/* 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([44, 0, -14, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -1/2*w^2 - w + 2]) primes_array = [ [4, 2, -1/2*w^3 + w^2 + 4*w - 8],\ [11, 11, 1/2*w^3 - 3/2*w^2 - 4*w + 11],\ [11, 11, -1/2*w^2 - w + 2],\ [11, 11, -1/2*w^2 + w + 2],\ [19, 19, 1/2*w^3 - 1/2*w^2 - 4*w + 5],\ [19, 19, 1/2*w^3 + w^2 - 4*w - 9],\ [19, 19, 1/2*w^3 - w^2 - 4*w + 9],\ [19, 19, 1/2*w^3 + 1/2*w^2 - 4*w - 5],\ [25, 5, 1/2*w^2 - 1],\ [29, 29, 1/2*w^3 - 4*w - 1],\ [29, 29, -1/2*w^3 + 4*w - 1],\ [31, 31, -w - 1],\ [31, 31, w - 1],\ [41, 41, 1/2*w^3 + 1/2*w^2 - 4*w - 2],\ [41, 41, -1/2*w^3 + 1/2*w^2 + 4*w - 2],\ [49, 7, -1/2*w^3 + 1/2*w^2 + 5*w - 7],\ [49, 7, 3/2*w^3 - 7/2*w^2 - 13*w + 29],\ [59, 59, -1/2*w^3 - 3/2*w^2 + 3*w + 10],\ [59, 59, 1/2*w^3 - 3/2*w^2 - 3*w + 10],\ [61, 61, 1/2*w^2 + w - 6],\ [61, 61, 1/2*w^2 - w - 6],\ [71, 71, w^3 - 5/2*w^2 - 8*w + 20],\ [71, 71, -w^3 + 5/2*w^2 + 10*w - 24],\ [81, 3, -3],\ [101, 101, -1/2*w^3 + 1/2*w^2 + 4*w - 1],\ [101, 101, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\ [109, 109, 3/2*w^2 + w - 12],\ [109, 109, 3/2*w^2 - w - 12],\ [149, 149, 1/2*w^3 + 2*w^2 - 4*w - 15],\ [149, 149, -1/2*w^3 + 2*w^2 + 4*w - 15],\ [151, 151, 1/2*w^3 - 1/2*w^2 - 4*w + 8],\ [151, 151, -w^3 + 5/2*w^2 + 8*w - 18],\ [151, 151, -w^3 + 3/2*w^2 + 10*w - 18],\ [151, 151, -1/2*w^3 - 1/2*w^2 + 4*w + 8],\ [179, 179, 1/2*w^3 + w^2 - 4*w - 5],\ [179, 179, -1/2*w^3 + w^2 + 4*w - 5],\ [181, 181, 1/2*w^3 - 5*w - 3],\ [181, 181, w^3 - 1/2*w^2 - 7*w - 1],\ [181, 181, -1/2*w^3 - 5/2*w^2 + 4*w + 15],\ [181, 181, 1/2*w^3 - 5*w + 3],\ [191, 191, w^3 - 2*w^2 - 7*w + 13],\ [191, 191, -w^3 - 2*w^2 + 7*w + 13],\ [199, 199, -5/2*w^2 - 2*w + 18],\ [199, 199, -5/2*w^2 + 2*w + 18],\ [241, 241, -3/2*w^3 + 7/2*w^2 + 14*w - 30],\ [241, 241, -3/2*w^3 + 5/2*w^2 + 16*w - 30],\ [251, 251, 3/2*w^2 - w - 13],\ [251, 251, 3/2*w^2 + w - 13],\ [269, 269, 1/2*w^3 + 1/2*w^2 - 3*w - 10],\ [269, 269, -w^3 + 1/2*w^2 + 7*w - 8],\ [269, 269, w^3 + 1/2*w^2 - 7*w - 8],\ [269, 269, -1/2*w^3 + 1/2*w^2 + 3*w - 10],\ [271, 271, -w^3 + 8*w + 5],\ [271, 271, -2*w^2 + 2*w + 15],\ [271, 271, 2*w^2 + 2*w - 15],\ [271, 271, w^3 - 8*w + 5],\ [281, 281, -2*w + 3],\ [281, 281, w^3 - 2*w^2 - 12*w + 25],\ [311, 311, 1/2*w^3 + 5/2*w^2 - 3*w - 17],\ [311, 311, -1/2*w^3 + 5/2*w^2 + 3*w - 17],\ [331, 331, -1/2*w^3 + 3/2*w^2 + 5*w - 10],\ [331, 331, 1/2*w^3 + 3/2*w^2 - 5*w - 10],\ [349, 349, -1/2*w^2 + 3*w - 3],\ [349, 349, -w^3 + 5/2*w^2 + 11*w - 25],\ [379, 379, 5/2*w^2 - w - 21],\ [379, 379, 5/2*w^2 + w - 21],\ [389, 389, 3/2*w^2 - w - 14],\ [389, 389, 1/2*w^3 - 5/2*w^2 - 3*w + 16],\ [389, 389, -1/2*w^3 - 5/2*w^2 + 3*w + 16],\ [389, 389, 3/2*w^2 + w - 14],\ [409, 409, w^3 + w^2 - 8*w - 7],\ [409, 409, -w^3 + w^2 + 8*w - 7],\ [419, 419, 3/2*w^3 - 5/2*w^2 - 15*w + 28],\ [419, 419, 3/2*w^3 - 7/2*w^2 - 13*w + 28],\ [439, 439, 1/2*w^2 + 2*w - 9],\ [439, 439, -3/2*w^2 + 2*w + 6],\ [439, 439, -3/2*w^2 - 2*w + 6],\ [439, 439, 1/2*w^2 - 2*w - 9],\ [449, 449, -w^3 + 