/* 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([2, 2, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13, 13, -w^2 + 3]) primes_array = [ [2, 2, -w],\ [3, 3, w + 1],\ [4, 2, -w^2 - w + 1],\ [13, 13, -w^2 + 3],\ [17, 17, -w + 3],\ [27, 3, w^3 - 2*w^2 - 3*w + 5],\ [31, 31, -w^2 - 2*w + 1],\ [41, 41, -w^2 + 5],\ [43, 43, w^3 - w^2 - 5*w - 1],\ [43, 43, w^3 - w^2 - 3*w + 1],\ [59, 59, -w - 3],\ [59, 59, -2*w^3 + 2*w^2 + 9*w - 5],\ [59, 59, -w^3 - 3*w^2 - w + 3],\ [59, 59, w^3 - 7*w + 1],\ [61, 61, -w^3 + w^2 + 2*w + 5],\ [61, 61, -w^3 - w^2 + 4*w + 3],\ [67, 67, 4*w^3 - 4*w^2 - 18*w + 7],\ [73, 73, -2*w^3 + 6*w - 3],\ [73, 73, -2*w + 3],\ [97, 97, w^3 - 2*w^2 - 5*w + 3],\ [101, 101, w^3 + w^2 - 5*w - 7],\ [101, 101, -w^3 - w^2 + 4*w + 5],\ [103, 103, 2*w^3 - 8*w - 1],\ [103, 103, w^2 - 2*w - 7],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, -w^3 + w^2 + 6*w - 3],\ [127, 127, -w^3 + w^2 + 6*w - 1],\ [131, 131, -2*w^3 + 3*w^2 + 10*w - 11],\ [137, 137, w^3 + w^2 - 6*w - 5],\ [139, 139, -3*w^3 + 2*w^2 + 15*w - 1],\ [149, 149, w^3 - 3*w^2 - 4*w + 11],\ [149, 149, -w^3 + 5*w - 1],\ [157, 157, -2*w^3 + 3*w^2 + 6*w - 1],\ [163, 163, 2*w^2 - 3],\ [163, 163, -2*w^3 + 2*w^2 + 7*w - 5],\ [167, 167, -2*w^3 + 2*w^2 + 8*w - 3],\ [167, 167, -2*w^2 + 2*w + 9],\ [173, 173, 2*w^3 - w^2 - 8*w + 3],\ [173, 173, 2*w^3 - 3*w^2 - 6*w + 3],\ [181, 181, 2*w^3 - 3*w^2 - 8*w + 5],\ [191, 191, -2*w^3 + w^2 + 10*w - 1],\ [193, 193, -w^3 + 3*w^2 + 2*w - 7],\ [193, 193, w^3 - 3*w - 3],\ [193, 193, 2*w^2 - 2*w - 3],\ [193, 193, w^3 - 7*w - 1],\ [197, 197, w^2 - 2*w - 5],\ [211, 211, w^2 - 4*w - 1],\ [229, 229, -w^3 + w^2 + 6*w - 7],\ [229, 229, -4*w^3 + 6*w^2 + 16*w - 13],\ [233, 233, 3*w^2 + 2*w - 5],\ [233, 233, 2*w^3 - 2*w^2 - 11*w + 7],\ [239, 239, -w^3 + w^2 + 7*w + 1],\ [241, 241, w^3 - 3*w^2 - 2*w + 9],\ [241, 241, w^3 + w^2 - 9*w - 5],\ [251, 251, 2*w^3 - 6*w + 1],\ [271, 271, 2*w^3 - w^2 - 8*w - 1],\ [271, 271, -2*w^2 + w + 7],\ [281, 281, 2*w^3 + 2*w^2 - 5*w - 1],\ [293, 293, w^3 + w^2 - 5*w - 1],\ [293, 293, -3*w + 7],\ [307, 307, -w^3 - 2*w^2 + 3*w + 5],\ [311, 311, -w^3 + 3*w^2 + 4*w - 7],\ [313, 313, 2*w^2 - 2*w - 5],\ [317, 317, -2*w^3 + 4*w^2 + 7*w - 13],\ [317, 317, -2*w^3 + 3*w^2 + 8*w - 11],\ [337, 337, 3*w^3 + 2*w^2 - 7*w + 1],\ [347, 347, 2*w^3 - 2*w^2 - 11*w + 1],\ [349, 349, -5*w^3 + 6*w^2 + 23*w - 13],\ [359, 359, 2*w^3 - 2*w^2 - 12*w + 9],\ [359, 359, -2*w^3 + 8*w + 5],\ [367, 367, -4*w^3 + 4*w^2 + 19*w - 5],\ [367, 367, 2*w^3 + w^2 - 10*w - 7],\ [383, 383, 2*w^3 - 2*w^2 - 7*w + 1],\ [389, 389, 2*w^2 - w - 5],\ [397, 397, 3*w^3 - 4*w^2 - 11*w + 9],\ [397, 397, 3*w^3 - 3*w^2 - 12*w + 7],\ [397, 397, 2*w^3 - 4*w^2 - 8*w + 15],\ [397, 397, -w^3 + 3*w^2 + w - 7],\ [409, 409, -w^3 - w^2 + 9*w - 1],\ [419, 419, 2*w^2 - 3*w - 7],\ [419, 419, 4*w^3 - 3*w^2 - 18*w + 3],\ [431, 431, -3*w^3 + w^2 + 17*w - 1],\ [431, 431, 3*w^3 - w^2 - 16*w - 1],\ [433, 433, -2*w^3 + 5*w^2 + 8*w - 19],\ [443, 443, 3*w - 5],\ [449, 449, -2*w^3 + 2*w^2 + 9*w - 9],\ [449, 449, -5*w^3 + 8*w^2 + 19*w - 17],\ [457, 457, -3*w^3 + 3*w^2 + 13*w - 9],\ [457, 457, -3*w^3 + 2*w^2 + 13*w + 1],\ [457, 457, -2*w^3 + w^2 + 8*w + 7],\ [457, 457, 3*w^3 - 3*w^2 - 15*w + 7],\ [461, 461, -2*w^3 + 2*w^2 + 9*w + 1],\ [479, 479, -w^3 + w^2 + 7*w - 9],\ [487, 487, -w^3 - w^2 + w - 3],\ [499, 499, -2*w^3 + 7*w - 3],\ [499, 499, -5*w^3 + 7*w^2 + 20*w - 15],\ [541, 541, -3*w^3 + 4*w^2 + 13*w - 7],\ [547, 547, -w^3 - w^2 + 3*w + 5],\ [557, 557, 4*w - 1],\ [563, 563, 2*w^3 - w^2 - 6*w - 1],\ [571, 571, w^3 - w^2 - w - 3],\ [587, 587, -2*w^3 + 2*w^2 + 10*w + 1],\ [593, 593, 2*w^3 - 2*w^2 - 6*w + 3],\ [613, 613, -5*w^3 + 5*w^2 + 23*w - 7],\ [613, 613, -w^3 + w^2 + 5*w - 7],\ [617, 617, -w - 5],\ [619, 619, -3*w^3 + 4*w^2 + 11*w - 7],\ [625, 5, -5],\ [643, 643, -3*w^3 + 3*w^2 + 14*w - 9],\ [643, 643, -3*w^2 - 4*w + 1],\ [653, 653, -w^3 + w^2 + 9*w + 3],\ [653, 653, -4*w^2 + 6*w + 11],\ [659, 659, -w^2 - 4*w + 1],\ [661, 661, -3*w^3 + 3*w^2 + 15*w - 5],\ [661, 661, w^3 + w^2 - 7*w - 11],\ [673, 673, 2*w^3 - 3*w^2 - 12*w + 1],\ [673, 673, -2*w^3 + w^2 + 10*w - 3],\ [683, 683, -w^3 - 2*w^2 + 5*w + 11],\ [691, 691, 4*w^3 - 3*w^2 - 18*w + 5],\ [709, 709, w^3 - 3*w - 7],\ [719, 719, 2*w^3 - 8*w + 1],\ [727, 727, -3*w^3 + 6*w^2 + 13*w - 19],\ [733, 733, w^3 - w^2 + 3],\ [739, 739, -w^3 + w^2 + 3*w - 7],\ [751, 751, -w^2 - 3],\ [773, 773, 2*w^3 - 2*w^2 - 11*w + 3],\ [787, 787, w^3 - w^2 - 3*w - 5],\ [797, 797, -2*w^3 + 2*w^2 + 5*w - 1],\ [797, 797, -7*w^3 + 8*w^2 + 31*w - 15],\ [809, 809, 4*w^3 - 6*w^2 - 17*w + 13],\ [809, 809, 3*w^2 - 4*w - 5],\ [811, 811, 2*w^2 + 4*w + 3],\ [811, 811, -3*w^3 + 3*w^2 + 12*w - 5],\ [821, 821, 2*w^3 - 10*w - 1],\ [821, 821, 6*w^3 - 10*w^2 - 24*w + 29],\ [823, 823, -5*w^3 + 3*w^2 + 24*w - 1],\ [823, 823, w^3 + w^2 + w + 3],\ [827, 827, -4*w^3 + 3*w^2 + 16*w - 7],\ [829, 829, 2*w^3 - 4*w^2 - 6*w + 11],\ [841, 29, w^3 - 3*w^2 - 5*w + 3],\ [841, 29, -3*w^3 + 3*w^2 + 13*w - 1],\ [857, 857, -4*w^3 + 6*w^2 + 13*w - 7],\ [857, 857, -3*w^3 + w^2 + 15*w + 1],\ [859, 859, -4*w^2 + 3*w + 17],\ [863, 863, -4*w^3 + 8*w^2 + 14*w - 21],\ [877, 877, -w^3 - w^2 + 6*w - 1],\ [881, 881, -5*w - 1],\ [883, 883, -4*w^3 + 4*w^2 + 21*w - 13],\ [883, 883, 2*w^3 - 11*w - 1],\ [887, 887, -3*w^3 - w^2 + 8*w - 5],\ [907, 907, w^3 - w^2 - w + 5],\ [911, 911, 2*w^2 - 5*w - 5],\ [919, 919, -w^3 + 3*w^2 + 6*w - 3],\ [919, 919, 5*w^2 + 4*w - 9],\ [929, 929, w^3 + 3*w^2 - 8*w - 17],\ [937, 937, -4*w^3 + 4*w^2 + 17*w - 7],\ [953, 953, -2*w^3 + 2*w^2 + 7*w + 5],\ [953, 953, 3*w^3 - 4*w^2 - 11*w + 3],\ [967, 967, 4*w^3 - 2*w^2 - 17*w + 3],\ [971, 971, w^3 - 3*w^2 - 8*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 12*w + 13],\ [991, 991, -2*w^3 - 2*w^2 + 8*w + 7],\ [991, 991, w^3 + w^2 - 10*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 + 4*x^9 - 6*x^8 - 37*x^7 - x^6 + 112*x^5 + 56*x^4 - 114*x^3 - 81*x^2 + 9*x + 8 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/2*e^9 - 3/2*e^8 + 4*e^7 + 13*e^6 - 19/2*e^5 - 73/2*e^4 + 5*e^3 + 71/2*e^2 + 3*e - 6, 1/2*e^9 + 3/2*e^8 - 4*e^7 - 13*e^6 + 19/2*e^5 + 73/2*e^4 - 4*e^3 - 69/2*e^2 - 7*e + 3, 1, 1/2*e^9 + 2*e^8 - 7/2*e^7 - 19*e^6 + 9/2*e^5 + 58*e^4 + 21/2*e^3 - 117/2*e^2 - 39/2*e + 6, -e^9 - 2*e^8 + 10*e^7 + 16*e^6 - 34*e^5 - 37*e^4 + 41*e^3 + 23*e^2 - 6*e - 4, e^9 + 5/2*e^8 - 21/2*e^7 - 25*e^6 + 37*e^5 + 167/2*e^4 - 87/2*e^3 - 99*e^2 + 3/2*e + 18, 1/2*e^9 - 15/2*e^7 + 69/2*e^5 - 4*e^4 - 111/2*e^3 + 31/2*e^2 + 43/2*e - 8, 1/2*e^9 + 3/2*e^8 - 3*e^7 - 10*e^6 + 5/2*e^5 + 31/2*e^4 + 9*e^3 + 1/2*e^2 - 9*e, -e^9 - 3*e^8 + 8*e^7 + 25*e^6 - 22*e^5 - 67*e^4 + 27*e^3 + 60*e^2 - 15*e - 8, -1/2*e^8 + 1/2*e^7 + 9*e^6 - e^5 - 85/2*e^4 - 19/2*e^3 + 61*e^2 + 51/2*e - 10, -3/2*e^9 - 7/2*e^8 + 15*e^7 + 32*e^6 - 101/2*e^5 - 189/2*e^4 + 60*e^3 + 191/2*e^2 - 8*e - 16, e^9 + 3*e^8 - 8*e^7 - 26*e^6 + 19*e^5 + 73*e^4 - 9*e^3 - 68*e^2 - 8*e + 4, e^9 + 2*e^8 - 9*e^7 - 13*e^6 + 29*e^5 + 20*e^4 - 35*e^3 + 3*e^2 + 3*e - 8, -1/2*e^8 - 3/2*e^7 + 4*e^6 + 12*e^5 - 23/2*e^4 - 57/2*e^3 + 14*e^2 + 33/2*e - 6, -1/2*e^9 - e^8 + 13/2*e^7 + 13*e^6 - 49/2*e^5 - 52*e^4 + 41/2*e^3 + 135/2*e^2 + 39/2*e - 12, -1/2*e^9 - e^8 + 11/2*e^7 + 9*e^6 - 41/2*e^5 - 24*e^4 + 51/2*e^3 + 33/2*e^2 - 5/2*e, e^9 + 7/2*e^8 - 17/2*e^7 - 36*e^6 + 18*e^5 + 241/2*e^4 + 17/2*e^3 - 135*e^2 - 77/2*e + 18, 1/2*e^9 + e^8 - 11/2*e^7 - 8*e^6 + 47/2*e^5 + 17*e^4 - 97/2*e^3 - 15/2*e^2 + 83/2*e + 4, e^9 + 3*e^8 - 8*e^7 - 25*e^6 + 20*e^5 + 62*e^4 - 19*e^3 - 40*e^2 + 10*e - 6, -1/2*e^8 - 5/2*e^7 + e^6 + 18*e^5 + 21/2*e^4 - 67/2*e^3 - 29*e^2 + 19/2*e + 6, -3/2*e^9 - 9/2*e^8 + 12*e^7 + 37*e^6 - 65/2*e^5 - 191/2*e^4 + 35*e^3 + 153/2*e^2 - 7*e, 1/2*e^9 + e^8 - 7/2*e^7 - 5*e^6 + 13/2*e^5 + 3*e^4 - 3/2*e^3 + 3/2*e^2 + 1/2*e + 8, 3/2*e^9 + 3*e^8 - 33/2*e^7 - 29*e^6 + 121/2*e^5 + 91*e^4 - 153/2*e^3 - 197/2*e^2 + 25/2*e + 16, -1/2*e^8 - 3/2*e^7 + 3*e^6 + 11*e^5 - 5/2*e^4 - 49/2*e^3 - 7*e^2 + 29/2*e, -3/2*e^9 - 3*e^8 + 33/2*e^7 + 27*e^6 - 127/2*e^5 - 74*e^4 + 189/2*e^3 + 117/2*e^2 - 79/2*e - 8, -3/2*e^9 - 3*e^8 + 31/2*e^7 + 27*e^6 - 107/2*e^5 - 81*e^4 + 127/2*e^3 + 187/2*e^2 - 15/2*e - 30, -4*e^9 - 21/2*e^8 + 71/2*e^7 + 91*e^6 - 99*e^5 - 497/2*e^4 + 147/2*e^3 + 218*e^2 + 75/2*e - 16, 3*e^9 + 8*e^8 - 27*e^7 - 70*e^6 + 80*e^5 + 195*e^4 - 78*e^3 - 178*e^2 - 3*e + 22, 1/2*e^9 + 3/2*e^8 - 2*e^7 - 6*e^6 - 5/2*e^5 - 25/2*e^4 + 12*e^3 + 103/2*e^2 - e - 12, -1/2*e^9 - 5/2*e^8 + 18*e^6 + 41/2*e^5 - 73/2*e^4 - 58*e^3 + 27/2*e^2 + 33*e + 10, 5/2*e^9 + 11/2*e^8 - 25*e^7 - 46*e^6 + 175/2*e^5 + 233/2*e^4 - 116*e^3 - 179/2*e^2 + 28*e + 6, -e^9 - 4*e^8 + 7*e^7 + 38*e^6 - 10*e^5 - 117*e^4 - 15*e^3 + 117*e^2 + 29*e - 18, -2*e^9 - 11/2*e^8 + 35/2*e^7 + 47*e^6 - 50*e^5 - 253/2*e^4 + 87/2*e^3 + 115*e^2 + 25/2*e - 28, 3/2*e^9 + 7/2*e^8 - 14*e^7 - 28*e^6 + 91/2*e^5 + 137/2*e^4 - 53*e^3 - 109/2*e^2 + 2*e + 10, 1/2*e^9 + 2*e^8 - 5/2*e^7 - 17*e^6 - 9/2*e^5 + 45*e^4 + 75/2*e^3 - 73/2*e^2 - 87/2*e + 4, 5/2*e^9 + 9/2*e^8 - 28*e^7 - 39*e^6 + 223/2*e^5 + 211/2*e^4 - 172*e^3 - 177/2*e^2 + 68*e + 4, -e^8 - e^7 + 15*e^6 + 13*e^5 - 68*e^4 - 43*e^3 + 98*e^2 + 35*e - 14, 1/2*e^9 - 1/2*e^8 - 8*e^7 + 5*e^6 + 77/2*e^5 - 31/2*e^4 - 62*e^3 + 29/2*e^2 + 20*e - 6, -5/2*e^9 - 9*e^8 + 37/2*e^7 + 81*e^6 - 75/2*e^5 - 237*e^4 + 1/2*e^3 + 461/2*e^2 + 91/2*e - 28, -e^9 - 7/2*e^8 + 13/2*e^7 + 28*e^6 - 11*e^5 - 145/2*e^4 - 1/2*e^3 + 71*e^2 + 27/2*e - 28, -2*e^9 - 7/2*e^8 + 39/2*e^7 + 22*e^6 - 70*e^5 - 53/2*e^4 + 213/2*e^3 - 21*e^2 - 97/2*e + 4, e^9 + 3/2*e^8 - 23/2*e^7 - 13*e^6 + 42*e^5 + 59/2*e^4 - 91/2*e^3 - 9*e^2 - 7/2*e - 6, -11/2*e^9 - 15*e^8 + 103/2*e^7 + 141*e^6 - 305/2*e^5 - 429*e^4 + 241/2*e^3 + 867/2*e^2 + 121/2*e - 42, 3/2*e^8 + 9/2*e^7 - 10*e^6 - 31*e^5 + 39/2*e^4 + 109/2*e^3 - 15*e^2 - 11/2*e + 6, 3/2*e^9 + 3*e^8 - 35/2*e^7 - 31*e^6 + 137/2*e^5 + 105*e^4 - 189/2*e^3 - 245/2*e^2 + 43/2*e + 18, 1/2*e^9 + 7/2*e^8 - 2*e^7 - 37*e^6 - 9/2*e^5 + 269/2*e^4 + 22*e^3 - 359/2*e^2 - 23*e + 42, -2*e^8 - 6*e^7 + 13*e^6 + 43*e^5 - 22*e^4 - 91*e^3 + 5*e^2 + 53*e + 2, -e^9 - 3/2*e^8 + 23/2*e^7 + 18*e^6 - 34*e^5 - 133/2*e^4 + 9/2*e^3 + 78*e^2 + 99/2*e - 2, -7/2*e^9 - 9*e^8 + 69/2*e^7 + 85*e^6 - 223/2*e^5 - 260*e^4 + 213/2*e^3 + 523/2*e^2 + 61/2*e - 26, 7/2*e^9 + 19/2*e^8 - 31*e^7 - 85*e^6 + 169/2*e^5 + 493/2*e^4 - 49*e^3 - 487/2*e^2 - 60*e + 30, 7/2*e^9 + 11*e^8 - 57/2*e^7 - 100*e^6 + 131/2*e^5 + 294*e^4 - 23/2*e^3 - 583/2*e^2 - 123/2*e + 36, -3/2*e^9 - 9/2*e^8 + 11*e^7 + 37*e^6 - 45/2*e^5 - 203/2*e^4 + e^3 + 205/2*e^2 + 29*e - 26, -3/2*e^9 - 5*e^8 + 23/2*e^7 + 44*e^6 - 51/2*e^5 - 126*e^4 + 19/2*e^3 + 253/2*e^2 + 23/2*e - 18, -1/2*e^9 - 3/2*e^8 + 4*e^7 + 14*e^6 - 15/2*e^5 - 89/2*e^4 - 6*e^3 + 97/2*e^2 + 8*e - 4, 3*e^7 + 10*e^6 - 16*e^5 - 67*e^4 + 14*e^3 + 119*e^2 + 12*e - 32, 3/2*e^9 + 9/2*e^8 - 12*e^7 - 39*e^6 + 59/2*e^5 + 227/2*e^4 - 19*e^3 - 255/2*e^2 - 2*e + 32, 3*e^9 + 7*e^8 - 28*e^7 - 58*e^6 + 88*e^5 + 149*e^4 - 96*e^3 - 116*e^2 + 8*e - 2, -1/2*e^9 + 17/2*e^7 + 2*e^6 - 83/2*e^5 - 7*e^4 + 131/2*e^3 - 19/2*e^2 - 35/2*e + 26, 2*e^8 + 3*e^7 - 25*e^6 - 29*e^5 + 106*e^4 + 88*e^3 - 152*e^2 - 84*e + 14, -e^9 - 7/2*e^8 + 17/2*e^7 + 32*e^6 - 25*e^5 - 183/2*e^4 + 55/2*e^3 + 75*e^2 + 3/2*e + 8, -11/2*e^9 - 25/2*e^8 + 59*e^7 + 124*e^6 - 417/2*e^5 - 797/2*e^4 + 246*e^3 + 863/2*e^2 - 17*e - 60, -3*e^6 - 10*e^5 + 14*e^4 + 56*e^3 - 13*e^2 - 68*e, -1/2*e^9 - 2*e^8 + 13/2*e^7 + 29*e^6 - 41/2*e^5 - 121*e^4 + 19/2*e^3 + 323/2*e^2 + 29/2*e - 40, -5/2*e^9 - 15/2*e^8 + 21*e^7 + 66*e^6 - 115/2*e^5 - 375/2*e^4 + 53*e^3 + 363/2*e^2 + 7*e - 34, 13/2*e^9 + 33/2*e^8 - 60*e^7 - 146*e^6 + 355/2*e^5 + 825/2*e^4 - 152*e^3 - 777/2*e^2 - 45*e + 54, 1/2*e^9 + 1/2*e^8 - 5*e^7 + e^6 + 43/2*e^5 - 59/2*e^4 - 54*e^3 + 151/2*e^2 + 57*e - 16, -e^9 - 5*e^8 + 2*e^7 + 39*e^6 + 25*e^5 - 95*e^4 - 89*e^3 + 76*e^2 + 76*e - 6, 5/2*e^9 + 8*e^8 - 41/2*e^7 - 75*e^6 + 87/2*e^5 + 228*e^4 + 29/2*e^3 - 467/2*e^2 - 153/2*e + 18, -e^9 - 7/2*e^8 + 17/2*e^7 + 34*e^6 - 20*e^5 - 211/2*e^4 + 1/2*e^3 + 114*e^2 + 57/2*e - 38, -3*e^9 - 7*e^8 + 33*e^7 + 74*e^6 - 113*e^5 - 251*e^4 + 101*e^3 + 279*e^2 + 56*e - 16, -1/2*e^9 - e^8 + 7/2*e^7 + 4*e^6 - 13/2*e^5 + 10*e^4 + 15/2*e^3 - 77/2*e^2 - 49/2*e + 4, 2*e^9 + 7*e^8 - 15*e^7 - 62*e^6 + 33*e^5 + 176*e^4 - 16*e^3 - 156*e^2 - 10*e + 2, -3*e^9 - 4*e^8 + 38*e^7 + 41*e^6 - 157*e^5 - 131*e^4 + 220*e^3 + 124*e^2 - 39*e + 14, -1/2*e^9 - 1/2*e^8 + 6*e^7 + 2*e^6 - 55/2*e^5 + 1/2*e^4 + 43*e^3 + 5/2*e^2 - 2*e - 22, -1/2*e^9 - 2*e^8 + 3/2*e^7 + 15*e^6 + 19/2*e^5 - 33*e^4 - 69/2*e^3 + 35/2*e^2 + 47/2*e + 2, -3/2*e^9 + 51/2*e^7 + 7*e^6 - 251/2*e^5 - 39*e^4 + 401/2*e^3 + 99/2*e^2 - 103/2*e + 2, -3/2*e^9 - 11/2*e^8 + 11*e^7 + 48*e^6 - 57/2*e^5 - 281/2*e^4 + 36*e^3 + 293/2*e^2 - 10*e - 20, -2*e^8 - 9*e^7 + 7*e^6 + 67*e^5 + 19*e^4 - 136*e^3 - 59*e^2 + 54*e + 8, e^8 + 3*e^7 - 10*e^6 - 28*e^5 + 34*e^4 + 79*e^3 - 36*e^2 - 58*e - 14, -7/2*e^9 - 19/2*e^8 + 33*e^7 + 89*e^6 - 203/2*e^5 - 547/2*e^4 + 101*e^3 + 591/2*e^2 + e - 44, 7/2*e^9 + 10*e^8 - 63/2*e^7 - 93*e^6 + 177/2*e^5 + 276*e^4 - 139/2*e^3 - 517/2*e^2 - 47/2*e + 6, -3*e^9 - 23/2*e^8 + 33/2*e^7 + 93*e^6 - 4*e^5 - 469/2*e^4 - 167/2*e^3 + 185*e^2 + 189/2*e - 20, -3*e^9 - 6*e^8 + 32*e^7 + 53*e^6 - 119*e^5 - 151*e^4 + 167*e^3 + 148*e^2 - 65*e - 32, e^9 - 2*e^8 - 23*e^7 + 5*e^6 + 123*e^5 + 30*e^4 - 207*e^3 - 81*e^2 + 70*e + 12, 2*e^9 + 9/2*e^8 - 47/2*e^7 - 47*e^6 + 96*e^5 + 321/2*e^4 - 279/2*e^3 - 175*e^2 + 57/2*e - 4, -3/2*e^9 + 1/2*e^8 + 25*e^7 - 2*e^6 - 255/2*e^5 + 3/2*e^4 + 232*e^3 + 1/2*e^2 - 101*e - 10, -3/2*e^9 - 9/2*e^8 + 16*e^7 + 53*e^6 - 91/2*e^5 - 407/2*e^4 - 3*e^3 + 539/2*e^2 + 92*e - 38, -2*e^9 - 7/2*e^8 + 37/2*e^7 + 22*e^6 - 56*e^5 - 47/2*e^4 + 117/2*e^3 - 37*e^2 - 33/2*e + 26, 3/2*e^9 + 3*e^8 - 27/2*e^7 - 20*e^6 + 81/2*e^5 + 31*e^4 - 75/2*e^3 + 11/2*e^2 - 21/2*e - 18, -1/2*e^8 - 7/2*e^7 + 31*e^5 + 37/2*e^4 - 171/2*e^3 - 42*e^2 + 147/2*e + 6, 2*e^9 + 17/2*e^8 - 25/2*e^7 - 79*e^6 + 12*e^5 + 485/2*e^4 + 59/2*e^3 - 265*e^2 - 55/2*e + 50, 5/2*e^9 + 7/2*e^8 - 30*e^7 - 31*e^6 + 247/2*e^5 + 169/2*e^4 - 191*e^3 - 147/2*e^2 + 68*e + 6, 3/2*e^9 + 3/2*e^8 - 19*e^7 - 10*e^6 + 173/2*e^5 + 29/2*e^4 - 152*e^3 + 7/2*e^2 + 75*e + 6, -1/2*e^9 + 2*e^8 + 19/2*e^7 - 27*e^6 - 107/2*e^5 + 123*e^4 + 211/2*e^3 - 387/2*e^2 - 113/2*e + 40, 7/2*e^9 + 11/2*e^8 - 41*e^7 - 46*e^6 + 347/2*e^5 + 233/2*e^4 - 296*e^3 - 179/2*e^2 + 144*e + 8, 5/2*e^9 + 15/2*e^8 - 26*e^7 - 83*e^6 + 165/2*e^5 + 595/2*e^4 - 61*e^3 - 685/2*e^2 - 58*e + 22, -5/2*e^9 - 9/2*e^8 + 27*e^7 + 40*e^6 - 199/2*e^5 - 237/2*e^4 + 131*e^3 + 255/2*e^2 - 31*e - 20, -1/2*e^8 - 11/2*e^7 - 11*e^6 + 29*e^5 + 169/2*e^4 - 53/2*e^3 - 140*e^2 - 33/2*e + 12, e^9 + 2*e^8 - 12*e^7 - 22*e^6 + 50*e^5 + 84*e^4 - 73*e^3 - 108*e^2 + 5*e + 4, 5/2*e^9 + 15/2*e^8 - 22*e^7 - 71*e^6 + 121/2*e^5 + 449/2*e^4 - 43*e^3 - 503/2*e^2 - 25*e + 36, e^9 + 4*e^8 - 9*e^7 - 42*e^6 + 25*e^5 + 137*e^4 - 30*e^3 - 145*e^2 + 32*e + 36, -3/2*e^9 - 11/2*e^8 + 6*e^7 + 41*e^6 + 41/2*e^5 - 177/2*e^4 - 106*e^3 + 87/2*e^2 + 89*e + 6, -5*e^9 - 15*e^8 + 43*e^7 + 139*e^6 - 105*e^5 - 410*e^4 + 26*e^3 + 393*e^2 + 104*e - 30, -e^9 + 1/2*e^8 + 33/2*e^7 - 6*e^6 - 81*e^5 + 71/2*e^4 + 251/2*e^3 - 83*e^2 - 47/2*e + 38, -5/2*e^9 - 15/2*e^8 + 25*e^7 + 78*e^6 - 155/2*e^5 - 533/2*e^4 + 48*e^3 + 611/2*e^2 + 79*e - 24, -3/2*e^9 - 6*e^8 + 19/2*e^7 + 53*e^6 - 27/2*e^5 - 157*e^4 - 19/2*e^3 + 319/2*e^2 + 33/2*e - 6, -4*e^9 - 12*e^8 + 35*e^7 + 109*e^6 - 100*e^5 - 319*e^4 + 97*e^3 + 316*e^2 - 4*e - 50, e^9 + 9/2*e^8 - 3/2*e^7 - 27*e^6 - 20*e^5 + 53/2*e^4 + 71/2*e^3 + 45*e^2 + 63/2*e - 32, -5/2*e^9 - 4*e^8 + 57/2*e^7 + 39*e^6 - 203/2*e^5 - 126*e^4 + 185/2*e^3 + 285/2*e^2 + 101/2*e - 28, -2*e^9 - 15/2*e^8 + 21/2*e^7 + 59*e^6 - 4*e^5 - 299/2*e^4 - 49/2*e^3 + 132*e^2 - 23/2*e - 10, 5/2*e^9 + 15/2*e^8 - 16*e^7 - 58*e^6 + 31/2*e^5 + 285/2*e^4 + 54*e^3 - 251/2*e^2 - 66*e + 26, 3*e^9 + 19/2*e^8 - 43/2*e^7 - 75*e^6 + 44*e^5 + 349/2*e^4 - 59/2*e^3 - 113*e^2 + 51/2*e, -1/2*e^9 + 3/2*e^8 + 13*e^7 - 4*e^6 - 135/2*e^5 - 43/2*e^4 + 96*e^3 + 125/2*e^2 + e - 14, 9/2*e^9 + 13*e^8 - 81/2*e^7 - 116*e^6 + 251/2*e^5 + 330*e^4 - 291/2*e^3 - 605/2*e^2 + 39/2*e + 20, 5*e^9 + 13*e^8 - 49*e^7 - 127*e^6 + 148*e^5 + 400*e^4 - 104*e^3 - 415*e^2 - 96*e + 44, -3*e^9 - 15/2*e^8 + 51/2*e^7 + 56*e^6 - 74*e^5 - 231/2*e^4 + 153/2*e^3 + 45*e^2 + 11/2*e + 6, 5/2*e^9 + 13/2*e^8 - 25*e^7 - 62*e^6 + 173/2*e^5 + 393/2*e^4 - 111*e^3 - 429/2*e^2 + 24*e + 28, -1/2*e^9 + 1/2*e^8 + 10*e^7 - 87/2*e^5 + 7/2*e^4 + 44*e^3 - 89/2*e^2 + 20*e + 28, 2*e^9 + 17/2*e^8 - 17/2*e^7 - 68*e^6 - 11*e^5 + 357/2*e^4 + 129/2*e^3 - 173*e^2 - 67/2*e + 30, -1/2*e^9 - 1/2*e^8 + 2*e^7 - 7*e^6 - 3/2*e^5 + 119/2*e^4 + 22*e^3 - 197/2*e^2 - 64*e + 24, -5/2*e^9 - 3/2*e^8 + 38*e^7 + 22*e^6 - 363/2*e^5 - 173/2*e^4 + 305*e^3 + 189/2*e^2 - 114*e + 8, -4*e^9 - 9*e^8 + 37*e^7 + 70*e^6 - 123*e^5 - 172*e^4 + 164*e^3 + 153*e^2 - 55*e - 34, 1/2*e^9 + 4*e^8 + 9/2*e^7 - 25*e^6 - 99/2*e^5 + 32*e^4 + 207/2*e^3 + 27/2*e^2 - 53/2*e + 4, 2*e^9 + 8*e^8 - 10*e^7 - 64*e^6 - 2*e^5 + 163*e^4 + 52*e^3 - 145*e^2 - 33*e + 32, -e^9 - 9/2*e^8 + 5/2*e^7 + 39*e^6 + 29*e^5 - 237/2*e^4 - 239/2*e^3 + 138*e^2 + 203/2*e - 22, e^9 + 2*e^8 - 10*e^7 - 12*e^6 + 39*e^5 + 11*e^4 - 52*e^3 + 21*e^2 - 18*e - 6, -15/2*e^9 - 37/2*e^8 + 72*e^7 + 165*e^6 - 453/2*e^5 - 931/2*e^4 + 213*e^3 + 833/2*e^2 + 60*e - 18, 1/2*e^9 + 5/2*e^8 - 4*e^7 - 28*e^6 + 17/2*e^5 + 207/2*e^4 - 7*e^3 - 275/2*e^2 + 15*e + 38, -3/2*e^9 - 13/2*e^8 + 4*e^7 + 44*e^6 + 45/2*e^5 - 149/2*e^4 - 66*e^3 + 13/2*e^2 + 29*e + 10, 5/2*e^9 + 3*e^8 - 67/2*e^7 - 37*e^6 + 279/2*e^5 + 142*e^4 - 377/2*e^3 - 351/2*e^2 + 55/2*e, 7*e^9 + 21*e^8 - 58*e^7 - 184*e^6 + 150*e^5 + 520*e^4 - 99*e^3 - 498*e^2 - 74*e + 60, -13/2*e^9 - 39/2*e^8 + 50*e^7 + 163*e^6 - 213/2*e^5 - 859/2*e^4 + 10*e^3 + 723/2*e^2 + 100*e - 16, 7/2*e^9 + 19/2*e^8 - 37*e^7 - 104*e^6 + 233/2*e^5 + 737/2*e^4 - 64*e^3 - 853/2*e^2 - 134*e + 30, -5/2*e^9 - 3*e^8 + 55/2*e^7 + 19*e^6 - 203/2*e^5 - 18*e^4 + 251/2*e^3 - 91/2*e^2 - 29/2*e + 18, -3/2*e^8 - 3/2*e^7 + 15*e^6 + 6*e^5 - 103/2*e^4 + 7/2*e^3 + 63*e^2 - 35/2*e - 16, -3*e^9 - 19/2*e^8 + 53/2*e^7 + 94*e^6 - 68*e^5 - 613/2*e^4 + 43/2*e^3 + 346*e^2 + 