/* 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([25, 5, -11, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, 1/5*w^3 - 1/5*w^2 - 11/5*w]) primes_array = [ [5, 5, 1/5*w^3 + 4/5*w^2 - 11/5*w - 7],\ [5, 5, 1/5*w^3 - 6/5*w^2 - 1/5*w + 4],\ [11, 11, w + 1],\ [11, 11, 1/5*w^3 - 1/5*w^2 - 11/5*w + 2],\ [16, 2, 2],\ [19, 19, -1/5*w^3 + 1/5*w^2 + 1/5*w + 1],\ [19, 19, 1/5*w^3 - 1/5*w^2 - 11/5*w],\ [19, 19, -2/5*w^3 + 2/5*w^2 + 17/5*w],\ [19, 19, w - 1],\ [29, 29, w^2 - w - 8],\ [29, 29, 2/5*w^3 - 2/5*w^2 - 7/5*w + 2],\ [31, 31, 1/5*w^3 - 1/5*w^2 - 1/5*w + 2],\ [31, 31, 2/5*w^3 - 2/5*w^2 - 17/5*w + 3],\ [61, 61, -2/5*w^3 - 3/5*w^2 + 12/5*w + 5],\ [61, 61, -4/5*w^3 - 6/5*w^2 + 39/5*w + 15],\ [61, 61, 3/5*w^3 + 2/5*w^2 - 18/5*w - 3],\ [61, 61, 7/5*w^3 + 3/5*w^2 - 62/5*w - 13],\ [71, 71, 1/5*w^3 - 6/5*w^2 - 6/5*w + 4],\ [71, 71, w^2 - 8],\ [79, 79, 3/5*w^3 + 12/5*w^2 - 33/5*w - 22],\ [79, 79, 1/5*w^3 + 4/5*w^2 - 11/5*w - 9],\ [81, 3, -3],\ [101, 101, 3/5*w^3 + 7/5*w^2 - 28/5*w - 15],\ [101, 101, 1/5*w^3 + 9/5*w^2 - 16/5*w - 16],\ [121, 11, 3/5*w^3 - 3/5*w^2 - 18/5*w + 1],\ [131, 131, 1/5*w^3 + 4/5*w^2 - 16/5*w - 8],\ [131, 131, w^2 - 2*w - 2],\ [149, 149, 4/5*w^3 + 1/5*w^2 - 29/5*w - 5],\ [149, 149, 4/5*w^3 - 9/5*w^2 - 19/5*w + 6],\ [151, 151, 2/5*w^3 + 3/5*w^2 - 17/5*w - 3],\ [151, 151, -2/5*w^3 + 7/5*w^2 + 7/5*w - 8],\ [151, 151, 4/5*w^3 + 1/5*w^2 - 29/5*w - 2],\ [151, 151, -4/5*w^3 + 9/5*w^2 + 19/5*w - 9],\ [179, 179, -3/5*w^3 + 8/5*w^2 + 18/5*w - 6],\ [179, 179, 2/5*w^3 + 3/5*w^2 - 12/5*w - 6],\ [211, 211, 1/5*w^3 + 4/5*w^2 - 6/5*w - 10],\ [211, 211, 2/5*w^3 - 7/5*w^2 - 12/5*w + 2],\ [229, 229, 6/5*w^3 - 11/5*w^2 - 41/5*w + 11],\ [229, 229, 2*w^2 - 2*w - 9],\ [229, 229, -4/5*w^3 - 1/5*w^2 + 19/5*w + 2],\ [229, 229, -3/5*w^3 + 3/5*w^2 + 28/5*w - 3],\ [239, 239, 11/5*w^3 + 4/5*w^2 - 96/5*w - 19],\ [239, 239, -6/5*w^3 + 1/5*w^2 + 51/5*w + 3],\ [241, 241, 1/5*w^3 + 4/5*w^2 - 1/5*w - 6],\ [241, 241, 4/5*w^3 - 4/5*w^2 - 29/5*w - 1],\ [251, 251, -1/5*w^3 + 6/5*w^2 + 11/5*w - 12],\ [251, 251, -1/5*w^3 + 11/5*w^2 + 1/5*w - 15],\ [269, 269, 2/5*w^3 + 3/5*w^2 - 17/5*w - 2],\ [269, 269, -2/5*w^3 + 7/5*w^2 + 7/5*w - 9],\ [271, 271, 1/5*w^3 - 1/5*w^2 + 4/5*w],\ [271, 271, 3/5*w^3 - 3/5*w^2 - 28/5*w + 2],\ [281, 281, w^3 - 3*w^2 - 4*w + 13],\ [281, 281, -3/5*w^3 + 3/5*w^2 + 28/5*w - 6],\ [281, 