/* 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([-1, 1, 6, -2, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([35, 35, 2*w^5 - 11*w^3 - 4*w^2 + 7*w + 1]) primes_array = [ [5, 5, -w^4 + w^3 + 4*w^2 - 2*w - 1],\ [7, 7, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w - 3],\ [19, 19, w^5 - w^4 - 5*w^3 + 2*w^2 + 4*w],\ [23, 23, -w^2 + w + 2],\ [25, 5, w^5 + w^4 - 6*w^3 - 7*w^2 + 4*w + 2],\ [41, 41, 2*w^5 - w^4 - 10*w^3 + 6*w - 1],\ [47, 47, w^3 - w^2 - 4*w],\ [53, 53, w^5 - 5*w^3 - 3*w^2 + w + 3],\ [59, 59, 2*w^5 - 11*w^3 - 4*w^2 + 8*w],\ [61, 61, w^2 - 2*w - 2],\ [64, 2, -2],\ [67, 67, -w^4 + 6*w^2 + w - 3],\ [67, 67, -2*w^4 + w^3 + 10*w^2 - 6],\ [73, 73, w^5 - 5*w^3 - 2*w^2 + 2*w - 2],\ [73, 73, -w^5 - w^4 + 7*w^3 + 6*w^2 - 8*w - 2],\ [79, 79, w^5 - w^4 - 5*w^3 + 3*w^2 + 5*w - 1],\ [83, 83, 2*w^5 - 11*w^3 - 4*w^2 + 6*w],\ [89, 89, -2*w^5 + 11*w^3 + 4*w^2 - 7*w - 2],\ [97, 97, w^5 - w^4 - 5*w^3 + 3*w^2 + 2*w - 2],\ [97, 97, w^5 - w^4 - 6*w^3 + 3*w^2 + 7*w - 1],\ [97, 97, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 5*w + 4],\ [101, 101, w^5 - 6*w^3 - 3*w^2 + 6*w + 2],\ [103, 103, -w^5 - w^4 + 5*w^3 + 8*w^2 - 5],\ [107, 107, 2*w^4 - w^3 - 9*w^2 + w + 2],\ [109, 109, 2*w^5 - 10*w^3 - 5*w^2 + 4*w + 1],\ [113, 113, -w^4 + 6*w^2 + 2*w - 3],\ [125, 5, 2*w^5 - 10*w^3 - 6*w^2 + 5*w + 6],\ [127, 127, 2*w^5 - w^4 - 11*w^3 + 10*w],\ [131, 131, 2*w^5 - w^4 - 11*w^3 + 9*w + 1],\ [137, 137, -w^5 + 2*w^4 + 6*w^3 - 9*w^2 - 9*w + 5],\ [139, 139, -w^5 - 2*w^4 + 7*w^3 + 11*w^2 - 5*w - 5],\ [157, 157, 2*w^5 - 10*w^3 - 5*w^2 + 5*w + 1],\ [167, 167, -2*w^5 + 10*w^3 + 5*w^2 - 3*w + 1],\ [173, 173, 4*w^5 + 2*w^4 - 22*w^3 - 19*w^2 + 10*w + 5],\ [179, 179, 2*w^5 - w^4 - 11*w^3 + 10*w + 1],\ [179, 179, 2*w^5 - 11*w^3 - 5*w^2 + 8*w + 1],\ [181, 181, -4*w^5 - w^4 + 22*w^3 + 14*w^2 - 12*w - 4],\ [191, 191, w^4 + w^3 - 6*w^2 - 4*w + 2],\ [191, 191, -3*w^5 + 18*w^3 + 5*w^2 - 15*w - 1],\ [193, 193, -w^4 + w^3 + 6*w^2 - 2*w - 7],\ [197, 197, -3*w^5 + 