/* 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([41, 13, -12, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1, 1, 1]) primes_array = [ [9, 3, -w^3 + 3*w^2 + 5*w - 15],\ [9, 3, -w^3 + 8*w + 8],\ [16, 2, 2],\ [19, 19, w + 1],\ [19, 19, -w^2 + 6],\ [19, 19, -w^2 + 2*w + 5],\ [19, 19, -w + 2],\ [25, 5, 2*w^2 - 2*w - 13],\ [29, 29, -w^2 + 9],\ [29, 29, -w^2 + 2*w + 6],\ [29, 29, w^2 - 7],\ [29, 29, -w^2 + 2*w + 8],\ [31, 31, -2*w^2 + w + 12],\ [31, 31, 2*w^2 - 3*w - 11],\ [41, 41, -w],\ [41, 41, -w + 1],\ [49, 7, w^3 + 2*w^2 - 10*w - 20],\ [49, 7, w^3 - 5*w^2 - 3*w + 27],\ [61, 61, 2*w^2 - 3*w - 14],\ [61, 61, 2*w^2 - w - 15],\ [71, 71, -w^3 + w^2 + 7*w - 5],\ [71, 71, w^3 - 2*w^2 - 6*w + 2],\ [79, 79, w^3 - 2*w^2 - 6*w + 4],\ [79, 79, 3*w^2 - 2*w - 18],\ [89, 89, 2*w^3 - 6*w^2 - 11*w + 33],\ [89, 89, -4*w^2 + 3*w + 25],\ [101, 101, w^3 + w^2 - 9*w - 12],\ [101, 101, w^3 - 4*w^2 - 4*w + 19],\ [109, 109, -w^3 + 3*w^2 + 6*w - 19],\ [109, 109, -2*w^2 + w + 18],\ [121, 11, -3*w^2 + 3*w + 19],\ [121, 11, 3*w^2 - 3*w - 20],\ [131, 131, 2*w^2 - 3*w - 15],\ [131, 131, 2*w^2 - w - 16],\ [139, 139, 3*w^2 - 4*w - 21],\ [139, 139, -w^3 - w^2 + 7*w + 13],\ [151, 151, 4*w^2 - 3*w - 27],\ [151, 151, 2*w^3 - w^2 - 13*w - 8],\ [151, 151, w^3 + 3*w^2 - 13*w - 27],\ [151, 151, 4*w^2 - 5*w - 26],\ [179, 179, w^3 - 3*w^2 - 5*w + 11],\ [179, 179, 3*w^3 - 11*w^2 - 14*w + 61],\ [179, 179, 2*w^3 - 2*w^2 - 12*w + 3],\ [179, 179, w^3 - 8*w - 4],\ [181, 181, -w - 4],\ [181, 181, w^3 - 5*w^2 - 3*w + 25],\ [181, 181, w^3 + 2*w^2 - 10*w - 18],\ [181, 181, w - 5],\ [229, 229, w^2 - 2*w - 11],\ [229, 229, w^2 - 12],\ [239, 239, 6*w^2 - 7*w - 42],\ [239, 239, 2*w^3 - 2*w^2 - 14*w - 3],\ [241, 241, w^3 - 4*w^2 - 4*w + 18],\ [241, 241, 3*w^2 - 2*w - 16],\ [269, 269, 3*w^2 - 4*w - 22],\ [269, 269, -w^3 + 6*w + 8],\ [281, 281, w^3 - w^2 - 9*w + 4],\ [281, 281, 2*w^3 - 9*w^2 - 8*w + 49],\ [311, 311, -2*w^3 - w^2 + 17*w + 19],\ [311, 311, 2*w^3 - 7*w^2 - 9*w + 33],\ [331, 331, w^3 + 2*w^2 - 9*w - 21],\ [331, 331, w^3 - 5*w^2 - 