/* 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([2, 2, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13, 13, -w^2 + 3]) primes_array = [ [2, 2, -w],\ [3, 3, w + 1],\ [4, 2, -w^2 - w + 1],\ [13, 13, -w^2 + 3],\ [17, 17, -w + 3],\ [27, 3, w^3 - 2*w^2 - 3*w + 5],\ [31, 31, -w^2 - 2*w + 1],\ [41, 41, -w^2 + 5],\ [43, 43, w^3 - w^2 - 5*w - 1],\ [43, 43, w^3 - w^2 - 3*w + 1],\ [59, 59, -w - 3],\ [59, 59, -2*w^3 + 2*w^2 + 9*w - 5],\ [59, 59, -w^3 - 3*w^2 - w + 3],\ [59, 59, w^3 - 7*w + 1],\ [61, 61, -w^3 + w^2 + 2*w + 5],\ [61, 61, -w^3 - w^2 + 4*w + 3],\ [67, 67, 4*w^3 - 4*w^2 - 18*w + 7],\ [73, 73, -2*w^3 + 6*w - 3],\ [73, 73, -2*w + 3],\ [97, 97, w^3 - 2*w^2 - 5*w + 3],\ [101, 101, w^3 + w^2 - 5*w - 7],\ [101, 101, -w^3 - w^2 + 4*w + 5],\ [103, 103, 2*w^3 - 8*w - 1],\ [103, 103, w^2 - 2*w - 7],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, -w^3 + w^2 + 6*w - 3],\ [127, 127, -w^3 + w^2 + 6*w - 1],\ [131, 131, -2*w^3 + 3*w^2 + 10*w - 11],\ [137, 137, w^3 + w^2 - 6*w - 5],\ [139, 139, -3*w^3 + 2*w^2 + 15*w - 1],\ [149, 149, w^3 - 3*w^2 - 4*w + 11],\ [149, 149, -w^3 + 5*w - 1],\ [157, 157, -2*w^3 + 3*w^2 + 6*w - 1],\ [163, 163, 2*w^2 - 3],\ [163, 163, -2*w^3 + 2*w^2 + 7*w - 5],\ [167, 167, -2*w^3 + 2*w^2 + 8*w - 3],\ [167, 167, -2*w^2 + 2*w + 9],\ [173, 173, 2*w^3 - w^2 - 8*w + 3],\ [173, 173, 2*w^3 - 3*w^2 - 6*w + 3],\ [181, 181, 2*w^3 - 3*w^2 - 8*w + 5],\ [191, 191, -2*w^3 + w^2 + 10*w - 1],\ [193, 193, -w^3 + 3*w^2 + 2*w - 7],\ [193, 193, w^3 - 3*w - 3],\ [193, 193, 2*w^2 - 2*w - 3],\ [193, 193, w^3 - 7*w - 1],\ [197, 197, w^2 - 2*w - 5],\ [211, 211, w^2 - 4*w - 1],\ [229, 229, -w^3 + w^2 + 6*w - 7],\ [229, 229, -4*w^3 + 6*w^2 + 16*w - 13],\ [233, 233, 3*w^2 + 2*w - 5],\ [233, 233, 2*w^3 - 2*w^2 - 11*w + 7],\ [239, 239, -w^3 + w^2 + 7*w + 1],\ [241, 241, w^3 - 3*w^2 - 2*w + 9],\ [241, 241, w^3 + w^2 - 9*w - 5],\ [251, 251, 2*w^3 - 6*w + 1],\ [271, 271, 2*w^3 - w^2 - 8*w - 1],\ [271, 271, -2*w^2 + w + 7],\ [281, 281, 2*w^3 + 2*w^2 - 5*w - 1],\ [293, 293, w^3 + w^2 - 5*w - 1],\ [293, 