/*
  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.<x> = PolynomialRing(QQ)
g = P([1, 7, 11, -2, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1])

primes_array = [
[5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5],\
[9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6],\
[11, 11, w - 1],\
[25, 5, w^3 + w^2 - 4*w - 3],\
[29, 29, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w],\
[41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1],\
[59, 59, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 24*w + 7],\
[59, 59, -w^5 + 8*w^3 + 2*w^2 - 15*w - 8],\
[61, 61, w^5 - 7*w^3 - 2*w^2 + 12*w + 4],\
[61, 61, -w^5 + 7*w^3 - 11*w - 1],\
[64, 2, 2],\
[71, 71, w^3 + w^2 - 5*w - 3],\
[71, 71, -3*w^5 + w^4 + 21*w^3 - w^2 - 33*w - 9],\
[79, 79, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w - 5],\
[81, 3, 2*w^5 - w^4 - 13*w^3 + w^2 + 19*w + 8],\
[89, 89, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 7],\
[89, 89, -w^5 + 8*w^3 + w^2 - 16*w - 5],\
[89, 89, -3*w^5 + w^4 + 20*w^3 - 30*w - 11],\
[89, 89, -w^5 + 7*w^3 + 2*w^2 - 11*w - 4],\
[89, 89, -2*w^5 + 14*w^3 + 3*w^2 - 22*w - 8],\
[89, 89, 2*w^5 - w^4 - 14*w^3 + 3*w^2 + 22*w + 6],\
[101, 101, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 22*w + 6],\
[101, 101, w^2 - w - 4],\
[101, 101, -3*w^5 + w^4 + 20*w^3 - 2*w^2 - 29*w - 7],\
[109, 109, w^4 - w^3 - 5*w^2 + 4*w + 5],\
[121, 11, w^5 - 7*w^3 - 2*w^2 + 10*w + 6],\
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 4*w - 3],\
[131, 131, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w - 6],\
[131, 131, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 11],\
[131, 131, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 2],\
[139, 139, -w^5 + 6*w^3 + w^2 - 8*w - 1],\
[151, 151, -w^3 + w^2 + 4*w - 2],\
[179, 179, w^4 - 6*w^2 + 6],\
[181, 181, w^3 + w^2 - 3*w],\
[191, 191, 3*w^5 - w^4 - 20*w^3 + 2*w^2 + 28*w + 5],\
[199, 199, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w - 2],\
[199, 199, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 15],\
[211, 211, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 9],\
[229, 229, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],\
[229, 229, -w^4 + 2*w^3 + 6*w^2 - 7*w - 6],\
[239, 239, -w^5 + w^4 + 7*w^3 - 3*w^2 - 13*w - 6],\
[239, 239, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 10],\
[239, 239, w^3 - w^2 - 4*w + 1],\
[239, 239, 5*w^5 - 2*w^4 - 34*w^3 + 2*w^2 + 53*w + 17],\
[241, 241, -w^5 + 7*w^3 + w^2 - 13*w - 4],\
[241, 241, -3*w^5 + w^4 + 21*w^3 - 35*w - 10],\
[241, 241, -w^5 + 7*w^3 - 11*w],\
[251, 251, 3*w^5 - w^4 - 21*w^3 + 35*w + 11],\
[251, 251, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 3],\
[269, 269, -w^5 + 8*w^3 + 3*w^2 - 16*w - 8],\
[269, 269, -2*w^5 + w^4 + 13*w^3 - w^2 - 21*w - 9],\
[269, 269, 3*w^5 - 21*w^3 - 3*w^2 + 32*w + 12],\
[271, 271, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 14],\
[281, 281, -w^5 + 8*w^3 + 3*w^2 - 16*w - 11],\
[281, 281, 4*w^5 - w^4 - 29*w^3 + 49*w + 13],\
[281, 281, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 5],\
[281, 281, -5*w^5 + 3*w^4 + 33*w^3 - 8*w^2 - 50*w - 12],\
[311, 311, 2*w^5 - w^4 - 14*w^3 + w^2 + 21*w + 9],\
[311, 311, -3*w^5 + 20*w^3 + 3*w^2 - 30*w - 10],\
[311, 311, 5*w^5 - 2*w^4 - 35*w^3 + 2*w^2 + 57*w + 19],\
[331, 331, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 7],\
[349, 349, -6*w^5 + 3*w^4 + 41*w^3 - 7*w^2 - 64*w - 17],\
[349, 349, 4*w^5 - w^4 - 29*w^3 - w^2 + 50*w + 17],\
[349, 349, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 17],\
[359, 359, w^5 - 6*w^3 - w^2 + 5*w + 3],\
[379, 379, -w^5 + w^4 + 8*w^3 - 3*w^2 - 17*w - 3],\
[379, 379, 2*w^5 - 14*w^3 - 4*w^2 + 22*w + 11],\
[379, 379, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 13],\
[379, 379, 4*w^5 - 2*w^4 - 27*w^3 + 3*w^2 + 43*w + 14],\
[389, 389, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 44*w + 13],\
[401, 401, -2*w^5 + 2*w^4 + 13*w^3 - 6*w^2 - 20*w - 6],\
[409, 409, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w],\
[419, 419, -5*w^5 + w^4 + 34*w^3 + 2*w^2 - 53*w - 19],\
[419, 419, 2*w^5 - w^4 - 14*w^3 + 4*w^2 + 23*w + 3],\
[421, 421, -w^5 - w^4 + 8*w^3 + 6*w^2 - 13*w - 7],\
[421, 421, 2*w^5 - 2*w^4 - 13*w^3 + 8*w^2 + 18*w + 2],\
[421, 421, 4*w^5 - w^4 - 26*w^3 + 37*w + 11],\
[431, 431, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 9],\
[431, 431, w^5 - 8*w^3 - w^2 + 14*w + 2],\
[449, 449, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 38*w + 9],\
[449, 449, -3*w^5 + w^4 + 20*w^3 - 31*w - 14],\
[461, 461, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 23*w + 4],\
[461, 461, -4*w^5 + 2*w^4 + 26*w^3 - 5*w^2 - 36*w - 9],\
[461, 461, -4*w^5 + 2*w^4 + 27*w^3 - 3*w^2 - 42*w - 15],\
[491, 491, -3*w^5 + w^4 + 20*w^3 - 29*w - 10],\
[491, 491, -5*w^5 + w^4 + 35*w^3 + 2*w^2 - 56*w - 18],\
[491, 491, 2*w^5 - 14*w^3 - 4*w^2 + 24*w + 13],\
[491, 491, -3*w^5 + w^4 + 21*w^3 - 2*w^2 - 33*w - 10],\
[499, 499, 6*w^5 - 3*w^4 - 40*w^3 + 6*w^2 + 61*w + 18],\
[499, 499, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 17],\
