/* 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([11, 9, -9, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([55,55,w^3 + 2*w^2 - 5*w - 6]) primes_array = [ [5, 5, -2*w^3 - 2*w^2 + 13*w + 8],\ [11, 11, 2*w^3 + 3*w^2 - 12*w - 11],\ [11, 11, -w^3 - 2*w^2 + 6*w + 9],\ [11, 11, w^3 + w^2 - 7*w - 4],\ [11, 11, w - 1],\ [16, 2, 2],\ [19, 19, -w^2 + 4],\ [19, 19, 2*w^3 + 2*w^2 - 13*w - 6],\ [19, 19, 3*w^3 + 4*w^2 - 18*w - 16],\ [19, 19, -w^3 - w^2 + 5*w + 3],\ [49, 7, 2*w^3 + 3*w^2 - 13*w - 15],\ [59, 59, -3*w^3 - 4*w^2 + 19*w + 14],\ [59, 59, 3*w^3 + 4*w^2 - 18*w - 17],\ [59, 59, 2*w^3 + 3*w^2 - 11*w - 13],\ [59, 59, -w^3 - 2*w^2 + 7*w + 9],\ [71, 71, 3*w^3 + 3*w^2 - 17*w - 10],\ [71, 71, -2*w^3 - w^2 + 14*w + 2],\ [71, 71, 5*w^3 + 7*w^2 - 30*w - 25],\ [71, 71, -3*w^3 - 4*w^2 + 16*w + 16],\ [81, 3, -3],\ [89, 89, -2*w^3 - 2*w^2 + 13*w + 4],\ [89, 89, 3*w^3 + 4*w^2 - 17*w - 16],\ [89, 89, 3*w^3 + 4*w^2 - 18*w - 18],\ [89, 89, -4*w^3 - 5*w^2 + 25*w + 18],\ [139, 139, -w^3 + 6*w + 1],\ [139, 139, -3*w^3 - 3*w^2 + 19*w + 8],\ [139, 139, 4*w^3 + 5*w^2 - 24*w - 21],\ [139, 139, -2*w^3 - 2*w^2 + 11*w + 5],\ [151, 151, -6*w^3 - 7*w^2 + 37*w + 27],\ [151, 151, 3*w^3 + 5*w^2 - 19*w - 17],\ [151, 151, -6*w^3 - 8*w^2 + 37*w + 31],\ [151, 151, 4*w^3 + 6*w^2 - 25*w - 26],\ [191, 191, 5*w^3 + 7*w^2 - 31*w - 26],\ [191, 191, -2*w^3 - 3*w^2 + 10*w + 13],\ [191, 191, -5*w^3 - 7*w^2 + 31*w + 29],\ [191, 191, 2*w^3 + 4*w^2 - 13*w - 17],\ [199, 199, 2*w^3 + 4*w^2 - 11*w - 20],\ [199, 199, -2*w^3 - 2*w^2 + 11*w + 3],\ [199, 199, 3*w^3 + 5*w^2 - 17*w - 17],\ [199, 199, 3*w^3 + 3*w^2 - 19*w - 6],\ [211, 211, 3*w^3 + 5*w^2 - 18*w - 19],\ [211, 211, -3*w^3 - 5*w^2 + 18*w + 21],\ [211, 211, 2*w^3 + 4*w^2 - 12*w - 17],\ [211, 211, -4*w^3 - 6*w^2 + 24*w + 23],\ [229, 229, 2*w^3 + 4*w^2 - 13*w - 19],\ [229, 229, -2*w^3 - 3*w^2 + 10*w + 15],\ [229, 229, -5*w^3 - 7*w^2 + 31*w + 24],\ [229, 229, 2*w^3 + 2*w^2 - 14*w - 3],\ [269, 269, 2*w^3 + w^2 - 11*w - 1],\ [269, 269, -6*w^3 - 7*w^2 + 37*w + 24],\ [269, 269, 5*w^3 + 6*w^2 - 29*w - 24],\ [269, 269, 3*w^3 + 2*w^2 - 19*w - 7],\ [281, 281, -4*w^3 - 6*w^2 + 25*w + 25],\ [281, 281, -5*w^3 - 