/* 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([19, 14, -13, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, -w]) primes_array = [ [4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3],\ [5, 5, 3/19*w^3 + 5/19*w^2 - 27/19*w - 1],\ [5, 5, -3/19*w^3 + 14/19*w^2 + 8/19*w - 2],\ [9, 3, -2/19*w^3 + 3/19*w^2 + 37/19*w - 4],\ [19, 19, -w],\ [19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 1],\ [19, 19, 4/19*w^3 - 6/19*w^2 - 55/19*w + 2],\ [19, 19, w - 1],\ [29, 29, -5/19*w^3 - 2/19*w^2 + 64/19*w + 2],\ [29, 29, 10/19*w^3 - 34/19*w^2 - 71/19*w + 9],\ [29, 29, 4/19*w^3 - 6/19*w^2 - 55/19*w + 4],\ [29, 29, -w + 3],\ [49, 7, 5/19*w^3 - 17/19*w^2 - 64/19*w + 11],\ [49, 7, 6/19*w^3 - 9/19*w^2 - 92/19*w - 1],\ [71, 71, 3/19*w^3 + 5/19*w^2 - 46/19*w - 1],\ [71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w],\ [71, 71, 6/19*w^3 - 9/19*w^2 - 73/19*w + 4],\ [71, 71, -3/19*w^3 + 14/19*w^2 + 27/19*w - 3],\ [101, 101, 7/19*w^3 - 1/19*w^2 - 63/19*w - 3],\ [101, 101, -9/19*w^3 + 23/19*w^2 + 81/19*w - 5],\ [101, 101, 9/19*w^3 - 4/19*w^2 - 100/19*w],\ [101, 101, 7/19*w^3 - 20/19*w^2 - 44/19*w + 6],\ [121, 11, 6/19*w^3 - 9/19*w^2 - 54/19*w + 1],\ [121, 11, -6/19*w^3 + 9/19*w^2 + 54/19*w - 2],\ [139, 139, 9/19*w^3 - 4/19*w^2 - 100/19*w - 2],\ [139, 139, -7/19*w^3 + 1/19*w^2 + 63/19*w + 1],\ [139, 139, 7/19*w^3 - 20/19*w^2 - 44/19*w + 4],\ [139, 139, w - 5],\ [149, 149, -1/19*w^3 + 11/19*w^2 - 10/19*w - 6],\ [149, 149, -3/19*w^3 - 5/19*w^2 + 46/19*w],\ [149, 149, -3/19*w^3 + 14/19*w^2 + 27/19*w - 2],\ [149, 149, 1/19*w^3 + 8/19*w^2 - 9/19*w - 6],\ [169, 13, 14/19*w^3 - 40/19*w^2 - 126/19*w + 13],\ [169, 13, 10/19*w^3 - 34/19*w^2 - 52/19*w + 7],\ [191, 191, -10/19*w^3 + 15/19*w^2 + 109/19*w - 6],\ [191, 191, 6/19*w^3 - 9/19*w^2 - 35/19*w - 2],\ [191, 191, -6/19*w^3 + 9/19*w^2 + 35/19*w - 4],\ [191, 191, 10/19*w^3 - 15/19*w^2 - 109/19*w],\ [211, 211, 1/19*w^3 + 8/19*w^2 - 28/19*w - 8],\ [211, 211, 1/19*w^3 - 11/19*w^2 - 9/19*w - 1],\ [211, 211, -1/19*w^3 - 8/19*w^2 + 28/19*w - 2],\ [211, 211, -1/19*w^3 + 11/19*w^2 + 9/19*w - 9],\ [239, 239, 4/19*w^3 - 25/19*w^2 - 17/19*w + 12],\ [239, 239, -1/19*w^3 - 8/19*w^2 - 29/19*w + 5],\ [239, 239, 10/19*w^3 - 15/19*w^2 - 128/19*w + 1],\ [239, 239, -4/19*w^3 - 13/19*w^2 + 