[499, 499, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w - 4],\
[499, 499, -3*w^5 + w^4 + 19*w^3 - 2*w^2 - 26*w - 8],\
[509, 509, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 11],\
[509, 509, -2*w^5 + 16*w^3 + 2*w^2 - 30*w - 9],\
[521, 521, 3*w^5 - 21*w^3 - 3*w^2 + 34*w + 10],\
[521, 521, -3*w^5 + w^4 + 19*w^3 - 26*w - 9],\
[521, 521, 4*w^5 - w^4 - 27*w^3 + 40*w + 15],\
[521, 521, -3*w^5 + 22*w^3 + 3*w^2 - 37*w - 11],\
[541, 541, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 18],\
[569, 569, -6*w^5 + 2*w^4 + 40*w^3 - 2*w^2 - 60*w - 19],\
[569, 569, -w^5 + w^4 + 7*w^3 - 2*w^2 - 12*w - 6],\
[571, 571, 4*w^5 - w^4 - 28*w^3 + 43*w + 14],\
[571, 571, -4*w^5 + 2*w^4 + 28*w^3 - 4*w^2 - 45*w - 14],\
[599, 599, -w^5 + w^4 + 7*w^3 - 2*w^2 - 13*w - 7],\
[601, 601, 4*w^5 - w^4 - 26*w^3 + 38*w + 13],\
[601, 601, 4*w^5 - 2*w^4 - 28*w^3 + 5*w^2 + 44*w + 11],\
[601, 601, 3*w^5 - w^4 - 21*w^3 + 2*w^2 + 35*w + 9],\
[619, 619, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 13],\
[619, 619, -4*w^5 + w^4 + 26*w^3 - 36*w - 12],\
[619, 619, w^4 - w^3 - 6*w^2 + 4*w + 4],\
[631, 631, -3*w^5 + w^4 + 20*w^3 - 30*w - 9],\
[631, 631, -5*w^5 + 2*w^4 + 35*w^3 - 3*w^2 - 57*w - 15],\
[641, 641, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 16],\
[641, 641, -5*w^5 + 2*w^4 + 34*w^3 - 2*w^2 - 52*w - 18],\
[659, 659, 3*w^5 - w^4 - 20*w^3 + w^2 + 32*w + 9],\
[659, 659, -4*w^5 + w^4 + 27*w^3 - w^2 - 40*w - 11],\
[661, 661, 4*w^5 - w^4 - 26*w^3 + 38*w + 12],\
[661, 661, -w^5 + 6*w^3 - 8*w + 1],\
[691, 691, 3*w^5 - 20*w^3 - 3*w^2 + 29*w + 9],\
[691, 691, w^5 + w^4 - 8*w^3 - 7*w^2 + 14*w + 9],\
[691, 691, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 2],\
[701, 701, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 9],\
[701, 701, 5*w^5 - 2*w^4 - 33*w^3 + 3*w^2 + 48*w + 14],\
[701, 701, w^4 + 3*w^3 - 3*w^2 - 10*w - 1],\
[701, 701, -2*w^5 + w^4 + 14*w^3 - 3*w^2 - 24*w - 3],\
[709, 709, -2*w^5 + 2*w^4 + 14*w^3 - 7*w^2 - 22*w - 5],\
[709, 709, -3*w^5 + 21*w^3 + 4*w^2 - 34*w - 11],\
[719, 719, 5*w^5 - 2*w^4 - 35*w^3 + 3*w^2 + 58*w + 17],\
[719, 719, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 37*w + 11],\
[719, 719, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 12],\
[719, 719, 2*w^5 - 16*w^3 - 3*w^2 + 30*w + 10],\
[739, 739, -5*w^5 + w^4 + 34*w^3 + w^2 - 51*w - 17],\
[751, 751, -w^5 - w^4 + 9*w^3 + 7*w^2 - 18*w - 10],\
[761, 761, 4*w^5 - 2*w^4 - 28*w^3 + 3*w^2 + 46*w + 16],\
[761, 761, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 12],\
[769, 769, -4*w^5 + w^4 + 28*w^3 - 44*w - 12],\
[769, 769, -w^4 + w^3 + 3*w^2 - 3*w + 1],\
[809, 809, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 1],\
[811, 811, -2*w^5 + 15*w^3 + 2*w^2 - 24*w - 8],\
[811, 811, -w^5 + 9*w^3 + w^2 - 18*w - 6],\
[821, 821, -w^5 + 8*w^3 + 3*w^2 - 17*w - 9],\
[821, 821, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 8],\
[821, 821, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 46*w + 11],\
[821, 821, 5*w^5 - 2*w^4 - 34*w^3 + 4*w^2 + 51*w + 13],\
[829, 829, -2*w^5 + w^4 + 15*w^3 - w^2 - 28*w - 10],\
[829, 829, -6*w^5 + 3*w^4 + 42*w^3 - 7*w^2 - 68*w - 21],\
[829, 829, 4*w^5 - 2*w^4 - 26*w^3 + 5*w^2 + 38*w + 12],\
[829, 829, w^5 - 7*w^3 - 3*w^2 + 11*w + 6],\
[839, 839, 3*w^5 - 2*w^4 - 20*w^3 + 5*w^2 + 32*w + 11],\
[839, 839, -w^4 + w^3 + 6*w^2 - 3*w - 4],\
[841, 29, -3*w^5 + w^4 + 22*w^3 - 38*w - 11],\
[911, 911, 3*w^5 - w^4 - 21*w^3 + 36*w + 12],\
[919, 919, -w^5 - w^4 + 7*w^3 + 6*w^2 - 12*w - 5],\
[941, 941, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w],\
[941, 941, 4*w^5 - w^4 - 29*w^3 + 48*w + 15],\
[971, 971, -4*w^5 + w^4 + 27*w^3 + w^2 - 41*w - 13],\
[991, 991, w^5 - w^4 - 8*w^3 + 3*w^2 + 16*w + 2],\
[991, 991, -4*w^5 + 3*w^4 + 27*w^3 - 9*w^2 - 42*w - 10]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^15 + 7*x^14 - 22*x^13 - 237*x^12 + 9*x^11 + 2807*x^10 + 2194*x^9 - 15492*x^8 - 15198*x^7 + 45065*x^6 + 38286*x^5 - 72076*x^4 - 36653*x^3 + 56862*x^2 + 7630*x - 13354
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1504363229540792067/146160698785720231801*e^14 + 11760786763522312777/146160698785720231801*e^13 - 23208336507342952576/146160698785720231801*e^12 - 373458701580536154521/146160698785720231801*e^11 - 297323830557380770642/146160698785720231801*e^10 + 3912025430771508715355/146160698785720231801*e^9 + 6493839506203570904652/146160698785720231801*e^8 - 17240286741835736767803/146160698785720231801*e^7 - 36427028596378027798851/146160698785720231801*e^6 + 34307569429378539535789/146160698785720231801*e^5 + 82996918369984897152272/146160698785720231801*e^4 - 32130081221752538733025/146160698785720231801*e^3 - 77695884679714210476650/146160698785720231801*e^2 + 13653494734526964614402/146160698785720231801*e + 21626703098563862878576/146160698785720231801, -481402907265757658/146160698785720231801*e^14 - 3917794344914564981/146160698785720231801*e^13 + 6654685380014286643/146160698785720231801*e^12 + 123980137464721654216/146160698785720231801*e^11 + 