/* 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, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([17, 17, -w - 3]) primes_array = [ [5, 5, w + 1],\ [5, 5, w - 1],\ [7, 7, -w + 2],\ [8, 2, 2],\ [11, 11, -w^2 + 2*w + 2],\ [17, 17, -w - 3],\ [17, 17, -w^2 + 2*w + 1],\ [17, 17, -w^2 + w + 4],\ [23, 23, -w^2 + 3],\ [27, 3, -3],\ [29, 29, w^2 - w - 8],\ [29, 29, w^2 - w - 3],\ [29, 29, w^2 - w - 1],\ [31, 31, w^2 - 2],\ [37, 37, 2*w - 5],\ [43, 43, w^2 - 2*w - 5],\ [47, 47, w^2 - 3*w - 2],\ [49, 7, w^2 + w - 4],\ [53, 53, w^2 - 2*w - 6],\ [71, 71, w - 5],\ [79, 79, w^2 - 10],\ [83, 83, -2*w^2 + 3*w + 7],\ [89, 89, 2*w^2 - w - 9],\ [97, 97, 3*w^2 - 4*w - 15],\ [107, 107, w^2 - 2*w - 10],\ [121, 11, w^2 - 5*w + 3],\ [127, 127, 2*w^2 - 3*w - 13],\ [131, 131, 3*w + 4],\ [137, 137, 2*w^2 - 3*w - 12],\ [139, 139, 2*w^2 - 3*w - 6],\ [149, 149, w^2 + w - 9],\ [151, 151, 2*w^2 - 11],\ [157, 157, w^2 + w - 8],\ [163, 163, 2*w^2 + w - 4],\ [173, 173, 3*w - 4],\ [179, 179, -w^2 + 2*w - 3],\ [193, 193, 3*w - 5],\ [197, 197, -w^2 + 3*w - 4],\ [197, 197, w^2 - 3*w - 7],\ [199, 199, 2*w^2 - w - 7],\ [211, 211, w^2 + 2*w - 5],\ [223, 223, 2*w^2 - 3*w - 3],\ [227, 227, w^2 - 2*w - 11],\ [227, 227, 2*w^2 + w - 9],\ [227, 227, 2*w^2 - 5],\ [229, 229, 2*w^2 - 13],\ [233, 233, 4*w - 3],\ [241, 241, 3*w^2 - w - 18],\ [257, 257, 2*w^2 + 2*w - 7],\ [269, 269, w^2 - w - 11],\ [271, 271, 2*w^2 - 2*w - 3],\ [277, 277, 2*w^2 - 4*w - 9],\ [277, 277, 2*w^2 - w - 5],\ [277, 277, w^2 + 2*w - 6],\ [281, 281, w^2 + 4*w - 3],\ [293, 293, 2*w^2 - 3*w - 17],\ [311, 311, w^2 - 12],\ [311, 311, 2*w^2 - 5*w - 6],\ [311, 311, 3*w^2 - 6*w - 10],\ [313, 313, -w^2 + 2*w - 4],\ [337, 337, -w^2 - 2*w - 4],\ [337, 337, w^2 + 2*w - 7],\ [337, 337, w^2 + 2*w - 12],\ [347, 347, -w^2 + 6*w - 6],\ [349, 349, -w - 7],\ [353, 353, 2*w^2 - 19],\ [359, 359, 2*w - 9],\ [383, 383, w^2 + 2*w - 16],\ [383, 383, w^2 + 3*w - 16],\ [383, 383, w^2 + 3*w - 5],\ [389, 389, -3*w^2 + 6*w + 5],\ [397, 397, 3*w^2 - 2*w - 13],\ [397, 397, 2*w^2 - 2*w - 17],\ [397, 397, w^2 + 2*w - 11],\ [401, 401, 3*w - 11],\ [401, 401, w^2 + w - 14],\ [401, 401, w - 8],\ [409, 409, -w^2 - w - 4],\ [409, 409, w^2 - 4*w - 6],\ [409, 409, 3*w^2 - 5*w - 14],\ [421, 421, w^2 + 2*w - 10],\ [433, 433, 4*w^2 - 