/* 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([-98, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([3, 3, -842*w + 8767]) primes_array = [ [2, 2, -17*w - 160],\ [2, 2, -17*w + 177],\ [3, 3, -842*w + 8767],\ [7, 7, -2*w + 21],\ [7, 7, 2*w + 19],\ [13, 13, -12*w - 113],\ [13, 13, 12*w - 125],\ [17, 17, 182*w - 1895],\ [17, 17, 182*w + 1713],\ [23, 23, -512*w - 4819],\ [23, 23, 512*w - 5331],\ [25, 5, -5],\ [29, 29, 22*w - 229],\ [29, 29, 22*w + 207],\ [43, 43, 114*w + 1073],\ [43, 43, 114*w - 1187],\ [47, 47, 8*w - 83],\ [47, 47, -8*w - 75],\ [61, 61, -1172*w - 11031],\ [61, 61, 1172*w - 12203],\ [71, 71, 216*w + 2033],\ [71, 71, 216*w - 2249],\ [83, 83, 8932*w - 93001],\ [83, 83, -2196*w + 22865],\ [109, 109, -4*w - 39],\ [109, 109, 4*w - 43],\ [121, 11, -11],\ [131, 131, 5564*w - 57933],\ [137, 137, 2*w - 17],\ [137, 137, -2*w - 15],\ [149, 149, 18*w - 187],\ [149, 149, 18*w + 169],\ [151, 151, -1502*w - 14137],\ [151, 151, -1502*w + 15639],\ [173, 173, -6*w - 55],\ [173, 173, 6*w - 61],\ [193, 193, 808*w - 8413],\ [193, 193, -808*w - 7605],\ [197, 197, 2*w - 15],\ [197, 197, -2*w - 13],\ [211, 211, -70*w + 729],\ [211, 211, -70*w - 659],\ [227, 227, 284*w + 2673],\ [227, 227, 284*w - 2957],\ [251, 251, 124*w - 1291],\ [251, 251, 124*w + 1167],\ [257, 257, 42*w + 395],\ [257, 257, 42*w - 437],\ [271, 271, 410*w + 3859],\ [271, 271, 410*w - 4269],\ [277, 277, 4*w - 45],\ [277, 277, -4*w - 41],\ [281, 281, -3550*w - 33413],\ [281, 281, 3550*w - 36963],\ [283, 283, 2*w - 27],\ [283, 283, -2*w - 25],\ [293, 293, 2*w - 11],\ [293, 293, -2*w - 9],\ [307, 307, -6*w - 59],\ [307, 307, 6*w - 65],\ [337, 337, 376*w - 3915],\ [337, 337, 376*w + 3539],\ [347, 347, -4*w - 33],\ [347, 347, -4*w + 37],\ [359, 359, -8*w - 73],\ [359, 359, -8*w + 81],\ [361, 19, -19],\ [367, 367, -774*w + 8059],\ [367, 367, -774*w - 7285],\ [379, 379, -30*w + 313],\ [379, 379, -30*w - 283],\ [389, 389, 2*w - 3],\ [389, 389, -2*w - 1],\ [397, 397, -172*w + 1791],\ [397, 397, -172*w - 1619],\ [401, 401, 6*w - 59],\ [401, 401, 6*w + 53],\ [409, 409, -40*w - 377],\ [409, 409, 40*w - 417],\ [419, 419, 100*w - 1041],\ [419, 419, -100*w - 941],\ [421, 421, 308*w + 2899],\ [421, 421, 308*w - 3207],\ [439, 439, 274*w - 2853],\ [439, 439, 274*w + 2579],\ [443, 443, -52*w - 489],\ [443, 443, 52*w - 541],\ [449, 449, 