/* 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([23, 23, -w + 4]) primes_array = [ [3, 3, w + 1],\ [7, 7, w - 1],\ [8, 2, 2],\ [9, 3, -w^2 + 2*w + 4],\ [11, 11, -w^2 + 2*w + 2],\ [13, 13, -w^2 + w + 4],\ [19, 19, w + 3],\ [19, 19, -w^2 + 2*w + 5],\ [19, 19, -w^2 + 3*w + 2],\ [23, 23, w^2 - w - 3],\ [23, 23, -w^2 + 2],\ [23, 23, -w + 4],\ [31, 31, w^2 - 5],\ [43, 43, w^2 - 3*w - 3],\ [49, 7, w^2 - 6],\ [53, 53, 2*w - 5],\ [61, 61, 2*w^2 - 2*w - 9],\ [71, 71, 2*w - 3],\ [73, 73, 2*w^2 - 5*w - 5],\ [83, 83, w^2 - w - 9],\ [97, 97, 2*w^2 - 3*w - 7],\ [103, 103, w^2 - 3*w - 6],\ [109, 109, w^2 - 4*w - 3],\ [121, 11, 2*w^2 - w - 7],\ [125, 5, -5],\ [127, 127, w^2 + w - 5],\ [131, 131, w^2 - 11],\ [137, 137, 3*w^2 - 7*w - 8],\ [137, 137, 2*w^2 - 5*w - 6],\ [137, 137, -w^2 + w - 2],\ [139, 139, 3*w^2 - 2*w - 16],\ [139, 139, 3*w - 2],\ [139, 139, -w^2 + 3*w - 3],\ [151, 151, w^2 + w - 11],\ [157, 157, 2*w^2 - 3*w - 3],\ [163, 163, w^2 - w - 10],\ [169, 13, 2*w^2 - 3*w - 4],\ [173, 173, -3*w^2 + 6*w + 8],\ [191, 191, -4*w^2 + 7*w + 15],\ [193, 193, 2*w^2 - 3],\ [197, 197, w^2 - 3*w - 11],\ [199, 199, 3*w^2 - 5*w - 16],\ [211, 211, w^2 - 4*w - 9],\ [223, 223, 2*w^2 - w - 4],\ [227, 227, 3*w - 4],\ [229, 229, w^2 + w - 8],\ [241, 241, w^2 - 4*w - 6],\ [251, 251, w - 7],\ [257, 257, w^2 - 4*w - 7],\ [263, 263, 3*w^2 - 5*w - 10],\ [263, 263, 2*w^2 - 5*w - 15],\ [263, 263, -w^2 + 6*w - 1],\ [269, 269, -w^2 - w + 14],\ [277, 277, 2*w^2 - 5*w - 8],\ [277, 277, w^2 + 3*w - 3],\ [277, 277, 3*w^2 - 4*w - 12],\ [281, 281, -2*w - 7],\ [293, 293, 3*w^2 - 2*w - 12],\ [307, 307, 2*w^2 + w - 8],\ [313, 313, w^2 + 4*w - 2],\ [317, 317, 3*w^2 - 6*w - 5],\ [331, 331, 4*w^2 - 4*w - 19],\ [337, 337, -5*w^2 + 8*w + 21],\ [347, 347, 3*w^2 - 6*w - 13],\ [347, 347, 3*w^2 - 5*w - 22],\ [347, 347, 3*w^2 - 5*w - 9],\ [349, 349, w^2 - 5*w - 11],\ [353, 353, -w^2 + 6*w - 7],\ [359, 359, -4*w^2 + 8*w + 11],\ [367, 367, 3*w^2 - 4*w - 11],\ [373, 373, w^2 + 2*w - 6],\ [379, 379, 5*w^2 - 9*w - 18],\ [409, 409, -w^2 - 4],\ [439, 439, 3*w^2 - 6*w - 14],\ [443, 443, -w^2 - 2*w + 13],\ [443, 443, 2*w^2 - 15],\ [443, 443, 3*w^2 - 13],\ [449, 449, w^2 + 2*w - 7],\ [449, 449, 2*w^2 - 6*w - 7],\ [449, 449, 3*w^2 - 3*w - 11],\ [461, 461, -w^2 - 2*w - 5],\ [467, 467, 3*w^2 - 5*w - 7],\ [479, 479, -w^2 + 6*w - 4],\ [491, 491, 3*w^2 - 5*w - 6],\ [499, 499, w^2 - 5*w - 8],\ [509, 509, 3*w^2 - 6*w - 19],\ [521, 521, 3*w^2 - 2*w - 10],\ [523, 523, 4*w - 9],\ [541, 541, 3*w^2 - 3*w - 10],\ [547, 547, 2*w^2 + w - 20],\ [547, 547, w^2 - 6*w - 5],\ [547, 547, 6*w^2 - 11*w - 24],\ [557, 557, -5*w^2 + 11*w + 11],\ [563, 