/* 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([2, 2, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([17, 17, -w + 3]) primes_array = [ [2, 2, -w],\ [3, 3, w + 1],\ [4, 2, -w^2 - w + 1],\ [13, 13, -w^2 + 3],\ [17, 17, -w + 3],\ [27, 3, w^3 - 2*w^2 - 3*w + 5],\ [31, 31, -w^2 - 2*w + 1],\ [41, 41, -w^2 + 5],\ [43, 43, w^3 - w^2 - 5*w - 1],\ [43, 43, w^3 - w^2 - 3*w + 1],\ [59, 59, -w - 3],\ [59, 59, -2*w^3 + 2*w^2 + 9*w - 5],\ [59, 59, -w^3 - 3*w^2 - w + 3],\ [59, 59, w^3 - 7*w + 1],\ [61, 61, -w^3 + w^2 + 2*w + 5],\ [61, 61, -w^3 - w^2 + 4*w + 3],\ [67, 67, 4*w^3 - 4*w^2 - 18*w + 7],\ [73, 73, -2*w^3 + 6*w - 3],\ [73, 73, -2*w + 3],\ [97, 97, w^3 - 2*w^2 - 5*w + 3],\ [101, 101, w^3 + w^2 - 5*w - 7],\ [101, 101, -w^3 - w^2 + 4*w + 5],\ [103, 103, 2*w^3 - 8*w - 1],\ [103, 103, w^2 - 2*w - 7],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, -w^3 + w^2 + 6*w - 3],\ [127, 127, -w^3 + w^2 + 6*w - 1],\ [131, 131, -2*w^3 + 3*w^2 + 10*w - 11],\ [137, 137, w^3 + w^2 - 6*w - 5],\ [139, 139, -3*w^3 + 2*w^2 + 15*w - 1],\ [149, 149, w^3 - 3*w^2 - 4*w + 11],\ [149, 149, -w^3 + 5*w - 1],\ [157, 157, -2*w^3 + 3*w^2 + 6*w - 1],\ [163, 163, 2*w^2 - 3],\ [163, 163, -2*w^3 + 2*w^2 + 7*w - 5],\ [167, 167, -2*w^3 + 2*w^2 + 8*w - 3],\ [167, 167, -2*w^2 + 2*w + 9],\ [173, 173, 2*w^3 - w^2 - 8*w + 3],\ [173, 173, 2*w^3 - 3*w^2 - 6*w + 3],\ [181, 181, 2*w^3 - 3*w^2 - 8*w + 5],\ [191, 191, -2*w^3 + w^2 + 10*w - 1],\ [193, 193, -w^3 + 3*w^2 + 2*w - 7],\ [193, 193, w^3 - 3*w - 3],\ [193, 193, 2*w^2 - 2*w - 3],\ [193, 193, w^3 - 7*w - 1],\ [197, 197, w^2 - 2*w - 5],\ [211, 211, w^2 - 4*w - 1],\ [229, 229, -w^3 + w^2 + 6*w - 7],\ [229, 229, -4*w^3 + 6*w^2 + 16*w - 13],\ [233, 233, 3*w^2 + 2*w - 5],\ [233, 233, 2*w^3 - 2*w^2 - 11*w + 7],\ [239, 239, -w^3 + w^2 + 7*w + 1],\ [241, 241, w^3 - 3*w^2 - 2*w + 9],\ [241, 241, w^3 + w^2 - 9*w - 5],\ [251, 251, 2*w^3 - 6*w + 1],\ [271, 271, 2*w^3 - w^2 - 8*w - 1],\ [271, 271, -2*w^2 + w + 7],\ [281, 281, 2*w^3 + 2*w^2 - 5*w - 1],\ [293, 293, w^3 + w^2 - 5*w - 1],\ [293, 293, -3*w + 7],\ [307, 307, -w^3 - 2*w^2 + 3*w + 5],\ [311, 311, -w^3 + 3*w^2 + 4*w - 7],\ [313, 313, 2*w^2 - 2*w - 5],\ [317, 317, -2*w^3 + 4*w^2 + 7*w - 13],\ [317, 317, -2*w^3 + 3*w^2 + 8*w - 11],\ [337, 337, 3*w^3 + 2*w^2 - 7*w + 1],\ [347, 347, 2*w^3 - 2*w^2 - 11*w + 1],\ [349, 349, -5*w^3 + 6*w^2 + 23*w - 13],\ [359, 359, 2*w^3 - 2*w^2 - 12*w + 9],\ [359, 359, -2*w^3 + 8*w + 5],\ [367, 367, -4*w^3 + 4*w^2 + 19*w - 5],\ [367, 367, 2*w^3 + w^2 - 10*w - 7],\ [383, 383, 2*w^3 - 2*w^2 - 7*w + 1],\ [389, 389, 2*w^2 - w - 5],\ [397, 397, 3*w^3 - 4*w^2 - 11*w + 9],\ [397, 397, 3*w^3 - 3*w^2 - 12*w + 7],\ [397, 397, 2*w^3 - 4*w^2 - 8*w + 15],\ [397, 397, -w^3 + 3*w^2 + w - 7],\ [409, 409, -w^3 - w^2 + 9*w - 1],\ [419, 419, 2*w^2 - 3*w - 7],\ [419, 419, 4*w^3 - 3*w^2 - 18*w + 3],\ [431, 431, -3*w^3 + w^2 + 17*w - 1],\ [431, 431, 3*w^3 - w^2 - 16*w - 1],\ [433, 433, -2*w^3 + 5*w^2 + 8*w - 19],\ [443, 443, 3*w - 5],\ [449, 449, -2*w^3 + 2*w^2 + 9*w - 9],\ [449, 449, -5*w^3 + 8*w^2 + 19*w - 17],\ [457, 457, -3*w^3 + 3*w^2 + 13*w - 9],\ [457, 457, -3*w^3 + 2*w^2 + 13*w + 1],\ [457, 457, -2*w^3 + w^2 + 8*w + 7],\ [457, 457, 3*w^3 - 3*w^2 - 15*w + 7],\ [461, 461, -2*w^3 + 2*w^2 + 9*w + 1],\ [479, 479, -w^3 + w^2 + 7*w - 9],\ [487, 487, -w^3 - w^2 + w - 3],\ [499, 499, -2*w^3 + 7*w - 3],\ [499, 499, -5*w^3 + 7*w^2 + 20*w - 15],\ [541, 541, -3*w^3 + 4*w^2 + 13*w - 7],\ [547, 547, -w^3 - w^2 + 3*w + 5],\ [557, 557, 4*w - 1],\ [563, 563, 2*w^3 - w^2 - 6*w - 1],\ [571, 571, w^3 - w^2 - w - 3],\ [587, 587, -2*w^3 + 2*w^2 + 10*w + 1],\ [593, 593, 2*w^3 - 2*w^2 - 6*w + 3],\ [613, 613, -5*w^3 + 5*w^2 + 23*w - 7],\ [613, 613, -w^3 + w^2 + 5*w - 7],\ [617, 617, -w - 5],\ [619, 619, -3*w^3 + 4*w^2 + 11*w - 7],\ [625, 5, -5],\ [643, 643, -3*w^3 + 3*w^2 + 14*w - 9],\ [643, 643, -3*w^2 - 4*w + 1],\ [653, 653, -w^3 + w^2 + 9*w + 3],\ [653, 653, -4*w^2 + 6*w + 11],\ [659, 659, -w^2 - 4*w + 1],\ [661, 661, -3*w^3 + 3*w^2 + 15*w - 5],\ [661, 661, w^3 + w^2 - 7*w - 11],\ [673, 673, 2*w^3 - 3*w^2 - 12*w + 1],\ [673, 673, -2*w^3 + w^2 + 10*w - 3],\ [683, 683, -w^3 - 2*w^2 + 5*w + 11],\ [691, 691, 4*w^3 - 3*w^2 - 18*w + 5],\ [709, 709, w^3 - 3*w - 7],\ [719, 719, 2*w^3 - 8*w + 1],\ [727, 727, -3*w^3 + 6*w^2 + 13*w - 19],\ [733, 733, w^3 - w^2 + 3],\ [739, 739, -w^3 + w^2 + 3*w - 7],\ [751, 751, -w^2 - 3],\ [773, 773, 2*w^3 - 2*w^2 - 11*w + 3],\ [787, 787, w^3 - w^2 - 3*w - 5],\ [797, 797, -2*w^3 + 2*w^2 + 5*w - 1],\ [797, 797, -7*w^3 + 8*w^2 + 31*w - 15],\ [809, 809, 4*w^3 - 6*w^2 - 17*w + 13],\ [809, 809, 3*w^2 - 4*w - 5],\ [811, 811, 2*w^2 + 4*w + 3],\ [811, 811, -3*w^3 + 3*w^2 + 12*w - 5],\ [821, 821, 2*w^3 - 10*w - 1],\ [821, 821, 6*w^3 - 10*w^2 - 24*w + 29],\ [823, 823, -5*w^3 + 3*w^2 + 24*w - 1],\ [823, 823, w^3 + w^2 + w + 3],\ [827, 827, -4*w^3 + 3*w^2 + 16*w - 7],\ [829, 829, 2*w^3 - 4*w^2 - 6*w + 11],\ [841, 29, w^3 - 3*w^2 - 5*w + 3],\ [841, 29, -3*w^3 + 3*w^2 + 13*w - 1],\ [857, 857, -4*w^3 + 6*w^2 + 13*w - 7],\ [857, 857, -3*w^3 + w^2 + 15*w + 1],\ [859, 859, -4*w^2 + 3*w + 17],\ [863, 863, -4*w^3 + 8*w^2 + 14*w - 21],\ [877, 877, -w^3 - w^2 + 6*w - 1],\ [881, 881, -5*w - 1],\ [883, 883, -4*w^3 + 4*w^2 + 21*w - 13],\ [883, 883, 2*w^3 - 11*w - 1],\ [887, 887, -3*w^3 - w^2 + 8*w - 5],\ [907, 907, w^3 - w^2 - w + 5],\ [911, 911, 2*w^2 - 5*w - 5],\ [919, 919, -w^3 + 3*w^2 + 6*w - 3],\ [919, 919, 5*w^2 + 4*w - 9],\ [929, 929, w^3 + 3*w^2 - 8*w - 17],\ [937, 937, -4*w^3 + 4*w^2 + 17*w - 7],\ [953, 953, -2*w^3 + 2*w^2 + 7*w + 5],\ [953, 953, 3*w^3 - 4*w^2 - 11*w + 3],\ [967, 967, 4*w^3 - 2*w^2 - 17*w + 3],\ [971, 971, w^3 - 3*w^2 - 8*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 12*w + 13],\ [991, 991, -2*w^3 - 2*w^2 + 8*w + 7],\ [991, 991, w^3 + w^2 - 10*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^15 - 5*x^14 - 11*x^13 + 87*x^12 + 3*x^11 - 580*x^10 + 406*x^9 + 1830*x^8 - 2012*x^7 - 2671*x^6 + 3809*x^5 + 1359*x^4 - 2752*x^3 + 62*x^2 + 508*x - 66 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -69/400*e^14 + 89/200*e^13 + 1213/400*e^12 - 761/100*e^11 - 8299/400*e^10 + 19963/400*e^9 + 5519/80*e^8 - 12497/80*e^7 - 44827/400*e^6 + 46769/200*e^5 + 30513/400*e^4 - 3557/25*e^3 - 358/25*e^2 + 4109/200*e + 161/200, 1027/400*e^14 - 1587/200*e^13 - 17379/400*e^12 + 14063/100*e^11 + 110717/400*e^10 - 385429/400*e^9 - 63897/80*e^8 + 254911/80*e^7 + 366141/400*e^6 - 1025427/200*e^5 - 1279/400*e^4 + 86781/25*e^3 - 10611/25*e^2 - 125347/200*e + 18137/200, -1887/400*e^14 + 2947/200*e^13 + 31799/400*e^12 - 26103/100*e^11 - 201377/400*e^10 + 715249/400*e^9 + 115037/80*e^8 - 473171/80*e^7 - 641121/400*e^6 + 1906187/200*e^5 - 37101/400*e^4 - 162061/25*e^3 + 20741/25*e^2 + 237407/200*e - 33997/200, -1, 759/80*e^14 - 1199/40*e^13 - 12743/80*e^12 + 10631/20*e^11 + 80249/80*e^10 - 291713/80*e^9 - 45413/16*e^8 + 193347/16*e^7 + 247497/80*e^6 - 780799/40*e^5 + 23677/80*e^4 + 66572/5*e^3 - 8332/5*e^2 - 97639/40*e + 13789/40, 751/200*e^14 - 1181/100*e^13 - 12627/200*e^12 + 10469/50*e^11 + 79721/200*e^10 - 287277/200*e^9 - 45341/40*e^8 + 190503/40*e^7 + 250833/200*e^6 - 770301/100*e^5 + 15273/200*e^4 + 131656/25*e^3 - 15836/25*e^2 - 96611/100*e + 13081/100, -1427/400*e^14 + 2187/200*e^13 + 24179/400*e^12 - 19363/100*e^11 - 154317/400*e^10 + 530229/400*e^9 + 89337/80*e^8 - 350511/80*e^7 - 516541/400*e^6 + 1411427/200*e^5 + 13679/400*e^4 - 120156/25*e^3 + 14111/25*e^2 + 177747/200*e - 22737/200, -457/400*e^14 + 617/200*e^13 + 8089/400*e^12 - 5433/100*e^11 - 55047/400*e^10 + 147439/400*e^9 + 35467/80*e^8 - 96061/80*e^7 - 261431/400*e^6 + 377657/200*e^5 + 124989/400*e^4 - 30796/25*e^3 + 1101/25*e^2 + 42177/200*e - 4067/200, -1959/200*e^14 + 3079/100*e^13 + 32943/200*e^12 - 27271/50*e^11 - 208089/200*e^10 + 747393/200*e^9 + 118509/40*e^8 - 494707/40*e^7 - 658497/200*e^6 + 1995059/100*e^5 - 34957/200*e^4 - 339729/25*e^3 + 41549/25*e^2 + 248199/100*e - 34829/100, 1079/200*e^14 - 1649/100*e^13 - 18283/200*e^12 + 14551/50*e^11 + 117009/200*e^10 - 396933/200*e^9 - 68389/40*e^8 + 261247/40*e^7 + 408857/200*e^6 - 1046729/100*e^5 - 39183/200*e^4 + 177199/25*e^3 - 20294/25*e^2 - 130019/100*e + 18849/100, -262/25*e^14 + 819/25*e^13 + 4424/25*e^12 - 14537/25*e^11 - 28102/25*e^10 + 99799/25*e^9 + 16157/5*e^8 - 66176/5*e^7 - 92196/25*e^6 + 534424/25*e^5 + 749/25*e^4 - 364051/25*e^3 + 41306/25*e^2 + 66314/25*e - 8844/25, -881/200*e^14 + 1361/100*e^13 + 14937/200*e^12 - 12089/50*e^11 - 95351/200*e^10 + 332287/200*e^9 + 55171/40*e^8 - 220613/40*e^7 - 318223/200*e^6 + 892781/100*e^5 + 6237/200*e^4 - 152911/25*e^3 + 17891/25*e^2 + 114341/100*e - 15411/100, -1823/400*e^14 + 2863/200*e^13 + 30671/400*e^12 - 25387/100*e^11 - 193633/400*e^10 + 696521/400*e^9 + 109933/80*e^8 - 461419/80*e^7 - 603409/400*e^6 + 1861023/200*e^5 - 47029/400*e^4 - 158169/25*e^3 + 19489/25*e^2 + 229703/200*e - 32613/200, 3377/400*e^14 - 5237/200*e^13 - 57129/400*e^12 + 46413/100*e^11 + 363967/400*e^10 - 1272479/400*e^9 - 210227/80*e^8 + 842301/80*e^7 + 1208591/400*e^6 - 3396077/200*e^5 - 11229/400*e^4 + 289331/25*e^3 - 34961/25*e^2 - 428297/200*e + 59987/200, 3121/400*e^14 - 4901/200*e^13 - 52617/400*e^12 + 43549/100*e^11 + 332991/400*e^10 - 1197567/400*e^9 - 189651/80*e^8 + 795373/80*e^7 + 1046543/400*e^6 - 3217821/200*e^5 + 76883/400*e^4 + 274838/25*e^3 - 33878/25*e^2 - 405481/200*e + 54851/200, 151/200*e^14 - 231/100*e^13 - 2527/200*e^12 + 2019/50*e^11 + 15921/200*e^10 - 54577/200*e^9 - 9101/40*e^8 + 35643/40*e^7 + 52233/200*e^6 - 141951/100*e^5 - 2827/200*e^4 + 23881/25*e^3 - 2536/25*e^2 - 17311/100*e + 2581/100, 1687/100*e^14 - 2647/50*e^13 - 28399/100*e^12 + 23453/25*e^11 + 179677/100*e^10 - 642949/100*e^9 - 102657/20*e^8 + 425651/20*e^7 + 576421/100*e^6 - 1716537/50*e^5 + 15501/100*e^4 + 584519/25*e^3 - 69039/25*e^2 - 214057/50*e + 28997/50, 4603/400*e^14 - 7143/200*e^13 - 77731/400*e^12 + 63207/100*e^11 + 494213/400*e^10 - 1729781/400*e^9 - 284833/80*e^8 + 1142559/80*e^7 + 1635349/400*e^6 - 4594303/200*e^5 - 25631/400*e^4 + 389809/25*e^3 - 45854/25*e^2 - 570483/200*e + 78193/200, 899/200*e^14 - 1369/100*e^13 - 15223/200*e^12 + 12081/50*e^11 + 97029/200*e^10 - 329273/200*e^9 - 55969/40*e^8 + 216187/40*e^7 + 318517/200*e^6 - 861749/100*e^5 + 8277/200*e^4 + 144544/25*e^3 - 20164/25*e^2 - 105739/100*e + 16469/100, -543/100*e^14 + 833/50*e^13 + 9211/100*e^12 - 7367/25*e^11 - 58953/100*e^10 + 201361/100*e^9 + 34353/20*e^8 - 132679/20*e^7 - 202269/100*e^6 + 531093/50*e^5 + 11411/100*e^4 - 178766/25*e^3 + 21721/25*e^2 + 64673/50*e - 9633/50, 3587/200*e^14 - 5647/100*e^13 - 60299/200*e^12 + 50053/50*e^11 + 380477/200*e^10 - 1372749/200*e^9 - 216097/40*e^8 + 909191/40*e^7 + 1190421/200*e^6 - 3667987/100*e^5 + 84801/200*e^4 + 624722/25*e^3 - 77107/25*e^2 - 457707/100*e + 65097/100, 303/20*e^14 - 483/10*e^13 - 5071/20*e^12 + 4282/5*e^11 + 31793/20*e^10 - 117501/20*e^9 - 17865/4*e^8 + 