15338*w - 159701],\ [449, 449, -6918*w + 72031],\ [457, 457, 17352*w - 180671],\ [457, 457, 6224*w - 64805],\ [461, 461, 614*w - 6393],\ [461, 461, 614*w + 5779],\ [479, 479, 192*w - 1999],\ [479, 479, 192*w + 1807],\ [487, 487, -94*w + 979],\ [487, 487, -94*w - 885],\ [491, 491, -20*w - 187],\ [491, 491, 20*w - 207],\ [503, 503, -16*w + 165],\ [503, 503, 16*w + 149],\ [509, 509, 2890*w - 30091],\ [509, 509, -2890*w - 27201],\ [521, 521, 11970*w - 124633],\ [521, 521, -10286*w + 107099],\ [577, 577, -1104*w - 10391],\ [577, 577, 1104*w - 11495],\ [593, 593, 134*w + 1261],\ [593, 593, 134*w - 1395],\ [601, 601, -8*w - 79],\ [601, 601, 8*w - 87],\ [613, 613, -2492*w - 23455],\ [613, 613, 2492*w - 25947],\ [617, 617, 226*w - 2353],\ [617, 617, 226*w + 2127],\ [631, 631, 2*w - 33],\ [631, 631, -2*w - 31],\ [677, 677, -62*w - 583],\ [677, 677, 62*w - 645],\ [691, 691, 1798*w - 18721],\ [691, 691, -1798*w - 16923],\ [739, 739, 74*w + 697],\ [739, 739, 74*w - 771],\ [743, 743, 48*w - 499],\ [743, 743, 48*w + 451],\ [757, 757, -44*w + 459],\ [757, 757, -44*w - 415],\ [761, 761, 14*w + 129],\ [761, 761, 14*w - 143],\ [769, 769, 16*w + 153],\ [769, 769, 16*w - 169],\ [773, 773, 4574*w - 47625],\ [773, 773, -39938*w + 415839],\ [787, 787, 3846*w + 36199],\ [787, 787, 3846*w - 40045],\ [809, 809, 30*w + 281],\ [809, 809, -30*w + 311],\ [811, 811, 1070*w - 11141],\ [811, 811, -1070*w - 10071],\ [829, 829, -4*w - 47],\ [829, 829, 4*w - 51],\ [857, 857, -18*w + 185],\ [857, 857, 18*w + 167],\ [877, 877, -196*w - 1845],\ [877, 877, -196*w + 2041],\ [881, 881, -26*w - 243],\ [881, 881, 26*w - 269],\ [907, 907, -14*w - 135],\ [907, 907, -14*w + 149],\ [937, 937, 8*w - 89],\ [937, 937, -8*w - 81],\ [941, 941, 294*w - 3061],\ [941, 941, 294*w + 2767],\ [947, 947, 4*w - 27],\ [947, 947, -4*w - 23],\ [961, 31, -31],\ [971, 971, -1604*w + 16701],\ [971, 971, 1604*w + 15097],\ [983, 983, 144*w - 1499],\ [983, 983, 144*w + 1355],\ [991, 991, -10*w - 99],\ [991, 991, 10*w - 109],\ [997, 997, 604*w - 6289],\ [997, 997, 604*w + 5685]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 18*x^8 + 115*x^6 - 314*x^4 + 335*x^2 - 91 K. = NumberField(heckePol) hecke_eigenvalues_array = [-e, e, 1, -4/19*e^8 + 51/19*e^6 - 178/19*e^4 + 141/19*e^2 - 6/19, -4/19*e^8 + 51/19*e^6 - 178/19*e^4 + 141/19*e^2 - 6/19, 10/19*e^8 - 137/19*e^6 + 559/19*e^4 - 723/19*e^2 + 224/19, 10/19*e^8 - 137/19*e^6 + 559/19*e^4 - 723/19*e^2 + 224/19, -5/19*e^9 + 78/19*e^7 - 403/19*e^5 + 789/19*e^3 - 416/19*e, 5/19*e^9 - 78/19*e^7 + 403/19*e^5 - 789/19*e^3 + 416/19*e, -3/19*e^9 + 43/19*e^7 - 181/19*e^5 + 196/19*e^3 + 43/19*e, 3/19*e^9 - 43/19*e^7 + 181/19*e^5 - 196/19*e^3 - 43/19*e, 7/19*e^8 - 94/19*e^6 + 359/19*e^4 - 356/19*e^2 - 94/19, -3/19*e^9 + 43/19*e^7 - 200/19*e^5 + 367/19*e^3 - 242/19*e, 3/19*e^9 - 43/19*e^7 + 200/19*e^5 - 367/19*e^3 + 242/19*e, -21/19*e^8 + 301/19*e^6 - 1343/19*e^4 + 2018/19*e^2 - 649/19, -21/19*e^8 + 301/19*e^6 - 1343/19*e^4 + 2018/19*e^2 - 649/19, 9/19*e^9 - 129/19*e^7 + 562/19*e^5 - 740/19*e^3 + 4/19*e, -9/19*e^9 + 129/19*e^7 - 562/19*e^5 + 740/19*e^3 - 4/19*e, 9/19*e^8 - 110/19*e^6 + 353/19*e^4 - 208/19*e^2 - 91/19, 9/19*e^8 - 110/19*e^6 + 353/19*e^4 - 208/19*e^2 - 91/19, -8/19*e^9 + 121/19*e^7 - 584/19*e^5 + 985/19*e^3 - 430/19*e, 8/19*e^9 - 121/19*e^7 + 584/19*e^5 - 985/19*e^3 + 430/19*e, -e^7 + 12*e^5 - 38*e^3 + 23*e, e^7 - 12*e^5 + 38*e^3 - 23*e, 1/19*e^8 - 27/19*e^6 + 206/19*e^4 - 477/19*e^2 + 144/19, 1/19*e^8 - 27/19*e^6 + 206/19*e^4 - 477/19*e^2 + 144/19, -15/19*e^8 + 215/19*e^6 - 943/19*e^4 + 1417/19*e^2 - 849/19, 0, -6/19*e^9 + 86/19*e^7 - 400/19*e^5 + 734/19*e^3 - 465/19*e, 6/19*e^9 - 86/19*e^7 + 400/19*e^5 - 734/19*e^3 + 465/19*e, -15/19*e^9 + 234/19*e^7 - 1190/19*e^5 + 2234/19*e^3 - 1134/19*e, 15/19*e^9 - 234/19*e^7 + 1190/19*e^5 - 2234/19*e^3 + 1134/19*e, -8/19*e^8 + 102/19*e^6 - 337/19*e^4 + 187/19*e^2 - 50/19, -8/19*e^8 + 102/19*e^6 - 337/19*e^4 + 187/19*e^2 - 50/19, 6/19*e^9 - 86/19*e^7 + 381/19*e^5 - 563/19*e^3 + 275/19*e, -6/19*e^9 + 86/19*e^7 - 381/19*e^5 + 563/19*e^3 - 275/19*e, 17/19*e^8 - 231/19*e^6 + 899/19*e^4 - 927/19*e^2 + 73/19, 17/19*e^8 - 231/19*e^6 + 899/19*e^4 - 927/19*e^2 + 73/19, -5/19*e^9 + 59/19*e^7 - 156/19*e^5 - 85/19*e^3 + 249/19*e, 5/19*e^9 - 59/19*e^7 + 156/19*e^5 + 85/19*e^3 - 249/19*e, 27/19*e^8 - 368/19*e^6 + 1515/19*e^4 - 1992/19*e^2 + 544/19, 27/19*e^8 - 368/19*e^6 + 1515/19*e^4 - 1992/19*e^2 + 544/19, -22/19*e^9 + 328/19*e^7 - 1568/19*e^5 + 2761/19*e^3 - 1515/19*e, 22/19*e^9 - 328/19*e^7 + 1568/19*e^5 - 2761/19*e^3 + 1515/19*e, e^9 - 14*e^7 + 60*e^5 - 88*e^3 + 37*e, -e^9 + 14*e^7 - 60*e^5 + 88*e^3 - 37*e, 4/19*e^9 - 51/19*e^7 + 178/19*e^5 - 141/19*e^3 + 120/19*e, -4/19*e^9 + 51/19*e^7 - 178/19*e^5 + 141/19*e^3 - 120/19*e, -20/19*e^8 + 293/19*e^6 - 1327/19*e^4 + 1959/19*e^2 - 695/19, -20/19*e^8 + 293/19*e^6 - 1327/19*e^4 + 1959/19*e^2 - 695/19, -14/19*e^8 + 188/19*e^6 - 737/19*e^4 + 769/19*e^2 + 17/19, -14/19*e^8 + 188/19*e^6 - 737/19*e^4 + 769/19*e^2 + 17/19, 4*e^3 - 26*e, -4*e^3 + 26*e, 41/19*e^8 - 575/19*e^6 + 2480/19*e^4 - 3616/19*e^2 + 1154/19, 41/19*e^8 - 575/19*e^6 + 2480/19*e^4 - 3616/19*e^2 + 1154/19, 13/19*e^9 - 199/19*e^7 + 987/19*e^5 - 1831/19*e^3 + 1131/19*e, -13/19*e^9 + 199/19*e^7 - 987/19*e^5 + 1831/19*e^3 - 1131/19*e, -29/19*e^8 + 384/19*e^6 - 1452/19*e^4 + 1445/19*e^2 - 224/19, -29/19*e^8 + 384/19*e^6 - 1452/19*e^4 + 1445/19*e^2 - 224/19, e^8 - 16*e^6 + 84*e^4 - 162*e^2 + 78, e^8 - 16*e^6 + 84*e^4 - 162*e^2 + 78, -13/19*e^9 + 180/19*e^7 - 740/19*e^5 + 824/19*e^3 + 351/19*e, 13/19*e^9 - 180/19*e^7 + 740/19*e^5 - 824/19*e^3 - 351/19*e, 15/19*e^9 - 196/19*e^7 + 715/19*e^5 - 657/19*e^3 - 25/19*e, -15/19*e^9 + 196/19*e^7 - 715/19*e^5 + 657/19*e^3 + 25/19*e, -4/19*e^8 + 70/19*e^6 - 425/19*e^4 + 920/19*e^2 - 6/19, -28/19*e^8 + 414/19*e^6 - 1911/19*e^4 + 3058/19*e^2 - 1315/19, -28/19*e^8 + 414/19*e^6 - 1911/19*e^4 + 3058/19*e^2 - 1315/19, -45/19*e^8 + 645/19*e^6 - 2829/19*e^4 + 4099/19*e^2 - 1426/19, -45/19*e^8 + 645/19*e^6 - 2829/19*e^4 + 4099/19*e^2 - 1426/19, 10/19*e^9 - 156/19*e^7 + 787/19*e^5 - 1426/19*e^3 + 528/19*e, -10/19*e^9 + 156/19*e^7 - 787/19*e^5 + 1426/19*e^3 - 528/19*e, -17/19*e^8 + 231/19*e^6 - 937/19*e^4 + 1079/19*e^2 - 54/19, -17/19*e^8 + 231/19*e^6 - 937/19*e^4 + 1079/19*e^2 - 54/19, 18/19*e^9 - 277/19*e^7 + 1390/19*e^5 - 2658/19*e^3 + 1680/19*e, -18/19*e^9 + 277/19*e^7 - 1390/19*e^5 + 2658/19*e^3 - 1680/19*e, -5/19*e^8 + 59/19*e^6 - 118/19*e^4 - 408/19*e^2 + 686/19, -5/19*e^8 + 59/19*e^6 - 118/19*e^4 - 408/19*e^2 + 686/19, -1/19*e^9 + 27/19*e^7 - 225/19*e^5 + 762/19*e^3 - 1113/19*e, 1/19*e^9 - 27/19*e^7 + 225/19*e^5 - 762/19*e^3 + 1113/19*e, 14/19*e^8 - 207/19*e^6 + 1003/19*e^4 - 1928/19*e^2 + 1237/19, 14/19*e^8 - 207/19*e^6 + 1003/19*e^4 - 1928/19*e^2 + 1237/19, -11/19*e^8 + 145/19*e^6 - 518/19*e^4 + 326/19*e^2 + 12/19, -11/19*e^8 + 145/19*e^6 - 518/19*e^4 + 326/19*e^2 + 12/19, 2*e^7 - 27*e^5 + 98*e^3 - 71*e, -2*e^7 + 27*e^5 - 98*e^3 + 71*e, -2*e^7 + 26*e^5 - 94*e^3 + 89*e, 2*e^7 - 26*e^5 + 94*e^3 - 89*e, -60/19*e^8 + 