563, 3*w^2 - 6*w - 16],\ [569, 569, 4*w^2 - 5*w - 17],\ [587, 587, 5*w^2 - 8*w - 20],\ [593, 593, 5*w - 3],\ [593, 593, 3*w^2 - w - 17],\ [593, 593, w - 9],\ [613, 613, 2*w^2 - w - 19],\ [613, 613, 3*w^2 - 4*w - 5],\ [613, 613, 3*w^2 - w - 8],\ [617, 617, 3*w^2 - 2*w - 9],\ [617, 617, -w^2 + w - 5],\ [617, 617, 4*w^2 - 6*w - 15],\ [619, 619, -w^2 + 3*w - 6],\ [631, 631, 4*w^2 - 7*w - 21],\ [641, 641, -w^2 - 3*w + 20],\ [643, 643, 3*w^2 - 14],\ [643, 643, w^2 - w - 13],\ [643, 643, 2*w^2 - 9*w + 2],\ [647, 647, 2*w^2 - 6*w - 9],\ [653, 653, 3*w^2 - 5],\ [659, 659, 6*w^2 - 11*w - 21],\ [661, 661, w^2 - 6*w - 6],\ [661, 661, w^2 + 3*w - 6],\ [661, 661, 5*w^2 - 7*w - 22],\ [673, 673, w^2 - 6*w - 12],\ [677, 677, 4*w^2 - 7*w - 22],\ [677, 677, 3*w^2 - 7*w - 12],\ [677, 677, -2*w^2 - 3],\ [683, 683, -2*w - 9],\ [683, 683, 4*w^2 - 7*w - 12],\ [683, 683, 3*w^2 - 3*w - 8],\ [691, 691, 2*w^2 + w - 11],\ [701, 701, 3*w^2 - 3*w - 5],\ [709, 709, -w^2 - 2*w - 6],\ [727, 727, 3*w^2 - w - 6],\ [727, 727, 3*w^2 - w - 27],\ [727, 727, 3*w^2 - w - 5],\ [733, 733, -2*w^2 + 9*w - 5],\ [739, 739, 3*w^2 - 4*w - 23],\ [743, 743, 2*w^2 - 7*w - 7],\ [743, 743, 3*w^2 - w - 20],\ [743, 743, 3*w^2 - 2*w - 7],\ [757, 757, -w - 9],\ [757, 757, 4*w^2 - 2*w - 29],\ [757, 757, 2*w^2 - 3*w - 18],\ [761, 761, 3*w^2 - 2*w - 6],\ [761, 761, 3*w^2 - 2*w - 25],\ [773, 773, -5*w - 12],\ [787, 787, -3*w - 10],\ [809, 809, 4*w^2 - w - 19],\ [821, 821, 5*w^2 - 10*w - 19],\ [823, 823, -4*w - 11],\ [827, 827, -7*w - 5],\ [827, 827, 2*w^2 - 6*w - 13],\ [827, 827, -w^2 - 2*w + 18],\ [839, 839, 6*w^2 - 9*w - 26],\ [839, 839, 5*w^2 - 12*w - 13],\ [839, 839, w - 10],\ [857, 857, -w^2 + 4*w - 8],\ [859, 859, 3*w^2 - 8*w - 10],\ [859, 859, 4*w^2 - 9*w - 14],\ [859, 859, 3*w^2 - 26],\ [863, 863, 2*w^2 + 3*w - 7],\ [877, 877, -5*w^2 + 11*w + 9],\ [877, 877, -5*w^2 + 10*w + 13],\ [877, 877, -w^2 + w - 6],\ [881, 881, w^2 - 3*w - 14],\ [883, 883, -w^2 + 3*w - 7],\ [887, 887, -3*w^2 + 6*w - 2],\ [907, 907, w^2 + 3*w - 8],\ [911, 911, 4*w^2 - 6*w - 29],\ [937, 937, -6*w^2 + 11*w + 25],\ [953, 953, 6*w^2 - 6*w - 29],\ [961, 31, -w^2 + 7*w - 5],\ [967, 967, 2*w^2 + w - 14],\ [971, 971, 5*w^2 - 3*w - 27],\ [971, 971, 4*w - 15],\ [971, 971, w^2 - 2*w - 14],\ [977, 977, 3*w^2 - 5*w - 24],\ [983, 983, w^2 - 4*w - 15],\ [991, 991, 6*w^2 - 10*w - 23],\ [991, 991, 5*w^2 - 6*w - 22],\ [991, 991, 3*w^2 + w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^18 - 44*x^16 + 791*x^14 - 7461*x^12 + 39425*x^10 - 115322*x^8 + 173000*x^6 - 116288*x^4 + 34960*x^2 - 3872 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 2371/10016*e^16 - 51701/5008*e^14 + 1835185/10016*e^12 - 16974321/10016*e^10 + 86851437/10016*e^8 - 7484880/313*e^6 + 19790787/626*e^4 - 9503825/626*e^2 + 1468311/626, -2815/5008*e^16 + 122813/5008*e^14 - 2181025/5008*e^12 + 10096347/2504*e^10 - 6467786/313*e^8 + 286215695/5008*e^6 - 190370381/2504*e^4 + 46500655/1252*e^2 - 3671079/626, -61761/220352*e^17 + 122487/10016*e^15 - 47860971/220352*e^13 + 443207071/220352*e^11 - 2272267499/220352*e^9 + 1572412855/55088*e^7 - 1047800835/27544*e^5 + 64314660/3443*e^3 - 40827979/13772*e, 55205/55088*e^17 - 437923/10016*e^15 + 42775781/55088*e^13 - 792127653/110176*e^11 + 4060123983/110176*e^9 - 11232865297/110176*e^7 + 7476885987/55088*e^5 - 1830332611/27544*e^3 + 144948307/13772*e, -4777/110176*e^17 + 18913/10016*e^15 - 3685459/110176*e^13 + 16998189/55088*e^11 - 43303269/27544*e^9 + 474113381/110176*e^7 - 308367201/55088*e^5 + 70595863/27544*e^3 - 5051143/13772*e, -17017/20032*e^16 + 371219/10016*e^14 - 13185115/20032*e^12 + 122073611/20032*e^10 - 625616327/20032*e^8 + 108149519/1252*e^6 - 287782913/2504*e^4 + 70340639/1252*e^2 - 11116039/1252, -8951/27544*e^17 + 17735/1252*e^15 - 6919883/27544*e^13 + 63935621/27544*e^11 - 326546283/27544*e^9 + 448749799/13772*e^7 - 588817175/13772*e^5 + 138334969/6886*e^3 - 10371341/3443*e, -411681/220352*e^17 + 816431/10016*e^15 - 318987179/220352*e^13 + 2953411919/220352*e^11 - 15136747643/220352*e^9 + 10467582155/55088*e^7 - 6964465623/27544*e^5 + 851327765/6886*e^3 - 269139539/13772*e, 48649/110176*e^17 - 192949/10016*e^15 + 37690591/110176*e^13 - 174460291/55088*e^11 + 446964121/27544*e^9 - 4943213877/110176*e^7 + 3285682647/55088*e^5 - 801298051/27544*e^3 + 63264805/13772*e, 81207/220352*e^17 - 160965/10016*e^15 + 62845965/220352*e^13 - 581256977/220352*e^11 + 2973906149/220352*e^9 - 2050073171/55088*e^7 + 1354640557/27544*e^5 - 81214550/3443*e^3 + 50148221/13772*e, 1, -19715/20032*e^16 + 430179/10016*e^14 - 15284185/20032*e^12 + 141572341/20032*e^10 - 726061185/20032*e^8 + 502677709/5008*e^6 - 41908178/313*e^4 + 20625972/313*e^2 - 13141207/1252, 688207/220352*e^17 - 1365035/10016*e^15 + 533445349/220352*e^13 - 4940573845/220352*e^11 + 25334018097/220352*e^9 - 4383761361/13772*e^7 + 2922217047/6886*e^5 - 2872421323/13772*e^3 + 456866299/13772*e, 38941/20032*e^16 - 849543/10016*e^14 + 30177911/20032*e^12 - 279453831/20032*e^10 + 1432649411/20032*e^8 - 247812369/1252*e^6 + 660276579/2504*e^4 - 161932127/1252*e^2 + 25694983/1252, 8773/10016*e^16 - 191371/5008*e^14 + 6796767/10016*e^12 - 62921671/10016*e^10 + 322421795/10016*e^8 - 111444799/1252*e^6 + 148189235/1252*e^4 - 36155861/626*e^2 + 