/* 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, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 5, w^2 - 2*w - 3]) primes_array = [ [5, 5, -w - 1],\ [5, 5, w + 2],\ [7, 7, w + 3],\ [7, 7, -w + 2],\ [7, 7, -w + 1],\ [8, 2, 2],\ [13, 13, -w^2 + w + 4],\ [19, 19, -w^2 + 5],\ [23, 23, -w^2 - w + 3],\ [27, 3, 3],\ [29, 29, w^2 - w - 3],\ [31, 31, w^2 - w - 8],\ [37, 37, -w - 4],\ [43, 43, 2*w^2 - 4*w - 3],\ [47, 47, w^2 - 3],\ [53, 53, 2*w^2 - w - 11],\ [59, 59, w^2 - 2*w - 4],\ [67, 67, w^2 + w - 8],\ [71, 71, w^2 + w - 11],\ [73, 73, -w^2 + 4*w - 2],\ [89, 89, 2*w^2 + w - 12],\ [89, 89, w^2 - 10],\ [89, 89, w - 5],\ [97, 97, w^2 - 2*w - 5],\ [101, 101, 2*w^2 - w - 17],\ [103, 103, -2*w^2 - 2*w + 7],\ [109, 109, w^2 - 3*w - 3],\ [127, 127, 2*w^2 + w - 9],\ [137, 137, 2*w^2 + w - 13],\ [137, 137, -2*w^2 + 3*w + 8],\ [137, 137, w^2 - 2*w - 10],\ [139, 139, 2*w - 7],\ [163, 163, -3*w - 5],\ [163, 163, 2*w^2 - 3*w - 3],\ [163, 163, 2*w^2 + w - 14],\ [169, 13, -w^2 + 5*w - 5],\ [173, 173, w - 6],\ [179, 179, -2*w^2 + 6*w - 3],\ [181, 181, 2*w^2 - w - 9],\ [193, 193, w^2 + 2*w - 6],\ [193, 193, -w^2 - 2*w - 3],\ [193, 193, w^2 + 2*w - 11],\ [229, 229, w^2 - 3*w - 13],\ [233, 233, w^2 + 2*w - 7],\ [241, 241, -w^2 + 2*w - 3],\ [251, 251, 2*w^2 - 2*w - 13],\ [263, 263, -w^2 + 3*w - 4],\ [269, 269, 2*w^2 - 2*w - 5],\ [269, 269, 3*w^2 + w - 26],\ [271, 271, 2*w^2 + w - 7],\ [281, 281, 2*w^2 - 2*w - 15],\ [283, 283, 2*w^2 + 2*w - 3],\ [293, 293, w - 7],\ [307, 307, -w^2 - 4*w - 6],\ [311, 311, 2*w^2 + 3*w - 8],\ [313, 313, w^2 - 3*w - 6],\ [347, 347, w^2 + 3*w - 5],\ [353, 353, 3*w^2 - 5*w - 6],\ [359, 359, 2*w^2 + w - 5],\ [361, 19, 2*w^2 - w - 4],\ [367, 367, 4*w^2 - 3*w - 20],\ [367, 367, 2*w^2 + w - 4],\ [367, 367, -w^2 - 3*w - 5],\ [373, 373, w^2 - 3*w - 7],\ [373, 373, 4*w - 3],\ [373, 373, 3*w^2 - 16],\ [379, 379, -w^2 + 4*w - 6],\ [397, 397, -3*w^2 + 4*w + 9],\ [397, 397, -3*w - 10],\ [397, 397, 2*w^2 - 5],\ [401, 401, -3*w^2 + 2*w + 14],\ [409, 409, w^2 - w - 13],\ [419, 419, w^2 - 3*w - 8],\ [419, 419, 3*w^2 - 5*w - 4],\ [419, 419, 3*w^2 + 2*w - 17],\ [421, 421, 4*w^2 + w - 22],\ [421, 421, 2*w^2 - w - 19],\ [421, 421, 3*w^2 - 6*w - 8],\ [431, 431, -w^2 + 5*w - 8],\ [433, 433, w^2 + 3*w - 6],\ [439, 439, -w^2 + 6*w - 7],\ [439, 439, 3*w^2 + 3*w - 14],\ [439, 439, -w^2 - w - 4],\ [457, 457, -w - 8],\ [461, 461, 2*w^2 - 3*w - 11],\ [467, 467, 2*w^2 - 19],\ [467, 467, w^2 - 13],\ [467, 467, 2*w^2 + 2*w - 13],\ [479, 479, 2*w^2 + w - 20],\ [487, 487, 2*w^2 + 2*w - 17],\ [499, 499, 4*w - 5],\ [509, 509, 2*w^2 - 5*w - 6],\ [521, 521, 4*w^2 - 4*w - 17],\ [529, 23, 3*w^2 - 4*w - 8],\ [541, 541, -w^2 - 4*w - 7],\ [547, 547, -3*w^2 + 5*w + 11],\ [557, 557, 3*w^2 - 2*w - 13],\ [557, 