77903/4*e^7 + 95789/20*e^6 - 314833/10*e^5 + 11689/20*e^4 + 107521/5*e^3 - 13181/5*e^2 - 39413/10*e + 5393/10, 793/40*e^14 - 1253/20*e^13 - 13321/40*e^12 + 11117/10*e^11 + 83903/40*e^10 - 305231/40*e^9 - 47435/8*e^8 + 202413/8*e^7 + 256919/40*e^6 - 817793/20*e^5 + 29379/40*e^4 + 139518/5*e^3 - 17893/5*e^2 - 102333/20*e + 14603/20, -39/5*e^14 + 251/10*e^13 + 1301/10*e^12 - 2229/5*e^11 - 4049/5*e^10 + 30641/10*e^9 + 2235*e^8 - 20357/2*e^7 - 11187/5*e^6 + 164891/10*e^5 - 6869/10*e^4 - 56432/5*e^3 + 8097/5*e^2 + 10378/5*e - 1543/5, -473/40*e^14 + 733/20*e^13 + 8001/40*e^12 - 6497/10*e^11 - 50943/40*e^10 + 178111/40*e^9 + 29379/8*e^8 - 117845/8*e^7 - 168279/40*e^6 + 474553/20*e^5 + 1061/40*e^4 - 80623/5*e^3 + 9628/5*e^2 + 59333/20*e - 8043/20, 1017/100*e^14 - 1577/50*e^13 - 17209/100*e^12 + 13973/25*e^11 + 109807/100*e^10 - 383059/100*e^9 - 63787/20*e^8 + 253601/20*e^7 + 376011/100*e^6 - 1022917/50*e^5 - 30309/100*e^4 + 348654/25*e^3 - 36499/25*e^2 - 128137/50*e + 16727/50, 91/400*e^14 - 171/200*e^13 - 1307/400*e^12 + 1479/100*e^11 + 5861/400*e^10 - 39757/400*e^9 - 481/80*e^8 + 26103/80*e^7 - 49547/400*e^6 - 106691/200*e^5 + 125593/400*e^4 + 9473/25*e^3 - 5863/25*e^2 - 13451/200*e + 6921/200, -1551/100*e^14 + 2431/50*e^13 + 26127/100*e^12 - 21569/25*e^11 - 165221/100*e^10 + 592177/100*e^9 + 94021/20*e^8 - 392623/20*e^7 - 517533/100*e^6 + 1585451/50*e^5 - 43373/100*e^4 - 540387/25*e^3 + 69422/25*e^2 + 198211/50*e - 28581/50, -243/200*e^14 + 333/100*e^13 + 4311/200*e^12 - 2967/50*e^11 - 29253/200*e^10 + 81761/200*e^9 + 18513/40*e^8 - 54379/40*e^7 - 126869/200*e^6 + 220393/100*e^5 + 34611/200*e^4 - 38058/25*e^3 + 5123/25*e^2 + 30923/100*e - 5933/100, -2637/400*e^14 + 4297/200*e^13 + 43749/400*e^12 - 38153/100*e^11 - 269827/400*e^10 + 1048899/400*e^9 + 146087/80*e^8 - 697081/80*e^7 - 681571/400*e^6 + 2826537/200*e^5 - 333751/400*e^4 - 242636/25*e^3 + 37366/25*e^2 + 359757/200*e - 55047/200, -2063/200*e^14 + 3203/100*e^13 + 34751/200*e^12 - 28297/50*e^11 - 220273/200*e^10 + 773201/200*e^9 + 126413/40*e^8 - 510019/40*e^7 - 719129/200*e^6 + 2048763/100*e^5 - 2149/200*e^4 - 347603/25*e^3 + 42043/25*e^2 + 255343/100*e - 35853/100, -191/40*e^14 + 311/20*e^13 + 3167/40*e^12 - 2759/10*e^11 - 19521/40*e^10 + 75737/40*e^9 + 10573/8*e^8 - 50203/8*e^7 - 49833/40*e^6 + 202611/20*e^5 - 22133/40*e^4 - 34461/5*e^3 + 5131/5*e^2 + 24991/20*e - 3821/20, 23/25*e^14 - 51/25*e^13 - 421/25*e^12 + 848/25*e^11 + 3033/25*e^10 - 5321/25*e^9 - 2148/5*e^8 + 3104/5*e^7 + 18709/25*e^6 - 20621/25*e^5 - 13346/25*e^4 + 10029/25*e^3 + 1676/25*e^2 - 1156/25*e + 326/25, -1053/80*e^14 + 1593/40*e^13 + 17941/80*e^12 - 14077/20*e^11 - 115603/80*e^10 + 384371/80*e^9 + 68199/16*e^8 - 252985/16*e^7 - 415459/80*e^6 + 1011753/40*e^5 + 55081/80*e^4 - 85124/5*e^3 + 9259/5*e^2 + 123213/40*e - 16343/40, 2317/400*e^14 - 3577/200*e^13 - 39109/400*e^12 + 31573/100*e^11 + 248707/400*e^10 - 861459/400*e^9 - 143687/80*e^8 + 566921/80*e^7 + 836211/400*e^6 - 2268817/200*e^5 - 50009/400*e^4 + 191176/25*e^3 - 20706/25*e^2 - 276237/200*e + 35127/200, -8941/400*e^14 + 14121/200*e^13 + 150357/400*e^12 - 125329/100*e^11 - 949011/400*e^10 + 3442707/400*e^9 + 539031/80*e^8 - 2284473/80*e^7 - 2966403/400*e^6 + 9237441/200*e^5 - 219943/400*e^4 - 788898/25*e^3 + 96188/25*e^2 + 1160301/200*e - 158871/200, -1151/100*e^14 + 878/25*e^13 + 19577/100*e^12 - 15544/25*e^11 - 125821/100*e^10 + 425427/100*e^9 + 73881/20*e^8 - 280873/20*e^7 - 444333/100*e^6 + 563838/25*e^5 + 46577/100*e^4 - 381387/25*e^3 + 42372/25*e^2 + 139011/50*e - 19131/50, 749/100*e^14 - 597/25*e^13 - 12523/100*e^12 + 10581/25*e^11 + 78379/100*e^10 - 290273/100*e^9 - 43859/20*e^8 + 192467/20*e^7 + 231067/100*e^6 - 389237/25*e^5 + 40277/100*e^4 + 266538/25*e^3 - 34928/25*e^2 - 98689/50*e + 13869/50, -549/50*e^14 + 869/25*e^13 + 9223/50*e^12 - 15412/25*e^11 - 58179/50*e^10 + 211473/50*e^9 + 33069/10*e^8 - 140167/10*e^7 - 183117/50*e^6 + 565974/25*e^5 - 10377/50*e^4 - 385926/25*e^3 + 46356/25*e^2 + 70614/25*e - 10069/25, -2717/100*e^14 + 2126/25*e^13 + 45759/100*e^12 - 37673/25*e^11 - 289607/100*e^10 + 1032709/100*e^9 + 165407/20*e^8 - 683571/20*e^7 - 924711/100*e^6 + 1377921/25*e^5 - 40041/100*e^4 - 938254/25*e^3 + 115349/25*e^2 + 345237/50*e - 48477/50, 143/100*e^14 - 283/50*e^13 - 2211/100*e^12 + 2542/25*e^11 + 12053/100*e^10 - 70961/100*e^9 - 4853/20*e^8 + 48079/20*e^7 - 4631/100*e^6 - 199543/50*e^5 + 67589/100*e^4 + 70341/25*e^3 - 13096/25*e^2 - 26573/50*e + 4733/50, -148/25*e^14 + 877/50*e^13 + 5067/50*e^12 - 7723/25*e^11 - 16458/25*e^10 + 105017/50*e^9 + 9858/5*e^8 - 68813/10*e^7 - 62284/25*e^6 + 547917/50*e^5 + 24167/50*e^4 - 183954/25*e^3 + 20224/25*e^2 + 33856/25*e - 5051/25, 2713/200*e^14 - 4303/100*e^13 - 45501/200*e^12 + 38197/50*e^11 + 285623/200*e^10 - 1049251/200*e^9 - 160163/40*e^8 + 696009/40*e^7 + 842279/200*e^6 - 2811163/100*e^5 + 157799/200*e^4 + 478603/25*e^3 - 65168/25*e^2 - 348193/100*e + 51703/100, -1231/400*e^14 + 2111/200*e^13 + 19887/400*e^12 - 18739/100*e^11 - 117201/400*e^10 + 515337/400*e^9 + 57501/80*e^8 - 342763/80*e^7 - 169073/400*e^6 + 1390831/200*e^5 - 339413/400*e^4 - 119168/25*e^3 + 22308/25*e^2 + 174591/200*e - 29461/200, -1831/400*e^14 + 3111/200*e^13 + 30087/400*e^12 - 27839/100*e^11 - 182601/400*e^10 + 773137/400*e^9 + 95781/80*e^8 - 520563/80*e^7 - 400473/400*e^6 + 2146231/200*e^5 - 304013/400*e^4 - 188018/25*e^3 + 26758/25*e^2 + 281991/200*e - 40461/200, 659/25*e^14 - 