/* 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([29, 11, -10, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, w^2 - 2*w - 5]) primes_array = [ [11, 11, -w - 1],\ [11, 11, w^2 - 5],\ [11, 11, -w^2 + 2*w + 4],\ [11, 11, w - 2],\ [16, 2, 2],\ [19, 19, w^2 - 2*w - 5],\ [19, 19, -w^2 + 6],\ [25, 5, -2*w^2 + 2*w + 11],\ [29, 29, w],\ [29, 29, 2*w^2 - w - 10],\ [29, 29, -2*w^2 + 3*w + 9],\ [29, 29, w - 1],\ [31, 31, w^3 - 6*w - 6],\ [31, 31, -w^3 + 3*w^2 + 3*w - 11],\ [41, 41, w^3 - 4*w^2 - 2*w + 16],\ [41, 41, w^3 - 5*w^2 - 2*w + 24],\ [59, 59, w^3 - w^2 - 5*w - 2],\ [59, 59, 2*w^2 - w - 13],\ [61, 61, w^3 - w^2 - 6*w + 3],\ [61, 61, -w^3 + 2*w^2 + 5*w - 3],\ [71, 71, 2*w^2 - w - 16],\ [71, 71, -w^3 + 3*w^2 + 4*w - 10],\ [71, 71, -w^3 + 7*w + 4],\ [71, 71, w^3 - 5*w^2 - 2*w + 23],\ [79, 79, -w^3 + 4*w^2 + 3*w - 16],\ [79, 79, w^3 + w^2 - 8*w - 10],\ [81, 3, -3],\ [131, 131, 4*w^2 - 5*w - 24],\ [131, 131, 4*w^2 - 3*w - 25],\ [139, 139, w^2 + w - 9],\ [139, 139, -w^3 + w^2 + 6*w - 5],\ [149, 149, w^3 - w^2 - 4*w + 2],\ [149, 149, w^3 - 2*w^2 - 3*w + 2],\ [151, 151, -w^3 + 7*w + 3],\ [151, 151, -w^3 + 3*w^2 + 4*w - 9],\ [179, 179, -w^3 - 2*w^2 + 10*w + 16],\ [179, 179, -w^3 + 3*w^2 + 3*w - 6],\ [179, 179, w^3 - 6*w - 1],\ [179, 179, w^3 - 5*w^2 - 3*w + 23],\ [191, 191, w^3 - 6*w^2 - w + 27],\ [191, 191, w^3 + 3*w^2 - 10*w - 21],\ [199, 199, -w^3 + 2*w^2 + 6*w - 4],\ [199, 199, -4*w^2 + 3*w + 22],\ [199, 199, 4*w^2 - 5*w - 21],\ [199, 199, 3*w^2 - 4*w - 12],\ [239, 239, -w^3 + w^2 + 4*w - 6],\ [239, 239, 2*w^3 - 5*w^2 - 9*w + 17],\ [239, 239, 2*w^3 - w^2 - 13*w - 5],\ [239, 239, w^3 - 8*w^2 + 2*w + 41],\ [241, 241, -w^3 + 5*w^2 + 4*w - 25],\ [241, 241, w^3 - 6*w - 8],\ [241, 241, -w^3 + 3*w^2 + 3*w - 13],\ [241, 241, w^3 - 5*w^2 + w + 19],\ [269, 269, w^2 - 2*w - 10],\ [269, 269, w^2 - 11],\ [271, 271, w^3 + 2*w^2 - 8*w - 18],\ [271, 271, 2*w^3 - 13*w - 10],\ [271, 271, 2*w^3 + w^2 - 15*w - 16],\ [271, 271, w^3 - 5*w^2 - w + 23],\ [289, 17, 2*w^2 - 11],\ [289, 17, -2*w^2 + 4*w + 9],\ [311, 311, w^3 - 4*w^2 - 3*w + 10],\ [311, 311, w^3 - 7*w^2 - w + 34],\ [331, 331, w^3 - w^2 - 7*w + 4],\ [331, 331, w^3 - 2*w^2 - 6*w + 3],\ [349, 349, w^3 + w^2 - 6*w - 12],\ [349, 349, -w^3 + 4*w^2 + w - 16],\ [361, 19, 4*w^2 - 4*w - 21],\ [379, 379, w^3 - 3*w^2 - 3*w + 15],\ [379, 379, 2*w^3 - 2*w^2 - 12*w + 1],\ [379, 379, -2*w^3 + 4*w^2 + 10*w - 11],\ [379, 379, w^3 - 6*w - 10],\ [401, 401, -2*w^3 + 7*w^2 + 8*w - 30],\ [401, 401, -w^3 + 2*w^2 + 6*w - 2],\ [419, 419, 5*w^2 - 4*w - 26],\ [419, 419, 5*w^2 - 6*w - 25],\ [421, 421, 3*w^2 - w - 20],\ [421, 421, -2*w^3 + 2*w^2 + 10*w + 3],\ [431, 431, w^2 - 3*w - 5],\ [431, 431, w^2 + w - 7],\ [449, 449, 2*w^3 - 13*w - 7],\ [449, 449, -2*w^3 + 6*w^2 + 