557, 3*w^2 - 2*w - 27],\ [557, 557, 2*w^2 - 3*w - 12],\ [563, 563, -w^2 + 6*w - 6],\ [569, 569, 2*w^2 + 4*w - 7],\ [571, 571, w^2 + 3*w - 12],\ [587, 587, 2*w^2 - 3*w - 18],\ [593, 593, 3*w^2 - 4*w - 14],\ [601, 601, 2*w^2 + 3*w - 10],\ [613, 613, 3*w^2 - w - 26],\ [613, 613, 2*w^2 + 5*w - 5],\ [613, 613, 3*w^2 + 2*w - 29],\ [617, 617, -w^2 + 2*w - 5],\ [619, 619, w^2 + 3*w - 9],\ [619, 619, -3*w^2 + 8*w + 5],\ [619, 619, 4*w^2 + 3*w - 17],\ [643, 643, 3*w^2 + 4*w - 12],\ [653, 653, 4*w^2 - 3*w - 19],\ [659, 659, -3*w^2 - 2*w + 25],\ [659, 659, 3*w^2 - 14],\ [659, 659, 3*w^2 + w - 13],\ [661, 661, -3*w^2 + 3*w + 10],\ [677, 677, -4*w + 13],\ [677, 677, 4*w^2 + w - 21],\ [677, 677, 2*w^2 - 3*w - 17],\ [691, 691, w^2 - 5*w - 5],\ [701, 701, -2*w^2 + 9*w - 8],\ [709, 709, -5*w - 6],\ [719, 719, 5*w - 11],\ [727, 727, 4*w^2 - w - 22],\ [739, 739, -2*w^2 + 5*w - 4],\ [743, 743, 2*w^2 + 3*w - 11],\ [757, 757, w^2 - 4*w - 8],\ [757, 757, -5*w - 7],\ [757, 757, w^2 + 2*w - 16],\ [761, 761, 5*w - 4],\ [769, 769, 4*w^2 - 7*w - 7],\ [769, 769, 3*w^2 - w - 13],\ [769, 769, 4*w^2 - 5*w - 18],\ [773, 773, 2*w^2 + 5*w + 5],\ [787, 787, w^2 - 3*w - 17],\ [797, 797, 3*w^2 - 3*w - 19],\ [797, 797, w^2 - 4*w - 13],\ [797, 797, 3*w^2 + 2*w - 24],\ [809, 809, 3*w^2 + 2*w - 20],\ [823, 823, 4*w^2 - 3*w - 25],\ [827, 827, 3*w^2 + 5*w - 10],\ [829, 829, w^2 - 4*w - 9],\ [839, 839, 2*w^2 + 5*w - 6],\ [841, 29, 3*w^2 + 2*w - 10],\ [863, 863, w^2 + 4*w - 20],\ [877, 877, 3*w^2 + 3*w - 7],\ [881, 881, 7*w^2 + w - 42],\ [887, 887, -w^2 + 7*w - 9],\ [907, 907, 3*w^2 - w - 12],\ [911, 911, 3*w^2 - 3*w - 5],\ [919, 919, 5*w^2 - 29],\ [929, 929, w - 10],\ [937, 937, w^2 + 4*w - 15],\ [937, 937, w^2 - 2*w - 16],\ [937, 937, 3*w^2 - w - 27],\ [941, 941, 4*w^2 - 3*w - 18],\ [947, 947, 4*w^2 + w - 20],\ [947, 947, 4*w^2 - 7*w - 13],\ [947, 947, 3*w^2 - 2*w - 28],\ [961, 31, 5*w^2 - 2*w - 28],\ [971, 971, 4*w^2 - 3*w - 26],\ [971, 971, -4*w^2 - 7*w + 3],\ [971, 971, 5*w - 9],\ [977, 977, 5*w^2 - w - 29],\ [983, 983, 2*w^2 + 2*w - 23],\ [991, 991, 2*w^2 + 3*w - 13],\ [997, 997, -w^2 + w - 6]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 + x^7 - 39*x^6 - 19*x^5 + 469*x^4 - 32*x^3 - 1808*x^2 + 960*x + 576 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, 1, e, 209/66862*e^7 + 797/267448*e^6 - 25883/267448*e^5 - 20395/267448*e^4 + 194089/267448*e^3 + 219045/267448*e^2 - 20554/33431*e - 136977/33431, 2861/802344*e^7 + 5695/1604688*e^6 - 72835/534896*e^5 - 111841/1604688*e^4 + 2423107/1604688*e^3 + 295657/1604688*e^2 - 434003/100293*e + 14679/66862, 5761/802344*e^7 + 31379/1604688*e^6 - 131519/534896*e^5 - 864053/1604688*e^4 + 3986879/1604688*e^3 + 5285453/1604688*e^2 - 1562297/200586*e - 30807/66862, 872/100293*e^7 + 13781/1604688*e^6 - 171553/534896*e^5 - 284867/1604688*e^4 + 5428481/1604688*e^3 + 446105/1604688*e^2 - 898837/100293*e + 226691/66862, 26585/3209376*e^7 + 76571/3209376*e^6 - 275095/1069792*e^5 - 1944497/3209376*e^4 + 7203359/3209376*e^3 + 4778113/1604688*e^2 - 2789927/401172*e + 185711/66862, -8413/1604688*e^7 - 43411/1604688*e^6 + 69375/534896*e^5 + 1193257/1604688*e^4 - 807943/1604688*e^3 - 3871043/802344*e^2 - 260951/200586*e + 219805/33431, 4115/401172*e^7 + 4043/401172*e^6 - 49359/133724*e^5 - 86513/401172*e^4 + 1502687/401172*e^3 + 18806/100293*e^2 - 1029961/100293*e + 145150/33431, 6623/802344*e^7 + 3217/401172*e^6 - 37621/133724*e^5 - 73849/401172*e^4 + 1042477/401172*e^3 + 732359/802344*e^2 - 626789/100293*e + 35891/33431, 3313/1069792*e^7 - 13757/1069792*e^6 - 129405/1069792*e^5 + 369655/1069792*e^4 + 1155175/1069792*e^3 - 666375/534896*e^2 + 12041/133724*e - 387883/66862, -1733/534896*e^7 - 13369/534896*e^6 + 22423/534896*e^5 + 380867/534896*e^4 + 344299/534896*e^3 - 608435/133724*e^2 - 355765/66862*e + 128478/33431, 383/267448*e^7 - 9427/534896*e^6 - 56267/534896*e^5 + 232845/534896*e^4 + 1086153/534896*e^3 - 910277/534896*e^2 - 349245/33431*e + 43007/66862, 11627/1604688*e^7 + 46715/1604688*e^6 - 116327/534896*e^5 - 1243913/1604688*e^4 + 2648783/1604688*e^3 + 1022869/200586*e^2 - 344807/200586*e - 244270/33431, 4471/401172*e^7 + 10349/200586*e^6 - 27103/66862*e^5 - 307529/200586*e^4 + 902879/200586*e^3 + 4174783/401172*e^2 - 1576124/100293*e - 126314/33431, 6619/534896*e^7 + 18267/534896*e^6 - 215045/534896*e^5 - 472313/534896*e^4 + 1884719/534896*e^3 + 347225/66862*e^2 - 491687/66862*e - 138264/33431, -1529/1604688*e^7 + 18337/1604688*e^6 + 37627/534896*e^5 - 615043/1604688*e^4 - 2582099/1604688*e^3 + 2236853/802344*e^2 + 2382161/200586*e - 118143/33431, 9119/802344*e^7 + 11081/200586*e^6 - 22611/66862*e^5 - 147841/100293*e^4 + 516629/200586*e^3 + 6723473/802344*e^2 - 483731/100293*e - 150977/33431, 2005/401172*e^7 - 11293/802344*e^6 - 64551/267448*e^5 + 293347/802344*e^4 + 2840783/802344*e^3 - 1217587/802344*e^2 - 1582031/100293*e + 28843/33431, -18073/802344*e^7 - 50221/802344*e^6 + 209537/267448*e^5 + 1438999/802344*e^4 - 6278737/802344*e^3 - 2434765/200586*e^2 + 2264575/100293*e + 427986/33431, 6845/1604688*e^7 + 1607/1604688*e^6 - 55539/534896*e^5 + 66427/1604688*e^4 + 9467/1604688*e^3 - 1409171/802344*e^2 + 1402885/200586*e + 153485/33431, 6155/3209376*e^7 - 13207/3209376*e^6 - 126717/1069792*e^5 + 585445/3209376*e^4 + 6940085/3209376*e^3 - 3837377/1604688*e^2 - 4677869/401172*e + 716621/66862, -13339/1604688*e^7 - 63703/1604688*e^6 + 124611/534896*e^5 + 1649101/1604688*e^4 - 3033451/1604688*e^3 - 2022877/401172*e^2 + 1536349/200586*e - 