^5 + 24*e^4 - 103*e^3 - 174*e^2 + 155*e + 220, 9*e^5 + 13*e^4 - 73*e^3 - 100*e^2 + 109*e + 142, 10*e^5 + 21*e^4 - 76*e^3 - 150*e^2 + 101*e + 188, -2*e^5 - e^4 + 18*e^3 + 14*e^2 - 33*e - 40, -10*e^5 - 16*e^4 + 78*e^3 + 110*e^2 - 111*e - 128, -6*e^5 - 14*e^4 + 40*e^3 + 94*e^2 - 34*e - 104, 26*e^5 + 44*e^4 - 200*e^3 - 314*e^2 + 274*e + 384, -16*e^5 - 32*e^4 + 120*e^3 + 238*e^2 - 158*e - 316, 16*e^5 + 30*e^4 - 120*e^3 - 222*e^2 + 158*e + 300, -17*e^5 - 24*e^4 + 134*e^3 + 175*e^2 - 200*e - 236, -9*e^5 - 4*e^4 + 74*e^3 + 23*e^2 - 112*e - 24, e^5 + 13*e^4 - 4*e^3 - 102*e^2 - 6*e + 124, -15*e^5 - 17*e^4 + 116*e^3 + 120*e^2 - 162*e - 172, 9*e^5 + 6*e^4 - 66*e^3 - 33*e^2 + 76*e + 20, -15*e^5 - 34*e^4 + 114*e^3 + 251*e^2 - 148*e - 328, -6*e^5 - 8*e^4 + 44*e^3 + 57*e^2 - 48*e - 66, 7*e^5 + 5*e^4 - 56*e^3 - 30*e^2 + 73*e + 12, 7*e^5 + 16*e^4 - 56*e^3 - 124*e^2 + 95*e + 168, 10*e^5 + 16*e^4 - 76*e^3 - 117*e^2 + 96*e + 158, 5*e^5 + 5*e^4 - 34*e^3 - 42*e^2 + 24*e + 72, -19*e^5 - 31*e^4 + 146*e^3 + 236*e^2 - 192*e - 332, 4*e^5 + 5*e^4 - 28*e^3 - 28*e^2 + 28*e + 20, -12*e^5 - 23*e^4 + 92*e^3 + 164*e^2 - 124*e - 196, 2*e^5 - 2*e^4 - 16*e^3 + 18*e^2 + 24*e - 26, -2*e^5 - 6*e^4 + 16*e^3 + 46*e^2 - 24*e - 70, -17*e^5 - 24*e^4 + 134*e^3 + 181*e^2 - 188*e - 254, -9*e^5 - 16*e^4 + 74*e^3 + 113*e^2 - 124*e - 138, 17*e^5 + 17*e^4 - 130*e^3 - 112*e^2 + 178*e + 136, -7*e^5 - 29*e^4 + 50*e^3 + 218*e^2 - 58*e - 276, -14*e^5 - 28*e^4 + 110*e^3 + 198*e^2 - 160*e - 238, -6*e^5 - 12*e^4 + 50*e^3 + 102*e^2 - 80*e - 170, e^5 + 6*e^4 - 7*e^3 - 46*e^2 + 15*e + 56, -e^5 - 5*e^4 + 12*e^3 + 44*e^2 - 33*e - 80, -17*e^5 - 32*e^4 + 132*e^3 + 234*e^2 - 183*e - 308, -3*e^5 - 9*e^4 + 23*e^3 + 68*e^2 - 39*e - 102, -25*e^5 - 41*e^4 + 193*e^3 + 300*e^2 - 269*e - 394, 3*e^5 + 12*e^4 - 17*e^3 - 90*e^2 + 5*e + 120, 5*e^5 + 12*e^4 - 34*e^3 - 84*e^2 + 30*e + 122, -19*e^5 - 30*e^4 + 146*e^3 + 214*e^2 - 198*e - 242, -9*e^5 - 9*e^4 + 64*e^3 + 62*e^2 - 59*e - 80, 23*e^5 + 38*e^4 - 176*e^3 - 280*e^2 + 227*e + 364, 23*e^5 + 42*e^4 - 168*e^3 - 300*e^2 + 204*e + 384, -41*e^5 - 78*e^4 + 312*e^3 + 570*e^2 - 420*e - 728, -9*e^5 - 23*e^4 + 66*e^3 + 166*e^2 - 78*e - 196, 15*e^5 + 19*e^4 - 114*e^3 - 128*e^2 + 150*e + 152, 6*e^5 + 26*e^4 - 48*e^3 - 208*e^2 + 80*e + 294, 6*e^5 + 18*e^4 - 48*e^3 - 132*e^2 + 64*e + 150, -e^5 + 10*e^4 + 12*e^3 - 76*e^2 - 29*e + 84, -17*e^5 - 21*e^4 + 132*e^3 + 146*e^2 - 187*e - 192, -13*e^5 - 18*e^4 + 104*e^3 + 132*e^2 - 159*e - 180, -5*e^5 - 13*e^4 + 32*e^3 + 92*e^2 - 14*e - 114, -13*e^5 - 15*e^4 + 104*e^3 + 106*e^2 - 153*e - 136, 27*e^5 + 37*e^4 - 208*e^3 - 262*e^2 + 278*e + 318, -17*e^5 - 20*e^4 + 132*e^3 + 144*e^2 - 178*e - 214, -e^5 + 2*e^4 + 12*e^3 - 18*e^2 - 38*e + 2, 6*e^5 + 14*e^4 - 52*e^3 - 116*e^2 + 90*e + 184, 22*e^5 + 44*e^4 - 172*e^3 - 320*e^2 + 246*e + 408, -17*e^5 - 35*e^4 + 132*e^3 + 264*e^2 - 191*e - 360, -e^5 + 12*e^3 - 2*e^2 - 25*e + 12, -8*e^5 - 2*e^4 + 60*e^3 + 9*e^2 - 76*e - 14, 8*e^5 + 26*e^4 - 60*e^3 - 201*e^2 + 76*e + 274, -26*e^5 - 46*e^4 + 200*e^3 + 340*e^2 - 280*e - 452, 6*e^5 + 18*e^4 - 40*e^3 - 136*e^2 + 40*e + 188, 18*e^5 + 26*e^4 - 134*e^3 - 186*e^2 + 166*e + 256, -22*e^5 - 44*e^4 + 166*e^3 + 326*e^2 - 214*e - 412, 26*e^5 + 40*e^4 - 208*e^3 - 294*e^2 + 312*e + 382, 7*e^5 + 13*e^4 - 50*e^3 - 100*e^2 + 56*e + 140, -17*e^5 - 31*e^4 + 130*e^3 + 234*e^2 - 176*e - 328, 10*e^5 + 22*e^4 - 80*e^3 - 164*e^2 + 124*e + 230, 10*e^5 + 18*e^4 - 80*e^3 - 136*e^2 + 116*e + 198, 21*e^5 + 39*e^4 - 162*e^3 - 276*e^2 + 232*e + 332, -3*e^5 - 13*e^4 + 18*e^3 + 86*e^2 - 16*e - 88, 33*e^5 + 44*e^4 - 258*e^3 - 309*e^2 + 372*e + 388, 4*e^5 + 14*e^4 - 23*e^3 - 104*e^2 + 9*e + 124, 9*e^5 - 4*e^4 - 78*e^3 + 31*e^2 + 132*e - 24, -32*e^5 - 55*e^4 + 247*e^3 + 404*e^2 - 345*e - 546, 11*e^5 + 29*e^4 - 80*e^3 - 218*e^2 + 91*e + 264, -21*e^5 - 26*e^4 + 160*e^3 + 184*e^2 - 211*e - 260, 40*e^5 + 58*e^4 - 312*e^3 - 414*e^2 + 440*e + 516, 8*e^5 + 2*e^4 - 72*e^3 - 18*e^2 + 136*e + 36, -3*e^5 + 15*e^4 + 22*e^3 - 128*e^2 - 22*e + 188, 5*e^5 + 25*e^4 - 38*e^3 - 190*e^2 + 46*e + 240, -26*e^5 - 30*e^4 + 204*e^3 + 212*e^2 - 286*e - 262, -10*e^5 - 8*e^4 + 84*e^3 + 56*e^2 - 146*e - 70, -31*e^5 - 46*e^4 + 244*e^3 + 343*e^2 - 348*e - 464, -15*e^5 - 22*e^4 + 124*e^3 + 155*e^2 - 204*e - 184, -8*e^5 - 12*e^4 + 68*e^3 + 82*e^2 - 134*e - 102, -24*e^5 - 22*e^4 + 188*e^3 + 158*e^2 - 250*e - 214, 14*e^5 + 24*e^4 - 104*e^3 - 163*e^2 + 132*e + 206, -18*e^5 - 36*e^4 + 136*e^3 + 255*e^2 - 180*e - 282, 6*e^5 + 19*e^4 - 40*e^3 - 144*e^2 + 38*e + 188, 15*e^5 + 24*e^4 - 122*e^3 - 182*e^2 + 184*e + 254, -26*e^5 - 43*e^4 + 200*e^3 + 316*e^2 - 278*e - 428, 23*e^5 + 44*e^4 - 182*e^3 - 324*e^2 + 272*e + 426, -21*e^5 - 42*e^4 + 160*e^3 + 301*e^2 - 208*e - 370, 11*e^5 + 10*e^4 - 80*e^3 - 55*e^2 + 88*e + 30, 12*e^5 + 9*e^4 - 96*e^3 - 58*e^2 + 142*e + 94, 12*e^5 + 11*e^4 - 96*e^3 - 78*e^2 + 146*e + 134] 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, w^3 - 2*w^2 - 5*w + 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]