2*w + 27],\ [349, 349, 2*w^3 - w^2 - 15*w - 4],\ [349, 349, -2*w^3 + 5*w^2 + 11*w - 18],\ [359, 359, -w^3 + 6*w^2 - 31],\ [359, 359, -w^3 - 3*w^2 + 9*w + 26],\ [379, 379, 2*w^3 - 5*w^2 - 11*w + 20],\ [379, 379, 2*w^3 - 14*w - 11],\ [401, 401, w^3 - 3*w^2 - 4*w + 16],\ [401, 401, -2*w^3 + 4*w^2 + 11*w - 16],\ [401, 401, 2*w^3 - 2*w^2 - 13*w - 3],\ [401, 401, w^3 - 7*w - 10],\ [409, 409, w^3 - 4*w^2 - 4*w + 17],\ [409, 409, 2*w^3 - 6*w^2 - 9*w + 22],\ [409, 409, -2*w^3 + 15*w + 9],\ [409, 409, -w^3 + 3*w^2 + 6*w - 12],\ [419, 419, -w^3 + 5*w^2 + 3*w - 24],\ [419, 419, w^3 + 2*w^2 - 10*w - 17],\ [421, 421, w^3 + 3*w^2 - 12*w - 25],\ [421, 421, -w^3 - w^2 + 9*w + 7],\ [431, 431, -w^3 - 2*w^2 + 12*w + 20],\ [431, 431, w^3 + 3*w^2 - 10*w - 28],\ [431, 431, -w^3 + 6*w^2 + w - 34],\ [431, 431, -w^3 + 5*w^2 + 5*w - 29],\ [439, 439, w^3 - 7*w^2 - 2*w + 39],\ [439, 439, w^3 + 4*w^2 - 13*w - 31],\ [449, 449, -w^3 - 4*w^2 + 13*w + 34],\ [449, 449, 6*w^2 - 5*w - 36],\ [461, 461, -w^3 + 5*w^2 + w - 25],\ [461, 461, 2*w^3 - 15*w - 12],\ [461, 461, -2*w^3 + 6*w^2 + 9*w - 25],\ [461, 461, w^3 + 2*w^2 - 8*w - 20],\ [479, 479, -w^3 - 4*w^2 + 12*w + 31],\ [479, 479, 2*w^3 - 15*w - 16],\ [479, 479, -2*w^3 + 6*w^2 + 9*w - 29],\ [479, 479, w^3 - 7*w^2 - w + 38],\ [491, 491, w^2 - 3*w - 7],\ [491, 491, -2*w^3 + 3*w^2 + 11*w - 2],\ [491, 491, 4*w^2 - 2*w - 29],\ [491, 491, w^2 + w - 9],\ [499, 499, 5*w^2 - 6*w - 33],\ [499, 499, 5*w^2 - 4*w - 34],\ [509, 509, 2*w - 3],\ [509, 509, -2*w - 1],\ [541, 541, -w^3 - 4*w^2 + 12*w + 29],\ [541, 541, -w^3 + 7*w^2 + w - 36],\ [599, 599, -w^3 - w^2 + 8*w + 7],\ [599, 599, w^3 - 4*w^2 - 3*w + 13],\ [619, 619, w^2 - 3*w - 6],\ [619, 619, w^2 + w - 8],\ [641, 641, -2*w^3 + 16*w + 11],\ [641, 641, -2*w^3 + 6*w^2 + 10*w - 25],\ [659, 659, 2*w^3 + w^2 - 16*w - 16],\ [659, 659, 2*w^3 - 7*w^2 - 8*w + 29],\ [691, 691, -w^3 + 5*w^2 + 3*w - 23],\ [691, 691, -w^3 + 3*w^2 + 6*w - 11],\ [701, 701, w^3 - w^2 - 9*w + 3],\ [701, 701, 2*w^3 - w^2 - 14*w - 5],\ [709, 709, 2*w^3 - 3*w^2 - 11*w + 6],\ [719, 719, w^2 - 2*w - 12],\ [719, 719, -w^2 + 13],\ [739, 739, -2*w^3 + 8*w^2 + 7*w - 36],\ [739, 739, w^2 + 2*w - 13],\ [751, 751, -2*w^3 + 5*w^2 + 10*w - 20],\ [751, 751, 2*w^3 - w^2 - 14*w - 7],\ [761, 761, w^3 + 4*w^2 - 12*w - 32],\ [761, 761, -w^3 + 7*w^2 + w - 39],\ [769, 769, -2*w^3 - 4*w^2 + 23*w + 45],\ [769, 769, 2*w^3 - 5*w^2 - 9*w + 21],\ [769, 769, 2*w^3 + 2*w^2 - 18*w - 31],\ [769, 769, 2*w^3 - 10*w^2 - 9*w + 62],\ [811, 811, -w^3 + 10*w + 5],\ [811, 811, -5*w^2 + 8*w + 30],\ [811, 811, w^3 - 8*w^2 + 2*w + 43],\ [811, 811, 2*w^3 - 2*w^2 - 13*w + 2],\ [829, 829, -2*w^3 - 2*w^2 + 18*w + 25],\ [829, 829, -2*w^3 + 8*w^2 + 8*w - 39],\ [859, 859, -w^3 - 4*w^2 + 12*w + 33],\ [859, 859, -w^3 + 7*w^2 + w - 40],\ [919, 919, w^3 - 4*w^2 - 3*w + 24],\ [919, 919, -w^3 + 5*w^2 + w - 26],\ [929, 929, 5*w^2 - 7*w - 28],\ [929, 929, -w^3 + 2*w^2 + 6*w - 13],\ [929, 929, w^3 - w^2 - 7*w - 6],\ [929, 929, -2*w^3 + 2*w^2 + 14*w - 5],\ [941, 941, -2*w^3 + 3*w^2 + 11*w - 1],\ [941, 941, 2*w^3 - 3*w^2 - 11*w + 11],\ [961, 31, 5*w^2 - 5*w - 33],\ [971, 971, -w^3 - 3*w^2 + 11*w + 22],\ [971, 971, 7*w^2 - 5*w - 45],\ [971, 971, 7*w^2 - 9*w - 43],\ [971, 971, w^3 - 6*w^2 - 2*w + 29],\ [991, 991, w^3 - 3*w^2 - 3*w + 15],\ [991, 991, -w^3 + 5*w^2 + 2*w - 29]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 + 2*x^5 - 35*x^4 - 46*x^3 + 310*x^2 + 116*x - 375 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, e, -1/42*e^5 + 7/12*e^3 - 9/28*e^2 - 73/42*e + 167/28, 1/84*e^5 + 1/12*e^4 - 1/4*e^3 - 43/21*e^2 + 19/42*e + 165/28, -1/12*e^4 + 1/12*e^3 + 11/6*e^2 - 31/12*e - 5/2, -1/12*e^4 + 1/12*e^3 + 11/6*e^2 - 31/12*e - 5/2, 1/84*e^5 + 1/12*e^4 - 1/4*e^3 - 43/21*e^2 + 19/42*e + 165/28, 1/84*e^5 + 1/12*e^4 - 1/4*e^3 - 43/21*e^2 + 19/42*e + 333/28, 1/42*e^5 - 5/6*e^3 + 1/14*e^2 + 241/42*e - 5/7, -1/84*e^5 + 5/12*e^3 + 13/28*e^2 - 241/84*e - 65/14, -1/84*e^5 + 5/12*e^3 + 13/28*e^2 - 241/84*e - 65/14, 1/42*e^5 - 5/6*e^3 + 1/14*e^2 + 241/42*e - 5/7, -1/42*e^5 - 1/12*e^4 + 2/3*e^3 + 127/84*e^2 - 121/28*e - 43/28, -1/42*e^5 - 1/12*e^4 + 2/3*e^3 + 127/84*e^2 - 121/28*e - 43/28, -1/4*e^3 - 1/4*e^2 + 4*e + 1/4, -1/4*e^3 - 1/4*e^2 + 4*e + 1/4, -1/84*e^5 - 1/12*e^4 + 1/2*e^3 + 193/84*e^2 - 229/42*e - 50/7, -1/84*e^5 - 1/12*e^4 + 1/2*e^3 + 193/84*e^2 - 229/42*e - 50/7, -1/42*e^5 + 1/12*e^4 + 3/4*e^3 - 40/21*e^2 - 349/84*e + 31/14, -1/42*e^5 + 1/12*e^4 + 3/4*e^3 - 40/21*e^2 - 349/84*e + 31/14, -1/21*e^5 + 17/12*e^3 + 17/28*e^2 - 157/21*e - 233/28, -1/21*e^5 + 17/12*e^3 + 17/28*e^2 - 157/21*e - 233/28, 5/84*e^5 + 1/12*e^4 - 23/12*e^3 - 40/21*e^2 + 167/14*e + 125/28, 5/84*e^5 + 1/12*e^4 - 23/12*e^3 - 40/21*e^2 + 167/14*e + 125/28, 1/21*e^5 - 5/3*e^3 + 1/7*e^2 + 304/21*e - 10/7, 1/21*e^5 - 5/3*e^3 + 1/7*e^2 + 304/21*e - 10/7, 1/84*e^5 - 2/3*e^3 + 2/7*e^2 + 577/84*e - 143/28, 1/84*e^5 - 2/3*e^3 + 2/7*e^2 + 577/84*e - 143/28, 5/84*e^5 + 1/4*e^4 - 19/12*e^3 - 85/14*e^2 + 191/21*e + 475/28, 5/84*e^5 + 1/4*e^4 - 19/12*e^3 - 85/14*e^2 + 191/21*e + 475/28, 1/84*e^5 - 1/6*e^4 + 145/42*e^2 - 361/84*e + 291/28, 1/28*e^5 - 5/4*e^3 + 17/28*e^2 + 297/28*e + 83/14, 1/84*e^5 + 1/12*e^3 - 27/28*e^2 - 683/84*e + 78/7, 1/84*e^5 + 1/12*e^3 - 27/28*e^2 - 683/84*e + 78/7, 1/28*e^5 + 1/12*e^4 - 13/12*e^3 - 41/42*e^2 + 130/21*e - 135/28, 1/28*e^5 + 1/12*e^4 - 13/12*e^3 - 41/42*e^2 + 130/21*e - 135/28, -1/4*e^3 + 3/4*e^2 + 6*e - 39/4, 5/84*e^5 + 1/6*e^4 - 7/4*e^3 - 377/84*e^2 + 715/84*e + 103/7, 5/84*e^5 + 1/6*e^4 - 7/4*e^3 - 377/84*e^2 + 715/84*e + 103/7, -1/4*e^3 + 3/4*e^2 + 6*e - 39/4, 1/84*e^5 + 1/3*e^3 + 2/7*e^2 - 1019/84*e + 25/28, -1/7*e^5 - 1/4*e^4 + 4*e^3 + 135/28*e^2 - 621/28*e - 335/28, -1/7*e^5 - 1/4*e^4 + 4*e^3 + 135/28*e^2 - 621/28*e - 335/28, 1/84*e^5 + 1/3*e^3 + 2/7*e^2 - 1019/84*e + 25/28, -1/28*e^5 - 1/6*e^4 + 17/12*e^3 + 341/84*e^2 - 989/84*e - 139/14, -1/42*e^5 - 1/4*e^4 + 5/6*e^3 + 173/28*e^2 - 629/84*e - 463/28, -1/42*e^5 - 1/4*e^4 + 5/6*e^3 + 173/28*e^2 - 629/84*e - 463/28, -1/28*e^5 - 1/6*e^4 + 17/12*e^3 + 341/84*e^2 - 989/84*e - 139/14, 1/84*e^5 + 1/6*e^4 + 1/6*e^3 - 50/21*e^2 - 195/28*e - 115/28, 1/84*e^5 + 1/6*e^4 + 