1/2*w^2 + 6*w - 1],\ [449, 449, 1/2*w^2 + 2*w - 5],\ [449, 449, 1/2*w^2 - 2*w - 5],\ [449, 449, w^3 + 1/2*w^2 - 6*w - 1],\ [461, 461, w^3 + 3/2*w^2 - 7*w - 9],\ [461, 461, -w^3 + 3/2*w^2 + 7*w - 9],\ [491, 491, -1/2*w^3 - 1/2*w^2 + 6*w + 7],\ [491, 491, -5/2*w^2 + w + 16],\ [491, 491, 5/2*w^2 + w - 16],\ [491, 491, 1/2*w^3 - 1/2*w^2 - 6*w + 7],\ [499, 499, -1/2*w^3 + 5/2*w^2 + 4*w - 19],\ [499, 499, 1/2*w^3 + 5/2*w^2 - 4*w - 19],\ [541, 541, -1/2*w^3 + 3/2*w^2 + 4*w - 7],\ [541, 541, 1/2*w^3 + 3/2*w^2 - 4*w - 7],\ [569, 569, 1/2*w^2 + 2*w - 2],\ [569, 569, 1/2*w^2 - 2*w - 2],\ [571, 571, -2*w^3 + 9/2*w^2 + 17*w - 39],\ [571, 571, 1/2*w^3 - 1/2*w^2 - 5*w - 2],\ [571, 571, -1/2*w^3 - 1/2*w^2 + 5*w - 2],\ [571, 571, w^3 - 5/2*w^2 - 11*w + 27],\ [599, 599, -w^3 + 2*w^2 + 8*w - 13],\ [599, 599, w^3 + 2*w^2 - 8*w - 13],\ [601, 601, 1/2*w^2 + 2*w - 4],\ [601, 601, 1/2*w^2 - 2*w - 4],\ [619, 619, -1/2*w^3 + 2*w^2 + 6*w - 13],\ [619, 619, 1/2*w^3 + 2*w^2 - 6*w - 13],\ [631, 631, -w^3 - 1/2*w^2 + 6*w - 2],\ [631, 631, w^3 - 1/2*w^2 - 6*w - 2],\ [641, 641, w^3 - 8*w - 1],\ [641, 641, -1/2*w^3 - 1/2*w^2 + 5*w - 1],\ [641, 641, 1/2*w^3 - 1/2*w^2 - 5*w - 1],\ [641, 641, w^3 - 8*w + 1],\ [661, 661, -1/2*w^3 + 7/2*w^2 + 2*w - 25],\ [661, 661, 3/2*w^3 - 9/2*w^2 - 11*w + 32],\ [661, 661, -5/2*w^3 + 13/2*w^2 + 23*w - 56],\ [661, 661, 1/2*w^3 + 7/2*w^2 - 2*w - 25],\ [691, 691, 1/2*w^3 + 7/2*w^2 - 3*w - 28],\ [691, 691, -1/2*w^3 + 7/2*w^2 + 3*w - 28],\ [701, 701, -1/2*w^3 + 1/2*w^2 + 5*w - 10],\ [701, 701, 3/2*w^3 - 5/2*w^2 - 17*w + 34],\ [709, 709, 1/2*w^3 - 5/2*w^2 - 6*w + 17],\ [709, 709, w^3 + 5/2*w^2 - 7*w - 14],\ [709, 709, -w^3 + 5/2*w^2 + 7*w - 14],\ [709, 709, -1/2*w^3 - 5/2*w^2 + 6*w + 17],\ [719, 719, -w^3 + 7/2*w^2 + 8*w - 23],\ [719, 719, w^3 + 7/2*w^2 - 8*w - 23],\ [751, 751, 7/2*w^2 + 2*w - 27],\ [751, 751, 7/2*w^2 - 2*w - 27],\ [761, 761, -1/2*w^3 + 3/2*w^2 + 3*w - 13],\ [761, 761, 1/2*w^3 + 3/2*w^2 - 3*w - 13],\ [769, 769, -w^3 + 7/2*w^2 + 8*w - 25],\ [769, 769, w^3 + 7/2*w^2 - 8*w - 25],\ [809, 809, 2*w^3 - 7/2*w^2 - 20*w + 40],\ [809, 809, -1/2*w^2 + 2*w - 4],\ [811, 811, -1/2*w^2 - 3*w + 8],\ [811, 811, 1/2*w^3 + 3/2*w^2 - 3*w - 18],\ [811, 811, -1/2*w^3 + 3/2*w^2 + 3*w - 18],\ [811, 811, 1/2*w^2 - 3*w - 8],\ [821, 821, 3/2*w^3 - 7/2*w^2 - 16*w + 37],\ [821, 821, -3/2*w^3 + 7/2*w^2 + 12*w - 29],\ [839, 839, 3*w^2 - 2*w - 23],\ [839, 839, 3*w^2 + 2*w - 23],\ [841, 29, -5/2*w^2 + 16],\ [859, 859, 5/2*w^2 + 3*w - 16],\ [859, 859, 5/2*w^2 - 3*w - 16],\ [911, 911, 3*w^2 - 2*w - 17],\ [911, 911, 3*w^2 + 2*w - 17],\ [919, 919, 3*w^2 - w - 23],\ [919, 919, -2*w^2 + 3*w + 15],\ [919, 919, -2*w^2 - 3*w + 15],\ [919, 919, 3*w^2 + w - 23],\ [941, 941, 3/2*w^2 - 3*w - 2],\ [941, 941, 2*w^3 - 11/2*w^2 - 17*w + 42],\ [961, 31, -w^2 + 13],\ [971, 971, 1/2*w^3 + 1/2*w^2 - 6*w - 5],\ [971, 971, -1/2*w^3 + 1/2*w^2 + 6*w - 5],\ [991, 991, w^3 + 3/2*w^2 - 8*w - 8],\ [991, 991, -w^3 + 3/2*w^2 + 8*w - 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + 5*x^7 - 4*x^6 - 49*x^5 - 46*x^4 + 58*x^3 + 65*x^2 - 18*x - 17 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -116/617*e^7 - 465/617*e^6 + 675/617*e^5 + 4084/617*e^4 + 2968/617*e^3 - 1309/617*e^2 - 2152/617*e - 1289/617, 1, 10/617*e^7 + 72/617*e^6 - 5/617*e^5 - 501/617*e^4 - 575/617*e^3 - 1302/617*e^2 - 857/617*e + 526/617, -23/617*e^7 - 289/617*e^6 - 297/617*e^5 + 3065/617*e^4 + 4716/617*e^3 - 4903/617*e^2 - 5001/617*e + 1505/617, -168/617*e^7 - 716/617*e^6 + 1318/617*e^5 + 7553/617*e^4 + 1022/617*e^3 - 13172/617*e^2 - 1521/617*e + 5601/617, 247/617*e^7 + 1038/617*e^6 - 1666/617*e^5 - 10462/617*e^4 - 4639/617*e^3 + 14856/617*e^2 + 7029/617*e - 4037/617, 97/617*e^7 + 575/617*e^6 - 357/617*e^5 - 6032/617*e^4 - 4035/617*e^3 + 10323/617*e^2 + 1374/617*e - 6991/617, -257/617*e^7 - 1110/617*e^6 + 1671/617*e^5 + 10963/617*e^4 + 5214/617*e^3 - 14171/617*e^2 - 6789/617*e + 4128/617, -486/617*e^7 - 1895/617*e^6 + 3945/617*e^5 + 19536/617*e^4 + 2648/617*e^3 - 30877/617*e^2 - 6229/617*e + 10099/617, 438/617*e^7 + 2043/617*e^6 - 2070/617*e^5 - 19229/617*e^4 - 15930/617*e^3 + 16272/617*e^2 + 14168/617*e - 3122/617, -161/617*e^7 - 789/617*e^6 + 389/617*e^5 + 6647/617*e^4 + 8949/617*e^3 + 231/617*e^2 - 4157/617*e - 3039/617, 10/617*e^7 + 72/617*e^6 - 5/617*e^5 - 1118/617*e^4 - 1192/617*e^3 + 4868/617*e^2 + 2845/617*e - 4410/617, 374/617*e^7 + 1212/617*e^6 - 3889/617*e^5 - 13061/617*e^4 + 6260/617*e^3 + 25592/617*e^2 - 4040/617*e - 10067/617, 340/617*e^7 + 1831/617*e^6 - 787/617*e^5 - 17034/617*e^4 - 20167/617*e^3 + 12496/617*e^2 + 18371/617*e - 3094/617, 143/617*e^7 + 536/617*e^6 - 997/617*e^5 - 4758/617*e^4 - 2361/617*e^3 + 1619/617*e^2 + 3355/617*e + 488/617, -366/617*e^7 - 1648/617*e^6 + 2034/617*e^5 + 15992/617*e^4 + 10556/617*e^3 - 17502/617*e^2 - 8492/617*e + 4071/617, -263/617*e^7 - 783/617*e^6 + 2908/617*e^5 + 8302/617*e^4 - 6164/617*e^3 - 15611/617*e^2 + 5078/617*e + 4923/617, 37/617*e^7 + 143/617*e^6 - 327/617*e^5 - 1175/617*e^4 + 649/617*e^3 - 992/617*e^2 - 3356/617*e + 4661/617, -55/617*e^7 - 396/617*e^6 - 281/617*e^5 + 3064/617*e^4 + 6556/617*e^3 + 2842/617*e^2 - 2382/617*e - 1659/617, -204/617*e^7 - 605/617*e^6 + 2570/617*e^5 + 7629/617*e^4 - 7397/617*e^3 - 23663/617*e^2 + 3045/617*e + 14690/617, 486/617*e^7 + 1895/617*e^6 - 3328/617*e^5 - 17685/617*e^4 - 8201/617*e^3 + 14835/617*e^2 + 8080/617*e - 844/617, -7/617*e^7 - 544/617*e^6 - 2156/617*e^5 + 3374/617*e^4 + 20455/617*e^3 + 10660/617*e^2 - 14640/617*e - 5551/617, 228/617*e^7 + 531/617*e^6 - 3199/617*e^5 - 6240/617*e^4 + 12187/617*e^3 + 16466/617*e^2 - 13493/617*e - 8615/617, 287/617*e^7 + 709/617*e^6 - 2920/617*e^5 - 5679/617*e^4 + 4784/617*e^3 - 2075/617*e^2 - 9973/617*e + 4854/617, 167/617*e^7 + 462/617*e^6 - 2243/617*e^5 - 6454/617*e^4 + 6748/617*e^3 + 24038/617*e^2 + 1545/617*e - 14415/617, 537/617*e^7 + 2509/617*e^6 - 2428/617*e^5 - 23757/617*e^4 - 20697/617*e^3 + 23373/617*e^2 + 19813/617*e - 9144/617, 734/617*e^7 + 3187/617*e^6 - 4686/617*e^5 - 31097/617*e^4 - 15057/617*e^3 + 34867/617*e^2 + 10766/617*e - 