281, -6/5*w^3 + 26/5*w^2 + 11/5*w - 16],\ [281, 281, w^3 + w^2 - 8*w - 9],\ [289, 17, 2/5*w^3 + 3/5*w^2 - 7/5*w - 5],\ [289, 17, 4/5*w^3 - 9/5*w^2 - 29/5*w + 8],\ [311, 311, -w^2 + 2*w + 11],\ [311, 311, -1/5*w^3 + 6/5*w^2 + 1/5*w - 1],\ [311, 311, 1/5*w^3 + 4/5*w^2 - 16/5*w + 1],\ [311, 311, -1/5*w^3 - 4/5*w^2 + 11/5*w + 10],\ [349, 349, -1/5*w^3 - 9/5*w^2 + 11/5*w + 16],\ [349, 349, 2/5*w^3 - 12/5*w^2 - 7/5*w + 7],\ [359, 359, -4/5*w^3 + 4/5*w^2 + 19/5*w - 1],\ [359, 359, -w^3 + 3*w^2 + 5*w - 12],\ [359, 359, w^3 - w^2 - 7*w + 2],\ [359, 359, 4/5*w^3 + 6/5*w^2 - 29/5*w - 11],\ [379, 379, 4/5*w^3 + 6/5*w^2 - 34/5*w - 9],\ [379, 379, 3/5*w^3 - 3/5*w^2 - 28/5*w + 7],\ [389, 389, w^2 - 3*w - 8],\ [389, 389, -4/5*w^3 + 14/5*w^2 + 19/5*w - 16],\ [401, 401, -3*w^2 + 2*w + 23],\ [401, 401, 1/5*w^3 - 16/5*w^2 + 4/5*w + 11],\ [409, 409, -w^3 + 2*w^2 + 3*w - 7],\ [409, 409, 7/5*w^3 - 2/5*w^2 - 57/5*w - 2],\ [419, 419, -1/5*w^3 + 1/5*w^2 + 16/5*w - 2],\ [419, 419, 1/5*w^3 - 1/5*w^2 - 16/5*w],\ [421, 421, 2/5*w^3 + 3/5*w^2 - 27/5*w - 3],\ [421, 421, 1/5*w^3 + 4/5*w^2 + 4/5*w - 3],\ [439, 439, -w^3 + 3*w^2 + 5*w - 16],\ [439, 439, -4/5*w^3 - 6/5*w^2 + 29/5*w + 7],\ [439, 439, -3/5*w^3 + 13/5*w^2 + 3/5*w - 11],\ [439, 439, 4/5*w^3 + 6/5*w^2 - 39/5*w - 10],\ [449, 449, 2/5*w^3 - 12/5*w^2 - 2/5*w + 5],\ [449, 449, 4/5*w^3 - 24/5*w^2 - 4/5*w + 15],\ [461, 461, -1/5*w^3 - 4/5*w^2 - 4/5*w + 4],\ [461, 461, 2*w^2 - 2*w - 11],\ [461, 461, 3/5*w^3 + 2/5*w^2 - 33/5*w - 4],\ [479, 479, -w^3 + 3*w^2 + 6*w - 14],\ [479, 479, -3/5*w^3 + 3/5*w^2 + 28/5*w + 3],\ [499, 499, 2/5*w^3 + 8/5*w^2 - 17/5*w - 6],\ [499, 499, -3/5*w^3 + 13/5*w^2 + 13/5*w - 17],\ [509, 509, -w^3 + 2*w^2 + 4*w - 6],\ [509, 509, 6/5*w^3 - 1/5*w^2 - 46/5*w - 4],\ [521, 521, -2/5*w^3 + 2/5*w^2 + 7/5*w - 7],\ [521, 521, -3/5*w^3 + 3/5*w^2 + 23/5*w - 8],\ [529, 23, -7/5*w^3 + 17/5*w^2 + 42/5*w - 15],\ [529, 23, 2/5*w^3 + 13/5*w^2 - 27/5*w - 21],\ [541, 541, 1/5*w^3 - 11/5*w^2 - 1/5*w + 10],\ [541, 541, 3/5*w^3 - 8/5*w^2 - 13/5*w + 13],\ [541, 541, -2*w^2 + w + 13],\ [541, 541, 3/5*w^3 + 2/5*w^2 - 23/5*w + 2],\ [569, 569, w^3 - 2*w^2 - 5*w + 7],\ [569, 569, -1/5*w^3 + 1/5*w^2 + 1/5*w - 6],\ [571, 571, w^2 + w - 9],\ [571, 571, -2/5*w^3 + 12/5*w^2 + 7/5*w - 12],\ [571, 571, 1/5*w^3 + 9/5*w^2 - 11/5*w - 11],\ [571, 571, -2/5*w^3 + 7/5*w^2 + 17/5*w - 4],\ [601, 