/* 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([-28, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7,7,-6*w - 29]) primes_array = [ [2, 2, -w + 6],\ [2, 2, w + 5],\ [7, 7, 6*w - 35],\ [7, 7, -6*w - 29],\ [9, 3, 3],\ [11, 11, 4*w + 19],\ [11, 11, 4*w - 23],\ [13, 13, -2*w + 11],\ [13, 13, 2*w + 9],\ [25, 5, -5],\ [31, 31, 2*w - 13],\ [31, 31, -2*w - 11],\ [41, 41, -8*w - 39],\ [41, 41, 8*w - 47],\ [53, 53, -26*w - 125],\ [53, 53, 26*w - 151],\ [61, 61, -14*w + 81],\ [61, 61, -14*w - 67],\ [83, 83, 2*w - 15],\ [83, 83, -2*w - 13],\ [97, 97, 2*w - 5],\ [97, 97, -2*w - 3],\ [109, 109, 2*w - 3],\ [109, 109, -2*w - 1],\ [113, 113, 2*w - 1],\ [127, 127, 8*w - 45],\ [127, 127, 8*w + 37],\ [131, 131, -50*w + 291],\ [131, 131, 50*w + 241],\ [139, 139, 6*w - 37],\ [139, 139, -6*w - 31],\ [149, 149, 20*w + 97],\ [149, 149, 20*w - 117],\ [157, 157, -12*w - 59],\ [157, 157, 12*w - 71],\ [163, 163, 4*w - 19],\ [163, 163, 4*w + 15],\ [173, 173, 4*w + 23],\ [173, 173, 4*w - 27],\ [211, 211, 2*w - 19],\ [211, 211, -2*w - 17],\ [227, 227, -4*w - 13],\ [227, 227, 4*w - 17],\ [233, 233, 6*w + 25],\ [233, 233, -6*w + 31],\ [239, 239, -14*w - 69],\ [239, 239, 14*w - 83],\ [241, 241, 46*w + 221],\ [241, 241, -46*w + 267],\ [251, 251, 22*w - 129],\ [251, 251, 22*w + 107],\ [257, 257, -34*w + 197],\ [257, 257, -34*w - 163],\ [277, 277, 4*w - 29],\ [277, 277, -4*w - 25],\ [283, 283, 4*w - 15],\ [283, 283, -4*w - 11],\ [289, 17, -17],\ [307, 307, 68*w - 395],\ [307, 307, 68*w + 327],\ [311, 311, 10*w - 61],\ [311, 311, -10*w - 51],\ [313, 313, -32*w - 155],\ [313, 313, 32*w - 187],\ [317, 317, -18*w - 85],\ [317, 317, 18*w - 103],\ [331, 331, -4*w - 9],\ [331, 331, 4*w - 13],\ [337, 337, -16*w - 79],\ [337, 337, 16*w - 95],\ [347, 347, -12*w + 67],\ [347, 347, 12*w + 55],\ [353, 353, 14*w - 79],\ [353, 353, 14*w + 65],\ [361, 19, -19],\ [367, 367, -32*w - 153],\ [367, 367, -32*w + 185],\ [383, 383, 56*w + 269],\ [383, 383, 56*w - 325],\ [389, 389, -4*w - 27],\ [389, 389, 4*w - 31],\ [401, 401, 8*w - 51],\ [401, 401, -8*w - 43],\ [421, 421, 12*w - 73],\ [421, 421, -12*w - 61],\ [439, 439, -8*w - 33],\ [439, 439, 8*w - 41],\ [443, 443, -4*w - 1],\ [443, 443, 4*w - 5],\ [461, 461, -30*w + 173],\ [461, 461, 30*w + 143],\ [463, 463, 2*w - 25],\ [463, 463, -2*w - 23],\ [467, 467, 34*w + 165],\ [467, 467, 34*w - 199],\ [503, 503, -26*w - 127],\ [503, 503, 26*w - 153],\ [509, 509, 4*w - 