7*w - 18],\ [461, 461, w^3 - w^2 - 8*w + 3],\ [461, 461, -w^3 + 2*w^2 + 7*w - 5],\ [491, 491, w^3 - 3*w^2 - 6*w + 15],\ [491, 491, w^3 - 9*w - 7],\ [499, 499, 4*w^2 - 6*w - 23],\ [499, 499, -4*w^2 + 2*w + 25],\ [509, 509, 2*w^3 - 3*w^2 - 11*w + 6],\ [521, 521, -w^3 + 3*w^2 + 2*w - 12],\ [521, 521, -w^3 + 4*w^2 + 2*w - 19],\ [529, 23, w^3 - 7*w^2 - w + 35],\ [529, 23, -w^3 + 3*w^2 + 4*w - 5],\ [541, 541, 2*w^3 - w^2 - 12*w - 5],\ [541, 541, w^3 - 2*w^2 - 7*w + 9],\ [569, 569, w^3 - 8*w - 2],\ [569, 569, -w^3 + 3*w^2 + 5*w - 9],\ [599, 599, -w^3 - 4*w^2 + 10*w + 25],\ [599, 599, -w^3 + 7*w^2 - 36],\ [601, 601, 5*w^2 - 6*w - 26],\ [601, 601, -2*w^3 + 8*w^2 + 6*w - 33],\ [601, 601, -2*w^3 - 2*w^2 + 16*w + 21],\ [601, 601, 5*w^2 - 4*w - 27],\ [619, 619, w^3 + 4*w^2 - 11*w - 26],\ [619, 619, w^3 - 3*w^2 - 5*w + 18],\ [641, 641, -w^3 + 3*w^2 + 6*w - 14],\ [641, 641, -w^3 + 9*w + 6],\ [659, 659, -w^3 - 4*w^2 + 10*w + 28],\ [659, 659, -w^3 + 6*w^2 - w - 27],\ [659, 659, -w^3 - 3*w^2 + 8*w + 23],\ [659, 659, -w^3 + 7*w^2 - w - 33],\ [691, 691, w^3 - w^2 - 8*w + 2],\ [691, 691, 2*w^3 - 2*w^2 - 11*w + 1],\ [701, 701, -w^3 - w^2 + 7*w + 15],\ [701, 701, -w^3 + 4*w^2 + 2*w - 20],\ [709, 709, -2*w^3 - w^2 + 15*w + 15],\ [709, 709, 2*w^3 - 7*w^2 - 7*w + 27],\ [719, 719, -w^3 - 4*w^2 + 13*w + 26],\ [719, 719, w^3 - 7*w^2 - 2*w + 34],\ [739, 739, 2*w^3 + 2*w^2 - 15*w - 24],\ [739, 739, -2*w^3 + 8*w^2 + 5*w - 35],\ [751, 751, -w^3 - 3*w^2 + 9*w + 25],\ [751, 751, -w^3 + 6*w^2 - 30],\ [761, 761, 3*w^3 - 2*w^2 - 16*w - 8],\ [761, 761, -3*w^3 + 7*w^2 + 11*w - 23],\ [769, 769, -2*w^3 + 4*w^2 + 11*w - 10],\ [769, 769, w^3 + 2*w^2 - 9*w - 12],\ [809, 809, -3*w^3 + 3*w^2 + 16*w + 4],\ [809, 809, w^3 + 5*w^2 - 12*w - 30],\ [811, 811, -w^3 - 4*w^2 + 10*w + 27],\ [811, 811, -2*w^3 + 5*w^2 + 9*w - 14],\ [811, 811, -2*w^3 + w^2 + 13*w + 2],\ [811, 811, -w^3 + 7*w^2 - w - 32],\ [821, 821, 2*w^3 - 8*w^2 - 7*w + 35],\ [821, 821, -2*w^3 - 2*w^2 + 17*w + 22],\ [829, 829, -3*w^3 + 20*w + 13],\ [829, 829, -w^3 + 7*w^2 - w - 36],\ [829, 829, w^3 + 4*w^2 - 10*w - 31],\ [829, 829, 2*w^3 - 3*w^2 - 11*w + 14],\ [859, 859, -w^3 + 7*w^2 - 3*w - 31],\ [859, 859, 7*w^2 - 9*w - 39],\ [859, 859, 7*w^2 - 5*w - 41],\ [859, 859, 3*w^3 - 4*w^2 - 17*w + 2],\ [929, 929, w^3 + 5*w^2 - 14*w - 31],\ [929, 929, -2*w^3 + 4*w^2 + 10*w - 5],\ [929, 929, w^3 - 9*w^2 + 4*w + 44],\ [929, 929, -w^3 + 8*w^2 + w - 39],\ [941, 941, -w^3 + 7*w^2 - 34],\ [941, 941, w^3 + 4*w^2 - 11*w - 28],\ [961, 31, -5*w^2 + 5*w + 28],\ [971, 971, -3*w^3 + w^2 + 19*w + 14],\ [971, 971, -3*w^3 + 8*w^2 + 12*w - 31],\ [991, 991, -w^3 - 5*w^2 + 11*w + 35],\ [991, 991, w^3 - 8*w^2 + 2*w + 40]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 24*x^7 + 232*x^6 - 1156*x^5 + 