120846929671884645685/146160698785720231801*e^10 - 1289560328884793589121/146160698785720231801*e^9 - 2368199449061829170770/146160698785720231801*e^8 + 5599783751094904074232/146160698785720231801*e^7 + 13057061024127687657139/146160698785720231801*e^6 - 10810058939091681536959/146160698785720231801*e^5 - 29395517822671857503347/146160698785720231801*e^4 + 9632017356518942414473/146160698785720231801*e^3 + 26534902530157807572758/146160698785720231801*e^2 - 4078009106494034368856/146160698785720231801*e - 6879847594187901980502/146160698785720231801, -2862270168039425134/146160698785720231801*e^14 - 22548037740141301670/146160698785720231801*e^13 + 43435825802176883659/146160698785720231801*e^12 + 718493423291352470464/146160698785720231801*e^11 + 599151168627617312779/146160698785720231801*e^10 - 7577283347570988461101/146160698785720231801*e^9 - 12921226149810575123741/146160698785720231801*e^8 + 33823699139456063201808/146160698785720231801*e^7 + 73579177120341421501624/146160698785720231801*e^6 - 68903087070066397125477/146160698785720231801*e^5 - 172357049136259300050399/146160698785720231801*e^4 + 66913841799985030558436/146160698785720231801*e^3 + 167429982748129757136606/146160698785720231801*e^2 - 29448694558840429505570/146160698785720231801*e - 48922313490213699060662/146160698785720231801, 3371352195470066360/146160698785720231801*e^14 + 26170699159654000246/146160698785720231801*e^13 - 53596193347548311064/146160698785720231801*e^12 - 836694985295869033380/146160698785720231801*e^11 - 625468913696283651477/146160698785720231801*e^10 + 8880169585145710809145/146160698785720231801*e^9 + 14318668208223482884202/146160698785720231801*e^8 - 40097464647824247056344/146160698785720231801*e^7 - 82190581114183316386379/146160698785720231801*e^6 + 83099849456624619253853/146160698785720231801*e^5 + 192289581308063835647636/146160698785720231801*e^4 - 81569929349421381736497/146160698785720231801*e^3 - 184948057751710587379952/146160698785720231801*e^2 + 35371376510506330356759/146160698785720231801*e + 52968987942433797496658/146160698785720231801, -1552406045668750059/146160698785720231801*e^14 - 12386254658102930354/146160698785720231801*e^13 + 21996581194760146160/146160698785720231801*e^12 + 389969300929715247194/146160698785720231801*e^11 + 370595692713837016089/146160698785720231801*e^10 - 4014799679343772779007/146160698785720231801*e^9 - 7407378361763562188298/146160698785720231801*e^8 + 17083895799027667686169/146160698785720231801*e^7 + 41044849631714407642019/146160698785720231801*e^6 - 31749540694581113731707/146160698785720231801*e^5 - 93772119953494975734947/146160698785720231801*e^4 + 26965998372103548648502/146160698785720231801*e^3 + 88856748219979758559365/146160698785720231801*e^2 - 11960226593228313926766/146160698785720231801*e - 24971780415614304869778/146160698785720231801, 1, -3621359265104992739/146160698785720231801*e^14 - 28082224501900602039/146160698785720231801*e^13 + 57804779515516703458/146160698785720231801*e^12 + 897644789893569764233/146160698785720231801*e^11 + 661047707874647730754/146160698785720231801*e^10 - 9527079781494594502591/146160698785720231801*e^9 - 15197009309913117668916/146160698785720231801*e^8 + 43077218160411992411915/146160698785720231801*e^7 + 86879147416184019133963/146160698785720231801*e^6 - 89922346878279806547744/146160698785720231801*e^5 - 201733730847500801440269/146160698785720231801*e^4 + 90390278368614928323017/146160698785720231801*e^3 + 192385519682009018779902/146160698785720231801*e^2 - 40418887584645958180304/146160698785720231801*e - 54558876689256037015962/146160698785720231801, 899561993049662133/146160698785720231801*e^14 + 6671658673287553874/146160698785720231801*e^13 - 17244836305366585745/146160698785720231801*e^12 - 221960041147181592759/146160698785720231801*e^11 - 81523991990960951467/146160698785720231801*e^10 + 2530481714332283347059/146160698785720231801*e^9 + 3085077056628717416199/146160698785720231801*e^8 - 12842379589369769414407/146160698785720231801*e^7 - 19903999899638410357208/146160698785720231801*e^6 + 31262004936005495482994/146160698785720231801*e^5 + 50954094189389938910720/146160698785720231801*e^4 - 35540281176007651679562/146160698785720231801*e^3 - 53016426523932692643482/146160698785720231801*e^2 + 15332520422569946086272/146160698785720231801*e + 17047742108539907264968/146160698785720231801, 232178559727782031/146160698785720231801*e^14 + 2774156625876869530/146160698785720231801*e^13 + 2407510773131576260/146160698785720231801*e^12 - 80818221447577754325/146160698785720231801*e^11 - 241544710835711588705/146160698785720231801*e^10 + 697632364092968268631/146160698785720231801*e^9 + 3160484001021050434211/146160698785720231801*e^8 - 1837720854719275035372/146160698785720231801*e^7 - 15981662084846418399815/146160698785720231801*e^6 - 477164823266649198883/146160698785720231801*e^5 + 35806766081125518487355/146160698785720231801*e^4 + 4241352489780565556606/146160698785720231801*e^3 - 34028962779393691968098/146160698785720231801*e^2 - 4585516294733194516/146160698785720231801*e + 9440452829786915311550/146160698785720231801, -351682979259545449/146160698785720231801*e^14 - 2643405753271749789/146160698785720231801*e^13 + 5870921871762744932/146160698785720231801*e^12 + 83105749849979847883/146160698785720231801*e^11 + 50007632213764088257/146160698785720231801*e^10 - 859720577625508749271/146160698785720231801*e^9 - 1205824828059061533791/146160698785720231801*e^8 + 3803815235283567566932/146160698785720231801*e^7 + 6265979841444416744709/146160698785720231801*e^6 - 8367066834649922491600/146160698785720231801*e^5 - 12090852585198390554967/146160698785720231801*e^4 + 10795124724995881849479/146160698785720231801*e^3 + 8648675500776062480906/146160698785720231801*e^2 - 6364273812697708463774/146160698785720231801*e - 1816905059674402703936/146160698785720231801, 2685392287129037130/146160698785720231801*e^14 + 20711126789450370775/146160698785720231801*e^13 - 42547390543012304709/146160698785720231801*e^12 - 659573539627520427004/146160698785720231801*e^11 - 503378095184801041522/146160698785720231801*e^10 + 6940516747909036851089/146160698785720231801*e^9 + 11471515169222881679141/146160698785720231801*e^8 - 30737184627283787358651/146160698785720231801*e^7 - 65835470216236465889283/146160698785720231801*e^6 + 61046308832486071179268/146160698785720231801*e^5 + 153924495835719795956657/146160698785720231801*e^4 - 55921493723331624494151/146160698785720231801*e^3 - 147386369895101478595776/146160698785720231801*e^2 + 23792322356790740990772/146160698785720231801*e + 41192579702639320431199/146160698785720231801, 3073051728510043733/146160698785720231801*e^14 + 24656889412727588210/146160698785720231801*e^13 - 44622061082888699305/146160698785720231801*e^12 - 785877871676160530812/146160698785720231801*e^11 - 711327921174717327250/146160698785720231801*e^10 + 8297132953126575260043/146160698785720231801*e^9 + 14670339310930347886934/146160698785720231801*e^8 - 37197903098105405886534/146160698785720231801*e^7 - 83213952487319090971564/146160698785720231801*e^6 + 76865457255407779757624/146160698785720231801*e^5 + 195715190961054360925682/146160698785720231801*e^4 - 77070954725795011737342/146160698785720231801*e^3 - 191130982112102415020358/146160698785720231801*e^2 + 34494709716797879194797/146160698785720231801*e + 55548317469184965654924/146160698785720231801, -1222202049124590363/146160698785720231801*e^14 - 8769786405838115315/146160698785720231801*e^13 + 22830195838851585076/146160698785720231801*e^12 + 279368732843566597676/146160698785720231801*e^11 + 105185824777768011255/146160698785720231801*e^10 - 2943879624945985157463/146160698785720231801*e^9 - 3646126751845311955386/146160698785720231801*e^8 + 13100425744382304833626/146160698785720231801*e^7 + 20825108864389688702889/146160698785720231801*e^6 - 26255336816284073790876/146160698785720231801*e^5 - 44977299123972488410557/146160698785720231801*e^4 + 23424177169165865895974/146160698785720231801*e^3 + 37753924665528492837986/146160698785720231801*e^2 - 7407543430853749943572/146160698785720231801*e - 9641442313955229320572/146160698785720231801, -4046290012619144808/146160698785720231801*e^14 - 31249997344773165878/146160698785720231801*e^13 + 64698811003988560083/146160698785720231801*e^12 + 997177060254196614614/146160698785720231801*e^11 + 735408602349985208425/146160698785720231801*e^10 - 10541869829556032649947/146160698785720231801*e^9 - 16959740901714724650443/146160698785720231801*e^8 + 47215519372359323284018/146160698785720231801*e^7 + 97180144135134633035910/146160698785720231801*e^6 - 96261318475094611970309/146160698785720231801*e^5 - 226726293742155896370435/146160698785720231801*e^4 + 91845826486342961164406/146160698785720231801*e^3 + 218055662471491068308264/146160698785720231801*e^2 - 38356754409407226247848/146160698785720231801*e - 63234441790807289729180/146160698785720231801, 1960765784412320297/146160698785720231801*e^14 + 16124185532453503945/146160698785720231801*e^13 - 25244883003023319025/146160698785720231801*e^12 - 506226459725116509807/146160698785720231801*e^11 - 551689534658613941076/146160698785720231801*e^10 + 5187168841789348284686/146160698785720231801*e^9 + 10293027793111448912389/146160698785720231801*e^8 - 21950467293537052695206/146160698785720231801*e^7 - 56465131308324727680125/146160698785720231801*e^6 + 41033003495573435428030/146160698785720231801*e^5 + 129054424658429776530473/146160698785720231801*e^4 - 37527113798559272178296/146160698785720231801*e^3 - 122190312884405780610052/146160698785720231801*e^2 + 19462965490563796879636/146160698785720231801*e + 33148638577712233434602/146160698785720231801, 1496069640723106321/146160698785720231801*e^14 + 11136021048395828764/146160698785720231801*e^13 - 26382005451277143938/146160698785720231801*e^12 - 359302677050502634887/146160698785720231801*e^11 - 195641193269344631983/146160698785720231801*e^10 + 3879086121813906438563/146160698785720231801*e^9 + 5505417019804336284815/146160698785720231801*e^8 - 18049275425005460989057/146160698785720231801*e^7 - 32765296296430057961504/146160698785720231801*e^6 + 39225292695743255811798/146160698785720231801*e^5 + 77856878568700046519170/146160698785720231801*e^4 - 40601493932671690903193/146160698785720231801*e^3 - 75410488764315240551325/146160698785720231801*e^2 + 17279472480963750953738/146160698785720231801*e + 22376957005397198858840/146160698785720231801, -1272105279941790990/146160698785720231801*e^14 - 9636428259059892630/146160698785720231801*e^13 + 20027980073132884481/146160698785720231801*e^12 + 301041579769393420782/146160698785720231801*e^11 + 230857158672138235543/146160698785720231801*e^10 - 3048225198290755394819/146160698785720231801*e^9 - 5124326496953631965340/146160698785720231801*e^8 + 12498743621681127708311/146160698785720231801*e^7 + 28017487577841051878285/146160698785720231801*e^6 - 21245527096523137974085/146160698785720231801*e^5 - 61056646287823647124021/146160698785720231801*e^4 + 14682302338429931218060/146160698785720231801*e^3 + 53695670414281837497866/146160698785720231801*e^2 - 5778094081174951124512/146160698785720231801*e - 13332549588517996588618/146160698785720231801, -1025394963863865481/146160698785720231801*e^14 - 7582374539910630009/146160698785720231801*e^13 + 17698119982499333855/146160698785720231801*e^12 + 240651260489840681527/146160698785720231801*e^11 + 139963998055383226309/146160698785720231801*e^10 - 2515523548696496295588/146160698785720231801*e^9 - 3712268450207662134340/146160698785720231801*e^8 + 11001974180316784868916/146160698785720231801*e^7 + 21264453940687682454510/146160698785720231801*e^6 - 21384746113611487452819/146160698785720231801*e^5 - 48359580037605419344502/146160698785720231801*e^4 + 19099826530599826737832/146160698785720231801*e^3 + 45190890295148001780184/146160698785720231801*e^2 - 8068314805766348043962/146160698785720231801*e - 14131559106175732577058/146160698785720231801, 1385992289472554048/146160698785720231801*e^14 + 10584555717128081342/146160698785720231801*e^13 - 24017766484522061212/146160698785720231801*e^12 - 345814977941034742177/146160698785720231801*e^11 - 204794975650422828944/146160698785720231801*e^10 + 3819057050602118844675/146160698785720231801*e^9 + 5554056242565595520650/146160698785720231801*e^8 - 18427986344090366850240/146160698785720231801*e^7 - 34082851899358280262686/146160698785720231801*e^6 + 41822255027016059913595/146160698785720231801*e^5 + 85408411196099471087318/146160698785720231801*e^4 - 43659886899835382438344/146160698785720231801*e^3 - 87892942039743356291312/146160698785720231801*e^2 + 17494338948294912885086/146160698785720231801*e + 27186989243433674077090/146160698785720231801, -2183150815142562240/146160698785720231801*e^14 - 16878442661439017436/146160698785720231801*e^13 + 36234447783906589140/146160698785720231801*e^12 + 545890972670913752243/146160698785720231801*e^11 + 364659921561061805810/146160698785720231801*e^10 - 5916983790272326762980/146160698785720231801*e^9 - 9010349245695144299780/146160698785720231801*e^8 + 27657166013630842242311/146160698785720231801*e^7 + 53342987567052622175914/146160698785720231801*e^6 - 59955893669675898761437/146160698785720231801*e^5 - 128861328007016629804662/146160698785720231801*e^4 + 60033453912514390501050/146160698785720231801*e^3 + 128153893968511467273378/146160698785720231801*e^2 - 23906465855372159712516/146160698785720231801*e - 38336944403822548437406/146160698785720231801, 2354865293075448363/146160698785720231801*e^14 + 17888793957394156747/146160698785720231801*e^13 - 39927610366775226229/146160698785720231801*e^12 - 574667854729869072385/146160698785720231801*e^11 - 354428065200868491270/146160698785720231801*e^10 + 6154719820214627492749/146160698785720231801*e^9 + 9072668852895815485450/146160698785720231801*e^8 - 28232694225357042081264/146160698785720231801*e^7 - 52832251535908590671367/146160698785720231801*e^6 + 59774627690323270589812/146160698785720231801*e^5 + 123908287532621947967345/146160698785720231801*e^4 - 58806717500269762883681/146160698785720231801*e^3 - 118988804881645763687842/146160698785720231801*e^2 + 23263368270435461232707/146160698785720231801*e + 33990892357161966980068/146160698785720231801, 755278915729127142/146160698785720231801*e^14 + 5896301646760827217/146160698785720231801*e^13 - 10235536658998816728/146160698785720231801*e^12 - 179018430240093259731/146160698785720231801*e^11 - 182365152041490833244/146160698785720231801*e^10 + 1705218477414579933360/146160698785720231801*e^9 + 3357609922941129264499/146160698785720231801*e^8 - 6067981031006393810905/146160698785720231801*e^7 - 16538640456576922466346/146160698785720231801*e^6 + 6818548563121435420994/146160698785720231801*e^5 + 30076595024118081529434/146160698785720231801*e^4 + 1024582687383568806606/146160698785720231801*e^3 - 18282002681398347071562/146160698785720231801*e^2 - 4072684380608411167812/146160698785720231801*e + 2177384804384029259958/146160698785720231801, -3158683544343413299/146160698785720231801*e^14 - 24967450131790388698/146160698785720231801*e^13 + 47414752747548925482/146160698785720231801*e^12 + 794856561434092132739/146160698785720231801*e^11 + 678248970317752390520/146160698785720231801*e^10 - 8369116845091990536769/146160698785720231801*e^9 - 14454570100888475089878/146160698785720231801*e^8 + 37269520017488667437501/146160698785720231801*e^7 + 82273463851911243375185/146160698785720231801*e^6 - 75805943457066780658063/146160698785720231801*e^5 - 193443645543671419576921/146160698785720231801*e^4 + 74358385034204079576389/146160698785720231801*e^3 + 189291451408461555124796/146160698785720231801*e^2 - 34708069720998239351932/146160698785720231801*e - 54889181328568666227040/146160698785720231801, -6028276126921912499/146160698785720231801*e^14 - 47095752325901632076/146160698785720231801*e^13 + 95434781603248608900/146160698785720231801*e^12 + 1510333033411175315247/146160698785720231801*e^11 + 1137760700797724238813/146160698785720231801*e^10 - 16124267032257025453539/146160698785720231801*e^9 - 25929410456958139956397/146160698785720231801*e^8 + 73579439695173875519791/146160698785720231801*e^7 + 149246830199908610659242/146160698785720231801*e^6 - 155009348906228283566587/146160698785720231801*e^5 - 350338619666748961476833/146160698785720231801*e^4 + 154589490425524475352033/146160698785720231801*e^3 + 337516474945782882108164/146160698785720231801*e^2 - 66864054508813942956500/146160698785720231801*e - 97162455118481285624124/146160698785720231801, 5166638562320664843/146160698785720231801*e^14 + 40757092313360271606/146160698785720231801*e^13 - 77485482572607099890/146160698785720231801*e^12 - 1292323382840283148361/146160698785720231801*e^11 - 1096925748094037277034/146160698785720231801*e^10 + 13497136380248306187318/146160698785720231801*e^9 + 23203148589396419698200/146160698785720231801*e^8 - 59126860543979286858920/146160698785720231801*e^7 - 129953914363252596060561/146160698785720231801*e^6 + 116282143735423799995439/146160698785720231801*e^5 + 297635409737115044288493/146160698785720231801*e^4 - 106771101841761602065995/146160698785720231801*e^3 - 281877673148398058792910/146160698785720231801*e^2 + 45021170620498286435362/146160698785720231801*e + 80507328164943931184844/146160698785720231801, -1643411045638169702/146160698785720231801*e^14 - 12409301887597706504/146160698785720231801*e^13 + 27951217754656286869/146160698785720231801*e^12 + 399915178155136245232/146160698785720231801*e^11 + 250904793882909071592/146160698785720231801*e^10 - 4309314747511862534514/146160698785720231801*e^9 - 6495193634207574017281/146160698785720231801*e^8 + 20004709660762796684157/146160698785720231801*e^7 + 38577592040586104512686/146160698785720231801*e^6 - 43463831523378163711804/146160698785720231801*e^5 - 92748732986109993754897/146160698785720231801*e^4 + 45464250090165163712205/146160698785720231801*e^3 + 90849972354988693415574/146160698785720231801*e^2 - 20402139499351317882508/146160698785720231801*e - 26193192129659747647240/146160698785720231801, 6666076253561254911/146160698785720231801*e^14 + 51795857354848975182/146160698785720231801*e^13 - 106333171587230207595/146160698785720231801*e^12 - 1658015086572466897436/146160698785720231801*e^11 - 1226045775145604968788/146160698785720231801*e^10 + 17638362373113836588551/146160698785720231801*e^9 + 28211399718122781347448/146160698785720231801*e^8 - 79974710441213904283680/146160698785720231801*e^7 - 162133897109464312923189/146160698785720231801*e^6 + 166893871987108796230911/146160698785720231801*e^5 + 379697865796551737290368/146160698785720231801*e^4 - 165736455661252442359568/146160698785720231801*e^3 - 366014527909476096463284/146160698785720231801*e^2 + 73179330030458649092879/146160698785720231801*e + 104949967179448228397124/146160698785720231801, -4401209657144542513/146160698785720231801*e^14 - 33962723214886966748/146160698785720231801*e^13 + 70730882674993279341/146160698785720231801*e^12 + 1084631628208967359978/146160698785720231801*e^11 + 788174459351467868930/146160698785720231801*e^10 - 11482019415937249841520/146160698785720231801*e^9 - 18310619660712873381887/146160698785720231801*e^8 + 51503152557587167735791/146160698785720231801*e^7 + 104906842512700748310915/146160698785720231801*e^6 - 104794609582961477537197/146160698785720231801*e^5 - 243972457358836448707301/146160698785720231801*e^4 + 98184601450554530200799/146160698785720231801*e^3 + 233213216427178444795656/146160698785720231801*e^2 - 40042953376139747656796/146160698785720231801*e - 68299355233434700791606/146160698785720231801, -4095063824200995679/146160698785720231801*e^14 - 31251038179847124918/146160698785720231801*e^13 + 67734834535057696461/146160698785720231801*e^12 + 998356275562419757949/146160698785720231801*e^11 + 662261375312115216752/146160698785720231801*e^10 - 10584872801589850588587/146160698785720231801*e^9 - 16091788524931047237504/146160698785720231801*e^8 + 47772019615311027639644/146160698785720231801*e^7 + 