/* 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, 1, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -w^3 + w^2 + 6*w + 1]) primes_array = [ [2, 2, w],\ [2, 2, -1/2*w^3 + w^2 + 3/2*w],\ [11, 11, 1/2*w^3 - w^2 - 5/2*w + 4],\ [11, 11, -w^3 + w^2 + 6*w + 1],\ [13, 13, -w^3 + w^2 + 6*w - 3],\ [19, 19, -1/2*w^3 + w^2 + 5/2*w],\ [23, 23, -1/2*w^3 + 2*w^2 - 1/2*w - 2],\ [31, 31, -w^3 + w^2 + 6*w - 1],\ [31, 31, 1/2*w^3 - 7/2*w],\ [43, 43, 1/2*w^3 - w^2 - 9/2*w + 2],\ [67, 67, w^2 - w - 5],\ [67, 67, -1/2*w^3 + 11/2*w + 2],\ [73, 73, w^2 + w + 1],\ [79, 79, 1/2*w^3 + w^2 - 5/2*w - 2],\ [81, 3, -3],\ [83, 83, 2*w^3 - 2*w^2 - 12*w + 5],\ [83, 83, -1/2*w^3 - w^2 + 1/2*w + 2],\ [89, 89, -3/2*w^3 + 2*w^2 + 17/2*w - 2],\ [89, 89, 3/2*w^3 - 2*w^2 - 21/2*w + 2],\ [97, 97, 1/2*w^3 - w^2 - 1/2*w - 2],\ [97, 97, -w^3 + w^2 + 8*w + 1],\ [103, 103, 2*w^3 - 2*w^2 - 14*w + 1],\ [103, 103, w^2 - w - 3],\ [107, 107, -3/2*w^3 + 2*w^2 + 21/2*w - 4],\ [109, 109, 5/2*w^3 - 3*w^2 - 33/2*w + 4],\ [109, 109, -1/2*w^3 + w^2 + 9/2*w - 4],\ [113, 113, -w^3 + w^2 + 8*w - 3],\ [113, 113, 1/2*w^3 - w^2 - 1/2*w + 2],\ [121, 11, 5/2*w^3 - 2*w^2 - 31/2*w + 2],\ [127, 127, -3/2*w^3 + w^2 + 23/2*w],\ [127, 127, -1/2*w^3 + 11/2*w],\ [131, 131, w^2 - 3*w - 3],\ [137, 137, 1/2*w^3 - w^2 - 5/2*w + 6],\ [139, 139, -3/2*w^3 + 2*w^2 + 13/2*w + 2],\ [151, 151, -1/2*w^3 + 2*w^2 + 3/2*w - 10],\ [157, 157, 7/2*w^3 - 5*w^2 - 47/2*w + 10],\ [157, 157, 7/2*w^3 - 4*w^2 - 45/2*w + 4],\ [167, 167, 1/2*w^3 + w^2 - 5/2*w - 4],\ [167, 167, 2*w + 5],\ [173, 173, -w^3 + w^2 + 4*w - 7],\ [181, 181, w^3 - 2*w^2 - 9*w + 1],\ [193, 193, -1/2*w^3 + 2*w^2 + 3/2*w - 8],\ [197, 197, -1/2*w^3 - w^2 + 13/2*w + 2],\ [197, 197, -w^3 + w^2 + 4*w - 1],\ [197, 197, w^3 - 2*w^2 - 7*w + 7],\ [197, 197, -2*w^3 + 3*w^2 + 13*w - 11],\ [199, 199, -2*w^3 + 3*w^2 + 11*w - 5],\ [239, 239, -w^3 + 2*w^2 + 5*w - 1],\ [239, 239, 7/2*w^3 - 4*w^2 - 45/2*w + 6],\ [241, 241, 1/2*w^3 - 2*w^2 - 7/2*w + 8],\ [257, 257, 3/2*w^3 - 2*w^2 - 17/2*w - 4],\ [257, 257, 1/2*w^3 - 7/2*w - 6],\ [257, 257, 7/2*w^3 - 5*w^2 - 43/2*w + 10],\ [257, 257, 3*w^3 - 4*w^2 - 19*w + 7],\ [269, 269, 1/2*w^3 + w^2 + 3/2*w + 2],\ [269, 269, -2*w^3 + 3*w^2 + 11*w - 11],\ [277, 277, 5/2*w^3 - 4*w^2 - 35/2*w + 8],\ [281, 281, -3/2*w^3 + w^2 + 23/2*w - 2],\ [283, 283, -w^3 - w^2 + 8*w + 11],\ [283, 283, -3*w^2 + 3*w + 19],\ [311, 311, 3/2*w^3 - 2*w^2 - 17/2*w - 2],\ [331, 331, -4*w^3 + 7*w^2 + 25*w - 21],\ [337, 337, -5/2*w^3 + 2*w^2 + 35/2*w + 4],\ [337, 