33],\ [509, 509, -4*w - 29],\ [521, 521, -10*w + 53],\ [521, 521, 10*w + 43],\ [529, 23, -23],\ [547, 547, 14*w - 85],\ [547, 547, -14*w - 71],\ [557, 557, 66*w + 317],\ [557, 557, 66*w - 383],\ [563, 563, 2*w - 27],\ [563, 563, -2*w - 25],\ [569, 569, -64*w + 373],\ [569, 569, 64*w + 309],\ [587, 587, 12*w + 53],\ [587, 587, -12*w + 65],\ [593, 593, 8*w + 45],\ [593, 593, 8*w - 53],\ [601, 601, -26*w - 123],\ [601, 601, 26*w - 149],\ [617, 617, 6*w - 23],\ [617, 617, -6*w - 17],\ [647, 647, 24*w - 137],\ [647, 647, -24*w - 113],\ [653, 653, 28*w - 165],\ [653, 653, -28*w - 137],\ [677, 677, -22*w - 103],\ [677, 677, 22*w - 125],\ [691, 691, 20*w - 113],\ [691, 691, 20*w + 93],\ [709, 709, -10*w - 41],\ [709, 709, 10*w - 51],\ [719, 719, -8*w + 37],\ [719, 719, -8*w - 29],\ [727, 727, -22*w - 109],\ [727, 727, 22*w - 131],\ [739, 739, 46*w - 269],\ [739, 739, -46*w - 223],\ [761, 761, -6*w - 13],\ [761, 761, 6*w - 19],\ [769, 769, 110*w - 639],\ [769, 769, 110*w + 529],\ [773, 773, 4*w - 37],\ [773, 773, -4*w - 33],\ [787, 787, 2*w - 31],\ [787, 787, -2*w - 29],\ [809, 809, 56*w + 271],\ [809, 809, -56*w + 327],\ [821, 821, 6*w - 17],\ [821, 821, -6*w - 11],\ [823, 823, 38*w - 223],\ [823, 823, -38*w - 185],\ [827, 827, 132*w - 767],\ [827, 827, 132*w + 635],\ [841, 29, -29],\ [853, 853, -76*w + 443],\ [853, 853, 76*w + 367],\ [863, 863, 14*w - 87],\ [863, 863, -14*w - 73],\ [911, 911, 2*w - 33],\ [911, 911, -2*w - 31],\ [919, 919, -6*w - 41],\ [919, 919, 6*w - 47],\ [929, 929, 50*w + 239],\ [929, 929, 50*w - 289],\ [953, 953, 6*w - 11],\ [953, 953, -6*w - 5],\ [967, 967, -8*w - 25],\ [967, 967, 8*w - 33],\ [991, 991, 16*w + 71],\ [991, 991, -16*w + 87]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 3*x^9 - 12*x^8 + 40*x^7 + 37*x^6 - 162*x^5 - 7*x^4 + 199*x^3 - 5*x^2 - 80*x - 12 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/2*e^8 + 6*e^6 - e^5 - 41/2*e^4 + 15/2*e^3 + 18*e^2 - 13/2*e - 4, e, -1/2*e^9 + e^8 + 7*e^7 - 12*e^6 - 61/2*e^5 + 79/2*e^4 + 44*e^3 - 47/2*e^2 - 27*e - 4, -1, 3/2*e^9 - 1/2*e^8 - 19*e^7 + 8*e^6 + 145/2*e^5 - 34*e^4 - 173/2*e^3 + 39/2*e^2 + 77/2*e + 4, 3/2*e^9 - e^8 - 19*e^7 + 14*e^6 + 143/2*e^5 - 109/2*e^4 - 79*e^3 + 75/2*e^2 + 32*e - 1, -5/2*e^9 + e^8 + 33*e^7 - 15*e^6 - 271/2*e^5 + 123/2*e^4 + 187*e^3 - 77/2*e^2 - 89*e - 12, -2*e^9 + 2*e^8 + 27*e^7 - 25*e^6 - 113*e^5 + 85*e^4 + 155*e^3 - 42*e^2 - 79*e - 18, 5/2*e^9 - 2*e^8 - 34*e^7 + 26*e^6 + 289/2*e^5 - 189/2*e^4 - 204*e^3 + 127/2*e^2 + 94*e + 8, e^7 - 12*e^5 + e^4 + 40*e^3 - 7*e^2 - 29*e, -5/2*e^9 - e^8 + 33*e^7 + 9*e^6 - 279/2*e^5 - 41/2*e^4 + 215*e^3 + 65/2*e^2 - 103*e - 25, -5/2*e^9 + 3/2*e^8 + 32*e^7 - 21*e^6 - 247/2*e^5 + 82*e^4 + 293/2*e^3 - 111/2*e^2 - 119/2*e - 2, 9/2*e^9 - 5/2*e^8 - 61*e^7 + 33*e^6 + 521/2*e^5 - 119*e^4 - 759/2*e^3 + 119/2*e^2 + 361/2*e + 32, 1/2*e^9 - 2*e^8 - 6*e^7 + 25*e^6 + 35/2*e^5 - 179/2*e^4 + 3*e^3 + 151/2*e^2 - 2*e - 10, e^9 - e^8 - 13*e^7 + 14*e^6 + 52*e^5 - 57*e^4 - 69*e^3 + 54*e^2 + 37*e - 4, 11/2*e^9 - 4*e^8 - 74*e^7 + 53*e^6 + 623/2*e^5 - 391/2*e^4 - 443*e^3 + 247/2*e^2 + 225*e + 30, -e^9 + 14*e^7 - 65*e^5 - 4*e^4 + 116*e^3 + 30*e^2 - 70*e - 26, -11/2*e^9 + 3*e^8 + 69*e^7 - 44*e^6 - 513/2*e^5 + 355/2*e^4 + 280*e^3 - 229/2*e^2 - 112*e - 17, -3/2*e^9 + 1/2*e^8 + 23*e^7 - 5*e^6 - 235/2*e^5 + 8*e^4 + 447/2*e^3 + 55/2*e^2 - 257/2*e - 32, 11/2*e^9 - 4*e^8 - 76*e^7 + 51*e^6 + 667/2*e^5 - 357/2*e^4 - 507*e^3 + 191/2*e^2 + 261*e + 41, 5/2*e^9 - e^8 - 34*e^7 + 15*e^6 + 295/2*e^5 - 127/2*e^4 - 227*e^3 + 101/2*e^2 + 114*e + 20, 8*e^9 - 6*e^8 - 107*e^7 + 79*e^6 + 444*e^5 - 289*e^4 - 605*e^3 + 180*e^2 + 278*e + 40, -3/2*e^9 + 1/2*e^8 + 16*e^7 - 9*e^6 - 77/2*e^5 + 41*e^4 - 41/2*e^3 - 47/2*e^2 + 83/2*e + 14, -1/2*e^9 - 1/2*e^8 + 8*e^7 + 6*e^6 - 87/2*e^5 - 21*e^4 + 179/2*e^3 + 45/2*e^2 - 89/2*e - 12, 3/2*e^9 - 17*e^7 + 2*e^6 + 101/2*e^5 - 23/2*e^4 - 21*e^3 - 21/2*e^2 - 7*e + 5, -3*e^9 + 2*e^8 + 41*e^7 - 27*e^6 - 177*e^5 + 102*e^4 + 265*e^3 - 71*e^2 - 146*e - 10, 5/2*e^9 + 1/2*e^8 - 32*e^7 - 3*e^6 + 251/2*e^5 - 319/2*e^3 - 25/2*e^2 + 113/2*e + 12, -7/2*e^9 - 3/2*e^8 + 44*e^7 + 12*e^6 - 339/2*e^5 - 16*e^4 + 435/2*e^3 + 21/2*e^2 - 167/2*e, 11/2*e^9 + 3*e^8 - 71*e^7 - 27*e^6 + 583/2*e^5 + 109/2*e^4 - 439*e^3 - 91/2*e^2 + 212*e + 42, -2*e^9 + 3*e^8 + 25*e^7 - 38*e^6 - 90*e^5 + 135*e^4 + 82*e^3 - 94*e^2 - 31*e - 2, -4*e^9 + 2*e^8 + 54*e^7 - 27*e^6 - 228*e^5 + 100*e^4 + 320*e^3 - 55*e^2 - 138*e - 20, -2*e^9 - 3*e^8 + 24*e^7 + 33*e^6 - 87*e^5 - 103*e^4 + 106*e^3 + 105*e^2 - 33*e - 18, -9*e^9 + 4*e^8 + 118*e^7 - 58*e^6 - 478*e^5 + 227*e^4 + 640*e^3 - 113*e^2 - 299*e - 58, -5/2*e^9 + 4*e^8 + 33*e^7 - 51*e^6 - 261/2*e^5 + 369/2*e^4 + 150*e^3 - 281/2*e^2 - 65*e - 6, 21/2*e^9 - 11/2*e^8 - 145*e^7 + 73*e^6 + 1281/2*e^5 - 266*e^4 - 1999/2*e^3 + 275/2*e^2 + 1025/2*e + 90, -15/2*e^9 + 9/2*e^8 + 95*e^7 - 64*e^6 - 715/2*e^5 + 250*e^4 + 