3*w - 20],\ [439, 439, w^2 - 4*w - 9],\ [443, 443, 3*w^2 - 16],\ [457, 457, w^2 - 4*w - 8],\ [461, 461, 4*w - 7],\ [487, 487, w^2 - 5*w - 13],\ [491, 491, 4*w^2 - 6*w - 19],\ [491, 491, 4*w^2 - 4*w - 19],\ [491, 491, 3*w^2 + w - 8],\ [503, 503, -5*w - 3],\ [509, 509, 2*w^2 + w - 12],\ [523, 523, w^2 - 5*w - 4],\ [523, 523, 2*w^2 - 6*w - 5],\ [523, 523, 2*w^2 - 3*w - 18],\ [529, 23, 3*w^2 - 5*w - 7],\ [541, 541, -w^2 - 2*w - 5],\ [557, 557, 3*w^2 - w - 11],\ [563, 563, 3*w^2 - 5*w - 21],\ [571, 571, 3*w^2 - 17],\ [587, 587, -5*w - 7],\ [599, 599, w^2 + 3*w - 7],\ [607, 607, 3*w^2 - 5*w - 6],\ [613, 613, 4*w^2 - 3*w - 19],\ [617, 617, 2*w^2 + w - 14],\ [631, 631, w^2 - 5*w - 5],\ [631, 631, 4*w^2 - 8*w - 13],\ [631, 631, 2*w^2 + w - 22],\ [641, 641, -w^2 - 5],\ [647, 647, 4*w^2 - w - 17],\ [647, 647, 2*w^2 - 5*w - 9],\ [647, 647, 5*w^2 - 6*w - 23],\ [653, 653, 3*w^2 - 5*w - 5],\ [659, 659, w^2 - 5*w - 12],\ [661, 661, w^2 - 6*w - 3],\ [661, 661, 3*w^2 - 5*w - 4],\ [661, 661, 3*w^2 + w - 6],\ [683, 683, 3*w^2 + w - 5],\ [691, 691, 2*w^2 + 2*w - 21],\ [691, 691, 3*w^2 - 5*w - 17],\ [691, 691, 3*w^2 + 2*w - 12],\ [701, 701, 3*w^2 - 4*w - 8],\ [709, 709, 3*w^2 - 7*w - 9],\ [719, 719, -2*w^2 - w - 3],\ [727, 727, w^2 - 14],\ [733, 733, -3*w - 10],\ [739, 739, 2*w^2 + 3*w - 8],\ [739, 739, 5*w - 6],\ [739, 739, 2*w^2 - w - 19],\ [743, 743, 4*w^2 - 5*w - 16],\ [743, 743, 5*w^2 - 3*w - 25],\ [743, 743, 2*w^2 - 5*w - 10],\ [761, 761, w^2 + 4*w - 6],\ [773, 773, -5*w^2 + 7*w + 25],\ [787, 787, 3*w^2 - 20],\ [797, 797, 3*w^2 + w - 15],\ [809, 809, 4*w^2 - 3*w - 18],\ [821, 821, 2*w^2 - 5*w - 11],\ [821, 821, 2*w^2 + 2*w - 11],\ [821, 821, 3*w^2 - 4*w - 6],\ [827, 827, 5*w - 7],\ [853, 853, -w^2 + w - 6],\ [859, 859, w^2 + 3*w - 12],\ [863, 863, 3*w^2 - 3*w - 8],\ [863, 863, w^2 + 3*w - 11],\ [863, 863, w^2 - 5*w - 9],\ [881, 881, w^2 + 4*w - 18],\ [881, 881, w^2 - 5*w - 17],\ [881, 881, 4*w^2 - 4*w - 17],\ [883, 883, 5*w - 8],\ [883, 883, 3*w^2 - 3*w - 4],\ [883, 883, 4*w^2 - 6*w - 27],\ [887, 887, w^2 - w - 14],\ [887, 887, 3*w^2 - w - 26],\ [887, 887, 2*w^2 - 5*w - 14],\ [911, 911, 2*w^2 + 4*w - 7],\ [919, 919, 3*w^2 - 3*w - 7],\ [929, 929, 3*w^2 - w - 5],\ [941, 941, 5*w^2 - 24],\ [947, 947, 3*w^2 - w - 6],\ [947, 947, 3*w^2 + 2*w - 