337, -2*w^3 + 3*w^2 + 11*w - 9],\ [347, 347, 2*w^3 - 4*w^2 - 12*w + 13],\ [347, 347, 5/2*w^3 - 5*w^2 - 29/2*w + 20],\ [347, 347, -1/2*w^3 - 1/2*w - 6],\ [347, 347, -1/2*w^3 + 3*w^2 + 1/2*w - 16],\ [349, 349, 1/2*w^3 + w^2 - 9/2*w - 4],\ [353, 353, -1/2*w^3 + 2*w^2 + 7/2*w],\ [359, 359, 3/2*w^3 - w^2 - 19/2*w + 2],\ [373, 373, -2*w^3 + 2*w^2 + 12*w + 1],\ [373, 373, -1/2*w^3 + w^2 + 9/2*w - 6],\ [379, 379, w^2 - w - 9],\ [379, 379, -2*w^3 + 3*w^2 + 13*w - 5],\ [383, 383, w^2 + w - 5],\ [389, 389, 9/2*w^3 - 6*w^2 - 59/2*w + 14],\ [397, 397, 2*w^2 - 2*w - 15],\ [401, 401, -1/2*w^3 + 2*w^2 + 3/2*w - 4],\ [419, 419, -3/2*w^3 + w^2 + 15/2*w - 2],\ [419, 419, w^3 + w^2 - 8*w - 15],\ [431, 431, -5/2*w^3 + 4*w^2 + 27/2*w - 16],\ [431, 431, 2*w^3 - 4*w^2 - 10*w + 11],\ [443, 443, 1/2*w^3 - 3*w^2 - 5/2*w + 14],\ [449, 449, 1/2*w^3 + w^2 - 9/2*w - 6],\ [457, 457, -w^3 + 2*w^2 + 7*w - 9],\ [461, 461, 4*w^3 - 5*w^2 - 27*w + 7],\ [487, 487, 2*w^2 - 9],\ [499, 499, 3/2*w^3 - w^2 - 15/2*w - 2],\ [499, 499, 3/2*w^3 - 4*w^2 - 17/2*w + 16],\ [503, 503, -5/2*w^3 + 3*w^2 + 37/2*w],\ [509, 509, -3*w^3 + 3*w^2 + 18*w + 7],\ [521, 521, -1/2*w^3 - 2*w^2 + 11/2*w + 18],\ [521, 521, -5/2*w^3 + 4*w^2 + 31/2*w - 8],\ [523, 523, -1/2*w^3 + 2*w^2 + 11/2*w],\ [523, 523, -1/2*w^3 - w^2 + 9/2*w],\ [547, 547, -7/2*w^3 + 6*w^2 + 45/2*w - 18],\ [547, 547, -w^3 - w^2 + 12*w + 5],\ [547, 547, 3/2*w^3 - w^2 - 19/2*w + 4],\ [547, 547, w^3 - w^2 - 6*w - 5],\ [557, 557, 1/2*w^3 + w^2 - 9/2*w - 12],\ [557, 557, 3/2*w^3 - 2*w^2 - 21/2*w],\ [557, 557, 2*w^3 - 2*w^2 - 12*w + 1],\ [557, 557, w^3 - 3*w^2 - 6*w + 11],\ [569, 569, w^3 - 2*w^2 - 7*w + 1],\ [577, 577, w^3 + w^2 - 6*w - 5],\ [599, 599, -3/2*w^3 + 3*w^2 + 15/2*w - 10],\ [607, 607, -5/2*w^3 + 3*w^2 + 25/2*w + 4],\ [613, 613, w^3 - 9*w + 1],\ [619, 619, 3*w^2 - w - 17],\ [619, 619, w^3 - 3*w^2 - 6*w + 13],\ [625, 5, -5],\ [631, 631, 11/2*w^3 - 7*w^2 - 71/2*w + 16],\ [631, 631, -3/2*w^3 + 2*w^2 + 13/2*w],\ [643, 643, w^2 - 3*w - 5],\ [653, 653, 2*w^2 - 2*w - 11],\ [659, 659, 5*w^3 - 3*w^2 - 36*w - 9],\ [659, 659, -w^3 + 7*w - 1],\ [673, 673, 5/2*w^3 - 2*w^2 - 31/2*w - 4],\ [677, 677, 13/2*w^3 - 6*w^2 - 87/2*w + 2],\ [691, 691, -3/2*w^3 + 2*w^2 + 13/2*w - 2],\ [701, 701, -w^3 + 3*w^2 + 4*w - 13],\ [701, 701, w^3 - 2*w^2 - 9*w + 3],\ [709, 709, -w^2 - 5*w - 1],\ [739, 739, 3/2*w^3 - w^2 - 15/2*w],\ [743, 743, -2*w^3 + w^2 + 15*w + 1],\ [751, 751, -2*w^3 + 4*w^2 + 12*w - 11],\ [757, 757, -6*w^3 + 9*w^2 + 39*w - 23],\ [757, 757, -w^3 - w^2 + 8*w + 3],\ [757, 757, 13/2*w^3 - 8*w^2 - 83/2*w + 16],\ [757, 757, 3*w^3 - 4*w^2 - 17*w + 3],\ [761, 761, 7/2*w^3 - 5*w^2 - 47/2*w + 12],\ [769, 769, -3*w^2 + 7*w + 3],\ [773, 773, -3/2*w^3 - w^2 + 19/2*w + 4],\ [787, 787, -4*w^3 + 5*w^2 + 23*w - 17],\ [787, 787, 1/2*w^3 - w^2 - 9/2*w - 4],\ [809, 809, -2*w^3 + 2*w^2 + 16*w + 3],\ [809, 809, -4*w^3 + 5*w^2 + 25*w - 9],\ [811, 811, 3*w^3 - 3*w^2 - 20*w + 5],\ [811, 811, w^3 - 3*w^2 - 6*w + 17],\ [823, 823, 5/2*w^3 - w^2 - 33/2*w - 10],\ [829, 829, 5/2*w^3 - 3*w^2 - 33/2*w + 2],\ [829, 829, -3*w^3 + 2*w^2 + 23*w - 1],\ [839, 839, -11/2*w^3 + 7*w^2 + 67/2*w - 18],\ [853, 853, -w^3 + 2*w^2 + 3*w - 5],\ [853, 853, -5*w^3 + 7*w^2 + 32*w - 15],\ [857, 857, 3/2*w^3 - 5*w^2 - 15/2*w + 26],\ [859, 859, -w^3 + 3*w^2 + 4*w - 17],\ [863, 863, 4*w^3 - 4*w^2 - 26*w + 3],\ [877, 877, w^3 - 5*w - 5],\ [887, 887, 3/2*w^3 - w^2 - 11/2*w + 8],\ [907, 907, -9/2*w^3 + 7*w^2 + 53/2*w - 24],\ [919, 919, 7/2*w^3 - 6*w^2 - 41/2*w + 22],\ [929, 929, -2*w^3 + 3*w^2 + 11*w - 1],\ [937, 937, 2*w^3 - 4*w^2 - 12*w + 7],\ [947, 947, 9/2*w^3 - 5*w^2 - 61/2*w + 10],\ [953, 953, -1/2*w^3 + 2*w^2 + 3/2*w + 2],\ [961, 31, -1/2*w^3 + 2*w^2 - 1/2*w - 6],\ [977, 977, 5/2*w^3 - 2*w^2 - 31/2*w],\ [983, 983, -5/2*w^3 + 6*w^2 + 27/2*w - 24],\ [983, 983, -3/2*w^3 + 2*w^2 + 21/2*w - 10],\ [983, 983, -w^3 + 4*w^2 + 7*w - 15],\ [983, 983, -1/2*w^3 + 3*w^2 - 3/2*w - 4],\ [997, 997, 1/2*w^3 - w^2 - 5/2*w - 4],\ [997, 997, 1/2*w^3 + w^2 - 17/2*w - 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 4*x^9 - 4*x^8 + 30*x^7 - 7*x^6 - 72*x^5 + 43*x^4 + 54*x^3 - 41*x^2 + 2*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e^3 - e^2 - 3*e + 2, e, e^8 - 2*e^7 - 8*e^6 + 14*e^5 + 20*e^4 - 28*e^3 - 13*e^2 + 14*e - 4, -1, -e^9 + 4*e^8 + 5*e^7 - 32*e^6 + e^5 + 82*e^4 - 32*e^3 - 66*e^2 + 35*e + 2, e^8 - 3*e^7 - 6*e^6 + 19*e^5 + 12*e^4 - 35*e^3 - 8*e^2 + 16*e - 1, -e^6 + 3*e^5 + 4*e^4 - 15*e^3 - e^2 + 16*e - 4, -e^7 + 2*e^6 + 4*e^5 - 8*e^4 + 6*e^2 - 9*e + 2, 2*e^9 - 7*e^8 - 9*e^7 + 48*e^6 - e^5 - 102*e^4 + 40*e^3 + 65*e^2 - 35*e + 3, -3*e^9 + 10*e^8 + 18*e^7 - 76*e^6 - 25*e^5 + 186*e^4 - 17*e^3 - 148*e^2 + 36*e + 9, -e^9 + 2*e^8 + 9*e^7 - 16*e^6 - 30*e^5 + 43*e^4 + 42*e^3 - 42*e^2 - 15*e + 10, e^9 - 4*e^8 - 4*e^7 + 28*e^6 - 3*e^5 - 62*e^4 + 26*e^3 + 42*e^2 - 30*e + 6, -e^9 + 7*e^8 - 2*e^7 - 52*e^6 + 43*e^5 + 128*e^4 - 98*e^3 - 110*e^2 + 49*e + 10, -5*e^8 + 8*e^7 + 43*e^6 - 56*e^5 - 122*e^4 + 116*e^3 + 113*e^2 - 66*e - 4, -2*e^9 + 6*e^8 + 12*e^7 - 44*e^6 - 