/* 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([29, 3, -12, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4]) primes_array = [ [4, 2, 1/2*w^3 - 2*w^2 - 2*w + 15/2],\ [4, 2, -w^2 + w + 8],\ [5, 5, -1/4*w^3 + 1/2*w^2 + 1/2*w - 9/4],\ [5, 5, 1/2*w^3 - w^2 - 4*w + 9/2],\ [19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4],\ [19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 41/4],\ [29, 29, w],\ [29, 29, 1/4*w^3 - 1/2*w^2 - 1/2*w + 1/4],\ [29, 29, 1/4*w^3 - 1/2*w^2 - 5/2*w + 9/4],\ [29, 29, -1/2*w^3 + w^2 + 4*w - 5/2],\ [41, 41, 3/4*w^3 - 5/2*w^2 - 7/2*w + 47/4],\ [41, 41, 1/4*w^3 + 1/2*w^2 - 5/2*w - 15/4],\ [61, 61, -3/2*w^3 + 3*w^2 + 11*w - 21/2],\ [61, 61, w^3 - 2*w^2 - 4*w + 6],\ [79, 79, 3/4*w^3 - 5/2*w^2 - 7/2*w + 27/4],\ [79, 79, 1/4*w^3 + 1/2*w^2 - 5/2*w - 35/4],\ [81, 3, -3],\ [89, 89, 7/4*w^3 - 11/2*w^2 - 21/2*w + 119/4],\ [89, 89, 1/4*w^3 + 3/2*w^2 - 3/2*w - 23/4],\ [109, 109, -1/2*w^3 + 3*w^2 + 2*w - 41/2],\ [109, 109, -5/4*w^3 + 7/2*w^2 + 9/2*w - 45/4],\ [121, 11, -3/4*w^3 + 3/2*w^2 + 9/2*w - 23/4],\ [121, 11, -1/4*w^3 + 1/2*w^2 + 3/2*w - 21/4],\ [131, 131, -1/2*w^3 + w^2 + 5*w - 3/2],\ [131, 131, 3/4*w^3 - 1/2*w^2 - 7/2*w - 1/4],\ [139, 139, -5/4*w^3 + 11/2*w^2 + 9/2*w - 73/4],\ [139, 139, -1/4*w^3 + 7/2*w^2 - 3/2*w - 113/4],\ [149, 149, -1/4*w^3 + 3/2*w^2 + 1/2*w - 49/4],\ [149, 149, 1/4*w^3 - 3/2*w^2 - 1/2*w + 13/4],\ [151, 151, 1/2*w^3 - 3*w^2 - w + 23/2],\ [151, 151, -1/4*w^3 + 3/2*w^2 + 3/2*w - 45/4],\ [151, 151, 3/4*w^3 - 3/2*w^2 - 7/2*w + 11/4],\ [151, 151, -2*w^3 + 6*w^2 + 7*w - 20],\ [169, 13, -1/4*w^3 + 1/2*w^2 + 1/2*w - 25/4],\ [169, 13, 1/2*w^3 - w^2 - 4*w + 17/2],\ [179, 179, -1/4*w^3 + 1/2*w^2 + 7/2*w - 21/4],\ [179, 179, 1/4*w^3 - 1/2*w^2 - 7/2*w - 3/4],\ [181, 181, 1/2*w^3 - 3*w - 7/2],\ [181, 181, -5/4*w^3 + 7/2*w^2 + 15/2*w - 57/4],\ [191, 191, -3/4*w^3 + 5/2*w^2 + 9/2*w - 39/4],\ [191, 191, w^2 - 8],\ [199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 43/4],\ [199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 81/4],\ [199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 75/4],\ [199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 49/4],\ [229, 229, -1/2*w^3 + 2*w^2 + w - 21/2],\ [229, 229, -3/4*w^3 + 5/2*w^2 + 7/2*w - 55/4],\ [239, 239, 3/2*w^3 - 4*w^2 - 9*w + 35/2],\ [239, 239, 3/2*w^3 - 5*w^2 - 7*w + 45/2],\ [241, 241, -5/4*w^3 + 9/2*w^2 + 13/2*w - 93/4],\ [241, 241, -1/4*w^3 - 1/2*w^2 - 1/2*w + 3/4],\ [251, 251, -w^3 + 3*w^2 + 8*w - 13],\ [251, 251, -7/4*w^3 + 13/2*w^2 + 13/2*w - 99/4],\ [269, 269, -9/4*w^3 + 13/2*w^2 + 15/2*w - 85/4],\ [269, 269, -3/4*w^3 + 5/2*w^2 + 3/2*w - 47/4],\ [271, 271, 5/4*w^3 - 5/2*w^2 - 21/2*w + 53/4],\ [271, 271, 5/4*w^3 - 1/2*w^2 - 23/2*w - 23/4],\ [271, 271, 7/4*w^3 - 11/2*w^2 - 13/2*w + 83/4],\ [271, 271, -1/2*w^3 + w^2 - 13/2],\ [281, 281, 3/4*w^3 - 1/2*w^2 - 13/2*w - 1/4],\ [281, 281, -w^3 + 3*w^2 + 4*w - 13],\ [311, 311, -1/4*w^3 + 1/2*w^2 - 1/2*w - 5/4],\ [311, 311, 7/4*w^3 - 13/2*w^2 - 19/2*w + 155/4],\ [311, 311, -1/4*w^3 + 7/2*w^2 + 1/2*w - 49/4],\ [311, 311, -3/4*w^3 + 3/2*w^2 + 13/2*w - 23/4],\ [331, 331, -3/4*w^3 + 1/2*w^2 + 15/2*w + 5/4],\ [331, 331, -3/4*w^3 + 5/2*w^2 + 3/2*w - 39/4],\ [349, 349, -1/4*w^3 + 1/2*w^2 + 7/2*w - 17/4],\ [349, 349, 1/4*w^3 - 1/2*w^2 - 7/2*w + 1/4],\ [359, 359, -5/4*w^3 - 1/2*w^2 + 25/2*w + 55/4],\ [359, 359, w^2 - 2*w - 2],\ [359, 359, -9/4*w^3 + 15/2*w^2 + 17/2*w - 113/4],\ [359, 359, -1/4*w^3 + 3/2*w^2 - 1/2*w - 45/4],\ [361, 19, -w^3 + 2*w^2 + 6*w - 8],\ [379, 379, -5/4*w^3 + 5/2*w^2 + 17/2*w - 37/4],\ [379, 379, -5/4*w^3 + 7/2*w^2 + 9/2*w - 41/4],\ [379, 379, 5/4*w^3 - 3/2*w^2 - 21/2*w - 3/4],\ [379, 379, -w^3 + 2*w^2 + 5*w - 7],\ [389, 389, 9/4*w^3 - 17/2*w^2 - 15/2*w + 117/4],\ [389, 389, -3/4*w^3 - 5/2*w^2 + 21/2*w + 113/4],\ [401, 401, -3/4*w^3 - 7/2*w^2 + 23/2*w + 149/4],\ [401, 401, 11/4*w^3 - 21/2*w^2 - 19/2*w + 143/4],\ [409, 409, -3/4*w^3 + 5/2*w^2 + 9/2*w - 31/4],\ [409, 409, w^2 - 10],\ [421, 421, 5/4*w^3 - 5/2*w^2 - 19/2*w + 49/4],\ [421, 421, -1/4*w^3 + 5/2*w^2 - 1/2*w - 41/4],\ [421, 421, 5/4*w^3 - 5/2*w^2 - 7/2*w + 41/4],\ [421, 421, 9/4*w^3 - 9/2*w^2 - 35/2*w + 77/4],\ [431, 431, 7/4*w^3 - 9/2*w^2 - 11/2*w + 59/4],\ [431, 431, 5/4*w^3 - 9/2*w^2 - 13/2*w + 85/4],\ [431, 431, 5/4*w^3 - 5/2*w^2 - 11/2*w + 33/4],\ [431, 431, -2*w^2 + w + 12],\ [439, 439, -1/2*w^3 + w^2 + 5*w - 7/2],\ [439, 439, 2*w - 1],\ [461, 461, -7/4*w^3 + 13/2*w^2 + 21/2*w - 163/4],\ [461, 461, 3/2*w^3 - 5*w^2 - 4*w + 31/2],\ [491, 491, 5/4*w^3 - 3/2*w^2 - 17/2*w + 21/4],\ [491, 491, -7/4*w^3 + 9/2*w^2 + 19/2*w - 83/4],\ [509, 509, -3/2*w^3 + 4*w^2 + 7*w - 27/2],\ [509, 509, -3/2*w^3 + 3*w^2 + 10*w - 27/2],\ [521, 521, -5/4*w^3 + 3/2*w^2 + 11/2*w - 17/4],\ [521, 521, -5/2*w^3 + 6*w^2 + 17*w - 53/2],\ [521, 521, -1/2*w^3 + 3*w^2 + w - 31/2],\ [541, 541, 9/4*w^3 - 7/2*w^2 - 35/2*w + 37/4],\ [541, 541, w^3 - 2*w^2 - 8*w + 