2*w^4 + 16*w^3 - 3*w^2 - 12*w + 1],\ [197, 197, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 7*w - 5],\ [197, 197, -w^5 + w^4 + 6*w^3 - 3*w^2 - 9*w + 1],\ [211, 211, -2*w^5 + w^4 + 10*w^3 - w^2 - 4*w + 4],\ [223, 223, 2*w^5 - 10*w^3 - 6*w^2 + 5*w + 4],\ [227, 227, w^5 - 7*w^3 - w^2 + 9*w],\ [227, 227, -2*w^5 + w^4 + 9*w^3 - 2*w + 1],\ [229, 229, w^5 + w^4 - 5*w^3 - 6*w^2 - 2*w - 2],\ [233, 233, -2*w^5 - w^4 + 12*w^3 + 8*w^2 - 8*w - 4],\ [269, 269, 3*w^5 - 16*w^3 - 6*w^2 + 8*w],\ [269, 269, -2*w^5 + 12*w^3 + 3*w^2 - 12*w - 1],\ [277, 277, 3*w^5 - w^4 - 17*w^3 - w^2 + 16*w],\ [289, 17, -2*w^5 - w^4 + 12*w^3 + 8*w^2 - 10*w - 3],\ [307, 307, w^4 - 5*w^2 - 2*w - 1],\ [307, 307, 3*w^5 - w^4 - 16*w^3 - 3*w^2 + 12*w + 3],\ [307, 307, -w^4 - w^3 + 5*w^2 + 6*w - 2],\ [311, 311, -w^4 - w^3 + 7*w^2 + 4*w - 4],\ [311, 311, 3*w^5 - w^4 - 17*w^3 - 2*w^2 + 16*w + 2],\ [313, 313, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w],\ [317, 317, 2*w^5 + w^4 - 12*w^3 - 8*w^2 + 7*w],\ [331, 331, 2*w^5 - 2*w^4 - 10*w^3 + 5*w^2 + 8*w - 5],\ [337, 337, w^5 - 6*w^3 - 3*w^2 + 6*w],\ [347, 347, -2*w^5 + 2*w^4 + 10*w^3 - 6*w^2 - 7*w + 2],\ [347, 347, 3*w^5 + w^4 - 17*w^3 - 11*w^2 + 9*w + 2],\ [349, 349, -2*w^5 + 11*w^3 + 5*w^2 - 7*w - 6],\ [367, 367, -w^5 - 2*w^4 + 5*w^3 + 13*w^2 + 2*w - 5],\ [367, 367, 2*w^5 + 2*w^4 - 10*w^3 - 16*w^2 - w + 6],\ [373, 373, 3*w^5 - w^4 - 17*w^3 - w^2 + 15*w + 1],\ [373, 373, 2*w^4 - 2*w^3 - 9*w^2 + 2*w + 4],\ [379, 379, 2*w^5 + w^4 - 11*w^3 - 10*w^2 + 5*w + 7],\ [389, 389, w^2 - 5],\ [389, 389, w^5 - 7*w^3 + 8*w],\ [397, 397, -2*w^5 - w^4 + 12*w^3 + 9*w^2 - 7*w - 5],\ [397, 397, -3*w^5 - w^4 + 18*w^3 + 10*w^2 - 14*w - 2],\ [397, 397, -2*w^5 - 2*w^4 + 12*w^3 + 13*w^2 - 6*w - 4],\ [419, 419, 2*w^5 + 2*w^4 - 11*w^3 - 14*w^2 + 2*w + 5],\ [419, 419, -w^5 + 4*w^3 + 3*w^2 + w - 2],\ [433, 433, -w^5 + 5*w^3 + 4*w^2 - w - 3],\ [433, 433, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 6*w - 4],\ [439, 439, 4*w^5 + 2*w^4 - 22*w^3 - 