7*w^2 + 31*w + 27],\ [281, 281, w^2 + 2*w - 7],\ [281, 281, 3*w^3 + 5*w^2 - 19*w - 18],\ [331, 331, -2*w^3 - 3*w^2 + 12*w + 7],\ [331, 331, w^3 + w^2 - 7*w - 8],\ [331, 331, w^3 + 2*w^2 - 6*w - 13],\ [331, 331, w - 5],\ [349, 349, 2*w^3 + 5*w^2 - 16*w - 12],\ [349, 349, 2*w^3 + 4*w^2 - 15*w - 10],\ [349, 349, 8*w^3 + 9*w^2 - 50*w - 32],\ [349, 349, 2*w^3 + 4*w^2 - 15*w - 9],\ [401, 401, 4*w^3 + 3*w^2 - 21*w - 12],\ [401, 401, 3*w^3 + 2*w^2 - 16*w - 9],\ [401, 401, -3*w^3 - 6*w^2 + 20*w + 19],\ [401, 401, -4*w^3 - 3*w^2 + 27*w + 9],\ [409, 409, -5*w^3 - 6*w^2 + 31*w + 20],\ [409, 409, 3*w^3 + 4*w^2 - 20*w - 12],\ [409, 409, -3*w^3 - 5*w^2 + 17*w + 23],\ [409, 409, 4*w^3 + 5*w^2 - 23*w - 21],\ [419, 419, -4*w^3 - 4*w^2 + 21*w + 18],\ [419, 419, -4*w^3 - 4*w^2 + 20*w + 19],\ [419, 419, -3*w^3 - 4*w^2 + 16*w + 18],\ [419, 419, -2*w^3 - w^2 + 8*w + 10],\ [421, 421, -6*w^3 - 7*w^2 + 36*w + 26],\ [421, 421, 5*w^3 + 5*w^2 - 31*w - 17],\ [421, 421, 3*w^3 + 2*w^2 - 18*w - 6],\ [421, 421, 4*w^3 + 4*w^2 - 23*w - 14],\ [431, 431, 6*w^3 + 7*w^2 - 36*w - 25],\ [431, 431, -3*w^3 - 2*w^2 + 18*w + 5],\ [431, 431, 4*w^3 + 4*w^2 - 23*w - 15],\ [431, 431, -5*w^3 - 5*w^2 + 31*w + 18],\ [439, 439, w^3 + w^2 - 4*w - 1],\ [439, 439, w^3 + 3*w^2 - 6*w - 10],\ [439, 439, 3*w^3 + 3*w^2 - 20*w - 7],\ [439, 439, 5*w^3 + 7*w^2 - 30*w - 30],\ [479, 479, -4*w^3 - 5*w^2 + 25*w + 15],\ [479, 479, -5*w^3 - 6*w^2 + 32*w + 21],\ [479, 479, 5*w^3 + 7*w^2 - 29*w - 28],\ [479, 479, 2*w^2 + w - 9],\ [491, 491, 7*w^3 + 8*w^2 - 43*w - 31],\ [491, 491, 6*w^3 + 6*w^2 - 37*w - 24],\ [491, 491, 4*w^3 + 3*w^2 - 24*w - 6],\ [491, 491, 5*w^3 + 5*w^2 - 29*w - 21],\ [509, 509, -4*w^3 - 5*w^2 + 25*w + 14],\ [509, 509, -3*w^3 - 4*w^2 + 17*w + 20],\ [509, 509, -6*w^3 - 7*w^2 + 38*w + 25],\ [509, 509, -6*w^3 - 8*w^2 + 35*w + 31],\ [541, 541, 9*w^3 + 12*w^2 - 55*w - 46],\ [541, 541, w^3 + 4*w^2 - 7*w - 17],\ [541, 541, -4*w^3 - 5*w^2 + 21*w + 19],\ [541, 541, -4*w^3 - 3*w^2 + 27*w + 8],\ [571, 571, -3*w^3 - 6*w^2 + 18*w + 23],\ [571, 571, 6*w^3 + 9*w^2 - 36*w - 37],\ [571, 571, 7*w^3 + 10*w^2 - 42*w - 36],\ [571, 571, 2*w^3 + 5*w^2 - 12*w - 24],\ [619, 619, -9*w^3 - 11*w^2 + 55*w + 39],\ [619, 619, -5*w^3 - 4*w^2 + 32*w + 14],\ [619, 619, 7*w^3 + 9*w^2 - 42*w - 36],\ [619, 619, 4*w^3 + 6*w^2 - 26*w - 27],\ [631, 631, 2*w^3 + 5*w^2 - 12*w - 21],\ [631, 631, -7*w^3 - 10*w^2 + 42*w + 39],\ [631, 631, 4*w^3 + 4*w^2 - 27*w - 13],\ [631, 631, w^3 + w^2 - 3*w - 4],\ [641, 641, -9*w^3 - 10*w^2 + 56*w + 36],\ [641, 641, -5*w^3 - 9*w^2 + 30*w + 32],\ [641, 641, -3*w^3 - 6*w^2 + 19*w + 21],\ [641, 641, 4*w^3 + 3*w^2 - 22*w - 10],\ [701, 701, -2*w^3 - 5*w^2 + 14*w + 20],\ [701, 701, -6*w^3 - 7*w^2 + 36*w + 34],\ [701, 701, 4*w^3 + 6*w^2 - 23*w - 17],\ [701, 701, -9*w^3 - 12*w^2 + 56*w + 46],\ [719, 719, 3*w^3 + 5*w^2 - 17*w - 25],\ [719, 719, -3*w^3 - 2*w^2 + 17*w + 3],\ [719, 719, 7*w^3 + 8*w^2 - 43*w - 26],\ [719, 719, -6*w^3 - 7*w^2 + 35*w + 29],\ [751, 751, 2*w^3 + 2*w^2 - 15*w - 4],\ [751, 751, 5*w^3 + 8*w^2 - 30*w - 34],\ [751, 751, w^3 + w^2 - 9*w - 5],\ [751, 751, -4*w^3 - 7*w^2 + 24*w + 26],\ [769, 769, 6*w^3 + 8*w^2 - 37*w - 27],\ [769, 769, -w^3 - 3*w^2 + 7*w + 16],\ [769, 769, 2*w^3 + w^2 - 14*w - 5],\ [769, 769, -3*w^3 - 4*w^2 + 16*w + 19],\ [821, 821, 6*w^3 + 6*w^2 - 37*w - 23],\ [821, 821, 5*w^3 + 5*w^2 - 29*w - 20],\ [821, 821, -7*w^3 - 8*w^2 + 42*w + 27],\ [821, 821, 4*w^3 + 3*w^2 - 24*w - 7],\ [829, 829, 7*w^3 + 8*w^2 - 44*w - 28],\ [829, 829, 7*w^3 + 9*w^2 - 41*w - 35],\ [829, 829, -2*w^3 - w^2 + 10*w + 2],\ [829, 829, 2*w^3 - 13*w + 2],\ [839, 839, 4*w^3 + 8*w^2 - 25*w - 26],\ [839, 839, -3*w^3 - 3*w^2 + 15*w + 16],\ [839, 839, -w^3 - 4*w^2 + 8*w + 10],\ [839, 839, -3*w^3 - 7*w^2 + 18*w + 26],\ [841, 29, -5*w^3 - 5*w^2 + 30*w + 16],\ [841, 29, -5*w^3 - 5*w^2 + 30*w + 19],\ [859, 859, 5*w^3 + 6*w^2 - 32*w - 20],\ [859, 859, -4*w^3 - 5*w^2 + 23*w + 23],\ [859, 859, -5*w^3 - 6*w^2 + 31*w + 18],\ [859, 859, -2*w^3 - w^2 + 13*w + 6],\ [911, 911, 9*w^3 + 12*w^2 - 56*w - 48],\ [911, 911, 6*w^3 + 5*w^2 - 38*w - 14],\ [911, 911, 7*w^3 + 8*w^2 - 40*w - 28],\ [911, 911, 10*w^3 + 12*w^2 - 61*w - 46],\ [929, 929, -7*w^3 - 10*w^2 + 39*w + 39],\ [929, 929, -10*w^3 - 13*w^2 + 60*w + 45],\ [929, 929, -6*w^3 - 7*w^2 + 32*w + 29],\ [929, 929, -3*w^3 - w^2 + 12*w + 12],\ [961, 31, -5*w^3 - 