/* 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([-67, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([6,6,-5*w + 41]) primes_array = [ [2, 2, -27*w + 221],\ [3, 3, -w + 8],\ [3, 3, -w - 8],\ [7, 7, -11*w + 90],\ [7, 7, -11*w - 90],\ [11, 11, 6*w - 49],\ [11, 11, 6*w + 49],\ [17, 17, 4*w + 33],\ [17, 17, -4*w + 33],\ [25, 5, -5],\ [29, 29, -70*w + 573],\ [29, 29, 151*w - 1236],\ [31, 31, -w - 6],\ [31, 31, w - 6],\ [37, 37, -21*w - 172],\ [37, 37, -21*w + 172],\ [43, 43, 2*w - 15],\ [43, 43, 2*w + 15],\ [67, 67, -w],\ [73, 73, -3*w - 26],\ [73, 73, -3*w + 26],\ [79, 79, 92*w - 753],\ [79, 79, 313*w - 2562],\ [89, 89, -5*w - 42],\ [89, 89, -5*w + 42],\ [139, 139, 10*w + 81],\ [139, 139, 10*w - 81],\ [149, 149, 19*w - 156],\ [149, 149, -19*w - 156],\ [157, 157, -102*w + 835],\ [157, 157, 561*w - 4592],\ [169, 13, -13],\ [173, 173, 2*w - 21],\ [173, 173, -2*w - 21],\ [179, 179, 87*w - 712],\ [179, 179, 87*w + 712],\ [181, 181, 3*w - 28],\ [181, 181, 3*w + 28],\ [191, 191, 15*w - 122],\ [191, 191, 15*w + 122],\ [193, 193, 36*w + 295],\ [193, 193, -36*w + 295],\ [239, 239, 12*w + 97],\ [239, 239, 12*w - 97],\ [241, 241, -183*w + 1498],\ [241, 241, 480*w - 3929],\ [251, 251, 45*w + 368],\ [251, 251, 45*w - 368],\ [257, 257, -w - 18],\ [257, 257, w - 18],\ [269, 269, 41*w + 336],\ [269, 269, -41*w + 336],\ [271, 271, 40*w - 327],\ [271, 271, -40*w - 327],\ [277, 277, 426*w - 3487],\ [277, 277, -237*w + 1940],\ [293, 293, -998*w + 8169],\ [293, 293, 107*w - 876],\ [311, 311, 804*w - 6581],\ [311, 311, 141*w - 1154],\ [317, 317, -7*w + 60],\ [317, 317, -7*w - 60],\ [331, 331, 254*w - 2079],\ [331, 331, 475*w - 3888],\ [347, 347, -3*w - 16],\ [347, 347, 3*w - 16],\ [349, 349, -9*w - 76],\ [349, 349, -9*w + 76],\ [361, 19, -19],\ [367, 367, 7*w + 54],\ [367, 367, 7*w - 54],\ [379, 379, 5*w + 36],\ [379, 379, 5*w - 36],\ [383, 383, 168*w - 1375],\ [383, 383, 831*w - 6802],\ [389, 389, 34*w - 279],\ [389, 389, -34*w - 279],\ [397, 397, -6*w - 53],\ [397, 397, -6*w + 53],\ [421, 421, -3*w - 32],\ [421, 421, 3*w - 32],\ [443, 443, -27*w - 220],\ [443, 443, -27*w + 220],\ [449, 449, -4*w - 39],\ [449, 449, 4*w - 39],\ [457, 457, 51*w + 418],\ [457, 457, -51*w + 418],\ [461, 461, 2*w - 27],\ [461, 461, -2*w - 27],\ [463, 463, 136*w + 1113],\ [463, 463, 136*w - 1113],\ [487, 487, 32*w + 261],\ [487, 487, -32*w + 261],\ [499, 499, -62*w - 507],\ [499, 499, 62*w - 507],\ [503, 503, -3*w - 10],\ [503, 503, 3*w - 10],\ [509, 509, -w - 24],\ [509, 509, w - 24],\ [529, 23, -23],\ [547, 547, 47*w + 384],\ [547, 547, -47*w + 384],\ [557, 557, 14*w - 117],\ [557, 557, 14*w + 117],\ [563, 563, 6*w + 43],\ [563, 563, 6*w - 43],\ [569, 569, -56*w - 459],\ [569, 569, 56*w - 459],\ [587, 587, -3*w - 4],\ [587, 587, 3*w - 4],\ [599, 599, 3*w - 2],\ [599, 599, -3*w - 2],\ [601, 601, 117*w - 958],\ [601, 601, 117*w + 958],\ [613, 613, 6*w - 55],\ [613, 613, -6*w - 55],\ [617, 617, -269*w + 2202],\ [617, 617, 836*w - 6843],\ [631, 631, -4*w - 21],\ [631, 631, 4*w - 21],\ [647, 647, 21*w - 170],\ [647, 647, 21*w + 170],\ [683, 683, 18*w + 145],\ [683, 683, 18*w - 145],\ [709, 709, 30*w - 247],\ [709, 709, 30*w + 247],\ [727, 727, 416*w - 3405],\ [727, 727, 637*w - 5214],\ [739, 739, 158*w - 1293],\ [739, 739, 158*w + 1293],\ [761, 761, -100*w - 819],\ [761, 761, -100*w + 819],\ [773, 773, 122*w + 999],\ [773, 773, 122*w - 999],\ [787, 787, -1322*w + 10821],\ [787, 787, -217*w + 1776],\ [797, 797, 674*w - 5517],\ [797, 797, -431*w + 3528],\ [811, 811, 14*w - 111],\ [811, 811, 14*w + 111],\ [821, 821, 2*w - 33],\ [821, 821, -2*w - 33],\ [829, 829, -66*w - 541],\ [829, 829, 66*w - 541],\ [853, 853, -171*w - 1400],\ [853, 853, 171*w - 1400],\ [877, 877, 54*w - 443],\ [877, 877, -54*w - 443],\ [881, 881, 1300*w - 10641],\ [881, 881, -247*w + 2022],\ [883, 883, 31*w + 252],\ [883, 883, 31*w - 252],\ [919, 919, 13*w + 102],\ [919, 919, 13*w - 102],\ [953, 953, 4*w - 45],\ [953, 953, -4*w - 45],\ [977, 977, -71*w - 582],\ [977, 977, 71*w - 582],\ [983, 983, 36*w - 293],\ [983, 983, 36*w + 293],\ [991, 991, -4*w - 9],\ [991, 991, 4*w - 9],\ [997, 997, 3*w - 40],\ [997, 997, -3*w - 40]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + x^7 - 20*x^6 - 17*x^5 + 129*x^4 + 85*x^3 - 296*x^2 - 109*x + 194 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -1, -27/538*e^7 - 11/538*e^6 + 417/538*e^5 + 91/269*e^4 - 834/269*e^3 - 1187/538*e^2 + 502/269*e + 910/269, 77/1076*e^7 - 69/538*e^6 - 759/538*e^5 + 2161/1076*e^4 + 4381/538*e^3 - 8949/1076*e^2 - 13693/1076*e + 4349/538, -25/1076*e^7 - 15/269*e^6 + 104/269*e^5 + 577/1076*e^4 - 1101/538*e^3 - 43/1076*e^2 + 3251/1076*e - 1419/538, 39/538*e^7 - 7/269*e^6 - 346/269*e^5 + 305/538*e^4 + 1922/269*e^3 - 1633/538*e^2 - 6621/538*e + 987/269, -11/538*e^7 - 67/269*e^6 + 70/269*e^5 + 1997/538*e^4 - 280/269*e^3 - 8175/538*e^2 + 957/538*e + 4067/269, 25/1076*e^7 + 15/269*e^6 - 104/269*e^5 - 577/1076*e^4 + 1101/538*e^3 + 43/1076*e^2 - 4327/1076*e + 2495/538, -21/1076*e^7 - 79/538*e^6 + 207/538*e^5 + 2443/1076*e^4 - 1097/538*e^3 - 9591/1076*e^2 + 2365/1076*e + 3607/538, -29/1076*e^7 + 19/538*e^6 + 209/538*e^5 - 1289/1076*e^4 - 567/538*e^3 + 9505/1076*e^2 - 1243/1076*e - 5907/538, -25/538*e^7 - 30/269*e^6 + 208/269*e^5 + 1115/538*e^4 - 832/269*e^3 - 5961/538*e^2 + 561/538*e + 3423/269, -33/269*e^7 + 3/538*e^6 + 1109/538*e^5 - 123/538*e^4 - 2487/269*e^3 + 223/269*e^2 + 3859/538*e - 77/269, -79/1076*e^7 - 41/538*e^6 + 625/538*e^5 + 941/1076*e^4 - 2769/538*e^3 - 2417/1076*e^2 + 8487/1076*e + 401/538, 41/1076*e^7 + 103/538*e^6 - 481/538*e^5 - 3335/1076*e^4 + 3269/538*e^3 + 13499/1076*e^2 - 11637/1076*e - 3225/538, 1/269*e^7 - 49/538*e^6 - 1/538*e^5 + 933/538*e^4 + 2/269*e^3 - 2656/269*e^2 - 1519/538*e + 4665/269, 38/269*e^7 + 21/538*e^6 - 1383/538*e^5 - 323/538*e^4 + 3573/269*e^3 + 485/269*e^2 - 7957/538*e + 1075/269, -103/1076*e^7 - 8/269*e^6 + 450/269*e^5 + 1043/1076*e^4 - 4407/538*e^3 - 6461/1076*e^2 + 10037/1076*e + 373/538, -181/1076*e^7 - 1/269*e^6 + 796/269*e^5 - 643/1076*e^4 - 7713/538*e^3 + 6489/1076*e^2 + 16823/1076*e - 5367/538, 237/1076*e^7 + 123/538*e^6 - 1875/538*e^5 - 3899/1076*e^4 + 8307/538*e^3 + 16935/1076*e^2 - 19005/1076*e - 6045/538, -25/1076*e^7 - 15/269*e^6 + 104/269*e^5 + 577/1076*e^4 - 563/538*e^3 + 1033/1076*e^2 - 1053/1076*e - 4109/538, 79/1076*e^7 + 41/538*e^6 - 625/538*e^5 - 941/1076*e^4 + 2769/538*e^3 + 3493/1076*e^2 - 8487/1076*e - 3091/538, 63/1076*e^7 - 16/269*e^6 - 176/269*e^5 + 741/1076*e^4 + 63/538*e^3 - 1355/1076*e^2 + 6355/1076*e - 3289/538, 177/1076*e^7 + 51/538*e^6 - 1591/538*e^5 - 1223/1076*e^4 + 8247/538*e^3 + 907/1076*e^2 - 22393/1076*e + 5183/538, -29/1076*e^7 + 19/538*e^6 + 209/538*e^5 - 213/1076*e^4 - 29/538*e^3 - 2331/1076*e^2 - 7699/1076*e + 4853/538, -77/1076*e^7 - 100/269*e^6 + 514/269*e^5 + 6985/1076*e^4 - 7609/538*e^3 - 33015/1076*e^2 + 27143/1076*e + 13943/538, -43/538*e^7 - 157/538*e^6 + 963/538*e^5 + 1470/269*e^4 - 3271/269*e^3 - 15181/538*e^2 + 5233/269*e + 6361/269, 21/269*e^7 + 47/538*e^6 - 559/538*e^5 - 313/538*e^4 + 580/269*e^3 - 93/269*e^2 + 3609/538*e + 1125/269, -69/269*e^7 - 58/269*e^6 + 1245/269*e^5 + 764/269*e^4 - 6325/269*e^3 - 2077/269*e^2 + 7617/269*e + 377/269, 117/538*e^7 - 21/269*e^6 - 1038/269*e^5 + 915/538*e^4 + 5228/269*e^3 - 5437/538*e^2 - 13945/538*e + 3768/269, 21/1076*e^7 + 79/538*e^6 + 331/538*e^5 - 3519/1076*e^4 - 5897/538*e^3 + 21427/1076*e^2 + 35295/1076*e - 13829/538, -52/269*e^7 + 127/538*e^6 + 1935/538*e^5 - 2517/538*e^4 - 5484/269*e^3 + 6571/269*e^2 + 19539/538*e - 7743/269, -85/1076*e^7 - 51/269*e^6 + 246/269*e^5 + 4329/1076*e^4 - 85/538*e^3 - 24679/1076*e^2 - 11973/1076*e + 11423/538, 205/1076*e^7 - 23/538*e^6 - 1867/538*e^5 + 1617/1076*e^4 + 9889/538*e^3 - 12129/1076*e^2 - 29133/1076*e + 8623/538, 45/538*e^7 - 161/538*e^6 - 695/538*e^5 + 1552/269*e^4 + 1390/269*e^3 - 17031/538*e^2 - 2630/269*e + 11485/269, 23/538*e^7 + 109/538*e^6 - 415/538*e^5 - 486/269*e^4 + 1368/269*e^3 - 563/538*e^2 - 3287/269*e + 4286/269, 265/1076*e^7 + 49/538*e^6 - 2151/538*e^5 - 1059/1076*e^4 + 9949/538*e^3 + 6051/1076*e^2 - 25745/1076*e - 6909/538, 113/1076*e^7 + 14/269*e^6 - 384/269*e^5 + 663/1076*e^4 + 2265/538*e^3 - 10953/1076*e^2 + 3081/1076*e + 7619/538, -49/1076*e^7 - 5/538*e^6 + 483/538*e^5 - 397/1076*e^4 - 2201/538*e^3 + 4521/1076*e^2 - 1655/1076*e - 1447/538, -49/538*e^7 + 259/538*e^6 + 1235/538*e^5 - 1947/269*e^4 - 4084/269*e^3 + 16895/538*e^2 + 5494/269*e - 10324/269, 39/538*e^7 - 7/269*e^6 - 346/269*e^5 + 843/538*e^4 + 1922/269*e^3 - 7551/538*e^2 - 3931/538*e + 7174/269, -75/269*e^7 + 89/269*e^6 + 1248/269*e^5 - 1497/269*e^4 - 6068/269*e^3 + 6596/269*e^2 + 8677/269*e - 5824/269, 211/1076*e^7 + 307/538*e^6 - 1465/538*e^5 - 9841/1076*e^4 + 3977/538*e^3 + 44565/1076*e^2 + 8005/1076*e - 25533/538, 17/1076*e^7 - 141/538*e^6 + 63/538*e^5 + 3761/1076*e^4 - 1597/538*e^3 - 13141/1076*e^2 + 3363/1076*e + 5893/538, 129/1076*e^7 - 84/269*e^6 - 655/269*e^5 + 3823/1076*e^4 + 7661/538*e^3 - 6105/1076*e^2 - 25211/1076*e - 5095/538, -25/1076*e^7 - 15/269*e^6 + 104/269*e^5 + 1653/1076*e^4 - 1101/538*e^3 - 9727/1076*e^2 + 4327/1076*e + 10955/538, 26/269*e^7 + 71/538*e^6 - 833/538*e^5 - 1835/538*e^4 + 1666/269*e^3 + 6264/269*e^2 - 1027/538*e - 6216/269, -125/1076*e^7 - 75/269*e^6 + 520/269*e^5 + 5037/1076*e^4 - 5505/538*e^3 - 22811/1076*e^2 + 23787/1076*e + 8507/538, 119/1076*e^7 - 90/269*e^6 - 721/269*e^5 + 5345/1076*e^4 + 9803/538*e^3 - 24199/1076*e^2 - 32949/1076*e + 17579/538, 9/269*e^7 - 86/269*e^6 - 139/269*e^5 + 1643/269*e^4 + 1094/269*e^3 - 8302/269*e^2 - 4818/269*e + 10781/269, 13/269*e^7 - 99/538*e^6 - 551/538*e^5 + 1907/538*e^4 + 1371/269*e^3 - 4131/269*e^2 + 159/538*e + 1196/269, -183/1076*e^7 - 56/269*e^6 + 729/269*e^5 + 3535/1076*e^4 - 6101/538*e^3 - 15637/1076*e^2 + 10541/1076*e + 16599/538, -37/269*e^7 + 199/538*e^6 + 1651/538*e^5 - 3317/538*e^4 - 5185/269*e^3 + 7350/269*e^2 + 15315/538*e - 7439/269, 169/1076*e^7 - 60/269*e^6 - 660/269*e^5 + 5267/1076*e^4 + 5011/538*e^3 - 31645/1076*e^2 - 2867/1076*e + 19879/538, 79/269*e^7 - 105/538*e^6 - 2769/538*e^5 + 1077/538*e^4 + 6883/269*e^3 + 265/269*e^2 - 17243/538*e - 4568/269, -27/269*e^7 + 258/269*e^6 + 417/269*e^5 - 4122/269*e^4 - 1668/269*e^3 + 17105/269*e^2 + 735/269*e - 14320/269, -148/269*e^7 - 11/538*e^6 + 5259/538*e^5 - 87/538*e^4 - 13208/269*e^3 + 1424/269*e^2 + 31401/538*e - 7429/269, -29/538*e^7 + 19/269*e^6 + 209/269*e^5 - 213/538*e^4 - 836/269*e^3 - 2331/538*e^2 + 2523/538*e + 4315/269, -54/269*e^7 + 225/538*e^6 + 1937/538*e^5 - 3307/538*e^4 - 4681/269*e^3 + 5427/269*e^2 + 10203/538*e - 1471/269, 107/1076*e^7 - 33/538*e^6 - 901/538*e^5 + 2975/1076*e^4 + 4411/538*e^3 - 24607/1076*e^2 - 9847/1076*e + 22407/538, -277/1076*e^7 + 49/269*e^6 + 1077/269*e^5 - 3463/1076*e^4 - 9423/538*e^3 + 17213/1076*e^2 + 23023/1076*e - 13549/538, 81/269*e^7 + 33/269*e^6 - 1520/269*e^5 - 815/269*e^4 + 7694/269*e^3 + 4906/269*e^2 - 7047/269*e - 4922/269, -195/1076*e^7 + 152/269*e^6 + 1134/269*e^5 - 10133/1076*e^4 - 14721/538*e^3 + 51743/1076*e^2 + 42789/1076*e - 40443/538, -63/1076*e^7 + 16/269*e^6 + 176/269*e^5 + 335/1076*e^4 + 475/538*e^3 - 9405/1076*e^2 - 16039/1076*e + 9745/538, 609/1076*e^7 - 65/269*e^6 - 2598/269*e^5 + 6087/1076*e^4 + 25357/538*e^3 - 38205/1076*e^2 - 60515/1076*e + 32587/538, 107/269*e^7 - 66/269*e^6 - 1802/269*e^5 + 1361/269*e^4 + 8284/269*e^3 - 8467/269*e^2 - 8502/269*e + 