1/6*e^3 - 50/21*e^2 - 195/28*e - 115/28, 3/28*e^5 + 1/4*e^4 - 13/4*e^3 - 69/14*e^2 + 130/7*e + 155/28, 3/28*e^5 + 1/4*e^4 - 13/4*e^3 - 69/14*e^2 + 130/7*e + 155/28, -1/21*e^5 + 1/6*e^4 + e^3 - 223/42*e^2 - 55/42*e + 363/14, -1/21*e^5 + 1/6*e^4 + e^3 - 223/42*e^2 - 55/42*e + 363/14, -1/4*e^4 + 1/4*e^3 + 15/2*e^2 - 19/4*e - 55/2, -1/4*e^4 + 1/4*e^3 + 15/2*e^2 - 19/4*e - 55/2, 1/28*e^5 - 3/4*e^3 + 3/28*e^2 + 17/28*e + 3/7, 1/28*e^5 - 3/4*e^3 + 3/28*e^2 + 17/28*e + 3/7, -11/84*e^5 + 49/12*e^3 - 11/28*e^2 - 2231/84*e + 59/7, -11/84*e^5 + 49/12*e^3 - 11/28*e^2 - 2231/84*e + 59/7, 1/21*e^5 + 1/12*e^4 - e^3 - 163/84*e^2 + 341/84*e + 177/28, 1/21*e^5 + 1/12*e^4 - e^3 - 163/84*e^2 + 341/84*e + 177/28, -1/14*e^5 - 1/12*e^4 + 4/3*e^3 + 199/84*e^2 + 269/84*e - 535/28, -1/14*e^5 - 1/12*e^4 + 4/3*e^3 + 199/84*e^2 + 269/84*e - 535/28, -1/14*e^5 - 1/4*e^4 + 3/2*e^3 + 169/28*e^2 - 139/28*e - 675/28, -1/14*e^5 - 1/4*e^4 + 3/2*e^3 + 169/28*e^2 - 139/28*e - 675/28, 1/12*e^5 + 1/6*e^4 - 7/3*e^3 - 13/6*e^2 + 65/4*e - 25/4, 1/12*e^5 + 1/6*e^4 - 7/3*e^3 - 13/6*e^2 + 65/4*e - 25/4, 1/28*e^5 - 7/4*e^3 - 53/28*e^2 + 549/28*e + 164/7, -1/28*e^5 + 1/2*e^3 - 19/14*e^2 + 95/28*e + 107/28, -1/28*e^5 + 1/2*e^3 - 19/14*e^2 + 95/28*e + 107/28, 1/28*e^5 - 7/4*e^3 - 53/28*e^2 + 549/28*e + 164/7, 1/7*e^5 + 1/12*e^4 - 49/12*e^3 - 59/42*e^2 + 1933/84*e + 45/14, 1/4*e^4 - 29/4*e^2 - 9/4*e + 165/4, 1/4*e^4 - 29/4*e^2 - 9/4*e + 165/4, 1/7*e^5 + 1/12*e^4 - 49/12*e^3 - 59/42*e^2 + 1933/84*e + 45/14, -5/42*e^5 - 1/2*e^4 + 41/12*e^3 + 319/28*e^2 - 382/21*e - 845/28, -5/42*e^5 - 1/2*e^4 + 41/12*e^3 + 319/28*e^2 - 382/21*e - 845/28, -1/12*e^5 - 5/12*e^4 + 25/12*e^3 + 49/6*e^2 - 8*e - 59/4, -1/12*e^5 - 5/12*e^4 + 25/12*e^3 + 49/6*e^2 - 8*e - 59/4, 5/42*e^5 + 1/4*e^4 - 19/6*e^3 - 165/28*e^2 + 1381/84*e + 467/28, -2/21*e^5 - 1/4*e^4 + 25/12*e^3 + 40/7*e^2 - 59/84*e - 162/7, -2/21*e^5 - 1/4*e^4 + 25/12*e^3 + 40/7*e^2 - 59/84*e - 162/7, 5/42*e^5 + 1/4*e^4 - 19/6*e^3 - 165/28*e^2 + 1381/84*e + 467/28, -1/21*e^5 + 1/4*e^4 + 5/3*e^3 - 179/28*e^2 - 985/84*e + 355/28, -1/21*e^5 + 1/4*e^4 + 5/3*e^3 - 179/28*e^2 - 985/84*e + 355/28, -5/84*e^5 + 1/4*e^4 + 25/12*e^3 - 83/14*e^2 - 697/42*e + 225/28, -5/84*e^5 + 1/4*e^4 + 25/12*e^3 - 83/14*e^2 - 697/42*e + 225/28, -1/12*e^5 - 1/4*e^4 + 8/3*e^3 + 21/4*e^2 - 119/6*e - 1/2, 5/84*e^5 - 1/4*e^4 - 25/12*e^3 + 111/14*e^2 + 697/42*e - 953/28, 5/84*e^5 - 1/4*e^4 - 25/12*e^3 + 111/14*e^2 + 697/42*e - 953/28, -1/12*e^5 - 1/4*e^4 + 8/3*e^3 + 21/4*e^2 - 119/6*e - 1/2, 1/84*e^5 - 11/12*e^3 + 1/28*e^2 + 661/84*e - 55/7, -1/28*e^5 - 1/4*e^4 + e^3 + 151/28*e^2 - 159/14*e - 195/14, -1/28*e^5 - 1/4*e^4 + e^3 + 151/28*e^2 - 159/14*e - 195/14, 1/84*e^5 - 11/12*e^3 + 1/28*e^2 + 661/84*e - 55/7, -3/28*e^5 - 1/4*e^4 + 7/2*e^3 + 173/28*e^2 - 200/7*e - 137/14, 1/4*e^4 - 25/4*e^2 - 9/4*e + 93/4, 1/4*e^4 - 25/4*e^2 - 9/4*e + 93/4, -3/28*e^5 - 1/4*e^4 + 7/2*e^3 + 173/28*e^2 - 200/7*e - 137/14, -1/42*e^5 + 1/12*e^4 + 1/2*e^3 - 181/84*e^2 + 239/84*e - 15/28, -1/42*e^5 + 1/12*e^4 + 1/2*e^3 - 181/84*e^2 + 239/84*e - 15/28, -1/21*e^5 + 23/12*e^3 - 25/28*e^2 - 388/21*e + 145/28, -1/21*e^5 + 23/12*e^3 - 25/28*e^2 - 388/21*e + 145/28, 1/14*e^5 + 1/6*e^4 - 29/12*e^3 - 437/84*e^2 + 323/21*e + 801/28, 1/14*e^5 + 1/6*e^4 - 29/12*e^3 - 437/84*e^2 + 323/21*e + 801/28, 1/4*e^3 - 3/4*e^2 - 4*e + 15/4, 1/4*e^3 - 3/4*e^2 - 4*e + 15/4, 5/84*e^5 + 1/4*e^4 - 4/3*e^3 - 219/28*e^2 + 65/21*e + 355/7, 5/84*e^5 + 1/4*e^4 - 4/3*e^3 - 219/28*e^2 + 65/21*e + 355/7, 11/84*e^5 - 10/3*e^3 + 8/7*e^2 + 971/84*e - 173/28, 11/84*e^5 - 10/3*e^3 + 8/7*e^2 + 971/84*e - 173/28, 1/84*e^5 + 1/4*e^4 + 1/3*e^3 - 167/28*e^2 - 302/21*e + 85/7, 1/84*e^5 + 1/4*e^4 + 1/3*e^3 - 167/28*e^2 - 302/21*e + 85/7, 1/42*e^5 + 1/4*e^4 - 13/12*e^3 - 45/7*e^2 + 1637/84*e + 431/14, 1/42*e^5 + 1/4*e^4 - 13/12*e^3 - 45/7*e^2 + 1637/84*e + 431/14, -17/84*e^5 - 1/2*e^4 + 35/6*e^3 + 71/7*e^2 - 2795/84*e - 369/28, -17/84*e^5 - 1/2*e^4 + 35/6*e^3 + 71/7*e^2 - 2795/84*e - 369/28, -5/42*e^5 + 19/6*e^3 - 33/14*e^2 - 449/42*e + 270/7, 1/28*e^5 - 7/4*e^3 + 31/28*e^2 + 717/28*e - 130/7, 1/28*e^5 - 7/4*e^3 + 