5705115/626, -289073/220352*e^17 + 573309/10016*e^15 - 224012411/220352*e^13 + 2074274555/220352*e^11 - 10632786399/220352*e^9 + 459706581/3443*e^7 - 1224359597/6886*e^5 + 1200041281/13772*e^3 - 190381505/13772*e, -42235/20032*e^16 + 921431/10016*e^14 - 32732385/20032*e^12 + 303113893/20032*e^10 - 1553937793/20032*e^8 + 1075109099/5008*e^6 - 358003093/1252*e^4 + 87753851/626*e^2 - 27838043/1252, 307267/220352*e^17 - 609283/10016*e^15 + 238007073/220352*e^13 - 2202983289/220352*e^11 + 11285064949/220352*e^9 - 3898434913/27544*e^7 + 2588615577/13772*e^5 - 1258734113/13772*e^3 + 197558323/13772*e, 9499/5008*e^16 - 103613/1252*e^14 + 7360621/5008*e^12 - 68149407/5008*e^10 + 349253899/5008*e^8 - 482943403/2504*e^6 + 80284897/313*e^4 - 78377717/626*e^2 + 6181447/313, 656067/220352*e^17 - 1301311/10016*e^15 + 508560289/220352*e^13 - 4710401073/220352*e^11 + 24156712541/220352*e^9 - 4181092199/13772*e^7 + 2788753799/6886*e^5 - 2745849839/13772*e^3 + 437632527/13772*e, 410665/220352*e^17 - 407105/5008*e^15 + 318010163/220352*e^13 - 2942904157/220352*e^11 + 15071132661/220352*e^9 - 20815752527/110176*e^7 + 13809417607/55088*e^5 - 3349507171/27544*e^3 + 65510916/3443*e, 539661/220352*e^17 - 133817/1252*e^15 + 418437271/220352*e^13 - 3876574397/220352*e^11 + 19888147269/220352*e^9 - 27557296953/110176*e^7 + 18407613343/55088*e^5 - 4549209901/27544*e^3 + 91073245/3443*e, -368637/110176*e^17 + 365569/2504*e^15 - 285703127/110176*e^13 + 2645829025/110176*e^11 - 13565309345/110176*e^9 + 18774441967/55088*e^7 - 12509655753/27544*e^5 + 3070721811/13772*e^3 - 121979617/3443*e, 14857/10016*e^16 - 324223/5008*e^14 + 11521667/10016*e^12 - 106748915/10016*e^10 + 547693239/10016*e^8 - 94868769/626*e^6 + 63380371/313*e^4 - 62688447/626*e^2 + 10048373/626, -14137/10016*e^16 + 308349/5008*e^14 - 10950491/10016*e^12 + 101368999/10016*e^10 - 519414779/10016*e^8 + 359073001/2504*e^6 - 119378823/626*e^4 + 29140135/313*e^2 - 9198153/626, 849/1252*e^16 - 74069/2504*e^14 + 164395/313*e^12 - 12174117/2504*e^10 + 62382581/2504*e^8 - 172544271/2504*e^6 + 28708453/313*e^4 - 28125669/626*e^2 + 2232886/313, 2273/1252*e^17 - 396789/5008*e^15 + 1762387/1252*e^13 - 65308547/5008*e^11 + 335041033/5008*e^9 - 928389909/5008*e^7 + 620000385/2504*e^5 - 153117895/1252*e^3 + 12252181/626*e, -365697/110176*e^17 + 362663/2504*e^15 - 283441563/110176*e^13 + 2625006093/110176*e^11 - 13459456309/110176*e^9 + 18629955947/55088*e^7 - 12415882739/27544*e^5 + 3049152303/13772*e^3 - 121167988/3443*e, -1035/10016*e^16 + 22545/5008*e^14 - 799625/10016*e^12 + 7393633/10016*e^10 - 37852301/10016*e^8 + 13080945/1252*e^6 - 4354694/313*e^4 + 