293, -3*w + 7],\ [307, 307, -w^3 - 2*w^2 + 3*w + 5],\ [311, 311, -w^3 + 3*w^2 + 4*w - 7],\ [313, 313, 2*w^2 - 2*w - 5],\ [317, 317, -2*w^3 + 4*w^2 + 7*w - 13],\ [317, 317, -2*w^3 + 3*w^2 + 8*w - 11],\ [337, 337, 3*w^3 + 2*w^2 - 7*w + 1],\ [347, 347, 2*w^3 - 2*w^2 - 11*w + 1],\ [349, 349, -5*w^3 + 6*w^2 + 23*w - 13],\ [359, 359, 2*w^3 - 2*w^2 - 12*w + 9],\ [359, 359, -2*w^3 + 8*w + 5],\ [367, 367, -4*w^3 + 4*w^2 + 19*w - 5],\ [367, 367, 2*w^3 + w^2 - 10*w - 7],\ [383, 383, 2*w^3 - 2*w^2 - 7*w + 1],\ [389, 389, 2*w^2 - w - 5],\ [397, 397, 3*w^3 - 4*w^2 - 11*w + 9],\ [397, 397, 3*w^3 - 3*w^2 - 12*w + 7],\ [397, 397, 2*w^3 - 4*w^2 - 8*w + 15],\ [397, 397, -w^3 + 3*w^2 + w - 7],\ [409, 409, -w^3 - w^2 + 9*w - 1],\ [419, 419, 2*w^2 - 3*w - 7],\ [419, 419, 4*w^3 - 3*w^2 - 18*w + 3],\ [431, 431, -3*w^3 + w^2 + 17*w - 1],\ [431, 431, 3*w^3 - w^2 - 16*w - 1],\ [433, 433, -2*w^3 + 5*w^2 + 8*w - 19],\ [443, 443, 3*w - 5],\ [449, 449, -2*w^3 + 2*w^2 + 9*w - 9],\ [449, 449, -5*w^3 + 8*w^2 + 19*w - 17],\ [457, 457, -3*w^3 + 3*w^2 + 13*w - 9],\ [457, 457, -3*w^3 + 2*w^2 + 13*w + 1],\ [457, 457, -2*w^3 + w^2 + 8*w + 7],\ [457, 457, 3*w^3 - 3*w^2 - 15*w + 7],\ [461, 461, -2*w^3 + 2*w^2 + 9*w + 1],\ [479, 479, -w^3 + w^2 + 7*w - 9],\ [487, 487, -w^3 - w^2 + w - 3],\ [499, 499, -2*w^3 + 7*w - 3],\ [499, 499, -5*w^3 + 7*w^2 + 20*w - 15],\ [541, 541, -3*w^3 + 4*w^2 + 13*w - 7],\ [547, 547, -w^3 - w^2 + 3*w + 5],\ [557, 557, 4*w - 1],\ [563, 563, 2*w^3 - w^2 - 6*w - 1],\ [571, 571, w^3 - w^2 - w - 3],\ [587, 587, -2*w^3 + 2*w^2 + 10*w + 1],\ [593, 593, 2*w^3 - 2*w^2 - 6*w + 3],\ [613, 613, -5*w^3 + 5*w^2 + 23*w - 7],\ [613, 613, -w^3 + w^2 + 5*w - 7],\ [617, 617, -w - 5],\ [619, 619, -3*w^3 + 4*w^2 + 11*w - 7],\ [625, 5, -5],\ [643, 643, -3*w^3 + 3*w^2 + 14*w - 9],\ [643, 643, -3*w^2 - 4*w + 1],\ [653, 653, -w^3 + w^2 + 9*w + 3],\ [653, 653, -4*w^2 + 6*w + 11],\ [659, 659, -w^2 - 4*w + 1],\ [661, 661, -3*w^3 + 3*w^2 + 15*w - 5],\ [661, 661, w^3 + w^2 - 7*w - 11],\ [673, 673, 2*w^3 - 3*w^2 - 12*w + 1],\ [673, 673, -2*w^3 + w^2 + 10*w - 3],\ [683, 683, -w^3 - 2*w^2 + 5*w + 11],\ [691, 691, 4*w^3 - 3*w^2 - 18*w + 5],\ [709, 709, w^3 - 3*w - 7],\ [719, 719, 2*w^3 - 8*w + 1],\ [727, 727, -3*w^3 + 6*w^2 + 13*w - 19],\ [733, 733, w^3 - w^2 + 3],\ [739, 739, -w^3 + w^2 + 3*w - 7],\ [751, 751, -w^2 - 3],\ [773, 773, 2*w^3 - 2*w^2 - 11*w + 3],\ [787, 787, w^3 - w^2 - 3*w - 5],\ [797, 797, -2*w^3 + 2*w^2 + 5*w - 1],\ [797, 797, -7*w^3 + 8*w^2 + 31*w - 15],\ [809, 809, 4*w^3 - 6*w^2 - 17*w + 13],\ [809, 809, 3*w^2 - 4*w - 5],\ [811, 811, 2*w^2 + 4*w + 3],\ [811, 811, -3*w^3 + 3*w^2 + 12*w - 5],\ [821, 821, 2*w^3 - 10*w - 1],\ [821, 821, 6*w^3 - 10*w^2 - 24*w + 29],\ [823, 823, -5*w^3 + 3*w^2 + 24*w - 1],\ [823, 823, w^3 + w^2 + w + 3],\ [827, 827, -4*w^3 + 3*w^2 + 16*w - 7],\ [829, 829, 2*w^3 - 4*w^2 - 6*w + 11],\ [841, 29, w^3 - 3*w^2 - 5*w + 3],\ [841, 29, -3*w^3 + 3*w^2 + 13*w - 1],\ [857, 857, -4*w^3 + 6*w^2 + 13*w - 7],\ [857, 857, -3*w^3 + w^2 + 15*w + 1],\ [859, 859, -4*w^2 + 3*w + 17],\ [863, 863, -4*w^3 + 8*w^2 + 14*w - 21],\ [877, 877, -w^3 - w^2 + 6*w - 1],\ [881, 881, -5*w - 1],\ [883, 883, -4*w^3 + 4*w^2 + 21*w - 13],\ [883, 883, 2*w^3 - 11*w - 1],\ [887, 887, -3*w^3 - w^2 + 8*w - 5],\ [907, 907, w^3 - w^2 - w + 5],\ [911, 911, 2*w^2 - 5*w - 5],\ [919, 919, -w^3 + 3*w^2 + 6*w - 3],\ [919, 919, 5*w^2 + 4*w - 9],\ [929, 929, w^3 + 3*w^2 - 8*w - 17],\ [937, 937, -4*w^3 + 4*w^2 + 17*w - 7],\ [953, 953, -2*w^3 + 2*w^2 + 7*w + 5],\ [953, 953, 3*w^3 - 4*w^2 - 11*w + 3],\ [967, 967, 4*w^3 - 2*w^2 - 17*w + 3],\ [971, 971, w^3 - 3*w^2 - 8*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 12*w + 13],\ [991, 991, -2*w^3 - 2*w^2 + 8*w + 7],\ [991, 991, w^3 + w^2 - 10*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^15 - 6*x^14 - 7*x^13 + 99*x^12 - 66*x^11 - 567*x^10 + 730*x^9 + 1359*x^8 - 2232*x^7 - 1376*x^6 + 2784*x^5 + 349*x^4 - 1291*x^3 + 189*x^2 + 81*x - 15 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/8*e^14 + 3/4*e^13 + 7/8*e^12 - 95/8*e^11 + 55/8*e^10 + 127/2*e^9 - 141/2*e^8 - 1091/8*e^7 + 709/4*e^6 + 