31/28*e^2 + 717/28*e - 130/7, 11/84*e^5 + 1/12*e^4 - 35/12*e^3 + 17/21*e^2 + 36/7*e - 425/28, 11/84*e^5 + 1/12*e^4 - 35/12*e^3 + 17/21*e^2 + 36/7*e - 425/28, 1/14*e^5 - 1/6*e^4 - 31/12*e^3 + 305/84*e^2 + 505/21*e + 31/28, 1/14*e^5 - 1/6*e^4 - 31/12*e^3 + 305/84*e^2 + 505/21*e + 31/28, 1/12*e^5 + 1/2*e^4 - 8/3*e^3 - 23/2*e^2 + 211/12*e + 71/4, 1/12*e^5 + 1/2*e^4 - 8/3*e^3 - 23/2*e^2 + 211/12*e + 71/4, -11/84*e^5 - 1/3*e^4 + 19/6*e^3 + 323/42*e^2 - 473/28*e - 905/28, -7/12*e^4 - 2/3*e^3 + 187/12*e^2 + 95/12*e - 225/4, -7/12*e^4 - 2/3*e^3 + 187/12*e^2 + 95/12*e - 225/4, -11/84*e^5 - 1/3*e^4 + 19/6*e^3 + 323/42*e^2 - 473/28*e - 905/28, 11/84*e^5 + 1/3*e^4 - 53/12*e^3 - 583/84*e^2 + 921/28*e + 109/7, -2/21*e^5 - 1/6*e^4 + 7/4*e^3 + 221/84*e^2 + 79/42*e - 403/28, -2/21*e^5 - 1/6*e^4 + 7/4*e^3 + 221/84*e^2 + 79/42*e - 403/28, 11/84*e^5 + 1/3*e^4 - 53/12*e^3 - 583/84*e^2 + 921/28*e + 109/7, -1/21*e^5 + 2/3*e^3 - 8/7*e^2 + 32/21*e + 115/7, -1/21*e^5 + 2/3*e^3 - 8/7*e^2 + 32/21*e + 115/7, -13/84*e^5 - 1/3*e^4 + 4*e^3 + 160/21*e^2 - 893/84*e - 885/28, -13/84*e^5 - 1/3*e^4 + 4*e^3 + 160/21*e^2 - 893/84*e - 885/28, 1/14*e^5 + 1/2*e^4 - 5/4*e^3 - 309/28*e^2 - 9/7*e + 1095/28, 1/14*e^5 + 1/2*e^4 - 5/4*e^3 - 309/28*e^2 - 9/7*e + 1095/28, -2/21*e^5 - 1/4*e^4 + 31/12*e^3 + 59/14*e^2 - 731/84*e + 285/14, 11/84*e^5 - 1/4*e^4 - 49/12*e^3 + 79/14*e^2 + 542/21*e - 355/28, 11/84*e^5 - 1/4*e^4 - 49/12*e^3 + 79/14*e^2 + 542/21*e - 355/28, -2/21*e^5 - 1/4*e^4 + 31/12*e^3 + 59/14*e^2 - 731/84*e + 285/14, -1/4*e^4 - e^3 + 13/4*e^2 + 49/4*e + 111/4, -1/4*e^4 - e^3 + 13/4*e^2 + 49/4*e + 111/4, 1/84*e^5 - 2/3*e^3 - 12/7*e^2 - 179/84*e + 1061/28, 1/4*e^4 + 3/2*e^3 - 19/4*e^2 - 105/4*e + 63/4, -1/14*e^5 + 1/4*e^4 + 5/2*e^3 - 209/28*e^2 - 713/28*e + 487/28, -1/14*e^5 + 1/4*e^4 + 5/2*e^3 - 209/28*e^2 - 713/28*e + 487/28, 1/4*e^4 + 3/2*e^3 - 19/4*e^2 - 105/4*e + 63/4, 1/7*e^5 + e^4 - 17/4*e^3 - 583/28*e^2 + 234/7*e + 951/28, 1/7*e^5 + e^4 - 17/4*e^3 - 583/28*e^2 + 234/7*e + 951/28] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]