4271287/626*e^2 - 668103/626, 613/626*e^16 - 53479/1252*e^14 + 949549/1252*e^12 - 8789413/1252*e^10 + 22517131/626*e^8 - 31131436/313*e^6 + 165608011/1252*e^4 - 20213574/313*e^2 + 3187861/313, 6723/10016*e^16 - 146635/5008*e^14 + 5206497/10016*e^12 - 48173845/10016*e^10 + 246594345/10016*e^8 - 170103407/2504*e^6 + 112519823/1252*e^4 - 13522364/313*e^2 + 4183477/626, -711/10016*e^16 + 15433/5008*e^14 - 543973/10016*e^12 + 4975613/10016*e^10 - 24983953/10016*e^8 + 8313281/1252*e^6 - 10138313/1252*e^4 + 1865699/626*e^2 - 171885/626, 4289/2504*e^16 - 187137/2504*e^14 + 3323619/2504*e^12 - 7693389/626*e^10 + 78860453/1252*e^8 - 436247987/2504*e^6 + 290172351/1252*e^4 - 70876901/626*e^2 + 5597517/313, 585579/220352*e^17 - 1161347/10016*e^15 + 453774217/220352*e^13 - 4201703169/220352*e^11 + 21537174829/220352*e^9 - 7448519965/27544*e^7 + 1239532699/3443*e^5 - 2427474837/13772*e^3 + 384480923/13772*e, 931/5008*e^16 - 10133/1252*e^14 + 717873/5008*e^12 - 6622015/5008*e^10 + 33750663/5008*e^8 - 46233005/2504*e^6 + 30137881/1252*e^4 - 6946029/626*e^2 + 504360/313, 311725/220352*e^17 - 309207/5008*e^15 + 241735223/220352*e^13 - 2239731625/220352*e^11 + 11491929577/220352*e^9 - 15926220875/110176*e^7 + 10641941065/55088*e^5 - 2632277419/27544*e^3 + 105403955/6886*e, 163137/220352*e^17 - 323671/10016*e^15 + 126541771/220352*e^13 - 1172736575/220352*e^11 + 6019750667/220352*e^9 - 4174322583/55088*e^7 + 2793360475/27544*e^5 - 346656085/6886*e^3 + 111207651/13772*e, 231435/110176*e^17 - 459229/5008*e^15 + 179567041/110176*e^13 - 1664535077/110176*e^11 + 8547398833/110176*e^9 - 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61824065903/110176*e^7 + 41220080397/55088*e^5 - 10134489181/27544*e^3 + 806176857/13772*e, -96479/20032*e^16 + 2105157/10016*e^14 - 74793725/20032*e^12 + 692737085/20032*e^10 - 3552154737/20032*e^8 + 307303055/626*e^6 - 1638367709/2504*e^4 + 402332529/1252*e^2 - 63945077/1252, -38571/20032*e^16 + 841429/10016*e^14 - 29885329/20032*e^12 + 276659017/20032*e^10 - 1417447309/20032*e^8 + 489739321/2504*e^6 - 650492025/2504*e^4 + 158178451/1252*e^2 - 24815465/1252, -27853/3443*e^17 + 1767453/5008*e^15 - 21577676/3443*e^13 + 3195980957/55088*e^11 - 16375572735/55088*e^9 + 45275185671/55088*e^7 - 30092310019/27544*e^5 + 7336505149/13772*e^3 - 577918499/6886*e, 26069/5008*e^16 - 568749/2504*e^14 + 20204183/5008*e^12 - 187102019/5008*e^10 + 959237583/5008*e^8 - 663736037/1252*e^6 + 442178653/626*e^4 - 108497484/313*e^2 + 17234107/313, -147055/55088*e^17 + 36473/313*e^15 - 114087593/55088*e^13 + 1057509463/55088*e^11 - 5430120043/55088*e^9 + 7536174221/27544*e^7 - 