55/19*w + 10],\ [241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w - 4],\ [241, 241, -6/19*w^3 + 9/19*w^2 + 92/19*w],\ [241, 241, 6/19*w^3 - 9/19*w^2 - 92/19*w + 5],\ [241, 241, -2/19*w^3 + 3/19*w^2 + 56/19*w + 1],\ [269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 11],\ [269, 269, 8/19*w^3 - 12/19*w^2 - 129/19*w + 11],\ [269, 269, -10/19*w^3 + 34/19*w^2 + 71/19*w - 8],\ [269, 269, -13/19*w^3 + 48/19*w^2 + 60/19*w - 8],\ [289, 17, 30/19*w^3 - 7/19*w^2 - 384/19*w - 14],\ [289, 17, 11/19*w^3 - 45/19*w^2 - 80/19*w + 17],\ [311, 311, -12/19*w^3 + 37/19*w^2 + 108/19*w - 15],\ [311, 311, -24/19*w^3 + 55/19*w^2 + 273/19*w - 22],\ [311, 311, -8/19*w^3 - 7/19*w^2 + 110/19*w + 4],\ [311, 311, 4/19*w^3 + 13/19*w^2 - 36/19*w - 7],\ [331, 331, -1/19*w^3 - 8/19*w^2 + 66/19*w - 2],\ [331, 331, -6/19*w^3 + 28/19*w^2 + 35/19*w - 9],\ [331, 331, 20/19*w^3 - 68/19*w^2 - 161/19*w + 22],\ [331, 331, 16/19*w^3 - 62/19*w^2 - 87/19*w + 15],\ [359, 359, 13/19*w^3 - 48/19*w^2 - 79/19*w + 11],\ [359, 359, -7/19*w^3 + 20/19*w^2 + 101/19*w - 13],\ [359, 359, -15/19*w^3 + 51/19*w^2 + 116/19*w - 17],\ [359, 359, 3/19*w^3 + 5/19*w^2 - 84/19*w + 5],\ [379, 379, 3/19*w^3 + 5/19*w^2 - 65/19*w - 9],\ [379, 379, 25/19*w^3 - 9/19*w^2 - 339/19*w - 11],\ [379, 379, -25/19*w^3 + 66/19*w^2 + 282/19*w - 28],\ [379, 379, 3/19*w^3 - 14/19*w^2 - 46/19*w + 12],\ [389, 389, -13/19*w^3 + 48/19*w^2 + 136/19*w - 24],\ [389, 389, 11/19*w^3 - 7/19*w^2 - 118/19*w + 2],\ [389, 389, -3/19*w^3 + 14/19*w^2 + 46/19*w - 10],\ [389, 389, -13/19*w^3 - 9/19*w^2 + 193/19*w + 15],\ [409, 409, 2/19*w^3 - 3/19*w^2 - 56/19*w],\ [409, 409, 6/19*w^3 - 9/19*w^2 - 92/19*w + 4],\ [409, 409, -6/19*w^3 + 9/19*w^2 + 92/19*w - 1],\ [409, 409, -2/19*w^3 + 3/19*w^2 + 56/19*w - 3],\ [431, 431, -6/19*w^3 + 9/19*w^2 + 130/19*w - 13],\ [431, 431, 12/19*w^3 - 37/19*w^2 - 108/19*w + 11],\ [431, 431, 10/19*w^3 - 15/19*w^2 - 166/19*w + 14],\ [431, 431, -8/19*w^3 + 31/19*w^2 + 34/19*w - 8],\ [461, 461, 5/19*w^3 - 17/19*w^2 - 45/19*w + 1],\ [461, 461, -3/19*w^3 + 14/19*w^2 + 8/19*w - 8],\ [461, 461, 3/19*w^3 + 5/19*w^2 - 27/19*w - 7],\ [461, 461, 5/19*w^3 + 2/19*w^2 - 64/19*w + 2],\ [479, 479, 5/19*w^3 - 17/19*w^2 - 26/19*w + 7],\ [479, 479, 1/19*w^3 - 11/19*w^2 - 28/19*w + 7],\ [479, 