91841592221859410672422/146160698785720231801*e^6 - 99288360901431379464810/146160698785720231801*e^5 - 210534705028219298749281/146160698785720231801*e^4 + 97997539060399699695144/146160698785720231801*e^3 + 197778275058341568086978/146160698785720231801*e^2 - 40853681294956466370542/146160698785720231801*e - 56314406032305284110440/146160698785720231801, 3836167650174416924/146160698785720231801*e^14 + 31003255920460614059/146160698785720231801*e^13 - 51866300236965902843/146160698785720231801*e^12 - 970865527474694124550/146160698785720231801*e^11 - 985667920383112034962/146160698785720231801*e^10 + 9894315322699939403861/146160698785720231801*e^9 + 18843257972086712240923/146160698785720231801*e^8 - 41357036638936698233955/146160698785720231801*e^7 - 102097922512907084990450/146160698785720231801*e^6 + 74830508349644223056752/146160698785720231801*e^5 + 226539840572193964780873/146160698785720231801*e^4 - 62170886411111300100871/146160698785720231801*e^3 - 205884506459724906624622/146160698785720231801*e^2 + 27138409737355405920680/146160698785720231801*e + 54353775154884416439078/146160698785720231801, -239882437892990875/146160698785720231801*e^14 - 3273993554995977931/146160698785720231801*e^13 - 2322579058180469102/146160698785720231801*e^12 + 108947814509219346243/146160698785720231801*e^11 + 266924292706849705179/146160698785720231801*e^10 - 1250509040614450019173/146160698785720231801*e^9 - 3907397326961979662875/146160698785720231801*e^8 + 6545808041709675253142/146160698785720231801*e^7 + 23156641148353485794316/146160698785720231801*e^6 - 17607518247372256775769/146160698785720231801*e^5 - 63289959075701564998363/146160698785720231801*e^4 + 25439840280837084412510/146160698785720231801*e^3 + 73728847691007696921640/146160698785720231801*e^2 - 16412648709213783884656/146160698785720231801*e - 24395443475884310341908/146160698785720231801, 607220670017193484/146160698785720231801*e^14 + 4164665769858698299/146160698785720231801*e^13 - 13188860066262219308/146160698785720231801*e^12 - 137936555868035591015/146160698785720231801*e^11 + 3879131334948120522/146160698785720231801*e^10 + 1566981422222042228206/146160698785720231801*e^9 + 1271658396009988674559/146160698785720231801*e^8 - 8018306776401157719579/146160698785720231801*e^7 - 8338296177780941568458/146160698785720231801*e^6 + 20470977435524504689489/146160698785720231801*e^5 + 19635205371332133821457/146160698785720231801*e^4 - 26272951423061117479130/146160698785720231801*e^3 - 18717631168835380216674/146160698785720231801*e^2 + 13086759633978839461994/146160698785720231801*e + 5361038519775314803724/146160698785720231801, -3803408144246282037/146160698785720231801*e^14 - 30576566937117611982/146160698785720231801*e^13 + 53313973097362056877/146160698785720231801*e^12 + 965219515901296638584/146160698785720231801*e^11 + 930705193069791398490/146160698785720231801*e^10 - 9991514732806542385688/146160698785720231801*e^9 - 18470029798896073982488/146160698785720231801*e^8 + 43013222412089577109531/146160698785720231801*e^7 + 102588014420807708067192/146160698785720231801*e^6 - 82051889118541876165718/146160698785720231801*e^5 - 235439426838838847854372/146160698785720231801*e^4 + 73802838244576730734961/146160698785720231801*e^3 + 224314347603222062034110/146160698785720231801*e^2 - 34933353879817723581680/146160698785720231801*e - 64033832291408371696750/146160698785720231801, 3650990518035275010/146160698785720231801*e^14 + 28447760004469716646/146160698785720231801*e^13 - 58397074812147264342/146160698785720231801*e^12 - 917080189519815785415/146160698785720231801*e^11 - 684429741948098954300/146160698785720231801*e^10 + 9889392186226245358269/146160698785720231801*e^9 + 15955738814741552598664/146160698785720231801*e^8 - 45978688717736563175254/146160698785720231801*e^7 - 94080190501305015985055/146160698785720231801*e^6 + 100149483489446051352374/146160698785720231801*e^5 + 228479074634672522962188/146160698785720231801*e^4 - 105131065873415542851870/146160698785720231801*e^3 - 228245377339507486186654/146160698785720231801*e^2 + 47611180584451451088791/146160698785720231801*e + 66736936310582297587232/146160698785720231801, 3440264794343517916/146160698785720231801*e^14 + 27199875035665499857/146160698785720231801*e^13 - 51305441510675237286/146160698785720231801*e^12 - 864225171541919167700/146160698785720231801*e^11 - 746608151120781186122/146160698785720231801*e^10 + 9066760194792900104514/146160698785720231801*e^9 + 15772463533830953458087/146160698785720231801*e^8 - 40142136516951557600818/146160698785720231801*e^7 - 89353409356784470123965/146160698785720231801*e^6 + 81138673788840893610079/146160698785720231801*e^5 + 209310233327556500981665/146160698785720231801*e^4 - 79787561361744654839993/146160698785720231801*e^3 - 204988503287384927786757/146160698785720231801*e^2 + 37592586840846009646442/146160698785720231801*e + 60139096810011937252170/146160698785720231801, -4534954974423059918/146160698785720231801*e^14 - 