129*e^5 - 167*e^4 - 55*e^3 + 52*e^2 + 11*e - 19/8, -1/4*e^14 + 5/4*e^13 + 21/8*e^12 - 41/2*e^11 + 5/8*e^10 + 465/4*e^9 - 311/4*e^8 - 275*e^7 + 993/4*e^6 + 2263/8*e^5 - 565/2*e^4 - 427/4*e^3 + 917/8*e^2 + 39/8*e - 61/8, -1, 1/8*e^14 - 3/8*e^13 - 9/4*e^12 + 7*e^11 + 57/4*e^10 - 48*e^9 - 71/2*e^8 + 1193/8*e^7 + 113/8*e^6 - 1683/8*e^5 + 279/4*e^4 + 929/8*e^3 - 157/2*e^2 - 21/2*e + 9, -5/8*e^14 + 29/8*e^13 + 21/4*e^12 - 497/8*e^11 + 227/8*e^10 + 1523/4*e^9 - 396*e^8 - 8311/8*e^7 + 10373/8*e^6 + 10759/8*e^5 - 13417/8*e^4 - 2875/4*e^3 + 6267/8*e^2 + 109/2*e - 367/8, 1/8*e^14 - 5/4*e^13 + 9/8*e^12 + 19*e^11 - 161/4*e^10 - 377/4*e^9 + 531/2*e^8 + 1385/8*e^7 - 2657/4*e^6 - 124*e^5 + 5705/8*e^4 + 193/8*e^3 - 2299/8*e^2 + 53/4*e + 16, -5/8*e^14 + 11/4*e^13 + 8*e^12 - 187/4*e^11 - 163/8*e^10 + 282*e^9 - 345/4*e^8 - 5959/8*e^7 + 1751/4*e^6 + 7269/8*e^5 - 5183/8*e^4 - 3555/8*e^3 + 1371/4*e^2 + 261/8*e - 171/8, 5/8*e^14 - 31/8*e^13 - 31/8*e^12 + 505/8*e^11 - 191/4*e^10 - 355*e^9 + 1905/4*e^8 + 6681/8*e^7 - 10943/8*e^6 - 1755/2*e^5 + 12675/8*e^4 + 1425/4*e^3 - 1327/2*e^2 - 65/8*e + 143/4, -1/8*e^14 + e^13 - 1/2*e^12 - 113/8*e^11 + 57/2*e^10 + 235/4*e^9 - 737/4*e^8 - 429/8*e^7 + 410*e^6 - 479/8*e^5 - 357*e^4 + 285/4*e^3 + 855/8*e^2 + 45/8*e - 25/2, -1/4*e^14 + 11/8*e^13 + 21/8*e^12 - 191/8*e^11 + 15/8*e^10 + 297/2*e^9 - 193/2*e^8 - 410*e^7 + 2699/8*e^6 + 4263/8*e^5 - 424*e^4 - 2509/8*e^3 + 365/2*e^2 + 275/4*e - 93/8, 3/4*e^14 - 17/4*e^13 - 45/8*e^12 + 271/4*e^11 - 307/8*e^10 - 1467/4*e^9 + 1747/4*e^8 + 804*e^7 - 4857/4*e^6 - 6107/8*e^5 + 5281/4*e^4 + 282*e^3 - 4107/8*e^2 - 187/8*e + 255/8, 1/2*e^14 - 5/2*e^13 - 25/4*e^12 + 183/4*e^11 + 19/2*e^10 - 307*e^9 + 297/2*e^8 + 1877/2*e^7 - 1405/2*e^6 - 5339/4*e^5 + 4407/4*e^4 + 3009/4*e^3 - 1193/2*e^2 - 225/4*e + 33, 1/4*e^14 - 7/8*e^13 - 4*e^12 + 31/2*e^11 + 167/8*e^10 - 99*e^9 - 137/4*e^8 + 281*e^7 - 195/8*e^6 - 1453/4*e^5 + 925/8*e^4 + 781/4*e^3 - 339/4*e^2 - 269/8*e + 45/8, 7/8*e^14 - 35/8*e^13 - 77/8*e^12 + 295/4*e^11 + 23/8*e^10 - 1755/4*e^9 + 1055/4*e^8 + 9061/8*e^7 - 7467/8*e^6 - 1337*e^5 + 4705/4*e^4 + 4905/8*e^3 - 4153/8*e^2 - 211/8*e + 203/8, -1/4*e^13 + 1/2*e^12 + 47/8*e^11 - 87/8*e^10 - 207/4*e^9 + 86*e^8 + 837/4*e^7 - 1181/4*e^6 - 383*e^5 + 3273/8*e^4 + 2243/8*e^3 - 1509/8*e^2 - 95/2*e + 65/8, -3/8*e^14 + 3/2*e^13 + 25/4*e^12 - 119/4*e^11 - 253/8*e^10 + 439/2*e^9 + 69/4*e^8 - 5929/8*e^7 + 525/2*e^6 + 9093/8*e^5 - 4847/8*e^4 - 5529/8*e^3 + 773/2*e^2 + 643/8*e - 181/8, 5/8*e^14 - 35/8*e^13 - 13/8*e^12 + 69*e^11 - 665/8*e^10 - 1469/4*e^9 + 2649/4*e^8 + 6283/8*e^7 - 13987/8*e^6 - 2951/4*e^5 + 7575/4*e^4 + 2141/8*e^3 - 5943/8*e^2 + 35/8*e + 323/8, -1/2*e^14 + 7/4*e^13 + 17/2*e^12 - 261/8*e^11 - 395/8*e^10 + 897/4*e^9 + 106*e^8 - 2821/4*e^7 - 61/4*e^6 + 2059/2*e^5 - 1631/8*e^4 - 4825/8*e^3 + 1479/8*e^2 + 129/2*e - 107/8, -3/4*e^13 + 9/4*e^12 + 13*e^11 - 79/2*e^10 - 163/2*e^9 + 249*e^8 + 234*e^7 - 2767/4*e^6 - 1363/4*e^5 + 3423/4*e^4 + 239*e^3 - 1589/4*e^2 - 51*e + 55/2, -5/8*e^14 + 13/4*e^13 + 53/8*e^12 - 219/4*e^11 + 5/4*e^10 + 1305/4*e^9 - 200*e^8 - 6813/8*e^7 + 2673/4*e^6 + 4193/4*e^5 - 6539/8*e^4 - 4311/8*e^3 + 2963/8*e^2 + 111/2*e - 57/2, -7/4*e^14 + 75/8*e^13 + 137/8*e^12 - 159*e^11 + 137/4*e^10 + 3823/4*e^9 - 802*e^8 - 10051/4*e^7 + 21627/8*e^6 + 24467/8*e^5 - 27693/8*e^4 - 6045/4*e^3 + 12683/8*e^2 + 237/2*e - 375/4, 3/8*e^14 - 5/4*e^13 - 27/4*e^12 + 93/4*e^11 + 351/8*e^10 - 315/2*e^9 - 495/4*e^8 + 3797/8*e^7 + 527/4*e^6 - 5017/8*e^5 + 185/8*e^4 + 2453/8*e^3 - 93*e^2 - 117/8*e + 67/8, -5/8*e^14 + 7/2*e^13 + 27/4*e^12 - 253/4*e^11 + 45/8*e^10 + 835/2*e^9 - 1145/4*e^8 - 10023/8*e^7 + 2251/2*e^6 + 14107/8*e^5 - 13241/8*e^4 - 8015/8*e^3 + 1753/2*e^2 + 669/8*e - 499/8, 3/8*e^14 - 5/4*e^13 - 53/8*e^12 + 93/4*e^11 + 83/2*e^10 - 633/4*e^9 - 215/2*e^8 + 3871/8*e^7 + 331/4*e^6 - 657*e^5 + 729/8*e^4 + 2553/8*e^3 - 1079/8*e^2 - 39/4*e + 37/4, 9/8*e^14 - 23/4*e^13 - 12*e^12 + 387/4*e^11 - 17/8*e^10 - 575*e^9 + 1481/4*e^8 + 11931/8*e^7 - 5103/4*e^6 - 14481/8*e^5 + 13043/8*e^4 + 7271/8*e^3 - 3099/4*e^2 - 609/8*e + 471/8, -1/8*e^14 - 5/8*e^13 + 13/2*e^12 + 5*e^11 - 