479, 7/19*w^3 - 1/19*w^2 - 82/19*w + 1],\ [479, 479, -5/19*w^3 + 17/19*w^2 + 64/19*w - 3],\ [499, 499, -11/19*w^3 + 7/19*w^2 + 118/19*w + 2],\ [499, 499, 9/19*w^3 - 23/19*w^2 - 62/19*w + 4],\ [499, 499, -9/19*w^3 + 4/19*w^2 + 81/19*w],\ [499, 499, -11/19*w^3 + 26/19*w^2 + 99/19*w - 8],\ [509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 9],\ [509, 509, -1/19*w^3 + 11/19*w^2 + 47/19*w - 7],\ [509, 509, -6/19*w^3 - 10/19*w^2 + 73/19*w + 2],\ [509, 509, -9/19*w^3 + 4/19*w^2 + 138/19*w - 2],\ [529, 23, -4/19*w^3 + 6/19*w^2 + 74/19*w - 1],\ [529, 23, 4/19*w^3 - 6/19*w^2 - 74/19*w + 3],\ [571, 571, 1/19*w^3 + 8/19*w^2 - 66/19*w + 6],\ [571, 571, -9/19*w^3 + 23/19*w^2 + 119/19*w - 15],\ [571, 571, -11/19*w^3 + 26/19*w^2 + 156/19*w - 18],\ [571, 571, 3/19*w^3 + 5/19*w^2 - 103/19*w + 9],\ [599, 599, 6/19*w^3 - 9/19*w^2 - 16/19*w - 2],\ [599, 599, -14/19*w^3 + 21/19*w^2 + 164/19*w - 7],\ [599, 599, -2/19*w^3 + 22/19*w^2 + 18/19*w - 13],\ [599, 599, -6/19*w^3 + 9/19*w^2 + 16/19*w - 3],\ [601, 601, 23/19*w^3 - 63/19*w^2 - 264/19*w + 31],\ [601, 601, -36/19*w^3 - 3/19*w^2 + 476/19*w + 23],\ [601, 601, 36/19*w^3 - 111/19*w^2 - 362/19*w + 46],\ [601, 601, -16/19*w^3 + 43/19*w^2 + 125/19*w - 8],\ [619, 619, -5/19*w^3 + 17/19*w^2 + 45/19*w - 11],\ [619, 619, 5/19*w^3 - 17/19*w^2 - 26/19*w - 2],\ [619, 619, -5/19*w^3 - 2/19*w^2 + 45/19*w - 4],\ [619, 619, -7/19*w^3 + 20/19*w^2 + 63/19*w - 12],\ [691, 691, 7/19*w^3 - 1/19*w^2 - 120/19*w],\ [691, 691, 3/19*w^3 - 14/19*w^2 - 65/19*w + 6],\ [691, 691, -3/19*w^3 - 5/19*w^2 + 84/19*w + 2],\ [691, 691, 7/19*w^3 - 20/19*w^2 - 101/19*w + 6],\ [701, 701, -7/19*w^3 + 20/19*w^2 + 63/19*w - 2],\ [701, 701, 5/19*w^3 - 17/19*w^2 - 26/19*w + 8],\ [701, 701, -7/19*w^3 + 20/19*w^2 + 82/19*w - 4],\ [701, 701, -7/19*w^3 + 1/19*w^2 + 82/19*w - 2],\ [719, 719, -8/19*w^3 + 31/19*w^2 + 53/19*w - 12],\ [719, 719, 8/19*w^3 - 31/19*w^2 - 53/19*w + 6],\ [719, 719, -8/19*w^3 - 7/19*w^2 + 91/19*w + 2],\ [719, 719, 8/19*w^3 + 7/19*w^2 - 91/19*w - 8],\ [739, 739, 9/19*w^3 - 23/19*w^2 - 43/19*w + 3],\ [739, 739, -16/19*w^3 + 24/19*w^2 + 163/19*w - 9],\ [739, 739, 16/19*w^3 - 24/19*w^2 - 163/19*w],\ [739, 739, -9/19*w^3 + 4/19*w^2 + 62/19*w],\ [769, 769, 24/19*w^3 - 74/19*w^2 - 254/19*w + 35],\ [769, 769, -3/19*w^3 + 33/19*w^2 - 30/19*w - 11],\ [769, 769, 3/19*w^3 + 24/19*w^2 - 27/19*w - 11],\ [769, 769, 24/19*w^3 + 2/19*w^2 - 330/19*w - 19],\ [811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w],\ [811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 7],\ [811, 811, 5/19*w^3 + 2/19*w^2 - 102/19*w - 2],\ [811, 811, -5/19*w^3 + 17/19*w^2 + 83/19*w - 5],\ [821, 821, -6/19*w^3 - 10/19*w^2 + 111/19*w + 13],\ [821, 821, 1/19*w^3 + 8/19*w^2 + 10/19*w - 12],\ [821, 821, -1/19*w^3 + 11/19*w^2 - 29/19*w - 11],\ [821, 821, -6/19*w^3 + 28/19*w^2 + 73/19*w - 18],\ [839, 839, -2*w^3 + 26*w + 23],\ [839, 839, 18/19*w^3 - 65/19*w^2 - 143/19*w + 24],\ [839, 839, -18/19*w^3 - 11/19*w^2 + 219/19*w + 14],\ [839, 839, 2*w^3 - 6*w^2 - 20*w + 47],\ [859, 859, 10/19*w^3 - 34/19*w^2 - 109/19*w + 19],\ [859, 859, 3/19*w^3 + 24/19*w^2 - 46/19*w - 14],\ [859, 859, -17/19*w^3 + 35/19*w^2 + 210/19*w - 14],\ [859, 859, -10/19*w^3 - 4/19*w^2 + 147/19*w + 12],\ [911, 911, -1/19*w^3 + 11/19*w^2 + 28/19*w - 9],\ [911, 911, -5/19*w^3 + 17/19*w^2 + 64/19*w - 1],\ [911, 911, 5/19*w^3 + 2/19*w^2 - 83/19*w + 3],\ [911, 911, 1/19*w^3 + 8/19*w^2 - 47/19*w - 7],\ [941, 941, 11/19*w^3 - 7/19*w^2 - 99/19*w - 5],\ [941, 941, -1/19*w^3 + 11/19*w^2 + 28/19*w - 10],\ [941, 941, -13/19*w^3 + 10/19*w^2 + 136/19*w - 4],\ [941, 941, -6/19*w^3 + 28/19*w^2 - 3/19*w - 6],\ [961, 31, 10/19*w^3 - 15/19*w^2 - 90/19*w + 2],\ [961, 31, -10/19*w^3 + 15/19*w^2 + 90/19*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 18*x^6 + 95*x^4 - 168*x^2 + 56 K. = NumberField(heckePol) hecke_eigenvalues_array = [-3/26*e^6 + 22/13*e^4 - 147/26*e^2 + 59/13, e, -1/52*e^7 + 3/26*e^5 + 81/52*e^3 - 79/13*e, -3/13*e^6 + 44/13*e^4 - 147/13*e^2 + 92/13, -1, -2/13*e^6 + 38/13*e^4 - 189/13*e^2 + 174/13, -5/26*e^6 + 41/13*e^4 - 323/26*e^2 + 146/13, -2/13*e^6 + 25/13*e^4 - 46/13*e^2 - 8/13, -3/26*e^7 + 22/13*e^5 - 147/26*e^3 + 59/13*e, 17/52*e^7 - 129/26*e^5 + 911/52*e^3 - 178/13*e, -5/26*e^7 + 41/13*e^5 - 349/26*e^3 + 211/13*e, 3*e, -9/13*e^6 + 132/13*e^4 - 441/13*e^2 + 302/13, 19/26*e^6 - 135/13*e^4 + 801/26*e^2 - 118/13, 7/26*e^7 - 47/13*e^5 + 213/26*e^3 + 92/13*e, -7/26*e^7 + 47/13*e^5 - 213/26*e^3 - 92/13*e, 7/52*e^7 - 47/26*e^5 + 213/52*e^3 - 19/13*e, 1/52*e^7 - 3/26*e^5 - 133/52*e^3 + 