785/2*e^3 - 307/2*e^2 - 291/2*e - 12, -8*e^9 + 2*e^8 + 104*e^7 - 33*e^6 - 419*e^5 + 140*e^4 + 570*e^3 - 51*e^2 - 281*e - 64, 1/2*e^9 + 1/2*e^8 - 9*e^7 - 7*e^6 + 111/2*e^5 + 32*e^4 - 263/2*e^3 - 105/2*e^2 + 171/2*e + 30, -3/2*e^9 - e^8 + 19*e^7 + 9*e^6 - 149/2*e^5 - 33/2*e^4 + 100*e^3 - 1/2*e^2 - 42*e + 16, e^9 - e^8 - 13*e^7 + 13*e^6 + 49*e^5 - 46*e^4 - 43*e^3 + 24*e^2 - 2*e + 14, e^9 - 17*e^7 + 99*e^5 - 2*e^4 - 221*e^3 + 12*e^2 + 134*e + 6, -9/2*e^9 + 1/2*e^8 + 56*e^7 - 12*e^6 - 413/2*e^5 + 59*e^4 + 445/2*e^3 - 17/2*e^2 - 133/2*e - 22, 5/2*e^9 + 2*e^8 - 35*e^7 - 20*e^6 + 331/2*e^5 + 95/2*e^4 - 310*e^3 - 35/2*e^2 + 170*e + 17, -1/2*e^9 + 7/2*e^8 + 12*e^7 - 39*e^6 - 165/2*e^5 + 119*e^4 + 371/2*e^3 - 177/2*e^2 - 247/2*e + 2, -7*e^9 + 9*e^8 + 95*e^7 - 114*e^6 - 399*e^5 + 407*e^4 + 546*e^3 - 296*e^2 - 281*e - 18, 3*e^9 + 2*e^8 - 34*e^7 - 17*e^6 + 107*e^5 + 27*e^4 - 83*e^3 - 8*e^2 + 3*e - 8, 11/2*e^9 - 1/2*e^8 - 75*e^7 + 10*e^6 + 657/2*e^5 - 42*e^4 - 1035/2*e^3 - 37/2*e^2 + 523/2*e + 50, -7/2*e^9 + 4*e^8 + 45*e^7 - 53*e^6 - 343/2*e^5 + 403/2*e^4 + 187*e^3 - 347/2*e^2 - 74*e + 22, -9*e^9 - e^8 + 119*e^7 + e^6 - 499*e^5 + 38*e^4 + 742*e^3 - 6*e^2 - 345*e - 46, -11*e^9 + 8*e^8 + 147*e^7 - 104*e^6 - 609*e^5 + 372*e^4 + 828*e^3 - 207*e^2 - 385*e - 63, 10*e^9 - 11*e^8 - 132*e^7 + 142*e^6 + 530*e^5 - 516*e^4 - 662*e^3 + 369*e^2 + 308*e + 18, -2*e^9 + 2*e^8 + 27*e^7 - 26*e^6 - 111*e^5 + 96*e^4 + 139*e^3 - 74*e^2 - 57*e, 3*e^9 - 3*e^8 - 33*e^7 + 43*e^6 + 86*e^5 - 175*e^4 + 22*e^3 + 148*e^2 - 60*e - 33, -19/2*e^9 + 9*e^8 + 130*e^7 - 116*e^6 - 1113/2*e^5 + 841/2*e^4 + 794*e^3 - 595/2*e^2 - 385*e - 29, -9/2*e^9 + 5*e^8 + 56*e^7 - 65*e^6 - 395/2*e^5 + 469/2*e^4 + 158*e^3 - 305/2*e^2 - 27*e + 9, 3/2*e^9 - 3/2*e^8 - 23*e^7 + 20*e^6 + 229/2*e^5 - 81*e^4 - 397/2*e^3 + 199/2*e^2 + 177/2*e - 22, -4*e^9 + 4*e^8 + 53*e^7 - 50*e^6 - 212*e^5 + 167*e^4 + 253*e^3 - 66*e^2 - 106*e - 43, -6*e^9 + 5*e^8 + 81*e^7 - 64*e^6 - 342*e^5 + 229*e^4 + 484*e^3 - 150*e^2 - 237*e - 30, 11*e^9 - 4*e^8 - 153*e^7 + 55*e^6 + 686*e^5 - 204*e^4 - 1103*e^3 + 83*e^2 + 571*e + 102, -8*e^9 + 2*e^8 + 105*e^7 - 34*e^6 - 428*e^5 + 156*e^4 + 580*e^3 - 122*e^2 - 243*e - 8, 25/2*e^9 - 3*e^8 - 170*e^7 + 47*e^6 + 1475/2*e^5 - 385/2*e^4 - 1129*e^3 + 143/2*e^2 + 550*e + 102, 9/2*e^9 - 13/2*e^8 - 61*e^7 + 78*e^6 + 505/2*e^5 - 252*e^4 - 645/2*e^3 + 247/2*e^2 + 299/2*e + 28, -17/2*e^9 + 11/2*e^8 + 114*e^7 - 73*e^6 - 953/2*e^5 + 266*e^4 + 