3149*x^4 - 4522*x^3 + 2741*x^2 + 214*x - 639 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/2*e^7 + 155/14*e^6 - 1339/14*e^5 + 5653/14*e^4 - 845*e^3 + 5207/7*e^2 - 555/14*e - 2549/14, -13/98*e^7 + 281/98*e^6 - 2361/98*e^5 + 9609/98*e^4 - 9479/49*e^3 + 7332/49*e^2 + 129/14*e - 3629/98, e, 95/98*e^7 - 2103/98*e^6 + 18129/98*e^5 - 76147/98*e^4 + 78900/49*e^3 - 68336/49*e^2 + 983/14*e + 32223/98, 45/98*e^7 - 977/98*e^6 + 8219/98*e^5 - 33445/98*e^4 + 33219/49*e^3 - 27102/49*e^2 + 27/2*e + 12129/98, -1, 121/98*e^7 - 2679/98*e^6 + 23075/98*e^5 - 96695/98*e^4 + 99720/49*e^3 - 85534/49*e^2 + 1009/14*e + 40671/98, -101/98*e^7 + 2223/98*e^6 - 19041/98*e^5 + 79435/98*e^4 - 81771/49*e^3 + 70418/49*e^2 - 883/14*e - 34235/98, 3/14*e^7 - 9/2*e^6 + 73/2*e^5 - 1999/14*e^4 + 1908/7*e^3 - 1514/7*e^2 + 125/14*e + 687/14, 61/98*e^7 - 1353/98*e^6 + 11645/98*e^5 - 48611/98*e^4 + 49793/49*e^3 - 42447/49*e^2 + 559/14*e + 19543/98, -13/49*e^7 + 288/49*e^6 - 2473/49*e^5 + 10274/49*e^4 - 20820/49*e^3 + 17198/49*e^2 - 27/7*e - 3832/49, -75/98*e^7 + 1647/98*e^6 - 14095/98*e^5 + 58887/98*e^4 - 60951/49*e^3 + 53220/49*e^2 - 857/14*e - 25787/98, -23/98*e^7 + 523/98*e^6 - 4651/98*e^5 + 20255/98*e^4 - 21859/49*e^3 + 19678/49*e^2 - 281/14*e - 9115/98, -141/98*e^7 + 3135/98*e^6 - 27109/98*e^5 + 114053/98*e^4 - 118257/49*e^3 + 102708/49*e^2 - 1583/14*e - 48675/98, 97/98*e^7 - 2143/98*e^6 + 18433/98*e^5 - 77243/98*e^4 + 79857/49*e^3 - 69030/49*e^2 + 139/2*e + 32763/98, -75/49*e^7 + 1661/49*e^6 - 14319/49*e^5 + 60119/49*e^4 - 124450/49*e^3 + 107392/49*e^2 - 97*e - 25605/49, 8/7*e^7 - 178/7*e^6 + 1546/7*e^5 - 6563/7*e^4 + 13802/7*e^3 - 1743*e^2 + 708/7*e + 2927/7, -11/49*e^7 + 248/49*e^6 - 2169/49*e^5 + 9178/49*e^4 - 18906/49*e^3 + 15712/49*e^2 + 47/7*e - 3978/49, -11/7*e^7 + 242/7*e^6 - 2073/7*e^5 + 8650/7*e^4 - 17793/7*e^3 + 15234/7*e^2 - 590/7*e - 3678/7, 44/49*e^7 - 978/49*e^6 + 8452/49*e^5 - 35529/49*e^4 + 73566/49*e^3 - 63562/49*e^2 + 410/7*e + 15310/49, -11/49*e^7 + 227/49*e^6 - 1784/49*e^5 + 6595/49*e^4 - 11311/49*e^3 + 7032/49*e^2 + 144/7*e - 1703/49, 9/49*e^7 - 194/49*e^6 + 1641/49*e^5 - 6850/49*e^4 + 14444/49*e^3 - 13372/49*e^2 + 155/7*e + 3914/49, -85/98*e^7 + 1861/98*e^6 - 15839/98*e^5 + 65501/98*e^4 - 66520/49*e^3 + 55892/49*e^2 - 433/14*e - 26737/98, -117/49*e^7 + 2592/49*e^6 - 22355/49*e^5 + 93936/49*e^4 - 194926/49*e^3 + 169776/49*e^2 - 1293/7*e - 40956/49, 6/7*e^7 - 19*e^6 + 164*e^5 - 4831/7*e^4 + 10054/7*e^3 - 8814/7*e^2 + 530/7*e + 2137/7, -58/49*e^7 + 1300/49*e^6 - 11350/49*e^5 + 48318/49*e^4 - 101664/49*e^3 + 89903/49*e^2 - 814/7*e - 21484/49, -48/49*e^7 + 1058/49*e^6 - 9060/49*e^5 + 37672/49*e^4 - 76904/49*e^3 + 65064/49*e^2 - 299/7*e - 15802/49, 53/98*e^7 - 1165/98*e^6 + 9981/98*e^5 - 41763/98*e^4 + 43319/49*e^3 - 37984/49*e^2 + 759/14*e + 17453/98, 159/98*e^7 - 3537/98*e^6 + 30615/98*e^5 - 128985/98*e^4 + 133975/49*e^3 - 116654/49*e^2 + 279/2*e + 54753/98, 97/49*e^7 - 2136/49*e^6 + 18321/49*e^5 - 76578/49*e^4 + 157803/49*e^3 - 135134/49*e^2 + 712/7*e + 32560/49, -139/98*e^7 + 3067/98*e^6 - 26259/98*e^5 + 109023/98*e^4 - 110979/49*e^3 + 93663/49*e^2 - 969/14*e - 44383/98, 19/49*e^7 - 422/49*e^6 + 3609/49*e^5 - 14794/49*e^4 + 29208/49*e^3 - 23196/49*e^2 - 13/7*e + 5858/49, -9/14*e^7 + 29/2*e^6 - 255/2*e^5 + 7663/14*e^4 - 8139/7*e^3 + 7244/7*e^2 - 837/14*e - 3335/14, 117/49*e^7 - 2592/49*e^6 + 22355/49*e^5 - 93936/49*e^4 + 194828/49*e^3 - 168992/49*e^2 + 1111/7*e + 40956/49, 51/49*e^7 - 1118/49*e^6 + 9565/49*e^5 - 40002/49*e^4 + 82960/49*e^3 - 72634/49*e^2 + 669/7*e + 16808/49, -53/49*e^7 + 1158/49*e^6 - 9869/49*e^5 + 41098/49*e^4 - 84874/49*e^3 + 74022/49*e^2 - 603/7*e - 18426/49, -33/98*e^7 + 807/98*e^6 - 7613/98*e^5 + 34695/98*e^4 - 38698/49*e^3 + 35902/49*e^2 - 717/14*e - 16995/98, 107/49*e^7 - 2385/49*e^6 + 20723/49*e^5 - 87889/49*e^4 + 184474/49*e^3 - 162850/49*e^2 + 1439/7*e + 38347/49, 205/98*e^7 - 4569/98*e^6 + 39693/98*e^5 - 168361/98*e^4 + 176958/49*e^3 - 157200/49*e^2 + 2945/14*e + 75321/98, 285/98*e^7 - 6267/98*e^6 + 53617/98*e^5 - 223275/98*e^4 + 229105/49*e^3 - 196132/49*e^2 + 2447/14*e + 93295/98, 76/49*e^7 - 1681/49*e^6 + 14520/49*e^5 - 61353/49*e^4 + 128592/49*e^3 - 113427/49*e^2 + 912/7*e + 27737/49, 5/7*e^7 - 115/7*e^6 + 1035/7*e^5 - 654*e^4 + 10140/7*e^3 - 9670/7*e^2 + 1031/7*e + 331, -27/49*e^7 + 582/49*e^6 - 4825/49*e^5 + 19080/49*e^4 - 35786/49*e^3 + 25710/49*e^2 + 151/7*e - 4784/49, -51/14*e^7 + 1123/14*e^6 - 9631/14*e^5 + 40267/14*e^4 - 41585/7*e^3 + 35976/7*e^2 - 3503/14*e - 17219/14, -51/98*e^7 + 1125/98*e^6 - 9579/98*e^5 + 39197/98*e^4 - 38785/49*e^3 + 31214/49*e^2 - 97/14*e - 14561/98, -192/49*e^7 + 4260/49*e^6 - 36786/49*e^5 + 154720/49*e^4 - 321287/49*e^3 + 279996/49*e^2 - 299*e - 68234/49, -141/49*e^7 + 3100/49*e^6 - 26500/49*e^5 + 110140/49*e^4 - 225293/49*e^3 + 192354/49*e^2 - 1314/7*e - 45112/49, 3/2*e^7 - 67/2*e^6 + 583/2*e^5 - 2475/2*e^4 + 2600*e^3 - 2300*e^2 + 265/2*e + 1119/2, -227/49*e^7 + 5023/49*e^6 - 43261/49*e^5 + 181453/49*e^4 - 375460/49*e^3 + 325034/49*e^2 - 2265/7*e - 78237/49, 135/98*e^7 - 2945/98*e^6 + 24979/98*e^5 - 103037/98*e^4 + 104557/49*e^3 - 88054/49*e^2 + 921/14*e + 40125/98, -10/49*e^7 + 207/49*e^6 - 1632/49*e^5 + 6047/49*e^4 - 10452/49*e^3 + 7122/49*e^2 - 64/7*e - 1041/49, -39/49*e^7 + 843/49*e^6 - 7083/49*e^5 + 28925/49*e^4 - 58099/49*e^3 + 48696/49*e^2 - 362/7*e - 11181/49, -59/98*e^7 + 1327/98*e^6 - 11663/98*e^5 + 50119/98*e^4 - 53197/49*e^3 + 46786/49*e^2 - 545/14*e - 20879/98, -2*e^7 + 312/7*e^6 - 2710/7*e^5 + 