18*w^2 + 9*w + 4],\ [439, 439, w^5 + w^4 - 5*w^3 - 9*w^2 + 6],\ [439, 439, -3*w^5 + 2*w^4 + 16*w^3 - 3*w^2 - 13*w + 2],\ [443, 443, -3*w^5 + w^4 + 15*w^3 + 3*w^2 - 8*w - 2],\ [449, 449, -w^5 + w^4 + 5*w^3 - 4*w^2 - 2*w + 3],\ [449, 449, 3*w^5 - 16*w^3 - 8*w^2 + 9*w + 4],\ [449, 449, w^4 + w^3 - 6*w^2 - 6*w + 5],\ [449, 449, -w^5 + w^4 + 6*w^3 - 5*w^2 - 7*w + 4],\ [457, 457, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 6*w + 4],\ [457, 457, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 5*w - 4],\ [461, 461, -2*w^4 + w^3 + 10*w^2 + w - 5],\ [463, 463, -w^5 + w^4 + 6*w^3 - 4*w^2 - 5*w + 4],\ [487, 487, -3*w^4 + 2*w^3 + 14*w^2 - w - 7],\ [487, 487, 3*w^5 + w^4 - 18*w^3 - 10*w^2 + 14*w + 3],\ [491, 491, -3*w^5 + w^4 + 16*w^3 + w^2 - 12*w + 2],\ [491, 491, 3*w^5 - w^4 - 16*w^3 - 2*w^2 + 12*w + 3],\ [499, 499, 4*w^5 - 22*w^3 - 9*w^2 + 15*w + 4],\ [499, 499, w^4 + w^3 - 7*w^2 - 6*w + 6],\ [523, 523, w^4 - 2*w^3 - 4*w^2 + 5*w + 2],\ [529, 23, -w^5 + 7*w^3 + w^2 - 10*w - 1],\ [541, 541, w^5 + 2*w^4 - 8*w^3 - 10*w^2 + 9*w + 3],\ [557, 557, w^5 - w^4 - 5*w^3 + 3*w^2 + 5*w - 5],\ [557, 557, 4*w^5 - 22*w^3 - 8*w^2 + 14*w + 1],\ [563, 563, 2*w^5 - w^4 - 12*w^3 + 2*w^2 + 13*w - 1],\ [563, 563, -w^5 - 2*w^4 + 6*w^3 + 13*w^2 - 2*w - 6],\ [563, 563, -w^5 + w^4 + 4*w^3 - 2*w^2 + w + 3],\ [569, 569, -3*w^5 + w^4 + 16*w^3 + w^2 - 9*w + 1],\ [599, 599, -w^4 - w^3 + 7*w^2 + 6*w - 5],\ [607, 607, -w^5 + 6*w^3 + 3*w^2 - 7*w - 1],\ [613, 613, -w^5 - 2*w^4 + 7*w^3 + 12*w^2 - 4*w - 7],\ [619, 619, 4*w^5 - w^4 - 22*w^3 - 3*w^2 + 16*w],\ [653, 653, 2*w^5 - 2*w^4 - 10*w^3 + 4*w^2 + 7*w],\ [653, 653, -2*w^5 + w^4 + 12*w^3 - w^2 - 14*w + 1],\ [659, 659, -2*w^5 - w^4 + 11*w^3 + 11*w^2 - 5*w - 7],\ [661, 661, 2*w^5 - 11*w^3 - 3*w^2 + 7*w],\ [661, 661, 2*w^5 - w^4 - 11*w^3 + 11*w + 2],\ [673, 673, -w^4 - w^3 + 5*w^2 + 7*w - 1],\ [677, 677, 3*w^5 - 16*w^3 - 7*w^2 + 10*w + 3],\ [677, 677, w^5 + 3*w^4 - 6*w^3 - 18*w^2 + 12],\ [691, 691, w^5 - w^4 - 4*w^3 + 2*w^2 - 