/* 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([6, 0, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13,13,-w^3 + 4*w + 1]) primes_array = [ [2, 2, -w^2 + w + 2],\ [3, 3, w^2 - w - 3],\ [11, 11, -w^2 + w + 1],\ [11, 11, -w^2 - w + 1],\ [13, 13, w^3 - 4*w + 1],\ [13, 13, -w^3 + 4*w + 1],\ [25, 5, -w^2 - 2*w + 1],\ [25, 5, w^2 - 2*w - 1],\ [37, 37, w^3 - 3*w - 1],\ [37, 37, w^3 - 3*w + 1],\ [59, 59, w^2 - w - 5],\ [59, 59, -w^2 - w + 5],\ [61, 61, -w^3 + w^2 + 4*w - 7],\ [61, 61, w^3 - 3*w^2 - 6*w + 11],\ [73, 73, 2*w^2 - w - 5],\ [73, 73, 2*w - 1],\ [73, 73, -2*w - 1],\ [73, 73, 2*w^2 + w - 5],\ [83, 83, 2*w^3 + w^2 - 9*w - 7],\ [83, 83, -2*w^3 + w^2 + 7*w + 1],\ [107, 107, w^3 + w^2 - 4*w - 1],\ [107, 107, -w^3 + w^2 + 4*w - 1],\ [109, 109, -w^3 + 2*w^2 + 5*w - 11],\ [109, 109, w^3 + 2*w^2 - 5*w - 11],\ [121, 11, 2*w^2 - 5],\ [131, 131, 3*w^3 - 2*w^2 - 14*w + 11],\ [131, 131, 3*w^3 - 12*w + 5],\ [157, 157, -3*w^3 + 2*w^2 + 13*w - 11],\ [157, 157, -w^3 + 2*w^2 + 7*w - 5],\ [167, 167, w^2 + 2*w - 5],\ [167, 167, -w^3 + w^2 + w + 1],\ [167, 167, 3*w^3 - w^2 - 9*w - 5],\ [167, 167, w^2 - 2*w - 5],\ [169, 13, -w^2 + 7],\ [179, 179, -w^3 + w^2 + 6*w - 1],\ [179, 179, w^3 + w^2 - 6*w - 1],\ [181, 181, -w^3 + 5*w - 5],\ [181, 181, w^3 - 5*w - 5],\ [191, 191, -2*w^3 + 2*w^2 + 6*w - 1],\ [191, 191, -2*w^2 + 2*w + 7],\ [191, 191, -4*w^2 + 4*w + 11],\ [191, 191, -2*w^3 + 8*w + 5],\ [227, 227, -w^3 + 2*w^2 + 5*w - 5],\ [227, 227, w^3 + 2*w^2 - 5*w - 5],\ [229, 229, -w^3 + 3*w + 5],\ [229, 229, -w^3 - 4*w^2 + 7*w + 13],\ [239, 239, -w^3 + w^2 + 5*w - 1],\ [239, 239, 2*w^3 - 4*w^2 - 12*w + 13],\ [239, 239, 2*w^3 - 2*w^2 - 10*w + 7],\ [239, 239, w^3 + w^2 - 5*w - 1],\ [241, 241, 2*w^3 - w^2 - 8*w + 5],\ [241, 241, -3*w^2 + 4*w + 7],\ [241, 241, -2*w^3 + w^2 + 6*w + 1],\ [241, 241, -2*w^3 - w^2 + 8*w + 5],\ [251, 251, -w^3 + 2*w - 5],\ [251, 251, 3*w^3 - 2*w^2 - 12*w + 13],\ [263, 263, 2*w^3 - 2*w^2 - 8*w + 11],\ [263, 263, -w^3 + w^2 + 3*w - 7],\ [263, 263, 3*w^3 - w^2 - 11*w + 11],\ [263, 263, -2*w^3 + 6*w - 7],\ [277, 277, -3*w^2 - w + 11],\ [277, 277, 3*w^2 - w - 11],\ [311, 311, -w^3 + 5*w^2 + 7*w - 19],\ [311, 311, 2*w^3 - 3*w^2 - 8*w + 17],\ [311, 311, -2*w^3 + 6*w - 5],\ [311, 311, -2*w^3 - 2*w^2 + 8*w + 5],\ [337, 337, -2*w^3 + 8*w + 1],\ [337, 337, -w^3 + 3*w^2 + 5*w - 11],\ [337, 