/* 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([16, 2, 2]) 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 + 6*x^5 - 15*x^4 - 100*x^3 + 128*x^2 + 472*x - 667 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e - 2, 1, 1/7*e^5 + 5/7*e^4 - 6/7*e^3 - 38/7*e^2 + 5/7*e + 40/7, -1/7*e^5 - 5/7*e^4 + 13/7*e^3 + 59/7*e^2 - 61/7*e - 124/7, 1/7*e^5 + 5/7*e^4 - 13/7*e^3 - 59/7*e^2 + 61/7*e + 82/7, -1/7*e^5 - 5/7*e^4 + 6/7*e^3 + 38/7*e^2 - 5/7*e - 26/7, -e^2 - 2*e + 6, -1/7*e^5 - 12/7*e^4 - 22/7*e^3 + 143/7*e^2 + 254/7*e - 642/7, 1/7*e^5 + 12/7*e^4 + 15/7*e^3 - 157/7*e^2 - 198/7*e + 635/7, -1/7*e^5 + 2/7*e^4 + 41/7*e^3 - 39/7*e^2 - 306/7*e + 443/7, 1/7*e^5 - 2/7*e^4 - 34/7*e^3 + 67/7*e^2 + 278/7*e - 562/7, -2/7*e^5 - 10/7*e^4 + 19/7*e^3 + 104/7*e^2 - 59/7*e - 206/7, 2/7*e^5 + 10/7*e^4 - 19/7*e^3 - 90/7*e^2 + 87/7*e + 80/7, 1/7*e^5 - 2/7*e^4 - 34/7*e^3 + 60/7*e^2 + 257/7*e - 492/7, -1/7*e^5 - 12/7*e^4 - 22/7*e^3 + 136/7*e^2 + 247/7*e - 558/7, -1/7*e^5 + 2/7*e^4 + 34/7*e^3 - 60/7*e^2 - 264/7*e + 478/7, 1/7*e^5 + 12/7*e^4 + 22/7*e^3 - 136/7*e^2 - 240/7*e + 558/7, 1/7*e^5 + 12/7*e^4 + 22/7*e^3 - 157/7*e^2 - 275/7*e + 789/7, -1/7*e^5 + 2/7*e^4 + 34/7*e^3 - 81/7*e^2 - 313/7*e + 695/7, -4/7*e^5 - 27/7*e^4 + 10/7*e^3 + 306/7*e^2 + 134/7*e - 972/7, 4/7*e^5 + 13/7*e^4 - 66/7*e^3 - 82/7*e^2 + 426/7*e - 400/7, 3/7*e^5 + 22/7*e^4 - 4/7*e^3 - 282/7*e^2 - 174/7*e + 1002/7, -3/7*e^5 - 8/7*e^4 + 60/7*e^3 + 30/7*e^2 - 442/7*e + 510/7, 6/7*e^5 + 30/7*e^4 - 64/7*e^3 - 333/7*e^2 + 226/7*e + 695/7, -6/7*e^5 - 30/7*e^4 + 64/7*e^3 + 291/7*e^2 - 310/7*e - 289/7, 2/7*e^5 + 10/7*e^4 - 19/7*e^3 - 104/7*e^2 + 80/7*e + 227/7, -2/7*e^5 - 10/7*e^4 + 19/7*e^3 + 90/7*e^2 - 108/7*e - 101/7, 3/7*e^5 + 15/7*e^4 - 32/7*e^3 - 149/7*e^2 + 148/7*e + 183/7, -3/7*e^5 - 15/7*e^4 + 32/7*e^3 + 163/7*e^2 - 120/7*e - 309/7, -4*e^4 - 16*e^3 + 59*e^2 + 150*e - 338, 4*e^4 + 16*e^3 - 53*e^2 - 138*e + 277, -3/7*e^5 - 15/7*e^4 + 39/7*e^3 + 184/7*e^2 - 183/7*e - 407/7, 3/7*e^5 + 15/7*e^4 - 39/7*e^3 - 170/7*e^2 + 211/7*e + 239/7, -e^4 - 3*e^3 + 21*e^2 + 37*e - 119, -e^4 - 5*e^3 + 15*e^2 + 51*e - 101, 11/7*e^5 + 48/7*e^4 - 143/7*e^3 - 460/7*e^2 + 755/7*e + 300/7, 2/7*e^5 + 17/7*e^4 + 2/7*e^3 - 209/7*e^2 - 102/7*e + 689/7, -2/7*e^5 - 3/7*e^4 + 54/7*e^3 + 27/7*e^2 - 374/7*e + 249/7, -11/7*e^5 - 62/7*e^4 + 87/7*e^3 + 670/7*e^2 - 