209/13*e, 3/26*e^7 - 9/13*e^5 - 217/26*e^3 + 435/13*e, 17/52*e^7 - 129/26*e^5 + 911/52*e^3 - 152/13*e, -11/52*e^7 + 85/26*e^5 - 565/52*e^3 - 11/13*e, -9/26*e^7 + 79/13*e^5 - 779/26*e^3 + 541/13*e, -1/13*e^6 + 6/13*e^4 + 55/13*e^2 - 108/13, 21/26*e^6 - 154/13*e^4 + 899/26*e^2 - 10/13, 6/13*e^6 - 101/13*e^4 + 424/13*e^2 - 392/13, 5/13*e^6 - 82/13*e^4 + 362/13*e^2 - 266/13, -10/13*e^6 + 138/13*e^4 - 360/13*e^2 - 14/13, -6/13*e^6 + 88/13*e^4 - 294/13*e^2 + 210/13, 3/13*e^7 - 57/13*e^5 + 316/13*e^3 - 521/13*e, -5/13*e^7 + 82/13*e^5 - 362/13*e^3 + 409/13*e, -2/13*e^7 + 38/13*e^5 - 189/13*e^3 + 135/13*e, 5/26*e^7 - 41/13*e^5 + 349/26*e^3 - 159/13*e, 4/13*e^6 - 50/13*e^4 + 118/13*e^2 - 36/13, -10/13*e^6 + 138/13*e^4 - 347/13*e^2 - 92/13, 4/13*e^7 - 50/13*e^5 + 66/13*e^3 + 250/13*e, -10/13*e^7 + 164/13*e^5 - 698/13*e^3 + 818/13*e, 21/52*e^7 - 167/26*e^5 + 1315/52*e^3 - 330/13*e, 15/26*e^7 - 123/13*e^5 + 1073/26*e^3 - 646/13*e, -1/13*e^6 + 6/13*e^4 + 29/13*e^2 + 48/13, 4/13*e^6 - 63/13*e^4 + 248/13*e^2 - 400/13, 16/13*e^6 - 226/13*e^4 + 667/13*e^2 - 274/13, -5/13*e^6 + 82/13*e^4 - 362/13*e^2 + 370/13, -29/52*e^7 + 217/26*e^5 - 1447/52*e^3 + 218/13*e, -1/13*e^7 + 6/13*e^5 + 81/13*e^3 - 420/13*e, 2*e^3 - 16*e, -9/26*e^7 + 79/13*e^5 - 727/26*e^3 + 320/13*e, 5/13*e^6 - 82/13*e^4 + 349/13*e^2 - 396/13, -1/2*e^6 + 8*e^4 - 63/2*e^2 + 18, 6/13*e^6 - 88/13*e^4 + 242/13*e^2 + 24/13, 4, -29/52*e^7 + 191/26*e^5 - 771/52*e^3 - 211/13*e, -9/52*e^7 + 27/26*e^5 + 625/52*e^3 - 607/13*e, 5/13*e^7 - 69/13*e^5 + 180/13*e^3 + 85/13*e, -3/52*e^7 + 35/26*e^5 - 485/52*e^3 + 166/13*e, 6/13*e^6 - 88/13*e^4 + 294/13*e^2 - 132/13, -3/13*e^6 + 44/13*e^4 - 147/13*e^2 + 92/13, -5/13*e^7 + 56/13*e^5 + 15/13*e^3 - 644/13*e, 19/52*e^7 - 161/26*e^5 + 1425/52*e^3 - 423/13*e, 33/52*e^7 - 229/26*e^5 + 1227/52*e^3 + 46/13*e, -25/52*e^7 + 205/26*e^5 - 1875/52*e^3 + 664/13*e, -8/13*e^6 + 100/13*e^4 - 171/13*e^2 - 214/13, -5/13*e^6 + 82/13*e^4 - 362/13*e^2 + 318/13, 9/13*e^6 - 145/13*e^4 + 623/13*e^2 - 536/13, 3/13*e^6 - 44/13*e^4 + 134/13*e^2 + 38/13, 27/52*e^7 - 237/26*e^5 + 2233/52*e^3 - 558/13*e, -15/26*e^7 + 123/13*e^5 - 1073/26*e^3 + 594/13*e, 25/52*e^7 - 231/26*e^5 + 2499/52*e^3 - 950/13*e, -19/52*e^7 + 135/26*e^5 - 697/52*e^3 - 188/13*e, 21/13*e^6 - 308/13*e^4 + 