337, w^3 + 3*w^2 - 5*w - 11],\ [337, 337, 2*w^3 - 8*w + 1],\ [347, 347, w^3 - 3*w^2 - 6*w + 13],\ [347, 347, -w^3 - 3*w^2 + 6*w + 13],\ [349, 349, -w^3 + 4*w - 5],\ [349, 349, w^3 - 4*w - 5],\ [361, 19, 4*w^3 - 2*w^2 - 17*w + 13],\ [361, 19, 2*w^3 - 2*w^2 - 11*w + 7],\ [373, 373, -2*w^3 - 5*w^2 + 13*w + 17],\ [373, 373, 2*w^3 - w^2 - 7*w + 1],\ [383, 383, 4*w^3 - w^2 - 16*w + 13],\ [383, 383, w^2 + 2*w - 7],\ [383, 383, w^2 - 2*w - 7],\ [383, 383, 2*w^3 + 3*w^2 - 6*w - 5],\ [397, 397, -w^3 + 2*w^2 + 7*w - 7],\ [397, 397, w^3 + 2*w^2 - 7*w - 7],\ [419, 419, 5*w^2 - 5*w - 11],\ [419, 419, 3*w^2 - 3*w - 5],\ [421, 421, w^3 + 4*w^2 - 5*w - 17],\ [421, 421, -w^3 + 4*w^2 + 5*w - 17],\ [433, 433, w^3 - w^2 - 7*w + 1],\ [433, 433, 3*w - 1],\ [433, 433, -3*w - 1],\ [433, 433, 5*w^3 - 3*w^2 - 21*w + 19],\ [443, 443, w^3 - 4*w^2 - 6*w + 17],\ [443, 443, -3*w^3 + 6*w^2 + 16*w - 25],\ [467, 467, -w^3 + w^2 + 2*w - 5],\ [467, 467, w^3 + w^2 - 2*w - 5],\ [491, 491, 3*w^3 - w^2 - 14*w + 7],\ [491, 491, -3*w^3 - w^2 + 14*w + 7],\ [529, 23, 3*w^2 - 11],\ [529, 23, 3*w^2 - 7],\ [541, 541, 3*w^3 + 2*w^2 - 10*w - 1],\ [541, 541, 3*w^3 - 4*w^2 - 16*w + 17],\ [563, 563, w^3 + 2*w^2 - 2*w - 7],\ [563, 563, -w^3 + 2*w^2 + 2*w - 7],\ [587, 587, -2*w^3 + w^2 + 5*w - 5],\ [587, 587, 2*w^3 + w^2 - 5*w - 5],\ [613, 613, 3*w^3 - 13*w - 1],\ [613, 613, 3*w^3 - 13*w + 1],\ [659, 659, w^3 + 3*w^2 - 4*w - 5],\ [659, 659, -w^3 + 3*w^2 + 4*w - 5],\ [661, 661, w^3 + 4*w^2 - 9*w - 13],\ [661, 661, -3*w^3 + 4*w^2 + 7*w - 5],\ [673, 673, -2*w^3 + 7*w + 1],\ [673, 673, w^3 + w^2 - 7*w - 5],\ [673, 673, -w^3 + w^2 + 7*w - 5],\ [673, 673, 2*w^3 - 7*w + 1],\ [683, 683, -2*w^3 - w^2 + 9*w + 1],\ [683, 683, 2*w^3 - w^2 - 9*w + 1],\ [709, 709, -3*w^3 + 2*w^2 + 8*w + 1],\ [709, 709, -w^3 + 4*w^2 - 2*w - 7],\ [733, 733, 2*w^3 - 5*w^2 - 11*w + 19],\ [733, 733, -2*w^3 + w^2 + 7*w - 11],\ [743, 743, 2*w^3 + 2*w^2 - 11*w - 5],\ [743, 743, 2*w^3 - w^2 - 8*w - 1],\ [743, 743, -2*w^3 - w^2 + 8*w - 1],\ [743, 743, -2*w^3 + 2*w^2 + 11*w - 5],\ [757, 757, 2*w^3 + 3*w^2 - 3*w + 1],\ [757, 757, -2*w^3 + 5*w^2 + 11*w - 17],\ [827, 827, -5*w^3 + 4*w^2 + 21*w - 23],\ [827, 827, -w^3 + w - 7],\ [829, 829, 2*w^3 - 3*w^2 - 9*w + 17],\ [829, 829, -2*w^3 - 3*w^2 + 9*w + 17],\ [841, 29, 2*w^2 - w - 13],\ [841, 29, 2*w^2 + w - 13],\ [853, 853, -w^3 + 6*w - 