/* 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([3, -3, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [3, 3, w],\ [5, 5, w - 1],\ [7, 7, w^3 - w^2 - 4*w + 1],\ [11, 11, -w^2 + w + 2],\ [13, 13, -w^3 + w^2 + 3*w - 1],\ [16, 2, 2],\ [17, 17, -w^3 + 5*w + 2],\ [29, 29, -w^2 + w + 1],\ [37, 37, -w^3 + 2*w^2 + 4*w - 4],\ [41, 41, -w^3 + w^2 + 5*w + 1],\ [41, 41, w^2 - 5],\ [47, 47, w^3 - w^2 - 5*w - 2],\ [47, 47, -w^3 + 2*w^2 + 4*w - 1],\ [53, 53, w^3 - 4*w - 4],\ [53, 53, 2*w^3 - 2*w^2 - 9*w + 1],\ [61, 61, -w^3 + w^2 + 6*w - 2],\ [71, 71, w^3 - w^2 - 6*w - 2],\ [103, 103, 2*w^3 - 2*w^2 - 8*w + 1],\ [103, 103, -3*w^3 + 3*w^2 + 13*w - 5],\ [109, 109, 2*w^3 - w^2 - 8*w - 4],\ [109, 109, 2*w^3 - w^2 - 9*w - 1],\ [113, 113, -2*w^3 + w^2 + 11*w - 1],\ [113, 113, 2*w^3 - w^2 - 10*w - 4],\ [125, 5, 2*w^3 - 3*w^2 - 10*w + 4],\ [131, 131, -2*w^3 + w^2 + 9*w - 1],\ [139, 139, 2*w^3 - 4*w^2 - 7*w + 5],\ [139, 139, 3*w^3 - w^2 - 16*w - 5],\ [149, 149, w^2 + w - 4],\ [149, 149, 3*w^3 - 3*w^2 - 13*w + 1],\ [151, 151, w^2 - 2*w - 8],\ [157, 157, w^3 - w^2 - 7*w - 2],\ [157, 157, -2*w^2 + w + 7],\ [167, 167, 2*w^3 - 2*w^2 - 7*w + 5],\ [173, 173, -w^3 + 6*w - 2],\ [173, 173, -w^3 + 2*w^2 + 5*w - 7],\ [181, 181, -3*w^3 + 2*w^2 + 14*w + 1],\ [191, 191, -w^3 + 2*w^2 + 2*w - 5],\ [191, 191, -w^3 + 2*w^2 + 6*w - 5],\ [193, 193, -w^3 + 3*w^2 + 4*w - 4],\ [193, 193, 2*w^3 + 3*w^2 - 13*w - 20],\ [197, 197, w^3 - 2*w - 2],\ [199, 199, 2*w^3 - w^2 - 11*w - 2],\ [211, 211, -2*w^3 + 9*w + 5],\ [223, 223, -w^3 + w^2 + 4*w - 5],\ [223, 223, w^2 - 3*w - 2],\ [229, 229, 2*w^3 - 2*w^2 - 7*w + 1],\ [241, 241, 3*w^2 - 2*w - 13],\ [241, 241, -w^3 + w^2 + 5*w + 4],\ [257, 257, -3*w^3 + w^2 + 15*w + 8],\ [263, 263, -3*w^3 + 5*w^2 + 9*w - 7],\ [263, 263, 2*w^3 - w^2 - 9*w + 2],\ [263, 263, -w^3 + 4*w^2 + 2*w - 16],\ [263, 263, w^3 - w^2 - 2*w - 2],\ [271, 271, -3*w - 1],\ [281, 281, 2*w^3 - 3*w^2 - 8*w + 2],\ [281, 281, 3*w^3 - 4*w^2 - 12*w + 4],\ [283, 283, w^3 - 5*w - 7],\ [293, 293, -2*w^3 + w^2 + 10*w - 1],\ [307, 307, w^3 - 3*w^2 - 3*w + 8],\ [307, 307, 3*w^3 - 15*w - 10],\ [311, 311, 2*w^3 - 3*w^2 - 7*w + 7],\ [313, 313, -w^3 + 7*w + 2],\ [337, 337, 3*w^3 - 17*w - 10],\ [337, 337, 2*w^3 - 2*w^2 - 9*w - 5],\ [343, 7, -2*w^3 + w^2 + 8*w + 2],\ [347, 347, -3*w^3 + 17*w + 14],\ [347, 347, -3*w^3 - w^2 + 17*w + 13],\ [349, 349, 2*w^3 - w^2 - 8*w - 1],\ [349, 349, -w^3 + 3*w^2 + 4*w - 8],\ [353, 353, -w^3 - w^2 + 7*w + 4],\ [359, 359, -2*w^3 + 9*w + 10],\ [367, 367, 3*w^3 - 4*w^2 - 9*w + 4],\ [367, 367, -w^3 + w^2 + 4*w + 4],\ [367, 367, -w^3 + 3*w^2 + 3*w - 7],\ [373, 373, -w^2 + w - 2],\ [373, 373, -2*w^3 + 2*w^2 + 11*w - 2],\ [379, 379, -2*w^3 + 4*w^2 + 7*w - 8],\ [379, 379, -w^2 - 2],\ [389, 389, -w^3 - 2*w^2 + 5*w + 11],\ [397, 397, -2*w^3 + 4*w^2 + 7*w - 7],\ [401, 401, w^3 - 3*w^2 - 2*w + 10],\ [401, 401, -2*w^3 + 11*w + 4],\ [401, 401, 3*w^3 - 2*w^2 - 14*w - 4],\ [401, 401, -3*w^3 + 4*w^2 + 15*w - 5],\ [421, 421, -w^3 + w^2 + 7*w - 1],\ [421, 421, -2*w^3 + 2*w^2 + 9*w - 7],\ [433, 433, w^2 - w - 8],\ [439, 439, -w^3 + 