81*e^10 + 43/2*e^9 + 386*e^8 - 2037/8*e^7 - 5825/8*e^6 + 4461/8*e^5 + 1981/4*e^4 - 3105/8*e^3 - 181/4*e^2 + 233/4*e - 17/4, 3/4*e^14 - 31/8*e^13 - 71/8*e^12 + 559/8*e^11 + 55/8*e^10 - 459*e^9 + 256*e^8 + 1362*e^7 - 8727/8*e^6 - 14957/8*e^5 + 1606*e^4 + 8113/8*e^3 - 3271/4*e^2 - 151/2*e + 399/8, -e^14 + 7*e^13 + 13/4*e^12 - 451/4*e^11 + 249/2*e^10 + 624*e^9 - 2065/2*e^8 - 1444*e^7 + 2823*e^6 + 6217/4*e^5 - 12783/4*e^4 - 2943/4*e^3 + 2677/2*e^2 + 325/4*e - 84, -e^14 + 33/8*e^13 + 119/8*e^12 - 149/2*e^11 - 127/2*e^10 + 1961/4*e^9 + 15/2*e^8 - 2915/2*e^7 + 3809/8*e^6 + 16051/8*e^5 - 7733/8*e^4 - 1108*e^3 + 4705/8*e^2 + 417/4*e - 61/2, -1/8*e^14 + 7/8*e^13 - 5/8*e^12 - 81/8*e^11 + 111/4*e^10 + 18*e^9 - 609/4*e^8 + 907/8*e^7 + 1719/8*e^6 - 645/2*e^5 + 233/8*e^4 + 841/4*e^3 - 142*e^2 + 17/8*e + 21/4, -3/8*e^14 + 9/8*e^13 + 53/8*e^12 - 147/8*e^11 - 183/4*e^10 + 101*e^9 + 689/4*e^8 - 1663/8*e^7 - 3247/8*e^6 + 105*e^5 + 4023/8*e^4 + 287/4*e^3 - 467/2*e^2 - 149/8*e + 63/4, 1/2*e^14 - 15/8*e^13 - 17/2*e^12 + 34*e^11 + 417/8*e^10 - 224*e^9 - 583/4*e^8 + 2647/4*e^7 + 1581/8*e^6 - 895*e^5 - 697/8*e^4 + 991/2*e^3 - 131/4*e^2 - 555/8*e + 7/8, 3/8*e^14 - 25/8*e^13 + 9/8*e^12 + 185/4*e^11 - 641/8*e^10 - 861/4*e^9 + 2119/4*e^8 + 2569/8*e^7 - 9641/8*e^6 - 307/4*e^5 + 1076*e^4 - 743/8*e^3 - 2523/8*e^2 + 125/8*e + 163/8, 3/8*e^14 - 23/8*e^13 - 3/8*e^12 + 383/8*e^11 - 257/4*e^10 - 565/2*e^9 + 2087/4*e^8 + 5943/8*e^7 - 12143/8*e^6 - 3907/4*e^5 + 14947/8*e^4 + 2291/4*e^3 - 3373/4*e^2 - 411/8*e + 181/4, -1/4*e^14 + 9/4*e^13 - 1/2*e^12 - 311/8*e^11 + 469/8*e^10 + 963/4*e^9 - 941/2*e^8 - 663*e^7 + 5745/4*e^6 + 3409/4*e^5 - 14943/8*e^4 - 3513/8*e^3 + 7133/8*e^2 + 91/4*e - 435/8, -1/4*e^14 + 3/2*e^13 + 15/8*e^12 - 27*e^11 + 149/8*e^10 + 711/4*e^9 - 927/4*e^8 - 534*e^7 + 1621/2*e^6 + 6065/8*e^5 - 4397/4*e^4 - 1781/4*e^3 + 4015/8*e^2 + 343/8*e - 141/8, -5/4*e^14 + 45/8*e^13 + 33/2*e^12 - 197/2*e^11 - 361/8*e^10 + 618*e^9 - 733/4*e^8 - 3409/2*e^7 + 8297/8*e^6 + 8383/4*e^5 - 12907/8*e^4 - 3787/4*e^3 + 3359/4*e^2 + 123/8*e - 