6556/617, -533/617*e^7 - 2110/617*e^6 + 4277/617*e^5 + 21212/617*e^4 + 1957/617*e^3 - 29200/617*e^2 + 2920/617*e + 7997/617, -136/617*e^7 - 609/617*e^6 + 685/617*e^5 + 6320/617*e^4 + 5352/617*e^3 - 10428/617*e^2 - 7842/617*e + 5680/617, 567/617*e^7 + 2108/617*e^6 - 4294/617*e^5 - 19707/617*e^4 - 5146/617*e^3 + 16382/617*e^2 - 651/617*e - 779/617, -294/617*e^7 - 1870/617*e^6 - 470/617*e^5 + 15840/617*e^4 + 26160/617*e^3 + 1012/617*e^2 - 10220/617*e - 11022/617, 450/617*e^7 + 1389/617*e^6 - 5161/617*e^5 - 15141/617*e^4 + 12996/617*e^3 + 30875/617*e^2 - 17587/617*e - 15201/617, 437/617*e^7 + 2406/617*e^6 - 1144/617*e^5 - 23066/617*e^4 - 24202/617*e^3 + 23436/617*e^2 + 23447/617*e - 8851/617, -368/617*e^7 - 1539/617*e^6 + 3269/617*e^5 + 16956/617*e^4 - 1052/617*e^3 - 35258/617*e^2 - 2891/617*e + 17293/617, 263/617*e^7 + 783/617*e^6 - 3525/617*e^5 - 10153/617*e^4 + 11100/617*e^3 + 32887/617*e^2 - 2610/617*e - 22816/617, 264/617*e^7 + 1654/617*e^6 + 1102/617*e^5 - 13103/617*e^4 - 31839/617*e^3 - 9446/617*e^2 + 24514/617*e + 9444/617, -1096/617*e^7 - 4436/617*e^6 + 7952/617*e^5 + 43927/617*e^4 + 14894/617*e^3 - 55728/617*e^2 - 23056/617*e + 10714/617, 117/617*e^7 + 1336/617*e^6 + 2101/617*e^5 - 11970/617*e^4 - 28631/617*e^3 + 4017/617*e^2 + 20021/617*e - 2237/617, -1092/617*e^7 - 4654/617*e^6 + 7333/617*e^5 + 45701/617*e^4 + 18983/617*e^3 - 54151/617*e^2 - 15748/617*e + 9567/617, -726/617*e^7 - 2389/617*e^6 + 7150/617*e^5 + 24156/617*e^4 - 8849/617*e^3 - 36649/617*e^2 + 8786/617*e + 16602/617, -547/617*e^7 - 3198/617*e^6 + 582/617*e^5 + 29194/617*e^4 + 37314/617*e^3 - 16518/617*e^2 - 25743/617*e - 5573/617, 1126/617*e^7 + 4652/617*e^6 - 7967/617*e^5 - 46047/617*e^4 - 17236/617*e^3 + 57992/617*e^2 + 24187/617*e - 12838/617, -33/617*e^7 - 361/617*e^6 - 1526/617*e^5 + 481/617*e^4 + 16397/617*e^3 + 23547/617*e^2 - 9080/617*e - 19999/617, -231/617*e^7 - 676/617*e^6 + 4126/617*e^5 + 11388/617*e^4 - 19727/617*e^3 - 49887/617*e^2 + 10480/617*e + 26597/617, 1023/617*e^7 + 3787/617*e^6 - 8224/617*e^5 - 36506/617*e^4 - 4835/617*e^3 + 40059/617*e^2 - 489/617*e - 11839/617, -140/617*e^7 - 391/617*e^6 + 1304/617*e^5 + 3312/617*e^4 - 588/617*e^3 - 282/617*e^2 - 4044/617*e - 3662/617, -1444/617*e^7 - 5831/617*e^6 + 10594/617*e^5 + 57413/617*e^4 + 17628/617*e^3 - 69527/617*e^2 - 19640/617*e + 14868/617, -968/617*e^7 - 4008/617*e^6 + 6654/617*e^5 + 38995/617*e^4 + 15555/617*e^3 - 43518/617*e^2 - 12554/617*e + 4243/617, -657/617*e^7 - 1522/617*e^6 + 9275/617*e^5 + 19280/617*e^4 - 32869/617*e^3 - 59577/617*e^2 + 19470/617*e + 36150/617, 206/617*e^7 + 496/617*e^6 - 3188/617*e^5 - 6742/617*e^4 + 14069/617*e^3 + 23526/617*e^2 - 17284/617*e - 11870/617, 851/617*e^7 + 3906/617*e^6 - 3819/617*e^5 - 35046/617*e^4 - 31965/617*e^3 + 16672/617*e^2 + 25234/617*e + 4781/617, -99/617*e^7 + 151/617*e^6 + 3443/617*e^5 + 2060/617*e^4 - 23615/617*e^3 - 31781/617*e^2 + 14716/617*e + 20830/617, 547/617*e^7 + 2581/617*e^6 - 3667/617*e^5 - 26726/617*e^4 - 8932/617*e^3 + 41815/617*e^2 + 5382/617*e - 