3*w^2 + 4*w - 7],\ [443, 443, -2*w^3 + w^2 + 10*w - 2],\ [449, 449, w^2 + 2*w - 4],\ [449, 449, 2*w^3 - 2*w^2 - 10*w - 1],\ [461, 461, 2*w^3 - 2*w^2 - 6*w + 5],\ [461, 461, -2*w^3 + 4*w^2 + 7*w - 13],\ [463, 463, -3*w^3 + 3*w^2 + 12*w - 4],\ [463, 463, w - 5],\ [467, 467, -3*w^3 + w^2 + 16*w + 8],\ [467, 467, 2*w^2 - 3*w - 10],\ [479, 479, 2*w^2 - 4*w - 1],\ [479, 479, -w^3 + 2*w^2 + 2*w - 7],\ [487, 487, -3*w^3 + 5*w^2 + 12*w - 10],\ [503, 503, w^3 + 2*w^2 - 8*w - 8],\ [509, 509, -3*w^3 + 5*w^2 + 11*w - 5],\ [521, 521, 2*w^2 - 3*w - 11],\ [523, 523, -2*w^3 - w^2 + 13*w + 11],\ [523, 523, -2*w^3 + 4*w^2 + 8*w - 7],\ [541, 541, 3*w^3 - 2*w^2 - 13*w + 1],\ [563, 563, w^3 - 3*w - 5],\ [563, 563, -w^3 + 3*w^2 + 2*w - 11],\ [569, 569, -2*w^3 + 4*w^2 + 9*w - 4],\ [569, 569, 3*w^2 - w - 14],\ [571, 571, -w^3 + 8*w - 1],\ [577, 577, 3*w^3 - 2*w^2 - 16*w + 1],\ [587, 587, -4*w^3 + 5*w^2 + 18*w - 7],\ [587, 587, 2*w^3 + w^2 - 10*w - 7],\ [599, 599, 2*w^3 + w^2 - 11*w - 8],\ [607, 607, w^3 - 3*w + 4],\ [613, 613, 3*w^3 - w^2 - 14*w - 5],\ [613, 613, 3*w^2 - w - 11],\ [619, 619, 2*w^2 - 5*w - 8],\ [631, 631, -2*w^3 - 2*w^2 + 12*w + 19],\ [647, 647, 2*w^3 - 2*w^2 - 11*w - 2],\ [653, 653, 3*w^3 - 5*w^2 - 8*w + 7],\ [677, 677, -2*w^3 + 4*w^2 + 5*w - 8],\ [683, 683, 2*w^3 + w^2 - 12*w - 8],\ [683, 683, -w^3 + 3*w^2 - 8],\ [683, 683, -2*w^3 + 3*w^2 + 11*w - 8],\ [683, 683, -2*w^3 + 3*w^2 + 10*w - 2],\ [691, 691, w^2 - 4*w - 1],\ [709, 709, 3*w^3 - 2*w^2 - 13*w - 2],\ [709, 709, w^3 - 2*w^2 - 3*w - 2],\ [727, 727, -w^3 + 4*w^2 + 2*w - 7],\ [727, 727, -w^3 + 8*w + 5],\ [733, 733, 3*w^2 - 2*w - 10],\ [733, 733, -w^3 + 5*w + 8],\ [757, 757, 3*w^3 - 14*w - 8],\ [761, 761, -w^3 + 3*w^2 + 5*w - 10],\ [773, 773, -2*w^3 + 3*w^2 + 9*w - 1],\ [787, 787, -w^3 + 4*w - 4],\ [797, 797, w^2 + 2*w - 5],\ [797, 797, w^3 + w^2 - 5*w - 1],\ [809, 809, w^3 + 3*w^2 - 9*w - 17],\ [811, 811, -4*w^2 + 3*w + 17],\ [811, 811, w^3 - 2*w^2 - 8*w + 2],\ [823, 823, -4*w^3 + 4*w^2 + 17*w - 4],\ [857, 857, 3*w^2 - w - 16],\ [881, 881, -2*w^3 + 9*w + 1],\ [883, 883, w^3 - w^2 - 4*w - 5],\ [887, 887, 3*w^2 + w - 10],\ [911, 911, w^3 - 3*w - 7],\ [919, 919, -w^3 + w^2 + 3*w - 7],\ [919, 919, 3*w^3 - 2*w^2 - 12*w + 2],\ [929, 929, 3*w^3 - w^2 - 16*w - 2],\ [929, 929, w^3 + w^2 - 6*w - 2],\ [941, 941, -3*w^3 + 5*w^2 + 14*w - 14],\ [941, 941, -w^3 + 2*w^2 + 6*w - 8],\ [947, 947, 3*w^3 - 3*w^2 - 13*w - 5],\ [947, 947, 3*w^3 - 4*w^2 - 12*w + 2],\ [953, 953, -3*w^3 + 5*w^2 + 10*w - 10],\ [961, 31, -w^3 + 4*w^2 + 3*w - 13],\ [961, 31, -4*w^3 + 3*w^2 + 17*w - 4],\ [967, 967, -w^3 - 4*w^2 + 9*w + 19],\ [967, 967, w^3 + 5*w^2 - 9*w - 26],\ [971, 971, -3*w^3 + 6*w^2 + 13*w - 7],\ [971, 971, w^3 + 2*w^2 - 7*w - 7],\ [977, 977, 2*w^3 - 3*w^2 - 4*w - 2],\ [983, 983, 3*w^3 - 5*w^2 - 7*w + 7],\ [991, 991, 2*w^2 - w - 13],\ [991, 991, w^3 - 8*w - 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^12 - 42*x^10 + 666*x^8 - 5120*x^6 + 20112*x^4 - 38240*x^2 + 27344 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1241/92216*e^10 + 5931/11527*e^8 - 324291/46108*e^6 + 