2058/25*e^13 - 11118/25*e^12 + 36509/25*e^11 + 70489/25*e^10 - 250468/25*e^9 - 40324/5*e^8 + 165937/5*e^7 + 225697/25*e^6 - 1338568/25*e^5 + 9782/25*e^4 + 910782/25*e^3 - 112317/25*e^2 - 166498/25*e + 23408/25, -32/5*e^14 + 99/5*e^13 + 544/5*e^12 - 1757/5*e^11 - 3492/5*e^10 + 12054/5*e^9 + 2044*e^8 - 7980*e^7 - 12161/5*e^6 + 64239/5*e^5 + 969/5*e^4 - 43531/5*e^3 + 4906/5*e^2 + 7944/5*e - 1144/5, 297/100*e^14 - 507/50*e^13 - 4869/100*e^12 + 4543/25*e^11 + 29387/100*e^10 - 126419/100*e^9 - 15167/20*e^8 + 85381/20*e^7 + 57951/100*e^6 - 353847/50*e^5 + 61831/100*e^4 + 125339/25*e^3 - 19584/25*e^2 - 48717/50*e + 7607/50, 813/100*e^14 - 1303/50*e^13 - 13601/100*e^12 + 11597/25*e^11 + 84923/100*e^10 - 319551/100*e^9 - 47023/20*e^8 + 212729/20*e^7 + 235979/100*e^6 - 862613/50*e^5 + 73299/100*e^4 + 294906/25*e^3 - 43136/25*e^2 - 107793/50*e + 16503/50, 939/100*e^14 - 1509/50*e^13 - 15703/100*e^12 + 13416/25*e^11 + 98269/100*e^10 - 369453/100*e^9 - 54969/20*e^8 + 246027/20*e^7 + 290237/100*e^6 - 999839/50*e^5 + 45097/100*e^4 + 344168/25*e^3 - 41433/25*e^2 - 128029/50*e + 16509/50, 1849/200*e^14 - 2769/100*e^13 - 31673/200*e^12 + 24531/50*e^11 + 205279/200*e^10 - 671423/200*e^9 - 121819/40*e^8 + 442757/40*e^7 + 745567/200*e^6 - 1772249/100*e^5 - 95773/200*e^4 + 298194/25*e^3 - 34064/25*e^2 - 218689/100*e + 30219/100, 5317/400*e^14 - 7977/200*e^13 - 90909/400*e^12 + 70573/100*e^11 + 588507/400*e^10 - 1929259/400*e^9 - 349647/80*e^8 + 1271121/80*e^7 + 2162811/400*e^6 - 5087217/200*e^5 - 345409/400*e^4 + 428226/25*e^3 - 45456/25*e^2 - 621637/200*e + 83327/200, 591/100*e^14 - 448/25*e^13 - 10057/100*e^12 + 7929/25*e^11 + 64661/100*e^10 - 217007/100*e^9 - 37981/20*e^8 + 143353/20*e^7 + 228753/100*e^6 - 288283/25*e^5 - 25657/100*e^4 + 195842/25*e^3 - 20952/25*e^2 - 71951/50*e + 8971/50, 4957/200*e^14 - 7667/100*e^13 - 83889/200*e^12 + 67933/50*e^11 + 534747/200*e^10 - 1861839/200*e^9 - 309207/40*e^8 + 1231741/40*e^7 + 1783931/200*e^6 - 4961307/100*e^5 - 31989/200*e^4 + 843542/25*e^3 - 101452/25*e^2 - 620277/100*e + 87867/100, -14571/400*e^14 + 22751/200*e^13 + 245667/400*e^12 - 201599/100*e^11 - 1556741/400*e^10 + 5526117/400*e^9 + 890321/80*e^8 - 3656703/80*e^7 - 4984693/400*e^6 + 14729871/200*e^5 - 213233/400*e^4 - 1251088/25*e^3 + 155453/25*e^2 + 1825531/200*e - 257201/200, -2441/200*e^14 + 3921/100*e^13 + 40657/200*e^12 - 34729/50*e^11 - 252911/200*e^10 + 952007/200*e^9 + 139891/40*e^8 - 630493/40*e^7 - 711703/200*e^6 + 2545441/100*e^5 - 179243/200*e^4 - 434371/25*e^3 + 59026/25*e^2 + 318401/100*e - 44971/100, -741/20*e^14 + 583/5*e^13 + 12467/20*e^12 - 10339/5*e^11 - 78771/20*e^10 + 283697/20*e^9 + 44855/4*e^8 - 188019/4*e^7 - 249003/20*e^6 + 379598/5*e^5 - 13393/20*e^4 - 258917/5*e^3 + 31242/5*e^2 + 95021/10*e - 12921/10, -1659/80*e^14 + 2599/40*e^13 + 27923/80*e^12 - 23031/20*e^11 - 176469/80*e^10 + 631413/80*e^9 + 100433/16*e^8 - 417967/16*e^7 - 554837/80*e^6 + 1684959/40*e^5 - 38737/80*e^4 - 143367/5*e^3 + 17972/5*e^2 + 210139/40*e - 29409/40, 29/40*e^14 - 79/20*e^13 - 393/40*e^12 + 741/10*e^11 + 1459/40*e^10 - 21743/40*e^9 + 321/8*e^8 + 15605/8*e^7 - 20573/40*e^6 - 69259/20*e^5 + 39467/40*e^4 + 13194/5*e^3 - 2724/5*e^2 - 10629/20*e + 1539/20, -953/50*e^14 + 1493/25*e^13 + 16031/50*e^12 - 26439/25*e^11 - 101313/50*e^10 + 362131/50*e^9 + 57763/10*e^8 - 239549/10*e^7 - 322149/50*e^6 + 965428/25*e^5 - 14669/50*e^4 - 657872/25*e^3 + 80632/25*e^2 + 121333/25*e - 16693/25, 3997/200*e^14 - 6257/100*e^13 - 67469/200*e^12 + 55543/50*e^11 + 428187/200*e^10 - 1525619/200*e^9 - 245487/40*e^8 + 1011801/40*e^7 + 1383851/200*e^6 - 4085097/100*e^5 + 36031/200*e^4 + 695057/25*e^3 - 83267/25*e^2 - 505517/100*e + 69807/100, 477/25*e^14 - 1499/25*e^13 - 8029/25*e^12 + 26577/25*e^11 + 50767/25*e^10 - 182229/25*e^9 - 28952/5*e^8 + 120676/5*e^7 + 161491/25*e^6 - 973329/25*e^5 + 7021/25*e^4 + 662446/25*e^3 - 80001/25*e^2 - 120694/25*e + 16724/25, -93/100*e^14 + 83/50*e^13 + 1761/100*e^12 - 667/25*e^11 - 13203/100*e^10 + 15911/100*e^9 + 9803/20*e^8 - 8569/20*e^7 - 90819/100*e^6 + 24793/50*e^5 + 72461/100*e^4 - 4566/25*e^3 - 3879/25*e^2 + 1473/50*e + 417/50, -1073/100*e^14 + 1663/50*e^13 + 18121/100*e^12 - 14712/25*e^11 - 115183/100*e^10 + 402471/100*e^9 + 66283/20*e^8 - 265669/20*e^7 - 377559/100*e^6 + 1066873/50*e^5 - 3079/100*e^4 - 360951/25*e^3 + 44731/25*e^2 + 131403/50*e - 19263/50, -129/25*e^14 + 821/50*e^13 + 4291/50*e^12 - 7254/25*e^11 - 13284/25*e^10 + 99041/50*e^9 + 7244/5*e^8 - 65189/10*e^7 - 34557/25*e^6 + 521091/50*e^5 - 30509/50*e^4 - 174942/25*e^3 + 29352/25*e^2 + 31588/25*e - 5423/25, -47/10*e^14 + 77/5*e^13 + 779/10*e^12 - 1366/5*e^11 - 4817/10*e^10 + 18769/10*e^9 + 2645/2*e^8 - 12479/2*e^7 - 13341/10*e^6 + 50667/5*e^5 - 3261/10*e^4 - 34778/5*e^3 + 4248/5*e^2 + 6257/5*e - 837/5, -1793/100*e^14 + 1404/25*e^13 + 30211/100*e^12 - 24917/25*e^11 - 191103/100*e^10 + 684161/100*e^9 + 108823/20*e^8 - 453659/20*e^7 - 601119/100*e^6 + 916184/25*e^5 - 42589/100*e^4 - 624866/25*e^3 + 78046/25*e^2 + 228873/50*e - 31733/50, 2447/400*e^14 - 3707/200*e^13 - 41719/400*e^12 + 32743/100*e^11 + 269537/400*e^10 - 893969/400*e^9 - 160237/80*e^8 + 588771/80*e^7 + 1001601/400*e^6 - 2359747/200*e^5 - 193619/400*e^4 + 199766/25*e^3 - 18571/25*e^2 - 295567/200*e + 33357/200, 1247/200*e^14 - 2007/100*e^13 - 20719/200*e^12 + 17793/50*e^11 + 128137/200*e^10 - 488169/200*e^9 - 69837/40*e^8 + 323451/40*e^7 + 335801/200*e^6 - 1304947/100*e^5 + 131981/200*e^4 + 221832/25*e^3 - 32567/25*e^2 - 160567/100*e + 25557/100, -1051/25*e^14 + 6599/50*e^13 + 35379/50*e^12 - 58476/25*e^11 - 111846/25*e^10 + 801579/50*e^9 + 63776/5*e^8 - 530621/10*e^7 - 355383/25*e^6 + 4278479/50*e^5 - 33171/50*e^4 - 1456298/25*e^3 + 177163/25*e^2 + 266922/25*e - 36887/25, -1363/400*e^14 + 2103/200*e^13 + 23051/400*e^12 - 18647/100*e^11 - 146173/400*e^10 + 511101/400*e^9 + 83033/80*e^8 - 337879/80*e^7 - 446429/400*e^6 + 1358863/200*e^5 - 70649/400*e^4 - 115364/25*e^3 + 16784/25*e^2 + 170243/200*e - 26153/200, 493/40*e^14 - 743/20*e^13 - 8441/40*e^12 + 6587/10*e^11 + 54763/40*e^10 - 180551/40*e^9 - 32671/8*e^8 + 119381/8*e^7 + 204499/40*e^6 - 480103/20*e^5 - 38461/40*e^4 + 81378/5*e^3 - 7868/5*e^2 - 59593/20*e + 7923/20, 49/80*e^14 - 69/40*e^13 - 793/80*e^12 + 581/20*e^11 + 4719/80*e^10 - 15023/80*e^9 - 2371/16*e^8 + 9293/16*e^7 + 7567/80*e^6 - 34509/40*e^5 + 13827/80*e^4 + 2652/5*e^3 - 912/5*e^2 - 4129/40*e + 339/40, -183/10*e^14 + 283/5*e^13 + 3091/10*e^12 - 5009/5*e^11 - 19653/10*e^10 + 68551/10*e^9 + 11325/2*e^8 - 45289/2*e^7 - 65039/10*e^6 + 182158/5*e^5 + 1241/10*e^4 - 123662/5*e^3 + 14402/5*e^2 + 22573/5*e - 3053/5, -19/16*e^14 + 23/8*e^13 + 347/16*e^12 - 203/4*e^11 - 2413/16*e^10 + 5453/16*e^9 + 7725/16*e^8 - 17219/16*e^7 - 10221/16*e^6 + 12679/8*e^5 + 1111/16*e^4 - 921*e^3 + 325*e^2 + 1259/8*e - 473/8, -427/40*e^14 + 647/20*e^13 + 7259/40*e^12 - 5723/10*e^11 - 46597/40*e^10 + 156549/40*e^9 + 27297/8*e^8 - 103351/8*e^7 - 163501/40*e^6 + 415347/20*e^5 + 17239/40*e^4 - 70452/5*e^3 + 7547/5*e^2 + 51827/20*e - 6697/20, 1039/80*e^14 - 1619/40*e^13 - 17463/80*e^12 + 14291/20*e^11 + 110209/80*e^10 - 389953/80*e^9 - 62605/16*e^8 + 256675/16*e^7 + 343617/80*e^6 - 1027939/40*e^5 + 31837/80*e^4 + 86842/5*e^3 - 11802/5*e^2 - 126759/40*e + 18829/40, 2539/80*e^14 - 3919/40*e^13 - 43043/80*e^12 + 34751/20*e^11 + 275029/80*e^10 - 953173/80*e^9 - 159681/16*e^8 + 631071/16*e^7 + 932277/80*e^6 - 2543399/40*e^5 - 44223/80*e^4 + 216177/5*e^3 - 24752/5*e^2 - 315459/40*e + 43729/40, 283/25*e^14 - 1767/50*e^13 - 9557/50*e^12 + 15683/25*e^11 + 30318/25*e^10 - 215307/50*e^9 - 17343/5*e^8 + 142713/10*e^7 + 96564/25*e^6 - 1151607/50*e^5 + 12743/50*e^4 + 391534/25*e^3 - 50904/25*e^2 - 70801/25*e + 10671/25, 9049/400*e^14 - 14269/200*e^13 - 152273/400*e^12 + 126681/100*e^11 + 961479/400*e^10 - 3480823/400*e^9 - 545739/80*e^8 + 2310277/80*e^7 + 2984567/400*e^6 - 9342349/200*e^5 + 284427/400*e^4 + 797422/25*e^3 - 101232/25*e^2 - 1167689/200*e + 170619/200, 2383/80*e^14 - 3723/40*e^13 - 40151/80*e^12 + 32967/20*e^11 + 254433/80*e^10 - 903201/80*e^9 - 145837/16*e^8 + 597571/16*e^7 + 826769/80*e^6 - 2408483/40*e^5 + 4749/80*e^4 + 204944/5*e^3 - 23864/5*e^2 - 299623/40*e + 40893/40, 829/200*e^14 - 1149/100*e^13 - 14733/200*e^12 + 10251/50*e^11 + 100459/200*e^10 - 282283/200*e^9 - 64519/40*e^8 + 186937/40*e^7 + 465907/200*e^6 - 749029/100*e^5 - 193833/200*e^4 + 125324/25*e^3 - 8544/25*e^2 - 89069/100*e + 14199/100, 9557/200*e^14 - 15017/100*e^13 - 160789/200*e^12 + 133133/50*e^11 + 1015547/200*e^10 - 3652139/200*e^9 - 577407/40*e^8 + 2419521/40*e^7 + 3182131/200*e^6 - 9764657/100*e^5 + 239511/200*e^4 + 1664042/25*e^3 - 208477/25*e^2 - 1221477/100*e + 171167/100, -5017/200*e^14 + 7777/100*e^13 + 84809/200*e^12 - 68873/50*e^11 - 539807/200*e^10 + 1886559/200*e^9 + 311427/40*e^8 - 1247341/40*e^7 - 1787911/200*e^6 + 5020417/100*e^5 + 17709/200*e^4 - 852202/25*e^3 + 102812/25*e^2 + 619737/100*e - 90027/100, 557/20*e^14 - 867/10*e^13 - 9389/20*e^12 + 7673/5*e^11 + 59507/20*e^10 - 210019/20*e^9 - 34075/4*e^8 + 138733/4*e^7 + 191751/20*e^6 - 557717/10*e^5 + 6171/20*e^4 + 189024/5*e^3 - 23719/5*e^2 - 68737/10*e + 9987/10, -6701/400*e^14 + 10081/200*e^13 + 114277/400*e^12 - 89069/100*e^11 - 737171/400*e^10 + 2431827/400*e^9 + 435431/80*e^8 - 1600473/80*e^7 - 2655283/400*e^6 + 6398401/200*e^5 + 347977/400*e^4 - 537528/25*e^3 + 60018/25*e^2 + 776461/200*e - 113031/200, 7239/400*e^14 - 11259/200*e^13 - 121903/400*e^12 + 99491/100*e^11 + 771769/400*e^10 - 2718553/400*e^9 - 441269/80*e^8 + 1792427/80*e^7 + 2474937/400*e^6 - 7190739/200*e^5 + 91397/400*e^4 + 608042/25*e^3 - 76252/25*e^2 - 886279/200*e + 124709/200, -1349/80*e^14 + 2169/40*e^13 + 22573/80*e^12 - 19281/20*e^11 - 141339/80*e^10 + 530683/80*e^9 + 79071/16*e^8 - 352977/16*e^7 - 416347/80*e^6 + 1430969/40*e^5 - 69967/80*e^4 - 122447/5*e^3 + 15287/5*e^2 + 179189/40*e - 24079/40, -5817/200*e^14 + 9077/100*e^13 + 98009/200*e^12 - 80323/50*e^11 - 621207/200*e^10 + 2198759/200*e^9 + 356307/40*e^8 - 1453101/40*e^7 - 2023711/200*e^6 + 5847517/100*e^5 - 8491/200*e^4 - 992977/25*e^3 + 117837/25*e^2 + 725437/100*e - 102827/100, -3951/100*e^14 + 3053/25*e^13 + 66877/100*e^12 - 54094/25*e^11 - 426521/100*e^10 + 1482427/100*e^9 + 247001/20*e^8 - 980773/20*e^7 - 1434333/100*e^6 + 1975763/25*e^5 + 53377/100*e^4 - 1344612/25*e^3 + 155422/25*e^2 + 494411/50*e - 67331/50, -1127/40*e^14 + 1787/20*e^13 + 18879/40*e^12 - 15843/10*e^11 - 118457/40*e^10 + 434769/40*e^9 + 66549/8*e^8 - 288283/8*e^7 - 354281/40*e^6 + 1165327/20*e^5 - 54261/40*e^4 - 199132/5*e^3 + 26222/5*e^2 + 146567/20*e - 21117/20, 1533/400*e^14 - 2673/200*e^13 - 24741/400*e^12 + 23777/100*e^11 + 145843/400*e^10 - 655491/400*e^9 - 72023/80*e^8 + 437289/80*e^7 + 228739/400*e^6 - 1781433/200*e^5 + 372359/400*e^4 + 153449/25*e^3 - 24494/25*e^2 - 221813/200*e + 28023/200, 111/20*e^14 - 181/10*e^13 - 1827/20*e^12 + 1599/5*e^11 + 11141/20*e^10 - 43717/20*e^9 - 5913/4*e^8 + 28875/4*e^7 + 25873/20*e^6 - 116191/10*e^5 + 16733/20*e^4 + 39392/5*e^3 - 6477/5*e^2 - 14091/10*e + 2441/10, 261/10*e^14 - 401/5*e^13 - 4427/10*e^12 + 7103/5*e^11 + 28321/10*e^10 - 97267/10*e^9 - 16491/2*e^8 + 64281/2*e^7 + 97193/10*e^6 - 258541/5*e^5 - 6737/10*e^4 + 175549/5*e^3 - 19649/5*e^2 - 32271/5*e + 4291/5, 3129/100*e^14 - 4849/50*e^13 - 52833/100*e^12 + 42876/25*e^11 + 336059/100*e^10 - 1172483/100*e^9 - 194079/20*e^8 + 773857/20*e^7 + 1124007/100*e^6 - 3109479/50*e^5 - 42333/100*e^4 + 1054748/25*e^3 - 120938/25*e^2 - 385969/50*e + 53099/50, 533/80*e^14 - 853/40*e^13 - 8981/80*e^12 + 7637/20*e^11 + 56683/80*e^10 - 212051/80*e^9 - 32015/16*e^8 + 142601/16*e^7 + 171099/80*e^6 - 586493/40*e^5 + 26279/80*e^4 + 51254/5*e^3 - 6304/5*e^2 - 77813/40*e + 10663/40, 213/16*e^14 - 329/8*e^13 - 3597/16*e^12 + 2909/4*e^11 + 22891/16*e^10 - 79579/16*e^9 - 66235/16*e^8 + 262933/16*e^7 + 77531/16*e^6 - 211889/8*e^5 - 5505/16*e^4 + 18071*e^3 - 1902*e^2 - 26709/8*e + 3439/8, -3077/100*e^14 + 4787/50*e^13 + 52029/100*e^12 - 42488/25*e^11 - 330967/100*e^10 + 1166679/100*e^9 + 190467/20*e^8 - 773341/20*e^7 - 1084391/100*e^6 + 3119827/50*e^5 - 4771/100*e^4 - 1060674/25*e^3 + 125144/25*e^2 + 386647/50*e - 51987/50, 591/400*e^14 - 1071/200*e^13 - 9407/400*e^12 + 9479/100*e^11 + 54561/400*e^10 - 259257/400*e^9 - 26541/80*e^8 + 170923/80*e^7 + 85953/400*e^6 - 684591/200*e^5 + 122693/400*e^4 + 57473/25*e^3 - 8063/25*e^2 - 76951/200*e + 9621/200, 2193/100*e^14 - 3433/50*e^13 - 36961/100*e^12 + 30417/25*e^11 + 234303/100*e^10 - 833711/100*e^9 - 134403/20*e^8 + 551709/20*e^7 + 764519/100*e^6 - 2223343/50*e^5 - 3861/100*e^4 + 756391/25*e^3 - 85746/25*e^2 - 276873/50*e + 36683/50, 139/100*e^14 - 309/50*e^13 - 2003/100*e^12 + 2766/25*e^11 + 9569/100*e^10 - 77253/100*e^9 - 2489/20*e^8 + 52687/20*e^7 - 27563/100*e^6 - 221889/50*e^5 + 77297/100*e^4 + 79893/25*e^3 - 10133/25*e^2 - 29579/50*e + 3009/50, -323/40*e^14 + 523/20*e^13 + 5371/40*e^12 - 4637/10*e^11 - 33333/40*e^10 + 127261/40*e^9 + 18385/8*e^8 - 84391/8*e^7 - 93549/40*e^6 + 341083/20*e^5 - 21529/40*e^4 - 58173/5*e^3 + 7378/5*e^2 + 42123/20*e - 6033/20, -1331/50*e^14 + 2086/25*e^13 + 22437/50*e^12 - 37028/25*e^11 - 142101/50*e^10 + 508537/50*e^9 + 81181/10*e^8 - 337413/10*e^7 - 453773/50*e^6 + 1364231/25*e^5 - 18663/50*e^4 - 932194/25*e^3 + 111964/25*e^2 + 171441/25*e - 24211/25, 1993/200*e^14 - 2983/100*e^13 - 34261/200*e^12 + 26467/50*e^11 + 223303/200*e^10 - 725411/200*e^9 - 133923/40*e^8 + 478729/40*e^7 + 844119/200*e^6 - 1914243/100*e^5 - 166161/200*e^4 + 319858/25*e^3 - 31048/25*e^2 - 227273/100*e + 28583/100, 3907/400*e^14 - 6067/200*e^13 - 65939/400*e^12 + 53783/100*e^11 + 417597/400*e^10 - 1473989/400*e^9 - 237497/80*e^8 + 974031/80*e^7 + 1291581/400*e^6 - 3909707/200*e^5 + 165361/400*e^4 + 329596/25*e^3 - 47251/25*e^2 - 477427/200*e + 74817/200, -4197/100*e^14 + 6607/50*e^13 + 70569/100*e^12 - 58593/25*e^11 - 445387/100*e^10 + 1608219/100*e^9 + 253007/20*e^8 - 1066361/20*e^7 - 1392951/100*e^6 + 4309197/50*e^5 - 103831/100*e^4 - 1471414/25*e^3 + 181584/25*e^2 + 540567/50*e - 75007/50, 1021/100*e^14 - 1551/50*e^13 - 17317/100*e^12 + 13674/25*e^11 + 110891/100*e^10 - 372367/100*e^9 - 64811/20*e^8 + 244353/20*e^7 + 387143/100*e^6 - 974221/50*e^5 - 37017/100*e^4 + 327177/25*e^3 - 38262/25*e^2 - 119181/50*e + 17651/50, -16531/400*e^14 + 25511/200*e^13 + 280187/400*e^12 - 226039/100*e^11 - 1790301/400*e^10 + 6193437/400*e^9 + 1040041/80*e^8 - 4094263/80*e^7 - 6090973/400*e^6 + 16460831/200*e^5 + 350487/400*e^4 - 1392968/25*e^3 + 156483/25*e^2 + 2018691/200*e - 271961/200, 1111/40*e^14 - 1751/20*e^13 - 18687/40*e^12 + 15539/10*e^11 + 117921/40*e^10 - 426737/40*e^9 - 66877/8*e^8 + 283027/8*e^7 + 365233/40*e^6 - 1143291/20*e^5 + 35533/40*e^4 + 194801/5*e^3 - 24836/5*e^2 - 141711/20*e + 20341/20, -3777/200*e^14 + 5837/100*e^13 + 64129/200*e^12 - 51813/50*e^11 - 410567/200*e^10 + 1422479/200*e^9 + 239107/40*e^8 - 942421/40*e^7 - 1406991/200*e^6 + 3799077/100*e^5 + 90429/200*e^4 - 645437/25*e^3 + 72272/25*e^2 + 470297/100*e - 64587/100, -5403/200*e^14 + 8593/100*e^13 + 90431/200*e^12 - 76207/50*e^11 - 566213/200*e^10 + 2091481/200*e^9 + 316393/40*e^8 - 1386419/40*e^7 - 1652149/200*e^6 + 5599653/100*e^5 - 327869/200*e^4 - 955268/25*e^3 + 129158/25*e^2 + 701883/100*e - 102693/100, 12951/400*e^14 - 19931/200*e^13 - 219327/400*e^12 + 176319/100*e^11 + 1400921/400*e^10 - 4823577/400*e^9 - 814581/80*e^8 + 3184363/80*e^7 + 4796633/400*e^6 - 12792251/200*e^5 - 339227/400*e^4 + 1083028/25*e^3 - 120518/25*e^2 - 1575111/200*e + 212181/200, -23637/400*e^14 + 37197/200*e^13 + 397749/400*e^12 - 330153/100*e^11 - 2511227/400*e^10 + 9068899/400*e^9 + 1425007/80*e^8 - 6017001/80*e^7 - 7785371/400*e^6 + 24321437/200*e^5 - 763351/400*e^4 - 2075411/25*e^3 + 264766/25*e^2 + 3047957/200*e - 429847/200, 3157/400*e^14 - 4917/200*e^13 - 53589/400*e^12 + 43833/100*e^11 + 342347/400*e^10 - 1209539/400*e^9 - 197967/80*e^8 + 806041/80*e^7 + 1134331/400*e^6 - 3269557/200*e^5 + 1111/400*e^4 + 279296/25*e^3 - 32901/25*e^2 - 408677/200*e + 50167/200, -821/200*e^14 + 1401/100*e^13 + 13517/200*e^12 - 12499/50*e^11 - 82691/200*e^10 + 345667/200*e^9 + 44591/40*e^8 - 231473/40*e^7 - 215843/200*e^6 + 948621/100*e^5 - 65183/200*e^4 - 165776/25*e^3 + 17706/25*e^2 + 126481/100*e - 15151/100, -761/100*e^14 + 1141/50*e^13 + 12997/100*e^12 - 10084/25*e^11 - 84031/100*e^10 + 275447/100*e^9 + 49831/20*e^8 - 181373/20*e^7 - 307063/100*e^6 + 725111/50*e^5 + 48597/100*e^4 - 243082/25*e^3 + 24592/25*e^2 + 87021/50*e - 9691/50, -713/50*e^14 + 1103/25*e^13 + 12101/50*e^12 - 19594/25*e^11 - 77373/50*e^10 + 269151/50*e^9 + 44893/10*e^8 - 178429/10*e^7 - 260629/50*e^6 + 719363/25*e^5 + 8601/50*e^4 - 487762/25*e^3 + 56447/25*e^2 + 87543/25*e - 12153/25, 7089/200*e^14 - 11209/100*e^13 - 119153/200*e^12 + 99491/50*e^11 + 751519/200*e^10 - 2733503/200*e^9 - 426339/40*e^8 + 1814637/40*e^7 + 2338487/200*e^6 - 7343389/100*e^5 + 190947/200*e^4 + 1255984/25*e^3 - 153654/25*e^2 - 925329/100*e + 126859/100, 439/400*e^14 - 659/200*e^13 - 7103/400*e^12 + 5491/100*e^11 + 42569/400*e^10 - 138953/400*e^9 - 21989/80*e^8 + 82747/80*e^7 + 82537/400*e^6 - 290339/200*e^5 + 108997/400*e^4 + 21242/25*e^3 - 9277/25*e^2 - 36479/200*e + 10309/200, -3949/400*e^14 + 5569/200*e^13 + 68373/400*e^12 - 48781/100*e^11 - 451779/400*e^10 + 1317123/400*e^9 + 278519/80*e^8 - 854537/80*e^7 - 1880067/400*e^6 + 3354249/200*e^5 + 598473/400*e^4 - 275397/25*e^3 + 25732/25*e^2 + 389389/200*e - 55719/200, 9233/400*e^14 - 14473/200*e^13 - 155041/400*e^12 + 127877/100*e^11 + 977743/400*e^10 - 3494391/400*e^9 - 555523/80*e^8 + 2304869/80*e^7 + 3064639/400*e^6 - 9256033/200*e^5 + 228059/400*e^4 + 784099/25*e^3 - 101519/25*e^2 - 1138313/200*e + 163723/200, -1671/200*e^14 + 2651/100*e^13 + 27967/200*e^12 - 23499/50*e^11 - 175041/200*e^10 + 644617/200*e^9 + 97621/40*e^8 - 427123/40*e^7 - 503793/200*e^6 + 1724471/100*e^5 - 120333/200*e^4 - 294251/25*e^3 + 41881/25*e^2 + 218531/100*e - 30701/100, -1783/50*e^14 + 2773/25*e^13 + 30091/50*e^12 - 49104/25*e^11 - 191093/50*e^10 + 672441/50*e^9 + 109853/10*e^8 - 444649/10*e^7 - 625539/50*e^6 + 1790883/25*e^5 - 3209/50*e^4 - 1219067/25*e^3 + 147527/25*e^2 + 224513/25*e - 31673/25, -21/20*e^14 + 51/10*e^13 + 297/20*e^12 - 469/5*e^11 - 1291/20*e^10 + 13467/20*e^9 + 91/4*e^8 - 9429/4*e^7 + 9897/20*e^6 + 40581/10*e^5 - 21763/20*e^4 - 14812/5*e^3 + 3012/5*e^2 + 5601/10*e - 571/10, -181/25*e^14 + 547/25*e^13 + 3062/25*e^12 - 9606/25*e^11 - 19576/25*e^10 + 65162/25*e^9 + 11436/5*e^8 - 42653/5*e^7 - 68173/25*e^6 + 340062/25*e^5 + 5237/25*e^4 - 229763/25*e^3 + 29253/25*e^2 + 43057/25*e - 6222/25, -13397/400*e^14 + 20457/200*e^13 + 227869/400*e^12 - 181193/100*e^11 - 1463787/400*e^10 + 4962219/400*e^9 + 858287/80*e^8 - 3278641/80*e^7 - 5141051/400*e^6 + 13179497/200*e^5 + 498769/400*e^4 - 1117066/25*e^3 + 124671/25*e^2 + 1634517/200*e - 221807/200, -132/5*e^14 + 409/5*e^13 + 2234/5*e^12 - 7252/5*e^11 - 14242/5*e^10 + 49719/5*e^9 + 8242*e^8 - 32914*e^7 - 47836/5*e^6 + 265334/5*e^5 + 1914/5*e^4 - 180536/5*e^3 + 20446/5*e^2 + 32944/5*e - 4464/5, -1769/100*e^14 + 2739/50*e^13 + 29913/100*e^12 - 24236/25*e^11 - 190599/100*e^10 + 663263/100*e^9 + 110299/20*e^8 - 438097/20*e^7 - 641127/100*e^6 + 1761319/50*e^5 + 30413/100*e^4 - 597228/25*e^3 + 66268/25*e^2 + 217609/50*e - 28839/50, -599/200*e^14 + 719/100*e^13 + 10823/200*e^12 - 6181/50*e^11 - 76329/200*e^10 + 163073/200*e^9 + 52389/40*e^8 - 102787/40*e^7 - 437817/200*e^6 + 388099/100*e^5 + 298723/200*e^4 - 59694/25*e^3 - 4936/25*e^2 + 35239/100*e - 3669/100, 2013/200*e^14 - 3053/100*e^13 - 34101/200*e^12 + 26797/50*e^11 + 218523/200*e^10 - 725851/200*e^9 - 128343/40*e^8 + 473169/40*e^7 + 780779/200*e^6 - 1870413/100*e^5 - 107201/200*e^4 + 310428/25*e^3 - 34643/25*e^2 - 221693/100*e + 30303/100, 277/8*e^14 - 423/4*e^13 - 4705/8*e^12 + 3741/2*e^11 + 30195/8*e^10 - 102295/8*e^9 - 88579/8*e^8 + 337425/8*e^7 + 106979/8*e^6 - 270851/4*e^5 - 13333/8*e^4 + 45816*e^3 - 4777*e^2 - 33309/4*e + 4403/4, 31/16*e^14 - 43/8*e^13 - 551/16*e^12 + 379/4*e^11 + 3809/16*e^10 - 10321/16*e^9 - 12769/16*e^8 + 33871/16*e^7 + 20785/16*e^6 - 27003/8*e^5 - 13747/16*e^4 + 2260*e^3 + 100*e^2 - 3215/8*e + 317/8, -201/400*e^14 + 781/200*e^13 + 1377/400*e^12 - 6969/100*e^11 + 10329/400*e^10 + 195127/400*e^9 - 24949/80*e^8 - 134453/80*e^7 + 422217/400*e^6 + 577501/200*e^5 - 558523/400*e^4 - 53378/25*e^3 + 14243/25*e^2 + 74961/200*e - 4731/200, -624/25*e^14 + 1963/25*e^13 + 10523/25*e^12 - 34924/25*e^11 - 66604/25*e^10 + 240423/25*e^9 + 37924/5*e^8 - 159932/5*e^7 - 208992/25*e^6 + 1295998/25*e^5 - 15777/25*e^4 - 885102/25*e^3 + 108212/25*e^2 + 160478/25*e - 22488/25, 5333/400*e^14 - 8173/200*e^13 - 90741/400*e^12 + 72577/100*e^11 + 582443/400*e^10 - 1993891/400*e^9 - 340223/80*e^8 + 1322649/80*e^7 + 2007739/400*e^6 - 5345533/200*e^5 - 122841/400*e^4 + 456999/25*e^3 - 52819/25*e^2 - 681613/200*e + 96823/200, 977/20*e^14 - 766/5*e^13 - 16459/20*e^12 + 13578/5*e^11 + 104227/20*e^10 - 372349/20*e^9 - 59599/4*e^8 + 246579/4*e^7 + 334351/20*e^6 - 497321/5*e^5 + 12001/20*e^4 + 338794/5*e^3 - 41174/5*e^2 - 124287/10*e + 17057/10, 7791/400*e^14 - 12171/200*e^13 - 131207/400*e^12 + 107779/100*e^11 + 830161/400*e^10 - 2952257/400*e^9 - 473421/80*e^8 + 1951683/80*e^7 + 2623953/400*e^6 - 7849091/200*e^5 + 186093/400*e^4 + 664398/25*e^3 - 86638/25*e^2 - 962351/200*e + 144621/200, 118/5*e^14 - 366/5*e^13 - 1996/5*e^12 + 6493/5*e^11 + 12703/5*e^10 - 44536/5*e^9 - 7316*e^8 + 29491*e^7 + 41739/5*e^6 - 237706/5*e^5 + 14/5*e^4 + 161584/5*e^3 - 19274/5*e^2 - 29556/5*e + 4186/5, 369/100*e^14 - 589/50*e^13 - 6213/100*e^12 + 5236/25*e^11 + 39299/100*e^10 - 143963/100*e^9 - 22419/20*e^8 + 95437/20*e^7 + 125127/100*e^6 - 383769/50*e^5 + 4487/100*e^4 + 129078/25*e^3 - 14793/25*e^2 - 46209/50*e + 6239/50, 