/* 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([20, 10, 2/19*w^3 - 3/19*w^2 + 1/19*w - 1]) 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^4 - 50*x^2 + 56*x + 184 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, -1/172*e^3 - 7/86*e^2 + 13/86*e + 77/43, 1/172*e^3 + 7/86*e^2 - 13/86*e - 120/43, e, -1/172*e^3 - 7/86*e^2 - 73/86*e + 77/43, 2/43*e^3 + 13/86*e^2 - 52/43*e - 57/43, -3/86*e^3 + 1/86*e^2 + 39/43*e - 54/43, -7/172*e^3 - 3/43*e^2 + 91/86*e + 195/43, 7/172*e^3 + 3/43*e^2 - 91/86*e + 192/43, -1/43*e^3 + 15/86*e^2 + 69/43*e - 122/43, 9/172*e^3 + 10/43*e^2 - 203/86*e - 48/43, -21/172*e^3 - 9/43*e^2 + 359/86*e + 198/43, 5/43*e^3 + 11/86*e^2 - 173/43*e + 266/43, -13/172*e^3 + 19/43*e^2 + 341/86*e - 461/43, 27/172*e^3 + 30/43*e^2 - 523/86*e - 316/43, 11/172*e^3 - 9/86*e^2 - 229/86*e + 486/43, -4/43*e^3 - 13/43*e^2 + 147/43*e + 415/43, 2/43*e^3 + 28/43*e^2 - 95/43*e - 616/43, 7/43*e^3 - 19/86*e^2 - 354/43*e + 338/43, 9/172*e^3 + 63/86*e^2 - 31/86*e - 693/43, -19/86*e^3 - 51/86*e^2 + 419/43*e + 45/43, -9/43*e^3 - 37/86*e^2 + 363/43*e - 66/43, 31/172*e^3 + 1/43*e^2 - 661/86*e + 150/43, 1/43*e^3 - 29/43*e^2 - 69/43*e + 681/43, -23/172*e^3 - 75/86*e^2 + 385/86*e + 610/43, -21/172*e^3 - 9/43*e^2 + 187/86*e - 60/43, 11/86*e^3 + 25/86*e^2 - 100/43*e - 146/43, -3/86*e^3 + 1/86*e^2 + 39/43*e + 419/43, -35/172*e^3 - 15/43*e^2 + 713/86*e - 143/43, 2/43*e^3 + 13/86*e^2 - 52/43*e + 416/43, 8/43*e^3 + 9/86*e^2 - 337/43*e + 73/43, -41/172*e^3 - 36/43*e^2 + 877/86*e + 233/43, 25/172*e^3 - 20/43*e^2 - 669/86*e + 526/43, -9/172*e^3 - 10/43*e^2 + 375/86*e + 564/43, 1/86*e^3 - 29/86*e^2 - 142/43*e + 792/43, 3/43*e^3 - 45/86*e^2 - 121/43*e + 538/43, -29/172*e^3 - 37/43*e^2 + 463/86*e + 470/43, 13/86*e^3 + 53/86*e^2 - 298/43*e - 196/43, -13/172*e^3 + 19/43*e^2 + 427/86*e - 418/43, -17/172*e^3 + 5/43*e^2 + 651/86*e - 669/43, 5/43*e^3 + 11/86*e^2 - 345/43*e - 293/43, 41/172*e^3 + 29/86*e^2 - 791/86*e + 283/43, -10/43*e^3 - 11/43*e^2 + 389/43*e + 70/43, -51/172*e^3 - 28/43*e^2 + 1007/86*e + 315/43, 1/4*e^3 - 21/2*e + 14, -19/86*e^3 - 4/43*e^2 + 419/43*e - 342/43, 7/86*e^3 - 31/86*e^2 - 91/43*e + 728/43, 21/86*e^3 + 18/43*e^2 - 445/43*e - 52/43, -7/43*e^3 - 67/86*e^2 + 182/43*e + 737/43, 9/43*e^3 + 37/86*e^2 - 277/43*e - 149/43, -6/43*e^3 - 39/86*e^2 + 156/43*e + 472/43, -33/172*e^3 - 8/43*e^2 + 515/86*e - 211/43, 9/86*e^3 - 3/86*e^2 - 117/43*e + 463/43, 15/172*e^3 - 12/43*e^2 - 625/86*e + 694/43, -11/86*e^3 - 