12],\ [541, 541, -1/4*w^3 - 3/2*w^2 + 7/2*w + 35/4],\ [541, 541, -3/4*w^3 + 9/2*w^2 + 5/2*w - 119/4],\ [569, 569, -w^3 + 3*w^2 + 6*w - 7],\ [569, 569, -7/4*w^3 + 9/2*w^2 + 23/2*w - 75/4],\ [599, 599, 1/4*w^3 + 5/2*w^2 - 9/2*w - 95/4],\ [599, 599, -7/4*w^3 + 13/2*w^2 + 15/2*w - 91/4],\ [619, 619, 9/4*w^3 - 13/2*w^2 - 19/2*w + 97/4],\ [619, 619, -7/4*w^3 + 3/2*w^2 + 29/2*w + 9/4],\ [619, 619, -1/4*w^3 + 3/2*w^2 - 3/2*w - 45/4],\ [619, 619, -1/4*w^3 - 1/2*w^2 + 9/2*w - 1/4],\ [631, 631, -9/4*w^3 + 13/2*w^2 + 15/2*w - 93/4],\ [631, 631, -13/4*w^3 + 21/2*w^2 + 39/2*w - 233/4],\ [631, 631, 7/4*w^3 - 9/2*w^2 - 15/2*w + 67/4],\ [631, 631, 1/4*w^3 + 7/2*w^2 - 3/2*w - 51/4],\ [641, 641, -1/4*w^3 + 5/2*w^2 + 1/2*w - 57/4],\ [641, 641, -w^3 + 4*w^2 + 5*w - 19],\ [661, 661, -2*w^3 + 20*w + 19],\ [661, 661, 5/4*w^3 - 11/2*w^2 - 13/2*w + 149/4],\ [691, 691, -5/4*w^3 + 3/2*w^2 + 13/2*w - 9/4],\ [691, 691, -7/4*w^3 + 11/2*w^2 + 23/2*w - 135/4],\ [739, 739, -2*w^3 + 7*w^2 + 10*w - 34],\ [739, 739, 1/4*w^3 + 5/2*w^2 - 7/2*w - 59/4],\ [751, 751, -1/2*w^3 + 3*w^2 + 2*w - 33/2],\ [751, 751, -3/4*w^3 + 7/2*w^2 + 7/2*w - 67/4],\ [761, 761, -w^3 + 4*w^2 + 5*w - 27],\ [761, 761, 7/4*w^3 - 9/2*w^2 - 15/2*w + 63/4],\ [769, 769, -5/4*w^3 + 1/2*w^2 + 25/2*w + 19/4],\ [769, 769, 3/2*w^3 - 5*w^2 - 4*w + 39/2],\ [769, 769, -3*w^3 + 10*w^2 + 11*w - 37],\ [769, 769, -7/4*w^3 + 5/2*w^2 + 27/2*w - 31/4],\ [811, 811, -w^3 + 3*w^2 + 6*w - 9],\ [811, 811, -3/4*w^3 + 7/2*w^2 + 5/2*w - 39/4],\ [811, 811, -1/4*w^3 + 5/2*w^2 - 1/2*w - 85/4],\ [811, 811, -5/4*w^3 + 7/2*w^2 + 17/2*w - 57/4],\ [821, 821, -3/4*w^3 + 3/2*w^2 + 3/2*w - 35/4],\ [821, 821, -5/4*w^3 + 11/2*w^2 + 9/2*w - 121/4],\ [829, 829, 7/4*w^3 - 13/2*w^2 - 19/2*w + 115/4],\ [829, 829, 1/4*w^3 - 7/2*w^2 - 1/2*w + 89/4],\ [839, 839, -3/4*w^3 + 5/2*w^2 + 3/2*w - 51/4],\ [839, 839, -3/4*w^3 + 1/2*w^2 + 15/2*w - 7/4],\ [911, 911, -3/4*w^3 + 1/2*w^2 + 11/2*w - 15/4],\ [911, 911, -3/4*w^3 + 7/2*w^2 + 3/2*w - 75/4],\ [929, 929, 9/4*w^3 - 9/2*w^2 - 35/2*w + 73/4],\ [929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 51/4],\ [929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 91/4],\ [929, 929, 5/2*w^3 - 4*w^2 - 19*w + 25/2],\ [961, 31, -5/4*w^3 + 5/2*w^2 + 15/2*w - 37/4],\ [961, 31, -1/2*w^3 + w^2 + 3*w - 19/2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + 2*x^7 - 14*x^6 - 22*x^5 + 53*x^4 + 66*x^3 - 44*x^2 - 40*x - 5 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/8*e^7 - 1/8*e^6 + 2*e^5 + 9/8*e^4 - 9*e^3 - 23/8*e^2 + 81/8*e + 5/4, e, -1/2*e^2 - 1/2*e + 3/2, 1/4*e^7 + 3/8*e^6 - 29/8*e^5 - 15/4*e^4 + 115/8*e^3 + 43/4*e^2 - 115/8*e - 53/8, 1, -1/8*e^7 - 1/4*e^6 + 15/8*e^5 + 25/8*e^4 - 61/8*e^3 - 87/8*e^2 + 5*e + 55/8, 3/8*e^7 + 5/8*e^6 - 23/4*e^5 - 53/8*e^4 + 103/4*e^3 + 143/8*e^2 - 253/8*e - 25/4, 1/4*e^7 + 3/8*e^6 - 27/8*e^5 - 13/4*e^4 + 89/8*e^3 + 25/4*e^2 - 33/8*e - 5/8, 1/8*e^6 - 1/8*e^5 - 5/2*e^4 + 11/8*e^3 + 23/2*e^2 - 17/8*e - 65/8, -1/8*e^6 - 3/8*e^5 + 7/4*e^4 + 33/8*e^3 - 27/4*e^2 - 71/8*e + 15/8, -5/8*e^7 - e^6 + 73/8*e^5 + 85/8*e^4 - 287/8*e^3 - 247/8*e^2 + 129/4*e + 89/8, -1/2*e^7 - 7/8*e^6 + 55/8*e^5 + 17/2*e^4 - 209/8*e^3 - 22*e^2 + 215/8*e + 79/8, -1/2*e^7 - 7/8*e^6 + 57/8*e^5 + 35/4*e^4 - 219/8*e^3 - 83/4*e^2 + 193/8*e + 29/8, -3/4*e^7 - e^6 + 23/2*e^5 + 41/4*e^4 - 99/2*e^3 - 121/4*e^2 + 223/4*e + 67/4, -9/8*e^7 - 2*e^6 + 125/8*e^5 + 155/8*e^4 - 471/8*e^3 - 373/8*e^2 + 207/4*e + 135/8, -1/4*e^7 - 1/8*e^6 + 29/8*e^5 - 1/4*e^4 - 107/8*e^3 + 15/4*e^2 + 103/8*e + 15/8, -1/2*e^7 - 1/2*e^6 + 15/2*e^5 + 15/4*e^4 - 59/2*e^3 - 17/4*e^2 + 26*e - 23/4, 1/2*e^7 + 9/8*e^6 - 61/8*e^5 - 27/2*e^4 + 275/8*e^3 + 81/2*e^2 - 337/8*e - 125/8, 3/4*e^7 + 7/4*e^6 - 10*e^5 - 75/4*e^4 + 73/2*e^3 + 203/4*e^2 - 109/4*e - 45/2, -9/8*e^7 - 9/4*e^6 + 121/8*e^5 + 181/8*e^4 - 439/8*e^3 - 459/8*e^2 + 189/4*e + 135/8, 7/8*e^7 + 3/2*e^6 - 99/8*e^5 - 119/8*e^4 + 373/8*e^3 + 289/8*e^2 - 157/4*e - 115/8, 5/8*e^7 + e^6 - 75/8*e^5 - 81/8*e^4 + 317/8*e^3 + 203/8*e^2 - 79/2*e - 69/8, -1/4*e^7 - 3/4*e^6 + 13/4*e^5 + 35/4*e^4 - 49/4*e^3 - 101/4*e^2 + 33/2*e + 7, 1/8*e^7 - 13/8*e^5 + 9/8*e^4 + 27/8*e^3 - 51/8*e^2 + 27/4*e + 69/8, -1/4*e^7 + 4*e^5 - 5/4*e^4 - 31/2*e^3 + 19/4*e^2 + 25/4*e - 3/4, 7/8*e^7 + 11/8*e^6 - 25/2*e^5 - 109/8*e^4 + 46*e^3 + 267/8*e^2 - 251/8*e - 15/2, e^7 + 13/8*e^6 - 111/8*e^5 - 63/4*e^4 + 409/8*e^3 + 165/4*e^2 - 335/8*e - 155/8, 5/8*e^7 + 3/4*e^6 - 73/8*e^5 - 59/8*e^4 + 267/8*e^3 + 185/8*e^2 - 89/4*e - 105/8, -3/4*e^7 - e^6 + 43/4*e^5 + 37/4*e^4 - 163/4*e^3 - 101/4*e^2 + 36*e + 65/4, -1/4*e^7 - 3/8*e^6 + 27/8*e^5 + 3*e^4 - 97/8*e^3 - 5*e^2 + 101/8*e - 41/8, 1/2*e^7 + 9/8*e^6 - 59/8*e^5 - 13*e^4 + 257/8*e^3 + 77/2*e^2 - 307/8*e - 161/8, 7/8*e^7 + 11/8*e^6 - 49/4*e^5 - 111/8*e^4 + 175/4*e^3 + 317/8*e^2 - 245/8*e - 83/4, 5/4*e^7 + 7/4*e^6 - 37/2*e^5 - 71/4*e^4 + 147/2*e^3 + 207/4*e^2 - 281/4*e - 32, 1/4*e^7 - 1/4*e^6 - 17/4*e^5 + 15/4*e^4 + 65/4*e^3 - 35/4*e^2 - 7*e + 5, 5/8*e^7 + 9/8*e^6 - 39/4*e^5 - 101/8*e^4 + 181/4*e^3 + 303/8*e^2 - 487/8*e - 105/4, 5/8*e^7 + 5/8*e^6 - 37/4*e^5 - 43/8*e^4 + 139/4*e^3 + 133/8*e^2 - 191/8*e - 10, -3/4*e^7 - 13/8*e^6 + 83/8*e^5 + 71/4*e^4 - 329/8*e^3 - 205/4*e^2 + 361/8*e + 135/8, 1/4*e^7 - 1/2*e^6 - 9/2*e^5 + 31/4*e^4 + 19*e^3 - 97/4*e^2 - 75/4*e + 27/4, 5/8*e^7 + 5/4*e^6 - 65/8*e^5 - 97/8*e^4 + 223/8*e^3 + 255/8*e^2 - 95/4*e - 131/8, 1/2*e^7 + 5/8*e^6 - 67/8*e^5 - 29/4*e^4 + 321/8*e^3 + 97/4*e^2 - 363/8*e - 159/8, 3/8*e^7 + 1/8*e^6 - 6*e^5 + 7/8*e^4 + 55/2*e^3 - 69/8*e^2 - 295/8*e + 23/4, 1/2*e^7 + 9/8*e^6 - 51/8*e^5 - 47/4*e^4 + 157/8*e^3 + 127/4*e^2 - 59/8*e - 75/8, -1/8*e^7 + 1/4*e^6 + 23/8*e^5 - 23/8*e^4 - 125/8*e^3 + 53/8*e^2 + 39/2*e - 65/8, e^7 + 15/8*e^6 - 121/8*e^5 - 41/2*e^4 + 535/8*e^3 + 56*e^2 - 677/8*e - 175/8, 3/4*e^7 + 5/4*e^6 - 43/4*e^5 - 23/2*e^4 + 181/4*e^3 + 49/2*e^2 - 113/2*e - 35/4, 7/8*e^7 + 3/2*e^6 - 95/8*e^5 - 109/8*e^4 + 349/8*e^3 + 255/8*e^2 - 165/4*e - 145/8, 1/2*e^7 + e^6 - 29/4*e^5 - 12*e^4 + 119/4*e^3 + 83/2*e^2 - 149/4*e - 45/2, -1/4*e^7 - 3/8*e^6 + 29/8*e^5 + 19/4*e^4 - 107/8*e^3 - 75/4*e^2 + 83/8*e + 85/8, -11/8*e^7 - 5/2*e^6 + 161/8*e^5 + 213/8*e^4 - 651/8*e^3 - 563/8*e^2 + 149/2*e + 165/8, -1/8*e^7 - 1/2*e^6 + 13/8*e^5 + 61/8*e^4 - 27/8*e^3 - 259/8*e^2 - 29/4*e + 241/8, -3/8*e^7 - 1/4*e^6 + 47/8*e^5 + 11/8*e^4 - 189/8*e^3 + 7/8*e^2 + 67/4*e - 59/8, 1/2*e^6 + e^5 - 21/4*e^4 - 7*e^3 + 41/4*e^2 + 15/2*e + 23/4, 3/4*e^7 + e^6 - 11*e^5 - 37/4*e^4 + 44*e^3 + 87/4*e^2 - 183/4*e - 57/4, 3/4*e^7 + 5/4*e^6 - 41/4*e^5 - 47/4*e^4 + 149/4*e^3 + 119/4*e^2 - 63/2*e - 20, 1/8*e^6 + 5/8*e^5 - 3/4*e^4 - 55/8*e^3 - 9/4*e^2 + 153/8*e - 15/8, 5/8*e^7 + 3/8*e^6 - 19/2*e^5 - 1/8*e^4 + 39*e^3 - 125/8*e^2 - 341/8*e + 21/2, -7/4*e^7 - 11/4*e^6 + 49/2*e^5 + 105/4*e^4 - 90*e^3 - 257/4*e^2 + 267/4*e + 22, -7/4*e^7 - 27/8*e^6 + 199/8*e^5 + 73/2*e^4 - 781/8*e^3 - 205/2*e^2 + 765/8*e + 251/8, -13/8*e^7 - 27/8*e^6 + 93/4*e^5 + 293/8*e^4 - 381/4*e^3 - 807/8*e^2 + 827/8*e + 48, -3/8*e^7 - 3/4*e^6 + 37/8*e^5 + 59/8*e^4 - 91/8*e^3 - 145/8*e^2 - 21/2*e - 19/8, -17/8*e^7 - 31/8*e^6 + 61/2*e^5 + 337/8*e^4 - 239/2*e^3 - 971/8*e^2 + 897/8*e + 89/2, 3/8*e^7 - 1/8*e^6 - 13/2*e^5 + 21/8*e^4 + 28*e^3 - 51/8*e^2 - 223/8*e - 43/4, -13/8*e^7 - 25/8*e^6 + 91/4*e^5 + 259/8*e^4 - 353/4*e^3 - 705/8*e^2 + 671/8*e + 37, 5/8*e^7 + 13/8*e^6 - 8*e^5 - 149/8*e^4 + 27*e^3 + 443/8*e^2 - 181/8*e - 