13],\ [947, 947, 3*w^2 - 5*w - 26],\ [961, 31, 4*w^2 - 5*w - 15],\ [967, 967, -5*w - 13],\ [967, 967, 4*w^2 - 21],\ [967, 967, 3*w^2 - 2*w - 7],\ [971, 971, w^2 + w - 16]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^10 - 48*x^8 + 785*x^6 - 4916*x^4 + 9216*x^2 - 2048 K. = NumberField(heckePol) hecke_eigenvalues_array = [-107/12832*e^8 + 106/401*e^6 - 31227/12832*e^4 + 22339/3208*e^2 - 1980/401, e, -47/51328*e^9 + 175/6416*e^7 - 9759/51328*e^5 - 4691/12832*e^3 + 7199/1604*e, 95/25664*e^8 - 147/1604*e^6 + 11535/25664*e^4 - 91/6416*e^2 + 1235/401, 329/102656*e^9 - 813/6416*e^7 + 170969/102656*e^5 - 211773/25664*e^3 + 9557/802*e, 1, 127/51328*e^9 - 507/6416*e^7 + 38383/51328*e^5 - 31349/12832*e^3 + 4505/1604*e, 101/25664*e^9 - 1119/6416*e^7 + 66293/25664*e^5 - 22553/1604*e^3 + 30515/1604*e, -91/102656*e^9 + 259/6416*e^7 - 69131/102656*e^5 + 122599/25664*e^3 - 7609/802*e, 5/1604*e^8 - 83/802*e^6 + 1789/1604*e^4 - 3703/802*e^2 + 238/401, -333/25664*e^8 + 701/1604*e^6 - 113373/25664*e^4 + 89265/6416*e^2 - 2324/401, 335/102656*e^9 - 523/3208*e^7 + 277055/102656*e^5 - 411367/25664*e^3 + 35633/1604*e, 5/3208*e^9 - 83/1604*e^7 + 1789/3208*e^5 - 4505/1604*e^3 + 3728/401*e, -351/102656*e^9 + 999/6416*e^7 - 251983/102656*e^5 + 384891/25664*e^3 - 19725/802*e, 25/102656*e^9 - 51/3208*e^7 + 31401/102656*e^5 - 41137/25664*e^3 - 3685/1604*e, 3/3208*e^8 - 65/802*e^6 + 4923/3208*e^4 - 2781/401*e^2 + 1114/401, 15/25664*e^8 + 19/1604*e^6 - 17089/25664*e^4 + 35949/6416*e^2 - 2612/401, -113/102656*e^9 + 11/1604*e^7 + 55167/102656*e^5 - 167839/25664*e^3 + 29007/1604*e, -199/25664*e^8 + 443/1604*e^6 - 79543/25664*e^4 + 80627/6416*e^2 - 4592/401, -55/12832*e^8 + 32/401*e^6 + 2777/12832*e^4 - 17929/3208*e^2 + 4986/401, 147/12832*e^8 - 295/802*e^6 + 45539/12832*e^4 - 40359/3208*e^2 + 7832/401, 163/102656*e^9 - 31/802*e^7 + 7635/102656*e^5 + 59901/25664*e^3 - 12317/1604*e, 169/102656*e^9 - 481/6416*e^7 + 113721/102656*e^5 - 139693/25664*e^3 + 3705/802*e, -77/3208*e^8 + 599/802*e^6 - 20493/3208*e^4 + 4813/401*e^2 + 4824/401, -279/25664*e^8 + 609/1604*e^6 - 108167/25664*e^4 + 103835/6416*e^2 - 2424/401, -177/25664*e^9 + 915/3208*e^7 - 101185/25664*e^5 + 132871/6416*e^3 - 27459/802*e, 253/25664*e^8 - 535/1604*e^6 + 84749/25664*e^4 - 66057/6416*e^2 + 