82958/33431, -32671/3209376*e^7 - 142117/3209376*e^6 + 382185/1069792*e^5 + 4275823/3209376*e^4 - 12670177/3209376*e^3 - 14458115/1604688*e^2 + 6792121/401172*e + 331791/66862, 10799/534896*e^7 + 5563/133724*e^6 - 86115/133724*e^5 - 35893/33431*e^4 + 713791/133724*e^3 + 3070681/534896*e^2 - 728181/66862*e - 493379/66862, 33049/1604688*e^7 + 76975/1604688*e^6 - 367611/534896*e^5 - 2233357/1604688*e^4 + 10781587/1604688*e^3 + 7498043/802344*e^2 - 4615603/200586*e + 27747/33431, -13207/802344*e^7 - 13255/200586*e^6 + 35211/66862*e^5 + 191219/100293*e^4 - 1011991/200586*e^3 - 11002369/802344*e^2 + 1591168/100293*e + 650333/33431, -785/534896*e^7 - 4793/267448*e^6 + 15891/267448*e^5 + 77937/267448*e^4 - 370909/267448*e^3 + 755619/534896*e^2 + 788613/66862*e - 1023829/66862, 23933/1604688*e^7 + 24749/401172*e^6 - 63691/133724*e^5 - 171113/100293*e^4 + 1758725/401172*e^3 + 17143931/1604688*e^2 - 3079829/200586*e - 290879/66862, -3367/401172*e^7 - 54167/802344*e^6 + 48675/267448*e^5 + 1595177/802344*e^4 - 94427/802344*e^3 - 11242901/802344*e^2 - 287755/100293*e + 513905/33431, -1581/534896*e^7 + 5011/534896*e^6 + 84579/534896*e^5 - 188129/534896*e^4 - 939417/534896*e^3 + 301759/66862*e^2 - 6957/66862*e - 561712/33431, -5831/267448*e^7 - 4599/133724*e^6 + 91805/133724*e^5 + 83543/133724*e^4 - 776347/133724*e^3 - 77923/267448*e^2 + 454238/33431*e - 258555/33431, 1769/534896*e^7 + 7165/534896*e^6 - 18259/534896*e^5 - 33519/534896*e^4 - 447751/534896*e^3 - 525341/133724*e^2 + 477087/66862*e + 346764/33431, 6569/267448*e^7 + 3935/66862*e^6 - 57993/66862*e^5 - 50159/33431*e^4 + 626895/66862*e^3 + 2186055/267448*e^2 - 1076220/33431*e - 114537/33431, -6669/1069792*e^7 + 12637/1069792*e^6 + 231549/1069792*e^5 - 760455/1069792*e^4 - 2431943/1069792*e^3 + 5085005/534896*e^2 + 943515/133724*e - 1301851/66862, -12739/1604688*e^7 - 33379/1604688*e^6 + 192319/534896*e^5 + 796609/1604688*e^4 - 8903095/1604688*e^3 - 324407/200586*e^2 + 5341369/200586*e - 273216/33431, -2877/133724*e^7 - 2831/66862*e^6 + 50915/66862*e^5 + 89139/66862*e^4 - 529855/66862*e^3 - 1443753/133724*e^2 + 879030/33431*e + 258886/33431, -901/401172*e^7 - 739/401172*e^6 + 2407/133724*e^5 + 35857/401172*e^4 + 338153/401172*e^3 - 418937/200586*e^2 - 683020/100293*e + 693058/33431, -823/33431*e^7 - 13155/267448*e^6 + 230237/267448*e^5 + 345693/267448*e^4 - 2330751/267448*e^3 - 2079415/267448*e^2 + 930948/33431*e + 420553/33431, 1895/534896*e^7 - 14549/534896*e^6 - 3685/534896*e^5 + 647303/534896*e^4 - 1077281/534896*e^3 - 1685353/133724*e^2 + 1002007/66862*e + 572578/33431, -11391/534896*e^7 - 42811/534896*e^6 + 420853/534896*e^5 + 1307097/534896*e^4 - 4708783/534896*e^3 - 2454045/133724*e^2 + 2135641/66862*e + 616622/33431, -16037/1069792*e^7 - 