601, -3/5*w^3 + 13/5*w^2 + 18/5*w - 11],\ [601, 601, -4/5*w^3 + 4/5*w^2 + 34/5*w + 1],\ [631, 631, 2/5*w^3 + 18/5*w^2 - 27/5*w - 30],\ [631, 631, 3/5*w^3 - 23/5*w^2 - 3/5*w + 15],\ [661, 661, -2*w^3 + 17*w + 12],\ [661, 661, -9/5*w^3 + 4/5*w^2 + 74/5*w + 1],\ [691, 691, -7/5*w^3 - 18/5*w^2 + 72/5*w + 35],\ [691, 691, 6/5*w^3 - 31/5*w^2 - 6/5*w + 19],\ [701, 701, -1/5*w^3 + 6/5*w^2 + 16/5*w - 6],\ [701, 701, 2/5*w^3 - 7/5*w^2 - 22/5*w + 8],\ [709, 709, -3/5*w^3 + 13/5*w^2 + 13/5*w - 18],\ [709, 709, 1/5*w^3 + 14/5*w^2 - 11/5*w - 20],\ [709, 709, -2/5*w^3 - 8/5*w^2 + 17/5*w + 5],\ [709, 709, 1/5*w^3 + 4/5*w^2 - 21/5*w - 10],\ [719, 719, -3/5*w^3 + 8/5*w^2 + 13/5*w - 12],\ [719, 719, 3/5*w^3 + 2/5*w^2 - 23/5*w + 1],\ [719, 719, -7/5*w^3 + 17/5*w^2 + 32/5*w - 14],\ [719, 719, 7/5*w^3 + 3/5*w^2 - 52/5*w - 8],\ [739, 739, 1/5*w^3 - 1/5*w^2 - 11/5*w - 5],\ [739, 739, w - 6],\ [761, 761, -4/5*w^3 + 9/5*w^2 + 19/5*w - 11],\ [761, 761, 4/5*w^3 + 1/5*w^2 - 29/5*w],\ [769, 769, 3/5*w^3 - 13/5*w^2 - 13/5*w + 8],\ [769, 769, -2/5*w^3 - 8/5*w^2 + 17/5*w + 15],\ [769, 769, 7/5*w^3 - 17/5*w^2 - 37/5*w + 18],\ [769, 769, -6/5*w^3 - 4/5*w^2 + 41/5*w + 5],\ [809, 809, -1/5*w^3 + 6/5*w^2 - 4/5*w - 14],\ [809, 809, -2/5*w^3 - 3/5*w^2 + 22/5*w - 4],\ [809, 809, -6/5*w^3 + 6/5*w^2 + 41/5*w - 5],\ [809, 809, w^3 - w^2 - 5*w + 4],\ [821, 821, -3/5*w^3 - 17/5*w^2 + 33/5*w + 30],\ [821, 821, -4/5*w^3 + 24/5*w^2 + 9/5*w - 15],\ [829, 829, 7/5*w^3 - 12/5*w^2 - 52/5*w + 10],\ [829, 829, -1/5*w^3 + 11/5*w^2 - 4/5*w - 19],\ [829, 829, -13/5*w^3 + 3/5*w^2 + 108/5*w + 10],\ [829, 829, -w^3 + 4*w^2 + 5*w - 23],\ [839, 839, 4/5*w^3 - 9/5*w^2 - 24/5*w + 4],\ [839, 839, 3/5*w^3 + 2/5*w^2 - 18/5*w - 8],\ [841, 29, -w^3 + w^2 + 6*w - 4],\ [859, 859, 6/5*w^3 - 11/5*w^2 - 36/5*w + 9],\ [859, 859, w^3 - 6*w - 3],\ [881, 881, 4/5*w^3 - 4/5*w^2 - 9/5*w - 1],\ [881, 881, 9/5*w^3 - 24/5*w^2 - 19/5*w + 14],\ [881, 881, -w^3 + 6*w + 2],\ [881, 881, 1/5*w^3 - 1/5*w^2 - 1/5*w - 6],\ [911, 911, w^3 - w^2 - 5*w + 1],\ [911, 911, 6/5*w^3 - 6/5*w^2 - 41/5*w + 2],\ [919, 919, -7/5*w^3 + 12/5*w^2 + 42/5*w - 7],\ [919, 919, -6/5*w^3 + 1/5*w^2 + 36/5*w + 5],\ [929, 929, -2/5*w^3 - 8/5*w^2 + 17/5*w + 16],\ [929, 929, -3/5*w^3 + 13/5*w^2 + 13/5*w - 7],\ [961, 31, w^3 - w^2 - 6*w + 2],\ [971, 971, 8/5*w^3 - 13/5*w^2 - 48/5*w + 6],\ [971, 971, -2/5*w^3 - 3/5*w^2 + 22/5*w],\ [971, 971, 7/5*w^3 - 7/5*w^2 - 57/5*w + 7],\ [971, 971, -1/5*w^3 + 6/5*w^2 - 4/5*w - 10],\ [991, 991, 2/5*w^3 + 8/5*w^2 - 22/5*w - 7],\ [991, 991, -2/5*w^3 + 12/5*w^2 + 2/5*w - 15]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 12*x^9 + 35*x^8 + 96*x^7 - 618*x^6 + 354*x^5 + 2511*x^4 - 3572*x^3 - 2269*x^2 + 5886*x - 2268 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -317/1044*e^9 + 347/116*e^8 - 2297/522*e^7 - 6305/174*e^6 + 8929/87*e^5 + 17357/174*e^4 - 52437/116*e^3 + 29131/1044*e^2 + 289897/522*e - 7790/29, -437/2088*e^9 + 1453/696*e^8 - 1795/522*e^7 - 2027/87*e^6 + 25091/348*e^5 + 4223/87*e^4 - 66579/232*e^3 + 115753/2088*e^2 + 318871/1044*e - 8711/58, -95/232*e^9 + 2747/696*e^8 - 446/87*e^7 - 2915/58*e^6 + 15297/116*e^5 + 9161/58*e^4 - 143341/232*e^3 - 3453/232*e^2 + 284479/348*e - 21827/58, -215/2088*e^9 + 267/232*e^8 - 803/261*e^7 - 1327/174*e^6 + 15203/348*e^5 - 2473/87*e^4 - 22329/232*e^3 + 266797/2088*e^2 - 28817/1044*e - 269/58, -100/261*e^9 + 1325/348*e^8 - 3295/522*e^7 - 3614/87*e^6 + 11243/87*e^5 + 13849/174*e^4 - 28645/58*e^3 + 111695/1044*e^2 + 128011/261*e - 6869/29, -1, 311/2088*e^9 - 887/696*e^8 + 122/261*e^7 + 3475/174*e^6 - 12011/348*e^5 - 16009/174*e^4 + 49581/232*e^3 + 189977/2088*e^2 - 368845/1044*e + 8395/58, -421/2088*e^9 + 1255/696*e^8 - 286/261*e^7 - 2428/87*e^6 + 18895/348*e^5 + 21875/174*e^4 - 75783/232*e^3 - 233809/2088*e^2 + 554687/1044*e - 12915/58, 79/348*e^9 - 689/348*e^8 + 37/58*e^7 + 1933/58*e^6 - 1699/29*e^5 - 9601/58*e^4 + 46141/116*e^3 + 57331/348*e^2 - 40453/58*e + 8742/29, 19/696*e^9 - 187/696*e^8 + 80/87*e^7 - 57/58*e^6 - 695/116*e^5 + 1018/29*e^4 - 10713/232*e^3 - 49085/696*e^2 + 59501/348*e - 4109/58, 977/2088*e^9 - 3191/696*e^8 + 1580/261*e^7 + 5219/87*e^6 - 54899/348*e^5 - 34957/174*e^4 + 176995/232*e^3 + 97097/2088*e^2 - 1090879/1044*e + 27805/58, -80/261*e^9 + 973/348*e^8 - 535/261*e^7 - 3709/87*e^6 + 7672/87*e^5 + 32429/174*e^4 - 30253/58*e^3 - 147893/1044*e^2 + 441649/522*e - 10982/29, -67/696*e^9 + 173/232*e^8 + 14/87*e^7 - 349/29*e^6 + 1709/116*e^5 + 3381/58*e^4 - 23379/232*e^3 - 48715/696*e^2 + 61001/348*e - 3527/58, -1175/2088*e^9 + 1211/232*e^8 - 2167/522*e^7 - 13933/174*e^6 + 59147/348*e^5 + 30701/87*e^4 - 233369/232*e^3 - 562379/2088*e^2 + 1698853/1044*e - 42321/58, -775/1044*e^9 + 1241/174*e^8 - 