860/19*e^6 - 3829/19*e^4 + 5858/19*e^2 - 2123/19, -60/19*e^8 + 860/19*e^6 - 3829/19*e^4 + 5858/19*e^2 - 2123/19, -3/19*e^9 + 81/19*e^7 - 656/19*e^5 + 1754/19*e^3 - 1002/19*e, 3/19*e^9 - 81/19*e^7 + 656/19*e^5 - 1754/19*e^3 + 1002/19*e, -6/19*e^9 + 86/19*e^7 - 381/19*e^5 + 601/19*e^3 - 256/19*e, 6/19*e^9 - 86/19*e^7 + 381/19*e^5 - 601/19*e^3 + 256/19*e, -6/19*e^8 + 48/19*e^6 + 37/19*e^4 - 387/19*e^2 - 370/19, -6/19*e^8 + 48/19*e^6 + 37/19*e^4 - 387/19*e^2 - 370/19, -4/19*e^9 + 89/19*e^7 - 615/19*e^5 + 1376/19*e^3 - 424/19*e, 4/19*e^9 - 89/19*e^7 + 615/19*e^5 - 1376/19*e^3 + 424/19*e, -26/19*e^9 + 341/19*e^7 - 1233/19*e^5 + 888/19*e^3 + 740/19*e, 26/19*e^9 - 341/19*e^7 + 1233/19*e^5 - 888/19*e^3 - 740/19*e, -31/19*e^9 + 438/19*e^7 - 1902/19*e^5 + 2684/19*e^3 - 455/19*e, 31/19*e^9 - 438/19*e^7 + 1902/19*e^5 - 2684/19*e^3 + 455/19*e, -18/19*e^9 + 239/19*e^7 - 915/19*e^5 + 948/19*e^3 + 11/19*e, 18/19*e^9 - 239/19*e^7 + 915/19*e^5 - 948/19*e^3 - 11/19*e, -18/19*e^8 + 277/19*e^6 - 1371/19*e^4 + 2449/19*e^2 - 1224/19, -18/19*e^8 + 277/19*e^6 - 1371/19*e^4 + 2449/19*e^2 - 1224/19, 14/19*e^9 - 169/19*e^7 + 509/19*e^5 - 161/19*e^3 - 74/19*e, -14/19*e^9 + 169/19*e^7 - 509/19*e^5 + 161/19*e^3 + 74/19*e, 46/19*e^8 - 634/19*e^6 + 2636/19*e^4 - 3455/19*e^2 + 392/19, 46/19*e^8 - 634/19*e^6 + 2636/19*e^4 - 3455/19*e^2 + 392/19, -16/19*e^8 + 166/19*e^6 - 313/19*e^4 - 348/19*e^2 + 90/19, -16/19*e^8 + 166/19*e^6 - 313/19*e^4 - 348/19*e^2 + 90/19, -13/19*e^9 + 180/19*e^7 - 721/19*e^5 + 672/19*e^3 + 560/19*e, 13/19*e^9 - 180/19*e^7 + 721/19*e^5 - 672/19*e^3 - 560/19*e, -33/19*e^8 + 435/19*e^6 - 1706/19*e^4 + 2213/19*e^2 - 971/19, -33/19*e^8 + 435/19*e^6 - 1706/19*e^4 + 2213/19*e^2 - 971/19, -13/19*e^9 + 161/19*e^7 - 493/19*e^5 - 107/19*e^3 + 1282/19*e, 13/19*e^9 - 161/19*e^7 + 493/19*e^5 + 107/19*e^3 - 1282/19*e, 39/19*e^8 - 559/19*e^6 + 2543/19*e^4 - 4258/19*e^2 + 2063/19, 39/19*e^8 - 559/19*e^6 + 2543/19*e^4 - 4258/19*e^2 + 2063/19, 2*e^8 - 29*e^6 + 129*e^4 - 181*e^2 + 23, 2*e^8 - 29*e^6 + 129*e^4 - 181*e^2 + 23, 29/19*e^9 - 384/19*e^7 + 1471/19*e^5 - 1578/19*e^3 + 110/19*e, -29/19*e^9 + 384/19*e^7 - 1471/19*e^5 + 1578/19*e^3 - 110/19*e, 1/19*e^8 - 8/19*e^6 + 35/19*e^4 - 363/19*e^2 + 1094/19, 1/19*e^8 - 8/19*e^6 + 35/19*e^4 - 363/19*e^2 + 1094/19, -2/19*e^9 + 16/19*e^7 + 25/19*e^5 - 186/19*e^3 - 516/19*e, 2/19*e^9 - 