/* 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, -2, 7, 2, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([125, 5, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 19*w + 2]) primes_array = [ [29, 29, -9*w^5 + 3*w^4 + 64*w^3 + 26*w^2 - 40*w - 10],\ [29, 29, w^5 - 7*w^3 - 5*w^2 + 2*w + 2],\ [29, 29, w^4 - w^3 - 6*w^2 + 2],\ [29, 29, 5*w^5 - w^4 - 36*w^3 - 19*w^2 + 21*w + 9],\ [29, 29, -w^5 + w^4 + 7*w^3 - 2*w^2 - 6*w + 1],\ [29, 29, 2*w^5 - 15*w^3 - 10*w^2 + 11*w + 5],\ [41, 41, 5*w^5 - w^4 - 36*w^3 - 18*w^2 + 21*w + 5],\ [41, 41, -5*w^5 + 2*w^4 + 36*w^3 + 11*w^2 - 25*w - 2],\ [41, 41, 6*w^5 - w^4 - 44*w^3 - 23*w^2 + 30*w + 8],\ [41, 41, 13*w^5 - 4*w^4 - 93*w^3 - 39*w^2 + 59*w + 16],\ [41, 41, -4*w^5 + 30*w^3 + 19*w^2 - 19*w - 8],\ [41, 41, w^5 - 7*w^3 - 6*w^2 + 2*w + 3],\ [49, 7, -5*w^5 + w^4 + 36*w^3 + 19*w^2 - 22*w - 6],\ [64, 2, -2],\ [71, 71, -8*w^5 + w^4 + 58*w^3 + 34*w^2 - 34*w - 16],\ [71, 71, -6*w^5 + 2*w^4 + 42*w^3 + 18*w^2 - 23*w - 6],\ [71, 71, -8*w^5 + 2*w^4 + 58*w^3 + 27*w^2 - 38*w - 10],\ [71, 71, 4*w^5 - 30*w^3 - 19*w^2 + 20*w + 8],\ [71, 71, -10*w^5 + 3*w^4 + 72*w^3 + 30*w^2 - 48*w - 10],\ [71, 71, -8*w^5 + 2*w^4 + 58*w^3 + 26*w^2 - 37*w - 8],\ [125, 5, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 19*w + 2],\ [139, 139, -w^5 - w^4 + 8*w^3 + 12*w^2 - 3*w - 5],\ [139, 139, -11*w^5 + 4*w^4 + 78*w^3 + 29*w^2 - 49*w - 11],\ [139, 139, -12*w^5 + 3*w^4 + 86*w^3 + 41*w^2 - 52*w - 18],\ [139, 139, -4*w^5 + w^4 + 28*w^3 + 15*w^2 - 14*w - 7],\ [139, 139, 8*w^5 - 2*w^4 - 58*w^3 - 27*w^2 + 39*w + 10],\ [139, 139, 7*w^5 - 2*w^4 - 51*w^3 - 21*w^2 + 35*w + 7],\ [169, 13, -8*w^5 + 2*w^4 + 57*w^3 + 28*w^2 - 34*w - 13],\ [169, 13, w^5 - w^4 - 6*w^3 + w^2 + 2*w - 2],\ [169, 13, -7*w^5 + w^4 + 51*w^3 + 29*w^2 - 32*w - 12],\ [181, 181, -5*w^5 + 36*w^3 + 26*w^2 - 18*w - 12],\ [181, 181, -6*w^5 + 44*w^3 + 30*w^2 - 23*w - 13],\ [181, 181, 9*w^5 - 4*w^4 - 64*w^3 - 19*w^2 + 44*w + 7],\ [181, 181, 2*w^4 - w^3 - 14*w^2 - 2*w + 8],\ [181, 181, -12*w^5 + 4*w^4 + 85*w^3 + 35*w^2 - 53*w - 16],\ [181, 181, -11*w^5 + 3*w^4 + 78*w^3 + 37*w^2 - 45*w - 18],\ [211, 211, -10*w^5 + 3*w^4 + 71*w^3 + 32*w^2 - 43*w - 15],\ [211, 211, -7*w^5 + 3*w^4 + 49*w^3 + 16*w^2 - 31*w - 5],\ [211, 211, 8*w^5 - w^4 - 58*w^3 - 34*w^2 + 35*w + 15],\ [211, 211, -w^4 + w^3 + 7*w^2 - 2*w - 4],\ [211, 211, 6*w^5 - 2*w^4 - 42*w^3 - 17*w^2 + 23*w + 6],\ [211, 211, w^3 - w^2 - 5*w],\ [239, 239, w^3 - w^2 - 5*w + 1],\ [239, 239, w^4 - w^3 - 7*w^2 + 2*w + 5],\ [239, 239, 8*w^5 - w^4 - 58*w^3 - 34*w^2 + 35*w + 14],\ [239, 239, 7*w^5 - 3*w^4 - 49*w^3 - 16*w^2 + 31*w + 6],\ [239, 239, 10*w^5 - 3*w^4 - 71*w^3 - 32*w^2 + 43*w + 14],\ [239, 239, -11*w^5 + 2*w^4 + 80*w^3 + 42*w^2 - 50*w - 18],\ [251, 251, 6*w^5 - w^4 - 44*w^3 - 23*w^2 + 31*w + 8],\ [251, 251, 11*w^5 - 2*w^4 - 79*w^3 - 43*w^2 + 47*w + 18],\ [251, 251, 10*w^5 - w^4 - 73*w^3 - 44*w^2 + 45*w + 18],\ [251, 251, -11*w^5 + 4*w^4 + 78*w^3 + 29*w^2 - 48*w - 13],\ [251, 251, 6*w^5 - 2*w^4 - 42*w^3 - 17*w^2 + 23*w + 5],\ [251, 251, -16*w^5 + 4*w^4 + 115*w^3 + 54*w^2 - 70*w - 22],\ [281, 281, 8*w^5 - 3*w^4 - 57*w^3 - 20*w^2 + 36*w + 7],\ [281, 281, 3*w^5 - w^4 - 22*w^3 - 8*w^2 + 18*w + 3],\ [281, 281, 2*w^5 - 2*w^4 - 13*w^3 + 2*w^2 + 9*w],\ [281, 281, w^5 + w^4 - 8*w^3 - 11*w^2 + 3*w + 4],\ [281, 281, w^5 - w^4 - 7*w^3 + 2*w^2 + 8*w - 2],\ [281, 281, -13*w^5 + 4*w^4 + 93*w^3 + 39*w^2 - 58*w - 15],\ [349, 349, 7*w^5 - 2*w^4 - 51*w^3 - 21*w^2 + 36*w + 5],\ [349, 349, 7*w^5 - w^4 - 51*w^3 - 28*w^2 + 32*w + 8],\ [349, 349, 3*w^5 - w^4 - 21*w^3 - 8*w^2 + 12*w],\ [349, 349, 10*w^5 - 2*w^4 - 72*w^3 - 38*w^2 + 45*w + 17],\ [349, 349, 7*w^5 - 2*w^4 - 50*w^3 - 23*w^2 + 33*w + 12],\ [349, 349, 17*w^5 - 5*w^4 - 122*w^3 - 53*w^2 + 79*w + 21],\ [379, 379, 2*w^5 - 14*w^3 - 11*w^2 + 7*w + 4],\ [379, 379, -10*w^5 + 3*w^4 + 71*w^3 + 32*w^2 - 42*w - 15],\ [379, 379, -15*w^5 + 5*w^4 + 106*w^3 + 44*w^2 - 63*w - 17],\ [379, 379, 2*w^5 - 3*w^4 - 12*w^3 + 9*w^2 + 8*w - 4],\ [379, 379, 4*w^5 - 29*w^3 - 20*w^2 + 14*w + 10],\ [379, 379, 13*w^5 - 2*w^4 - 94*w^3 - 53*w^2 + 55*w + 24],\ [419, 419, 3*w^5 - 2*w^4 - 20*w^3 - 4*w^2 + 12*w + 4],\ [419, 419, 3*w^5 - 22*w^3 - 16*w^2 + 15*w + 8],\ [419, 419, -11*w^5 + 4*w^4 + 77*w^3 + 31*w^2 - 45*w - 14],\ [419, 419, -19*w^5 + 5*w^4 + 137*w^3 + 62*w^2 - 87*w - 24],\ [419, 419, -16*w^5 + 5*w^4 + 114*w^3 + 48*w^2 - 72*w - 17],\ [419, 419, 17*w^5 - 5*w^4 - 121*w^3 - 54*w^2 + 73*w + 23],\ [421, 421, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 20*w + 1],\ [421, 421, 4*w^5 - 2*w^4 - 29*w^3 - 6*w^2 + 22*w + 1],\ [421, 421, -8*w^5 + 3*w^4 + 57*w^3 + 20*w^2 - 37*w - 10],\ [421, 421, -6*w^5 + 45*w^3 + 30*w^2 - 31*w - 14],\ [421, 421, 5*w^5 + w^4 - 38*w^3 - 31*w^2 + 22*w + 14],\ [421, 421, -6*w^5 + 3*w^4 + 41*w^3 + 12*w^2 - 24*w - 5],\ [449, 449, -9*w^5 + w^4 + 66*w^3 + 38*w^2 - 43*w - 16],\ [449, 449, 2*w^5 + w^4 - 16*w^3 - 17*w^2 + 11*w + 9],\ [449, 449, 10*w^5 - w^4 - 74*w^3 - 43*w^2 + 49*w + 18],\ [449, 449, 17*w^5 - 6*w^4 - 121*w^3 - 46*w^2 + 78*w + 16],\ [449, 449, -11*w^5 + 2*w^4 + 79*w^3 + 44*w^2 - 47*w - 21],\ [449, 449, 6*w^5 - w^4 - 