2216/261*e^7 - 16723/174*e^6 + 20897/87*e^5 + 29639/87*e^4 - 140293/116*e^3 - 60899/522*e^2 + 899429/522*e - 22779/29, 235/348*e^9 - 2261/348*e^8 + 519/58*e^7 + 4535/58*e^6 - 6167/29*e^5 - 12375/58*e^4 + 106393/116*e^3 - 14753/348*e^2 - 63315/58*e + 14622/29, 1063/2088*e^9 - 3349/696*e^8 + 2567/522*e^7 + 11891/174*e^6 - 55099/348*e^5 - 23371/87*e^4 + 196529/232*e^3 + 334063/2088*e^2 - 1326641/1044*e + 32599/58, 17/522*e^9 - 127/174*e^8 + 1109/261*e^7 - 407/174*e^6 - 7555/174*e^5 + 16901/174*e^4 + 1030/29*e^3 - 66281/261*e^2 + 94297/522*e - 509/29, 1763/2088*e^9 - 5791/696*e^8 + 3209/261*e^7 + 8738/87*e^6 - 99365/348*e^5 - 23813/87*e^4 + 290885/232*e^3 - 173755/2088*e^2 - 1605247/1044*e + 42887/58, -719/2088*e^9 + 809/232*e^8 - 3199/522*e^7 - 3257/87*e^6 + 42293/348*e^5 + 5804/87*e^4 - 106329/232*e^3 + 231175/2088*e^2 + 464329/1044*e - 12901/58, -107/696*e^9 + 989/696*e^8 - 130/87*e^7 - 1071/58*e^6 + 4903/116*e^5 + 3637/58*e^4 - 44771/232*e^3 - 23321/696*e^2 + 83825/348*e - 5521/58, 43/58*e^9 - 2611/348*e^8 + 1121/87*e^7 + 2416/29*e^6 - 7724/29*e^5 - 9723/58*e^4 + 31003/29*e^3 - 27253/116*e^2 - 202889/174*e + 17510/29, -779/1044*e^9 + 2401/348*e^8 - 1543/261*e^7 - 8857/87*e^6 + 38471/174*e^5 + 36961/87*e^4 - 144981/116*e^3 - 310415/1044*e^2 + 1021609/522*e - 24976/29, 271/174*e^9 - 1683/116*e^8 + 1159/87*e^7 + 12205/58*e^6 - 27059/58*e^5 - 24865/29*e^4 + 148695/58*e^3 + 202193/348*e^2 - 340772/87*e + 49572/29, 1/8*e^9 - 35/24*e^8 + 14/3*e^7 + 11/2*e^6 - 227/4*e^5 + 82*e^4 + 543/8*e^3 - 2071/8*e^2 + 2273/12*e - 57/2, 971/1044*e^9 - 752/87*e^8 + 1951/261*e^7 + 11152/87*e^6 - 48443/174*e^5 - 93797/174*e^4 + 182723/116*e^3 + 198949/522*e^2 - 642899/261*e + 31977/29, 303/232*e^9 - 2915/232*e^8 + 981/58*e^7 + 4480/29*e^6 - 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71/261*e^7 - 10379/87*e^6 + 16517/87*e^5 + 113629/174*e^4 - 84135/58*e^3 - 781021/1044*e^2 + 1415063/522*e - 32413/29, 601/2088*e^9 - 2221/696*e^8 + 2239/261*e^7 + 1723/87*e^6 - 41011/348*e^5 + 8018/87*e^4 + 51263/232*e^3 - 762905/2088*e^2 + 203383/1044*e - 2683/58, 3011/2088*e^9 - 3115/232*e^8 + 3230/261*e^7 + 16871/87*e^6 - 149393/348*e^5 - 136993/174*e^4 + 542849/232*e^3 + 1146695/2088*e^2 - 3708625/1044*e + 87103/58, 679/232*e^9 - 19505/696*e^8 + 2699/87*e^7 + 11372/29*e^6 - 109351/116*e^5 - 86923/58*e^4 + 1150189/232*e^3 + 