983083/23054*e^4 - 1291831/11527*e^2 + 1153846/11527, e, -73/46108*e^10 + 2113/46108*e^8 - 8227/23054*e^6 + 2421/23054*e^4 + 79916/11527*e^2 - 170736/11527, -165/46108*e^11 + 6355/46108*e^9 - 89141/46108*e^7 + 144455/11527*e^5 - 868651/23054*e^3 + 468509/11527*e, -231/46108*e^10 + 8897/46108*e^8 - 30623/11527*e^6 + 369893/23054*e^4 - 457052/11527*e^2 + 312408/11527, -1, 1083/92216*e^11 - 5083/11527*e^9 + 67818/11527*e^7 - 799347/23054*e^5 + 2035167/23054*e^3 - 854639/11527*e, -79/23054*e^11 + 1696/11527*e^9 - 53019/23054*e^7 + 183736/11527*e^5 - 536968/11527*e^3 + 471617/11527*e, -73/46108*e^10 + 2113/46108*e^8 - 8227/23054*e^6 + 2421/23054*e^4 + 91443/11527*e^2 - 239898/11527, 423/92216*e^11 - 3811/23054*e^9 + 46495/23054*e^7 - 221527/23054*e^5 + 297865/23054*e^3 + 82379/11527*e, -79/46108*e^11 + 848/11527*e^9 - 53019/46108*e^7 + 91868/11527*e^5 - 548495/23054*e^3 + 299207/11527*e, 197/92216*e^11 - 4667/46108*e^9 + 82521/46108*e^7 - 166051/11527*e^5 + 582367/11527*e^3 - 670940/11527*e, 925/92216*e^11 - 4235/11527*e^9 + 218253/46108*e^7 - 615611/23054*e^5 + 743336/11527*e^3 - 578486/11527*e, 197/92216*e^11 - 4667/46108*e^9 + 82521/46108*e^7 - 166051/11527*e^5 + 582367/11527*e^3 - 659413/11527*e, -779/46108*e^11 + 14827/23054*e^9 - 201799/23054*e^7 + 613190/11527*e^5 - 1658031/11527*e^3 + 1602187/11527*e, 233/46108*e^10 - 5481/46108*e^8 + 3892/11527*e^6 + 149861/23054*e^4 - 456560/11527*e^2 + 679802/11527, 265/92216*e^11 - 2115/23054*e^9 + 39971/46108*e^7 - 37791/23054*e^5 - 125315/11527*e^3 + 358532/11527*e, 584/11527*e^10 - 45335/23054*e^8 + 316064/11527*e^6 - 1963745/11527*e^4 + 5327156/11527*e^2 - 4933802/11527, 2119/46108*e^10 - 80915/46108*e^8 + 553985/23054*e^6 - 3400473/23054*e^4 + 4630238/11527*e^2 - 4384638/11527, 624/11527*e^10 - 47019/23054*e^8 + 631685/23054*e^6 - 1887604/11527*e^4 + 4938985/11527*e^2 - 4355574/11527, 1447/46108*e^10 - 52937/46108*e^8 + 169569/11527*e^6 - 1882203/23054*e^4 + 2196136/11527*e^2 - 1593770/11527, -2185/46108*e^11 + 83457/46108*e^9 - 1141321/46108*e^7 + 1740728/11527*e^5 - 9352037/23054*e^3 + 4378388/11527*e, -3129/92216*e^11 + 59733/46108*e^9 - 408515/23054*e^7 + 2498373/23054*e^5 - 6768375/23054*e^3 + 3270650/11527*e, -368/11527*e^11 + 56345/46108*e^9 - 385537/23054*e^7 + 2336059/23054*e^5 - 3040714/11527*e^3 + 2608573/11527*e, 485/11527*e^11 - 37709/23054*e^9 + 1052623/46108*e^7 - 3268687/23054*e^5 + 8848503/23054*e^3 - 4083723/11527*e, 5309/92216*e^10 - 24992/11527*e^8 + 1342677/46108*e^6 - 4018505/23054*e^4 + 5293658/11527*e^2 - 4769334/11527, 104/11527*e^10 - 15673/46108*e^8 + 53601/11527*e^6 - 671467/23054*e^4 + 913459/11527*e^2 - 668294/11527, 4237/92216*e^11 - 81769/46108*e^9 + 1134701/46108*e^7 - 1762324/11527*e^5 + 4824060/11527*e^3 - 4580819/11527*e, -1095/46108*e^11 + 21611/23054*e^9 - 307837/23054*e^7 + 980662/11527*e^5 - 2743494/11527*e^3 + 2637637/11527*e, -204/11527*e^10 + 8905/11527*e^8 - 284763/23054*e^6 + 1021433/11527*e^4 - 3176355/11527*e^2 + 3257174/11527, 221/11527*e^10 - 17373/23054*e^8 + 242213/23054*e^6 - 727122/11527*e^4 + 1784045/11527*e^2 - 1290446/11527, 1487/46108*e^10 - 53779/46108*e^8 + 341909/23054*e^6 - 1930585/23054*e^4 + 2493893/11527*e^2 - 2521224/11527, -99/46108*e^11 + 3813/46108*e^9 - 27895/23054*e^7 + 207927/23054*e^5 - 411599/11527*e^3 + 670718/11527*e, 2285/92216*e^11 - 42781/46108*e^9 + 566061/46108*e^7 - 817032/11527*e^5 + 1989768/11527*e^3 - 1486901/11527*e, -779/92216*e^11 + 14827/46108*e^9 - 201799/46108*e^7 + 306595/11527*e^5 - 834779/11527*e^3 + 899073/11527*e, 2567/46108*e^10 - 99567/46108*e^8 + 346687/11527*e^6 - 4297383/23054*e^4 + 5807262/11527*e^2 - 5407588/11527, -73/46108*e^11 + 2113/46108*e^9 - 8227/23054*e^7 + 2421/23054*e^5 + 91443/11527*e^3 - 309060/11527*e, 1411/92216*e^11 - 28395/46108*e^9 + 413875/46108*e^7 - 674067/11527*e^5 + 1908715/11527*e^3 - 1807726/11527*e, -1489/92216*e^10 + 30945/46108*e^8 - 472879/46108*e^6 + 822433/11527*e^4 - 2559535/11527*e^2 + 2827840/11527, -5711/92216*e^10 + 113997/46108*e^8 - 1639681/46108*e^6 + 2611200/11527*e^4 - 7144054/11527*e^2 + 6547464/11527, 249/11527*e^11 - 39409/46108*e^9 + 139971/11527*e^7 - 1753397/23054*e^5 + 2331895/11527*e^3 - 2013027/11527*e, 1919/46108*e^10 - 76705/46108*e^8 + 551657/23054*e^6 - 3504373/23054*e^4 + 4766760/11527*e^2 - 4358168/11527, 8053/92216*e^10 - 38552/11527*e^8 + 2111423/46108*e^6 - 6418041/23054*e^4 + 8494849/11527*e^2 - 7595212/11527, 445/23054*e^10 - 36025/46108*e^8 + 266259/23054*e^6 - 1796937/23054*e^4 + 2754903/11527*e^2 - 2924616/11527, 673/23054*e^10 - 13135/11527*e^8 + 364705/23054*e^6 - 1097015/11527*e^4 + 2721203/11527*e^2 - 2053586/11527, 4443/46108*e^10 - 169027/46108*e^8 + 574774/11527*e^6 - 6965333/23054*e^4 + 9260594/11527*e^2 - 8516878/11527, 1419/92216*e^10 - 21563/46108*e^8 + 200027/46108*e^6 - 154313/11527*e^4 + 93018/11527*e^2 + 38370/11527, 783/92216*e^10 - 11411/46108*e^8 + 94875/46108*e^6 - 46718/11527*e^4 - 55779/11527*e^2 - 56714/11527, 1281/92216*e^11 - 24145/46108*e^9 + 163531/23054*e^7 - 503637/11527*e^5 + 2858365/23054*e^3 - 1525357/11527*e, -1213/92216*e^11 + 12291/23054*e^9 - 358085/46108*e^7 + 1140207/23054*e^5 - 1497116/11527*e^3 + 1160062/11527*e, -79/23054*e^11 + 1696/11527*e^9 - 53019/23054*e^7 + 183736/11527*e^5 - 548495/11527*e^3 + 552306/11527*e, 3433/46108*e^11 - 32619/11527*e^9 + 886503/23054*e^7 - 2684530/11527*e^5 + 7157038/11527*e^3 - 6682972/11527*e, -759/23054*e^11 + 29233/23054*e^9 - 400827/23054*e^7 + 1202189/11527*e^5 - 3041359/11527*e^3 + 2461352/11527*e, 2983/46108*e^10 - 28810/11527*e^8 + 400288/11527*e^6 - 2495952/11527*e^4 + 6905153/11527*e^2 - 6583070/11527, -485/11527*e^11 + 37709/23054*e^9 - 1052623/46108*e^7 + 3268687/23054*e^5 - 8848503/23054*e^3 + 4095250/11527*e, -1031/92216*e^11 + 4658/11527*e^9 - 57984/11527*e^7 + 302684/11527*e^5 - 1282677/23054*e^3 + 439684/11527*e, 757/46108*e^10 - 32649/46108*e^8 + 259639/23054*e^6 - 1883321/23054*e^4 + 3039459/11527*e^2 - 3237262/11527, -73/23054*e^11 + 2113/23054*e^9 - 8227/11527*e^7 + 2421/11527*e^5 + 159832/11527*e^3 - 352999/11527*e, -1459/46108*e^10 + 55495/46108*e^8 - 375703/23054*e^6 + 2244833/23054*e^4 - 