223/7*e - 1490/7, -3/7*e^5 - 36/7*e^4 - 52/7*e^3 + 443/7*e^2 + 608/7*e - 1744/7, -3/7*e^5 - 29/7*e^4 - 17/7*e^3 + 359/7*e^2 + 279/7*e - 1296/7, 3/7*e^5 + 1/7*e^4 - 95/7*e^3 + 5/7*e^2 + 673/7*e - 650/7, 3/7*e^5 - 6/7*e^4 - 116/7*e^3 + 131/7*e^2 + 876/7*e - 1252/7, 2/7*e^5 + 10/7*e^4 - 19/7*e^3 - 90/7*e^2 + 108/7*e + 59/7, 5/7*e^5 + 39/7*e^4 + 5/7*e^3 - 456/7*e^2 - 311/7*e + 1523/7, -5/7*e^5 - 11/7*e^4 + 107/7*e^3 + 50/7*e^2 - 725/7*e + 745/7, -2/7*e^5 - 10/7*e^4 + 19/7*e^3 + 104/7*e^2 - 80/7*e - 269/7, -1/7*e^5 + 9/7*e^4 + 76/7*e^3 - 144/7*e^2 - 677/7*e + 1080/7, 1/7*e^5 + 19/7*e^4 + 36/7*e^3 - 304/7*e^2 - 443/7*e + 1426/7, 2/7*e^5 - 11/7*e^4 - 110/7*e^3 + 204/7*e^2 + 948/7*e - 1621/7, -2/7*e^5 - 31/7*e^4 - 58/7*e^3 + 440/7*e^2 + 676/7*e - 2061/7, -4/7*e^5 - 20/7*e^4 + 31/7*e^3 + 138/7*e^2 - 160/7*e + 106/7, 4/7*e^5 + 20/7*e^4 - 31/7*e^3 - 208/7*e^2 + 20/7*e + 538/7, -1/7*e^5 + 9/7*e^4 + 62/7*e^3 - 137/7*e^2 - 460/7*e + 849/7, 1/7*e^5 + 19/7*e^4 + 50/7*e^3 - 213/7*e^2 - 464/7*e + 901/7, 5/7*e^5 + 32/7*e^4 - 23/7*e^3 - 386/7*e^2 - 136/7*e + 1278/7, -5/7*e^5 - 18/7*e^4 + 79/7*e^3 + 120/7*e^2 - 508/7*e + 542/7, 1/7*e^5 + 12/7*e^4 + 15/7*e^3 - 164/7*e^2 - 184/7*e + 740/7, -1/7*e^5 + 2/7*e^4 + 41/7*e^3 - 46/7*e^2 - 348/7*e + 492/7, -2*e^4 - 9*e^3 + 26*e^2 + 81*e - 161, -2*e^4 - 7*e^3 + 32*e^2 + 67*e - 179, -3/7*e^5 - 8/7*e^4 + 53/7*e^3 + 37/7*e^2 - 330/7*e + 321/7, 3/7*e^5 + 22/7*e^4 + 3/7*e^3 - 233/7*e^2 - 174/7*e + 673/7, -2/7*e^5 - 17/7*e^4 - 16/7*e^3 + 188/7*e^2 + 228/7*e - 815/7, 2/7*e^5 + 3/7*e^4 - 40/7*e^3 + 36/7*e^2 + 332/7*e - 599/7, -2/7*e^5 + 11/7*e^4 + 89/7*e^3 - 260/7*e^2 - 780/7*e + 1761/7, 2/7*e^5 + 31/7*e^4 + 79/7*e^3 - 370/7*e^2 - 816/7*e + 1809/7, -10/7*e^5 - 50/7*e^4 + 102/7*e^3 + 562/7*e^2 - 302/7*e - 1352/7, -5*e^4 - 18*e^3 + 83*e^2 + 184*e - 461, -5*e^4 - 22*e^3 + 71*e^2 + 204*e - 433, 10/7*e^5 + 50/7*e^4 - 102/7*e^3 - 450/7*e^2 + 526/7*e + 204/7, 6*e^4 + 25*e^3 - 80*e^2 - 220*e + 442, -4/7*e^5 - 6/7*e^4 + 108/7*e^3 + 26/7*e^2 - 755/7*e + 848/7, 4/7*e^5 + 34/7*e^4 + 4/7*e^3 - 446/7*e^2 - 309/7*e + 1630/7, 6*e^4 + 23*e^3 - 86*e^2 - 208*e + 458, 3/7*e^5 - 20/7*e^4 - 165/7*e^3 + 383/7*e^2 + 1408/7*e - 2715/7, -3/7*e^5 - 50/7*e^4 - 115/7*e^3 + 653/7*e^2 + 1224/7*e - 3095/7, -2/7*e^5 + 18/7*e^4 + 131/7*e^3 - 344/7*e^2 - 1193/7*e + 2447/7, 2/7*e^5 + 38/7*e^4 + 93/7*e^3 - 538/7*e^2 - 1019/7*e + 2761/7, -2/7*e^5 - 3/7*e^4 + 54/7*e^3 + 13/7*e^2 - 374/7*e + 326/7, e^5 + 6*e^4 - 7*e^3 - 66*e^2 + 19*e + 166, -e^5 - 4*e^4 + 15*e^3 + 40*e^2 - 87*e - 16, 2/7*e^5 + 17/7*e^4 + 2/7*e^3 - 223/7*e^2 - 158/7*e + 710/7, 13/7*e^5 + 72/7*e^4 - 120/7*e^3 - 788/7*e^2 + 436/7*e + 1570/7, -13/7*e^5 - 58/7*e^4 + 176/7*e^3 + 620/7*e^2 - 884/7*e - 758/7, 9/7*e^5 + 66/7*e^4 - 12/7*e^3 - 734/7*e^2 - 284/7*e + 2124/7, -9/7*e^5 - 24/7*e^4 + 180/7*e^3 + 202/7*e^2 - 1116/7*e + 620/7, 11/7*e^5 + 69/7*e^4 - 52/7*e^3 - 754/7*e^2 - 99/7*e + 1994/7, -8/7*e^5 - 47/7*e^4 + 62/7*e^3 + 521/7*e^2 - 145/7*e - 1146/7, 8/7*e^5 + 33/7*e^4 - 118/7*e^3 - 339/7*e^2 + 621/7*e + 236/7, -11/7*e^5 - 41/7*e^4 + 164/7*e^3 + 334/7*e^2 - 965/7*e + 344/7, 3/7*e^5 - 34/7*e^4 - 221/7*e^3 + 572/7*e^2 + 1891/7*e - 3842/7, 4/7*e^5 + 34/7*e^4 + 4/7*e^3 - 425/7*e^2 - 218/7*e + 1546/7, -4/7*e^5 - 6/7*e^4 + 108/7*e^3 + 47/7*e^2 - 762/7*e + 666/7, -3/7*e^5 - 64/7*e^4 - 171/7*e^3 + 842/7*e^2 + 1721/7*e - 4208/7, -1/7*e^5 + 2/7*e^4 + 48/7*e^3 - 11/7*e^2 - 341/7*e + 135/7, -10/7*e^5 - 64/7*e^4 + 46/7*e^3 + 660/7*e^2 + 20/7*e - 1534/7, 10/7*e^5 + 36/7*e^4 - 158/7*e^3 - 352/7*e^2 + 820/7*e - 6/7, 1/7*e^5 + 12/7*e^4 + 8/7*e^3 - 171/7*e^2 - 135/7*e + 453/7, -5/7*e^5 - 25/7*e^4 + 37/7*e^3 + 246/7*e^2 - 67/7*e - 725/7, 5/7*e^5 + 25/7*e^4 - 37/7*e^3 - 176/7*e^2 + 207/7*e - 143/7, 1/7*e^5 - 2/7*e^4 - 34/7*e^3 + 95/7*e^2 + 376/7*e - 758/7, -1/7*e^5 - 12/7*e^4 - 22/7*e^3 + 171/7*e^2 + 268/7*e - 922/7, 4/7*e^5 + 34/7*e^4 + 25/7*e^3 - 390/7*e^2 - 470/7*e + 1371/7, -4/7*e^5 - 6/7*e^4 + 87/7*e^3 - 44/7*e^2 - 622/7*e + 967/7, -11/7*e^5 - 76/7*e^4 + 24/7*e^3 + 838/7*e^2 + 330/7*e - 2400/7, 11/7*e^5 + 34/7*e^4 - 192/7*e^3 - 250/7*e^2 + 1182/7*e - 764/7, 9/7*e^5 + 38/7*e^4 - 131/7*e^3 - 433/7*e^2 + 584/7*e + 619/7, -9/7*e^5 - 52/7*e^4 + 75/7*e^3 + 545/7*e^2 - 248/7*e - 913/7, 6/7*e^5 + 16/7*e^4 - 113/7*e^3 - 116/7*e^2 + 667/7*e - 474/7, -6/7*e^5 - 44/7*e^4 + 1/7*e^3 + 466/7*e^2 + 257/7*e - 1304/7, e^5 + 10*e^4 + 11*e^3 - 123*e^2 - 156*e + 514, -e^5 + 29*e^3 - 29*e^2 - 228*e + 374, -2/7*e^5 - 24/7*e^4 - 30/7*e^3 + 328/7*e^2 + 452/7*e - 1508/7, 2/7*e^5 - 4/7*e^4 - 82/7*e^3 + 92/7*e^2 + 612/7*e - 1180/7, 1/7*e^5 + 5/7*e^4 - 27/7*e^3 - 73/7*e^2 + 257/7*e + 26/7, -1/7*e^5 - 5/7*e^4 + 27/7*e^3 + 129/7*e^2 - 145/7*e - 516/7, 8*e^4 + 32*e^3 - 102*e^2 - 268*e + 518, 6/7*e^5 + 16/7*e^4 - 134/7*e^3 - 172/7*e^2 + 891/7*e - 292/7, -6/7*e^5 - 44/7*e^4 + 22/7*e^3 + 536/7*e^2 + 61/7*e - 1626/7, 4/7*e^5 - 15/7*e^4 - 192/7*e^3 + 254/7*e^2 + 1539/7*e - 2206/7, -4/7*e^5 - 55/7*e^4 - 88/7*e^3 + 726/7*e^2 + 981/7*e - 3100/7, -4/7*e^5 - 34/7*e^4 - 32/7*e^3 + 334/7*e^2 + 442/7*e - 1224/7, 4/7*e^5 + 6/7*e^4 - 80/7*e^3 + 30/7*e^2 + 510/7*e - 932/7, -2/7*e^5 + 11/7*e^4 + 110/7*e^3 - 190/7*e^2 - 878/7*e + 1446/7, 2/7*e^5 + 31/7*e^4 + 58/7*e^3 - 426/7*e^2 - 690/7*e + 1802/7, 12/7*e^5 + 32/7*e^4 - 240/7*e^3 - 267/7*e^2 + 1474/7*e - 948/7, -12/7*e^5 - 67/7*e^4 + 100/7*e^3 + 764/7*e^2 - 228/7*e - 1908/7, 12/7*e^5 + 53/7*e^4 - 156/7*e^3 - 484/7*e^2 + 900/7*e + 116/7, -12/7*e^5 - 88/7*e^4 + 16/7*e^3 + 981/7*e^2 + 402/7*e - 2916/7, -10/7*e^5 - 71/7*e^4 + 18/7*e^3 + 807/7*e^2 + 307/7*e - 2430/7, -1/7*e^5 - 5/7*e^4 + 13/7*e^3 + 31/7*e^2 - 61/7*e + 268/7, 1/7*e^5 + 5/7*e^4 - 13/7*e^3 - 87/7*e^2 - 51/7*e + 362/7, 10/7*e^5 + 29/7*e^4 - 186/7*e^3 - 205/7*e^2 + 1233/7*e - 776/7, -9/7*e^5 - 59/7*e^4 + 47/7*e^3 + 671/7*e^2 + 25/7*e - 1844/7, 9/7*e^5 + 31/7*e^4 - 159/7*e^3 - 307/7*e^2 + 927/7*e - 242/7, -2/7*e^5 - 17/7*e^4 + 5/7*e^3 + 265/7*e^2 + 137/7*e - 1081/7, 2/7*e^5 + 3/7*e^4 - 61/7*e^3 - 13/7*e^2 + 479/7*e - 543/7, 6/7*e^5 + 58/7*e^4 + 62/7*e^3 - 725/7*e^2 - 964/7*e + 3166/7, -6/7*e^5 - 2/7*e^4 + 162/7*e^3 - 185/7*e^2 - 1304/7*e + 2434/7, 10/7*e^5 + 64/7*e^4 - 39/7*e^3 - 660/7*e^2 - 83/7*e + 1548/7, -1/7*e^5 + 16/7*e^4 + 97/7*e^3 - 256/7*e^2 - 908/7*e + 1542/7, 1/7*e^5 + 26/7*e^4 + 71/7*e^3 - 374/7*e^2 - 688/7*e + 1846/7, -10/7*e^5 - 36/7*e^4 + 151/7*e^3 + 310/7*e^2 - 841/7*e + 90/7, 5/7*e^5 + 11/7*e^4 - 100/7*e^3 + 20/7*e^2 + 837/7*e - 1214/7, -5/7*e^5 - 39/7*e^4 - 12/7*e^3 + 484/7*e^2 + 395/7*e - 1992/7, 5*e^4 + 20*e^3 - 77*e^2 - 194*e + 433, -11/7*e^5 - 69/7*e^4 + 73/7*e^3 + 789/7*e^2 - 139/7*e - 2008/7, 12/7*e^5 + 88/7*e^4 + 12/7*e^3 - 1002/7*e^2 - 794/7*e + 3616/7, -12/7*e^5 - 32/7*e^4 + 212/7*e^3 + 78/7*e^2 - 1502/7*e + 2124/7, 11/7*e^5 + 41/7*e^4 - 185/7*e^3 - 425/7*e^2 + 1091/7*e + 90/7, -10/7*e^5 - 64/7*e^4 + 46/7*e^3 + 737/7*e^2 + 132/7*e - 2136/7, 10/7*e^5 + 36/7*e^4 - 158/7*e^3 - 275/7*e^2 + 1016/7*e - 524/7] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([16, 2, 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]