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53/4*e^13 - 43/2*e^12 + 439/2*e^11 - 517/8*e^10 - 2539/2*e^9 + 4379/4*e^8 + 25077/8*e^7 - 13201/4*e^6 - 28207/8*e^5 + 30275/8*e^4 + 12567/8*e^3 - 3043/2*e^2 - 675/8*e + 579/8, 9/8*e^14 - 6*e^13 - 53/4*e^12 + 443/4*e^11 + 43/8*e^10 - 1503/2*e^9 + 1797/4*e^8 + 18635/8*e^7 - 1945*e^6 - 26963/8*e^5 + 23645/8*e^4 + 15855/8*e^3 - 3101/2*e^2 - 1681/8*e + 891/8, 1/8*e^14 - 7/8*e^13 - 1/8*e^12 + 95/8*e^11 - 67/4*e^10 - 42*e^9 + 407/4*e^8 - 147/8*e^7 - 1087/8*e^6 + 979/4*e^5 - 739/8*e^4 - 569/2*e^3 + 183*e^2 + 521/8*e - 31/4, 33/8*e^14 - 167/8*e^13 - 347/8*e^12 + 2779/8*e^11 - 33/2*e^10 - 4047/2*e^9 + 5561/4*e^8 + 40393/8*e^7 - 37367/8*e^6 - 11449/2*e^5 + 46313/8*e^4 + 2555*e^3 - 10403/4*e^2 - 917/8*e + 144, -1/2*e^14 + 3*e^13 + 25/8*e^12 - 205/4*e^11 + 347/8*e^10 + 1259/4*e^9 - 1847/4*e^8 - 3491/4*e^7 + 1489*e^6 + 9349/8*e^5 - 7855/4*e^4 - 2411/4*e^3 + 7671/8*e^2 - 317/8*e - 451/8, -11/8*e^14 + 31/4*e^13 + 23/2*e^12 - 1037/8*e^11 + 60*e^10 + 3051/4*e^9 - 3317/4*e^8 - 15535/8*e^7 + 10623/4*e^6 + 18139/8*e^5 - 3401*e^4 - 2011/2*e^3 + 12711/8*e^2 - 15/8*e - 171/2, -15/8*e^14 + 45/4*e^13 + 13*e^12 - 737/4*e^11 + 951/8*e^10 + 1051*e^9 - 5087/4*e^8 - 20605/8*e^7 + 14589/4*e^6 + 24183/8*e^5 - 33109/8*e^4 - 12865/8*e^3 + 6641/4*e^2 + 1703/8*e - 649/8, -e^14 + 4*e^13 + 59/4*e^12 - 143/2*e^11 - 243/4*e^10 + 927/2*e^9 - 33/2*e^8 - 2691/2*e^7 + 582*e^6 + 7079/4*e^5 - 2415/2*e^4 - 1705/2*e^3 + 3241/4*e^2 + 49/4*e - 229/4, -11/8*e^14 + 75/8*e^13 + 29/8*e^12 - 1169/8*e^11 + 731/4*e^10 + 1517/2*e^9 - 5853/4*e^8 - 12167/8*e^7 + 31155/8*e^6 + 1200*e^5 - 34249/8*e^4 - 224*e^3 + 6845/4*e^2 - 695/8*e - 369/4, -e^14 + 47/8*e^13 + 109/8*e^12 - 963/8*e^11 - 171/8*e^10 + 1839/2*e^9 - 437*e^8 - 12829/4*e^7 + 18911/8*e^6 + 40069/8*e^5 - 16305/4*e^4 - 23487/8*e^3 + 2339*e^2 + 327/2*e - 919/8, 7/4*e^14 - 85/8*e^13 - 103/8*e^12 + 177*e^11 - 401/4*e^10 - 4153/4*e^9 + 1142*e^8 + 10639/4*e^7 - 26981/8*e^6 - 26049/8*e^5 + 31751/8*e^4 + 6773/4*e^3 - 13533/8*e^2 - 138*e + 303/4, 1/4*e^14 - 3/4*e^13 - 