7700/401, 55/12832*e^8 - 32/401*e^6 - 2777/12832*e^4 + 17929/3208*e^2 - 6590/401, 39/25664*e^8 - 111/1604*e^6 + 22295/25664*e^4 - 21379/6416*e^2 + 908/401, 63/102656*e^9 + 10/401*e^7 - 117969/102656*e^5 + 250113/25664*e^3 - 23241/1604*e, -815/102656*e^9 + 1021/3208*e^7 - 448799/102656*e^5 + 627607/25664*e^3 - 78765/1604*e, -267/51328*e^9 + 687/6416*e^7 + 1349/51328*e^5 - 63575/12832*e^3 + 1479/1604*e, 213/25664*e^9 - 2209/6416*e^7 + 121765/25664*e^5 - 75547/3208*e^3 + 43557/1604*e, -431/51328*e^9 + 1929/6416*e^7 - 177951/51328*e^5 + 189153/12832*e^3 - 26043/1604*e, 107/102656*e^9 + 189/6416*e^7 - 161253/102656*e^5 + 341769/25664*e^3 - 10733/802*e, 601/25664*e^8 - 1217/1604*e^6 + 181033/25664*e^4 - 125789/6416*e^2 + 9818/401, -699/102656*e^9 + 80/401*e^7 - 142955/102656*e^5 - 25349/25664*e^3 + 29409/1604*e, 149/6416*e^8 - 239/401*e^6 + 16741/6416*e^4 + 20895/1604*e^2 - 10698/401, -663/25664*e^8 + 1085/1604*e^6 - 96711/25664*e^4 - 11893/6416*e^2 + 4614/401, -249/51328*e^9 + 1695/6416*e^7 - 245001/51328*e^5 + 407511/12832*e^3 - 94293/1604*e, -345/102656*e^9 + 383/3208*e^7 - 145897/102656*e^5 + 210961/25664*e^3 - 43783/1604*e, -67/6416*e^9 + 2465/6416*e^7 - 29747/6416*e^5 + 139581/6416*e^3 - 57645/1604*e, -97/12832*e^8 + 91/802*e^6 + 17263/12832*e^4 - 54747/3208*e^2 + 4696/401, -579/102656*e^9 + 179/802*e^7 - 279667/102656*e^5 + 236579/25664*e^3 + 6909/1604*e, -23/102656*e^9 - 243/6416*e^7 + 106617/102656*e^5 - 120565/25664*e^3 - 2982/401*e, -423/51328*e^9 + 247/802*e^7 - 190487/51328*e^5 + 202391/12832*e^3 - 7905/802*e, 293/51328*e^9 - 1637/6416*e^7 + 201717/51328*e^5 - 303023/12832*e^3 + 60951/1604*e, 1683/102656*e^9 - 1051/1604*e^7 + 910787/102656*e^5 - 1205507/25664*e^3 + 113307/1604*e, 179/102656*e^9 + 25/802*e^7 - 222749/102656*e^5 + 524269/25664*e^3 - 49001/1604*e, 711/25664*e^8 - 1345/1604*e^6 + 175479/25664*e^4 - 77099/6416*e^2 - 10406/401, 147/51328*e^9 - 991/6416*e^7 + 135363/51328*e^5 - 198353/12832*e^3 + 40313/1604*e, -333/25664*e^8 + 701/1604*e^6 - 113373/25664*e^4 + 102097/6416*e^2 - 8740/401, 949/102656*e^9 - 575/1604*e^7 + 456965/102656*e^5 - 488677/25664*e^3 + 26773/1604*e, -169/51328*e^9 + 481/3208*e^7 - 113721/51328*e^5 + 152525/12832*e^3 - 8918/401*e, 533/102656*e^9 - 279/1604*e^7 + 184933/102656*e^5 - 166533/25664*e^3 + 5325/1604*e, -203/12832*e^8 + 331/802*e^6 - 21947/12832*e^4 - 38673/3208*e^2 + 9158/401, -25/1604*e^8 + 415/802*e^6 - 7341/1604*e^4 + 3277/802*e^2 + 11642/401, 187/6416*e^8 - 378/401*e^6 + 59851/6416*e^4 - 53567/1604*e^2 + 8120/401, -17/6416*e^8 + 251/802*e^6 - 43937/6416*e^4 + 65603/1604*e^2 - 14518/401, 295/12832*e^8 - 281/401*e^6 + 70263/12832*e^4 - 16407/3208*e^2 - 7568/401, 121/3208*e^8 - 442/401*e^6 + 25329/3208*e^4 - 4185/802*e^2 + 554/401, 757/51328*e^9 - 3723/6416*e^7 + 398533/51328*e^5 - 532907/12832*e^3 + 104293/1604*e, 743/102656*e^9 - 1251/6416*e^7 + 99671/102656*e^5 + 142669/25664*e^3 - 27451/802*e, 619/102656*e^9 - 2317/6416*e^7 + 678939/102656*e^5 - 1034143/25664*e^3 + 20959/401*e, -31/1604*e^8 + 675/802*e^6 - 18791/1604*e^4 + 43169/802*e^2 - 19280/401, 29/12832*e^8 + 5/401*e^6 - 26195/12832*e^4 + 68539/3208*e^2 - 6464/401, -73/6416*e^8 + 323/802*e^6 - 26761/6416*e^4 + 18651/1604*e^2 + 1818/401, 1353/25664*e^8 - 2617/1604*e^6 + 362841/25664*e^4 - 211133/6416*e^2 + 3554/401, -235/102656*e^9 + 1039/6416*e^7 - 356763/102656*e^5 + 684711/25664*e^3 - 43031/802*e, -139/12832*e^9 + 2949/6416*e^7 - 83739/12832*e^5 + 223083/6416*e^3 - 85433/1604*e, -523/102656*e^9 + 1797/6416*e^7 - 521403/102656*e^5 + 856159/25664*e^3 - 20246/401*e, 143/102656*e^9 - 1209/6416*e^7 + 475263/102656*e^5 - 855795/25664*e^3 + 21818/401*e, 97/3208*e^8 - 765/802*e^6 + 27649/3208*e^4 - 8917/401*e^2 + 464/401, -23/102656*e^9 - 161/1604*e^7 + 311929/102656*e^5 - 609785/25664*e^3 + 75089/1604*e, 751/25664*e^8 - 1027/1604*e^6 + 10143/25664*e^4 + 214453/6416*e^2 - 18708/401, 165/6416*e^8 - 785/802*e^6 + 75077/6416*e^4 - 68919/1604*e^2 + 6976/401, -421/25664*e^8 + 643/1604*e^6 - 26805/25664*e^4 - 113295/6416*e^2 + 16582/401, -81/6416*e^8 + 138/401*e^6 - 14225/6416*e^4 + 5413/1604*e^2 - 8222/401, 95/1604*e^8 - 1577/802*e^6 + 30783/1604*e^4 - 43089/802*e^2 + 3720/401, 483/12832*e^8 - 456/401*e^6 + 122131/12832*e^4 - 71427/3208*e^2 + 528/401, 199/51328*e^9 - 443/3208*e^7 + 79543/51328*e^5 - 67795/12832*e^3 - 4120/401*e, -605/102656*e^9 + 1105/6416*e^7 - 123437/102656*e^5 + 9697/25664*e^3 - 1727/802*e, -499/25664*e^8 + 865/1604*e^6 - 97059/25664*e^4 + 44951/6416*e^2 - 3680/401, 93/51328*e^9 - 5/6416*e^7 - 49491/51328*e^5 + 103065/12832*e^3 - 