1016/13*e^2 - 722/13, -19/26*e^6 + 135/13*e^4 - 853/26*e^2 + 118/13, -9/13*e^6 + 119/13*e^4 - 259/13*e^2 - 36/13, -19/26*e^6 + 135/13*e^4 - 801/26*e^2 + 118/13, -11/52*e^7 + 59/26*e^5 - 45/52*e^3 - 128/13*e, -1/2*e^7 + 8*e^5 - 61/2*e^3 + 17*e, -5/13*e^7 + 82/13*e^5 - 401/13*e^3 + 773/13*e, 17/52*e^7 - 129/26*e^5 + 911/52*e^3 - 126/13*e, 14/13*e^6 - 227/13*e^4 + 972/13*e^2 - 854/13, -5/13*e^6 + 82/13*e^4 - 349/13*e^2 + 266/13, 14/13*e^6 - 201/13*e^4 + 582/13*e^2 - 308/13, -11/26*e^6 + 85/13*e^4 - 747/26*e^2 + 602/13, -8/13*e^7 + 126/13*e^5 - 548/13*e^3 + 878/13*e, 1/13*e^7 - 6/13*e^5 - 55/13*e^3 + 186/13*e, -5/52*e^7 + 15/26*e^5 + 457/52*e^3 - 447/13*e, -21/52*e^7 + 167/26*e^5 - 1263/52*e^3 + 122/13*e, 47/52*e^7 - 349/26*e^5 + 2329/52*e^3 - 317/13*e, 24/13*e^7 - 378/13*e^5 + 1462/13*e^3 - 1347/13*e, 19/52*e^7 - 135/26*e^5 + 957/52*e^3 - 384/13*e, 5/26*e^7 - 28/13*e^5 + 37/26*e^3 + 75/13*e, -2/13*e^7 + 38/13*e^5 - 254/13*e^3 + 642/13*e, 15/13*e^7 - 220/13*e^5 + 709/13*e^3 - 252/13*e, 3/13*e^7 - 70/13*e^5 + 485/13*e^3 - 820/13*e, -71/52*e^7 + 551/26*e^5 - 4233/52*e^3 + 1021/13*e, -20/13*e^6 + 276/13*e^4 - 798/13*e^2 + 414/13, 14/13*e^6 - 214/13*e^4 + 764/13*e^2 - 230/13, 5/13*e^6 - 95/13*e^4 + 427/13*e^2 - 188/13, 19/26*e^6 - 161/13*e^4 + 1477/26*e^2 - 846/13, 23/26*e^7 - 173/13*e^5 + 1257/26*e^3 - 643/13*e, e^7 - 16*e^5 + 66*e^3 - 83*e, 23/26*e^7 - 173/13*e^5 + 1127/26*e^3 - 175/13*e, 35/52*e^7 - 261/26*e^5 + 1741/52*e^3 - 225/13*e, 4/13*e^6 - 50/13*e^4 + 79/13*e^2 + 380/13, 6/13*e^6 - 114/13*e^4 + 528/13*e^2 - 236/13, -16/13*e^6 + 226/13*e^4 - 758/13*e^2 + 794/13, -23/13*e^6 + 333/13*e^4 - 971/13*e^2 + 220/13, 21/13*e^6 - 321/13*e^4 + 1133/13*e^2 - 592/13, -5/13*e^6 + 95/13*e^4 - 401/13*e^2 + 136/13, 9/26*e^7 - 53/13*e^5 + 51/26*e^3 + 408/13*e, 1/2*e^7 - 7*e^5 + 43/2*e^3 - 20*e, 9/52*e^7 - 53/26*e^5 + 51/52*e^3 + 178/13*e, -17/52*e^7 + 129/26*e^5 - 963/52*e^3 + 373/13*e, -16/13*e^6 + 213/13*e^4 - 472/13*e^2 - 350/13, -2/13*e^6 + 12/13*e^4 + 84/13*e^2 - 294/13, -12/13*e^6 + 202/13*e^4 - 900/13*e^2 + 602/13, 21/13*e^6 - 308/13*e^4 + 977/13*e^2 - 462/13, 14/13*e^6 - 188/13*e^4 + 426/13*e^2 + 368/13, -55/26*e^6 + 399/13*e^4 - 2513/26*e^2 + 410/13, 69/26*e^6 - 493/13*e^4 + 2991/26*e^2 - 486/13, 5/13*e^6 - 43/13*e^4 - 