137/4, -7/8*e^7 - 7/8*e^6 + 27/2*e^5 + 63/8*e^4 - 56*e^3 - 197/8*e^2 + 431/8*e + 87/4, -1/4*e^6 + 1/2*e^5 + 19/4*e^4 - 17/2*e^3 - 89/4*e^2 + 45/2*e + 8, -3/8*e^7 - 13/8*e^6 + 15/4*e^5 + 143/8*e^4 - 35/4*e^3 - 377/8*e^2 - 15/8*e + 23, 3/4*e^7 + 5/4*e^6 - 41/4*e^5 - 45/4*e^4 + 141/4*e^3 + 79/4*e^2 - 17*e - 5, 19/8*e^7 + 15/4*e^6 - 279/8*e^5 - 307/8*e^4 + 1129/8*e^3 + 857/8*e^2 - 563/4*e - 365/8, -9/8*e^7 - 13/8*e^6 + 31/2*e^5 + 109/8*e^4 - 57*e^3 - 219/8*e^2 + 445/8*e + 55/4, 23/8*e^7 + 17/4*e^6 - 339/8*e^5 - 337/8*e^4 + 1373/8*e^3 + 887/8*e^2 - 709/4*e - 435/8, -3/8*e^7 + 1/4*e^6 + 57/8*e^5 - 31/8*e^4 - 303/8*e^3 + 73/8*e^2 + 127/2*e - 25/8, -1/2*e^7 - 9/8*e^6 + 53/8*e^5 + 45/4*e^4 - 211/8*e^3 - 129/4*e^2 + 285/8*e + 255/8, -e^7 - 17/8*e^6 + 121/8*e^5 + 103/4*e^4 - 523/8*e^3 - 325/4*e^2 + 553/8*e + 299/8, -1/2*e^7 - 3/2*e^6 + 6*e^5 + 16*e^4 - 18*e^3 - 71/2*e^2 + 6*e, -1/4*e^7 - 5/8*e^6 + 31/8*e^5 + 7*e^4 - 145/8*e^3 - 17*e^2 + 177/8*e + 45/8, 3/4*e^7 + 7/8*e^6 - 89/8*e^5 - 39/4*e^4 + 311/8*e^3 + 147/4*e^2 - 123/8*e - 225/8, -5/4*e^7 - 11/4*e^6 + 71/4*e^5 + 119/4*e^4 - 295/4*e^3 - 319/4*e^2 + 171/2*e + 55/2, -1/2*e^7 - 3/4*e^6 + 27/4*e^5 + 7*e^4 - 93/4*e^3 - 20*e^2 + 61/4*e + 15/4, -2*e^7 - 23/8*e^6 + 229/8*e^5 + 27*e^4 - 859/8*e^3 - 125/2*e^2 + 705/8*e + 75/8, -9/4*e^7 - 27/8*e^6 + 267/8*e^5 + 133/4*e^4 - 1085/8*e^3 - 341/4*e^2 + 993/8*e + 321/8, -5/8*e^7 - 13/8*e^6 + 17/2*e^5 + 141/8*e^4 - 34*e^3 - 363/8*e^2 + 225/8*e + 43/4, 1/4*e^7 + 5/8*e^6 - 39/8*e^5 - 41/4*e^4 + 217/8*e^3 + 167/4*e^2 - 281/8*e - 255/8, e^7 + 9/8*e^6 - 115/8*e^5 - 35/4*e^4 + 449/8*e^3 + 81/4*e^2 - 467/8*e - 75/8, -1/2*e^7 - 1/4*e^6 + 27/4*e^5 - 5/4*e^4 - 83/4*e^3 + 65/4*e^2 + 11/4*e - 23, e^7 + 13/8*e^6 - 113/8*e^5 - 17*e^4 + 415/8*e^3 + 103/2*e^2 - 293/8*e - 289/8, 9/8*e^7 + 17/8*e^6 - 16*e^5 - 185/8*e^4 + 129/2*e^3 + 563/8*e^2 - 565/8*e - 197/4, -5/4*e^7 - 21/8*e^6 + 133/8*e^5 + 27*e^4 - 471/8*e^3 - 143/2*e^2 + 363/8*e + 261/8, 1/4*e^7 + 1/4*e^6 - 9/2*e^5 - 15/4*e^4 + 25*e^3 + 79/4*e^2 - 165/4*e - 12, -5/8*e^7 - 1/2*e^6 + 71/8*e^5 + 29/8*e^4 - 237/8*e^3 - 79/8*e^2 + 18*e + 81/8, -2*e^7 - 3*e^6 + 29*e^5 + 59/2*e^4 - 114*e^3 - 149/2*e^2 + 114*e + 51/2, -5/4*e^7 - 21/8*e^6 + 149/8*e^5 + 123/4*e^4 - 639/8*e^3 - 383/4*e^2 + 675/8*e + 371/8, -5/8*e^7 - 1/2*e^6 + 85/8*e^5 + 49/8*e^4 - 395/8*e^3 - 227/8*e^2 + 247/4*e + 305/8, 13/8*e^7 + 3*e^6 - 189/8*e^5 - 257/8*e^4 + 747/8*e^3 + 687/8*e^2 - 325/4*e - 265/8, -5/4*e^7 - 