5*w^2 + 30*w + 17],\ [961, 31, -5*w^3 - 5*w^2 + 30*w + 18],\ [991, 991, 10*w^3 + 12*w^2 - 61*w - 45],\ [991, 991, -6*w^3 - 9*w^2 + 38*w + 38],\ [991, 991, 6*w^3 + 8*w^2 - 37*w - 38],\ [991, 991, -8*w^3 - 11*w^2 + 49*w + 43]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 + 3*x^4 - 39*x^3 - 119*x^2 + 322*x + 920 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, e, 1, 5/16*e^4 - 1/2*e^3 - 155/16*e^2 + 67/8*e + 117/2, -3/8*e^4 + 1/2*e^3 + 97/8*e^2 - 33/4*e - 79, 7/16*e^4 - 3/4*e^3 - 221/16*e^2 + 101/8*e + 169/2, -1/8*e^4 + 1/4*e^3 + 33/8*e^2 - 17/4*e - 27, -3/16*e^4 + 1/4*e^3 + 105/16*e^2 - 33/8*e - 91/2, 7/16*e^4 - 3/4*e^3 - 221/16*e^2 + 101/8*e + 175/2, 1/16*e^4 - 1/4*e^3 - 27/16*e^2 + 43/8*e + 21/2, 3/4*e^4 - 5/4*e^3 - 49/2*e^2 + 22*e + 166, 7/16*e^4 - 3/4*e^3 - 221/16*e^2 + 109/8*e + 179/2, -11/16*e^4 + 5/4*e^3 + 353/16*e^2 - 177/8*e - 283/2, -9/16*e^4 + 3/4*e^3 + 283/16*e^2 - 99/8*e - 217/2, e^4 - 5/4*e^3 - 129/4*e^2 + 41/2*e + 208, -7/16*e^4 + 3/4*e^3 + 237/16*e^2 - 109/8*e - 203/2, -5/16*e^4 + 3/4*e^3 + 159/16*e^2 - 111/8*e - 129/2, 1/4*e^3 + 1/4*e^2 - 13/2*e - 6, 1/8*e^4 - 1/4*e^3 - 41/8*e^2 + 21/4*e + 43, -1/4*e^4 + 1/4*e^3 + 8*e^2 - 5*e - 54, -1/4*e^4 + 1/4*e^3 + 8*e^2 - 5*e - 46, -5/16*e^4 + 1/4*e^3 + 151/16*e^2 - 23/8*e - 97/2, -7/16*e^4 + 3/4*e^3 + 221/16*e^2 - 117/8*e - 167/2, -1/4*e^4 + 1/4*e^3 + 8*e^2 - 2*e - 56, -27/16*e^4 + 5/2*e^3 + 869/16*e^2 - 333/8*e - 703/2, -17/16*e^4 + 2*e^3 + 535/16*e^2 - 271/8*e - 401/2, 7/8*e^4 - 3/2*e^3 - 229/8*e^2 + 97/4*e + 197, 9/16*e^4 - 1/2*e^3 - 279/16*e^2 + 47/8*e + 201/2, -9/16*e^4 + 3/4*e^3 + 299/16*e^2 - 107/8*e - 245/2, 1/16*e^4 - 39/16*e^2 - 17/8*e + 25/2, -9/16*e^4 + 1/2*e^3 + 279/16*e^2 - 55/8*e - 217/2, -15/16*e^4 + 3/2*e^3 + 481/16*e^2 - 193/8*e - 391/2, -1/8*e^4 + 1/4*e^3 + 25/8*e^2 - 21/4*e - 11, 5/2*e^4 - 15/4*e^3 - 325/4*e^2 + 123/2*e + 530, -31/16*e^4 + 5/2*e^3 + 993/16*e^2 - 313/8*e - 791/2, -15/16*e^4 + 3/2*e^3 + 449/16*e^2 - 177/8*e - 303/2, -5/8*e^4 + 5/4*e^3 + 157/8*e^2 - 85/4*e - 125, 3/16*e^4 - 1/2*e^3 - 77/16*e^2 + 93/8*e + 35/2, 9/16*e^4 - 3/4*e^3 - 283/16*e^2 + 99/8*e + 217/2, -17/16*e^4 + 7/4*e^3 + 515/16*e^2 - 235/8*e - 361/2, -9/8*e^4 + 7/4*e^3 + 293/8*e^2 - 125/4*e - 243, -1/8*e^4 + 23/8*e^2 + 1/4*e - 5, -3/2*e^4 + 11/4*e^3 + 189/4*e^2 - 99/2*e - 290, 3/8*e^4 - 3/4*e^3 - 91/8*e^2 + 63/4*e + 69, -7/4*e^4 + 9/4*e^3 + 113/2*e^2 - 37*e - 360, -13/16*e^4 + e^3 + 427/16*e^2 - 147/8*e - 361/2, -3/8*e^4 + 3/4*e^3 + 99/8*e^2 - 71/4*e - 85, 7/16*e^4 - 1/2*e^3 - 249/16*e^2 + 81/8*e + 243/2, 27/16*e^4 - 3*e^3 - 877/16*e^2 + 405/8*e + 735/2, -3/2*e^4 + 9/4*e^3 + 191/4*e^2 - 73/2*e - 298, 21/16*e^4 - 7/4*e^3 - 655/16*e^2 + 223/8*e + 509/2, 1/8*e^4 - 39/8*e^2 - 9/4*e + 45, 5/16*e^4 - 1/2*e^3 - 155/16*e^2 + 67/8*e + 137/2, 3/4*e^4 - 3/4*e^3 - 24*e^2 + 13*e + 142, -15/16*e^4 + 7/4*e^3 + 453/16*e^2 - 245/8*e - 335/2, 23/16*e^4 - 2*e^3 - 721/16*e^2 + 249/8*e + 547/2, -9/8*e^4 + 7/4*e^3 + 269/8*e^2 - 117/4*e - 183, 23/16*e^4 - 3*e^3 - 721/16*e^2 + 425/8*e + 559/2, 5/16*e^4 - 1/4*e^3 - 183/16*e^2 + 39/8*e + 169/2, 3/16*e^4 - 1/4*e^3 - 105/16*e^2 + 41/8*e + 95/2, 9/16*e^4 - 1/2*e^3 - 311/16*e^2 + 71/8*e + 293/2, -9/8*e^4 + 9/4*e^3 + 289/8*e^2 - 157/4*e - 229, -5/8*e^4 + e^3 + 179/8*e^2 - 79/4*e - 165, -15/16*e^4 + e^3 + 457/16*e^2 - 129/8*e - 315/2, -25/16*e^4 + 2*e^3 + 831/16*e^2 - 239/8*e - 685/2, -9/16*e^4 + 5/4*e^3 + 307/16*e^2 - 163/8*e - 305/2, 3/8*e^4 - 1/2*e^3 - 89/8*e^2 + 41/4*e + 65, -21/16*e^4 + 7/4*e^3 + 671/16*e^2 - 231/8*e - 573/2, 5/16*e^4 - 1/2*e^3 - 171/16*e^2 + 75/8*e + 137/2, -13/16*e^4 + 3/2*e^3 + 419/16*e^2 - 227/8*e - 357/2, -3/2*e^4 + 2*e^3 + 93/2*e^2 - 32*e - 276, -1/8*e^4 - 1/4*e^3 + 37/8*e^2 + 19/4*e - 19, -31/16*e^4 + 7/2*e^3 + 961/16*e^2 - 497/8*e - 739/2, -9/16*e^4 + e^3 + 255/16*e^2 - 111/8*e - 133/2, -25/16*e^4 + 3*e^3 + 799/16*e^2 - 431/8*e - 665/2, 27/16*e^4 - 11/4*e^3 - 841/16*e^2 + 401/8*e + 627/2, 39/16*e^4 - 7/2*e^3 - 1273/16*e^2 + 449/8*e + 1019/2, -33/16*e^4 + 11/4*e^3 + 1075/16*e^2 - 355/8*e - 897/2, 15/8*e^4 - 11/4*e^3 - 471/8*e^2 + 175/4*e + 351, -5/16*e^4 + 1/4*e^3 + 151/16*e^2 - 23/8*e - 109/2, 5/2*e^4 - 15/4*e^3 - 325/4*e^2 + 127/2*e + 538, -25/16*e^4 + 7/4*e^3 + 811/16*e^2 - 203/8*e - 653/2, -27/16*e^4 + 9/4*e^3 + 881/16*e^2 - 313/8*e - 727/2, 5/4*e^4 - 5/4*e^3 - 41*e^2 + 21*e + 264, 51/16*e^4 - 5*e^3 - 1621/16*e^2 + 661/8*e + 1251/2, 15/16*e^4 - 3/2*e^3 - 465/16*e^2 + 177/8*e + 347/2, -3/4*e^4 + 3/4*e^3 + 26*e^2 - 13*e - 176, -1/4*e^4 + 1/4*e^3 + 11*e^2 - 6*e - 90, 13/16*e^4 - 3/2*e^3 - 371/16*e^2 + 219/8*e + 257/2, -17/16*e^4 + 5/4*e^3 + 555/16*e^2 - 171/8*e - 493/2, -15/16*e^4 + 5/4*e^3 + 445/16*e^2 - 181/8*e - 287/2, -9/8*e^4 + 9/4*e^3 + 273/8*e^2 - 165/4*e - 203, -33/16*e^4 + 9/4*e^3 + 1051/16*e^2 - 267/8*e - 837/2, 7/16*e^4 - 1/2*e^3 - 265/16*e^2 + 65/8*e + 271/2, -11/8*e^4 + 5/2*e^3 + 345/8*e^2 - 201/4*e - 267, 33/16*e^4 - 7/2*e^3 - 1039/16*e^2 + 463/8*e + 809/2, -1/16*e^4 - 1/2*e^3 + 31/16*e^2 + 49/8*e + 7/2, 1/8*e^4 - 1/2*e^3 - 43/8*e^2 + 27/4*e + 47, 11/16*e^4 - 1/2*e^3 - 373/16*e^2 + 53/8*e + 291/2, -3/8*e^4 + e^3 + 93/8*e^2 - 65/4*e - 69, -3/8*e^4 + 5/4*e^3 + 95/8*e^2 - 83/4*e - 87, -23/16*e^4 + 5/2*e^3 + 761/16*e^2 - 337/8*e - 667/2, -9/8*e^4 + 7/4*e^3 + 293/8*e^2 - 125/4*e - 225, 19/8*e^4 - 13/4*e^3 - 615/8*e^2 + 203/4*e + 495, -13/16*e^4 + e^3 + 427/16*e^2 - 163/8*e - 357/2, -25/16*e^4 + 9/4*e^3 + 835/16*e^2 - 299/8*e - 685/2, -1/2*e^4 + 1/4*e^3 + 59/4*e^2 - 3/2*e - 74, 11/4*e^4 - 17/4*e^3 - 171/2*e^2 + 72*e + 508, 19/16*e^4 - 7/4*e^3 - 593/16*e^2 + 241/8*e + 439/2, 1/2*e^4 - 3/4*e^3 - 57/4*e^2 + 31/2*e + 70, 19/16*e^4 - 5/4*e^3 - 601/16*e^2 + 193/8*e + 455/2, -17/16*e^4 + 2*e^3 + 535/16*e^2 - 279/8*e - 405/2, -23/16*e^4 + 5/2*e^3 + 713/16*e^2 - 313/8*e - 527/2, -5/4*e^4 + 5/2*e^3 + 161/4*e^2 - 93/2*e - 270, 7/16*e^4 - 1/2*e^3 - 233/16*e^2 + 129/8*e + 199/2, 1/2*e^4 - e^3 - 31/2*e^2 + 17*e + 104, -15/16*e^4 + 7/4*e^3 + 501/16*e^2 - 229/8*e - 423/2, -e^4 + 7/4*e^3 + 119/4*e^2 - 55/2*e - 160, -7/8*e^4 + 5/4*e^3 + 243/8*e^2 - 103/4*e - 231, -7/16*e^4 + 1/2*e^3 + 217/16*e^2 - 65/8*e - 155/2, -25/16*e^4 + 7/4*e^3 + 795/16*e^2 - 219/8*e - 609/2, -49/16*e^4 + 5*e^3 + 1511/16*e^2 - 671/8*e - 1101/2, 39/16*e^4 - 7/2*e^3 - 1241/16*e^2 + 497/8*e + 963/2, 5/8*e^4 - e^3 - 187/8*e^2 + 63/4*e + 187, 1/4*e^3 - 7/4*e^2 - 5/2*e + 24, -61/16*e^4 + 21/4*e^3 + 1935/16*e^2 - 695/8*e - 1525/2, -19/8*e^4 + 9/2*e^3 + 593/8*e^2 - 309/4*e - 445, 53/16*e^4 - 11/2*e^3 - 1659/16*e^2 + 771/8*e + 1309/2, 35/16*e^4 - 13/4*e^3 - 1145/16*e^2 + 