22207/1069792*e^6 + 708097/1069792*e^5 + 749981/1069792*e^4 - 9432755/1069792*e^3 - 2824157/534896*e^2 + 4304515/133724*e - 49877/66862, -2173/802344*e^7 + 2335/1604688*e^6 + 29309/534896*e^5 + 320447/1604688*e^4 + 1802179/1604688*e^3 - 8495699/1604688*e^2 - 1708580/100293*e + 1048103/66862, -1192/100293*e^7 - 39323/802344*e^6 + 52079/267448*e^5 + 1014989/802344*e^4 + 1605697/802344*e^3 - 5430431/802344*e^2 - 2431549/100293*e + 347905/33431, -11141/1604688*e^7 - 130469/1604688*e^6 + 135065/534896*e^5 + 4328423/1604688*e^4 - 4847729/1604688*e^3 - 4262965/200586*e^2 + 2684705/200586*e + 611016/33431, -1535/802344*e^7 - 3515/200586*e^6 + 6563/66862*e^5 + 56572/100293*e^4 - 281831/200586*e^3 - 3139337/802344*e^2 + 378368/100293*e - 277947/33431, 1697/802344*e^7 - 6929/401172*e^6 - 10003/133724*e^5 + 154073/401172*e^4 - 70277/401172*e^3 - 419407/802344*e^2 + 869632/100293*e - 302187/33431, -13207/802344*e^7 - 13255/200586*e^6 + 35211/66862*e^5 + 191219/100293*e^4 - 1011991/200586*e^3 - 10200025/802344*e^2 + 1390582/100293*e + 182299/33431, 53551/3209376*e^7 + 154345/3209376*e^6 - 513213/1069792*e^5 - 3533707/3209376*e^4 + 9233269/3209376*e^3 + 5427125/1604688*e^2 - 345433/401172*e + 281699/66862, 126257/3209376*e^7 + 283883/3209376*e^6 - 1335399/1069792*e^5 - 7434785/3209376*e^4 + 32356175/3209376*e^3 + 21828925/1604688*e^2 - 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223153/1604688*e^6 + 1160757/534896*e^5 + 5027707/1604688*e^4 - 31095709/1604688*e^3 - 2115053/200586*e^2 + 9726601/200586*e - 351292/33431, -76103/802344*e^7 - 67115/200586*e^6 + 201591/66862*e^5 + 909838/100293*e^4 - 5415773/200586*e^3 - 43744601/802344*e^2 + 7312253/100293*e + 1276299/33431, -8021/100293*e^7 - 427067/1604688*e^6 + 1355535/534896*e^5 + 11746637/1604688*e^4 - 35709071/1604688*e^3 - 68292695/1604688*e^2 + 6259582/100293*e + 336599/66862, -9383/401172*e^7 - 31087/802344*e^6 + 149387/267448*e^5 + 536113/802344*e^4 - 375859/802344*e^3 + 1104995/802344*e^2 - 2160311/100293*e - 388855/33431, 35975/1069792*e^7 + 63049/1069792*e^6 - 1343863/1069792*e^5 - 1385387/1069792*e^4 + 15255317/1069792*e^3 + 2691209/534896*e^2 - 6459385/133724*e - 683007/66862, 3743/133724*e^7 + 1289/133724*e^6 - 124243/133724*e^5 + 46209/133724*e^4 + 1167589/133724*e^3 - 612481/66862*e^2 - 907377/33431*e + 1185024/33431, -25027/267448*e^7 - 144093/534896*e^6 + 1754683/534896*e^5 + 4159443/534896*e^4 - 18223833/534896*e^3 - 26945523/534896*e^2 + 3690729/33431*e + 1467145/66862, 42691/802344*e^7 + 86887/802344*e^6 - 508467/267448*e^5 - 2385325/802344*e^4 + 14699419/802344*e^3 + 3678499/200586*e^2 - 3424087/100293*e - 759916/33431, 29143/1069792*e^7 + 81489/1069792*e^6 - 1153455/1069792*e^5 - 2611619/1069792*e^4 + 13046621/1069792*e^3 + 