15762/269, -42/269*e^7 - 363/538*e^6 + 1387/538*e^5 + 5199/538*e^4 - 3043/269*e^3 - 9767/269*e^2 + 5425/538*e + 9048/269, -29/1076*e^7 + 19/538*e^6 + 747/538*e^5 - 213/1076*e^4 - 7561/538*e^3 + 1973/1076*e^2 + 33189/1076*e - 3755/538, -39/538*e^7 + 7/269*e^6 + 346/269*e^5 - 305/538*e^4 - 1922/269*e^3 + 1633/538*e^2 + 8235/538*e - 2870/269, 89/1076*e^7 + 53/538*e^6 - 1031/538*e^5 - 3539/1076*e^4 + 6545/538*e^3 + 26967/1076*e^2 - 19041/1076*e - 21461/538, 261/1076*e^7 + 367/538*e^6 - 1881/538*e^5 - 12071/1076*e^4 + 6717/538*e^3 + 55411/1076*e^2 - 3877/1076*e - 29151/538, 13/269*e^7 + 85/269*e^6 + 128/269*e^5 - 1333/269*e^4 - 3202/269*e^3 + 5284/269*e^2 + 8822/269*e - 2032/269, -59/269*e^7 - 34/269*e^6 + 971/269*e^5 + 49/269*e^4 - 4691/269*e^3 + 2567/269*e^2 + 7016/269*e - 3276/269, -31/538*e^7 - 91/269*e^6 + 75/269*e^5 + 2889/538*e^4 + 1314/269*e^3 - 11007/538*e^2 - 13443/538*e + 5030/269, -92/269*e^7 + 102/269*e^6 + 1660/269*e^5 - 1761/269*e^4 - 8792/269*e^3 + 8439/269*e^2 + 12577/269*e - 8195/269, -191/1076*e^7 + 255/538*e^6 + 2267/538*e^5 - 8267/1076*e^4 - 15255/538*e^3 + 34663/1076*e^2 + 53739/1076*e - 14973/538, 309/1076*e^7 + 24/269*e^6 - 1350/269*e^5 + 99/1076*e^4 + 13759/538*e^3 - 15049/1076*e^2 - 34415/1076*e + 25781/538, -493/1076*e^7 - 215/538*e^6 + 4629/538*e^5 + 6063/1076*e^4 - 25241/538*e^3 - 21335/1076*e^2 + 64949/1076*e + 2339/538, 411/1076*e^7 + 9/538*e^6 - 4205/538*e^5 - 469/1076*e^4 + 24621/538*e^3 + 793/1076*e^2 - 68575/1076*e + 2497/538, -185/538*e^7 - 175/538*e^6 + 2917/538*e^5 + 1301/269*e^4 - 6372/269*e^3 - 8711/538*e^2 + 7644/269*e - 171/269, 51/538*e^7 + 499/538*e^6 - 967/538*e^5 - 4177/269*e^4 + 2741/269*e^3 + 38049/538*e^2 - 3160/269*e - 19174/269, 293/1076*e^7 + 122/269*e^6 - 1079/269*e^5 - 7365/1076*e^4 + 8901/538*e^3 + 28523/1076*e^2 - 16883/1076*e - 2931/538, -75/1076*e^7 + 179/538*e^6 + 355/538*e^5 - 7415/1076*e^4 - 1151/538*e^3 + 42911/1076*e^2 + 16747/1076*e - 27391/538, 21/269*e^7 - 111/269*e^6 - 414/269*e^5 + 1592/269*e^4 + 1656/269*e^3 - 5204/269*e^2 + 2477/269*e + 2201/269, -161/538*e^7 - 247/269*e^6 + 1049/269*e^5 + 7611/538*e^4 - 2851/269*e^3 - 33719/538*e^2 - 519/538*e + 18149/269, -33/538*e^7 - 133/538*e^6 + 689/538*e^5 + 1247/269*e^4 - 1647/269*e^3 - 13765/538*e^2 + 494/269*e + 13815/269, 249/538*e^7 + 245/269*e^6 - 2147/269*e^5 - 7447/538*e^4 + 10740/269*e^3 + 31331/538*e^2 - 27581/538*e - 12756/269, -465/1076*e^7 + 249/538*e^6 + 4353/538*e^5 - 8313/1076*e^4 - 24675/538*e^3 + 39873/1076*e^2 + 81881/1076*e - 24887/538, 16/269*e^7 - 123/269*e^6 - 277/269*e^5 + 1815/269*e^4 + 1915/269*e^3 - 6450/269*e^2 - 6234/269*e + 2548/269, 2/269*e^7 + 171/538*e^6 + 267/538*e^5 - 1631/538*e^4 - 1879/269*e^3 + 1413/269*e^2 + 11757/538*e - 2237/269, -57/269*e^7 - 83/269*e^6 + 970/269*e^5 + 1251/269*e^4 - 4956/269*e^3 - 5973/269*e^2 + 8456/269*e + 6592/269, 57/538*e^7 + 176/269*e^6 - 485/269*e^5 - 6093/538*e^4 + 2478/269*e^3 + 29645/538*e^2 - 5497/538*e - 13787/269, 131/538*e^7 - 58/269*e^6 - 907/269*e^5 + 1797/538*e^4 + 2821/269*e^3 - 6037/538*e^2 - 99/538*e + 108/269, -48/269*e^7 - 169/269*e^6 + 1100/269*e^5 + 2625/269*e^4 - 7090/269*e^3 - 10509/269*e^2 + 9825/269*e + 7420/269, 104/269*e^7 + 15/538*e^6 - 3601/538*e^5 + 461/538*e^4 + 9085/269*e^3 - 4265/269*e^2 - 22669/538*e + 14141/269, -64/269*e^7 + 177/538*e^6 + 1947/538*e^5 - 3491/538*e^4 - 3625/269*e^3 + 9660/269*e^2 + 3335/538*e - 15303/269, -52/269*e^7 + 198/269*e^6 + 1102/269*e^5 - 3276/269*e^4 - 7098/269*e^3 + 14910/269*e^2 + 12056/269*e - 15544/269, -417/1076*e^7 + 199/538*e^6 + 3803/538*e^5 - 7441/1076*e^4 - 20861/538*e^3 + 32897/1076*e^2 + 69097/1076*e - 14071/538, -193/1076*e^7 + 145/538*e^6 + 2133/538*e^5 - 7317/1076*e^4 - 14719/538*e^3 + 49121/1076*e^2 + 59293/1076*e - 34971/538, -47/269*e^7 - 59/269*e^6 + 696/269*e^5 + 805/269*e^4 - 2246/269*e^3 - 2405/269*e^2 - 1291/269*e - 3517/269, -143/1076*e^7 - 333/538*e^6 + 641/538*e^5 + 9821/1076*e^4 + 395/538*e^3 - 41177/1076*e^2 - 12845/1076*e + 27585/538, 89/269*e^7 - 57/538*e^6 - 3317/538*e^5 + 1261/538*e^4 + 9324/269*e^3 - 3430/269*e^2 - 27591/538*e + 4691/269, 63/269*e^7 - 333/269*e^6 - 1242/269*e^5 + 5583/269*e^4 + 7389/269*e^3 - 26641/269*e^2 - 14358/269*e + 29737/269, -39/1076*e^7 - 531/538*e^6 + 77/538*e^5 + 15297/1076*e^4 - 39/538*e^3 - 58085/1076*e^2 + 6083/1076*e + 30217/538, -615/1076*e^7 + 169/269*e^6 + 2666/269*e^5 - 13997/1076*e^4 - 26977/538*e^3 + 79427/1076*e^2 + 75025/1076*e - 54921/538, 45/1076*e^7 + 27/269*e^6 + 28/269*e^5 - 1469/1076*e^4 - 2645/538*e^3 + 5027/1076*e^2 + 12225/1076*e + 2877/538, 505/1076*e^7 + 34/269*e^6 - 2047/269*e^5 - 465/1076*e^4 + 17721/538*e^3 - 6233/1076*e^2 - 29947/1076*e + 12201/538, 197/538*e^7 + 75/269*e^6 - 1596/269*e^5 - 2115/538*e^4 + 7191/269*e^3 + 5891/538*e^2 - 14987/538*e + 4220/269, 555/1076*e^7 + 64/269*e^6 - 1986/269*e^5 - 2695/1076*e^4 + 14005/538*e^3 + 12145/1076*e^2 - 16005/1076*e - 19393/538, 189/1076*e^7 - 365/538*e^6 - 1325/538*e^5 + 14597/1076*e^4 + 4493/538*e^3 - 76157/1076*e^2 - 7297/1076*e + 43395/538, -347/1076*e^7 - 255/538*e^6 + 2037/538*e^5 + 7729/1076*e^4 - 3575/538*e^3 - 30897/1076*e^2 - 14465/1076*e + 5289/538, -167/538*e^7 + 729/538*e^6 + 3177/538*e^5 - 6471/269*e^4 - 9044/269*e^3 + 65069/538*e^2 + 14931/269*e - 39424/269, -157/269*e^7 - 54/269*e^6 + 3172/269*e^5 + 869/269*e^4 - 18606/269*e^3 - 2917/269*e^2 + 26033/269*e - 4222/269, 2/269*e^7 - 49/269*e^6 - 1/269*e^5 + 933/269*e^4 + 4/269*e^3 - 4774/269*e^2 - 981/269*e + 12020/269, -109/1076*e^7 + 96/269*e^6 + 518/269*e^5 - 9019/1076*e^4 - 6027/538*e^3 + 60585/1076*e^2 + 21319/1076*e - 41329/538, 83/538*e^7 + 253/538*e^6 - 983/538*e^5 - 1017/269*e^4 + 1428/269*e^3 - 4979/538*e^2 - 248/269*e + 12157/269, -41/538*e^7 - 475/538*e^6 + 155/538*e^5 + 3954/269*e^4 + 1573/269*e^3 - 37171/538*e^2 - 8035/269*e + 20710/269, -249/1076*e^7 + 12/269*e^6 + 1208/269*e^5 - 1699/1076*e^4 - 14237/538*e^3 + 11709/1076*e^2 + 46411/1076*e - 15489/538, -559/538*e^7 - 427/538*e^6 + 9829/538*e^5 + 2701/269*e^4 - 25038/269*e^3 - 14971/538*e^2 + 32252/269*e - 428/269, -283/538*e^7 - 195/538*e^6 + 4849/538*e^5 + 1173/269*e^4 - 11850/269*e^3 - 6125/538*e^2 + 13521/269*e - 3603/269, -485/1076*e^7 + 225/538*e^6 + 4627/538*e^5 - 7421/1076*e^4 - 24695/538*e^3 + 31661/1076*e^2 + 59949/1076*e - 15047/538, -219/1076*e^7 - 209/538*e^6 + 2005/538*e^5 + 6109/1076*e^4 - 10979/538*e^3 - 25469/1076*e^2 + 30351/1076*e + 19785/538, -73/1076*e^7 + 10/269*e^6 + 379/269*e^5 - 1371/1076*e^4 - 3839/538*e^3 + 14465/1076*e^2 + 8503/1076*e - 18153/538, 21/1076*e^7 - 459/538*e^6 - 745/538*e^5 + 13697/1076*e^4 + 7553/538*e^3 - 54969/1076*e^2 - 36797/1076*e + 23831/538, -191/538*e^7 - 297/538*e^6 + 3727/538*e^5 + 2457/269*e^4 - 10144/269*e^3 - 22903/538*e^2 + 11671/269*e + 13810/269, 71/269*e^7 - 251/538*e^6 - 2761/538*e^5 + 5449/538*e^4 + 8212/269*e^3 - 16685/269*e^2 - 31453/538*e + 23479/269, -235/1076*e^7 - 551/538*e^6 + 1471/538*e^5 + 18013/1076*e^4 - 2925/538*e^3 - 90573/1076*e^2 - 15601/1076*e + 58861/538, 63/1076*e^7 - 301/538*e^6 - 83/538*e^5 + 10963/1076*e^4 - 2627/538*e^3 - 48699/1076*e^2 + 15501/1076*e + 8009/538, 101/1076*e^7 + 175/538*e^6 - 765/538*e^5 - 7087/1076*e^4 + 2791/538*e^3 + 45667/1076*e^2 + 359/1076*e - 35973/538, 137/1076*e^7 + 3/538*e^6 - 1043/538*e^5 + 1637/1076*e^4 + 4441/538*e^3 - 19821/1076*e^2 - 8153/1076*e + 15179/538, 173/1076*e^7 - 169/538*e^6 - 1321/538*e^5 + 2829/1076*e^4 + 4477/538*e^3 + 7227/1076*e^2 + 9159/1076*e - 12217/538, -66/269*e^7 - 266/269*e^6 + 840/269*e^5 + 4181/269*e^4 - 3091/269*e^3 - 18653/269*e^2 + 6280/269*e + 18407/269, 71/1076*e^7 - 399/538*e^6 - 623/538*e^5 + 11467/1076*e^4 + 2223/538*e^3 - 46275/1076*e^2 - 1335/1076*e + 27207/538, 107/538*e^7 + 203/538*e^6 - 1533/538*e^5 - 2144/269*e^4 + 1990/269*e^3 + 27041/538*e^2 + 3281/269*e - 17405/269, 217/538*e^7 + 99/269*e^6 - 2139/269*e^5 - 1931/538*e^4 + 12591/269*e^3 + 115/538*e^2 - 39861/538*e + 7023/269, 277/1076*e^7 - 49/269*e^6 - 1077/269*e^5 + 3463/1076*e^4 + 8347/538*e^3 - 18289/1076*e^2 + 649/1076*e + 12473/538, 261/1076*e^7 - 171/538*e^6 - 2419/538*e^5 + 4069/1076*e^4 + 11559/538*e^3 - 8073/1076*e^2 - 11409/1076*e - 4941/538, -130/269*e^7 - 43/269*e^6 + 2217/269*e^5 + 418/269*e^4 - 9675/269*e^3 - 385/269*e^2 + 7544/269*e - 124/269, -439/1076*e^7 + 167/269*e^6 + 2106/269*e^5 - 8289/1076*e^4 - 21959/538*e^3 + 20851/1076*e^2 + 43573/1076*e + 1595/538, 62/269*e^7 - 174/269*e^6 - 1107/269*e^5 + 3637/269*e^4 + 6311/269*e^3 - 21026/269*e^2 - 10774/269*e + 23727/269, -83/269*e^7 + 16/269*e^6 + 1521/269*e^5 - 656/269*e^4 - 7967/269*e^3 + 