67/13*e^2 + 228/13, 10/13*e^6 - 164/13*e^4 + 750/13*e^2 - 896/13, 18/13*e^6 - 290/13*e^4 + 1207/13*e^2 - 994/13, 4/13*e^6 - 50/13*e^4 + 40/13*e^2 + 588/13, 32/13*e^6 - 452/13*e^4 + 1269/13*e^2 - 210/13, 9/13*e^7 - 106/13*e^5 + 77/13*e^3 + 647/13*e, -7/26*e^7 + 21/13*e^5 + 489/26*e^3 - 885/13*e, 4/13*e^7 - 37/13*e^5 - 129/13*e^3 + 783/13*e, 8/13*e^7 - 100/13*e^5 + 145/13*e^3 + 565/13*e, 7/26*e^7 - 47/13*e^5 + 161/26*e^3 + 300/13*e, 45/52*e^7 - 395/26*e^5 + 3635/52*e^3 - 904/13*e, 9/13*e^7 - 132/13*e^5 + 441/13*e^3 - 198/13*e, 17/13*e^7 - 258/13*e^5 + 911/13*e^3 - 686/13*e, -20/13*e^6 + 315/13*e^4 - 1136/13*e^2 + 492/13, 2*e^4 - 20*e^2 + 40, 22/13*e^6 - 340/13*e^4 + 1195/13*e^2 - 614/13, 2*e^6 - 32*e^4 + 122*e^2 - 86, -8/13*e^6 + 100/13*e^4 - 184/13*e^2 + 124/13, -11/26*e^6 + 46/13*e^4 + 215/26*e^2 - 646/13, 27/26*e^6 - 198/13*e^4 + 1297/26*e^2 + 54/13, -6/13*e^6 + 62/13*e^4 - 8/13*e^2 - 128/13, 28/13*e^6 - 389/13*e^4 + 982/13*e^2 + 268/13, -18/13*e^6 + 264/13*e^4 - 856/13*e^2 + 604/13, -33/26*e^6 + 229/13*e^4 - 1123/26*e^2 + 142/13, -14/13*e^6 + 188/13*e^4 - 543/13*e^2 + 646/13, -25/52*e^7 + 231/26*e^5 - 2551/52*e^3 + 989/13*e, -41/26*e^7 + 318/13*e^5 - 2425/26*e^3 + 997/13*e, -5/4*e^7 + 41/2*e^5 - 339/4*e^3 + 80*e, -1/26*e^7 + 16/13*e^5 - 309/26*e^3 + 271/13*e, 25/52*e^7 - 205/26*e^5 + 1927/52*e^3 - 807/13*e, 21/26*e^7 - 141/13*e^5 + 587/26*e^3 + 484/13*e, 15/13*e^7 - 246/13*e^5 + 1073/13*e^3 - 1266/13*e, 11/52*e^7 - 111/26*e^5 + 1241/52*e^3 - 171/13*e, 10/13*e^6 - 125/13*e^4 + 204/13*e^2 + 196/13, 21/26*e^6 - 141/13*e^4 + 691/26*e^2 - 322/13, -71/26*e^6 + 525/13*e^4 - 3453/26*e^2 + 742/13, 1/26*e^6 - 3/13*e^4 - 237/26*e^2 + 574/13, -125/52*e^7 + 973/26*e^5 - 7295/52*e^3 + 1539/13*e, 75/52*e^7 - 589/26*e^5 + 4533/52*e^3 - 1108/13*e, 41/26*e^7 - 305/13*e^5 + 2087/26*e^3 - 776/13*e, 7/26*e^7 - 73/13*e^5 + 941/26*e^3 - 974/13*e, 4/13*e^7 - 50/13*e^5 + 118/13*e^3 - 153/13*e, -9/26*e^7 + 79/13*e^5 - 831/26*e^3 + 879/13*e, 9/13*e^7 - 106/13*e^5 + 90/13*e^3 + 543/13*e, -99/52*e^7 + 739/26*e^5 - 5085/52*e^3 + 876/13*e, 25/13*e^6 - 358/13*e^4 + 1147/13*e^2 - 706/13, -42/13*e^6 + 616/13*e^4 - 2032/13*e^2 + 1002/13] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19, 19, -w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]