/* 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([-58, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9,9,w + 7]) primes_array = [ [2, 2, w],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [7, 7, -2*w + 15],\ [7, 7, -2*w - 15],\ [11, 11, w + 5],\ [11, 11, w + 6],\ [19, 19, w + 1],\ [19, 19, w + 18],\ [23, 23, w + 9],\ [23, 23, -w + 9],\ [25, 5, 5],\ [29, 29, w],\ [37, 37, w + 13],\ [37, 37, w + 24],\ [43, 43, w + 12],\ [43, 43, w + 31],\ [61, 61, w + 27],\ [61, 61, w + 34],\ [71, 71, 12*w - 91],\ [71, 71, 12*w + 91],\ [101, 101, w + 19],\ [101, 101, w + 82],\ [103, 103, -3*w + 25],\ [103, 103, -3*w - 25],\ [131, 131, w + 53],\ [131, 131, w + 78],\ [151, 151, 2*w - 9],\ [151, 151, -2*w - 9],\ [157, 157, w + 23],\ [157, 157, w + 134],\ [163, 163, w + 59],\ [163, 163, w + 104],\ [167, 167, -w - 15],\ [167, 167, w - 15],\ [169, 13, -13],\ [199, 199, -4*w + 27],\ [199, 199, -4*w - 27],\ [211, 211, w + 67],\ [211, 211, w + 144],\ [223, 223, 2*w - 3],\ [223, 223, -2*w - 3],\ [229, 229, w + 79],\ [229, 229, w + 150],\ [233, 233, 3*w - 17],\ [233, 233, -3*w - 17],\ [239, 239, 6*w + 43],\ [239, 239, 6*w - 43],\ [241, 241, -7*w + 51],\ [241, 241, -7*w - 51],\ [251, 251, w + 73],\ [251, 251, w + 178],\ [257, 257, -8*w - 63],\ [257, 257, -8*w + 63],\ [269, 269, w + 70],\ [269, 269, w + 199],\ [281, 281, 15*w + 113],\ [281, 281, 15*w - 113],\ [289, 17, -17],\ [293, 293, w + 75],\ [293, 293, w + 218],\ [307, 307, w + 66],\ [307, 307, w + 241],\ [313, 313, -6*w + 49],\ [313, 313, -6*w - 49],\ [317, 317, w + 117],\ [317, 317, w + 200],\ [331, 331, w + 148],\ [331, 331, w + 183],\ [353, 353, -3*w - 13],\ [353, 353, 3*w - 13],\ [379, 379, w + 171],\ [379, 379, w + 208],\ [383, 383, -w - 21],\ [383, 383, w - 21],\ [389, 389, w + 35],\ [389, 389, w + 354],\ [401, 401, 3*w - 11],\ [401, 401, -3*w - 11],\ [421, 421, w + 30],\ [421, 421, w + 391],\ [431, 431, -12*w - 89],\ [431, 431, -12*w + 89],\ [439, 439, 3*w - 31],\ [439, 439, -3*w - 31],\ [443, 443, w + 175],\ [443, 443, w + 268],\ [457, 457, -11*w - 81],\ [457, 457, -11*w + 81],\ [461, 461, w + 141],\ [461, 461, w + 320],\ [463, 463, 8*w + 57],\ [463, 463, 8*w - 57],\ [467, 467, w + 92],\ [467, 467, w + 375],\ [487, 487, -4*w - 21],\ [487, 487, 4*w - 21],\ [491, 491, w + 135],\ [491, 491, w + 356],\ [521, 521, -3*w - 1],\ [521, 521, 3*w - 1],\ [541, 541, w + 41],\ [541, 541, w + 500],\ [563, 563, w + 109],\ [563, 563, w + 454],\ [593, 593, -4*w - 39],\ [593, 593, 4*w - 39],\ [619, 619, w + 36],\ [619, 619, w + 583],\ [631, 631, -9*w + 73],\ [631, 631, -9*w - 73],\ [647, 647, 24*w - 181],\ [647, 647, 24*w + 181],\ [653, 653, w + 133],\ [653, 653, w + 520],\ [659, 659, w + 306],\ [659, 659, w + 353],\ [673, 673, 12*w + 95],\ [673, 673, 12*w - 95],\ [677, 677, w + 259],\ [677, 677, w + 418],\ [719, 719, -6*w - 37],\ [719, 719, 6*w - 37],\ [733, 733, w + 304],\ [733, 733, w + 429],\ [739, 739, w + 102],\ [739, 739, w + 637],\ [757, 757, w + 315],\ [757, 757, w + 442],\ [761, 761, -10*w + 81],\ [761, 761, -10*w - 81],\ [773, 773, w + 226],\ [773, 773, w + 547],\ [797, 797, w + 281],\ [797, 797, w + 516],\ [827, 827, w + 239],\ [827, 827, w + 588],\ [829, 829, w + 108],\ [829, 829, w + 721],\ [853, 853, w + 42],\ [853, 853, w + 811],\ [857, 857, 2*w - 33],\ [857, 857, -2*w - 33],\ [859, 859, w + 403],\ [859, 859, w + 456],\ [863, 863, 6*w - 35],\ [863, 863, -6*w - 35],\ [907, 907, w + 128],\ [907, 907, w + 779],\ [919, 919, 4*w - 3],\ [919, 919, -4*w - 3],\ [929, 929, 21*w - 157],\ [929, 929, 21*w + 157],\ [937, 937, 6*w - 55],\ [937, 937, -6*w - 55],\ [947, 947, w + 406],\ [947, 947, w + 541],\ [953, 953, 14*w + 111],\ [953, 953, 14*w - 111],\ [961, 31, -31],\ [971, 971, w + 143],\ [971, 971, w + 828],\ [977, 977, 9*w + 61],\ [977, 977, -9*w + 61],\ [991, 991, -21*w + 163],\ [991, 991, -21*w - 163],\ [997, 997, w + 105],\ [997, 997, w + 892]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^7 - 2*x^6 - 11*x^5 + 21*x^4 + 35*x^3 - 65*x^2 - 29*x + 55 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 0, 3*e^6 - 2*e^5 - 35*e^4 + 15*e^3 + 120*e^2 - 26*e - 114, -e^6 + e^5 + 12*e^4 - 8*e^3 - 43*e^2 + 14*e + 42, 3*e^6 - 2*e^5 - 36*e^4 + 16*e^3 + 127*e^2 - 30*e - 123, -e^4 + e^3 + 7*e^2 - 4*e - 7, -7*e^6 + 4*e^5 + 83*e^4 - 30*e^3 - 290*e^2 + 52*e + 282, 9*e^6 - 5*e^5 - 108*e^4 + 37*e^3 + 382*e^2 - 64*e - 374, -3*e^6 + 2*e^5 + 36*e^4 - 16*e^3 - 127*e^2 + 30*e + 121, 9*e^6 - 6*e^5 - 107*e^4 + 45*e^3 + 377*e^2 - 76*e - 370, -5*e^6 + 3*e^5 + 60*e^4 - 24*e^3 - 212*e^2 + 47*e + 205, -6*e^6 + 4*e^5 + 71*e^4 - 31*e^3 - 249*e^2 + 55*e + 243, e^6 - 13*e^4 + 50*e^2 - 55, -5*e^6 + 3*e^5 + 61*e^4 - 23*e^3 - 223*e^2 + 40*e + 226, 5*e^6 - 3*e^5 - 60*e^4 + 23*e^3 + 215*e^2 - 42*e - 214, 13*e^6 - 8*e^5 - 154*e^4 + 60*e^3 + 538*e^2 - 102*e - 524, -10*e^6 + 6*e^5 + 120*e^4 - 46*e^3 - 424*e^2 + 81*e + 411, -3*e^6 + e^5 + 38*e^4 - 8*e^3 - 142*e^2 + 14*e + 148, -11*e^6 + 7*e^5 + 129*e^4 - 53*e^3 - 444*e^2 + 91*e + 423, -8*e^6 + 4*e^5 + 96*e^4 - 30*e^3 - 339*e^2 + 52*e + 331, -6*e^6 + 5*e^5 + 70*e^4 - 39*e^3 - 239*e^2 + 64*e + 219, -9*e^6 + 6*e^5 + 108*e^4 - 46*e^3 - 385*e^2 + 80*e + 382, 3*e^6 - 2*e^5 - 38*e^4 + 16*e^3 + 147*e^2 - 27*e - 162, 6*e^6 - 3*e^5 - 71*e^4 + 23*e^3 + 244*e^2 - 39*e - 225, -19*e^6 + 11*e^5 + 226*e^4 - 82*e^3 - 791*e^2 + 143*e + 765, 5*e^6 - 4*e^5 - 57*e^4 + 28*e^3 + 195*e^2 - 38*e - 188, -2*e^6 + 2*e^5 + 24*e^4 - 17*e^3 - 85*e^2 + 33*e + 78, 16*e^6 - 11*e^5 - 186*e^4 + 84*e^3 + 633*e^2 - 147*e - 596, -31*e^6 + 22*e^5 + 365*e^4 - 167*e^3 - 1269*e^2 + 284*e + 1219, 20*e^6 - 15*e^5 - 235*e^4 + 113*e^3 + 817*e^2 - 187*e - 790, -8*e^6 + 4*e^5 + 98*e^4 - 29*e^3 - 359*e^2 + 46*e + 365, 6*e^6 - 3*e^5 - 75*e^4 + 25*e^3 + 279*e^2 - 53*e - 288, -14*e^6 + 9*e^5 + 165*e^4 - 69*e^3 - 568*e^2 + 126*e + 537, -18*e^6 + 11*e^5 + 214*e^4 - 82*e^3 - 752*e^2 + 140*e + 729, -15*e^6 + 9*e^5 + 181*e^4 - 68*e^3 - 647*e^2 + 116*e + 646, -4*e^6 + 3*e^5 + 48*e^4 - 24*e^3 - 172*e^2 + 42*e + 169, 2*e^6 - e^5 - 27*e^4 + 8*e^3 + 106*e^2 - 14*e - 106, 15*e^6 - 11*e^5 - 176*e^4 + 85*e^3 + 611*e^2 - 148*e - 601, -32*e^6 + 21*e^5 + 382*e^4 - 159*e^3 - 1353*e^2 + 273*e + 1334, -20*e^6 + 13*e^5 + 238*e^4 - 99*e^3 - 830*e^2 + 174*e + 784, 3*e^6 - 2*e^5 - 35*e^4 + 13*e^3 + 119*e^2 - 15*e - 112, -6*e^6 + 4*e^5 + 68*e^4 - 26*e^3 - 227*e^2 + 34*e + 218, 4*e^6 - 2*e^5 - 49*e^4 + 15*e^3 + 177*e^2 - 21*e - 185, -6*e^6 + 4*e^5 + 73*e^4 - 33*e^3 - 261*e^2 + 61*e + 255, -15*e^6 + 11*e^5 + 178*e^4 - 84*e^3 - 629*e^2 + 142*e + 613, 21*e^6 - 12*e^5 - 252*e^4 + 93*e^3 + 895*e^2 - 170*e - 888, -25*e^6 + 13*e^5 + 297*e^4 - 95*e^3 - 1040*e^2 + 166*e + 1006, 25*e^6 - 16*e^5 - 299*e^4 + 122*e^3 + 1062*e^2 - 208*e - 1061, 2*e^5 - 20*e^3 - 6*e^2 + 44*e + 18, -2*e^5 + 4*e^4 + 14*e^3 - 25*e^2 - 19*e + 18, -2*e^6 + 2*e^5 + 25*e^4 - 14*e^3 - 92*e^2 + 10*e + 98, 28*e^6 - 18*e^5 - 336*e^4 + 141*e^3 + 1185*e^2 - 257*e - 1143, 41*e^6 - 26*e^5 - 484*e^4 + 197*e^3 + 1686*e^2 - 346*e - 1634, 21*e^6 - 13*e^5 - 249*e^4 + 97*e^3 + 869*e^2 - 171*e - 841, 27*e^6 - 20*e^5 - 318*e^4 + 154*e^3 + 1104*e^2 - 262*e - 1057, -16*e^6 + 10*e^5 + 189*e^4 - 75*e^3 - 653*e^2 + 127*e + 617, 11*e^6 - 8*e^5 - 128*e^4 + 61*e^3 + 438*e^2 - 103*e - 425, -25*e^6 + 16*e^5 + 299*e^4 - 124*e^3 - 1059*e^2 + 220*e + 1030, 14*e^6 - 6*e^5 - 170*e^4 + 44*e^3 + 608*e^2 - 79*e - 606, 32*e^6 - 20*e^5 - 380*e^4 + 151*e^3 + 1331*e^2 - 265*e - 1285, -9*e^6 + 8*e^5 + 102*e^4 - 62*e^3 - 347*e^2 + 107*e + 350, 47*e^6 - 31*e^5 - 555*e^4 + 238*e^3 + 1927*e^2 - 415*e - 1847, -16*e^6 + 9*e^5 + 190*e^4 - 66*e^3 - 662*e^2 + 119*e + 628, -23*e^6 + 14*e^5 + 274*e^4 - 104*e^3 - 970*e^2 + 179*e + 956, 37*e^6 - 23*e^5 - 441*e^4 + 174*e^3 + 1551*e^2 - 299*e - 1519, -31*e^6 + 20*e^5 + 367*e^4 - 151*e^3 - 1287*e^2 + 265*e + 1264, 25*e^6 - 14*e^5 - 296*e^4 + 102*e^3 + 1031*e^2 - 173*e - 989, 3*e^6 - 2*e^5 - 33*e^4 + 16*e^3 + 100*e^2 - 27*e - 79, 21*e^6 - 13*e^5 - 248*e^4 + 98*e^3 + 863*e^2 - 172*e - 849, e^6 + e^5 - 11*e^4 - 10*e^3 + 33*e^2 + 18*e - 36, 43*e^6 - 28*e^5 - 509*e^4 + 211*e^3 + 1778*e^2 - 360*e - 1724, 21*e^6 - 16*e^5 - 247*e^4 + 127*e^3 + 860*e^2 - 226*e - 841, 23*e^6 - 17*e^5 - 269*e^4 + 131*e^3 + 931*e^2 - 232*e - 896, -15*e^6 + 9*e^5 + 178*e^4 - 64*e^3 - 625*e^2 + 104*e + 607, -4*e^6 + 5*e^5 + 47*e^4 - 41*e^3 - 164*e^2 + 66*e + 163, 17*e^6 - 11*e^5 - 199*e^4 + 84*e^3 + 687*e^2 - 150*e - 663, -21*e^6 + 12*e^5 + 252*e^4 - 91*e^3 - 889*e^2 + 160*e + 883, 6*e^6 - 2*e^5 - 78*e^4 + 16*e^3 + 300*e^2 - 31*e - 311, 44*e^6 - 27*e^5 - 523*e^4 + 204*e^3 + 1829*e^2 - 355*e - 1779, 27*e^6 - 16*e^5 - 322*e^4 + 120*e^3 + 1131*e^2 - 209*e - 1085, 6*e^6 - 4*e^5 - 73*e^4 + 34*e^3 + 266*e^2 - 72*e - 260, 38*e^6 - 25*e^5 - 449*e^4 + 190*e^3 + 1567*e^2 - 339*e - 1517, 17*e^6 - 12*e^5 - 201*e^4 + 93*e^3 + 700*e^2 - 157*e - 683, -33*e^6 + 22*e^5 + 394*e^4 - 169*e^3 - 1387*e^2 + 293*e + 1349, 20*e^6 - 12*e^5 - 235*e^4 + 89*e^3 + 800*e^2 - 152*e - 741, 36*e^6 - 23*e^5 - 424*e^4 + 171*e^3 + 1471*e^2 - 292*e - 1415, -26*e^6 + 17*e^5 + 310*e^4 - 127*e^3 - 1099*e^2 + 218*e + 1085, 25*e^6 - 17*e^5 - 299*e^4 + 130*e^3 + 1067*e^2 - 216*e - 1078, -67*e^6 + 45*e^5 + 796*e^4 - 344*e^3 - 2793*e^2 + 594*e + 2717, -3*e^6 + 3*e^5 + 32*e^4 - 22*e^3 - 99*e^2 + 32*e + 65, -55*e^6 + 37*e^5 + 654*e^4 - 280*e^3 - 2302*e^2 + 476*e + 2245, -49*e^6 + 32*e^5 + 577*e^4 - 240*e^3 - 2006*e^2 + 410*e + 1928, -13*e^6 + 8*e^5 + 151*e^4 - 60*e^3 - 515*e^2 + 100*e + 498, 50*e^6 - 35*e^5 - 590*e^4 + 271*e^3 + 2056*e^2 - 475*e - 1983, -24*e^6 + 15*e^5 + 284*e^4 - 117*e^3 - 984*e^2 + 209*e + 938, 64*e^6 - 42*e^5 - 759*e^4 + 318*e^3 + 2663*e^2 - 548*e - 2592, 35*e^6 - 24*e^5 - 417*e^4 + 183*e^3 + 1468*e^2 - 308*e - 1437, -19*e^6 + 11*e^5 + 225*e^4 - 83*e^3 - 791*e^2 + 148*e + 794, 6*e^6 - 5*e^5 - 67*e^4 + 38*e^3 + 214*e^2 - 65*e - 189, 48*e^6 - 30*e^5 - 571*e^4 + 230*e^3 + 2004*e^2 - 408*e - 1950, -e^6 + e^5 + 10*e^4 - 7*e^3 - 27*e^2 + 5*e + 25, 17*e^6 - 12*e^5 - 202*e^4 + 92*e^3 + 706*e^2 - 160*e - 693, -39*e^6 + 26*e^5 + 459*e^4 - 193*e^3 - 1604*e^2 + 318*e + 1562, -55*e^6 + 37*e^5 + 651*e^4 - 280*e^3 - 2280*e^2 + 478*e + 2210, e^6 + e^5 - 14*e^4 - 8*e^3 + 60*e^2 + 13*e - 65, 53*e^6 - 34*e^5 - 627*e^4 + 257*e^3 + 2194*e^2 - 444*e - 2135, 4*e^6 - 5*e^5 - 48*e^4 + 39*e^3 + 189*e^2 - 66*e - 230, -32*e^6 + 25*e^5 + 380*e^4 - 195*e^3 - 1342*e^2 + 342*e + 1324, -75*e^6 + 49*e^5 + 882*e^4 - 367*e^3 - 3065*e^2 + 624*e + 2974, 64*e^6 - 43*e^5 - 757*e^4 + 322*e^3 + 2651*e^2 - 541*e - 2593, 8*e^6 - 6*e^5 - 93*e^4 + 46*e^3 + 328*e^2 - 80*e - 338, 23*e^6 - 13*e^5 - 273*e^4 + 102*e^3 + 950*e^2 - 192*e - 900, 45*e^6 - 27*e^5 - 539*e^4 + 207*e^3 + 1905*e^2 - 364*e - 1850, 32*e^6 - 20*e^5 - 382*e^4 + 149*e^3 + 1350*e^2 - 250*e - 1323, 29*e^6 - 21*e^5 - 348*e^4 + 166*e^3 + 1235*e^2 - 303*e - 1207, -9*e^6 + 7*e^5 + 110*e^4 - 54*e^3 - 408*e^2 + 90*e + 444, -17*e^6 + 9*e^5 + 208*e^4 - 74*e^3 - 752*e^2 + 149*e + 766, -32*e^6 + 23*e^5 + 379*e^4 - 178*e^3 - 1337*e^2 + 313*e + 1306, 26*e^6 - 15*e^5 - 319*e^4 + 117*e^3 + 1159*e^2 - 210*e - 1169, 59*e^6 - 38*e^5 - 697*e^4 + 284*e^3 + 2434*e^2 - 480*e - 2376, 61*e^6 - 41*e^5 - 725*e^4 + 316*e^3 + 2547*e^2 - 558*e - 2464, -59*e^6 + 39*e^5 + 694*e^4 - 300*e^3 - 2405*e^2 + 535*e + 2315, 20*e^6 - 14*e^5 - 234*e^4 + 106*e^3 + 808*e^2 - 191*e - 775, 2*e^6 - e^5 - 25*e^4 + 8*e^3 + 102*e^2 - 20*e - 130, 58*e^6 - 37*e^5 - 689*e^4 + 284*e^3 + 2408*e^2 - 502*e - 2330, -5*e^6 + 3*e^5 + 57*e^4 - 22*e^3 - 177*e^2 + 27*e + 131, 33*e^6 - 23*e^5 - 391*e^4 + 173*e^3 + 1374*e^2 - 282*e - 1354, 13*e^6 - 6*e^5 - 155*e^4 + 47*e^3 + 531*e^2 - 101*e - 467, -82*e^6 + 50*e^5 + 977*e^4 - 385*e^3 - 3430*e^2 + 687*e + 3328, 66*e^6 - 43*e^5 - 774*e^4 + 320*e^3 + 2679*e^2 - 539*e - 2588, 26*e^6 - 19*e^5 - 302*e^4 + 144*e^3 + 1033*e^2 - 240*e - 987, 22*e^6 - 12*e^5 - 265*e^4 + 