44*w^3 - 22*w^2 + 28*w + 5],\ [461, 461, -6*w^5 + 3*w^4 + 42*w^3 + 10*w^2 - 28*w - 4],\ [461, 461, -15*w^5 + 5*w^4 + 107*w^3 + 43*w^2 - 70*w - 16],\ [461, 461, -10*w^5 + 2*w^4 + 73*w^3 + 36*w^2 - 46*w - 13],\ [461, 461, -9*w^5 + 2*w^4 + 66*w^3 + 31*w^2 - 46*w - 10],\ [461, 461, 12*w^5 - 4*w^4 - 85*w^3 - 34*w^2 + 50*w + 13],\ [461, 461, -18*w^5 + 4*w^4 + 130*w^3 + 64*w^2 - 81*w - 28],\ [491, 491, 17*w^5 - 5*w^4 - 121*w^3 - 54*w^2 + 73*w + 21],\ [491, 491, -10*w^5 + 4*w^4 + 70*w^3 + 26*w^2 - 43*w - 11],\ [491, 491, -6*w^5 + 3*w^4 + 41*w^3 + 12*w^2 - 23*w - 3],\ [491, 491, 2*w^5 - 16*w^3 - 9*w^2 + 16*w + 3],\ [491, 491, 20*w^5 - 5*w^4 - 144*w^3 - 68*w^2 + 90*w + 29],\ [491, 491, -6*w^5 + w^4 + 44*w^3 + 24*w^2 - 31*w - 13],\ [601, 601, -10*w^5 + 2*w^4 + 73*w^3 + 36*w^2 - 47*w - 12],\ [601, 601, -7*w^5 + 2*w^4 + 49*w^3 + 24*w^2 - 26*w - 10],\ [601, 601, -15*w^5 + 3*w^4 + 108*w^3 + 56*w^2 - 64*w - 24],\ [601, 601, -3*w^5 + 3*w^4 + 20*w^3 - 5*w^2 - 15*w + 3],\ [601, 601, 9*w^5 - 2*w^4 - 66*w^3 - 31*w^2 + 45*w + 11],\ [601, 601, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 63*w + 25],\ [631, 631, 5*w^5 - 2*w^4 - 35*w^3 - 13*w^2 + 20*w + 9],\ [631, 631, -10*w^5 + 4*w^4 + 71*w^3 + 24*w^2 - 47*w - 6],\ [631, 631, -5*w^5 + w^4 + 36*w^3 + 18*w^2 - 20*w - 9],\ [631, 631, -21*w^5 + 5*w^4 + 151*w^3 + 73*w^2 - 93*w - 31],\ [631, 631, 8*w^5 - 2*w^4 - 57*w^3 - 27*w^2 + 34*w + 8],\ [631, 631, -14*w^5 + 3*w^4 + 102*w^3 + 50*w^2 - 68*w - 19],\ [659, 659, 14*w^5 - 3*w^4 - 102*w^3 - 49*w^2 + 67*w + 19],\ [659, 659, 7*w^5 - 2*w^4 - 50*w^3 - 22*w^2 + 30*w + 5],\ [659, 659, -6*w^5 + 2*w^4 + 43*w^3 + 17*w^2 - 29*w - 10],\ [659, 659, -18*w^5 + 6*w^4 + 128*w^3 + 52*w^2 - 80*w - 21],\ [659, 659, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 64*w + 24],\ [659, 659, -16*w^5 + 5*w^4 + 114*w^3 + 48*w^2 - 72*w - 18],\ [701, 701, -7*w^5 + 4*w^4 + 49*w^3 + 9*w^2 - 34*w - 4],\ [701, 701, 15*w^5 - 3*w^4 - 108*w^3 - 57*w^2 + 65*w + 26],\ [701, 701, -12*w^5 + 2*w^4 + 87*w^3 + 48*w^2 - 55*w - 22],\ [701, 701, 7*w^5 - 3*w^4 - 49*w^3 - 16*w^2 + 28*w + 5],\ [701, 701, -8*w^5 + 2*w^4 + 57*w^3 + 27*w^2 - 32*w - 12],\ [701, 701, -9*w^5 + 3*w^4 + 64*w^3 + 26*w^2 - 38*w - 12],\ [729, 3, -3],\ [769, 769, -12*w^5 + w^4 + 88*w^3 + 53*w^2 - 54*w - 21],\ [769, 769, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 62*w + 25],\ [769, 769, -3*w^5 + 23*w^3 + 13*w^2 - 17*w - 1],\ [769, 769, 9*w^5 - 2*w^4 - 65*w^3 - 32*w^2 + 43*w + 12],\ [769, 769, -13*w^5 + 4*w^4 + 94*w^3 + 38*w^2 - 63*w - 14],\ [769, 769, 16*w^5 - 4*w^4 - 116*w^3 - 53*w^2 + 75*w + 21],\ [811, 811, 20*w^5 - 7*w^4 - 142*w^3 - 55*w^2 + 89*w + 21],\ [811, 811, 11*w^5 - 2*w^4 - 80*w^3 - 42*w^2 + 53*w + 17],\ [811, 811, -w^5 + 7*w^3 + 4*w^2 - w + 1],\ [811, 811, 9*w^5 - 2*w^4 - 64*w^3 - 34*w^2 + 35*w + 16],\ [811, 811, 5*w^5 - 2*w^4 - 35*w^3 - 13*w^2 + 20*w + 3],\ [811, 811, -7*w^5 + 52*w^3 + 34*w^2 - 31*w - 15],\ [839, 839, -14*w^5 + 5*w^4 + 99*w^3 + 38*w^2 - 60*w - 16],\ [839, 839, -20*w^5 + 6*w^4 + 143*w^3 + 62*w^2 - 90*w - 25],\ [839, 839, 7*w^5 - w^4 - 50*w^3 - 29*w^2 + 26*w + 12],\ [839, 839, -19*w^5 + 5*w^4 + 137*w^3 + 62*w^2 - 88*w - 22],\ [839, 839, -14*w^5 + 3*w^4 + 101*w^3 + 50*w^2 - 62*w - 21],\ [839, 839, -w^5 - w^4 + 9*w^3 + 11*w^2 - 10*w - 6],\ [881, 881, -14*w^5 + 3*w^4 + 102*w^3 + 49*w^2 - 67*w - 18],\ [881, 881, 12*w^5 - 5*w^4 - 84*w^3 - 29*w^2 + 52*w + 13],\ [881, 881, -3*w^5 + 2*w^4 + 21*w^3 + 2*w^2 - 15*w - 3],\ [881, 881, -3*w^5 + 21*w^3 + 16*w^2 - 8*w - 8],\ [881, 881, -17*w^5 + 4*w^4 + 123*w^3 + 58*w^2 - 79*w - 22],\ [881, 881, 19*w^5 - 5*w^4 - 136*w^3 - 64*w^2 + 83*w + 26],\ [911, 911, -6*w^5 + 2*w^4 + 44*w^3 + 15*w^2 - 32*w - 2],\ [911, 911, -15*w^5 + 4*w^4 + 107*w^3 + 51*w^2 - 66*w - 23],\ [911, 911, 13*w^5 - 4*w^4 - 94*w^3 - 37*w^2 + 63*w + 13],\ [911, 911, -15*w^5 + 3*w^4 + 109*w^3 + 55*w^2 - 71*w - 20],\ [911, 911, -7*w^5 + 3*w^4 + 48*w^3 + 17*w^2 - 25*w - 6],\ [911, 911, 12*w^5 - 4*w^4 - 86*w^3 - 34*w^2 + 55*w + 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 - 10*x^5 - 84*x^4 + 880*x^3 - 112*x^2 - 4224*x + 1728 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/1944*e^5 + 23/1944*e^4 + 7/486*e^3 - 277/243*e^2 + 152/81*e + 88/9, 7/1296*e^5 - 31/648*e^4 - 157/324*e^3 + 661/162*e^2 + 53/27*e - 32/3, e, -1/1944*e^5 - 1/486*e^4 + 95/972*e^3 + 121/486*e^2 - 388/81*e - 2/9, -7/3888*e^5 + 5/243*e^4 + 65/486*e^3 - 805/486*e^2 + 100/81*e + 20/9, -5/1944*e^5 + 17/972*e^4 + 58/243*e^3 - 745/486*e^2 - 104/81*e + 80/9, 1/1296*e^5 - 5/1296*e^4 - 17/162*e^3 + 26/81*e^2 + 77/27*e + 7/3, 1/1296*e^5 - 7/648*e^4 - 41/648*e^3 + 329/324*e^2 - 13/27*e - 8/3, 1/972*e^5 - 19/1944*e^4 - 109/972*e^3 + 433/486*e^2 + 391/162*e - 23/9, -1/432*e^5 + 1/54*e^4 + 25/108*e^3 - 179/108*e^2 - 23/9*e + 11, -5/2592*e^5 + 13/648*e^4 + 29/162*e^3 - 557/324*e^2 - 35/27*e + 23/3, 13/7776*e^5 - 55/3888*e^4 - 253/1944*e^3 + 1117/972*e^2 - 151/162*e + 11/9, 0, 4, 5/1296*e^5 - 13/324*e^4 - 29/81*e^3 + 557/162*e^2 + 167/54*e - 31/3, -7/1944*e^5 + 53/1944*e^4 + 601/1944*e^3 - 2113/972*e^2 - 43/81*e + 22/9, -19/7776*e^5 + 31/972*e^4 + 47/243*e^3 - 2779/972*e^2 + 128/81*e + 103/9, 17/3888*e^5 - 121/3888*e^4 - 443/972*e^3 + 667/243*e^2 + 490/81*e - 109/9, 1/864*e^5 - 7/432*e^4 - 7/216*e^3 + 151/108*e^2 - 85/18*e - 5, -13/3888*e^5 + 55/1944*e^4 + 167/486*e^3 - 2477/972*e^2 - 443/81*e + 131/9, -1, -1/486*e^5 + 11/1944*e^4 + 109/486*e^3 - 191/486*e^2 - 337/81*e - 26/9, 17/3888*e^5 - 37/972*e^4 - 181/486*e^3 + 775/243*e^2 + 85/81*e - 118/9, -5/3888*e^5 + 11/486*e^4 + 35/972*e^3 - 463/243*e^2 + 407/81*e + 4/9, -13/3888*e^5 + 41/972*e^4 + 253/972*e^3 - 896/243*e^2 + 97/81*e + 86/9, -1/243*e^5 + 49/1944*e^4 + 109/243*e^3 - 1057/486*e^2 - 647/81*e + 56/9, 25/3888*e^5 - 14/243*e^4 - 145/243*e^3 + 1208/243*e^2 + 395/81*e - 200/9, 1/432*e^5 - 7/216*e^4 - 4/27*e^3 + 151/54*e^2 - 28/9*e - 4, -7/1296*e^5 + 31/648*e^4 + 157/324*e^3 - 661/162*e^2 - 80/27*e + 56/3, 1/324*e^5 - 5/324*e^4 - 109/324*e^3 + 104/81*e^2 + 164/27*e - 2/3, -1/7776*e^5 + 13/972*e^4 - 37/972*e^3 - 1411/972*e^2 + 335/81*e + 121/9, -13/1944*e^5 + 55/972*e^4 + 1093/1944*e^3 - 4711/972*e^2 + 86/81*e + 136/9, -25/7776*e^5 + 85/3888*e^4 + 661/1944*e^3 - 1741/972*e^2 - 611/162*e + 1/9, 2/243*e^5 - 19/243*e^4 - 355/486*e^3 + 3221/486*e^2 + 347/162*e - 157/9, -1/3888*e^5 - 1/972*e^4 + 22/243*e^3 + 121/972*e^2 - 572/81*e - 1/9, 1/486*e^5 - 49/3888*e^4 - 109/486*e^3 + 325/243*e^2 + 283/81*e - 145/9, -5/1944*e^5 + 61/1944*e^4 + 383/1944*e^3 - 3083/972*e^2 + 139/81*e + 224/9, -31/3888*e^5 + 281/3888*e^4 + 703/972*e^3 - 1472/243*e^2 - 128/81*e + 59/9, -5/3888*e^5 + 17/1944*e^4 + 29/243*e^3 - 259/972*e^2 - 133/81*e - 185/9, -49/7776*e^5 + 199/3888*e^4 + 991/1944*e^3 - 4339/972*e^2 + 673/162*e + 115/9, 23/3888*e^5 - 29/486*e^4 - 101/243*e^3 + 2537/486*e^2 - 1417/162*e - 193/9, 95/7776*e^5 - 101/972*e^4 - 551/486*e^3 + 8495/972*e^2 + 494/81*e - 209/9, -1/1296*e^5 + 2/81*e^4 + 7/324*e^3 - 349/162*e^2 + 94/27*e + 2/3, 11/1944*e^5 - 59/972*e^4 - 397/972*e^3 + 1238/243*e^2 - 403/81*e - 140/9, -13/1296*e^5 + 55/648*e^4 + 307/324*e^3 - 599/81*e^2 - 218/27*e + 80/3, 1/216*e^5 - 5/216*e^4 - 59/108*e^3 + 52/27*e^2 + 106/9*e - 10, -5/1296*e^5 + 17/648*e^4 + 29/81*e^3 - 166/81*e^2 - 106/27*e - 2/3, 17/3888*e^5 - 101/1944*e^4 - 181/486*e^3 + 2225/486*e^2 + 139/81*e - 208/9, -1/243*e^5 + 179/3888*e^4 + 355/972*e^3 - 2191/486*e^2 - 134/81*e + 263/9, 1/216*e^5 - 11/216*e^4 - 55/216*e^3 + 481/108*e^2 - 113/9*e - 22, -19/7776*e^5 + 35/1944*e^4 + 47/243*e^3 - 943/972*e^2 + 20/81*e - 221/9, -5/1296*e^5 + 17/648*e^4 + 89/324*e^3 - 745/324*e^2 + 173/27*e + 7/3, 13/864*e^5 - 55/432*e^4 - 307/216*e^3 + 1171/108*e^2 + 173/18*e - 37, -1/108*e^5 + 