22845/1604*e, -31/12832*e^8 - 33/401*e^6 + 42161/12832*e^4 - 65633/3208*e^2 + 6412/401, 59/6416*e^9 - 2039/6416*e^7 + 23035/6416*e^5 - 114739/6416*e^3 + 82447/1604*e, 1351/25664*e^8 - 2673/1604*e^6 + 378807/25664*e^4 - 224267/6416*e^2 + 11548/401, 415/12832*e^8 - 811/802*e^6 + 113199/12832*e^4 - 64051/3208*e^2 + 364/401, 163/25664*e^9 - 2195/6416*e^7 + 161619/25664*e^5 - 143883/3208*e^3 + 149227/1604*e, 1417/102656*e^9 - 2429/6416*e^7 + 211225/102656*e^5 + 209155/25664*e^3 - 41115/802*e, 285/12832*e^8 - 441/802*e^6 + 34605/12832*e^4 - 3481/3208*e^2 + 9816/401, -463/25664*e^9 + 1071/1604*e^7 - 204799/25664*e^5 + 220411/6416*e^3 - 14841/401*e, -517/25664*e^8 + 1163/1604*e^6 - 210005/25664*e^4 + 205841/6416*e^2 - 12736/401, 323/12832*e^8 - 290/401*e^6 + 64883/12832*e^4 - 12179/3208*e^2 + 6794/401, -75/6416*e^8 + 211/802*e^6 - 4379/6416*e^4 - 5711/1604*e^2 - 4702/401, -273/51328*e^9 + 777/3208*e^7 - 207393/51328*e^5 + 367797/12832*e^3 - 24832/401*e, -1157/25664*e^8 + 2491/1604*e^6 - 413333/25664*e^4 + 327345/6416*e^2 - 4214/401, 105/25664*e^9 - 67/401*e^7 + 60025/25664*e^5 - 90009/6416*e^3 + 16202/401*e, -597/25664*e^8 + 1329/1604*e^6 - 238629/25664*e^4 + 229049/6416*e^2 - 9766/401, -77/102656*e^9 + 651/6416*e^7 - 232221/102656*e^5 + 285113/25664*e^3 + 5063/401*e, -43/12832*e^8 - 1/802*e^6 + 35301/12832*e^4 - 94713/3208*e^2 + 17328/401, 1263/102656*e^9 - 783/1604*e^7 + 670687/102656*e^5 - 896799/25664*e^3 + 96619/1604*e, -1247/51328*e^9 + 5957/6416*e^7 - 593103/51328*e^5 + 665833/12832*e^3 - 93775/1604*e, 431/102656*e^9 - 363/6416*e^7 - 78689/102656*e^5 + 211045/25664*e^3 - 3815/802*e, 41/3208*e^9 - 841/1604*e^7 + 22369/3208*e^5 - 50575/1604*e^3 + 7472/401*e, 177/3208*e^8 - 1429/802*e^6 + 56273/3208*e^4 - 24130/401*e^2 + 7982/401, -107/12832*e^8 + 106/401*e^6 - 31227/12832*e^4 + 22339/3208*e^2 - 1178/401, 47/12832*e^8 - 144/401*e^6 + 99583/12832*e^4 - 150095/3208*e^2 + 14054/401, 247/3208*e^8 - 1005/401*e^6 + 78111/3208*e^4 - 62151/802*e^2 + 20074/401, -129/12832*e^9 + 1191/3208*e^7 - 60913/12832*e^5 + 10748/401*e^3 - 49615/802*e, -167/3208*e^8 + 673/401*e^6 - 52695/3208*e^4 + 46161/802*e^2 - 22180/401, -1751/102656*e^9 + 2353/3208*e^7 - 1086535/102656*e^5 + 1474335/25664*e^3 - 134241/1604*e, -357/25664*e^9 + 4527/6416*e^7 - 