2525783759/6886*e^5 + 1260314893/6886*e^3 - 102061536/3443*e, -25935/10016*e^16 + 565939/5008*e^14 - 20110213/10016*e^12 + 186313809/10016*e^10 - 955874853/10016*e^8 + 662247833/2504*e^6 - 442366637/1252*e^4 + 54659450/313*e^2 - 17501569/626, 14553/10016*e^16 - 317465/5008*e^14 + 11274995/10016*e^12 - 104370335/10016*e^10 + 534702043/10016*e^8 - 369477337/2504*e^6 + 245411665/1252*e^4 - 29865288/313*e^2 + 9409291/626, -86131/20032*e^16 + 1878553/10016*e^14 - 66704473/20032*e^12 + 617311689/20032*e^10 - 3161397293/20032*e^8 + 545784283/1252*e^6 - 1448125625/2504*e^4 + 351094369/1252*e^2 - 54923169/1252, 59153/6886*e^17 - 234629/626*e^15 + 91676925/13772*e^13 - 424443587/6886*e^11 + 4351362181/13772*e^9 - 12039955519/13772*e^7 + 16031519969/13772*e^5 - 1963194397/3443*e^3 + 311044531/3443*e, 20299/5008*e^16 - 55354/313*e^14 + 15730445/5008*e^12 - 145673075/5008*e^10 + 746895911/5008*e^8 - 1033834185/2504*e^6 + 344540919/626*e^4 - 169285743/626*e^2 + 13450987/313, -5653/5008*e^16 + 61657/1252*e^14 - 4380515/5008*e^12 + 40573785/5008*e^10 - 208131021/5008*e^8 + 288398617/2504*e^6 - 48174798/313*e^4 + 47650927/626*e^2 - 3809519/313, 1007/1252*e^16 - 43911/1252*e^14 + 194807/313*e^12 - 3603009/626*e^10 + 36858551/1252*e^8 - 50788823/626*e^6 + 134062147/1252*e^4 - 16010463/313*e^2 + 2450255/313, 711/1252*e^16 - 62045/2504*e^14 + 550859/1252*e^12 - 10195053/2504*e^10 + 52185511/2504*e^8 - 143941517/2504*e^6 + 95098543/1252*e^4 - 22761547/626*e^2 + 1748297/313, -1426485/220352*e^17 + 2829507/10016*e^15 - 1105830743/220352*e^13 + 10243067179/220352*e^11 - 52535430007/220352*e^9 + 36378070831/55088*e^7 - 24272771133/27544*e^5 + 2990475387/6886*e^3 - 954782171/13772*e, -37331/5008*e^16 + 814473/2504*e^14 - 28934189/5008*e^12 + 267956241/5008*e^10 - 1373800745/5008*e^8 + 950583355/1252*e^6 - 1266404361/1252*e^4 + 155292876/313*e^2 - 24643922/313, 503649/220352*e^17 - 998641/10016*e^15 + 390078411/220352*e^13 - 3610223571/220352*e^11 + 18491330311/220352*e^9 - 6386395259/27544*e^7 + 4238743293/13772*e^5 - 2058607707/13772*e^3 + 322140697/13772*e, -470405/110176*e^17 + 932617/5008*e^15 - 364231911/110176*e^13 + 3370244023/110176*e^11 - 17255903787/110176*e^9 + 2977899027/6886*e^7 - 1973640600/3443*e^5 + 954635433/3443*e^3 - 297520065/6886*e, -33735/20032*e^16 + 735925/10016*e^14 - 26138949/20032*e^12 + 242006053/20032*e^10 - 1240286249/20032*e^8 + 53606761/313*e^6 - 570755207/2504*e^4 + 139631965/1252*e^2 - 22073417/1252, -1823263/220352*e^17 + 3616429/10016*e^15 - 1413311909/220352*e^13 + 13090273609/220352*e^11 - 67130723101/220352*e^9 + 46475039819/55088*e^7 - 30996091201/27544*e^5 + 1906932185/3443*e^3 - 1215292917/13772*e, -1223075/220352*e^17 + 606429/2504*e^15 - 947841921/220352*e^13 + 8777119163/220352*e^11 - 44995316043/220352*e^9 + 62259065543/110176*e^7 - 41461529139/55088*e^5 + 10161216639/27544*e^3 - 402596939/6886*e, -8637/10016*e^16 + 188463/5008*e^14 - 6695639/10016*e^12 + 62007447/10016*e^10 - 317879571/10016*e^8 + 27488432/313*e^6 - 146439051/1252*e^4 + 35907865/626*e^2 - 5704287/626, -89/10016*e^16 + 1857/5008*e^14 - 63123/10016*e^12 + 562063/10016*e^10 - 2813131/10016*e^8 + 1975949/2504*e^6 - 1465853/1252*e^4 + 245549/313*e^2 - 101871/626, 43905/220352*e^17 - 87165/10016*e^15 + 34109467/220352*e^13 - 316562731/220352*e^11 + 1628775295/220352*e^9 - 283598815/13772*e^7 + 383254067/13772*e^5 - 195762313/13772*e^3 + 33406225/13772*e, -63885/110176*e^17 + 126599/5008*e^15 - 49413103/110176*e^13 + 456829419/110176*e^11 - 2335893271/110176*e^9 + 1608666605/27544*e^7 - 1060901229/13772*e^5 + 126604862/3443*e^3 - 38966335/6886*e, 46323/20032*e^16 - 1010315/10016*e^14 + 35874985/20032*e^12 - 332013717/20032*e^10 + 1700453825/20032*e^8 - 1174465993/5008*e^6 + 194841865/626*e^4 - 47298500/313*e^2 + 29635911/1252, 19795/20032*e^16 - 431595/10016*e^14 + 15320105/20032*e^12 - 141730101/20032*e^10 + 725569793/20032*e^8 - 500828065/5008*e^6 + 41493500/313*e^4 - 20071185/313*e^2 + 12494631/1252, 1152331/220352*e^17 - 2285323/10016*e^15 + 892935897/220352*e^13 - 8268033489/220352*e^11 + 42380352205/220352*e^9 - 14657186829/27544*e^7 + 9757134363/13772*e^5 - 4778180065/13772*e^3 + 756843995/13772*e, 513437/220352*e^17 - 1018511/10016*e^15 + 398096511/220352*e^13 - 3688001419/220352*e^11 + 18919325239/220352*e^9 - 13105429705/55088*e^7 + 8751046325/27544*e^5 - 540177288/3443*e^3 + 345681475/13772*e, 21243/2504*e^16 - 231711/626*e^14 + 16461041/2504*e^12 - 152421199/2504*e^10 + 781312727/2504*e^8 - 1080966609/1252*e^6 + 719755885/626*e^4 - 176348356/313*e^2 + 27949830/313, 97189/20032*e^16 - 2119915/10016*e^14 + 75286543/20032*e^12 - 696922279/20032*e^10 + 3570811027/20032*e^8 - 1234047213/2504*e^6 + 1640365169/2504*e^4 - 399864641/1252*e^2 + 62984347/1252, -15379/2504*e^16 + 671119/2504*e^14 - 11921935/2504*e^12 + 27605709/626*e^10 - 141564687/626*e^8 + 1567914671/2504*e^6 - 522697687/626*e^4 + 257046163/626*e^2 - 20460364/313, 78663/10016*e^16 - 1716071/5008*e^14 + 60955013/10016*e^12 - 564381265/10016*e^10 + 2892624109/10016*e^8 - 2000387145/2504*e^6 + 332735863/313*e^4 - 162692484/313*e^2 + 51437427/626, 124601/20032*e^16 - 2718163/10016*e^14 + 96546331/20032*e^12 - 893883275/20032*e^10 + 4581162759/20032*e^8 - 791957923/1252*e^6 + 2107409001/2504*e^4 - 515083379/1252*e^2 + 81427455/1252, 1007/2504*e^16 - 43911/2504*e^14 + 779541/2504*e^12 - 1804165/626*e^10 + 18499231/1252*e^8 - 102466253/2504*e^6 + 68406865/1252*e^4 - 16896879/626*e^2 + 1350171/313, 836149/110176*e^17 - 1658067/5008*e^15 + 647734015/110176*e^13 - 5995924667/110176*e^11 + 30719451087/110176*e^9 - 21229993661/27544*e^7 + 3526412817/3443*e^5 - 1717750113/3443*e^3 + 540504633/6886*e, -1367573/220352*e^17 + 2712199/10016*e^15 - 1059737879/220352*e^13 + 9812753395/220352*e^11 - 50300902991/220352*e^9 + 34796895365/55088*e^7 - 23170091595/27544*e^5 + 2838816533/6886*e^3 - 900167639/13772*e, 171961/20032*e^16 - 3751747/10016*e^14 + 133280683/20032*e^12 - 1234311819/20032*e^10 + 6328539735/20032*e^8 - 273716149/313*e^6 + 2918135703/2504*e^4 - 716301567/1252*e^2 + 113776347/1252, -17187/20032*e^16 + 375167/10016*e^14 - 13337817/20032*e^12 + 123668989/20032*e^10 - 635385017/20032*e^8 + 441455667/5008*e^6 - 148404377/1252*e^4 + 37352305/626*e^2 - 12194107/1252, -26045/10016*e^16 + 568199/5008*e^14 - 20185895/10016*e^12 + 186975815/10016*e^10 - 959089779/10016*e^8 + 83045232/313*e^6 - 443711489/1252*e^4 + 109641555/626*e^2 - 17552779/626, 28205/10016*e^16 - 615195/5008*e^14 + 21846839/10016*e^12 - 202215375/10016*e^10 + 1035893579/10016*e^8 - 357852569/1252*e^6 + 475201303/1252*e^4 - 115478973/626*e^2 + 18110255/626, 17327/10016*e^16 - 378271/5008*e^14 + 13450757/10016*e^12 - 124750105/10016*e^10 + 641166941/10016*e^8 - 445650975/2504*e^6 + 299708731/1252*e^4 - 37693103/313*e^2 + 12328997/626, 69291/10016*e^16 - 1511625/5008*e^14 + 53694609/10016*e^12 - 497191873/10016*e^10 + 2548633717/10016*e^8 - 440762447/626*e^6 + 1173870371/1252*e^4 - 287546669/626*e^2 + 45570057/626, 95471/20032*e^16 - 2083309/10016*e^14 + 74025629/20032*e^12 - 685751325/20032*e^10 + 3517544097/20032*e^8 - 304519613/626*e^6 + 1626116283/2504*e^4 - 401112929/1252*e^2 + 64091905/1252, 568147/55088*e^17 - 281701/626*e^15 + 440291965/55088*e^13 - 4077058691/55088*e^11 + 20899837615/55088*e^9 - 28916353249/27544*e^7 + 4813534975/3443*e^5 - 4717583229/6886*e^3 + 374012486/3443*e, 1043083/220352*e^17 - 2068991/10016*e^15 + 808597177/220352*e^13 - 7489789881/220352*e^11 + 38414064741/220352*e^9 - 1662505908/3443*e^7 + 2218691705/3443*e^5 - 4374184835/13772*e^3 + 698131655/13772*e, -90181/10016*e^16 + 1967453/5008*e^14 - 69891359/10016*e^12 + 647238963/10016*e^10 - 3318339143/10016*e^8 + 2296142287/2504*e^6 - 382417786/313*e^4 + 187638188/313*e^2 - 59579361/626] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([23, 23, -w + 4])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]