17256/617, -589/617*e^7 - 3377/617*e^6 - 14/617*e^5 + 30311/617*e^4 + 47750/617*e^3 - 14875/617*e^2 - 41394/617*e - 1859/617, 505/617*e^7 + 1785/617*e^6 - 4880/617*e^5 - 18822/617*e^4 + 3972/617*e^3 + 31118/617*e^2 + 5773/617*e - 7372/617, -561/617*e^7 - 1818/617*e^6 + 5525/617*e^5 + 18049/617*e^4 - 7539/617*e^3 - 22963/617*e^2 + 13464/617*e + 7388/617, 476/617*e^7 + 1823/617*e^6 - 4557/617*e^5 - 19652/617*e^4 + 5331/617*e^3 + 38966/617*e^2 - 5871/617*e - 26667/617, -489/617*e^7 - 2040/617*e^6 + 2404/617*e^5 + 17280/617*e^4 + 16703/617*e^3 + 1104/617*e^2 - 9242/617*e - 8939/617, 1759/617*e^7 + 7482/617*e^6 - 11677/617*e^5 - 72886/617*e^4 - 31113/617*e^3 + 84044/617*e^2 + 21952/617*e - 26064/617, -59/617*e^7 - 178/617*e^6 + 955/617*e^5 + 3758/617*e^4 - 3086/617*e^3 - 19096/617*e^2 - 1669/617*e + 7509/617, 873/617*e^7 + 3941/617*e^6 - 3830/617*e^5 - 35778/617*e^4 - 35698/617*e^3 + 20101/617*e^2 + 35812/617*e + 2483/617, 717/617*e^7 + 2571/617*e^6 - 6220/617*e^5 - 25371/617*e^4 + 420/617*e^3 + 32021/617*e^2 + 6855/617*e - 3995/617, -959/617*e^7 - 3573/617*e^6 + 8809/617*e^5 + 38359/617*e^4 - 5015/617*e^3 - 72208/617*e^2 - 1664/617*e + 23720/617, 960/617*e^7 + 3827/617*e^6 - 6650/617*e^5 - 35756/617*e^4 - 13861/617*e^3 + 28641/617*e^2 + 406/617*e - 4417/617, 292/617*e^7 + 1362/617*e^6 - 2614/617*e^5 - 16110/617*e^4 - 131/617*e^3 + 40464/617*e^2 + 12736/617*e - 23265/617, -157/617*e^7 - 390/617*e^6 + 1004/617*e^5 + 2868/617*e^4 + 5634/617*e^3 + 4893/617*e^2 - 18444/617*e - 9122/617, 1712/617*e^7 + 7267/617*e^6 - 11345/617*e^5 - 71210/617*e^4 - 31804/617*e^3 + 85721/617*e^2 + 34186/617*e - 23230/617, -367/617*e^7 - 1902/617*e^6 + 1109/617*e^5 + 17708/617*e^4 + 20794/617*e^3 - 10955/617*e^2 - 26361/617*e - 9679/617, 489/617*e^7 + 189/617*e^6 - 9808/617*e^5 - 5557/617*e^4 + 53018/617*e^3 + 39001/617*e^2 - 47522/617*e - 18826/617, 56/617*e^7 + 650/617*e^6 + 589/617*e^5 - 6631/617*e^4 - 9390/617*e^3 + 9738/617*e^2 + 5443/617*e - 14207/617, 665/617*e^7 + 1703/617*e^6 - 8045/617*e^5 - 18817/617*e^4 + 21303/617*e^3 + 41136/617*e^2 - 12875/617*e - 8828/617, -55/617*e^7 + 838/617*e^6 + 3421/617*e^5 - 8659/617*e^4 - 29230/617*e^3 + 12714/617*e^2 + 35872/617*e - 10914/617, 384/617*e^7 + 1284/617*e^6 - 3277/617*e^5 - 12945/617*e^4 - 1102/617*e^3 + 20588/617*e^2 + 1890/617*e - 22498/617, -333/617*e^7 - 1287/617*e^6 + 2326/617*e^5 + 11192/617*e^4 + 4031/617*e^3 - 2178/617*e^2 + 4907/617*e - 7397/617, 1677/617*e^7 + 6398/617*e^6 - 13487/617*e^5 - 64212/617*e^4 - 9122/617*e^3 + 90278/617*e^2 + 9112/617*e - 38028/617, -641/617*e^7 - 3011/617*e^6 + 3097/617*e^5 + 27610/617*e^4 + 21741/617*e^3 - 16866/617*e^2 - 17934/617*e - 2990/617, 1176/617*e^7 + 5629/617*e^6 - 4907/617*e^5 - 52254/617*e^4 - 47876/617*e^3 + 37908/617*e^2 + 32859/617*e - 1570/617, -661/617*e^7 - 3155/617*e^6 + 1256/617*e^5 + 24910/617*e^4 + 41401/617*e^3 + 14737/617*e^2 - 33496/617*e - 16382/617, -107/617*e^7 - 1264/617*e^6 - 3340/617*e^5 + 7150/617*e^4 + 37928/617*e^3 + 35403/617*e^2 - 14708/617*e - 