306741/25664*e^5 + 117149/1604*e^3 - 159315/1604*e, -1109/25664*e^8 + 2231/1604*e^6 - 334565/25664*e^4 + 231937/6416*e^2 - 7600/401, -719/12832*e^8 + 761/401*e^6 - 252767/12832*e^4 + 215439/3208*e^2 - 13080/401, -27/3208*e^9 + 1873/6416*e^7 - 9019/3208*e^5 + 31945/6416*e^3 + 17239/1604*e, 891/102656*e^9 - 2721/6416*e^7 + 663339/102656*e^5 - 794175/25664*e^3 + 7407/401*e, -299/51328*e^9 + 313/802*e^7 - 410459/51328*e^5 + 721563/12832*e^3 - 69651/802*e, -245/102656*e^9 - 111/1604*e^7 + 390331/102656*e^5 - 957691/25664*e^3 + 144383/1604*e, 367/25664*e^8 - 551/1604*e^6 + 47263/25664*e^4 - 48843/6416*e^2 + 15598/401, 1587/102656*e^9 - 1441/3208*e^7 + 342627/102656*e^5 - 126075/25664*e^3 + 13413/1604*e, -783/102656*e^9 + 1735/6416*e^7 - 293631/102656*e^5 + 217003/25664*e^3 - 5691/802*e, 51/12832*e^8 - 88/401*e^6 + 41987/12832*e^4 - 50043/3208*e^2 + 14960/401, 295/3208*e^8 - 1124/401*e^6 + 76679/3208*e^4 - 46883/802*e^2 + 8224/401, -363/6416*e^8 + 663/401*e^6 - 79195/6416*e^4 + 28595/1604*e^2 - 6044/401, -29/12832*e^8 - 5/401*e^6 + 13363/12832*e^4 - 10795/3208*e^2 + 3256/401, -311/102656*e^9 + 515/6416*e^7 - 58023/102656*e^5 + 102211/25664*e^3 - 29891/802*e, -117/6416*e^9 + 2263/3208*e^7 - 60469/6416*e^5 + 169577/3208*e^3 - 79135/802*e, 349/12832*e^8 - 327/401*e^6 + 75469/12832*e^4 + 1371/3208*e^2 - 16590/401, 1129/102656*e^9 - 1437/3208*e^7 + 662521/102656*e^5 - 1010065/25664*e^3 + 126155/1604*e, -347/102656*e^9 + 1111/6416*e^7 - 283915/102656*e^5 + 346999/25664*e^3 - 6867/802*e, -173/12832*e^8 + 369/802*e^6 - 56125/12832*e^4 + 23601/3208*e^2 + 4324/401, 527/51328*e^9 - 883/3208*e^7 + 78847/51328*e^5 + 33061/12832*e^3 - 5998/401*e, -39/3208*e^8 + 222/401*e^6 - 25503/3208*e^4 + 30201/802*e^2 - 16086/401, 55/6416*e^9 - 1425/6416*e^7 + 3639/6416*e^5 + 96979/6416*e^3 - 102043/1604*e, 2991/102656*e^9 - 3439/3208*e^7 + 1350559/102656*e^5 - 1639975/25664*e^3 + 137529/1604*e, -1803/102656*e^9 + 4453/6416*e^7 - 979387/102656*e^5 + 1432799/25664*e^3 - 47664/401*e, 167/3208*e^8 - 673/401*e^6 + 49487/3208*e^4 - 30121/802*e^2 - 4286/401, 1253/102656*e^9 - 3011/6416*e^7 + 596533/102656*e^5 - 659313/25664*e^3 + 13596/401*e, 237/12832*e^9 - 291/401*e^7 + 122653/12832*e^5 - 159901/3208*e^3 + 35435/401*e, -131/12832*e^9 + 967/3208*e^7 - 32115/12832*e^5 + 