11482/7*e^4 - 3432*e^3 + 20971/7*e^2 - 960/7*e - 5030/7, -27/49*e^7 + 610/49*e^6 - 5371/49*e^5 + 23112/49*e^4 - 49555/49*e^3 + 45940/49*e^2 - 704/7*e - 10692/49, -1/49*e^7 - 8/49*e^6 + 345/49*e^5 - 2700/49*e^4 + 8402/49*e^3 - 9736/49*e^2 + 55/7*e + 3580/49, 171/98*e^7 - 3805/98*e^6 + 32887/98*e^5 - 138025/98*e^4 + 142265/49*e^3 - 121770/49*e^2 + 1341/14*e + 59197/98, 55/49*e^7 - 1240/49*e^6 + 10943/49*e^5 - 47409/49*e^4 + 102468/49*e^3 - 94338/49*e^2 + 1081/7*e + 23320/49, 31/49*e^7 - 690/49*e^6 + 5979/49*e^5 - 25304/49*e^4 + 53334/49*e^3 - 48373/49*e^2 + 607/7*e + 11282/49, 59/49*e^7 - 1292/49*e^6 + 11005/49*e^5 - 45618/49*e^4 + 93164/49*e^3 - 79236/49*e^2 + 430/7*e + 18982/49, 52/49*e^7 - 1138/49*e^6 + 9668/49*e^5 - 39864/49*e^4 + 80732/49*e^3 - 67840/49*e^2 + 265/7*e + 16882/49, 53/49*e^7 - 1179/49*e^6 + 10205/49*e^5 - 42946/49*e^4 + 88696/49*e^3 - 75548/49*e^2 + 63*e + 16683/49, 361/98*e^7 - 8081/98*e^6 + 70461/98*e^5 - 299517/98*e^4 + 314471/49*e^3 - 276894/49*e^2 + 4475/14*e + 133709/98, -145/49*e^7 + 3208/49*e^6 - 27605/49*e^5 + 115580/49*e^4 - 238578/49*e^3 + 206442/49*e^2 - 225*e - 48866/49, -51/49*e^7 + 1132/49*e^6 - 9887/49*e^5 + 42704/49*e^4 - 92858/49*e^3 + 86718/49*e^2 - 1009/7*e - 22408/49, 219/49*e^7 - 4849/49*e^6 + 41821/49*e^5 - 175935/49*e^4 + 366236/49*e^3 - 321176/49*e^2 + 2763/7*e + 76847/49, 26/7*e^7 - 82*e^6 + 704*e^5 - 20568/7*e^4 + 42186/7*e^3 - 35828/7*e^2 + 1172/7*e + 8614/7, 29/14*e^7 - 635/14*e^6 + 5421/14*e^5 - 22601/14*e^4 + 23351/7*e^3 - 20361/7*e^2 + 2301/14*e + 9733/14, 157/98*e^7 - 3469/98*e^6 + 29765/98*e^5 - 123857/98*e^4 + 126109/49*e^3 - 105502/49*e^2 + 807/14*e + 49089/98, -48/49*e^7 + 1072/49*e^6 - 9284/49*e^5 + 38904/49*e^4 - 79452/49*e^3 + 66016/49*e^2 - 114/7*e - 15620/49, 59/98*e^7 - 1285/98*e^6 + 10795/98*e^5 - 43581/98*e^4 + 42515/49*e^3 - 33402/49*e^2 - 111/14*e + 18093/98, 235/98*e^7 - 5211/98*e^6 + 45023/98*e^5 - 189771/98*e^4 + 197977/49*e^3 - 174526/49*e^2 + 483/2*e + 82483/98, 66/49*e^7 - 1474/49*e^6 + 12888/49*e^5 - 55306/49*e^4 + 118336/49*e^3 - 107971/49*e^2 + 1324/7*e + 25716/49, 237/49*e^7 - 5251/49*e^6 + 45327/49*e^5 - 190867/49*e^4 + 397672/49*e^3 - 348872/49*e^2 + 2909/7*e + 84101/49, -319/98*e^7 + 7059/98*e^6 - 60675/98*e^5 + 253233/98*e^4 - 259633/49*e^3 + 221636/49*e^2 - 2785/14*e - 105919/98, -5/49*e^7 + 128/49*e^6 - 1257/49*e^5 + 5939/49*e^4 - 13752/49*e^3 + 13606/49*e^2 - 291/7*e - 2456/49, 16/7*e^7 - 355/7*e^6 + 3076/7*e^5 - 13045/7*e^4 + 27520/7*e^3 - 24747/7*e^2 + 280*e + 5937/7, 39/49*e^7 - 829/49*e^6 + 6761/49*e^5 - 26223/49*e^4 + 48054/49*e^3 - 33142/49*e^2 - 531/7*e + 7639/49, 184/49*e^7 - 4086/49*e^6 + 35346/49*e^5 - 149104/49*e^4 + 310936/49*e^3 - 272414/49*e^2 + 2262/7*e + 65472/49, 285/98*e^7 - 6309/98*e^6 + 