181311/232*e^2 - 2551447/348*e + 188659/58, -3989/2088*e^9 + 4329/232*e^8 - 6890/261*e^7 - 39943/174*e^6 + 221405/348*e^5 + 57158/87*e^4 - 665075/232*e^3 + 264679/2088*e^2 + 3783265/1044*e - 102371/58, 1567/522*e^9 - 10153/348*e^8 + 19859/522*e^7 + 65963/174*e^6 - 173513/174*e^5 - 107974/87*e^4 + 279253/58*e^3 + 174827/1044*e^2 - 3437473/522*e + 90288/29, 61/232*e^9 - 1853/696*e^8 + 392/87*e^7 + 1713/58*e^6 - 10583/116*e^5 - 3671/58*e^4 + 80799/232*e^3 - 10229/232*e^2 - 117841/348*e + 8631/58, 5491/2088*e^9 - 17183/696*e^8 + 6880/261*e^7 + 29275/87*e^6 - 277357/348*e^5 - 106549/87*e^4 + 941605/232*e^3 + 1111645/2088*e^2 - 6065111/1044*e + 153871/58, 25/72*e^9 - 31/8*e^8 + 103/9*e^7 + 55/3*e^6 - 1807/12*e^5 + 551/3*e^4 + 2111/8*e^3 - 47729/72*e^2 + 9151/36*e + 135/2, 1679/1044*e^9 - 1869/116*e^8 + 14567/522*e^7 + 14857/87*e^6 - 95981/174*e^5 - 24625/87*e^4 + 236053/116*e^3 - 580675/1044*e^2 - 494786/261*e + 27664/29, -163/174*e^9 + 3149/348*e^8 - 2473/174*e^7 - 2821/29*e^6 + 8580/29*e^5 + 9909/58*e^4 - 32137/29*e^3 + 101317/348*e^2 + 91465/87*e - 14746/29, -937/522*e^9 + 947/58*e^8 - 2467/261*e^7 - 46379/174*e^6 + 90389/174*e^5 + 222179/174*e^4 - 96537/29*e^3 - 305150/261*e^2 + 2960377/522*e - 72106/29, -35/522*e^9 + 125/174*e^8 - 1675/522*e^7 + 529/87*e^6 + 1700/87*e^5 - 11413/87*e^4 + 8831/58*e^3 + 135559/522*e^2 - 296371/522*e + 6720/29, 3463/2088*e^9 - 10487/696*e^8 + 2224/261*e^7 + 42971/174*e^6 - 166699/348*e^5 - 207131/174*e^4 + 717053/232*e^3 + 2333401/2088*e^2 - 5540981/1044*e + 130595/58, 97/72*e^9 - 101/8*e^8 + 233/18*e^7 + 526/3*e^6 - 4891/12*e^5 - 3959/6*e^4 + 16987/8*e^3 + 23353/72*e^2 - 111557/36*e + 2789/2, 89/58*e^9 - 1246/87*e^8 + 1142/87*e^7 + 6054/29*e^6 - 13416/29*e^5 - 24837/29*e^4 + 148319/58*e^3 + 16871/29*e^2 - 340363/87*e + 50368/29, 1685/1044*e^9 - 5935/348*e^8 + 19247/522*e^7 + 13273/87*e^6 - 108005/174*e^5 + 410/87*e^4 + 221915/116*e^3 - 1225735/1044*e^2 - 289838/261*e + 19838/29, -1807/1044*e^9 + 923/58*e^8 - 3104/261*e^7 - 21404/87*e^6 + 89695/174*e^5 + 189955/174*e^4 - 360259/116*e^3 - 213997/261*e^2 + 1333891/261*e - 67141/29, -74/87*e^9 + 227/29*e^8 - 484/87*e^7 - 7127/58*e^6 + 14605/58*e^5 + 32435/58*e^4 - 88935/58*e^3 - 81295/174*e^2 + 440935/174*e - 31332/29, -1793/1044*e^9 + 2831/174*e^8 - 9005/522*e^7 - 39731/174*e^6 + 47074/87*e^5 + 75919/87*e^4 - 333063/116*e^3 - 223651/522*e^2 + 1115813/261*e - 56073/29, 2551/1044*e^9 - 4313/174*e^8 + 11906/261*e^7 + 43999/174*e^6 - 75500/87*e^5 - 27851/87*e^4 + 360197/116*e^3 - 596599/522*e^2 - 1423109/522*e + 43393/29, -394/261*e^9 + 4771/348*e^8 - 1928/261*e^7 - 39583/174*e^6 + 76213/174*e^5 + 96605/87*e^4 - 83202/29*e^3 - 1086589/1044*e^2 + 1294252/261*e - 63333/29, -595/174*e^9 + 11387/348*e^8 - 3551/87*e^7 - 12235/29*e^6 + 31394/29*e^5 + 79177/58*e^4 - 149359/29*e^3 - 77249/348*e^2 + 1203827/174*e - 93440/29, 463/174*e^9 - 2955/116*e^8 + 2845/87*e^7 + 9315/29*e^6 - 24270/29*e^5 - 57319/58*e^4 + 111690/29*e^3 + 25679/348*e^2 - 865489/174*e + 66174/29, 461/2088*e^9 - 1721/696*e^8 + 1793/261*e^7 + 1295/87*e^6 - 33167/348*e^5 + 6958/87*e^4 + 45523/232*e^3 - 694645/2088*e^2 + 117503/1044*e + 1941/58, 81/232*e^9 - 2645/696*e^8 + 1303/174*e^7 + 1245/29*e^6 - 17317/116*e^5 - 2651/29*e^4 + 144903/232*e^3 - 31017/232*e^2 - 251257/348*e + 23889/58, -157/348*e^9 + 511/116*e^8 - 620/87*e^7 - 2683/58*e^6 + 4078/29*e^5 + 4405/58*e^4 - 55967/116*e^3 + 42917/348*e^2 + 32122/87*e - 4519/29, -1205/261*e^9 + 3881/87*e^8 - 29765/522*e^7 - 100739/174*e^6 + 261569/174*e^5 + 330323/174*e^4 - 418361/58*e^3 - 176821/522*e^2 + 2553155/261*e - 131403/29, -3769/1044*e^9 + 2037/58*e^8 - 12950/261*e^7 - 37094/87*e^6 + 204853/174*e^5 + 206473/174*e^4 - 599621/116*e^3 + 61007/261*e^2 + 1647631/261*e - 85965/29, 13/232*e^9 + 71/696*e^8 - 1291/174*e^7 + 1971/58*e^6 + 2377/116*e^5 - 21379/58*e^4 + 105775/232*e^3 + 148215/232*e^2 - 485627/348*e + 35081/58, 7/18*e^9 - 19/4*e^8 + 151/9*e^7 + 71/6*e^6 - 1157/6*e^5 + 995/3*e^4 + 335/2*e^3 - 34501/36*e^2 + 7333/9*e - 178, 3547/2088*e^9 - 11599/696*e^8 + 5815/261*e^7 + 18880/87*e^6 - 200533/348*e^5 - 62431/87*e^4 + 644749/232*e^3 + 298405/2088*e^2 - 3970607/1044*e + 99563/58, 277/696*e^9 - 923/232*e^8 + 568/87*e^7 + 1281/29*e^6 - 15563/116*e^5 - 5363/58*e^4 + 118229/232*e^3 - 59939/696*e^2 - 167951/348*e + 13749/58, -919/1044*e^9 + 805/87*e^8 - 9481/522*e^7 - 16729/174*e^6 + 30074/87*e^5 + 11438/87*e^4 - 152461/116*e^3 + 124445/261*e^2 + 348631/261*e - 22585/29, -7435/2088*e^9 + 22825/696*e^8 - 13889/522*e^7 - 85343/174*e^6 + 363055/348*e^5 + 181987/87*e^4 - 1387869/232*e^3 - 3262771/2088*e^2 + 9863249/1044*e - 239789/58, 2503/2088*e^9 - 8351/696*e^8 + 10673/522*e^7 + 22535/174*e^6 - 143287/348*e^5 - 41081/174*e^4 + 361245/232*e^3 - 771695/2088*e^2 - 1570799/1044*e + 44347/58, -1375/696*e^9 + 4455/232*e^8 - 2311/87*e^7 - 6884/29*e^6 + 75117/116*e^5 + 20031/29*e^4 - 678075/232*e^3 + 54227/696*e^2 + 1288247/348*e - 101031/58, 259/696*e^9 - 3587/696*e^8 + 566/29*e^7 + 554/29*e^6 - 28269/116*e^5 + 17291/58*e^4 + 108939/232*e^3 - 687257/696*e^2 + 35917/116*e + 5071/58, 2123/1044*e^9 - 1619/87*e^8 + 4138/261*e^7 + 23269/87*e^6 - 99923/174*e^5 - 187295/174*e^4 + 361035/116*e^3 + 390667/522*e^2 - 1218836/261*e + 57859/29, 2245/2088*e^9 - 6833/696*e^8 + 1751/522*e^7 + 31313/174*e^6 - 113977/348*e^5 - 169199/174*e^4 + 555871/232*e^3 + 2125471/2088*e^2 - 4611473/1044*e + 112615/58, -2821/522*e^9 + 18091/348*e^8 - 34607/522*e^7 - 58126/87*e^6 + 150940/87*e^5 + 372617/174*e^4 - 238312/29*e^3 - 285335/1044*e^2 + 2861900/261*e - 148423/29, 2831/696*e^9 - 26935/696*e^8 + 1344/29*e^7 + 14676/29*e^6 - 147113/116*e^5 - 98257/58*e^4 + 1420343/232*e^3 + 315539/696*e^2 - 965603/116*e + 218435/58, -1811/1044*e^9 + 462/29*e^8 - 7733/522*e^7 - 38579/174*e^6 + 42925/87*e^5 + 73285/87*e^4 - 298189/116*e^3 - 126149/261*e^2 + 975032/261*e - 47443/29, -1219/522*e^9 + 7601/348*e^8 - 10463/522*e^7 - 27805/87*e^6 + 61570/87*e^5 + 229955/174*e^4 - 113860/29*e^3 - 972269/1044*e^2 + 1576883/261*e - 76078/29, 6763/2088*e^9 - 20773/696*e^8 + 13157/522*e^7 + 76571/174*e^6 - 331111/348*e^5 - 159496/87*e^4 + 1247797/232*e^3 + 2653951/2088*e^2 - 8781509/1044*e + 215329/58, -1385/696*e^9 + 4731/232*e^8 - 6637/174*e^7 - 12201/58*e^6 + 84717/116*e^5 + 8231/29*e^4 - 625597/232*e^3 + 666487/696*e^2 + 888823/348*e - 82781/58, -1364/261*e^9 + 1465/29*e^8 - 17452/261*e^7 - 111017/174*e^6 + 294275/174*e^5 + 342083/174*e^4 - 453903/58*e^3 - 46009/522*e^2 + 5311933/522*e - 137743/29, 251/696*e^9 - 2681/696*e^8 + 892/87*e^7 + 595/29*e^6 - 15485/116*e^5 + 4324/29*e^4 + 40095/232*e^3 - 365359/696*e^2 + 148357/348*e - 5269/58, 299/116*e^9 - 746/29*e^8 + 1190/29*e^7 + 17267/58*e^6 - 25952/29*e^5 - 20583/29*e^4 + 434261/116*e^3 - 14610/29*e^2 - 250835/58*e + 60461/29, -127/87*e^9 + 2419/174*e^8 - 1087/58*e^7 - 9625/58*e^6 + 25913/58*e^5 + 25741/58*e^4 - 110441/58*e^3 + 8168/87*e^2 + 64864/29*e - 29378/29] 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, 1/5*w^3 - 1/5*w^2 - 11/5*w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]