10885237/534896*e^2 - 5175553/133724*e - 2437239/66862, -25693/802344*e^7 - 74281/802344*e^6 + 272341/267448*e^5 + 2356699/802344*e^4 - 7114477/802344*e^3 - 5272675/200586*e^2 + 2482633/100293*e + 2278494/33431, 156679/1604688*e^7 + 367831/1604688*e^6 - 1774579/534896*e^5 - 8775277/1604688*e^4 + 53138491/1604688*e^3 + 4328453/200586*e^2 - 19826149/200586*e + 638064/33431, 10207/133724*e^7 + 36817/267448*e^6 - 770151/267448*e^5 - 986767/267448*e^4 + 8588997/267448*e^3 + 4852679/267448*e^2 - 3388644/33431*e + 660127/33431, -19787/267448*e^7 - 44577/267448*e^6 + 675519/267448*e^5 + 1163699/267448*e^4 - 6546221/267448*e^3 - 3735763/133724*e^2 + 2219859/33431*e + 1117634/33431, 4299/1069792*e^7 + 128345/1069792*e^6 + 296665/1069792*e^5 - 3474411/1069792*e^4 - 10013723/1069792*e^3 + 10694375/534896*e^2 + 6124547/133724*e - 1133961/66862, -19795/267448*e^7 - 20911/267448*e^6 + 696881/267448*e^5 + 514469/267448*e^4 - 6679243/267448*e^3 - 510851/66862*e^2 + 1788012/33431*e - 519974/33431, -15911/802344*e^7 - 5245/401172*e^6 + 126017/133724*e^5 + 197221/401172*e^4 - 5749909/401172*e^3 - 5307143/802344*e^2 + 6434123/100293*e + 329021/33431, -96293/1604688*e^7 - 366167/1604688*e^6 + 975139/534896*e^5 + 9928997/1604688*e^4 - 24053579/1604688*e^3 - 27111889/802344*e^2 + 7949249/200586*e - 388037/33431, -3399/267448*e^7 - 15997/267448*e^6 + 74883/267448*e^5 + 390399/267448*e^4 + 206327/267448*e^3 - 788623/133724*e^2 - 684465/33431*e + 421876/33431, 1639/33431*e^7 + 24817/267448*e^6 - 478095/267448*e^5 - 589087/267448*e^4 + 5301605/267448*e^3 + 2539949/267448*e^2 - 2110052/33431*e + 31677/33431, 1321/3209376*e^7 - 339089/3209376*e^6 - 342811/1069792*e^5 + 10078691/3209376*e^4 + 26002051/3209376*e^3 - 34304437/1604688*e^2 - 17354455/401172*e + 1736189/66862, -26225/1069792*e^7 - 138611/1069792*e^6 + 866925/1069792*e^5 + 4348185/1069792*e^4 - 8237879/1069792*e^3 - 17290609/534896*e^2 + 2264735/133724*e + 2189427/66862, 28975/401172*e^7 + 187451/802344*e^6 - 703919/267448*e^5 - 5378357/802344*e^4 + 23682263/802344*e^3 + 36401849/802344*e^2 - 10636526/100293*e - 802035/33431, 38843/802344*e^7 + 170555/802344*e^6 - 404239/267448*e^5 - 5027033/802344*e^4 + 11092223/802344*e^3 + 4618078/100293*e^2 - 4405190/100293*e - 2070944/33431, -173623/3209376*e^7 - 590329/3209376*e^6 + 1678477/1069792*e^5 + 16345435/3209376*e^4 - 36206533/3209376*e^3 - 52930217/1604688*e^2 + 8412961/401172*e + 2684833/66862, 25849/401172*e^7 + 128225/802344*e^6 - 521509/267448*e^5 - 3363455/802344*e^4 + 11894837/802344*e^3 + 21141635/802344*e^2 - 2766011/100293*e - 1086807/33431] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, -w - 1])] = 1 AL_eigenvalues[ZF.ideal([5, 5, w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]