4],\ [709, 709, -w^4 + w^3 + 3*w^2 - 2*w + 2],\ [709, 709, -2*w^5 - w^4 + 11*w^3 + 9*w^2 - 6*w - 1],\ [719, 719, 2*w^5 + 2*w^4 - 12*w^3 - 14*w^2 + 8*w + 5],\ [729, 3, -3],\ [739, 739, 4*w^5 - w^4 - 21*w^3 - 5*w^2 + 12*w + 3],\ [743, 743, -2*w^5 - w^4 + 10*w^3 + 11*w^2 - w - 6],\ [751, 751, -3*w^5 + w^4 + 17*w^3 + 2*w^2 - 15*w - 2],\ [751, 751, -2*w^5 + 3*w^4 + 10*w^3 - 11*w^2 - 10*w + 6],\ [757, 757, w^5 - 3*w^4 - 5*w^3 + 13*w^2 + 7*w - 6],\ [761, 761, -w^5 + w^4 + 6*w^3 - 3*w^2 - 6*w - 1],\ [787, 787, -3*w^5 - w^4 + 18*w^3 + 10*w^2 - 15*w - 2],\ [797, 797, 2*w^5 - 2*w^4 - 11*w^3 + 6*w^2 + 12*w - 1],\ [797, 797, w^2 - 2*w - 5],\ [809, 809, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 12*w - 3],\ [827, 827, 4*w^5 - 22*w^3 - 8*w^2 + 15*w + 1],\ [839, 839, 3*w^5 - w^4 - 16*w^3 - 3*w^2 + 10*w + 2],\ [839, 839, -w^5 + w^4 + 6*w^3 - 4*w^2 - 8*w + 1],\ [841, 29, -2*w^5 - w^4 + 11*w^3 + 9*w^2 - 7*w - 3],\ [853, 853, w^5 - 7*w^3 - w^2 + 7*w + 1],\ [857, 857, -2*w^5 + w^4 + 10*w^3 - w^2 - 6*w + 4],\ [863, 863, 3*w^5 - w^4 - 17*w^3 - 2*w^2 + 16*w],\ [877, 877, 2*w^5 - 10*w^3 - 5*w^2 + 3*w + 4],\ [887, 887, 2*w^5 + w^4 - 13*w^3 - 8*w^2 + 13*w + 5],\ [887, 887, 3*w^5 - 2*w^4 - 15*w^3 + 3*w^2 + 8*w - 4],\ [907, 907, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 17*w],\ [907, 907, -2*w^5 + 2*w^4 + 10*w^3 - 4*w^2 - 9*w + 1],\ [919, 919, -3*w^5 + 17*w^3 + 5*w^2 - 11*w],\ [929, 929, -3*w^5 + 17*w^3 + 6*w^2 - 11*w],\ [941, 941, 2*w^5 - w^4 - 11*w^3 - w^2 + 9*w + 2],\ [947, 947, -w^4 + 6*w^2 + 4*w - 4],\ [947, 947, -2*w^5 + w^4 + 11*w^3 - 11*w - 3],\ [947, 947, -4*w^5 + w^4 + 22*w^3 + 3*w^2 - 16*w - 1],\ [953, 953, -w^5 - 2*w^4 + 6*w^3 + 13*w^2 - 3*w - 8],\ [953, 953, 2*w^5 + 2*w^4 - 13*w^3 - 14*w^2 + 10*w + 6],\ [961, 31, 2*w^5 + w^4 - 12*w^3 - 10*w^2 + 9*w + 4],\ [967, 967, 2*w^5 - w^4 - 11*w^3 + w^2 + 11*w + 1],\ [967, 967, 2*w^5 - 2*w^4 - 11*w^3 + 6*w^2 + 13*w - 3],\ [983, 983, -4*w^5 + w^4 + 22*w^3 + 4*w^2 - 18*w - 2],\ [991, 991, 3*w^5 - 16*w^3 - 7*w^2 + 7*w + 2],\ [991, 991, -2*w^5 - w^4 + 12*w^3 + 8*w^2 - 11*w - 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 14*x^4 + 58*x^3 - 60*x^2 + 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, 1/14*e^4 - 5/7*e^3 + 9/7*e^2 + 13/7*e + 3/7, 2/7*e^4 - 20/7*e^3 + 50/7*e^2 - 11/7*e - 30/7, -5/14*e^4 + 32/7*e^3 - 122/7*e^2 + 131/7*e - 29/7, 3/7*e^4 - 37/7*e^3 + 138/7*e^2 - 153/7*e + 32/7, 4/7*e^4 - 40/7*e^3 + 100/7*e^2 - 43/7*e - 4/7, -2/7*e^4 + 13/7*e^3 + 13/7*e^2 - 108/7*e + 44/7, 2/7*e^4 - 34/7*e^3 + 148/7*e^2 - 67/7*e - 72/7, -3/14*e^4 + 22/7*e^3 - 83/7*e^2 + 24/7*e + 47/7, 9/14*e^4 - 66/7*e^3 + 277/7*e^2 - 247/7*e - 15/7, -1/7*e^4 + 10/7*e^3 - 25/7*e^2 + 9/7*e + 8/7, -6/7*e^4 + 67/7*e^3 - 199/7*e^2 + 75/7*e + 76/7, -6/7*e^4 + 81/7*e^3 - 311/7*e^2 + 236/7*e + 27/7, 1/7*e^4 - 17/7*e^3 + 88/7*e^2 - 135/7*e + 13/7, -e^4 + 13*e^3 - 48*e^2 + 36*e + 8, 5/7*e^4 - 78/7*e^3 + 335/7*e^2 - 276/7*e - 19/7, -1/7*e^4 + 17/7*e^3 - 88/7*e^2 + 100/7*e + 106/7, -1/7*e^4 + 17/7*e^3 - 60/7*e^2 - 40/7*e + 22/7, 4/7*e^4 - 68/7*e^3 + 310/7*e^2 - 253/7*e - 18/7, 3/7*e^4 - 37/7*e^3 + 138/7*e^2 - 139/7*e - 59/7, -4/7*e^4 + 61/7*e^3 - 261/7*e^2 + 232/7*e + 11/7, 6/7*e^4 - 67/7*e^3 + 234/7*e^2 - 313/7*e + 22/7, 9/7*e^4 - 118/7*e^3 + 449/7*e^2 - 389/7*e - 51/7, -4/7*e^4 + 47/7*e^3 - 163/7*e^2 + 169/7*e - 10/7, e^4 - 11*e^3 + 32*e^2 - 14*e - 10, -4/7*e^4 + 40/7*e^3 - 114/7*e^2 + 120/7*e + 46/7, -2/7*e^4 + 13/7*e^3 - 29/7*e^2 + 179/7*e - 110/7, e^4 - 15*e^3 + 64*e^2 - 58*e - 6, 10/7*e^4 - 121/7*e^3 + 418/7*e^2 - 335/7*e - 24/7, 2/7*e^4 + 1/7*e^3 - 125/7*e^2 + 255/7*e + 12/7, -2/7*e^4 + 6/7*e^3 + 83/7*e^2 - 269/7*e + 79/7, -1/7*e^4 + 38/7*e^3 - 228/7*e^2 + 170/7*e + 134/7, -2/7*e^4 + 34/7*e^3 - 134/7*e^2 - 17/7*e + 114/7, -3/14*e^4 + 29/7*e^3 - 160/7*e^2 + 213/7*e + 33/7, -3/7*e^4 + 58/7*e^3 - 278/7*e^2 + 202/7*e + 45/7, e^4 - 11*e^3 + 34*e^2 - 26*e, 13/14*e^4 - 72/7*e^3 + 194/7*e^2 + 29/7*e - 143/7, -6/7*e^4 + 81/7*e^3 - 311/7*e^2 + 236/7*e + 111/7, -8/7*e^4 + 