16*e^5 + 106*e^4 - 18*e^3 - 91*e^2 + 38*e + 13, 3*e^9 - 12*e^8 - 15*e^7 + 95*e^6 + e^5 - 245*e^4 + 75*e^3 + 209*e^2 - 79*e - 5, -3*e^9 + 6*e^8 + 27*e^7 - 50*e^6 - 78*e^5 + 130*e^4 + 71*e^3 - 103*e^2 - e - 2, -4*e^9 + 12*e^8 + 25*e^7 - 91*e^6 - 33*e^5 + 216*e^4 - 41*e^3 - 155*e^2 + 75*e, 4*e^9 - 12*e^8 - 26*e^7 + 88*e^6 + 50*e^5 - 206*e^4 - 14*e^3 + 150*e^2 - 33*e + 4, -4*e^9 + 13*e^8 + 26*e^7 - 105*e^6 - 38*e^5 + 273*e^4 - 38*e^3 - 230*e^2 + 82*e + 11, -2*e^8 + 6*e^7 + 14*e^6 - 44*e^5 - 34*e^4 + 101*e^3 + 32*e^2 - 71*e + 6, -e^9 + 4*e^8 + 6*e^7 - 36*e^6 - 4*e^5 + 110*e^4 - 26*e^3 - 116*e^2 + 29*e + 12, 3*e^8 - 7*e^7 - 24*e^6 + 49*e^5 + 70*e^4 - 107*e^3 - 74*e^2 + 73*e - 1, -3*e^9 + 10*e^8 + 13*e^7 - 62*e^6 + 110*e^4 - 50*e^3 - 46*e^2 + 45*e - 2, -3*e^9 + 9*e^8 + 17*e^7 - 60*e^6 - 21*e^5 + 119*e^4 - 22*e^3 - 63*e^2 + 41*e - 4, 2*e^9 - 6*e^8 - 14*e^7 + 47*e^6 + 31*e^5 - 120*e^4 - 17*e^3 + 98*e^2 - 15*e - 1, 4*e^9 - 14*e^8 - 21*e^7 + 101*e^6 + 19*e^5 - 232*e^4 + 30*e^3 + 176*e^2 - 28*e - 16, 5*e^9 - 18*e^8 - 25*e^7 + 134*e^6 + 6*e^5 - 321*e^4 + 110*e^3 + 249*e^2 - 126*e - 3, e^9 - e^8 - 10*e^7 + 9*e^6 + 27*e^5 - 22*e^4 - 10*e^3 + 16*e^2 - 18*e + 2, -e^9 + 13*e^7 + 4*e^6 - 64*e^5 - 22*e^4 + 126*e^3 + 30*e^2 - 71*e, -e^9 + 2*e^8 + 7*e^7 - 11*e^6 - 15*e^5 + 13*e^4 + 2*e^3 + 4*e^2 + 20*e + 5, -4*e^8 + 8*e^7 + 27*e^6 - 48*e^5 - 55*e^4 + 82*e^3 + 28*e^2 - 44*e + 3, 2*e^8 - 23*e^6 - e^5 + 81*e^4 + 10*e^3 - 91*e^2 - 15*e + 19, -2*e^9 + 8*e^8 + 9*e^7 - 62*e^6 + 5*e^5 + 156*e^4 - 53*e^3 - 128*e^2 + 37*e + 6, 5*e^9 - 17*e^8 - 28*e^7 + 131*e^6 + 22*e^5 - 325*e^4 + 78*e^3 + 263*e^2 - 90*e - 11, e^9 - 7*e^8 + 5*e^7 + 46*e^6 - 63*e^5 - 99*e^4 + 149*e^3 + 80*e^2 - 98*e - 6, -6*e^9 + 16*e^8 + 44*e^7 - 126*e^6 - 95*e^5 + 319*e^4 + 33*e^3 - 264*e^2 + 56*e + 18, -e^9 + e^8 + 10*e^7 - 2*e^6 - 47*e^5 - 10*e^4 + 104*e^3 + 22*e^2 - 71*e - 2, -e^9 + 6*e^8 - 5*e^7 - 35*e^6 + 63*e^5 + 58*e^4 - 148*e^3 - 22*e^2 + 95*e - 4, e^8 + 2*e^7 - 15*e^6 - 16*e^5 + 69*e^4 + 36*e^3 - 104*e^2 - 24*e + 21, 3*e^9 - 10*e^8 - 13*e^7 + 65*e^6 - 6*e^5 - 126*e^4 + 80*e^3 + 69*e^2 - 81*e - 1, -7*e^8 + 13*e^7 + 59*e^6 - 96*e^5 - 165*e^4 + 219*e^3 + 150*e^2 - 147*e + 5, e^9 - 4*e^8 - 10*e^7 + 42*e^6 + 30*e^5 - 136*e^4 - 22*e^3 + 138*e^2 - 18*e - 14, 4*e^9 - 11*e^8 - 30*e^7 + 87*e^6 + 71*e^5 - 225*e^4 - 39*e^3 + 191*e^2 - 33*e - 9, 4*e^9 - 16*e^8 - 14*e^7 + 113*e^6 - 28*e^5 - 255*e^4 + 120*e^3 + 189*e^2 - 70*e - 10, 6*e^8 - 14*e^7 - 41*e^6 + 88*e^5 + 95*e^4 - 164*e^3 - 76*e^2 + 90*e - 2, -e^9 + 6*e^8 - e^7 - 40*e^6 + 34*e^5 + 82*e^4 - 77*e^3 - 50*e^2 + 39*e, 5*e^9 - 14*e^8 - 38*e^7 + 112*e^6 + 92*e^5 - 290*e^4 - 61*e^3 + 250*e^2 - 26*e - 18, e^9 - 4*e^8 - 3*e^7 + 22*e^6 + 4*e^5 - 30*e^4 - 39*e^3 + 4*e^2 + 67*e - 8, -6*e^9 + 19*e^8 + 37*e^7 - 143*e^6 - 52*e^5 + 342*e^4 - 48*e^3 - 260*e^2 + 100*e + 16, -2*e^7 + 4*e^6 + 8*e^5 - 17*e^4 + 4*e^3 + 11*e^2 - 28*e + 4, 2*e^8 - 2*e^7 - 21*e^6 + 17*e^5 + 71*e^4 - 40*e^3 - 80*e^2 + 20*e + 8, 3*e^9 - 4*e^8 - 32*e^7 + 36*e^6 + 112*e^5 - 97*e^4 - 139*e^3 + 77*e^2 + 37*e - 3, 7*e^9 - 18*e^8 - 50*e^7 + 134*e^6 + 110*e^5 - 318*e^4 - 62*e^3 + 248*e^2 - 25*e - 26, -6*e^9 + 22*e^8 + 34*e^7 - 178*e^6 - 26*e^5 + 472*e^4 - 112*e^3 - 410*e^2 + 148*e + 12, -3*e^9 + 10*e^8 + 17*e^7 - 72*e^6 - 26*e^5 + 166*e^4 + 17*e^3 - 133*e^2 - 23*e + 20, -3*e^9 + 6*e^8 + 22*e^7 - 38*e^6 - 47*e^5 + 56*e^4 + 17*e^3 + 16*e^2 + 26*e - 24, -6*e^9 + 18*e^8 + 41*e^7 - 140*e^6 - 84*e^5 + 354*e^4 + 41*e^3 - 304*e^2 + 27*e + 36, 8*e^9 - 30*e^8 - 42*e^7 + 234*e^6 + 18*e^5 - 590*e^4 + 164*e^3 + 480*e^2 - 178*e - 16, 2*e^9 - 5*e^8 - 15*e^7 + 39*e^6 + 36*e^5 - 107*e^4 - 23*e^3 + 116*e^2 - 7*e - 19, 3*e^9 - 18*e^8 + 2*e^7 + 132*e^6 - 107*e^5 - 316*e^4 + 269*e^3 + 246*e^2 - 155*e + 4, e^9 - 3*e^8 - 4*e^7 + 17*e^6 + 2*e^5 - 32*e^4 + e^3 + 24*e^2 - 1, 5*e^9 - 10*e^8 - 44*e^7 + 80*e^6 + 126*e^5 - 201*e^4 - 112*e^3 + 154*e^2 - 8*e + 7, 5*e^9 - 10*e^8 - 45*e^7 + 77*e^6 + 143*e^5 - 184*e^4 - 178*e^3 + 137*e^2 + 56*e - 13, 6*e^9 - 15*e^8 - 48*e^7 + 124*e^6 + 120*e^5 - 335*e^4 - 76*e^3 + 305*e^2 - 40*e - 38, 3*e^9 - 8*e^8 - 23*e^7 + 71*e^6 + 39*e^5 - 199*e^4 + 45*e^3 + 167*e^2 - 101*e + 16, -2*e^9 + 7*e^8 + 10*e^7 - 48*e^6 - 10*e^5 + 101*e^4 - 8*e^3 - 61*e^2 + 18*e + 5, -2*e^9 + 4*e^8 + 14*e^7 - 22*e^6 - 32*e^5 + 23*e^4 + 26*e^3 + 17*e^2 - 2*e - 12, 2*e^9 - 10*e^8 - 6*e^7 + 86*e^6 - 36*e^5 - 245*e^4 + 143*e^3 + 234*e^2 - 107*e - 11, -2*e^9 + 6*e^8 + 10*e^7 - 36*e^6 - 13*e^5 + 64*e^4 + 3*e^3 - 26*e^2 + 4*e - 10, 8*e^8 - 18*e^7 - 56*e^6 + 115*e^5 + 131*e^4 - 217*e^3 - 108*e^2 + 116*e + 12, -8*e^9 + 27*e^8 + 46*e^7 - 207*e^6 - 43*e^5 + 503*e^4 - 110*e^3 - 386*e^2 + 136*e + 13, 2*e^9 - 13*e^8 + 2*e^7 + 103*e^6 - 88*e^5 - 269*e^4 + 254*e^3 + 231*e^2 - 204*e + 2, 4*e^9 - 9*e^8 - 36*e^7 + 75*e^6 + 112*e^5 - 203*e^4 - 124*e^3 + 175*e^2 + 14*e - 6, e^9 - 2*e^8 - 7*e^7 + 16*e^6 + 11*e^5 - 48*e^4 + 11*e^3 + 66*e^2 - 27*e - 20, -6*e^9 + 23*e^8 + 28*e^7 - 171*e^6 + 4*e^5 + 407*e^4 - 148*e^3 - 307*e^2 + 158*e - 2, -2*e^8 + 20*e^6 + 4*e^5 - 62*e^4 - 16*e^3 + 52*e^2 + 8*e + 8, -5*e^9 + 19*e^8 + 20*e^7 - 129*e^6 + 8*e^5 + 276*e^4 - 81*e^3 - 188*e^2 + 50*e + 17, -2*e^8 + 6*e^7 + 18*e^6 - 56*e^5 - 53*e^4 + 160*e^3 + 52*e^2 - 130*e + 6, -e^8 + 19*e^6 - 17*e^5 - 83*e^4 + 89*e^3 + 109*e^2 - 105*e - 17, -12*e^9 + 39*e^8 + 68*e^7 - 291*e^6 - 66*e^5 + 705*e^4 - 160*e^3 - 565*e^2 + 206*e + 16, -7*e^9 + 22*e^8 + 45*e^7 - 168*e^6 - 74*e^5 + 408*e^4 - 25*e^3 - 316*e^2 + 94*e + 25, -6*e^9 + 18*e^8 + 38*e^7 - 135*e^6 - 56*e^5 + 318*e^4 - 50*e^3 - 223*e^2 + 110*e - 12, -e^9 + 2*e^8 + 7*e^7 - 12*e^6 - 8*e^5 + 16*e^4 - 33*e^3 - 3*e^2 + 57*e + 6, 7*e^9 - 21*e^8 - 46*e^7 + 163*e^6 + 78*e^5 - 413*e^4 + 22*e^3 + 351*e^2 - 82*e - 25, e^8 - 3*e^7 - 4*e^6 + 21*e^5 - 6*e^4 - 45*e^3 + 25*e^2 + 36*e - 12, 13*e^9 - 46*e^8 - 69*e^7 + 352*e^6 + 34*e^5 - 872*e^4 + 259*e^3 + 700*e^2 - 295*e - 8, -14*e^9 + 44*e^8 + 82*e^7 - 323*e^6 - 96*e^5 + 749*e^4 - 142*e^3 - 545*e^2 + 230*e - 1, -7*e^9 + 28*e^8 + 36*e^7 - 228*e^6 - 5*e^5 + 602*e^4 - 169*e^3 - 518*e^2 + 170*e + 32, -8*e^9 + 31*e^8 + 37*e^7 - 237*e^6 + 16*e^5 + 582*e^4 - 222*e^3 - 455*e^2 + 187*e + 13, e^9 - 4*e^8 + 14*e^6 - 19*e^5 + 22*e^4 + 21*e^3 - 86*e^2 + 16*e + 35, e^9 + 4*e^8 - 22*e^7 - 32*e^6 + 123*e^5 + 88*e^4 - 247*e^3 - 86*e^2 + 148*e + 3, 6*e^7 - 13*e^6 - 42*e^5 + 81*e^4 + 88*e^3 - 132*e^2 - 54*e + 31, -4*e^9 + 18*e^8 + 11*e^7 - 130*e^6 + 59*e^5 + 296*e^4 - 230*e^3 - 214*e^2 + 196*e + 4, -5*e^9 + 8*e^8 + 49*e^7 - 58*e^6 - 173*e^5 + 126*e^4 + 240*e^3 - 88*e^2 - 83*e + 30, -7*e^9 + 25*e^8 + 32*e^7 - 175*e^6 + 8*e^5 + 383*e^4 - 183*e^3 - 260*e^2 + 192*e - 10, 9*e^9 - 31*e^8 - 44*e^7 + 218*e^6 + 21*e^5 - 491*e^4 + 125*e^3 + 366*e^2 - 116*e - 21, 7*e^9 - 28*e^8 - 27*e^7 + 204*e^6 - 38*e^5 - 484*e^4 + 216*e^3 + 384*e^2 - 154*e - 2, -2*e^9 + 8*e^8 + 9*e^7 - 64*e^6 + 13*e^5 + 170*e^4 - 113*e^3 - 152*e^2 + 135*e - 2, -4*e^9 + 14*e^8 + 28*e^7 - 126*e^6 - 44*e^5 + 372*e^4 - 48*e^3 - 357*e^2 + 108*e + 9, 6*e^9 - 24*e^8 - 26*e^7 + 177*e^6 - 10*e^5 - 430*e^4 + 150*e^3 + 351*e^2 - 156*e - 14, -6*e^8 + 11*e^7 + 51*e^6 - 76*e^5 - 153*e^4 + 169*e^3 + 150*e^2 - 120*e + 14, -2*e^9 + 9*e^8 + 4*e^7 - 59*e^6 + 27*e^5 + 123*e^4 - 74*e^3 - 88*e^2 + 44*e + 23, 9*e^9 - 34*e^8 - 43*e^7 + 249*e^6 + 9*e^5 - 584*e^4 + 168*e^3 + 441*e^2 - 174*e - 17, -3*e^9 + 4*e^8 + 33*e^7 - 30*e^6 - 136*e^5 + 68*e^4 + 229*e^3 - 40*e^2 - 115*e + 8, -2*e^9 + 8*e^8 + 6*e^7 - 64*e^6 + 46*e^5 + 165*e^4 - 210*e^3 - 141*e^2 + 206*e - 6, 9*e^9 - 26*e^8 - 61*e^7 + 196*e^6 + 118*e^5 - 464*e^4 - 27*e^3 + 335*e^2 - 67*e - 10, 3*e^9 - 17*e^8 - 2*e^7 + 119*e^6 - 73*e^5 - 258*e^4 + 201*e^3 + 147*e^2 - 149*e + 28, -2*e^9 + 2*e^8 + 24*e^7 - 26*e^6 - 93*e^5 + 112*e^4 + 120*e^3 - 168*e^2 - 24*e + 48, -5*e^8 + 11*e^7 + 39*e^6 - 78*e^5 - 97*e^4 + 167*e^3 + 61*e^2 - 102*e + 24, -6*e^9 + 17*e^8 + 32*e^7 - 106*e^6 - 40*e^5 + 200*e^4 - 6*e^3 - 131*e^2 + 6*e + 33, 4*e^9 - 10*e^8 - 24*e^7 + 60*e^6 + 46*e^5 - 105*e^4 - 44*e^3 + 64*e^2 + 40*e - 21, 3*e^9 - 5*e^8 - 23*e^7 + 28*e^6 + 64*e^5 - 40*e^4 - 80*e^3 + 8*e^2 + 48*e + 10, -10*e^9 + 34*e^8 + 61*e^7 - 265*e^6 - 86*e^5 + 675*e^4 - 79*e^3 - 562*e^2 + 182*e + 16, -7*e^9 + 19*e^8 + 52*e^7 - 151*e^6 - 114*e^5 + 386*e^4 + 37*e^3 - 321*e^2 + 79*e + 26, 2*e^9 - 3*e^8 - 21*e^7 + 22*e^6 + 83*e^5 - 45*e^4 - 150*e^3 + 25*e^2 + 119*e - 11, 5*e^9 - 14*e^8 - 33*e^7 + 104*e^6 + 60*e^5 - 252*e^4 + 4*e^3 + 196*e^2 - 53*e + 20, -10*e^9 + 33*e^8 + 59*e^7 - 244*e^6 - 92*e^5 + 593*e^4 - 4*e^3 - 496*e^2 + 68*e + 49, 6*e^9 - 20*e^8 - 28*e^7 + 138*e^6 - 3*e^5 - 302*e^4 + 142*e^3 + 226*e^2 - 133*e - 30, 4*e^9 - 20*e^8 - 5*e^7 + 145*e^6 - 96*e^5 - 339*e^4 + 285*e^3 + 252*e^2 - 198*e + 22, -5*e^9 + 18*e^8 + 27*e^7 - 136*e^6 - 27*e^5 + 342*e^4 - 44*e^3 - 304*e^2 + 45*e + 24, -2*e^9 + 19*e^8 - 11*e^7 - 151*e^6 + 140*e^5 + 401*e^4 - 341*e^3 - 356*e^2 + 245*e + 13, -3*e^9 + 6*e^8 + 25*e^7 - 33*e^6 - 91*e^5 + 39*e^4 + 175*e^3 + 13*e^2 - 147*e + 1, -2*e^9 + 8*e^8 + 19*e^7 - 80*e^6 - 60*e^5 + 256*e^4 + 65*e^3 - 272*e^2 - 2*e + 44, 2*e^9 + 2*e^8 - 30*e^7 - 8*e^6 + 123*e^5 - e^4 - 144*e^3 + 13*e^2 - 3*e + 14, -7*e^9 + 23*e^8 + 36*e^7 - 173*e^6 - 3*e^5 + 426*e^4 - 194*e^3 - 346*e^2 + 196*e, -e^9 + e^8 + 12*e^7 - 6*e^6 - 49*e^5 + 5*e^4 + 63*e^3 + 6*e^2 + 4*e + 15, 14*e^9 - 46*e^8 - 78*e^7 + 338*e^6 + 74*e^5 - 796*e^4 + 183*e^3 + 602*e^2 - 244*e - 12, -2*e^9 + 20*e^8 - 18*e^7 - 152*e^6 + 186*e^5 + 390*e^4 - 423*e^3 - 344*e^2 + 274*e - 4, -2*e^8 - 4*e^7 + 30*e^6 + 22*e^5 - 104*e^4 - 34*e^3 + 78*e^2 - 2*e + 24, -10*e^9 + 31*e^8 + 58*e^7 - 227*e^6 - 74*e^5 + 544*e^4 - 75*e^3 - 440*e^2 + 158*e + 31, -e^9 - 6*e^8 + 24*e^7 + 48*e^6 - 118*e^5 - 152*e^4 + 186*e^3 + 180*e^2 - 73*e + 2, -11*e^9 + 35*e^8 + 68*e^7 - 279*e^6 - 69*e^5 + 718*e^4 - 221*e^3 - 595*e^2 + 339*e + 4, -6*e^9 + 15*e^8 + 53*e^7 - 132*e^6 - 149*e^5 + 366*e^4 + 128*e^3 - 311*e^2 + 15*e - 7, -8*e^9 + 26*e^8 + 48*e^7 - 199*e^6 - 57*e^5 + 489*e^4 - 88*e^3 - 385*e^2 + 133*e - 5, -2*e^8 - 2*e^7 + 23*e^6 + 28*e^5 - 92*e^4 - 96*e^3 + 121*e^2 + 82*e - 25, 11*e^9 - 34*e^8 - 66*e^7 + 254*e^6 + 76*e^5 - 594*e^4 + 139*e^3 + 412*e^2 - 