54289/98*e^5 - 227069/98*e^4 + 233417/49*e^3 - 198638/49*e^2 + 1675/14*e + 95689/98, 583/98*e^7 - 12843/98*e^6 + 110043/98*e^5 - 458721/98*e^4 + 470923/49*e^3 - 403439/49*e^2 + 5305/14*e + 189169/98, -157/98*e^7 + 3441/98*e^6 - 29513/98*e^5 + 124333/98*e^4 - 130911/49*e^3 + 117878/49*e^2 - 2591/14*e - 56901/98, -1/98*e^7 + 41/98*e^6 - 537/98*e^5 + 3033/98*e^4 - 3737/49*e^3 + 2874/49*e^2 + 461/14*e - 1173/98, 11/7*e^7 - 250/7*e^6 + 2215/7*e^5 - 9578/7*e^4 + 20488/7*e^3 - 2630*e^2 + 1131/7*e + 4484/7, -589/98*e^7 + 13103/98*e^6 - 113489/98*e^5 + 478935/98*e^4 - 499029/49*e^3 + 436300/49*e^2 - 6631/14*e - 212195/98, 32/7*e^7 - 709/7*e^6 + 6122/7*e^5 - 25792/7*e^4 + 53752/7*e^3 - 47088/7*e^2 + 2672/7*e + 11229/7, -93/98*e^7 + 2063/98*e^6 - 17825/98*e^5 + 75051/98*e^4 - 77943/49*e^3 + 67740/49*e^2 - 1091/14*e - 33251/98, -109/49*e^7 + 2390/49*e^6 - 20369/49*e^5 + 84386/49*e^4 - 172080/49*e^3 + 146570/49*e^2 - 957/7*e - 35226/49, 160/49*e^7 - 3550/49*e^6 + 30704/49*e^5 - 129652/49*e^4 + 271210/49*e^3 - 239210/49*e^2 + 282*e + 58936/49, -3/98*e^7 + 39/98*e^6 - 71/98*e^5 - 1233/98*e^4 + 4077/49*e^3 - 9130/49*e^2 + 209/2*e + 4601/98, -271/49*e^7 + 6015/49*e^6 - 52035/49*e^5 + 219635/49*e^4 - 458434/49*e^3 + 401504/49*e^2 - 3099/7*e - 96599/49, -193/49*e^7 + 4245/49*e^6 - 36280/49*e^5 + 150571/49*e^4 - 306711/49*e^3 + 258612/49*e^2 - 1210/7*e - 61609/49, -206/49*e^7 + 4554/49*e^6 - 39138/49*e^5 + 163526/49*e^4 - 336204/49*e^3 + 287822/49*e^2 - 1614/7*e - 69578/49, 191/49*e^7 - 4212/49*e^6 + 36137/49*e^5 - 150924/49*e^4 + 310824/49*e^3 - 267892/49*e^2 + 1999/7*e + 63526/49, -171/49*e^7 + 3812/49*e^6 - 33097/49*e^5 + 140062/49*e^4 - 292615/49*e^3 + 255678/49*e^2 - 1854/7*e - 61360/49, -373/98*e^7 + 8265/98*e^6 - 71193/98*e^5 + 298225/98*e^4 - 307669/49*e^3 + 265140/49*e^2 - 3447/14*e - 127877/98, -30/49*e^7 + 663/49*e^6 - 5764/49*e^5 + 24728/49*e^4 - 53112/49*e^3 + 48379/49*e^2 - 456/7*e - 11838/49, 69/14*e^7 - 1541/14*e^6 + 13393/14*e^5 - 56677/14*e^4 + 59151/7*e^3 - 51677/7*e^2 + 779/2*e + 24965/14, -99/49*e^7 + 2134/49*e^6 - 17855/49*e^5 + 72410/49*e^4 - 143498/49*e^3 + 115928/49*e^2 - 67/7*e - 27080/49, -18/7*e^7 + 402/7*e^6 - 3492/7*e^5 + 14764/7*e^4 - 30792/7*e^3 + 26947/7*e^2 - 230*e - 6456/7, -209/49*e^7 + 4635/49*e^6 - 39979/49*e^5 + 167753/49*e^4 - 346768/49*e^3 + 299711/49*e^2 - 2137/7*e - 71879/49, 425/98*e^7 - 9473/98*e^6 + 82275/98*e^5 - 348561/98*e^4 + 365136/49*e^3 - 321726/49*e^2 + 5517/14*e + 155413/98, 66/49*e^7 - 1523/49*e^6 + 13672/49*e^5 - 59765/49*e^4 + 128920/49*e^3 - 116742/49*e^2 + 1226/7*e + 27333/49, -229/98*e^7 + 5063/98*e^6 - 43565/98*e^5 + 182549/98*e^4 - 188589/49*e^3 + 162329/49*e^2 - 1751/14*e - 78385/98, 163/49*e^7 - 3589/49*e^6 + 30775/49*e^5 - 128615/49*e^4 + 