28704/617, -13/617*e^7 - 834/617*e^6 - 3387/617*e^5 + 5032/617*e^4 + 33757/617*e^3 + 20326/617*e^2 - 31772/617*e - 15862/617, -1379/617*e^7 - 5363/617*e^6 + 11487/617*e^5 + 55699/617*e^4 + 4944/617*e^3 - 92181/617*e^2 - 19349/617*e + 34329/617, -347/617*e^7 - 1141/617*e^6 + 4184/617*e^5 + 13004/617*e^4 - 11823/617*e^3 - 28367/617*e^2 + 11413/617*e - 3691/617, 1457/617*e^7 + 4814/617*e^6 - 14611/617*e^5 - 50105/617*e^4 + 19570/617*e^3 + 84370/617*e^2 - 18309/617*e - 32324/617, -220/617*e^7 - 1584/617*e^6 - 507/617*e^5 + 16575/617*e^4 + 24373/617*e^3 - 28120/617*e^2 - 34208/617*e + 10640/617, 653/617*e^7 + 2357/617*e^6 - 5571/617*e^5 - 22905/617*e^4 + 1632/617*e^3 + 25916/617*e^2 - 21842/617*e - 9706/617, -523/617*e^7 - 1421/617*e^6 + 6740/617*e^5 + 15775/617*e^4 - 22681/617*e^3 - 31736/617*e^2 + 28594/617*e + 7906/617, 485/617*e^7 + 1641/617*e^6 - 5487/617*e^5 - 18437/617*e^4 + 13760/617*e^3 + 38658/617*e^2 - 18427/617*e - 11509/617, -790/617*e^7 - 3220/617*e^6 + 6565/617*e^5 + 33409/617*e^4 + 1001/617*e^3 - 55094/617*e^2 + 4769/617*e + 23848/617, -1222/617*e^7 - 5590/617*e^6 + 6164/617*e^5 + 52214/617*e^4 + 38798/617*e^3 - 41544/617*e^2 - 22500/617*e + 2112/617, -1059/617*e^7 - 3676/617*e^6 + 8859/617*e^5 + 34114/617*e^4 + 735/617*e^3 - 24636/617*e^2 + 10608/617*e - 5603/617, -78/617*e^7 + 549/617*e^6 + 3741/617*e^5 - 3126/617*e^4 - 27599/617*e^3 - 16869/617*e^2 + 17297/617*e + 17122/617, -583/617*e^7 - 3087/617*e^6 + 3068/617*e^5 + 32355/617*e^4 + 17172/617*e^3 - 52306/617*e^2 - 15624/617*e + 11537/617, 912/617*e^7 + 3358/617*e^6 - 6626/617*e^5 - 30513/617*e^4 - 12335/617*e^3 + 19589/617*e^2 + 18834/617*e + 7496/617, -822/617*e^7 - 2710/617*e^6 + 7198/617*e^5 + 25387/617*e^4 - 861/617*e^3 - 23286/617*e^2 + 1835/617*e + 8344/617, -120/617*e^7 + 370/617*e^6 + 4379/617*e^5 - 1392/617*e^4 - 32588/617*e^3 - 15226/617*e^2 + 40517/617*e + 2943/617, 306/617*e^7 + 3684/617*e^6 + 6634/617*e^5 - 30879/617*e^4 - 85465/617*e^3 - 6153/617*e^2 + 64845/617*e + 6964/617, -373/617*e^7 - 1575/617*e^6 + 3580/617*e^5 + 19366/617*e^4 - 4158/617*e^3 - 56202/617*e^2 + 6484/617*e + 36157/617, 614/617*e^7 + 3557/617*e^6 - 307/617*e^5 - 31872/617*e^4 - 46411/617*e^3 + 14705/617*e^2 + 41411/617*e - 10400/617, -438/617*e^7 - 1426/617*e^6 + 4538/617*e^5 + 15527/617*e^4 - 6899/617*e^3 - 32931/617*e^2 + 8044/617*e + 26568/617, 780/617*e^7 + 3765/617*e^6 - 2858/617*e^5 - 35376/617*e^4 - 36829/617*e^3 + 31716/617*e^2 + 35576/617*e - 10800/617, -1078/617*e^7 - 4800/617*e^6 + 5475/617*e^5 + 43889/617*e^4 + 33603/617*e^3 - 29196/617*e^2 - 17318/617*e + 4010/617, -1023/617*e^7 - 4404/617*e^6 + 6373/617*e^5 + 43293/617*e^4 + 23345/617*e^3 - 53633/617*e^2 - 25425/617*e + 18009/617, -1595/617*e^7 - 5931/617*e^6 + 12829/617*e^5 + 57389/617*e^4 + 8109/617*e^3 - 62577/617*e^2 + 26/617*e + 12972/617, 966/617*e^7 + 2266/617*e^6 - 12823/617*e^5 - 25074/617*e^4 + 43792/617*e^3 + 54761/617*e^2 - 46630/617*e - 13233/617, -2181/617*e^7 - 8546/617*e^6 + 17441/617*e^5 + 86871/617*e^4 + 14039/617*e^3 - 