92*e^3 + 934*e^2 - 162*e - 882, 61*e^6 - 39*e^5 - 727*e^4 + 293*e^3 + 2569*e^2 - 505*e - 2528, -28*e^6 + 18*e^5 + 323*e^4 - 135*e^3 - 1094*e^2 + 242*e + 1022, -e^6 + 3*e^5 + 15*e^4 - 35*e^3 - 66*e^2 + 86*e + 78, -37*e^6 + 27*e^5 + 431*e^4 - 203*e^3 - 1486*e^2 + 345*e + 1438, -30*e^6 + 18*e^5 + 359*e^4 - 134*e^3 - 1269*e^2 + 222*e + 1257, -7*e^6 + 8*e^5 + 82*e^4 - 70*e^3 - 288*e^2 + 139*e + 293, 44*e^6 - 29*e^5 - 522*e^4 + 222*e^3 + 1816*e^2 - 383*e - 1742, -5*e^6 + 6*e^5 + 49*e^4 - 49*e^3 - 137*e^2 + 95*e + 125, -45*e^6 + 26*e^5 + 540*e^4 - 202*e^3 - 1905*e^2 + 360*e + 1830, 55*e^6 - 38*e^5 - 643*e^4 + 289*e^3 + 2218*e^2 - 506*e - 2123, 30*e^6 - 20*e^5 - 355*e^4 + 154*e^3 + 1247*e^2 - 272*e - 1232, -52*e^6 + 30*e^5 + 623*e^4 - 228*e^3 - 2205*e^2 + 399*e + 2163, 2*e^6 - 4*e^5 - 21*e^4 + 33*e^3 + 76*e^2 - 59*e - 92, 10*e^6 - 10*e^5 - 111*e^4 + 76*e^3 + 363*e^2 - 137*e - 336, e^5 - 2*e^4 - 4*e^3 + 11*e^2 - 3*e + 6, -44*e^6 + 30*e^5 + 517*e^4 - 232*e^3 - 1791*e^2 + 412*e + 1739, 18*e^6 - 10*e^5 - 215*e^4 + 82*e^3 + 759*e^2 - 173*e - 736, 74*e^6 - 47*e^5 - 869*e^4 + 351*e^3 + 3009*e^2 - 603*e - 2900, -17*e^6 + 13*e^5 + 201*e^4 - 104*e^3 - 704*e^2 + 194*e + 675, -39*e^6 + 25*e^5 + 460*e^4 - 193*e^3 - 1593*e^2 + 339*e + 1517, 24*e^6 - 17*e^5 - 287*e^4 + 127*e^3 + 1025*e^2 - 205*e - 1022, 56*e^6 - 33*e^5 - 674*e^4 + 254*e^3 + 2396*e^2 - 455*e - 2365, -79*e^6 + 48*e^5 + 940*e^4 - 366*e^3 - 3295*e^2 + 644*e + 3190, -67*e^6 + 42*e^5 + 797*e^4 - 321*e^3 - 2799*e^2 + 564*e + 2713, 14*e^6 - 9*e^5 - 162*e^4 + 66*e^3 + 547*e^2 - 114*e - 513, -53*e^6 + 36*e^5 + 620*e^4 - 268*e^3 - 2139*e^2 + 444*e + 2048, -59*e^6 + 36*e^5 + 704*e^4 - 272*e^3 - 2482*e^2 + 470*e + 2407, 34*e^6 - 20*e^5 - 407*e^4 + 155*e^3 + 1429*e^2 - 286*e - 1390, -10*e^6 + 10*e^5 + 117*e^4 - 82*e^3 - 411*e^2 + 158*e + 387, 21*e^6 - 11*e^5 - 262*e^4 + 89*e^3 + 970*e^2 - 170*e - 992, 11*e^6 - 7*e^5 - 126*e^4 + 51*e^3 + 434*e^2 - 83*e - 449, -16*e^6 + 9*e^5 + 193*e^4 - 69*e^3 - 700*e^2 + 127*e + 724, -45*e^6 + 27*e^5 + 529*e^4 - 199*e^3 - 1830*e^2 + 341*e + 1767, -51*e^6 + 36*e^5 + 597*e^4 - 279*e^3 - 2060*e^2 + 489*e + 1987, 2*e^6 - e^5 - 22*e^4 + 6*e^3 + 67*e^2 + 7*e - 57, 62*e^6 - 43*e^5 - 733*e^4 + 332*e^3 + 2563*e^2 - 579*e - 2477] 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,-w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]