11/8*e^6 + 149/8*e^5 + 23/2*e^4 - 583/8*e^3 - 25*e^2 + 443/8*e + 31/8, -5/8*e^7 - 3/2*e^6 + 69/8*e^5 + 135/8*e^4 - 275/8*e^3 - 353/8*e^2 + 181/4*e + 51/8, 9/8*e^7 + 7/4*e^6 - 133/8*e^5 - 135/8*e^4 + 547/8*e^3 + 293/8*e^2 - 261/4*e - 1/8, 1/4*e^6 + 7/4*e^5 - 3/4*e^4 - 71/4*e^3 - 23/4*e^2 + 155/4*e + 31/2, -19/8*e^7 - 15/4*e^6 + 273/8*e^5 + 289/8*e^4 - 1063/8*e^3 - 683/8*e^2 + 126*e + 275/8, 3/4*e^7 + 9/4*e^6 - 17/2*e^5 - 103/4*e^4 + 41/2*e^3 + 313/4*e^2 + 15/4*e - 45, 13/4*e^7 + 43/8*e^6 - 361/8*e^5 - 203/4*e^4 + 1339/8*e^3 + 465/4*e^2 - 1115/8*e - 261/8, -5/8*e^7 - 11/8*e^6 + 41/4*e^5 + 143/8*e^4 - 203/4*e^3 - 497/8*e^2 + 575/8*e + 157/4, 3/8*e^7 + 17/8*e^6 - 15/4*e^5 - 211/8*e^4 + 39/4*e^3 + 621/8*e^2 - 65/8*e - 42, 9/4*e^7 + 15/4*e^6 - 32*e^5 - 36*e^4 + 123*e^3 + 84*e^2 - 397/4*e - 127/4, -5/4*e^7 - 3/2*e^6 + 19*e^5 + 53/4*e^4 - 159/2*e^3 - 115/4*e^2 + 317/4*e + 77/4, -3/4*e^7 - 3/2*e^6 + 10*e^5 + 59/4*e^4 - 71/2*e^3 - 137/4*e^2 + 131/4*e + 7/4, -17/8*e^7 - 33/8*e^6 + 59/2*e^5 + 347/8*e^4 - 227/2*e^3 - 985/8*e^2 + 929/8*e + 57, -1/8*e^7 + 11/8*e^5 - 19/8*e^4 - 25/8*e^3 + 109/8*e^2 + 1/2*e - 215/8, 1/8*e^7 + 9/8*e^6 - 109/8*e^4 - 19/2*e^3 + 303/8*e^2 + 195/8*e - 55/4, -1/8*e^7 + 15/8*e^5 - 15/8*e^4 - 65/8*e^3 + 121/8*e^2 + 6*e - 175/8, 13/4*e^7 + 43/8*e^6 - 379/8*e^5 - 215/4*e^4 + 1549/8*e^3 + 543/4*e^2 - 1657/8*e - 485/8, e^7 + 3/4*e^6 - 61/4*e^5 - 3*e^4 + 257/4*e^3 - 13/2*e^2 - 279/4*e + 45/4, -2*e^7 - 29/8*e^6 + 229/8*e^5 + 75/2*e^4 - 927/8*e^3 - 97*e^2 + 1049/8*e + 265/8, -5/8*e^7 - 5/8*e^6 + 35/4*e^5 + 25/8*e^4 - 121/4*e^3 + 33/8*e^2 + 67/8*e - 45/4, 1/4*e^7 + 5/4*e^6 - 9/4*e^5 - 27/2*e^4 + 17/4*e^3 + 28*e^2 + 8*e + 25/4, -9/4*e^7 - 21/8*e^6 + 281/8*e^5 + 53/2*e^4 - 1191/8*e^3 - 151/2*e^2 + 1155/8*e + 329/8, -17/8*e^7 - 17/8*e^6 + 31*e^5 + 129/8*e^4 - 116*e^3 - 235/8*e^2 + 725/8*e + 7/4, -11/4*e^7 - 17/4*e^6 + 159/4*e^5 + 83/2*e^4 - 619/4*e^3 - 101*e^2 + 132*e + 107/4, 17/4*e^7 + 51/8*e^6 - 491/8*e^5 - 123/2*e^4 + 1921/8*e^3 + 313/2*e^2 - 1869/8*e - 651/8, -5/2*e^7 - 43/8*e^6 + 277/8*e^5 + 233/4*e^4 - 1055/8*e^3 - 631/4*e^2 + 945/8*e + 521/8, -9/8*e^7 - 3/2*e^6 + 137/8*e^5 + 111/8*e^4 - 583/8*e^3 - 221/8*e^2 + 327/4*e - 9/8, -e^7 - 11/8*e^6 + 119/8*e^5 + 53/4*e^4 - 493/8*e^3 - 141/4*e^2 + 555/8*e + 301/8, 7/4*e^7 + 17/4*e^6 - 47/2*e^5 - 185/4*e^4 + 87*e^3 + 475/4*e^2 - 293/4*e - 28, 19/4*e^7 + 63/8*e^6 - 551/8*e^5 - 323/4*e^4 + 2181/8*e^3 + 875/4*e^2 - 2001/8*e - 749/8, -7/8*e^7 - 