7],\ [853, 853, -2*w^3 + w^2 + 11*w - 5],\ [863, 863, w^3 - 5*w^2 - 9*w + 13],\ [863, 863, 2*w^3 + 4*w^2 - 5*w - 11],\ [863, 863, -2*w^3 + 4*w^2 + 5*w - 11],\ [863, 863, w^3 - 3*w^2 - 7*w + 7],\ [877, 877, -w^3 - 3*w^2 + 4*w + 17],\ [877, 877, w^3 - 3*w^2 - 4*w + 17],\ [887, 887, -2*w^3 - w^2 + 10*w + 1],\ [887, 887, 2*w^3 + 2*w^2 - 9*w - 5],\ [887, 887, -2*w^3 + 2*w^2 + 9*w - 5],\ [887, 887, 2*w^3 - w^2 - 10*w + 1],\ [911, 911, -2*w^3 + 11*w - 5],\ [911, 911, -w^3 + w^2 + w - 5],\ [911, 911, w^3 + w^2 - w - 5],\ [911, 911, 2*w^3 - 11*w - 5],\ [937, 937, -4*w^3 - 2*w^2 + 16*w + 17],\ [937, 937, 3*w^3 - w^2 - 11*w - 1],\ [937, 937, -3*w^3 - 5*w^2 + 17*w + 19],\ [937, 937, -4*w^2 + 2*w + 13],\ [947, 947, -3*w^3 + 2*w^2 + 10*w + 1],\ [947, 947, 3*w^3 - 12*w - 7],\ [971, 971, w^3 + w^2 - 2*w - 7],\ [971, 971, -w^3 + w^2 + 2*w - 7],\ [983, 983, -w^3 - 3*w^2 + 7*w + 13],\ [983, 983, 2*w^3 - 2*w^2 - 7*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 7*w + 1],\ [983, 983, w^3 - 7*w^2 + 3*w + 17],\ [997, 997, -w^3 + 2*w^2 + 4*w - 13],\ [997, 997, 3*w^3 - 8*w^2 - 18*w + 29]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^14 - 23*x^12 + 209*x^10 - 953*x^8 + 2293*x^6 - 2811*x^4 + 1529*x^2 - 261 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/24*e^13 + 5/6*e^11 - 149/24*e^9 + 253/12*e^7 - 775/24*e^5 + 85/4*e^3 - 191/24*e, -1/12*e^13 + 5/3*e^11 - 155/12*e^9 + 295/6*e^7 - 1147/12*e^5 + 173/2*e^3 - 305/12*e, 1/6*e^13 - 43/12*e^11 + 355/12*e^9 - 701/6*e^7 + 1345/6*e^5 - 759/4*e^3 + 619/12*e, -1/4*e^12 + 5*e^10 - 151/4*e^8 + 265/2*e^6 - 855/4*e^4 + 271/2*e^2 - 85/4, -1, -3/8*e^12 + 15/2*e^10 - 451/8*e^8 + 783/4*e^6 - 2477/8*e^4 + 765/4*e^2 - 257/8, 1/4*e^12 - 5*e^10 + 149/4*e^8 - 251/2*e^6 + 727/4*e^4 - 169/2*e^2 + 31/4, -3/8*e^12 + 33/4*e^10 - 549/8*e^8 + 1065/4*e^6 - 3845/8*e^4 + 717/2*e^2 - 627/8, -1/4*e^10 + 15/4*e^8 - 37/2*e^6 + 32*e^4 - 43/4*e^2 - 9/4, 1/12*e^13 - 5/3*e^11 + 143/12*e^9 - 205/6*e^7 + 271/12*e^5 + 73/2*e^3 - 271/12*e, -7/24*e^13 + 73/12*e^11 - 1145/24*e^9 + 2065/12*e^7 - 6649/24*e^5 + 317/2*e^3 - 239/24*e, -1/8*e^12 + 5/2*e^10 - 149/8*e^8 + 249/4*e^6 - 703/8*e^4 + 167/4*e^2 - 47/8, -1/4*e^10 + 15/4*e^8 - 39/2*e^6 + 44*e^4 - 203/4*e^2 + 107/4, -1/4*e^12 + 5*e^10 - 149/4*e^8 + 253/2*e^6 - 775/4*e^4 + 247/2*e^2 - 119/4, 1/2*e^12 - 10*e^10 + 151/2*e^8 - 266*e^6 + 873/2*e^4 - 