265310/49*e^3 - 228594/49*e^2 + 215*e + 54923/49, 83/49*e^7 - 1835/49*e^6 + 15857/49*e^5 - 67205/49*e^4 + 142298/49*e^3 - 129331/49*e^2 + 1441/7*e + 32189/49, 219/98*e^7 - 4919/98*e^6 + 43039/98*e^5 - 183663/98*e^4 + 193751/49*e^3 - 171592/49*e^2 + 2825/14*e + 85051/98, 9/14*e^7 - 197/14*e^6 + 1689/14*e^5 - 7121/14*e^4 + 7509/7*e^3 - 6746/7*e^2 + 825/14*e + 3609/14, -64/49*e^7 + 1413/49*e^6 - 12150/49*e^5 + 50941/49*e^4 - 105642/49*e^3 + 92464/49*e^2 - 887/7*e - 22215/49, 324/49*e^7 - 7124/49*e^6 + 60924/49*e^5 - 253530/49*e^4 + 519984/49*e^3 - 445440/49*e^2 + 2792/7*e + 107136/49, -113/98*e^7 + 2533/98*e^6 - 22377/98*e^5 + 97953/98*e^4 - 108191/49*e^3 + 103079/49*e^2 - 2831/14*e - 52245/98, -57/49*e^7 + 1245/49*e^6 - 10589/49*e^5 + 43857/49*e^4 - 89388/49*e^3 + 75314/49*e^2 - 375/7*e - 16279/49, -88/49*e^7 + 1914/49*e^6 - 16134/49*e^5 + 65794/49*e^4 - 130864/49*e^3 + 106383/49*e^2 - 304/7*e - 24502/49, 151/98*e^7 - 3405/98*e^6 + 30043/98*e^5 - 129809/98*e^4 + 138869/49*e^3 - 123797/49*e^2 + 1805/14*e + 57129/98, -251/98*e^7 + 5447/98*e^6 - 45719/98*e^5 + 185071/98*e^4 - 182015/49*e^3 + 145960/49*e^2 - 561/14*e - 66923/98, -26/49*e^7 + 625/49*e^6 - 5926/49*e^5 + 27849/49*e^4 - 65993/49*e^3 + 67324/49*e^2 - 1027/7*e - 18787/49, -181/49*e^7 + 4019/49*e^6 - 34778/49*e^5 + 146893/49*e^4 - 307281/49*e^3 + 271130/49*e^2 - 354*e - 64165/49, 17/7*e^7 - 379/7*e^6 + 3285/7*e^5 - 13847/7*e^4 + 28764/7*e^3 - 25104/7*e^2 + 1639/7*e + 5833/7, 135/49*e^7 - 2994/49*e^6 + 25861/49*e^5 - 108868/49*e^4 + 226264/49*e^3 - 196982/49*e^2 + 1537/7*e + 46544/49, -4/7*e^7 + 82/7*e^6 - 640/7*e^5 + 2340/7*e^4 - 3905/7*e^3 + 310*e^2 + 647/7*e - 578/7, -39/14*e^7 + 869/14*e^6 - 7555/14*e^5 + 4583/2*e^4 - 33687/7*e^3 + 29572/7*e^2 - 2915/14*e - 2023/2, -268/49*e^7 + 5948/49*e^6 - 51418/49*e^5 + 216738/49*e^4 - 451888/49*e^3 + 397280/49*e^2 - 3574/7*e - 94900/49, 375/49*e^7 - 8270/49*e^6 + 71035/49*e^5 - 297466/49*e^4 + 615586/49*e^3 - 534678/49*e^2 + 3945/7*e + 128774/49, 635/98*e^7 - 14037/98*e^6 + 120803/98*e^5 - 506453/98*e^4 + 523833/49*e^3 - 453179/49*e^2 + 879/2*e + 217377/98, -155/98*e^7 + 3485/98*e^6 - 30651/98*e^5 + 132393/98*e^4 - 143135/49*e^3 + 133368/49*e^2 - 503/2*e - 65461/98, 52/49*e^7 - 1222/49*e^6 + 11208/49*e^5 - 50294/49*e^4 + 112190/49*e^3 - 106431/49*e^2 + 1318/7*e + 27550/49, -181/49*e^7 + 4026/49*e^6 - 34841/49*e^5 + 146676/49*e^4 - 303704/49*e^3 + 260924/49*e^2 - 1563/7*e - 61428/49, 251/49*e^7 - 5573/49*e^6 + 48127/49*e^5 - 202137/49*e^4 + 417636/49*e^3 - 358210/49*e^2 + 1913/7*e + 86159/49, -191/98*e^7 + 4107/98*e^6 - 34163/98*e^5 + 137127/98*e^4 - 133803/49*e^3 + 106268/49*e^2 - 93/14*e - 51759/98, -74/49*e^7 + 1641/49*e^6 - 14118/49*e^5 + 58885/49*e^4 - 120406/49*e^3 + 102092/49*e^2 - 558/7*e - 