25/86*e^2 + 358/43*e + 318/43, 6/43*e^3 + 39/86*e^2 - 328/43*e + 216/43, -7/86*e^3 + 31/86*e^2 + 263/43*e - 83/43, 25/172*e^3 + 3/86*e^2 - 411/86*e + 569/43, -15/86*e^3 - 19/43*e^2 + 238/43*e + 504/43, 55/172*e^3 + 41/86*e^2 - 1059/86*e - 21/43, -53/172*e^3 - 27/86*e^2 + 1033/86*e - 305/43, 25/172*e^3 + 23/43*e^2 - 497/86*e - 463/43, -15/172*e^3 + 12/43*e^2 + 367/86*e - 608/43, -1/4*e^3 - e^2 + 17/2*e + 6, -1/4*e^3 - 1/2*e^2 + 19/2*e + 7, 25/172*e^3 - 20/43*e^2 - 497/86*e + 397/43, 19/86*e^3 + 4/43*e^2 - 376/43*e + 514/43, 27/172*e^3 + 103/86*e^2 - 265/86*e - 1176/43, -1/86*e^3 + 36/43*e^2 - 30/43*e - 1093/43, -13/172*e^3 - 5/86*e^2 + 255/86*e + 313/43, 7/86*e^3 + 6/43*e^2 - 134/43*e + 384/43, -19/172*e^3 - 2/43*e^2 + 849/86*e - 214/43, 1/86*e^3 - 36/43*e^2 - 13/43*e + 706/43, 4/43*e^3 - 17/86*e^2 - 405/43*e + 316/43, -13/86*e^3 - 48/43*e^2 + 169/43*e + 712/43, 7/86*e^3 + 6/43*e^2 + 81/43*e + 298/43, 29/86*e^3 - 12/43*e^2 - 678/43*e + 264/43, -9/86*e^3 - 20/43*e^2 - 55/43*e + 612/43, -75/172*e^3 - 95/86*e^2 + 1577/86*e - 245/43, -29/172*e^3 - 31/86*e^2 + 979/86*e - 46/43, 9/43*e^3 - 49/86*e^2 - 449/43*e + 410/43, 5/43*e^3 - 16/43*e^2 - 431/43*e + 481/43, -57/172*e^3 - 49/43*e^2 + 1171/86*e + 46/43, 8/43*e^3 - 17/43*e^2 - 251/43*e + 632/43, -51/172*e^3 - 99/86*e^2 + 749/86*e + 573/43, 7/43*e^3 - 19/86*e^2 - 225/43*e + 80/43, -41/172*e^3 - 36/43*e^2 + 619/86*e + 18/43, -9/172*e^3 + 23/86*e^2 + 375/86*e + 693/43, 4/43*e^3 + 13/43*e^2 - 233/43*e + 918/43, 11/43*e^3 - 18/43*e^2 - 544/43*e + 224/43, -31/86*e^3 - 45/43*e^2 + 661/43*e - 214/43, -21/43*e^3 - 115/86*e^2 + 761/43*e + 233/43, 7/172*e^3 + 49/86*e^2 + 339/86*e - 539/43, 65/172*e^3 - 9/43*e^2 - 1275/86*e + 585/43, 1/86*e^3 + 7/43*e^2 - 228/43*e - 154/43, 11/86*e^3 - 9/43*e^2 - 229/43*e - 103/43, 5/86*e^3 - 59/86*e^2 - 323/43*e + 1337/43, -8/43*e^3 - 26/43*e^2 + 294/43*e - 245/43, -13/86*e^3 - 53/86*e^2 + 427/43*e + 884/43, -7/172*e^3 - 49/86*e^2 + 91/86*e + 1055/43, -7/86*e^3 - 49/43*e^2 + 91/43*e + 1250/43, -23/43*e^3 - 85/86*e^2 + 856/43*e - 97/43, 21/43*e^3 + 29/86*e^2 - 804/43*e + 326/43, -11/43*e^3 - 93/86*e^2 + 458/43*e + 894/43, 11/86*e^3 - 61/86*e^2 - 315/43*e + 1187/43, -9/172*e^3 - 10/43*e^2 + 31/86*e + 1080/43, 3/86*e^3 - 1/86*e^2 + 4/43*e + 1000/43, 33/86*e^3 + 75/86*e^2 - 687/43*e - 309/43, -27/86*e^3 + 9/86*e^2 + 609/43*e - 744/43, 29/86*e^3 + 31/43*e^2 - 635/43*e - 768/43, 7/172*e^3 - 37/86*e^2 + 81/86*e + 966/43, -12/43*e^3 + 4/43*e^2 + 