2927517/11527*e^2 + 2718088/11527, -8077/92216*e^10 + 78383/23054*e^8 - 2184553/46108*e^6 + 6757617/23054*e^4 - 8995690/11527*e^2 + 7912640/11527, -553/11527*e^11 + 83449/46108*e^9 - 278917/11527*e^7 + 3265707/23054*e^5 - 4070979/11527*e^3 + 3352024/11527*e, -4613/46108*e^10 + 178369/46108*e^8 - 619566/11527*e^6 + 7695435/23054*e^4 - 10528943/11527*e^2 + 9939908/11527, 43/23054*e^10 - 2963/46108*e^8 + 18061/23054*e^6 - 93647/23054*e^4 + 44808/11527*e^2 + 153454/11527, -1173/92216*e^10 + 24161/46108*e^8 - 366841/46108*e^6 + 638697/11527*e^4 - 1999513/11527*e^2 + 2068048/11527, -2359/46108*e^10 + 85967/46108*e^8 - 279542/11527*e^6 + 3321901/23054*e^4 - 4583987/11527*e^2 + 4485564/11527, 3775/92216*e^11 - 18218/11527*e^9 + 500341/23054*e^7 - 2993377/23054*e^5 + 7454519/23054*e^3 - 2873644/11527*e, 423/23054*e^11 - 7622/11527*e^9 + 383487/46108*e^7 - 523743/11527*e^5 + 2424849/23054*e^3 - 846238/11527*e, 4203/46108*e^10 - 163975/46108*e^8 + 1144449/23054*e^6 - 7043905/23054*e^4 + 9306845/11527*e^2 - 8277628/11527, -294/11527*e^10 + 21599/23054*e^8 - 275121/23054*e^6 + 743491/11527*e^4 - 1694921/11527*e^2 + 1414392/11527, 1513/46108*e^11 - 55479/46108*e^9 + 711627/46108*e^7 - 981593/11527*e^5 + 4460779/23054*e^3 - 1518358/11527*e, 1149/92216*e^11 - 21603/46108*e^9 + 293711/46108*e^7 - 457382/11527*e^5 + 1291186/11527*e^3 - 1220378/11527*e, -299/46108*e^10 + 8023/46108*e^8 - 9348/11527*e^6 - 195675/23054*e^4 + 739299/11527*e^2 - 1101024/11527, -2063/46108*e^10 + 18205/11527*e^8 - 437141/23054*e^6 + 1075034/11527*e^4 - 1993278/11527*e^2 + 1020564/11527, -2743/23054*e^10 + 208849/46108*e^8 - 1418049/23054*e^6 + 8538699/23054*e^4 - 11263125/11527*e^2 + 10313078/11527, 5367/46108*e^10 - 204615/46108*e^8 + 697266/11527*e^6 - 8467959/23054*e^4 + 11342396/11527*e^2 - 10665616/11527, -741/11527*e^10 + 113111/46108*e^8 - 778223/23054*e^6 + 4857687/23054*e^4 - 6835474/11527*e^2 + 6775938/11527, 9405/92216*e^10 - 87677/23054*e^8 + 2327269/46108*e^6 - 6896803/23054*e^4 + 9113254/11527*e^2 - 8563038/11527, -737/11527*e^10 + 52929/23054*e^8 - 332075/11527*e^6 + 1827832/11527*e^4 - 4461690/11527*e^2 + 4154886/11527, -4135/92216*e^11 + 76661/46108*e^9 - 1002567/46108*e^7 + 1432643/11527*e^5 - 3487967/11527*e^3 + 2759143/11527*e, -697/11527*e^10 + 51245/23054*e^8 - 664593/23054*e^6 + 1903973/11527*e^4 - 4849861/11527*e^2 + 4479520/11527, -3499/92216*e^11 + 66509/46108*e^9 - 454471/23054*e^7 + 2799947/23054*e^5 - 7681189/23054*e^3 + 3603482/11527*e, 4293/92216*e^11 - 80053/46108*e^9 + 527793/23054*e^7 - 1524511/11527*e^5 + 7524429/23054*e^3 - 3023769/11527*e, -1039/92216*e^11 + 23327/46108*e^9 - 96738/11527*e^7 + 728144/11527*e^5 - 4867185/23054*e^3 + 2823997/11527*e, -5927/92216*e^11 + 113965/46108*e^9 - 785825/23054*e^7 + 4832011/23054*e^5 - 13032689/23054*e^3 + 6084540/11527*e, 4199/46108*e^10 - 39820/11527*e^8 + 539234/11527*e^6 - 3252107/11527*e^4 + 8667291/11527*e^2 - 8002756/11527, -557/46108*e^10 + 28439/46108*e^8 - 257311/23054*e^6 + 1987221/23054*e^4 - 3199035/11527*e^2 + 3487440/11527, -3435/23054*e^10 + 265647/46108*e^8 - 1838987/23054*e^6 + 11277811/23054*e^4 - 14919049/11527*e^2 + 13271952/11527, 3925/46108*e^10 - 154665/46108*e^8 + 547322/11527*e^6 - 6854043/23054*e^4 + 9225265/11527*e^2 - 8401060/11527, -5559/92216*e^11 + 105481/46108*e^9 - 356569/11527*e^7 + 4259033/23054*e^5 - 10952669/23054*e^3 + 4725361/11527*e, 647/23054*e^11 - 12285/11527*e^9 + 662265/46108*e^7 - 972198/11527*e^5 + 4709735/23054*e^3 - 1719337/11527*e, -3223/92216*e^11 + 30073/23054*e^9 - 198537/11527*e^7 + 1147644/11527*e^5 - 5625513/23054*e^3 + 2258460/11527*e, -575/46108*e^11 + 20749/46108*e^9 - 66745/11527*e^7 + 790589/23054*e^5 - 1120418/11527*e^3 + 1208629/11527*e, -3467/46108*e^11 + 130039/46108*e^9 - 432614/11527*e^7 + 5074749/23054*e^5 - 6437829/11527*e^3 + 5503649/11527*e, -4599/46108*e^10 + 41925/11527*e^8 - 1071597/23054*e^6 + 2986829/11527*e^4 - 7183912/11527*e^2 + 6003890/11527, -2463/46108*e^10 + 92767/46108*e^8 - 626229/23054*e^6 + 3798115/23054*e^4 - 5109172/11527*e^2 + 4900468/11527, -373/92216*e^11 + 2107/23054*e^9 - 48/11527*e^7 - 232329/23054*e^5 + 1368237/23054*e^3 - 935804/11527*e, -3985/92216*e^11 + 19491/11527*e^9 - 276141/11527*e^7 + 3543997/23054*e^5 - 10242487/23054*e^3 + 5247694/11527*e, -2071/92216*e^11 + 41105/46108*e^9 - 592157/46108*e^7 + 962977/11527*e^5 - 2777366/11527*e^3 + 2813906/11527*e, 907/23054*e^11 - 71613/46108*e^9 + 511243/23054*e^7 - 3276509/23054*e^5 + 4617692/11527*e^3 - 4473950/11527*e, -55/23054*e^10 + 8079/46108*e^8 - 91191/23054*e^6 + 818907/23054*e^4 - 1449935/11527*e^2 + 1472724/11527, 89/23054*e^11 - 7205/46108*e^9 + 48641/23054*e^7 - 230285/23054*e^5 + 46098/11527*e^3 + 401788/11527*e, 2799/92216*e^11 - 26689/23054*e^9 + 727889/46108*e^7 - 2209463/23054*e^5 + 2949862/11527*e^3 - 2802141/11527*e, 327/92216*e^11 - 8917/46108*e^9 + 84667/23054*e^7 - 684489/23054*e^5 + 2377393/23054*e^3 - 1518132/11527*e, -104/11527*e^10 + 15673/46108*e^8 - 53601/11527*e^6 + 694521/23054*e^4 - 1097891/11527*e^2 + 1198536/11527, 12673/92216*e^10 - 121589/23054*e^8 + 3336343/46108*e^6 - 10140025/23054*e^4 + 13342017/11527*e^2 - 11895046/11527, 4967/46108*e^10 - 46167/11527*e^8 + 1216971/23054*e^6 - 3548280/11527*e^4 + 9056446/11527*e^2 - 7892304/11527, -1701/92216*e^11 + 34329/46108*e^9 - 127943/11527*e^7 + 1774231/23054*e^5 - 5667821/23054*e^3 + 3161167/11527*e, 1863/92216*e^11 - 34305/46108*e^9 + 111585/11527*e^7 - 1276835/23054*e^5 + 3086541/23054*e^3 - 1073397/11527*e, -3233/46108*e^11 + 63133/23054*e^9 - 1779877/46108*e^7 + 2817169/11527*e^5 - 15774401/23054*e^3 + 7705459/11527*e, 369/46108*e^11 - 3815/11527*e^9 + 225759/46108*e^7 - 356587/11527*e^5 + 1736391/23054*e^3 - 539311/11527*e, 14713/92216*e^10 - 69044/11527*e^8 + 3696677/46108*e^6 - 11039483/23054*e^4 + 14600734/11527*e^2 - 13586188/11527, -11795/92216*e^10 + 220681/46108*e^8 - 2922217/46108*e^6 + 4235947/11527*e^4 - 10485936/11527*e^2 + 8654916/11527, 178/11527*e^11 - 7205/11527*e^9 + 423709/46108*e^7 - 702637/11527*e^5 + 4184221/23054*e^3 - 2288974/11527*e, 453/23054*e^11 - 31751/46108*e^9 + 380273/46108*e^7 - 473577/11527*e^5 + 1808083/23054*e^3 - 439207/11527*e, -525/23054*e^11 + 39393/46108*e^9 - 132908/11527*e^7 + 1644655/23054*e^5 - 2401313/11527*e^3 + 2692198/11527*e, 235/46108*e^10 - 3398/11527*e^8 + 69377/11527*e^6 - 604643/11527*e^4 + 2145563/11527*e^2 - 2362438/11527, -3621/23054*e^10 + 275783/46108*e^8 - 1877437/23054*e^6 + 11384259/23054*e^4 - 15137264/11527*e^2 + 14005890/11527, 4073/23054*e^10 - 155475/23054*e^8 + 1057636/11527*e^6 - 6339131/11527*e^4 + 16257534/11527*e^2 - 13788946/11527, -831/46108*e^10 + 16527/23054*e^8 - 241135/23054*e^6 + 807169/11527*e^4 - 2398994/11527*e^2 + 2374462/11527, 6231/46108*e^10 - 59735/11527*e^8 + 1641123/23054*e^6 - 5029695/11527*e^4 + 13559676/11527*e^2 - 12495184/11527, -1423/92216*e^11 + 14837/23054*e^9 - 461967/46108*e^7 + 1690827/23054*e^5 - 2891100/11527*e^3 + 3488004/11527*e, 1157/23054*e^11 - 93665/46108*e^9 + 344984/11527*e^7 - 4584431/23054*e^5 + 6731638/11527*e^3 - 6799417/11527*e, 711/92216*e^11 - 3816/11527*e^9 + 244349/46108*e^7 - 907501/23054*e^5 + 1542461/11527*e^3 - 1813275/11527*e, 6045/92216*e^11 - 29234/11527*e^9 + 810949/23054*e^7 - 5003083/23054*e^5 + 13513967/23054*e^3 - 6427208/11527*e, 125/46108*e^11 - 5513/46108*e^9 + 83599/46108*e^7 - 120264/11527*e^5 + 296191/23054*e^3 + 366729/11527*e, 1215/23054*e^11 - 22874/11527*e^9 + 1230019/46108*e^7 - 3694225/23054*e^5 + 9832517/23054*e^3 - 4603891/11527*e, -101/46108*e^11 + 397/46108*e^9 + 62661/46108*e^7 - 473205/23054*e^5 + 2260469/23054*e^3 - 1566408/11527*e, 5889/92216*e^10 - 27959/11527*e^8 + 1492363/46108*e^6 - 4248241/23054*e^4 + 4884757/11527*e^2 - 3464820/11527, 27/23054*e^10 + 4/11527*e^8 - 25653/23054*e^6 + 215749/11527*e^4 - 1210079/11527*e^2 + 1983566/11527, -1283/46108*e^10 + 22437/23054*e^8 - 262073/23054*e^6 + 586019/11527*e^4 - 688310/11527*e^2 - 385220/11527, 2261/11527*e^10 - 172419/23054*e^8 + 1170294/11527*e^6 - 6987691/11527*e^4 + 17813240/11527*e^2 - 14819582/11527, -583/11527*e^10 + 85975/46108*e^8 - 277310/11527*e^6 + 3065043/23054*e^4 - 3396578/11527*e^2 + 2122990/11527, 619/11527*e^10 - 93617/46108*e^8 + 636063/23054*e^6 - 3912395/23054*e^4 + 5418328/11527*e^2 - 5217452/11527, 1693/46108*e^10 - 70795/46108*e^8 + 270594/11527*e^6 - 3725523/23054*e^4 + 5645156/11527*e^2 - 6026184/11527, 528/11527*e^10 - 20336/11527*e^8 + 568197/23054*e^6 - 1814443/11527*e^4 + 5211251/11527*e^2 - 4941042/11527, -391/11527*e^11 + 60587/46108*e^9 - 843761/46108*e^7 + 1311274/11527*e^5 - 7109911/23054*e^3 + 3363088/11527*e, -409/11527*e^11 + 16102/11527*e^9 - 231301/11527*e^7 + 1523112/11527*e^5 - 4560067/11527*e^3 + 4725887/11527*e, -1239/46108*e^10 + 39337/46108*e^8 - 193321/23054*e^6 + 607019/23054*e^4 + 41515/11527*e^2 - 826764/11527, 386/11527*e^11 - 30083/23054*e^9 + 420495/23054*e^7 - 1304942/11527*e^5 + 3544401/11527*e^3 - 3406549/11527*e, 8933/92216*e^11 - 174997/46108*e^9 + 2472087/46108*e^7 - 3907384/11527*e^5 + 10859543/11527*e^3 - 10431453/11527*e, -8/11527*e^11 + 2979/46108*e^9 - 75901/46108*e^7 + 363767/23054*e^5 - 1184169/23054*e^3 + 227859/11527*e, 597/92216*e^10 - 5101/11527*e^8 + 432987/46108*e^6 - 1807401/23054*e^4 + 2935677/11527*e^2 - 2979756/11527, 5757/92216*e^10 - 54647/23054*e^8 + 1470539/46108*e^6 - 4317109/23054*e^4 + 5386509/11527*e^2 - 4715986/11527, -311/46108*e^10 + 10581/46108*e^8 - 55261/23054*e^6 + 143901/23054*e^4 + 238458/11527*e^2 - 737488/11527, 2185/46108*e^11 - 83457/46108*e^9 + 1141321/46108*e^7 - 1740728/11527*e^5 + 9352037/23054*e^3 - 4470604/11527*e, 1097/46108*e^11 - 19903/23054*e^9 + 497223/46108*e^7 - 640096/11527*e^5 + 2426375/23054*e^3 - 584943/11527*e, -2531/46108*e^10 + 91893/46108*e^8 - 583679/23054*e^6 + 3209493/23054*e^4 - 3613119/11527*e^2 + 2126850/11527, 1517/92216*e^11 - 30087/46108*e^9 + 439085/46108*e^7 - 743871/11527*e^5 + 2342723/11527*e^3 - 2844678/11527*e, -7641/92216*e^11 + 148719/46108*e^9 - 2081729/46108*e^7 + 3251002/11527*e^5 - 8905429/11527*e^3 + 8447458/11527*e, -27/23054*e^10 - 4/11527*e^8 + 25653/23054*e^6 - 215749/11527*e^4 + 1233133/11527*e^2 - 2052728/11527, 3685/46108*e^10 - 69043/23054*e^8 + 458320/11527*e^6 - 2676708/11527*e^4 + 6816265/11527*e^2 - 6317490/11527, 1227/92216*e^11 - 24153/46108*e^9 + 85297/11527*e^7 - 1061645/23054*e^5 + 2788947/23054*e^3 - 1249170/11527*e, -357/92216*e^11 + 6351/46108*e^9 - 41039/23054*e^7 + 255961/23054*e^5 - 776563/23054*e^3 + 335718/11527*e, 1139/92216*e^11 - 4654/11527*e^9 + 192157/46108*e^7 - 323721/23054*e^5 - 55789/11527*e^3 + 840735/11527*e, 4597/92216*e^11 - 42779/23054*e^9 + 1125059/46108*e^7 - 3235179/23054*e^5 + 3945019/11527*e^3 - 3094605/11527*e, 3489/92216*e^11 - 31761/23054*e^9 + 201847/11527*e^7 - 1104452/11527*e^5 + 4987239/23054*e^3 - 1634585/11527*e, 4687/92216*e^11 - 89387/46108*e^9 + 305157/11527*e^7 - 3724753/23054*e^5 + 10061383/23054*e^3 - 4665351/11527*e, -2633/46108*e^11 + 102109/46108*e^9 - 1420099/46108*e^7 + 4389893/23054*e^5 - 11844409/23054*e^3 + 5482027/11527*e, 971/11527*e^10 - 155531/46108*e^8 + 1130131/23054*e^6 - 7376767/23054*e^4 + 10548541/11527*e^2 - 10355800/11527, -383/46108*e^10 + 7201/23054*e^8 - 90219/23054*e^6 + 220390/11527*e^4 - 495769/11527*e^2 + 1097918/11527, 2981/46108*e^10 - 29664/11527*e^8 + 842511/23054*e^6 - 2605978/11527*e^4 + 6769808/11527*e^2 - 5754014/11527, 289/23054*e^10 - 6788/11527*e^8 + 237729/23054*e^6 - 939166/11527*e^4 + 3150465/11527*e^2 - 3524224/11527, 695/11527*e^11 - 104627/46108*e^9 + 1399545/46108*e^7 - 4146385/23054*e^5 + 10841673/23054*e^3 - 5128584/11527*e, 6901/92216*e^11 - 135167/46108*e^9 + 477358/11527*e^7 - 3018590/11527*e^5 + 16734485/23054*e^3 - 7920118/11527*e, 1681/92216*e^11 - 28355/46108*e^9 + 77166/11527*e^7 - 592145/23054*e^5 + 372137/23054*e^3 + 419290/11527*e, -2849/92216*e^11 + 28393/23054*e^9 - 820687/46108*e^7 + 2663319/23054*e^5 - 3782913/11527*e^3 + 3586404/11527*e, -2981/46108*e^10 + 29664/11527*e^8 - 865565/23054*e^6 + 2905680/11527*e^4 - 8913830/11527*e^2 + 9580978/11527, -2003/11527*e^10 + 297755/46108*e^8 - 981239/11527*e^6 + 11456851/23054*e^4 - 14647388/11527*e^2 + 12926282/11527] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([16, 2, 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]