5517/269*e^2 + 6683/269*e - 10057/269, 19/269*e^7 + 207/269*e^6 - 144/269*e^5 - 2569/269*e^4 - 231/269*e^3 + 7909/269*e^2 + 1306/269*e - 10357/269, 205/538*e^7 - 23/269*e^6 - 1598/269*e^5 + 3/538*e^4 + 6392/269*e^3 + 7239/538*e^2 - 3309/538*e - 4558/269, -391/1076*e^7 - 396/269*e^6 + 1293/269*e^5 + 23787/1076*e^4 - 6847/538*e^3 - 99105/1076*e^2 - 18707/1076*e + 54913/538, -73/269*e^7 + 40/269*e^6 + 1247/269*e^5 - 26/269*e^4 - 5795/269*e^3 - 3289/269*e^2 + 3661/269*e + 9/269, -129/538*e^7 + 67/538*e^6 + 1275/538*e^5 - 701/269*e^4 + 1216/269*e^3 + 9333/538*e^2 - 13084/269*e - 7010/269, 169/1076*e^7 - 389/538*e^6 - 1589/538*e^5 + 14413/1076*e^4 + 8239/538*e^3 - 77913/1076*e^2 - 15241/1076*e + 52159/538, -955/1076*e^7 - 35/269*e^6 + 4188/269*e^5 + 1167/1076*e^4 - 42381/538*e^3 + 4383/1076*e^2 + 108909/1076*e - 14609/538, -123/538*e^7 - 309/269*e^6 + 905/269*e^5 + 10005/538*e^4 - 3620/269*e^3 - 44801/538*e^2 + 1555/538*e + 21780/269, -183/1076*e^7 + 157/538*e^6 + 2265/538*e^5 - 5611/1076*e^4 - 15247/538*e^3 + 30631/1076*e^2 + 51967/1076*e - 28593/538, 7/269*e^7 - 37/269*e^6 - 138/269*e^5 + 441/269*e^4 + 283/269*e^3 - 2183/269*e^2 + 3426/269*e + 10597/269, 41/269*e^7 + 206/269*e^6 - 693/269*e^5 - 3604/269*e^4 + 3041/269*e^3 + 17265/269*e^2 - 1953/269*e - 20707/269, -307/538*e^7 - 207/269*e^6 + 2834/269*e^5 + 5407/538*e^4 - 15909/269*e^3 - 15549/538*e^2 + 52533/538*e + 5784/269, -45/1076*e^7 - 27/269*e^6 + 241/269*e^5 + 3621/1076*e^4 - 2197/538*e^3 - 27623/1076*e^2 - 8997/1076*e + 13263/538, -515/1076*e^7 + 229/269*e^6 + 2788/269*e^5 - 14153/1076*e^4 - 37099/538*e^3 + 57003/1076*e^2 + 137341/1076*e - 22883/538, -375/538*e^7 - 181/269*e^6 + 2851/269*e^5 + 5427/538*e^4 - 11404/269*e^3 - 22703/538*e^2 + 18637/538*e + 9919/269, -13/269*e^7 + 184/269*e^6 + 410/269*e^5 - 2433/269*e^4 - 2178/269*e^3 + 7897/269*e^2 + 593/269*e - 7652/269, -425/1076*e^7 - 779/538*e^6 + 3267/538*e^5 + 23259/1076*e^4 - 14413/538*e^3 - 85735/1076*e^2 + 31057/1076*e + 28063/538, 35/269*e^7 - 639/538*e^6 - 1649/538*e^5 + 10597/538*e^4 + 5988/269*e^3 - 24634/269*e^2 - 25727/538*e + 31196/269, -153/1076*e^7 - 345/538*e^6 + 2123/538*e^5 + 14571/1076*e^4 - 15755/538*e^3 - 77563/1076*e^2 + 52585/1076*e + 36271/538, -171/1076*e^7 + 5/269*e^6 + 862/269*e^5 - 1089/1076*e^4 - 11469/538*e^3 + 5215/1076*e^2 + 62221/1076*e + 2087/538, -441/538*e^7 + 179/538*e^6 + 7887/538*e^5 - 1921/269*e^4 - 20616/269*e^3 + 24011/538*e^2 + 28464/269*e - 21362/269, -63/269*e^7 - 141/538*e^6 + 1139/538*e^5 + 2015/538*e^4 + 1488/269*e^3 - 5101/269*e^2 - 24277/538*e + 7116/269, -135/269*e^7 - 55/269*e^6 + 2354/269*e^5 + 103/269*e^4 - 11568/269*e^3 + 4018/269*e^2 + 14973/269*e - 8116/269] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2,2,27*w + 221])] = 1 AL_eigenvalues[ZF.ideal([3,3,w + 8])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]