570/43*e - 1206/43, -23/172*e^3 - 75/86*e^2 + 127/86*e + 1126/43, -11/43*e^3 - 25/43*e^2 + 673/43*e + 292/43, -19/43*e^3 - 8/43*e^2 + 752/43*e - 426/43, 31/172*e^3 - 41/86*e^2 - 1177/86*e + 967/43, 1/2*e^3 + e^2 - 19*e, -1/172*e^3 - 25/43*e^2 - 417/86*e + 808/43, -5/86*e^3 - 27/86*e^2 + 280/43*e + 426/43, 14/43*e^3 + 67/43*e^2 - 493/43*e - 958/43, -25/172*e^3 + 83/86*e^2 + 583/86*e - 1171/43, 9/86*e^3 + 20/43*e^2 - 289/43*e - 10/43, -3/86*e^3 + 22/43*e^2 + 211/43*e - 312/43, 23/172*e^3 + 161/86*e^2 - 41/86*e - 1857/43, 5/43*e^3 + 70/43*e^2 - 259/43*e - 1626/43, 47/172*e^3 - 15/86*e^2 - 1385/86*e + 1240/43, -14/43*e^3 - 24/43*e^2 + 751/43*e + 571/43, -3/86*e^3 - 21/43*e^2 + 39/43*e - 828/43, -3/86*e^3 - 21/43*e^2 + 39/43*e - 828/43, -7/43*e^3 - 67/86*e^2 + 225/43*e + 823/43, -8/43*e^3 - 26/43*e^2 + 208/43*e + 400/43, 13/172*e^3 - 19/43*e^2 - 255/86*e + 891/43, 6/43*e^3 - 2/43*e^2 - 156/43*e + 388/43, 13/172*e^3 + 5/86*e^2 + 3/86*e + 1235/43, -17/172*e^3 - 33/86*e^2 + 49/86*e + 1395/43, 14/43*e^3 + 91/86*e^2 - 536/43*e - 1302/43, -19/86*e^3 + 35/86*e^2 + 419/43*e - 1589/43, -19/86*e^3 + 35/86*e^2 + 419/43*e + 217/43, 14/43*e^3 + 91/86*e^2 - 536/43*e + 504/43, 37/172*e^3 + 1/86*e^2 - 739/86*e + 32/43, -11/43*e^3 - 25/43*e^2 + 415/43*e - 181/43, -7/86*e^3 - 6/43*e^2 + 177/43*e - 728/43, -19/172*e^3 + 39/86*e^2 + 161/86*e - 1633/43, 3/43*e^3 - 1/43*e^2 - 164/43*e - 580/43, 19/86*e^3 + 47/43*e^2 - 204/43*e - 1722/43, 77/172*e^3 + 109/86*e^2 - 1431/86*e - 726/43, 12/43*e^3 + 82/43*e^2 - 183/43*e - 2320/43, -29/86*e^3 + 12/43*e^2 + 592/43*e - 1081/43, -11/172*e^3 + 95/86*e^2 - 115/86*e - 2077/43, 85/172*e^3 + 79/86*e^2 - 1965/86*e + 421/43, -5/86*e^3 + 145/86*e^2 + 108/43*e - 2111/43, -73/172*e^3 + 5/86*e^2 + 1809/86*e - 313/43, 59/172*e^3 + 99/43*e^2 - 853/86*e - 2049/43, -19/43*e^3 - 51/43*e^2 + 752/43*e + 90/43, 19/172*e^3 + 45/43*e^2 - 591/86*e - 1592/43, 29/86*e^3 - 12/43*e^2 - 635/43*e + 522/43, 9/172*e^3 + 53/43*e^2 + 227/86*e - 1897/43, -7/86*e^3 + 117/86*e^2 + 177/43*e - 1631/43, -23/172*e^3 + 11/86*e^2 + 385/86*e - 379/43, 27/86*e^3 + 163/86*e^2 - 437/43*e - 1492/43, 8/43*e^3 + 26/43*e^2 - 251/43*e - 314/43, -51/172*e^3 - 28/43*e^2 + 1093/86*e - 932/43, 21/86*e^3 - 7/86*e^2 - 488/43*e - 568/43] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, -2/19*w^3 + 3/19*w^2 + 37/19*w - 3])] = -1 AL_eigenvalues[ZF.ideal([5, 5, 3/19*w^3 + 5/19*w^2 - 27/19*w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]