7/4*e^6 + 109/8*e^5 + 177/8*e^4 - 491/8*e^3 - 627/8*e^2 + 73*e + 411/8, -13/8*e^7 - 2*e^6 + 197/8*e^5 + 159/8*e^4 - 787/8*e^3 - 457/8*e^2 + 349/4*e + 215/8, 27/8*e^7 + 21/4*e^6 - 393/8*e^5 - 419/8*e^4 + 1551/8*e^3 + 1121/8*e^2 - 168*e - 545/8, 19/4*e^7 + 57/8*e^6 - 553/8*e^5 - 139/2*e^4 + 2203/8*e^3 + 180*e^2 - 2275/8*e - 741/8, -3/4*e^7 + 47/4*e^5 - 17/4*e^4 - 173/4*e^3 + 79/4*e^2 + 35/2*e - 53/4, 17/8*e^7 + 15/4*e^6 - 253/8*e^5 - 301/8*e^4 + 1119/8*e^3 + 759/8*e^2 - 717/4*e - 379/8, -13/8*e^7 - 11/4*e^6 + 181/8*e^5 + 233/8*e^4 - 647/8*e^3 - 703/8*e^2 + 201/4*e + 331/8, 9/4*e^7 + 17/4*e^6 - 121/4*e^5 - 44*e^4 + 413/4*e^3 + 241/2*e^2 - 70*e - 225/4, 2*e^7 + 29/8*e^6 - 225/8*e^5 - 69/2*e^4 + 895/8*e^3 + 76*e^2 - 901/8*e - 245/8, 1/8*e^7 + 1/2*e^6 - 7/8*e^5 - 27/8*e^4 - 11/8*e^3 - 63/8*e^2 + 27/2*e + 145/8, 4*e^7 + 13/2*e^6 - 229/4*e^5 - 263/4*e^4 + 871/4*e^3 + 697/4*e^2 - 709/4*e - 305/4, -5/4*e^7 - 3*e^6 + 65/4*e^5 + 133/4*e^4 - 225/4*e^3 - 401/4*e^2 + 43*e + 253/4, 1/2*e^7 + 13/8*e^6 - 45/8*e^5 - 67/4*e^4 + 147/8*e^3 + 169/4*e^2 - 225/8*e - 11/8, 3/4*e^7 + 7/4*e^6 - 21/2*e^5 - 39/2*e^4 + 85/2*e^3 + 59*e^2 - 155/4*e - 163/4, -7/2*e^7 - 49/8*e^6 + 399/8*e^5 + 253/4*e^4 - 1545/8*e^3 - 671/4*e^2 + 1395/8*e + 531/8, 5/8*e^7 + 3/2*e^6 - 65/8*e^5 - 131/8*e^4 + 191/8*e^3 + 329/8*e^2 + 35/4*e - 51/8, -11/8*e^7 - 3/2*e^6 + 161/8*e^5 + 75/8*e^4 - 655/8*e^3 - 13/8*e^2 + 159/2*e - 81/8, 1/8*e^7 + 3/4*e^6 - 5/8*e^5 - 67/8*e^4 - 9/8*e^3 + 245/8*e^2 - 3/4*e - 205/8, -13/4*e^7 - 45/8*e^6 + 375/8*e^5 + 231/4*e^4 - 1493/8*e^3 - 615/4*e^2 + 1421/8*e + 515/8, -3/4*e^6 - 3/2*e^5 + 23/2*e^4 + 35/2*e^3 - 49*e^2 - 47*e + 95/4, -41/8*e^7 - 63/8*e^6 + 76*e^5 + 649/8*e^4 - 308*e^3 - 1767/8*e^2 + 2305/8*e + 100, -7/4*e^7 - 11/4*e^6 + 103/4*e^5 + 53/2*e^4 - 425/4*e^3 - 129/2*e^2 + 219/2*e + 113/4, -2*e^7 - 11/4*e^6 + 61/2*e^5 + 28*e^4 - 261/2*e^3 - 167/2*e^2 + 132*e + 233/4, -5/2*e^7 - 21/4*e^6 + 141/4*e^5 + 229/4*e^4 - 555/4*e^3 - 631/4*e^2 + 567/4*e + 145/2, 5/4*e^7 + 27/8*e^6 - 115/8*e^5 - 139/4*e^4 + 289/8*e^3 + 351/4*e^2 + 63/8*e - 345/8, 9/8*e^7 + 7/4*e^6 - 145/8*e^5 - 175/8*e^4 + 655/8*e^3 + 645/8*e^2 - 351/4*e - 505/8, 13/4*e^7 + 19/4*e^6 - 50*e^5 - 193/4*e^4 + 437/2*e^3 + 529/4*e^2 - 959/4*e - 75, e^7 + 5/4*e^6 - 27/2*e^5 - 9*e^4 + 97/2*e^3 + 16*e^2 - 95/2*e - 77/4, 9/2*e^7 + 53/8*e^6 - 529/8*e^5 - 66*e^4 + 2091/8*e^3 + 349/2*e^2 - 1841/8*e - 629/8] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]