153/2*e - 62, 1/2*e^9 + 7/2*e^8 + 2*e^7 - 22*e^6 - 37/2*e^5 + 81/2*e^4 - e^3 - 57/2*e^2 + 47*e + 32, 5/2*e^9 + 23/2*e^8 - 11*e^7 - 102*e^6 - 49/2*e^5 + 593/2*e^4 + 151*e^3 - 591/2*e^2 - 149*e + 22, -e^9 - 4*e^8 + 9*e^7 + 51*e^6 - 10*e^5 - 207*e^4 - 60*e^3 + 282*e^2 + 98*e - 54, -5/2*e^9 - 13/2*e^8 + 24*e^7 + 64*e^6 - 139/2*e^5 - 419/2*e^4 + 36*e^3 + 469/2*e^2 + 74*e - 26, 1/2*e^9 - 2*e^8 - 19/2*e^7 + 22*e^6 + 95/2*e^5 - 82*e^4 - 155/2*e^3 + 183/2*e^2 + 43/2*e + 10, 15/2*e^9 + 19*e^8 - 149/2*e^7 - 176*e^6 + 509/2*e^5 + 528*e^4 - 643/2*e^3 - 1081/2*e^2 + 131/2*e + 78, 17/2*e^9 + 41/2*e^8 - 83*e^7 - 182*e^6 + 557/2*e^5 + 1039/2*e^4 - 339*e^3 - 989/2*e^2 + 57*e + 36, 5/2*e^9 + 19/2*e^8 - 16*e^7 - 83*e^6 + 29/2*e^5 + 475/2*e^4 + 81*e^3 - 469/2*e^2 - 152*e + 28, 5/2*e^9 + 13/2*e^8 - 18*e^7 - 45*e^6 + 69/2*e^5 + 163/2*e^4 - 5*e^3 - 41/2*e^2 - 20*e - 14, 7*e^9 + 20*e^8 - 57*e^7 - 169*e^6 + 142*e^5 + 453*e^4 - 86*e^3 - 399*e^2 - 67*e + 34, 7/2*e^9 + 11*e^8 - 63/2*e^7 - 104*e^6 + 193/2*e^5 + 320*e^4 - 227/2*e^3 - 673/2*e^2 + 53/2*e + 52, -8*e^9 - 20*e^8 + 74*e^7 + 174*e^6 - 227*e^5 - 483*e^4 + 240*e^3 + 446*e^2 - 32*e - 64, 13/2*e^9 + 29/2*e^8 - 69*e^7 - 140*e^6 + 483/2*e^5 + 881/2*e^4 - 267*e^3 - 947/2*e^2 - 23*e + 64, 7*e^9 + 45/2*e^8 - 113/2*e^7 - 203*e^6 + 131*e^5 + 1183/2*e^4 - 47/2*e^3 - 574*e^2 - 305/2*e + 58, -11/2*e^9 - 37/2*e^8 + 41*e^7 + 165*e^6 - 151/2*e^5 - 953/2*e^4 - 44*e^3 + 907/2*e^2 + 143*e - 28, -9*e^9 - 24*e^8 + 79*e^7 + 202*e^6 - 234*e^5 - 540*e^4 + 242*e^3 + 476*e^2 - 8*e - 52, -1/2*e^9 - 6*e^8 - 5/2*e^7 + 64*e^6 + 93/2*e^5 - 226*e^4 - 267/2*e^3 + 557/2*e^2 + 195/2*e - 46, -3*e^9 - 5*e^8 + 31*e^7 + 34*e^6 - 122*e^5 - 62*e^4 + 212*e^3 + 17*e^2 - 126*e + 14, -3/2*e^9 - 13/2*e^8 + 12*e^7 + 64*e^6 - 63/2*e^5 - 399/2*e^4 + 47*e^3 + 423/2*e^2 - 55*e - 60, 4*e^9 + 12*e^8 - 28*e^7 - 89*e^6 + 57*e^5 + 186*e^4 - 34*e^3 - 72*e^2 + 6*e - 36, 4*e^9 + 23/2*e^8 - 59/2*e^7 - 90*e^6 + 58*e^5 + 429/2*e^4 + 11/2*e^3 - 164*e^2 - 165/2*e + 30, 17/2*e^9 + 25*e^8 - 153/2*e^7 - 234*e^6 + 433/2*e^5 + 715*e^4 - 297/2*e^3 - 1469/2*e^2 - 245/2*e + 76, 2*e^9 + 27/2*e^8 - 1/2*e^7 - 119*e^6 - 75*e^5 + 687/2*e^4 + 439/2*e^3 - 334*e^2 - 323/2*e + 34, 2*e^9 + 15/2*e^8 - 33/2*e^7 - 77*e^6 + 33*e^5 + 513/2*e^4 + 29/2*e^3 - 286*e^2 - 89/2*e + 44, -3*e^9 - 13/2*e^8 + 69/2*e^7 + 69*e^6 - 129*e^5 - 455/2*e^4 + 365/2*e^3 + 245*e^2 - 191/2*e - 46, 1/2*e^9 + 5/2*e^8 + e^7 - 9*e^6 - 27/2*e^5 - 45/2*e^4 - 12*e^3 + 147/2*e^2 + 85*e + 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^2 + 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]