214*e + 22, 3*e^9 - 8*e^8 - 29*e^7 + 77*e^6 + 89*e^5 - 229*e^4 - 100*e^3 + 222*e^2 + 38*e - 25, -5*e^9 + 10*e^8 + 38*e^7 - 62*e^6 - 105*e^5 + 110*e^4 + 117*e^3 - 56*e^2 - 26*e + 19, 2*e^9 - 7*e^8 - 9*e^7 + 60*e^6 - 17*e^5 - 183*e^4 + 118*e^3 + 215*e^2 - 119*e - 29, -6*e^9 + 21*e^8 + 43*e^7 - 182*e^6 - 89*e^5 + 515*e^4 + 28*e^3 - 491*e^2 + 61*e + 65, -9*e^9 + 20*e^8 + 66*e^7 - 134*e^6 - 167*e^5 + 278*e^4 + 162*e^3 - 174*e^2 - 49*e - 6, 3*e^9 - 10*e^8 - 16*e^7 + 64*e^6 + 16*e^5 - 106*e^4 + 34*e^3 - 2*e^2 - 49*e + 48, 7*e^8 - 16*e^7 - 51*e^6 + 105*e^5 + 119*e^4 - 181*e^3 - 87*e^2 + 47*e - 3, 8*e^9 - 23*e^8 - 52*e^7 + 168*e^6 + 108*e^5 - 400*e^4 - 86*e^3 + 316*e^2 + 24*e - 25, 8*e^9 - 22*e^8 - 57*e^7 + 175*e^6 + 113*e^5 - 460*e^4 + 3*e^3 + 417*e^2 - 125*e - 48, -2*e^9 + 12*e^8 - 89*e^6 + 61*e^5 + 218*e^4 - 159*e^3 - 182*e^2 + 101*e + 17, -7*e^9 + 20*e^8 + 49*e^7 - 141*e^6 - 125*e^5 + 311*e^4 + 141*e^3 - 215*e^2 - 49*e + 6, -11*e^9 + 46*e^8 + 41*e^7 - 342*e^6 + 76*e^5 + 828*e^4 - 407*e^3 - 658*e^2 + 356*e + 14, -8*e^9 + 23*e^8 + 52*e^7 - 171*e^6 - 92*e^5 + 406*e^4 - 12*e^3 - 287*e^2 + 114*e - 29, 10*e^9 - 27*e^8 - 64*e^7 + 182*e^6 + 126*e^5 - 375*e^4 - 74*e^3 + 231*e^2 + 4*e - 13, e^9 - 6*e^8 - 13*e^7 + 82*e^6 + 30*e^5 - 309*e^4 + 28*e^3 + 345*e^2 - 92*e - 23, 2*e^9 - 8*e^8 - 8*e^7 + 58*e^6 - 16*e^5 - 128*e^4 + 104*e^3 + 71*e^2 - 113*e + 15, -11*e^9 + 48*e^8 + 43*e^7 - 363*e^6 + 59*e^5 + 883*e^4 - 345*e^3 - 691*e^2 + 269*e + 29, 6*e^9 - 26*e^8 - 25*e^7 + 202*e^6 - 22*e^5 - 526*e^4 + 178*e^3 + 482*e^2 - 152*e - 52, -4*e^8 + 3*e^7 + 46*e^6 - 34*e^5 - 146*e^4 + 92*e^3 + 118*e^2 - 61*e + 28, -8*e^8 + 12*e^7 + 65*e^6 - 81*e^5 - 164*e^4 + 161*e^3 + 123*e^2 - 92*e - 6, 2*e^9 - 11*e^8 - 11*e^7 + 105*e^6 - 8*e^5 - 317*e^4 + 125*e^3 + 277*e^2 - 172*e + 32, 12*e^9 - 45*e^8 - 55*e^7 + 326*e^6 - 2*e^5 - 753*e^4 + 237*e^3 + 545*e^2 - 197*e + 1, 10*e^8 - 12*e^7 - 101*e^6 + 98*e^5 + 332*e^4 - 232*e^3 - 372*e^2 + 142*e + 41, -14*e^9 + 41*e^8 + 92*e^7 - 310*e^6 - 164*e^5 + 753*e^4 - 6*e^3 - 596*e^2 + 172*e + 23, 11*e^9 - 35*e^8 - 66*e^7 + 257*e^6 + 96*e^5 - 592*e^4 + 41*e^3 + 406*e^2 - 110*e + 23, 8*e^9 - 24*e^8 - 54*e^7 + 187*e^6 + 93*e^5 - 457*e^4 + 24*e^3 + 343*e^2 - 103*e + 3, 6*e^9 - 9*e^8 - 63*e^7 + 93*e^6 + 198*e^5 - 294*e^4 - 174*e^3 + 303*e^2 - 27*e - 35, 4*e^9 - 17*e^8 - 10*e^7 + 115*e^6 - 49*e^5 - 239*e^4 + 142*e^3 + 142*e^2 - 62*e + 23] 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, -w^3 + w^2 + 6*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]