291*e^2 + 117/2, -3/8*e^12 + 33/4*e^10 - 553/8*e^8 + 1089/4*e^6 - 4021/8*e^4 + 767/2*e^2 - 663/8, -e^6 + 10*e^4 - 28*e^2 + 21, 1/8*e^13 - 9/4*e^11 + 115/8*e^9 - 147/4*e^7 + 175/8*e^5 + 33*e^3 - 155/8*e, -1/24*e^13 + 5/6*e^11 - 149/24*e^9 + 253/12*e^7 - 823/24*e^5 + 145/4*e^3 - 695/24*e, 5/12*e^13 - 103/12*e^11 + 401/6*e^9 - 727/3*e^7 + 4859/12*e^5 - 1061/4*e^3 + 112/3*e, 1/12*e^13 - 5/3*e^11 + 143/12*e^9 - 205/6*e^7 + 271/12*e^5 + 69/2*e^3 - 199/12*e, -1/8*e^12 + 13/4*e^10 - 243/8*e^8 + 503/4*e^6 - 1791/8*e^4 + 138*e^2 - 93/8, 1/4*e^12 - 23/4*e^10 + 97/2*e^8 - 181*e^6 + 1127/4*e^4 - 571/4*e^2 + 21, 1/8*e^12 - 5/2*e^10 + 153/8*e^8 - 277/4*e^6 + 943/8*e^4 - 331/4*e^2 + 171/8, -1/24*e^13 + 13/12*e^11 - 275/24*e^9 + 739/12*e^7 - 4087/24*e^5 + 215*e^3 - 2165/24*e, -1/2*e^13 + 21/2*e^11 - 83*e^9 + 302*e^7 - 985/2*e^5 + 595/2*e^3 - 36*e, 3/8*e^12 - 8*e^10 + 515/8*e^8 - 963/4*e^6 + 3317/8*e^4 - 1131/4*e^2 + 417/8, -1/8*e^12 + 13/4*e^10 - 235/8*e^8 + 447/4*e^6 - 1303/8*e^4 + 57*e^2 + 11/8, -1/8*e^13 + 13/4*e^11 - 255/8*e^9 + 591/4*e^7 - 2647/8*e^5 + 329*e^3 - 897/8*e, 3/4*e^13 - 31/2*e^11 + 485/4*e^9 - 885/2*e^7 + 2989/4*e^5 - 505*e^3 + 367/4*e, -1/8*e^13 + 5/2*e^11 - 157/8*e^9 + 313/4*e^7 - 1367/8*e^5 + 771/4*e^3 - 583/8*e, -5/8*e^13 + 53/4*e^11 - 855/8*e^9 + 1623/4*e^7 - 5795/8*e^5 + 531*e^3 - 809/8*e, 1/2*e^12 - 10*e^10 + 151/2*e^8 - 266*e^6 + 869/2*e^4 - 279*e^2 + 81/2, -1/6*e^13 + 23/6*e^11 - 100/3*e^9 + 406/3*e^7 - 1531/6*e^5 + 381/2*e^3 - 67/3*e, -5/12*e^13 + 53/6*e^11 - 853/12*e^9 + 1607/6*e^7 - 5615/12*e^5 + 321*e^3 - 619/12*e, 5/8*e^12 - 25/2*e^10 + 753/8*e^8 - 1313/4*e^6 + 4171/8*e^4 - 1251/4*e^2 + 363/8, -1/2*e^12 + 39/4*e^10 - 283/4*e^8 + 465/2*e^6 - 659/2*e^4 + 585/4*e^2 - 7/4, 7/12*e^13 - 73/6*e^11 + 1157/12*e^9 - 2155/6*e^7 + 7549/12*e^5 - 459*e^3 + 1283/12*e, 1/3*e^13 - 83/12*e^11 + 647/12*e^9 - 1159/6*e^7 + 937/3*e^5 - 823/4*e^3 + 767/12*e, 1/12*e^13 - 7/6*e^11 + 47/12*e^9 + 59/6*e^7 - 881/12*e^5 + 109*e^3 - 427/12*e, 1/6*e^13 - 49/12*e^11 + 451/12*e^9 - 971/6*e^7 + 1993/6*e^5 - 1197/4*e^3 + 919/12*e, -1/12*e^13 + 7/6*e^11 - 41/12*e^9 - 101/6*e^7 + 1253/12*e^5 - 154*e^3 + 553/12*e, -11/24*e^13 + 113/12*e^11 - 1789/24*e^9 + 3413/12*e^7 - 12749/24*e^5 + 857/2*e^3 - 2395/24*e, 3/4*e^12 - 15*e^10 + 457/4*e^8 - 825/2*e^6 + 2849/4*e^4 - 1045/2*e^2 + 515/4, 1/4*e^12 - 23/4*e^10 + 99/2*e^8 - 195*e^6 + 1383/4*e^4 - 1003/4*e^2 + 78, -1/2*e^13 + 11*e^11 - 183/2*e^9 + 356*e^7 - 1305/2*e^5 + 518*e^3 - 289/2*e, 1/8*e^13 - 9/4*e^11 + 119/8*e^9 - 175/4*e^7 + 431/8*e^5 - 20*e^3 + 49/8*e, -13/24*e^13 + 34/3*e^11 - 2129/24*e^9 + 3805/12*e^7 - 12043/24*e^5 + 1147/4*e^3 - 803/24*e, 1/12*e^13 - 29/12*e^11 + 157/6*e^9 - 401/3*e^7 + 3943/12*e^5 - 1375/4*e^3 + 293/3*e, e^12 - 20*e^10 + 152*e^8 - 546*e^6 + 938*e^4 - 692*e^2 + 155, -1/2*e^12 + 10*e^10 - 147/2*e^8 + 237*e^6 - 605/2*e^4 + 88*e^2 + 11/2, e^12 - 41/2*e^10 + 315/2*e^8 - 555*e^6 + 877*e^4 - 1053/2*e^2 + 185/2, -1/4*e^10 + 19/4*e^8 - 65/2*e^6 + 94*e^4 - 399/4*e^2 + 127/4, 1/6*e^13 - 17/6*e^11 + 46/3*e^9 - 49/3*e^7 - 575/6*e^5 + 491/2*e^3 - 350/3*e, -1/24*e^13 + 13/12*e^11 - 227/24*e^9 + 391/12*e^7 - 751/24*e^5 - 31*e^3 + 1051/24*e, 1/12*e^13 - 23/12*e^11 + 97/6*e^9 - 182/3*e^7 + 1147/12*e^5 - 181/4*e^3 + 2/3*e, 5/12*e^13 - 53/6*e^11 + 847/12*e^9 - 1571/6*e^7 + 5375/12*e^5 - 310*e^3 + 805/12*e, 1/2*e^13 - 21/2*e^11 + 83*e^9 - 303*e^7 + 1007/2*e^5 - 669/2*e^3 + 73*e, -1/8*e^13 + 3*e^11 - 217/8*e^9 + 461/4*e^7 - 1903/8*e^5 + 945/4*e^3 - 779/8*e, 3/2*e^10 - 23*e^8 + 119*e^6 - 235*e^4 + 297/2*e^2 - 19, -1/8*e^12 + 2*e^10 - 73/8*e^8 - 7/4*e^6 + 761/8*e^4 - 651/4*e^2 + 341/8, 1/12*e^13 - 13/6*e^11 + 239/12*e^9 - 475/6*e^7 + 1579/12*e^5 - 80*e^3 + 101/12*e, 7/24*e^13 - 67/12*e^11 + 953/24*e^9 - 1525/12*e^7 + 4105/24*e^5 - 61*e^3 - 265/24*e, -5/12*e^13 + 25/3*e^11 - 745/12*e^9 + 1247/6*e^7 - 3491/12*e^5 + 229/2*e^3 + 89/12*e, -1/2*e^11 + 9*e^9 - 60*e^7 + 182*e^5 - 493/2*e^3 + 116*e, e^12 - 41/2*e^10 + 321/2*e^8 - 595*e^6 + 1047*e^4 - 1549/2*e^2 + 371/2, 1/4*e^12 - 21/4*e^10 + 85/2*e^8 - 166*e^6 + 1263/4*e^4 - 993/4*e^2 + 39, -11/8*e^12 + 111/4*e^10 - 1689/8*e^8 + 2977/4*e^6 - 9573/8*e^4 + 745*e^2 - 935/8, 1/4*e^12 - 6*e^10 + 213/4*e^8 - 433/2*e^6 + 1619/4*e^4 - 629/2*e^2 + 307/4, -3/4*e^13 + 31/2*e^11 - 481/4*e^9 + 855/2*e^7 - 2685/4*e^5 + 358*e^3 - 3/4*e, e^11 - 35/2*e^9 + 111*e^7 - 311*e^5 + 376*e^3 - 295/2*e, -1/4*e^12 + 9/2*e^10 - 117/4*e^8 + 159/2*e^6 - 279/4*e^4 - 7*e^2 - 47/4, e^12 - 20*e^10 + 303/2*e^8 - 540*e^6 + 913*e^4 - 648*e^2 + 281/2, 1/8*e^12 - 9/4*e^10 + 127/8*e^8 - 231/4*e^6 + 935/8*e^4 - 108*e^2 + 113/8, 1/4*e^12 - 11/2*e^10 + 183/4*e^8 - 359/2*e^6 + 1359/4*e^4 - 291*e^2 + 361/4, -1/2*e^12 + 19/2*e^10 - 133/2*e^8 + 207*e^6 - 537/2*e^4 + 207/2*e^2 - 9/2, 9/8*e^12 - 45/2*e^10 + 1373/8*e^8 - 2485/4*e^6 + 8607/8*e^4 - 3131/4*e^2 + 1327/8, -1/2*e^13 + 10*e^11 - 149/2*e^9 + 251*e^7 - 731/2*e^5 + 181*e^3 - 39/2*e, -5/8*e^13 + 27/2*e^11 - 885/8*e^9 + 1701/4*e^7 - 6147/8*e^5 + 2335/4*e^3 - 1159/8*e, -1/2*e^11 + 10*e^9 - 75*e^7 + 256*e^5 - 743/2*e^3 + 149*e, 19/24*e^13 - 193/12*e^11 + 2969/24*e^9 - 5341/12*e^7 + 17965/24*e^5 - 1047/2*e^3 + 2831/24*e, -1/4*e^12 + 25/4*e^10 - 59*e^8 + 260*e^6 - 2139/4*e^4 + 1797/4*e^2 - 203/2, 1/2*e^12 - 21/2*e^10 + 83*e^8 - 303*e^6 + 999/2*e^4 - 615/2*e^2 + 58, -1/2*e^11 + 15/2*e^9 - 37*e^7 + 61*e^5 + 19/2*e^3 - 149/2*e, -1/4*e^11 + 23/4*e^9 - 99/2*e^7 + 191*e^5 - 1223/4*e^3 + 547/4*e, -1/8*e^12 + 4*e^10 - 329/8*e^8 + 705/4*e^6 - 2519/8*e^4 + 877/4*e^2 - 539/8, 9/8*e^12 - 47/2*e^10 + 1485/8*e^8 - 2737/4*e^6 + 9423/8*e^4 - 3423/4*e^2 + 1607/8, -2*e^12 + 83/2*e^10 - 651/2*e^8 + 1189*e^6 - 2008*e^4 + 2721/2*e^2 - 491/2, 1/4*e^12 - 6*e^10 + 217/4*e^8 - 459/2*e^6 + 1823/4*e^4 - 735/2*e^2 + 259/4, -1/4*e^12 + 15/4*e^10 - 17*e^8 + 11*e^6 + 357/4*e^4 - 741/4*e^2 + 173/2, 3/8*e^12 - 31/4*e^10 + 461/8*e^8 - 717/4*e^6 + 1477/8*e^4 + 40*e^2 - 485/8, 5/24*e^13 - 31/6*e^11 + 1153/24*e^9 - 2501/12*e^7 + 10259/24*e^5 - 1509/4*e^3 + 2347/24*e, 1/2*e^13 - 21/2*e^11 + 169/2*e^9 - 326*e^7 + 1235/2*e^5 - 1047/2*e^3 + 255/2*e, e^13 - 21*e^11 + 168*e^9 - 635*e^7 + 1143*e^5 - 883*e^3 + 217*e, -2/3*e^13 + 40/3*e^11 - 605/6*e^9 + 1066/3*e^7 - 1721/3*e^5 + 340*e^3 - 113/6*e, 9/8*e^13 - 23*e^11 + 1425/8*e^9 - 2581/4*e^7 + 8687/8*e^5 - 2909/4*e^3 + 979/8*e, 13/24*e^13 - 127/12*e^11 + 1883/24*e^9 - 3307/12*e^7 + 11275/24*e^5 - 719/2*e^3 + 2189/24*e, -1/4*e^12 + 5/2*e^10 + 5/4*e^8 - 153/2*e^6 + 957/4*e^4 - 247*e^2 + 259/4, 3/4*e^12 - 16*e^10 + 515/4*e^8 - 961/2*e^6 + 3301/4*e^4 - 1157/2*e^2 + 457/4, 5/8*e^12 - 47/4*e^10 + 635/8*e^8 - 895/4*e^6 + 1603/8*e^4 + 165/2*e^2 - 643/8, -1/4*e^12 + 9/2*e^10 - 123/4*e^8 + 209/2*e^6 - 803/4*e^4 + 213*e^2 - 249/4, -2/3*e^13 + 43/3*e^11 - 355/3*e^9 + 1405/3*e^7 - 2714/3*e^5 + 767*e^3 - 550/3*e, 1/4*e^13 - 5*e^11 + 145/4*e^9 - 225/2*e^7 + 519/4*e^5 - 45/2*e^3 - 9/4*e, -1/2*e^13 + 10*e^11 - 151/2*e^9 + 265*e^7 - 859/2*e^5 + 286*e^3 - 115/2*e, -1/24*e^13 + 5/6*e^11 - 173/24*e^9 + 421/12*e^7 - 2311/24*e^5 + 485/4*e^3 - 455/24*e, 1/2*e^12 - 21/2*e^10 + 171/2*e^8 - 338*e^6 + 1325/2*e^4 - 1161/2*e^2 + 305/2, -1/2*e^12 + 11*e^10 - 91*e^8 + 352*e^6 - 1295/2*e^4 + 519*e^2 - 123, 5/8*e^13 - 13*e^11 + 813/8*e^9 - 1461/4*e^7 + 4699/8*e^5 - 1413/4*e^3 + 543/8*e, -7/6*e^13 + 301/12*e^11 - 2461/12*e^9 + 4739/6*e^7 - 8641/6*e^5 + 4449/4*e^3 - 3001/12*e, -3/4*e^12 + 31/2*e^10 - 491/4*e^8 + 923/2*e^6 - 3285/4*e^4 + 588*e^2 - 385/4, 3/4*e^12 - 31/2*e^10 + 491/4*e^8 - 933/2*e^6 + 3469/4*e^4 - 697*e^2 + 601/4, -3/4*e^10 + 51/4*e^8 - 161/2*e^6 + 231*e^4 - 1153/4*e^2 + 439/4, 3/4*e^12 - 16*e^10 + 519/4*e^8 - 989/2*e^6 + 3569/4*e^4 - 1397/2*e^2 + 689/4, 1/4*e^12 - 17/4*e^10 + 49/2*e^8 - 44*e^6 - 233/4*e^4 + 871/4*e^2 - 96, -1/2*e^10 + 21/2*e^8 - 78*e^6 + 243*e^4 - 583/2*e^2 + 205/2, 5/8*e^13 - 13*e^11 + 837/8*e^9 - 1629/4*e^7 + 6179/8*e^5 - 2425/4*e^3 + 871/8*e, 1/6*e^13 - 17/6*e^11 + 89/6*e^9 - 28/3*e^7 - 761/6*e^5 + 577/2*e^3 - 799/6*e, 3/8*e^12 - 8*e^10 + 531/8*e^8 - 1087/4*e^6 + 4525/8*e^4 - 2091/4*e^2 + 1201/8, 1/8*e^12 - 3/4*e^10 - 65/8*e^8 + 313/4*e^6 - 1697/8*e^4 + 419/2*e^2 - 191/8, 3/4*e^12 - 31/2*e^10 + 491/4*e^8 - 929/2*e^6 + 3401/4*e^4 - 673*e^2 + 709/4, 3/4*e^12 - 33/2*e^10 + 547/4*e^8 - 1049/2*e^6 + 3669/4*e^4 - 616*e^2 + 361/4, 13/12*e^13 - 65/3*e^11 + 1949/12*e^9 - 3343/6*e^7 + 10183/12*e^5 - 959/2*e^3 + 1115/12*e, -1/12*e^13 + 8/3*e^11 - 353/12*e^9 + 871/6*e^7 - 3931/12*e^5 + 575/2*e^3 - 395/12*e, -3/4*e^13 + 16*e^11 - 515/4*e^9 + 959/2*e^7 - 3257/4*e^5 + 1101/2*e^3 - 513/4*e, -1/3*e^13 + 83/12*e^11 - 635/12*e^9 + 1075/6*e^7 - 736/3*e^5 + 283/4*e^3 + 541/12*e, -3/8*e^12 + 15/2*e^10 - 463/8*e^8 + 883/4*e^6 - 3557/8*e^4 + 1761/4*e^2 - 877/8, 7/8*e^12 - 77/4*e^10 + 1257/8*e^8 - 2305/4*e^6 + 7241/8*e^4 - 951/2*e^2 + 167/8, 7/4*e^13 - 36*e^11 + 1117/4*e^9 - 2007/2*e^7 + 6561/4*e^5 - 2017/2*e^3 + 411/4*e, -5/12*e^13 + 28/3*e^11 - 979/12*e^9 + 2087/6*e^7 - 8783/12*e^5 + 1333/2*e^3 - 2149/12*e, 5/8*e^12 - 59/4*e^10 + 1019/8*e^8 - 1959/4*e^6 + 6491/8*e^4 - 1019/2*e^2 + 989/8, 3/4*e^12 - 57/4*e^10 + 197/2*e^8 - 294*e^6 + 1349/4*e^4 - 293/4*e^2 - 25, -1/2*e^12 + 19/2*e^10 - 137/2*e^8 + 234*e^6 - 785/2*e^4 + 661/2*e^2 - 253/2, -3/8*e^12 + 39/4*e^10 - 749/8*e^8 + 1649/4*e^6 - 6637/8*e^4 + 660*e^2 - 1099/8, 1/2*e^12 - 25/2*e^10 + 112*e^8 - 437*e^6 + 1403/2*e^4 - 703/2*e^2 + 39, -1/2*e^12 + 17/2*e^10 - 103/2*e^8 + 130*e^6 - 227/2*e^4 + 21/2*e^2 - 67/2, 1/12*e^13 - 2/3*e^11 - 55/12*e^9 + 371/6*e^7 - 2489/12*e^5 + 455/2*e^3 - 433/12*e, 1/6*e^13 - 29/6*e^11 + 151/3*e^9 - 721/3*e^7 + 3271/6*e^5 - 1103/2*e^3 + 589/3*e, 5/8*e^13 - 55/4*e^11 + 907/8*e^9 - 1719/4*e^7 + 5955/8*e^5 - 1099/2*e^3 + 1389/8*e, 1/3*e^13 - 37/6*e^11 + 259/6*e^9 - 434/3*e^7 + 730/3*e^5 - 353/2*e^3 - 77/6*e, 3*e^12 - 61*e^10 + 941/2*e^8 - 1706*e^6 + 2921*e^4 - 2099*e^2 + 899/2, -1/4*e^12 + 15/4*e^10 - 41/2*e^8 + 59*e^6 - 467/4*e^4 + 395/4*e^2, 3/4*e^13 - 31/2*e^11 + 485/4*e^9 - 889/2*e^7 + 3073/4*e^5 - 562*e^3 + 447/4*e, 7/6*e^13 - 149/6*e^11 + 601/3*e^9 - 2260/3*e^7 + 7801/6*e^5 - 1719/2*e^3 + 304/3*e, 7/6*e^13 - 283/12*e^11 + 2167/12*e^9 - 3881/6*e^7 + 6463/6*e^5 - 2871/4*e^3 + 1543/12*e, 1/8*e^13 - 5/2*e^11 + 137/8*e^9 - 161/4*e^7 - 137/8*e^5 + 525/4*e^3 - 485/8*e, -1/24*e^13 + 5/6*e^11 - 233/24*e^9 + 877/12*e^7 - 6775/24*e^5 + 1737/4*e^3 - 3971/24*e, 1/6*e^13 - 43/12*e^11 + 349/12*e^9 - 665/6*e^7 + 1225/6*e^5 - 715/4*e^3 + 781/12*e, 1/4*e^13 - 9/2*e^11 + 111/4*e^9 - 121/2*e^7 - 53/4*e^5 + 167*e^3 - 419/4*e, -1/6*e^13 + 23/6*e^11 - 112/3*e^9 + 580/3*e^7 - 3181/6*e^5 + 1303/2*e^3 - 673/3*e, -11/8*e^12 + 28*e^10 - 1743/8*e^8 + 3227/4*e^6 - 11469/8*e^4 + 4275/4*e^2 - 1733/8, -7/4*e^12 + 143/4*e^10 - 278*e^8 + 1022*e^6 - 7161/4*e^4 + 5315/4*e^2 - 569/2, -3/2*e^10 + 43/2*e^8 - 98*e^6 + 146*e^4 - 69/2*e^2 - 47/2, -5/4*e^12 + 27*e^10 - 877/4*e^8 + 1641/2*e^6 - 5583/4*e^4 + 1905/2*e^2 - 823/4, 7/6*e^13 - 70/3*e^11 + 523/3*e^9 - 1780/3*e^7 + 5311/6*e^5 - 452*e^3 + 142/3*e, 19/24*e^13 - 89/6*e^11 + 2447/24*e^9 - 3679/12*e^7 + 8509/24*e^5 - 163/4*e^3 - 1531/24*e, 5/4*e^13 - 101/4*e^11 + 192*e^9 - 676*e^7 + 4355/4*e^5 - 2785/4*e^3 + 291/2*e, 4/3*e^13 - 341/12*e^11 + 2783/12*e^9 - 5413/6*e^7 + 5080/3*e^5 - 5513/4*e^3 + 4259/12*e, -1/2*e^13 + 23/2*e^11 - 103*e^9 + 450*e^7 - 1955/2*e^5 + 1891/2*e^3 - 270*e, -3/4*e^13 + 16*e^11 - 527/4*e^9 + 1047/2*e^7 - 4081/4*e^5 + 1739/2*e^3 - 833/4*e, -1/8*e^13 + 7/4*e^11 - 27/8*e^9 - 205/4*e^7 + 2225/8*e^5 - 819/2*e^3 + 923/8*e, 5/12*e^13 - 53/6*e^11 + 859/12*e^9 - 1649/6*e^7 + 6023/12*e^5 - 391*e^3 + 1153/12*e, 3/2*e^12 - 30*e^10 + 230*e^8 - 845*e^6 + 3023/2*e^4 - 1174*e^2 + 278, 17/8*e^12 - 173/4*e^10 + 2635/8*e^8 - 4575/4*e^6 + 13959/8*e^4 - 936*e^2 + 861/8] 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^3 + 4*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]