441/8*e + 999/2, -23/8*e^4 + 5*e^3 + 745/8*e^2 - 337/4*e - 607, 23/16*e^4 - 7/4*e^3 - 733/16*e^2 + 245/8*e + 539/2, -25/16*e^4 + 5/2*e^3 + 775/16*e^2 - 335/8*e - 625/2, 25/16*e^4 - 5/2*e^3 - 775/16*e^2 + 303/8*e + 541/2, 1/16*e^4 + 1/2*e^3 + 17/16*e^2 - 105/8*e - 67/2, 35/16*e^4 - 7/2*e^3 - 1133/16*e^2 + 517/8*e + 935/2, -5/8*e^4 + 5/4*e^3 + 157/8*e^2 - 117/4*e - 135, 5/8*e^4 - 3/2*e^3 - 151/8*e^2 + 95/4*e + 115, 29/8*e^4 - 21/4*e^3 - 917/8*e^2 + 353/4*e + 717, 71/16*e^4 - 7*e^3 - 2241/16*e^2 + 969/8*e + 1747/2, -21/8*e^4 + 4*e^3 + 667/8*e^2 - 279/4*e - 527, 19/16*e^4 - 7/4*e^3 - 641/16*e^2 + 257/8*e + 583/2, 11/8*e^4 - 9/4*e^3 - 375/8*e^2 + 147/4*e + 351, -53/16*e^4 + 21/4*e^3 + 1671/16*e^2 - 695/8*e - 1273/2, 3/4*e^4 - e^3 - 93/4*e^2 + 41/2*e + 144, 21/8*e^4 - 15/4*e^3 - 689/8*e^2 + 233/4*e + 549, -7/16*e^4 + 3/4*e^3 + 173/16*e^2 - 85/8*e - 83/2, -21/16*e^4 + 11/4*e^3 + 623/16*e^2 - 367/8*e - 425/2, -19/16*e^4 + 2*e^3 + 581/16*e^2 - 325/8*e - 411/2, 19/16*e^4 - 7/4*e^3 - 641/16*e^2 + 257/8*e + 555/2, 13/16*e^4 - 3/4*e^3 - 359/16*e^2 + 87/8*e + 181/2, 31/8*e^4 - 25/4*e^3 - 1011/8*e^2 + 431/4*e + 837, -61/16*e^4 + 23/4*e^3 + 1943/16*e^2 - 751/8*e - 1493/2, 23/8*e^4 - 5*e^3 - 729/8*e^2 + 333/4*e + 565, 21/16*e^4 - 7/4*e^3 - 655/16*e^2 + 215/8*e + 517/2, 11/8*e^4 - 11/4*e^3 - 355/8*e^2 + 207/4*e + 289, e^4 - 5/4*e^3 - 133/4*e^2 + 43/2*e + 230, -29/8*e^4 + 25/4*e^3 + 909/8*e^2 - 449/4*e - 695, 3/4*e^4 - 2*e^3 - 97/4*e^2 + 73/2*e + 138, 23/16*e^4 - 2*e^3 - 753/16*e^2 + 273/8*e + 631/2, 9/4*e^4 - 9/2*e^3 - 281/4*e^2 + 153/2*e + 420, 7/8*e^4 - 3/4*e^3 - 231/8*e^2 + 55/4*e + 217, -37/16*e^4 + 17/4*e^3 + 1223/16*e^2 - 615/8*e - 1053/2, 3/8*e^4 - 1/2*e^3 - 73/8*e^2 + 61/4*e + 17, -43/16*e^4 + 17/4*e^3 + 1329/16*e^2 - 601/8*e - 1011/2, 7/8*e^4 - 5/4*e^3 - 211/8*e^2 + 71/4*e + 137, -21/16*e^4 + 9/4*e^3 + 615/16*e^2 - 311/8*e - 393/2, 9/16*e^4 - e^3 - 303/16*e^2 + 151/8*e + 217/2, -47/16*e^4 + 17/4*e^3 + 1533/16*e^2 - 557/8*e - 1251/2] 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,-w^3 - w^2 + 5*w + 5])] = -1 AL_eigenvalues[ZF.ideal([11,11,-w^3 - 2*w^2 + 6*w + 9])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]