126092/617*e^2 - 27249/617*e + 40023/617, 604/617*e^7 + 2251/617*e^6 - 5855/617*e^5 - 23967/617*e^4 + 8460/617*e^3 + 43155/617*e^2 - 20049/617*e - 17096/617, -2228/617*e^7 - 10612/617*e^6 + 9752/617*e^5 + 99653/617*e^4 + 86771/617*e^3 - 85544/617*e^2 - 65609/617*e + 15709/617, -166/617*e^7 - 2059/617*e^6 - 4853/617*e^5 + 13993/617*e^4 + 58288/617*e^3 + 29264/617*e^2 - 47227/617*e - 10706/617, -972/617*e^7 - 3173/617*e^6 + 10358/617*e^5 + 35370/617*e^4 - 18767/617*e^3 - 79030/617*e^2 + 11605/617*e + 31921/617, 162/617*e^7 + 1660/617*e^6 + 1770/617*e^5 - 15767/617*e^4 - 29059/617*e^3 + 15434/617*e^2 + 30047/617*e - 12827/617, 1612/617*e^7 + 4696/617*e^6 - 19933/617*e^5 - 55094/617*e^4 + 56624/617*e^3 + 140080/617*e^2 - 36220/617*e - 62425/617, -518/617*e^7 - 1385/617*e^6 + 7663/617*e^5 + 19535/617*e^4 - 28213/617*e^3 - 71875/617*e^2 + 10581/617*e + 41487/617, -1177/617*e^7 - 4649/617*e^6 + 8301/617*e^5 + 44098/617*e^4 + 16158/617*e^3 - 44935/617*e^2 - 7538/617*e + 13734/617, -381/617*e^7 - 1139/617*e^6 + 6052/617*e^5 + 15818/617*e^4 - 27144/617*e^3 - 53803/617*e^2 + 24569/617*e + 20558/617, 589/617*e^7 + 909/617*e^6 - 11092/617*e^5 - 15503/617*e^4 + 57140/617*e^3 + 69788/617*e^2 - 42518/617*e - 27140/617, -140/617*e^7 + 1460/617*e^6 + 8091/617*e^5 - 9645/617*e^4 - 61671/617*e^3 - 29898/617*e^2 + 35444/617*e + 27805/617, -368/617*e^7 - 1539/617*e^6 + 3269/617*e^5 + 19424/617*e^4 + 1416/617*e^3 - 58087/617*e^2 - 21401/617*e + 29016/617, -1893/617*e^7 - 6349/617*e^6 + 19148/617*e^5 + 67136/617*e^4 - 25967/617*e^3 - 117438/617*e^2 + 11497/617*e + 34564/617, -707/617*e^7 - 3116/617*e^6 + 1896/617*e^5 + 23636/617*e^4 + 37876/617*e^3 + 26526/617*e^2 - 20669/617*e - 34967/617, 533/617*e^7 + 2727/617*e^6 - 1192/617*e^5 - 24297/617*e^4 - 32807/617*e^3 + 8839/617*e^2 + 34100/617*e - 4295/617, -148/617*e^7 + 45/617*e^6 + 4393/617*e^5 + 4700/617*e^4 - 26659/617*e^3 - 47243/617*e^2 + 4786/617*e + 27631/617, -495/617*e^7 - 4181/617*e^6 - 4997/617*e^5 + 34980/617*e^4 + 86152/617*e^3 + 5217/617*e^2 - 70798/617*e - 9378/617, 453/617*e^7 + 300/617*e^6 - 9173/617*e^5 - 7332/617*e^4 + 50152/617*e^3 + 45169/617*e^2 - 44190/617*e - 28247/617, -424/617*e^7 - 2189/617*e^6 + 2063/617*e^5 + 23587/617*e^4 + 16359/617*e^3 - 44996/617*e^2 - 18823/617*e + 17926/617, -1583/617*e^7 - 5351/617*e^6 + 15908/617*e^5 + 56541/617*e^4 - 22197/617*e^3 - 103504/617*e^2 + 15163/617*e + 41615/617, 271/617*e^7 + 964/617*e^6 - 1061/617*e^5 - 7839/617*e^4 - 14657/617*e^3 + 1489/617*e^2 + 31750/617*e - 7834/617, 1057/617*e^7 + 5636/617*e^6 - 3305/617*e^5 - 54128/617*e^4 - 54916/617*e^3 + 54389/617*e^2 + 62246/617*e - 9557/617, 921/617*e^7 + 5644/617*e^6 + 465/617*e^5 - 49659/617*e^4 - 77329/617*e^3 + 12494/617*e^2 + 60574/617*e + 9697/617, 1583/617*e^7 + 6585/617*e^6 - 10972/617*e^5 - 65179/617*e^4 - 22844/617*e^3 + 83760/617*e^2 + 11985/617*e - 28658/617, 790/617*e^7 + 4454/617*e^6 - 1012/617*e^5 - 42047/617*e^4 - 55297/617*e^3 + 35967/617*e^2 + 52612/617*e - 2253/617, 1331/617*e^7 + 4277/617*e^6 - 13314/617*e^5 - 43052/617*e^4 + 17560/617*e^3 + 59066/617*e^2 - 14668/617*e - 3906/617, 239/617*e^7 - 377/617*e^6 - 7832/617*e^5 - 2904/617*e^4 + 53202/617*e^3 + 55509/617*e^2 - 42139/617*e - 34444/617, 978/617*e^7 + 5314/617*e^6 - 2340/617*e^5 - 49985/617*e^4 - 56235/617*e^3 + 41599/617*e^2 + 46866/617*e - 8036/617, 88/617*e^7 + 140/617*e^6 - 1278/617*e^5 - 1694/617*e^4 + 4812/617*e^3 + 9397/617*e^2 - 2112/617*e - 19064/617, 1893/617*e^7 + 8817/617*e^6 - 9276/617*e^5 - 83795/617*e^4 - 64115/617*e^3 + 77950/617*e^2 + 45884/617*e - 10501/617, -2446/617*e^7 - 11071/617*e^6 + 13563/617*e^5 + 105392/617*e^4 + 67839/617*e^3 - 97759/617*e^2 - 43101/617*e + 11276/617, 1099/617*e^7 + 4581/617*e^6 - 9496/617*e^5 - 50309/617*e^4 + 3135/617*e^3 + 103957/617*e^2 - 10951/617*e - 57078/617, 477/617*e^7 + 2077/617*e^6 - 3015/617*e^5 - 21985/617*e^4 - 13545/617*e^3 + 39823/617*e^2 + 31742/617*e - 20321/617, -1742/617*e^7 - 8100/617*e^6 + 8892/617*e^5 + 79500/617*e^4 + 56975/617*e^3 - 96623/617*e^2 - 49508/617*e + 35226/617, -406/617*e^7 - 702/617*e^6 + 7607/617*e^5 + 13060/617*e^4 - 37738/617*e^3 - 65973/617*e^2 + 25169/617*e + 35285/617, -1138/617*e^7 - 3381/617*e^6 + 11675/617*e^5 + 32704/617*e^4 - 19711/617*e^3 - 36809/617*e^2 + 35333/617*e - 4082/617, -1526/617*e^7 - 6298/617*e^6 + 9401/617*e^5 + 57449/617*e^4 + 33449/617*e^3 - 35528/617*e^2 - 22608/617*e - 8819/617, 1100/617*e^7 + 4218/617*e^6 - 8571/617*e^5 - 41536/617*e^4 - 8954/617*e^3 + 49284/617*e^2 + 14939/617*e + 3564/617, 1260/617*e^7 + 4136/617*e^6 - 14204/617*e^5 - 47701/617*e^4 + 31823/617*e^3 + 112364/617*e^2 - 22836/617*e - 42933/617, -340/617*e^7 + 20/617*e^6 + 8191/617*e^5 + 4077/617*e^4 - 50171/617*e^3 - 39027/617*e^2 + 45180/617*e + 12966/617, 2000/617*e^7 + 7613/617*e^6 - 17659/617*e^5 - 81073/617*e^4 + 2847/617*e^3 + 148054/617*e^2 + 11849/617*e - 48433/617, 1412/617*e^7 + 5724/617*e^6 - 11195/617*e^5 - 58031/617*e^4 - 8384/617*e^3 + 80974/617*e^2 + 13004/617*e - 3841/617, 519/617*e^7 + 3490/617*e^6 + 1283/617*e^5 - 29889/617*e^4 - 49895/617*e^3 - 691/617*e^2 + 18394/617*e + 16070/617, -324/617*e^7 - 852/617*e^6 + 5098/617*e^5 + 11790/617*e^4 - 23943/617*e^3 - 40123/617*e^2 + 34307/617*e + 14548/617, -741/617*e^7 - 1880/617*e^6 + 9934/617*e^5 + 23365/617*e^4 - 30507/617*e^3 - 66780/617*e^2 + 2976/617*e + 31238/617, 685/617*e^7 + 3698/617*e^6 - 651/617*e^5 - 32159/617*e^4 - 50185/617*e^3 + 2129/617*e^2 + 47728/617*e + 19989/617, -808/617*e^7 - 2239/617*e^6 + 9659/617*e^5 + 25426/617*e^4 - 23878/617*e^3 - 60031/617*e^2 + 9520/617*e + 18212/617, -231/617*e^7 - 59/617*e^6 + 4126/617*e^5 - 952/617*e^4 - 21578/617*e^3 + 13664/617*e^2 + 33926/617*e - 15976/617, -187/617*e^7 - 1223/617*e^6 - 215/617*e^5 + 10541/617*e^4 + 15997/617*e^3 + 3863/617*e^2 - 10320/617*e - 21189/617, -1735/617*e^7 - 6322/617*e^6 + 15367/617*e^5 + 62552/617*e^4 - 5436/617*e^3 - 79518/617*e^2 + 2152/617*e + 3757/617] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, -1/2*w^2 - w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]