/* 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([211,211,w^4 - w^3 - 7*w^2 + 2*w + 4]) 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^5 + 7*x^4 - 66*x^3 - 262*x^2 + 1569*x - 449 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/10*e^4 - 47/40*e^3 + 57/40*e^2 + 263/8*e - 721/40, 1/80*e^4 + 1/10*e^3 - 9/40*e^2 - 5/2*e - 591/80, 1/80*e^4 - 1/40*e^3 - 17/20*e^2 + 17/8*e + 59/80, 3/8*e^3 + 9/8*e^2 - 127/8*e + 51/8, -3/80*e^4 - 4/5*e^3 - 33/40*e^2 + 26*e - 587/80, e, 1/16*e^4 + 1/2*e^3 - 15/8*e^2 - 12*e + 213/16, 1/80*e^4 - 1/40*e^3 - 3/5*e^2 + 21/8*e - 641/80, -1/80*e^4 - 1/10*e^3 + 9/40*e^2 + 5/2*e - 49/80, 1/10*e^4 + 47/40*e^3 - 37/40*e^2 - 247/8*e - 19/40, 1/8*e^4 + 5/4*e^3 - 5/2*e^2 - 131/4*e + 143/8, -1/20*e^4 - 2/5*e^3 + 7/5*e^2 + 10*e - 239/20, -7/80*e^4 - 23/40*e^3 + 27/10*e^2 + 83/8*e - 1073/80, 1/10*e^4 + 67/40*e^3 + 33/40*e^2 - 407/8*e + 251/40, -1/20*e^4 - 23/20*e^3 - 11/10*e^2 + 157/4*e - 419/20, -1/80*e^4 + 1/40*e^3 + 17/20*e^2 - 9/8*e - 459/80, 1/4*e^3 + e^2 - 35/4*e - 11/2, 1/20*e^4 + 9/10*e^3 + 3/5*e^2 - 28*e + 149/20, 9/80*e^4 + 23/20*e^3 - 81/40*e^2 - 119/4*e + 921/80, -3/80*e^4 - 7/40*e^3 + 4/5*e^2 - 9/8*e + 923/80, 19/80*e^4 + 12/5*e^3 - 161/40*e^2 - 61*e + 1391/80, -3/20*e^4 - 73/40*e^3 + 43/40*e^2 + 389/8*e - 69/40, 5/8*e^3 + 21/8*e^2 - 173/8*e - 85/8, -3/20*e^4 - 43/40*e^3 + 143/40*e^2 + 159/8*e + 511/40, 11/80*e^4 + 11/10*e^3 - 129/40*e^2 - 49/2*e - 441/80, -9/80*e^4 - 41/40*e^3 + 29/10*e^2 + 221/8*e - 1951/80, -9/80*e^4 - 61/40*e^3 + 23/20*e^2 + 365/8*e - 2091/80, -9/80*e^4 - 23/20*e^3 + 41/40*e^2 + 107/4*e + 1239/80, -3/20*e^4 - 19/20*e^3 + 89/20*e^2 + 61/4*e - 53/5, -13/80*e^4 - 41/20*e^3 + 77/40*e^2 + 235/4*e - 2437/80, -1/10*e^4 - 4/5*e^3 + 31/20*e^2 + 29/2*e + 317/20, -1/8*e^4 - 17/8*e^3 - 11/8*e^2 + 509/8*e, -3/40*e^4 - 27/20*e^3 - 3/20*e^2 + 177/4*e - 1467/40, 1/80*e^4 + 9/40*e^3 - 1/10*e^2 - 85/8*e + 279/80, -3/40*e^4 - 29/40*e^3 + 59/40*e^2 + 145/8*e - 49/5, -1/80*e^4 - 19/40*e^3 - 7/5*e^2 + 143/8*e + 1121/80, 1/20*e^4 - 19/40*e^3 - 191/40*e^2 + 187/8*e + 393/40, 9/80*e^4 + 7/5*e^3 - 31/40*e^2 - 37*e + 821/80, -23/80*e^4 - 14/5*e^3 + 207/40*e^2 + 139/2*e - 1567/80, 1, -3/80*e^4 + 3/40*e^3 + 9/5*e^2 - 79/8*e + 963/80, -13/80*e^4 - 57/40*e^3 + 71/20*e^2 + 269/8*e - 1567/80, 9/80*e^4 + 33/20*e^3 - 11/40*e^2 - 199/4*e + 1301/80, 3/20*e^4 + 6/5*e^3 - 21/5*e^2 - 27*e + 417/20, 7/40*e^4 + 51/40*e^3 - 191/40*e^2 - 211/8*e + 17/10, 3/80*e^4 + 11/20*e^3 - 27/40*e^2 - 71/4*e + 2227/80, 3/20*e^4 + 73/40*e^3 - 33/40*e^2 - 397/8*e - 301/40, -7/80*e^4 - 23/40*e^3 + 49/20*e^2 + 51/8*e - 733/80, -1/80*e^4 - 39/40*e^3 - 53/20*e^2 + 291/8*e - 1419/80, -9/40*e^4 - 51/20*e^3 + 71/20*e^2 + 287/4*e - 1901/40, -9/80*e^4 - 13/20*e^3 + 111/40*e^2 + 25/4*e + 1579/80, 13/80*e^4 + 31/20*e^3 - 137/40*e^2 - 157/4*e + 1757/80, -3/20*e^4 - 83/40*e^3 + 3/40*e^2 + 471/8*e + 211/40, -7/40*e^4 - 43/20*e^3 + 43/20*e^2 + 255/4*e - 1623/40, -17/80*e^4 - 11/5*e^3 + 103/40*e^2 + 53*e + 67/80, 3/10*e^4 + 151/40*e^3 - 91/40*e^2 - 835/8*e + 583/40, 5/16*e^4 + 31/8*e^3 - 5/2*e^2 - 859/8*e + 363/16, 3/40*e^4 - 1/40*e^3 - 159/40*e^2 + 93/8*e + 33/10, 21/80*e^4 + 89/40*e^3 - 117/20*e^2 - 397/8*e + 1199/80, 1/16*e^4 + 1/4*e^3 - 21/8*e^2 - 15/4*e + 193/16, -27/80*e^4 - 133/40*e^3 + 129/20*e^2 + 665/8*e - 3833/80, 1/80*e^4 - 9/10*e^3 - 169/40*e^2 + 69/2*e + 1169/80, 11/80*e^4 + 21/10*e^3 + 11/40*e^2 - 65*e + 519/80, -11/80*e^4 - 89/40*e^3 - 3/20*e^2 + 561/8*e - 3409/80, 23/80*e^4 + 43/10*e^3 + 13/40*e^2 - 126*e + 647/80, -1/40*e^4 + 3/10*e^3 + 49/20*e^2 - 35/2*e - 369/40, -1/20*e^4 - 33/20*e^3 - 8/5*e^2 + 259/4*e - 1109/20, 3/40*e^4 + 39/40*e^3 - 29/40*e^2 - 239/8*e + 151/20, -17/40*e^4 - 22/5*e^3 + 32/5*e^2 + 112*e - 623/40, -1/16*e^4 - e^3 + 1/8*e^2 + 61/2*e - 137/16, 1/40*e^4 - 21/20*e^3 - 89/20*e^2 + 183/4*e - 971/40, 3/8*e^4 + 4*e^3 - 11/2*e^2 - 103*e + 145/8, 13/80*e^4 + 127/40*e^3 + 17/10*e^2 - 843/8*e + 3387/80, -7/80*e^4 - 1/5*e^3 + 153/40*e^2 - 1/2*e + 1517/80, 9/80*e^4 + 2/5*e^3 - 221/40*e^2 - 5*e + 2801/80, 1/8*e^4 + e^3 - 4*e^2 - 28*e + 343/8, 3/16*e^4 + 13/8*e^3 - 13/4*e^2 - 265/8*e - 407/16, -7/20*e^4 - 107/40*e^3 + 347/40*e^2 + 443/8*e - 121/40, -7/40*e^4 - 31/40*e^3 + 241/40*e^2 + 19/8*e + 131/20, 23/80*e^4 + 61/20*e^3 - 197/40*e^2 - 331/4*e + 4027/80, 3/16*e^4 + e^3 - 51/8*e^2 - 13*e + 195/16, 29/80*e^4 + 29/10*e^3 - 331/40*e^2 - 62*e - 1119/80, -27/80*e^4 - 16/5*e^3 + 253/40*e^2 + 78*e - 2223/80, 1/4*e^4 + 2*e^3 - 23/4*e^2 - 83/2*e - 4, -3/16*e^4 - 11/4*e^3 + 13/8*e^2 + 347/4*e - 951/16, -1/16*e^4 - 1/2*e^3 + 5/8*e^2 + 17/2*e + 295/16, 1/8*e^4 + e^3 - 5/2*e^2 - 19*e - 157/8, 13/80*e^4 + 37/40*e^3 - 101/20*e^2 - 105/8*e + 7/80, 3/20*e^4 + 73/40*e^3 - 83/40*e^2 - 401/8*e + 1369/40, 3/16*e^4 + 11/4*e^3 - 3/8*e^2 - 333/4*e + 619/16, -13/80*e^4 - 87/40*e^3 + 9/5*e^2 + 511/8*e - 3787/80, 2/5*e^4 + 21/5*e^3 - 129/20*e^2 - 111*e + 757/20, -13/40*e^4 - 18/5*e^3 + 97/20*e^2 + 193/2*e - 1697/40, 7/80*e^4 + 53/40*e^3 + 1/20*e^2 - 329/8*e - 987/80, -21/40*e^4 - 183/40*e^3 + 473/40*e^2 + 847/8*e - 258/5, 1/16*e^4 - 3/8*e^3 - 4*e^2 + 203/8*e - 161/16, -37/80*e^4 - 153/40*e^3 + 219/20*e^2 + 693/8*e - 2343/80, 3/40*e^4 + 29/40*e^3 - 99/40*e^2 - 197/8*e + 383/10, -3/16*e^4 - 5/2*e^3 + 5/8*e^2 + 141/2*e + 89/16, 3/80*e^4 + 7/40*e^3 - 23/10*e^2 - 39/8*e + 2477/80, -1/8*e^4 - 5/8*e^3 + 35/8*e^2 + 61/8*e - 93/4, -3/40*e^4 - 49/40*e^3 + 49/40*e^2 + 365/8*e - 891/20, 31/80*e^4 + 229/40*e^3 - 3/5*e^2 - 1361/8*e + 3889/80, -37/80*e^4 - 203/40*e^3 + 36/5*e^2 + 1119/8*e - 5563/80, 21/80*e^4 + 57/20*e^3 - 159/40*e^2 - 311/4*e + 769/80, 51/80*e^4 + 259/40*e^3 - 48/5*e^2 - 1279/8*e + 429/80, -3/40*e^4 - 59/40*e^3 - 81/40*e^2 + 347/8*e + 96/5, 11/80*e^4 + 1/10*e^3 - 259/40*e^2 + 33/2*e - 1061/80, -1/16*e^4 + 1/8*e^3 + 11/2*e^2 - 65/8*e - 679/16, -1/8*e^4 - 19/8*e^3 - 3/8*e^2 + 663/8*e - 56, 5/16*e^4 + 5/2*e^3 - 61/8*e^2 - 54*e - 19/16, -9/40*e^4 - 107/40*e^3 + 77/40*e^2 + 591/8*e - 39/10, 3/8*e^4 + 41/8*e^3 - 5/8*e^2 - 1137/8*e - 15/4, 3/80*e^4 + 3/10*e^3 - 97/40*e^2 - 14*e + 2727/80, -17/40*e^4 - 121/40*e^3 + 521/40*e^2 + 529/8*e - 587/10, 3/2*e^3 + 19/4*e^2 - 64*e + 31/4, 19/80*e^4 + 29/10*e^3 - 121/40*e^2 - 169/2*e + 2431/80, -17/80*e^4 - 49/20*e^3 + 103/40*e^2 + 253/4*e - 1613/80, -9/80*e^4 - 33/20*e^3 + 71/40*e^2 + 229/4*e - 5141/80, 3/40*e^4 + 19/40*e^3 - 109/40*e^2 - 79/8*e + 561/20, -3/16*e^4 - 3*e^3 - 5/8*e^2 + 187/2*e - 139/16, -1/5*e^4 - 8/5*e^3 + 107/20*e^2 + 37*e - 951/20, 1/16*e^4 + 11/8*e^3 + 5/4*e^2 - 375/8*e + 579/16, -1/80*e^4 + 1/40*e^3 + 37/20*e^2 + 31/8*e - 299/80, -29/80*e^4 - 101/40*e^3 + 183/20*e^2 + 353/8*e + 49/80, -3/20*e^4 - 39/20*e^3 + 19/20*e^2 + 203/4*e - 53/5, -1/5*e^4 - 37/20*e^3 + 51/10*e^2 + 205/4*e - 483/10, -1/80*e^4 - 19/40*e^3 - 2/5*e^2 + 147/8*e - 3239/80, 21/40*e^4 + 26/5*e^3 - 209/20*e^2 - 135*e + 3149/40, -29/80*e^4 - 151/40*e^3 + 103/20*e^2 + 767/8*e - 1271/80, 27/80*e^4 + 16/5*e^3 - 293/40*e^2 - 157/2*e + 3943/80, 3/8*e^4 + 41/8*e^3 - 21/8*e^2 - 1229/8*e + 315/4, 13/40*e^4 + 139/40*e^3 - 159/40*e^2 - 715/8*e + 251/20, 37/80*e^4 + 163/40*e^3 - 189/20*e^2 - 767/8*e + 223/80, -7/20*e^4 - 71/20*e^3 + 141/20*e^2 + 385/4*e - 297/5, 7/16*e^4 + 15/4*e^3 - 79/8*e^2 - 351/4*e + 263/16, 7/16*e^4 + 11/2*e^3 - 31/8*e^2 - 153*e + 735/16, 1/16*e^4 + 5/4*e^3 + 13/8*e^2 - 145/4*e - 187/16, 11/80*e^4 + 69/40*e^3 + 3/20*e^2 - 361/8*e - 2311/80, 1/8*e^4 + 11/8*e^3 - 23/8*e^2 - 287/8*e + 221/4, -11/20*e^4 - 291/40*e^3 + 121/40*e^2 + 1659/8*e - 1383/40, 1/80*e^4 + 8/5*e^3 + 181/40*e^2 - 65*e - 251/80, -17/80*e^4 - 37/10*e^3 - 57/40*e^2 + 116*e - 4133/80, -3/80*e^4 + 17/10*e^3 + 267/40*e^2 - 149/2*e + 4973/80, -3/5*e^4 - 141/20*e^3 + 141/20*e^2 + 783/4*e - 1263/20, -17/80*e^4 - 29/20*e^3 + 303/40*e^2 + 143/4*e - 4933/80, -1/80*e^4 + 41/40*e^3 + 51/10*e^2 - 309/8*e - 1959/80, -1/2*e^4 - 21/4*e^3 + 35/4*e^2 + 555/4*e - 307/4, -1/80*e^4 - 3/5*e^3 - 71/40*e^2 + 43/2*e + 3271/80, -3/10*e^4 - 73/20*e^3 + 43/20*e^2 + 377/4*e + 231/20, 17/80*e^4 + 39/20*e^3 - 93/40*e^2 - 155/4*e - 2567/80, -9/40*e^4 - 97/40*e^3 + 197/40*e^2 + 545/8*e - 247/5, 9/80*e^4 + 111/40*e^3 + 23/5*e^2 - 735/8*e - 929/80, 17/40*e^4 + 29/10*e^3 - 62/5*e^2 - 105/2*e + 2143/40, -3/4*e^3 - 7/4*e^2 + 135/4*e - 77/4, -27/80*e^4 - 79/20*e^3 + 203/40*e^2 + 455/4*e - 7003/80, 7/20*e^4 + 107/40*e^3 - 307/40*e^2 - 415/8*e - 979/40] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([211,211,w^4 - w^3 - 7*w^2 + 2*w + 4])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]