23963/49, -95/98*e^7 + 2145/98*e^6 - 18899/98*e^5 + 81411/98*e^4 - 86985/49*e^3 + 78339/49*e^2 - 1429/14*e - 35695/98, -157/98*e^7 + 3441/98*e^6 - 29121/98*e^5 + 118649/98*e^4 - 117191/49*e^3 + 93868/49*e^2 - 99/14*e - 44357/98, 276/49*e^7 - 6066/49*e^6 + 51864/49*e^5 - 215711/49*e^4 + 441414/49*e^3 - 374839/49*e^2 + 1814/7*e + 89325/49, -33/98*e^7 + 779/98*e^6 - 7165/98*e^5 + 32035/98*e^4 - 35121/49*e^3 + 32206/49*e^2 - 1031/14*e - 13047/98, 7/2*e^7 - 1081/14*e^6 + 9281/14*e^5 - 38813/14*e^4 + 5729*e^3 - 34976/7*e^2 + 4605/14*e + 16425/14, -345/49*e^7 + 7635/49*e^6 - 65817/49*e^5 + 276623/49*e^4 - 574430/49*e^3 + 500012/49*e^2 - 3595/7*e - 121325/49, -24/49*e^7 + 508/49*e^6 - 4096/49*e^5 + 15518/49*e^4 - 26986/49*e^3 + 15816/49*e^2 + 65*e - 1706/49, 41/98*e^7 - 953/98*e^6 + 8801/98*e^5 - 40689/98*e^4 + 48063/49*e^3 - 49668/49*e^2 + 1527/14*e + 29725/98, 86/49*e^7 - 1853/49*e^6 + 15494/49*e^5 - 62899/49*e^4 + 125667/49*e^3 - 105184/49*e^2 + 97*e + 25411/49, -302/49*e^7 + 6677/49*e^6 - 57468/49*e^5 + 240907/49*e^4 - 498048/49*e^3 + 429990/49*e^2 - 2900/7*e - 102855/49, -263/98*e^7 + 5869/98*e^6 - 51043/98*e^5 + 216385/98*e^4 - 225977/49*e^3 + 195414/49*e^2 - 255/2*e - 96609/98, 48/49*e^7 - 1093/49*e^6 + 9816/49*e^5 - 43643/49*e^4 + 97680/49*e^3 - 94198/49*e^2 + 1464/7*e + 21913/49, -148/49*e^7 + 3247/49*e^6 - 27578/49*e^5 + 113171/49*e^4 - 226308/49*e^3 + 185144/49*e^2 - 82*e - 41227/49, 83/49*e^7 - 1849/49*e^6 + 16081/49*e^5 - 68388/49*e^4 + 144258/49*e^3 - 128323/49*e^2 + 1053/7*e + 31370/49, 5/14*e^7 - 117/14*e^6 + 1053/14*e^5 - 4537/14*e^4 + 4685/7*e^3 - 3804/7*e^2 - 155/14*e + 1745/14, 180/49*e^7 - 4006/49*e^6 + 34738/49*e^5 - 147010/49*e^4 + 308284/49*e^3 - 273754/49*e^2 + 393*e + 65568/49, -456/49*e^7 + 10107/49*e^6 - 87260/49*e^5 + 367369/49*e^4 - 764692/49*e^3 + 669152/49*e^2 - 5450/7*e - 160759/49, 351/49*e^7 - 7804/49*e^6 + 67611/49*e^5 - 285742/49*e^4 + 597322/49*e^3 - 525540/49*e^2 + 4587/7*e + 126228/49, -167/98*e^7 + 3725/98*e^6 - 32475/98*e^5 + 138577/98*e^4 - 146721/49*e^3 + 131064/49*e^2 - 2481/14*e - 63801/98, 13/14*e^7 - 291/14*e^6 + 2549/14*e^5 - 10951/14*e^4 + 11705/7*e^3 - 1514*e^2 + 1665/14*e + 4927/14, -311/98*e^7 + 6871/98*e^6 - 59207/98*e^5 + 249227/98*e^4 - 259921/49*e^3 + 228394/49*e^2 - 4021/14*e - 107847/98, 190/49*e^7 - 4227/49*e^6 + 36594/49*e^5 - 154191/49*e^4 + 320010/49*e^3 - 276438/49*e^2 + 1587/7*e + 65937/49, 18/49*e^7 - 374/49*e^6 + 2960/49*e^5 - 10998/49*e^4 + 18696/49*e^3 - 10406/49*e^2 - 471/7*e + 1738/49, -677/98*e^7 + 15059/98*e^6 - 130393/98*e^5 + 549993/98*e^4 - 572497/49*e^3 + 499127/49*e^2 - 7227/14*e - 240953/98] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19, 19, w^2 - 2*w - 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]