19/216*e^4 + 91/108*e^3 - 203/27*e^2 - 37/18*e + 11, -1/972*e^5 + 65/3888*e^4 + 7/243*e^3 - 649/486*e^2 + 493/81*e + 59/9, -11/3888*e^5 + 59/1944*e^4 + 397/1944*e^3 - 2719/972*e^2 + 161/81*e + 250/9, -1/288*e^5 + 1/48*e^4 + 25/72*e^3 - 23/12*e^2 - 5/2*e + 21, 7/1296*e^5 - 5/81*e^4 - 65/162*e^3 + 443/81*e^2 - 281/54*e - 35/3, -25/3888*e^5 + 14/243*e^4 + 145/243*e^3 - 4589/972*e^2 - 395/81*e + 155/9, 65/7776*e^5 - 31/486*e^4 - 377/486*e^3 + 5153/972*e^2 + 365/81*e - 17/9, -1/1944*e^5 + 25/972*e^4 + 7/486*e^3 - 1229/486*e^2 + 260/81*e + 52/9, -37/3888*e^5 + 169/1944*e^4 + 907/972*e^3 - 3715/486*e^2 - 941/81*e + 224/9, 2/243*e^5 - 179/1944*e^4 - 355/486*e^3 + 1948/243*e^2 + 268/81*e - 328/9, -13/1944*e^5 + 55/972*e^4 + 253/486*e^3 - 1117/243*e^2 + 221/81*e - 8/9, -5/3888*e^5 - 5/972*e^4 + 139/486*e^3 + 181/486*e^2 - 1024/81*e - 68/9, 19/1944*e^5 - 35/486*e^4 - 995/972*e^3 + 3101/486*e^2 + 1216/81*e - 358/9, -25/1944*e^5 + 251/1944*e^4 + 1079/972*e^3 - 5507/486*e^2 - 88/81*e + 328/9, 7/1944*e^5 - 53/1944*e^4 - 65/243*e^3 + 589/243*e^2 - 173/81*e - 202/9, 11/3888*e^5 - 4/243*e^4 - 80/243*e^3 + 403/243*e^2 + 352/81*e - 178/9, 5/486*e^5 - 163/1944*e^4 - 1009/972*e^3 + 1706/243*e^2 + 1145/81*e - 230/9, 1/972*e^5 - 23/972*e^4 + 53/972*e^3 + 865/486*e^2 - 979/81*e + 4/9, -19/3888*e^5 + 43/1944*e^4 + 457/972*e^3 - 377/243*e^2 - 257/81*e - 118/9, 17/1944*e^5 - 101/972*e^4 - 181/243*e^3 + 2225/243*e^2 + 35/81*e - 326/9, -1/81*e^5 + 19/162*e^4 + 191/162*e^3 - 1651/162*e^2 - 332/27*e + 110/3, -1/162*e^5 + 19/324*e^4 + 137/324*e^3 - 785/162*e^2 + 176/27*e + 28/3, 7/648*e^5 - 53/648*e^4 - 92/81*e^3 + 589/81*e^2 + 484/27*e - 118/3, 5/1296*e^5 - 1/81*e^4 - 29/81*e^3 + 107/162*e^2 + 88/27*e + 14/3, -19/3888*e^5 + 43/1944*e^4 + 619/972*e^3 - 997/486*e^2 - 1283/81*e + 98/9, 7/1296*e^5 - 31/648*e^4 - 46/81*e^3 + 1403/324*e^2 + 224/27*e - 53/3, 13/2592*e^5 - 4/81*e^4 - 167/324*e^3 + 1423/324*e^2 + 190/27*e - 43/3, -5/1296*e^5 + 43/1296*e^4 + 143/324*e^3 - 485/162*e^2 - 232/27*e + 55/3, -5/1296*e^5 + 13/324*e^4 + 259/648*e^3 - 1195/324*e^2 - 142/27*e + 70/3, -1/243*e^5 + 19/486*e^4 + 109/243*e^3 - 866/243*e^2 - 1321/162*e + 209/9, 11/7776*e^5 - 59/3888*e^4 - 401/1944*e^3 + 1481/972*e^2 + 1081/162*e - 71/9, 1/972*e^5 + 1/243*e^4 - 95/486*e^3 - 121/243*e^2 + 938/81*e + 76/9, -1/972*e^5 + 23/972*e^4 + 7/243*e^3 - 554/243*e^2 + 142/81*e + 248/9, -7/486*e^5 + 133/972*e^4 + 601/486*e^3 - 2788/243*e^2 - 118/81*e + 304/9, -1/648*e^5 - 1/162*e^4 + 17/81*e^3 + 20/81*e^2 - 136/27*e + 64/3, 31/1944*e^5 - 127/972*e^4 - 703/486*e^3 + 2728/243*e^2 + 526/81*e - 280/9, -1/36*e^4 + 1/6*e^3 + 25/9*e^2 - 40/3*e - 12, 1/324*e^5 - 19/648*e^4 - 55/324*e^3 + 176/81*e^2 - 293/54*e + 43/3, -1/3888*e^5 - 29/1944*e^4 + 7/972*e^3 + 1471/972*e^2 - 5/81*e + 35/9, 11/7776*e^5 + 11/1944*e^4 - 161/486*e^3 - 301/972*e^2 + 1310/81*e + 37/9, 11/864*e^5 - 53/432*e^4 - 257/216*e^3 + 1169/108*e^2 + 175/18*e - 35, -1/243*e^5 + 233/3888*e^4 + 355/972*e^3 - 2623/486*e^2 - 188/81*e + 317/9, -25/1944*e^5 + 197/1944*e^4 + 2563/1944*e^3 - 8557/972*e^2 - 1465/81*e + 418/9, 5/1296*e^5 - 43/1296*e^4 - 143/324*e^3 + 283/81*e^2 + 259/27*e - 121/3, -37/2592*e^5 + 151/1296*e^4 + 907/648*e^3 - 3265/324*e^2 - 635/54*e + 91/3, 7/432*e^5 - 17/108*e^4 - 157/108*e^3 + 368/27*e^2 + 73/18*e - 45, -1/162*e^5 + 19/324*e^4 + 247/648*e^3 - 1651/324*e^2 + 329/27*e + 52/3, 1/288*e^5 - 1/72*e^4 - 11/36*e^3 + 17/36*e^2 + e + 21, -1/324*e^5 + 19/648*e^4 + 34/81*e^3 - 785/324*e^2 - 407/27*e + 11/3, -1/3888*e^5 + 13/486*e^4 - 37/486*e^3 - 2579/972*e^2 + 670/81*e + 305/9, -41/7776*e^5 + 161/3888*e^4 + 1097/1944*e^3 - 3473/972*e^2 - 1879/162*e + 299/9, -11/972*e^5 + 91/972*e^4 + 239/243*e^3 - 3845/486*e^2 - 305/162*e + 361/9, 11/972*e^5 - 445/3888*e^4 - 239/243*e^3 + 2368/243*e^2 + 193/81*e - 91/9, 11/1944*e^5 - 8/243*e^4 - 1199/1944*e^3 + 2981/972*e^2 + 812/81*e - 50/9, -1/7776*e^5 - 7/486*e^4 + 125/972*e^3 + 1289/972*e^2 - 583/81*e + 67/9, 1/96*e^5 - 5/48*e^4 - 19/24*e^3 + 101/12*e^2 - 15/2*e - 19, -11/486*e^5 + 391/1944*e^4 + 1993/972*e^3 - 16973/972*e^2 - 710/81*e + 443/9, 11/1944*e^5 - 101/3888*e^4 - 721/972*e^3 + 455/243*e^2 + 1757/81*e - 95/9, 19/7776*e^5 - 1/243*e^4 - 47/243*e^3 + 565/972*e^2 - 155/81*e - 265/9, -1/1296*e^5 - 11/648*e^4 + 17/162*e^3 + 163/81*e^2 - 19/54*e - 127/3, 19/3888*e^5 - 97/1944*e^4 - 833/1944*e^3 + 4451/972*e^2 - 256/81*e - 296/9, 7/1296*e^5 - 11/324*e^4 - 211/324*e^3 + 517/162*e^2 + 431/27*e - 92/3, -17/3888*e^5 + 37/972*e^4 + 281/972*e^3 - 775/243*e^2 + 428/81*e + 46/9, -17/3888*e^5 + 47/1944*e^4 + 131/243*e^3 - 559/243*e^2 - 895/81*e + 82/9, 5/1296*e^5 - 1/81*e^4 - 29/81*e^3 + 107/162*e^2 + 61/27*e + 8/3, 11/972*e^5 - 59/486*e^4 - 239/243*e^3 + 5195/486*e^2 + 139/81*e - 424/9, -23/1944*e^5 + 205/1944*e^4 + 283/243*e^3 - 4399/486*e^2 - 1148/81*e + 224/9, 13/1944*e^5 - 85/3888*e^4 - 749/972*e^3 + 334/243*e^2 + 1426/81*e - 55/9, 101/7776*e^5 - 581/3888*e^4 - 2003/1944*e^3 + 12371/972*e^2 - 791/162*e - 395/9, -7/3888*e^5 - 41/1944*e^4 + 373/972*e^3 + 977/486*e^2 - 2473/162*e - 223/9, -41/3888*e^5 + 47/486*e^4 + 1951/1944*e^3 - 8053/972*e^2 - 1042/81*e + 184/9, 101/7776*e^5 - 169/1944*e^4 - 1285/972*e^3 + 7511/972*e^2 + 1400/81*e - 485/9, -79/3888*e^5 + 355/1944*e^4 + 1687/972*e^3 - 15119/972*e^2 - 152/81*e + 335/9, 16, -7/1296*e^5 + 11/324*e^4 + 211/324*e^3 - 517/162*e^2 - 377/27*e + 50/3, -1/1296*e^5 + 7/648*e^4 - 5/81*e^3 - 62/81*e^2 + 229/27*e - 16/3, 1/144*e^5 - 1/12*e^4 - 11/18*e^3 + 15/2*e^2 + 5/3*e - 38, -1/81*e^5 + 19/162*e^4 + 191/162*e^3 - 1651/162*e^2 - 305/27*e + 98/3, 13/3888*e^5 - 7/486*e^4 - 253/972*e^3 + 221/243*e^2 - 124/81*e + 4/9, 2/243*e^5 - 125/1944*e^4 - 218/243*e^3 + 2789/486*e^2 + 1348/81*e - 310/9, 23/1944*e^5 - 89/972*e^4 - 283/243*e^3 + 3967/486*e^2 + 1459/162*e - 359/9, 1/2592*e^5 - 1/81*e^4 + 37/324*e^3 + 187/324*e^2 - 371/27*e + 53/3, 5/1296*e^5 - 13/324*e^4 - 31/162*e^3 + 1195/324*e^2 - 272/27*e - 85/3, -7/648*e^5 + 97/1296*e^4 + 157/162*e^3 - 472/81*e^2 - 79/27*e - 17/3, 7/648*e^5 - 31/324*e^4 - 709/648*e^3 + 2563/324*e^2 + 430/27*e - 58/3, -125/7776*e^5 + 641/3888*e^4 + 2657/1944*e^3 - 14105/972*e^2 + 293/162*e + 455/9, -13/1296*e^5 + 55/648*e^4 + 307/324*e^3 - 599/81*e^2 - 245/27*e + 56/3, -1/3888*e^5 + 13/486*e^4 - 37/486*e^3 - 584/243*e^2 + 670/81*e - 64/9, 1/162*e^5 - 47/648*e^4 - 41/81*e^3 + 505/81*e^2 + 13/27*e - 100/3, 7/972*e^5 - 79/1944*e^4 - 763/972*e^3 + 1681/486*e^2 + 1058/81*e - 242/9, 1/162*e^5 - 47/648*e^4 - 137/324*e^3 + 505/81*e^2 - 185/27*e - 100/3, -1/108*e^5 + 2/27*e^4 + 91/108*e^3 - 331/54*e^2 - 53/9*e + 2, -1/243*e^5 + 49/1944*e^4 + 629/1944*e^3 - 1385/972*e^2 + 163/81*e - 214/9, 7/3888*e^5 - 5/243*e^4 - 73/243*e^3 + 805/486*e^2 + 2257/162*e - 29/9, -11/3888*e^5 + 59/1944*e^4 + 80/243*e^3 - 3205/972*e^2 - 649/81*e + 331/9, 25/7776*e^5 - 139/3888*e^4 - 175/1944*e^3 + 3091/972*e^2 - 2521/162*e - 145/9, -119/7776*e^5 + 143/972*e^4 + 337/243*e^3 - 12443/972*e^2 - 338/81*e + 359/9, 67/3888*e^5 - 569/3888*e^4 - 1603/972*e^3 + 3083/243*e^2 + 956/81*e - 401/9, -59/7776*e^5 + 211/1944*e^4 + 409/972*e^3 - 8837/972*e^2 + 1378/81*e + 209/9, 197/7776*e^5 - 929/3888*e^4 - 4295/1944*e^3 + 20063/972*e^2 + 985/162*e - 581/9, 1/972*e^5 + 151/3888*e^4 - 271/972*e^3 - 904/243*e^2 + 992/81*e + 283/9, -47/3888*e^5 + 149/1944*e^4 + 1139/972*e^3 - 6463/972*e^2 - 1018/81*e + 385/9, -61/3888*e^5 + 101/972*e^4 + 3203/1944*e^3 - 8333/972*e^2 - 2168/81*e + 290/9, 35/3888*e^5 - 173/1944*e^4 - 731/972*e^3 + 3593/486*e^2 + 647/162*e - 109/9] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([125, 5, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 19*w + 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]