16/19*e^7 - 25/19*e^5 + 186/19*e^3 + 516/19*e, -93/19*e^8 + 1352/19*e^6 - 6162/19*e^4 + 9914/19*e^2 - 4120/19, -93/19*e^8 + 1352/19*e^6 - 6162/19*e^4 + 9914/19*e^2 - 4120/19, 14/19*e^9 - 245/19*e^7 + 1478/19*e^5 - 3467/19*e^3 + 2073/19*e, -14/19*e^9 + 245/19*e^7 - 1478/19*e^5 + 3467/19*e^3 - 2073/19*e, -9/19*e^8 + 186/19*e^6 - 1246/19*e^4 + 2887/19*e^2 - 1296/19, -9/19*e^8 + 186/19*e^6 - 1246/19*e^4 + 2887/19*e^2 - 1296/19, -3/19*e^9 + 5/19*e^7 + 256/19*e^5 - 1115/19*e^3 + 803/19*e, 3/19*e^9 - 5/19*e^7 - 256/19*e^5 + 1115/19*e^3 - 803/19*e, 64/19*e^8 - 949/19*e^6 + 4387/19*e^4 - 6778/19*e^2 + 2300/19, 64/19*e^8 - 949/19*e^6 + 4387/19*e^4 - 6778/19*e^2 + 2300/19, -21/19*e^8 + 282/19*e^6 - 1172/19*e^4 + 1809/19*e^2 - 1105/19, -21/19*e^8 + 282/19*e^6 - 1172/19*e^4 + 1809/19*e^2 - 1105/19, -18/19*e^9 + 239/19*e^7 - 915/19*e^5 + 967/19*e^3 + 106/19*e, 18/19*e^9 - 239/19*e^7 + 915/19*e^5 - 967/19*e^3 - 106/19*e, -47/19*e^8 + 718/19*e^6 - 3488/19*e^4 + 5908/19*e^2 - 2493/19, -47/19*e^8 + 718/19*e^6 - 3488/19*e^4 + 5908/19*e^2 - 2493/19, -51/19*e^9 + 769/19*e^7 - 3742/19*e^5 + 6638/19*e^3 - 3240/19*e, 51/19*e^9 - 769/19*e^7 + 3742/19*e^5 - 6638/19*e^3 + 3240/19*e, 1/19*e^8 - 27/19*e^6 + 225/19*e^4 - 572/19*e^2 - 293/19, 1/19*e^8 - 27/19*e^6 + 225/19*e^4 - 572/19*e^2 - 293/19, -10/19*e^8 + 80/19*e^6 + 30/19*e^4 - 474/19*e^2 - 661/19, -10/19*e^8 + 80/19*e^6 + 30/19*e^4 - 474/19*e^2 - 661/19, 10/19*e^9 - 156/19*e^7 + 768/19*e^5 - 1217/19*e^3 + 262/19*e, -10/19*e^9 + 156/19*e^7 - 768/19*e^5 + 1217/19*e^3 - 262/19*e, -22/19*e^9 + 290/19*e^7 - 1055/19*e^5 + 690/19*e^3 + 1221/19*e, 22/19*e^9 - 290/19*e^7 + 1055/19*e^5 - 690/19*e^3 - 1221/19*e, 32/19*e^8 - 427/19*e^6 + 1709/19*e^4 - 2306/19*e^2 + 1815/19, -3/19*e^9 + 24/19*e^7 + 28/19*e^5 - 241/19*e^3 - 128/19*e, 3/19*e^9 - 24/19*e^7 - 28/19*e^5 + 241/19*e^3 + 128/19*e, -25/19*e^9 + 352/19*e^7 - 1426/19*e^5 + 1304/19*e^3 + 1017/19*e, 25/19*e^9 - 352/19*e^7 + 1426/19*e^5 - 1304/19*e^3 - 1017/19*e, 16/19*e^8 - 261/19*e^6 + 1396/19*e^4 - 2730/19*e^2 + 879/19, 16/19*e^8 - 261/19*e^6 + 1396/19*e^4 - 2730/19*e^2 + 879/19, 58/19*e^8 - 806/19*e^6 + 3360/19*e^4 - 4372/19*e^2 + 1189/19, 58/19*e^8 - 806/19*e^6 + 3360/19*e^4 - 4372/19*e^2 + 1189/19] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -842*w + 8767])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]