967/100*e^14 - 801/25*e^13 - 16109/100*e^12 + 14373/25*e^11 + 99657/100*e^10 - 399859/100*e^9 - 54017/20*e^8 + 269321/20*e^7 + 251961/100*e^6 - 554296/25*e^5 + 118491/100*e^4 + 387129/25*e^3 - 51874/25*e^2 - 146087/50*e + 19927/50, -3159/50*e^14 + 4904/25*e^13 + 53343/50*e^12 - 86842/25*e^11 - 338939/50*e^10 + 1189043/50*e^9 + 194949/10*e^8 - 785817/10*e^7 - 1111297/50*e^6 + 3160434/25*e^5 - 1207/50*e^4 - 2143166/25*e^3 + 257596/25*e^2 + 390099/25*e - 55029/25, -163/20*e^14 + 253/10*e^13 + 2751/20*e^12 - 2242/5*e^11 - 17453/20*e^10 + 61441/20*e^9 + 10001/4*e^8 - 40623/4*e^7 - 56349/20*e^6 + 163333/10*e^5 - 1349/20*e^4 - 55306/5*e^3 + 6636/5*e^2 + 20283/10*e - 2613/10, 1573/200*e^14 - 2363/100*e^13 - 26721/200*e^12 + 20787/50*e^11 + 171683/200*e^10 - 564871/200*e^9 - 101023/40*e^8 + 369989/40*e^7 + 613859/200*e^6 - 1473623/100*e^5 - 78021/200*e^4 + 248288/25*e^3 - 28478/25*e^2 - 188253/100*e + 26363/100, 13983/400*e^14 - 21923/200*e^13 - 235591/400*e^12 + 194427/100*e^11 + 1490193/400*e^10 - 5334241/400*e^9 - 848173/80*e^8 + 3532979/80*e^7 + 4665889/400*e^6 - 14246083/200*e^5 + 403309/400*e^4 + 1211974/25*e^3 - 156694/25*e^2 - 1778863/200*e + 257373/200, -5989/400*e^14 + 9209/200*e^13 + 101453/400*e^12 - 81641/100*e^11 - 647019/400*e^10 + 2239003/400*e^9 + 373759/80*e^8 - 1482417/80*e^7 - 2140987/400*e^6 + 5976289/200*e^5 - 9247/400*e^4 - 508292/25*e^3 + 64127/25*e^2 + 743429/200*e - 107359/200, -11391/200*e^14 + 17621/100*e^13 + 192507/200*e^12 - 155929/50*e^11 - 1225361/200*e^10 + 4267557/200*e^9 + 707701/40*e^8 - 2819063/40*e^7 - 4086553/200*e^6 + 11336341/100*e^5 + 108807/200*e^4 - 1923246/25*e^3 + 226576/25*e^2 + 1402951/100*e - 198321/100, 10509/400*e^14 - 16229/200*e^13 - 177693/400*e^12 + 143621/100*e^11 + 1131139/400*e^10 - 3930043/400*e^9 - 652439/80*e^8 + 2594577/80*e^7 + 3742547/400*e^6 - 10419909/200*e^5 - 40593/400*e^4 + 881927/25*e^3 - 105537/25*e^2 - 1288949/200*e + 173279/200, 5117/80*e^14 - 8057/40*e^13 - 86149/80*e^12 + 71513/20*e^11 + 544627/80*e^10 - 1964499/80*e^9 - 310167/16*e^8 + 1303609/16*e^7 + 1718371/80*e^6 - 5271097/40*e^5 + 105191/80*e^4 + 450041/5*e^3 - 54696/5*e^2 - 660557/40*e + 90407/40, 5207/200*e^14 - 8167/100*e^13 - 87839/200*e^12 + 72483/50*e^11 + 556697/200*e^10 - 1990089/200*e^9 - 317997/40*e^8 + 1318891/40*e^7 + 1767281/200*e^6 - 5319307/100*e^5 + 112661/200*e^4 + 904217/25*e^3 - 114002/25*e^2 - 660927/100*e + 92517/100, -19*e^14 + 61*e^13 + 318*e^12 - 1085*e^11 - 1991*e^10 + 7472*e^9 + 5563*e^8 - 24887*e^7 - 5818*e^6 + 40471*e^5 - 1108*e^4 - 27874*e^3 + 3557*e^2 + 5206*e - 710, -6779/400*e^14 + 10799/200*e^13 + 113683/400*e^12 - 95851/100*e^11 - 714709/400*e^10 + 2633333/400*e^9 + 403249/80*e^8 - 1747647/80*e^7 - 2179157/400*e^6 + 7065479/200*e^5 - 249617/400*e^4 - 602087/25*e^3 + 75622/25*e^2 + 869019/200*e - 123249/200, -649/50*e^14 + 1019/25*e^13 + 10923/50*e^12 - 18037/25*e^11 - 69229/50*e^10 + 247023/50*e^9 + 39829/10*e^8 - 163457/10*e^7 - 229967/50*e^6 + 659249/25*e^5 + 9823/50*e^4 - 449801/25*e^3 + 48056/25*e^2 + 83489/25*e - 10819/25, 699/100*e^14 - 1169/50*e^13 - 11623/100*e^12 + 10456/25*e^11 + 72029/100*e^10 - 289973/100*e^9 - 39489/20*e^8 + 194647/20*e^7 + 194917/100*e^6 - 797699/50*e^5 + 61977/100*e^4 + 276238/25*e^3 - 34403/25*e^2 - 100839/50*e + 13769/50, 24427/400*e^14 - 38187/200*e^13 - 411579/400*e^12 + 338263/100*e^11 + 2606517/400*e^10 - 9269229/400*e^9 - 1490257/80*e^8 + 6131991/80*e^7 + 8355941/400*e^6 - 24698227/200*e^5 + 300521/400*e^4 + 2097981/25*e^3 - 256386/25*e^2 - 3059547/200*e + 426537/200, 10109/200*e^14 - 15729/100*e^13 - 170693/200*e^12 + 139321/50*e^11 + 1084939/200*e^10 - 3817443/200*e^9 - 624999/40*e^8 + 2525337/40*e^7 + 3587747/200*e^6 - 10174009/100*e^5 - 62393/200*e^4 + 1730654/25*e^3 - 200849/25*e^2 - 1268749/100*e + 174479/100, -13379/400*e^14 + 20999/200*e^13 + 225483/400*e^12 - 186451/100*e^11 - 1426509/400*e^10 + 5122733/400*e^9 + 812009/80*e^8 - 3398807/80*e^7 - 4470557/400*e^6 + 13734079/200*e^5 - 367017/400*e^4 - 1171437/25*e^3 + 148672/25*e^2 + 1728219/200*e - 249849/200, 69/8*e^14 - 109/4*e^13 - 1157/8*e^12 + 965/2*e^11 + 7283/8*e^10 - 26427/8*e^9 - 20675/8*e^8 + 87325/8*e^7 + 23099/8*e^6 - 70181/4*e^5 + 207/8*e^4 + 11844*e^3 - 1255*e^2 - 8385/4*e + 1047/4, -1999/80*e^14 + 3159/40*e^13 + 33503/80*e^12 - 27991/20*e^11 - 210289/80*e^10 + 767433/80*e^9 + 118157/16*e^8 - 508171/16*e^7 - 629537/80*e^6 + 2050359/40*e^5 - 91317/80*e^4 - 174777/5*e^3 + 22517/5*e^2 + 257279/40*e - 34789/40, -2603/200*e^14 + 4243/100*e^13 + 43331/200*e^12 - 37757/50*e^11 - 269013/200*e^10 + 1040781/200*e^9 + 148073/40*e^8 - 693919/40*e^7 - 741949/200*e^6 + 2825203/100*e^5 - 209769/200*e^4 - 487818/25*e^3 + 63483/25*e^2 + 364083/100*e - 49593/100, 3649/80*e^14 - 5649/40*e^13 - 61793/80*e^12 + 50101/20*e^11 + 393999/80*e^10 - 1374343/80*e^9 - 227667/16*e^8 + 909845/16*e^7 + 1308847/80*e^6 - 3665569/40*e^5 - 15093/80*e^4 + 311437/5*e^3 - 37247/5*e^2 - 457969/40*e + 64059/40, -30*e^14 + 96*e^13 + 502*e^12 - 1705*e^11 - 3144*e^10 + 11718*e^9 + 8803*e^8 - 38919*e^7 - 9309*e^6 + 63028*e^5 - 1475*e^4 - 43108*e^3 + 5427*e^2 + 7894*e - 1106, -24231/400*e^14 + 38011/200*e^13 + 407887/400*e^12 - 336839/100*e^11 - 2579401/400*e^10 + 9234937/400*e^9 + 1471141/80*e^8 - 6113003/80*e^7 - 8201673/400*e^6 + 24636531/200*e^5 - 367413/400*e^4 - 2093193/25*e^3 + 253158/25*e^2 + 3048791/200*e - 420661/200] 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]