1327/2*e^3 - 291/2*e^2 - 611/2*e - 52, e^8 + 4*e^7 - 11*e^6 - 46*e^5 + 39*e^4 + 144*e^3 - 63*e^2 - 98*e + 8, -11/2*e^9 + 7/2*e^8 + 73*e^7 - 46*e^6 - 595/2*e^5 + 163*e^4 + 779/2*e^3 - 143/2*e^2 - 369/2*e - 24, -41/2*e^9 + 29/2*e^8 + 270*e^7 - 194*e^6 - 2181/2*e^5 + 720*e^4 + 2815/2*e^3 - 895/2*e^2 - 1259/2*e - 74, 5*e^9 - 4*e^8 - 69*e^7 + 50*e^6 + 301*e^5 - 169*e^4 - 451*e^3 + 79*e^2 + 244*e + 38, 14*e^9 - 9*e^8 - 191*e^7 + 117*e^6 + 823*e^5 - 414*e^4 - 1217*e^3 + 198*e^2 + 607*e + 116, -2*e^8 + 3*e^7 + 25*e^6 - 40*e^5 - 85*e^4 + 148*e^3 + 48*e^2 - 105*e - 10, -15*e^9 + 6*e^8 + 202*e^7 - 88*e^6 - 860*e^5 + 354*e^4 + 1274*e^3 - 214*e^2 - 637*e - 100, 7/2*e^9 - e^8 - 47*e^7 + 16*e^6 + 405/2*e^5 - 143/2*e^4 - 318*e^3 + 119/2*e^2 + 174*e + 8, -9/2*e^9 + 4*e^8 + 63*e^7 - 48*e^6 - 559/2*e^5 + 299/2*e^4 + 428*e^3 - 65/2*e^2 - 240*e - 62, -3*e^9 + 4*e^8 + 41*e^7 - 52*e^6 - 174*e^5 + 191*e^4 + 241*e^3 - 143*e^2 - 121*e - 14, -5/2*e^9 - 6*e^8 + 35*e^7 + 69*e^6 - 345/2*e^5 - 443/2*e^4 + 358*e^3 + 363/2*e^2 - 189*e - 48, 9/2*e^9 - 11/2*e^8 - 55*e^7 + 72*e^6 + 377/2*e^5 - 266*e^4 - 277/2*e^3 + 397/2*e^2 + 31/2*e - 18, 5/2*e^9 + 1/2*e^8 - 30*e^7 - e^6 + 211/2*e^5 - 21*e^4 - 219/2*e^3 + 81/2*e^2 + 57/2*e - 10, 3/2*e^9 - 7*e^8 - 26*e^7 + 80*e^6 + 281/2*e^5 - 493/2*e^4 - 252*e^3 + 279/2*e^2 + 179*e + 37, 14*e^9 - 8*e^8 - 194*e^7 + 107*e^6 + 860*e^5 - 398*e^4 - 1348*e^3 + 245*e^2 + 704*e + 106, 3/2*e^9 - 5*e^8 - 21*e^7 + 59*e^6 + 169/2*e^5 - 385/2*e^4 - 79*e^3 + 273/2*e^2 + 29*e - 23, -7/2*e^9 + 5/2*e^8 + 44*e^7 - 34*e^6 - 319/2*e^5 + 125*e^4 + 287/2*e^3 - 121/2*e^2 - 47/2*e - 14, -5*e^9 + 4*e^8 + 73*e^7 - 51*e^6 - 347*e^5 + 185*e^4 + 590*e^3 - 140*e^2 - 301*e - 30, 15/2*e^9 - 8*e^8 - 100*e^7 + 100*e^6 + 813/2*e^5 - 679/2*e^4 - 512*e^3 + 329/2*e^2 + 227*e + 66, -8*e^9 + 4*e^8 + 108*e^7 - 53*e^6 - 457*e^5 + 187*e^4 + 651*e^3 - 60*e^2 - 304*e - 70, -5*e^9 + 5*e^8 + 71*e^7 - 64*e^6 - 321*e^5 + 234*e^4 + 500*e^3 - 191*e^2 - 253*e - 2, -3*e^9 + 9*e^8 + 48*e^7 - 105*e^6 - 243*e^5 + 337*e^4 + 415*e^3 - 225*e^2 - 259*e - 20, 15/2*e^9 - 3/2*e^8 - 103*e^7 + 25*e^6 + 917/2*e^5 - 107*e^4 - 1507/2*e^3 + 73/2*e^2 + 855/2*e + 80, 7/2*e^9 - 5*e^8 - 43*e^7 + 64*e^6 + 285/2*e^5 - 455/2*e^4 - 69*e^3 + 297/2*e^2 - 17*e - 11, 1/2*e^9 - 7/2*e^8 - 8*e^7 + 43*e^6 + 77/2*e^5 - 155*e^4 - 113/2*e^3 + 309/2*e^2 + 97/2*e - 24, 15*e^9 - 8*e^8 - 197*e^7 + 112*e^6 + 799*e^5 - 437*e^4 - 1063*e^3 + 291*e^2 + 476*e + 