12365/1604*e^3 - 9619/802*e, -65/6416*e^8 + 185/401*e^6 - 39297/6416*e^4 + 35097/1604*e^2 - 4182/401, -45/51328*e^9 + 1089/6416*e^7 - 231037/51328*e^5 + 427087/12832*e^3 - 64127/1604*e, -897/102656*e^9 + 269/802*e^7 - 461457/102656*e^5 + 682593/25664*e^3 - 93465/1604*e, -1637/102656*e^9 + 1543/3208*e^7 - 405429/102656*e^5 + 259677/25664*e^3 - 57371/1604*e, 191/6416*e^8 - 266/401*e^6 + 8671/6416*e^4 + 25633/1604*e^2 + 3516/401, -21/6416*e^9 - 293/3208*e^7 + 32907/6416*e^5 - 159123/3208*e^3 + 80823/802*e, 75/3208*e^8 - 823/802*e^6 + 46083/3208*e^4 - 27019/401*e^2 + 20632/401, 199/102656*e^9 - 443/6416*e^7 + 130871/102656*e^5 - 388595/25664*e^3 + 50817/802*e, -1087/51328*e^9 + 2847/3208*e^7 - 638511/51328*e^5 + 825531/12832*e^3 - 33331/401*e, -931/102656*e^9 + 2403/6416*e^7 - 549331/102656*e^5 + 817007/25664*e^3 - 59585/802*e, -1069/12832*e^8 + 1074/401*e^6 - 320253/12832*e^4 + 213917/3208*e^2 - 526/401, 1223/25664*e^8 - 2247/1604*e^6 + 271415/25664*e^4 - 92819/6416*e^2 + 7478/401, 177/6416*e^8 - 257/401*e^6 + 11361/6416*e^4 + 28331/1604*e^2 - 18064/401, -615/25664*e^8 + 825/1604*e^6 + 7721/25664*e^4 - 229205/6416*e^2 + 23684/401, 1213/102656*e^9 - 2527/6416*e^7 + 402573/102656*e^5 - 325305/25664*e^3 + 4644/401*e, 1275/102656*e^9 - 699/1604*e^7 + 472235/102656*e^5 - 343211/25664*e^3 - 18713/1604*e, 2989/102656*e^9 - 6533/6416*e^7 + 1109885/102656*e^5 - 888001/25664*e^3 + 381/802*e, -15/1604*e^9 + 3195/6416*e^7 - 13387/1604*e^5 + 295387/6416*e^3 - 74635/1604*e, 2119/102656*e^9 - 6833/6416*e^7 + 1844407/102656*e^5 - 2751691/25664*e^3 + 58315/401*e, -421/51328*e^9 + 643/3208*e^7 - 52469/51328*e^5 + 40689/12832*e^3 - 15368/401*e, -339/25664*e^8 + 533/1604*e^6 - 39811/25664*e^4 - 14297/6416*e^2 - 8016/401, -73/25664*e^9 + 1125/3208*e^7 - 212825/25664*e^5 + 361907/6416*e^3 - 60845/802*e, 1557/25664*e^8 - 3321/1604*e^6 + 556453/25664*e^4 - 469049/6416*e^2 + 14226/401, -227/51328*e^9 + 431/1604*e^7 - 266643/51328*e^5 + 466171/12832*e^3 - 48665/802*e, 2497/102656*e^9 - 3137/3208*e^7 + 1341905/102656*e^5 - 1663241/25664*e^3 + 121483/1604*e, -1505/25664*e^8 + 3173/1604*e^6 - 535281/25664*e^4 + 508981/6416*e^2 - 23174/401] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([17, 17, -w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]