101/7*e^3 - 382/7*e^2 + 380/7*e - 20/7, -1/7*e^4 + 10/7*e^3 - 25/7*e^2 - 19/7*e + 92/7, -6/7*e^4 + 102/7*e^3 - 500/7*e^2 + 593/7*e + 13/7, e^4 - 14*e^3 + 56*e^2 - 47*e - 2, 11/7*e^4 - 152/7*e^3 + 597/7*e^2 - 463/7*e - 60/7, -1/14*e^4 + 5/7*e^3 - 16/7*e^2 + 22/7*e + 81/7, -6/7*e^4 + 81/7*e^3 - 318/7*e^2 + 292/7*e - 50/7, -e^4 + 16*e^3 - 76*e^2 + 91*e + 6, -9/7*e^4 + 118/7*e^3 - 470/7*e^2 + 522/7*e + 72/7, 11/14*e^4 - 83/7*e^3 + 379/7*e^2 - 473/7*e + 33/7, -8/7*e^4 + 122/7*e^3 - 529/7*e^2 + 499/7*e + 36/7, 5/7*e^4 - 57/7*e^3 + 188/7*e^2 - 171/7*e - 5/7, -e^4 + 16*e^3 - 74*e^2 + 81*e + 6, -e^4 + 10*e^3 - 26*e^2 + 16*e + 10, 10/7*e^4 - 121/7*e^3 + 446/7*e^2 - 482/7*e - 52/7, -3*e^3 + 22*e^2 - 18*e - 8, 2/7*e^4 - 27/7*e^3 + 120/7*e^2 - 200/7*e + 47/7, -5/7*e^4 + 57/7*e^3 - 188/7*e^2 + 143/7*e + 96/7, 15/14*e^4 - 124/7*e^3 + 555/7*e^2 - 428/7*e - 67/7, -13/7*e^4 + 165/7*e^3 - 605/7*e^2 + 467/7*e + 125/7, -31/14*e^4 + 211/7*e^3 - 825/7*e^2 + 689/7*e + 61/7, -13/7*e^4 + 165/7*e^3 - 612/7*e^2 + 586/7*e - 71/7, -19/7*e^4 + 239/7*e^3 - 867/7*e^2 + 731/7*e + 26/7, -13/7*e^4 + 165/7*e^3 - 633/7*e^2 + 698/7*e + 48/7, 15/7*e^4 - 185/7*e^3 + 655/7*e^2 - 513/7*e - 1/7, -16/7*e^4 + 230/7*e^3 - 960/7*e^2 + 893/7*e + 58/7, -1/2*e^4 + 7*e^3 - 27*e^2 + 21*e - 1, 8/7*e^4 - 115/7*e^3 + 466/7*e^2 - 338/7*e - 64/7, -8/7*e^4 + 80/7*e^3 - 242/7*e^2 + 366/7*e - 160/7, -1/7*e^4 + 10/7*e^3 - 53/7*e^2 + 247/7*e - 188/7, 1/7*e^4 - 17/7*e^3 + 102/7*e^2 - 163/7*e - 148/7, -1/7*e^4 + 17/7*e^3 - 60/7*e^2 - 82/7*e + 134/7, -1/14*e^4 - 23/7*e^3 + 201/7*e^2 - 265/7*e + 67/7, 25/14*e^4 - 139/7*e^3 + 414/7*e^2 - 200/7*e - 51/7, -9/7*e^4 + 111/7*e^3 - 372/7*e^2 + 158/7*e + 100/7, -39/14*e^4 + 223/7*e^3 - 736/7*e^2 + 641/7*e + 79/7, e^4 - 11*e^3 + 32*e^2 - 10*e - 21, -9/7*e^4 + 167/7*e^3 - 834/7*e^2 + 872/7*e + 72/7, 12/7*e^4 - 120/7*e^3 + 321/7*e^2 - 241/7*e - 47/7, 13/7*e^4 - 193/7*e^3 + 815/7*e^2 - 719/7*e - 97/7, 2*e^4 - 30*e^3 + 125*e^2 - 97*e - 9, -8/7*e^4 + 101/7*e^3 - 382/7*e^2 + 401/7*e - 69/7, 15/14*e^4 - 82/7*e^3 + 254/7*e^2 - 197/7*e - 11/7, 17/7*e^4 - 233/7*e^3 + 922/7*e^2 - 811/7*e - 24/7, -8/7*e^4 + 129/7*e^3 - 543/7*e^2 + 296/7*e + 190/7, 5/14*e^4 - 60/7*e^3 + 346/7*e^2 - 418/7*e - 27/7, -1/7*e^4 + 3/7*e^3 + 66/7*e^2 - 341/7*e + 176/7, -1/2*e^4 + 6*e^3 - 19*e^2 + 2*e + 31, 6/7*e^4 - 67/7*e^3 + 199/7*e^2 - 75/7*e - 132/7, 23/14*e^4 - 164/7*e^3 + 662/7*e^2 - 583/7*e + 27/7, -1/7*e^4 - 11/7*e^3 + 164/7*e^2 - 334/7*e - 20/7, 3/7*e^4 - 37/7*e^3 + 131/7*e^2 - 125/7*e + 60/7, 1/7*e^4 - 17/7*e^3 + 95/7*e^2 - 163/7*e - 64/7, -8/7*e^4 + 73/7*e^3 - 144/7*e^2 + 37/7*e - 146/7, -9/7*e^4 + 146/7*e^3 - 666/7*e^2 + 641/7*e - 68/7, -12/7*e^4 + 127/7*e^3 - 356/7*e^2 + 234/7*e - 184/7, 8/7*e^4 - 108/7*e^3 + 424/7*e^2 - 443/7*e + 132/7, 5/7*e^4 - 78/7*e^3 + 342/7*e^2 - 297/7*e + 72/7, 13/14*e^4 - 93/7*e^3 + 376/7*e^2 - 321/7*e + 95/7, 5/7*e^4 - 113/7*e^3 + 664/7*e^2 - 941/7*e - 26/7, -4/7*e^4 + 47/7*e^3 - 184/7*e^2 + 295/7*e + 32/7, 4/7*e^4 - 96/7*e^3 + 548/7*e^2 - 652/7*e - 4/7, 4/7*e^4 - 82/7*e^3 + 450/7*e^2 - 561/7*e + 10/7, 5/7*e^4 - 78/7*e^3 + 300/7*e^2 - 17/7*e - 166/7, -5/7*e^4 + 71/7*e^3 - 321/7*e^2 + 479/7*e - 156/7, 4/7*e^4 - 75/7*e^3 + 359/7*e^2 - 295/7*e - 46/7, -20/7*e^4 + 228/7*e^3 - 738/7*e^2 + 600/7*e + 20/7, -10/7*e^4 + 114/7*e^3 - 327/7*e^2 + 41/7*e - 4/7, -17/14*e^4 + 141/7*e^3 - 678/7*e^2 + 745/7*e + 145/7, -17/7*e^4 + 219/7*e^3 - 831/7*e^2 + 839/7*e - 102/7, 18/7*e^4 - 236/7*e^3 + 912/7*e^2 - 890/7*e - 46/7, -20/7*e^4 + 256/7*e^3 - 892/7*e^2 + 446/7*e + 216/7, -2/7*e^4 + 27/7*e^3 - 64/7*e^2 - 171/7*e + 30/7, 20/7*e^4 - 263/7*e^3 + 962/7*e^2 - 600/7*e - 118/7, -12/7*e^4 + 134/7*e^3 - 384/7*e^2 + 17/7*e + 306/7, -4/7*e^4 + 47/7*e^3 - 198/7*e^2 + 428/7*e - 122/7, 4/7*e^4 - 61/7*e^3 + 240/7*e^2 - 99/7*e - 74/7, -23/14*e^4 + 143/7*e^3 - 473/7*e^2 + 156/7*e + 281/7, -15/14*e^4 + 145/7*e^3 - 709/7*e^2 + 603/7*e + 25/7, -11/7*e^4 + 173/7*e^3 - 772/7*e^2 + 750/7*e + 4/7, -11/7*e^4 + 159/7*e^3 - 688/7*e^2 + 806/7*e - 80/7, e^4 - 13*e^3 + 41*e^2 + 14*e - 32, -e^4 + 4*e^3 + 24*e^2 - 62*e + 4, -6/7*e^4 + 67/7*e^3 - 213/7*e^2 + 138/7*e + 132/7, -1/7*e^4 + 31/7*e^3 - 179/7*e^2 + 128/7*e + 36/7, -3/14*e^4 + 43/7*e^3 - 244/7*e^2 + 157/7*e + 341/7, 3/7*e^4 - 51/7*e^3 + 194/7*e^2 + 22/7*e - 38/7, -3*e^4 + 38*e^3 - 134*e^2 + 80*e + 32, 3/7*e^4 - 51/7*e^3 + 208/7*e^2 - 69/7*e + 32/7, 20/7*e^4 - 263/7*e^3 + 1004/7*e^2 - 901/7*e + 64/7, -26/7*e^4 + 309/7*e^3 - 1028/7*e^2 + 696/7*e + 166/7, 4/7*e^4 - 47/7*e^3 + 128/7*e^2 + 104/7*e - 60/7, -5/2*e^4 + 34*e^3 - 132*e^2 + 110*e + 13, -19/14*e^4 + 102/7*e^3 - 255/7*e^2 - 30/7*e - 43/7, e^4 - 13*e^3 + 54*e^2 - 69*e - 14, -9/7*e^4 + 104/7*e^3 - 337/7*e^2 + 235/7*e + 184/7, 17/14*e^4 - 99/7*e^3 + 377/7*e^2 - 556/7*e - 47/7, 25/14*e^4 - 216/7*e^3 + 1037/7*e^2 - 1103/7*e - 79/7, 9/7*e^4 - 90/7*e^3 + 183/7*e^2 + 164/7*e - 58/7, -17/7*e^4 + 219/7*e^3 - 810/7*e^2 + 643/7*e + 150/7, -12/7*e^4 + 141/7*e^3 - 433/7*e^2 + 129/7*e + 222/7, 3*e^4 - 37*e^3 + 132*e^2 - 105*e - 19, -e^3 + 16*e^2 - 60*e + 34, -11/14*e^4 + 69/7*e^3 - 288/7*e^2 + 452/7*e - 61/7, -9/7*e^4 + 160/7*e^3 - 820/7*e^2 + 1061/7*e + 114/7, 10/7*e^4 - 121/7*e^3 + 446/7*e^2 - 482/7*e + 74/7, 17/7*e^4 - 247/7*e^3 + 1027/7*e^2 - 930/7*e - 10/7, -2*e^4 + 20*e^3 - 45*e^2 - 13*e + 12, 2*e^4 - 23*e^3 + 72*e^2 - 43*e + 7, -12/7*e^4 + 162/7*e^3 - 643/7*e^2 + 619/7*e + 26/7, e^4 - 12*e^3 + 42*e^2 - 39*e + 11, -17/7*e^4 + 212/7*e^3 - 712/7*e^2 + 223/7*e + 339/7, 6/7*e^4 - 11/7*e^3 - 284/7*e^2 + 744/7*e - 90/7, 3/14*e^4 + 6/7*e^3 - 99/7*e^2 - 24/7*e + 401/7, 16/7*e^4 - 216/7*e^3 + 792/7*e^2 - 438/7*e - 128/7, -20/7*e^4 + 242/7*e^3 - 815/7*e^2 + 502/7*e + 216/7, 18/7*e^4 - 229/7*e^3 + 800/7*e^2 - 393/7*e - 165/7, -1/7*e^4 + 59/7*e^3 - 389/7*e^2 + 429/7*e - 167/7, 2/7*e^4 - 13/7*e^3 - 27/7*e^2 + 94/7*e + 285/7] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, -w^4 + w^3 + 4*w^2 - 2*w - 1])] = -1 AL_eigenvalues[ZF.ideal([7, 7, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]