11/2*e^12 + 69/4*e^11 + 167/4*e^10 - 287/2*e^9 - 118*e^8 + 2063/4*e^7 + 161/4*e^6 - 2979/4*e^5 + 819/4*e^4 + 719/2*e^3 - 671/4*e^2 - 31/2*e + 17/4, 37/8*e^14 - 99/4*e^13 - 45*e^12 + 1657/4*e^11 - 665/8*e^10 - 2439*e^9 + 7893/4*e^8 + 49735/8*e^7 - 25655/4*e^6 - 58693/8*e^5 + 63859/8*e^4 + 28447/8*e^3 - 14561/4*e^2 - 2597/8*e + 1823/8, -5/8*e^13 + 7/4*e^12 + 33/4*e^11 - 185/8*e^10 - 29*e^9 + 321/4*e^8 + 31/4*e^7 + 55/8*e^6 + 95/4*e^5 - 2101/8*e^4 + 227/4*e^3 + 833/4*e^2 - 751/8*e - 195/8, 15/4*e^14 - 157/8*e^13 - 327/8*e^12 + 1367/4*e^11 - 10*e^10 - 8555/4*e^9 + 1411*e^8 + 23873/4*e^7 - 42381/8*e^6 - 62193/8*e^5 + 58421/8*e^4 + 8211/2*e^3 - 28767/8*e^2 - 352*e + 230, 3*e^13 - 41/4*e^12 - 187/4*e^11 + 171*e^10 + 246*e^9 - 1991/2*e^8 - 535*e^7 + 2444*e^6 + 2403/4*e^5 - 10295/4*e^4 - 1479/4*e^3 + 967*e^2 + 311/4*e - 129/2, -2*e^14 + 97/8*e^13 + 119/8*e^12 - 1613/8*e^11 + 895/8*e^10 + 2353/2*e^9 - 1291*e^8 - 11883/4*e^7 + 30689/8*e^6 + 28207/8*e^5 - 18271/4*e^4 - 14257/8*e^3 + 3985/2*e^2 + 194*e - 981/8, -3/8*e^14 + 9/4*e^13 + 3*e^12 - 165/4*e^11 + 187/8*e^10 + 284*e^9 - 1235/4*e^8 - 7545/8*e^7 + 4325/4*e^6 + 12955/8*e^5 - 11977/8*e^4 - 10093/8*e^3 + 2985/4*e^2 + 1971/8*e - 461/8, -13/4*e^14 + 151/8*e^13 + 199/8*e^12 - 2489/8*e^11 + 1387/8*e^10 + 3571/2*e^9 - 2075*e^8 - 4355*e^7 + 50031/8*e^6 + 38649/8*e^5 - 29923/4*e^4 - 17423/8*e^3 + 6503/2*e^2 + 369/2*e - 1605/8, 11/4*e^14 - 101/8*e^13 - 249/8*e^12 + 1609/8*e^11 + 321/8*e^10 - 1084*e^9 + 494*e^8 + 4665/2*e^7 - 11997/8*e^6 - 16551/8*e^5 + 1341*e^4 + 5107/8*e^3 - 1349/4*e^2 - 161/2*e + 129/8, e^14 - 9/2*e^13 - 121/8*e^12 + 691/8*e^11 + 235/4*e^10 - 1219/2*e^9 + 423/4*e^8 + 1931*e^7 - 1110*e^6 - 21417/8*e^5 + 17475/8*e^4 + 10435/8*e^3 - 5561/4*e^2 + 195/8*e + 185/2, 1/4*e^14 - 1/8*e^13 - 35/8*e^12 - 5*e^11 + 153/4*e^10 + 383/4*e^9 - 237*e^8 - 2019/4*e^7 + 6879/8*e^6 + 7399/8*e^5 - 10281/8*e^4 - 2153/4*e^3 + 4919/8*e^2 - 27/2*e - 95/4] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([13, 13, -w^2 + 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]