52, -2*e^9 - 2*e^8 + 19*e^7 + 18*e^6 - 31*e^5 - 41*e^4 - 61*e^3 + 56*e^2 + 55*e - 5, 8*e^9 - 6*e^8 - 111*e^7 + 78*e^6 + 490*e^5 - 281*e^4 - 758*e^3 + 165*e^2 + 421*e + 68, 17/2*e^9 - 8*e^8 - 106*e^7 + 106*e^6 + 767/2*e^5 - 789/2*e^4 - 368*e^3 + 553/2*e^2 + 131*e - 3, 5/2*e^9 - 2*e^8 - 26*e^7 + 30*e^6 + 109/2*e^5 - 251/2*e^4 + 70*e^3 + 197/2*e^2 - 84*e - 24, 11*e^9 - 5*e^8 - 148*e^7 + 70*e^6 + 625*e^5 - 267*e^4 - 896*e^3 + 138*e^2 + 424*e + 84, -19/2*e^9 + 9*e^8 + 123*e^7 - 117*e^6 - 963/2*e^5 + 845/2*e^4 + 581*e^3 - 519/2*e^2 - 258*e - 56, 9*e^9 - 8*e^8 - 114*e^7 + 106*e^6 + 426*e^5 - 393*e^4 - 451*e^3 + 265*e^2 + 178*e + 6, 13/2*e^9 - 3*e^8 - 86*e^7 + 43*e^6 + 703/2*e^5 - 337/2*e^4 - 471*e^3 + 197/2*e^2 + 218*e + 9, 11/2*e^9 - 7*e^8 - 79*e^7 + 85*e^6 + 729/2*e^5 - 569/2*e^4 - 594*e^3 + 347/2*e^2 + 340*e + 52, -15*e^9 + 14*e^8 + 208*e^7 - 178*e^6 - 915*e^5 + 633*e^4 + 1390*e^3 - 423*e^2 - 730*e - 94, 13*e^9 - 2*e^8 - 177*e^7 + 36*e^6 + 770*e^5 - 160*e^4 - 1190*e^3 + 46*e^2 + 598*e + 120, 2*e^9 - 4*e^8 - 24*e^7 + 48*e^6 + 76*e^5 - 154*e^4 - 29*e^3 + 67*e^2 + e + 7, 29/2*e^9 - 10*e^8 - 194*e^7 + 135*e^6 + 1617/2*e^5 - 1027/2*e^4 - 1122*e^3 + 743/2*e^2 + 522*e + 32, -17/2*e^9 + 7*e^8 + 116*e^7 - 86*e^6 - 991/2*e^5 + 557/2*e^4 + 709*e^3 - 165/2*e^2 - 358*e - 86, -15/2*e^9 + e^8 + 95*e^7 - 22*e^6 - 731/2*e^5 + 215/2*e^4 + 459*e^3 - 75/2*e^2 - 232*e - 40, 3/2*e^9 + 7/2*e^8 - 23*e^7 - 42*e^6 + 253/2*e^5 + 146*e^4 - 579/2*e^3 - 297/2*e^2 + 335/2*e + 58, -5*e^9 + 2*e^8 + 76*e^7 - 22*e^6 - 387*e^5 + 56*e^4 + 747*e^3 + 36*e^2 - 455*e - 114, 25/2*e^9 - 10*e^8 - 170*e^7 + 132*e^6 + 1445/2*e^5 - 983/2*e^4 - 1020*e^3 + 713/2*e^2 + 472*e + 42, -11*e^9 + 7*e^8 + 143*e^7 - 95*e^6 - 566*e^5 + 349*e^4 + 712*e^3 - 165*e^2 - 350*e - 76, 1/2*e^9 + e^8 - 2*e^7 - 8*e^6 - 43/2*e^5 + 17/2*e^4 + 97*e^3 + 25/2*e^2 - 61*e - 23, -14*e^9 + 12*e^8 + 188*e^7 - 155*e^6 - 781*e^5 + 553*e^4 + 1055*e^3 - 328*e^2 - 498*e - 66, -9/2*e^9 + 4*e^8 + 51*e^7 - 57*e^6 - 297/2*e^5 + 461/2*e^4 + 43*e^3 - 385/2*e^2 + 12*e + 36, 10*e^9 - 5*e^8 - 132*e^7 + 72*e^6 + 545*e^5 - 287*e^4 - 775*e^3 + 184*e^2 + 404*e + 60, 5*e^9 - 7*e^8 - 74*e^7 + 83*e^6 + 354*e^5 - 267*e^4 - 603*e^3 + 144*e^2 + 360*e + 67, -6*e^9 - 2*e^8 + 80*e^7 + 19*e^6 - 341*e^5 - 54*e^4 + 523*e^3 + 109*e^2 - 252*e - 74, -20*e^9 + 15*e^8 + 265*e^7 - 200*e^6 - 1081*e^5 + 745*e^4 + 1418*e^3 - 497*e^2 - 620*e - 67, -4*e^9 - 5*e^8 + 51*e^7 + 53*e^6 - 209*e^5 - 154*e^4 + 326*e^3 + 140*e^2 - 150*e - 34, 11*e^9 - 4*e^8 - 148*e^7 + 59*e^6 + 626*e^5 - 243*e^4 - 899*e^3 + 176*e^2 + 408*e + 20, -11/2*e^9 + 3*e^8 + 67*e^7 - 44*e^6 - 463/2*e^5 + 363/2*e^4 + 186*e^3 - 295/2*e^2 - 3*e + 38, 4*e^9 + 2*e^8 - 48*e^7 - 16*e^6 + 171*e^5 + 25*e^4 - 197*e^3 - 41*e^2 + 98*e + 18, -9/2*e^9 + 8*e^8 + 67*e^7 - 98*e^6 - 639/2*e^5 + 687/2*e^4 + 522*e^3 - 577/2*e^2 - 270*e + 6, 20*e^9 - 12*e^8 - 267*e^7 + 165*e^6 + 1115*e^5 - 631*e^4 - 1581*e^3 + 405*e^2 + 785*e + 111, 3/2*e^9 - 4*e^8 - 25*e^7 + 48*e^6 + 265/2*e^5 - 335/2*e^4 - 228*e^3 + 327/2*e^2 + 86*e - 27, 4*e^9 - 4*e^8 - 52*e^7 + 50*e^6 + 203*e^5 - 167*e^4 - 238*e^3 + 69*e^2 + 115*e + 18, -7/2*e^9 + 3*e^8 + 46*e^7 - 41*e^6 - 361/2*e^5 + 323/2*e^4 + 200*e^3 - 299/2*e^2 - 51*e + 35, -2*e^9 + 3*e^8 + 25*e^7 - 40*e^6 - 92*e^5 + 156*e^4 + 97*e^3 - 149*e^2 - 44*e + 10, 5/2*e^9 + 5*e^8 - 34*e^7 - 54*e^6 + 317/2*e^5 + 307/2*e^4 - 305*e^3 - 199/2*e^2 + 155*e + 40, 15*e^9 - 6*e^8 - 203*e^7 + 86*e^6 + 869*e^5 - 341*e^4 - 1284*e^3 + 211*e^2 + 609*e + 78, 11*e^9 - 12*e^8 - 140*e^7 + 153*e^6 + 522*e^5 - 536*e^4 - 526*e^3 + 307*e^2 + 185*e + 26, -9*e^9 - 5*e^8 + 119*e^7 + 51*e^6 - 503*e^5 - 147*e^4 + 769*e^3 + 189*e^2 - 344*e - 88, 17/2*e^9 - 6*e^8 - 107*e^7 + 83*e^6 + 801/2*e^5 - 639/2*e^4 - 444*e^3 + 415/2*e^2 + 187*e + 32, -11*e^9 + 9*e^8 + 157*e^7 - 110*e^6 - 722*e^5 + 361*e^4 + 1183*e^3 - 148*e^2 - 659*e - 124, 25*e^9 - 9*e^8 - 334*e^7 + 133*e^6 + 1403*e^5 - 535*e^4 - 2024*e^3 + 301*e^2 + 966*e + 154, 19*e^9 - 18*e^8 - 250*e^7 + 235*e^6 + 1000*e^5 - 855*e^4 - 1240*e^3 + 564*e^2 + 549*e + 44, -2*e^9 - e^8 + 37*e^7 + 13*e^6 - 233*e^5 - 46*e^4 + 552*e^3 + 36*e^2 - 338*e - 62, 23*e^9 - 12*e^8 - 313*e^7 + 165*e^6 + 1349*e^5 - 634*e^4 - 2012*e^3 + 423*e^2 + 991*e + 98, 2*e^9 + e^8 - 14*e^7 - 3*e^6 - 33*e^5 - 28*e^4 + 299*e^3 + 44*e^2 - 268*e - 66, -11/2*e^9 - 1/2*e^8 + 74*e^7 + 4*e^6 - 635/2*e^5 - 19*e^4 + 975/2*e^3 + 217/2*e^2 - 515/2*e - 74, -21*e^9 + 11*e^8 + 288*e^7 - 150*e^6 - 1255*e^5 + 568*e^4 + 1903*e^3 - 353*e^2 - 945*e - 136, 13*e^9 - 8*e^8 - 169*e^7 + 110*e^6 + 668*e^5 - 418*e^4 - 826*e^3 + 268*e^2 + 344*e + 4, -33/2*e^9 + 10*e^8 + 224*e^7 - 132*e^6 - 1917/2*e^5 + 961/2*e^4 + 1400*e^3 - 545/2*e^2 - 674*e - 97, 23*e^9 - 13*e^8 - 310*e^7 + 172*e^6 + 1314*e^5 - 618*e^4 - 1909*e^3 + 287*e^2 + 972*e + 178, 20*e^9 - 12*e^8 - 267*e^7 + 160*e^6 + 1112*e^5 - 582*e^4 - 1556*e^3 + 292*e^2 + 755*e + 138, 3*e^9 + 5*e^8 - 40*e^7 - 52*e^6 + 181*e^5 + 139*e^4 - 343*e^3 - 82*e^2 + 197*e + 22, 25/2*e^9 - 17/2*e^8 - 165*e^7 + 114*e^6 + 1345/2*e^5 - 419*e^4 - 1803/2*e^3 + 461/2*e^2 + 889/2*e + 72, 16*e^9 - 20*e^8 - 209*e^7 + 253*e^6 + 818*e^5 - 891*e^4 - 946*e^3 + 588*e^2 + 423*e + 26, -6*e^9 + 6*e^8 + 89*e^7 - 71*e^6 - 429*e^5 + 228*e^4 + 741*e^3 - 119*e^2 - 423*e - 50, 9*e^9 - 5*e^8 - 112*e^7 + 77*e^6 + 411*e^5 - 338*e^4 - 436*e^3 + 314*e^2 + 154*e - 14, -15*e^9 + 4*e^8 + 192*e^7 - 69*e^6 - 751*e^5 + 315*e^4 + 953*e^3 - 222*e^2 - 411*e - 20, -3/2*e^9 - e^8 + 14*e^7 + 6*e^6 - 37/2*e^5 + 5/2*e^4 - 66*e^3 + 19/2*e^2 + 51*e - 2, -23/2*e^9 + 6*e^8 + 165*e^7 - 80*e^6 - 1545/2*e^5 + 605/2*e^4 + 1318*e^3 - 435/2*e^2 - 706*e - 86, 25*e^9 - 24*e^8 - 331*e^7 + 312*e^6 + 1339*e^5 - 1134*e^4 - 1706*e^3 + 767*e^2 + 791*e + 55, -e^9 + 6*e^8 + 15*e^7 - 74*e^6 - 67*e^5 + 265*e^4 + 86*e^3 - 255*e^2 - 63*e + 50, -31/2*e^9 + 6*e^8 + 202*e^7 - 92*e^6 - 1623/2*e^5 + 769/2*e^4 + 1074*e^3 - 483/2*e^2 - 500*e - 86, -17/2*e^9 + 1/2*e^8 + 112*e^7 - 15*e^6 - 925/2*e^5 + 83*e^4 + 1311/2*e^3 - 63/2*e^2 - 595/2*e - 42, 3*e^9 - 2*e^8 - 32*e^7 + 33*e^6 + 74*e^5 - 154*e^4 + 59*e^3 + 157*e^2 - 90*e - 20, -7*e^9 + 2*e^8 + 84*e^7 - 32*e^6 - 283*e^5 + 131*e^4 + 213*e^3 - 41*e^2 - e - 14, 29/2*e^9 - 5/2*e^8 - 189*e^7 + 49*e^6 + 1535/2*e^5 - 241*e^4 - 2117/2*e^3 + 339/2*e^2 + 933/2*e + 46, 19*e^9 - 14*e^8 - 256*e^7 + 183*e^6 + 1079*e^5 - 662*e^4 - 1527*e^3 + 387*e^2 + 733*e + 138, 13*e^9 - 9*e^8 - 177*e^7 + 116*e^6 + 757*e^5 - 405*e^4 - 1097*e^3 + 186*e^2 + 542*e + 118, 21/2*e^9 - 7*e^8 - 138*e^7 + 94*e^6 + 1113/2*e^5 - 703/2*e^4 - 719*e^3 + 457/2*e^2 + 315*e + 15, 7*e^9 + 3*e^8 - 94*e^7 - 28*e^6 + 405*e^5 + 61*e^4 - 628*e^3 - 46*e^2 + 286*e + 20, -13/2*e^9 + 6*e^8 + 80*e^7 - 81*e^6 - 555/2*e^5 + 613/2*e^4 + 208*e^3 - 449/2*e^2 - 3*e + 36, -7/2*e^9 - 2*e^8 + 54*e^7 + 23*e^6 - 563/2*e^5 - 149/2*e^4 + 553*e^3 + 133/2*e^2 - 279*e - 48, 7/2*e^9 - 5/2*e^8 - 43*e^7 + 34*e^6 + 297/2*e^5 - 128*e^4 - 219/2*e^3 + 159/2*e^2 + 11/2*e + 2, -e^8 - 9*e^7 + 6*e^6 + 102*e^5 + 15*e^4 - 322*e^3 - 82*e^2 + 259*e + 84, -27*e^9 + 24*e^8 + 366*e^7 - 307*e^6 - 1549*e^5 + 1083*e^4 + 2194*e^3 - 626*e^2 - 1124*e - 178, 61/2*e^9 - 47/2*e^8 - 412*e^7 + 306*e^6 + 3473/2*e^5 - 1103*e^4 - 4873/2*e^3 + 1331/2*e^2 + 2341/2*e + 152] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7,7,-6*w - 29])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]