35830817751742388457/146160698785720231801*e^13 + 69917959381240041503/146160698785720231801*e^12 + 1150478004166205860342/146160698785720231801*e^11 + 927927960093753127646/146160698785720231801*e^10 - 12308365729879146075059/146160698785720231801*e^9 - 20511666284242432872475/146160698785720231801*e^8 + 56342569099507919653447/146160698785720231801*e^7 + 118735541450551928441837/146160698785720231801*e^6 - 119135941480946013754664/146160698785720231801*e^5 - 282832517695496331700392/146160698785720231801*e^4 + 119142687732314592668613/146160698785720231801*e^3 + 277211777255484024216142/146160698785720231801*e^2 - 51073990585335113877165/146160698785720231801*e - 81549865489877123562864/146160698785720231801, -72818861500891500/146160698785720231801*e^14 - 555187921546671313/146160698785720231801*e^13 + 1934058985051484018/146160698785720231801*e^12 + 21218394523704584619/146160698785720231801*e^11 - 8651776247007599526/146160698785720231801*e^10 - 296881303689619888569/146160698785720231801*e^9 - 117564881981686422523/146160698785720231801*e^8 + 1952874712564847981840/146160698785720231801*e^7 + 1102262812906193942979/146160698785720231801*e^6 - 6341464223957484620956/146160698785720231801*e^5 - 2342317012835299118250/146160698785720231801*e^4 + 9804805577125150210558/146160698785720231801*e^3 - 796011441636361970548/146160698785720231801*e^2 - 6166054808596531055173/146160698785720231801*e + 2290336964875530658928/146160698785720231801, -2686085622910433877/146160698785720231801*e^14 - 21686772141165437803/146160698785720231801*e^13 + 37156171089978397491/146160698785720231801*e^12 + 683186673394586611161/146160698785720231801*e^11 + 669659075965079974370/146160698785720231801*e^10 - 7047341013117411098826/146160698785720231801*e^9 - 13106758042606842797927/146160698785720231801*e^8 + 30187031402208691305127/146160698785720231801*e^7 + 72217655309742830058925/146160698785720231801*e^6 - 57272710581770620096880/146160698785720231801*e^5 - 164444779763410371569030/146160698785720231801*e^4 + 50655061167572670504293/146160698785720231801*e^3 + 156932611321486543308585/146160698785720231801*e^2 - 21684532491220489263324/146160698785720231801*e - 47319832175866566874354/146160698785720231801, -2577615159983160640/146160698785720231801*e^14 - 21350791771241712330/146160698785720231801*e^13 + 33324660383496681239/146160698785720231801*e^12 + 677090220880541198264/146160698785720231801*e^11 + 735483348055663677975/146160698785720231801*e^10 - 7073351329538064433555/146160698785720231801*e^9 - 13915710854951275182507/146160698785720231801*e^8 + 31003827769594839095595/146160698785720231801*e^7 + 77895968705661145470514/146160698785720231801*e^6 - 61138447953831647331624/146160698785720231801*e^5 - 181739406623992129680138/146160698785720231801*e^4 + 56793546833555337277051/146160698785720231801*e^3 + 173226028144325454851402/146160698785720231801*e^2 - 24158631359980436924433/146160698785720231801*e - 47483465695846892199388/146160698785720231801, -3949706732395280552/146160698785720231801*e^14 - 31007590039435859223/146160698785720231801*e^13 + 61119407646534063765/146160698785720231801*e^12 + 995540040691912037389/146160698785720231801*e^11 + 809656331991326495878/146160698785720231801*e^10 - 10645457634325229128448/146160698785720231801*e^9 - 18074619078163846659835/146160698785720231801*e^8 + 48643446045183721446891/146160698785720231801*e^7 + 106220328910505568785376/146160698785720231801*e^6 - 102508463896946353238619/146160698785720231801*e^5 - 259859028631054271732199/146160698785720231801*e^4 + 103374545102269119634969/146160698785720231801*e^3 + 265297723318163552549728/146160698785720231801*e^2 - 48281842462007787189722/146160698785720231801*e - 80284389057776980761708/146160698785720231801, -780184745713606757/146160698785720231801*e^14 - 7574448323957264357/146160698785720231801*e^13 + 3885501261114299601/146160698785720231801*e^12 + 232244507850629671480/146160698785720231801*e^11 + 414091840143007832541/146160698785720231801*e^10 - 2273480247816880315280/146160698785720231801*e^9 - 6096499975972665518064/146160698785720231801*e^8 + 8847452462685817223123/146160698785720231801*e^7 + 30720542825560159202812/146160698785720231801*e^6 - 14557219054597282488105/146160698785720231801*e^5 - 64089278175914453174928/146160698785720231801*e^4 + 12534544482321285066144/146160698785720231801*e^3 + 51369147104997764834000/146160698785720231801*e^2 - 6820556421557381694695/146160698785720231801*e - 10035483686140758396814/146160698785720231801, -7202453800792941920/146160698785720231801*e^14 - 56407732382813805377/146160698785720231801*e^13 + 110735900650402297713/146160698785720231801*e^12 + 1794621763400811165516/146160698785720231801*e^11 + 1450771111038477534342/146160698785720231801*e^10 - 18862579608193663675312/146160698785720231801*e^9 - 31681373261043389977454/146160698785720231801*e^8 + 83571863705670895383773/146160698785720231801*e^7 + 179422619572590167618504/146160698785720231801*e^6 - 167484287774966066627102/146160698785720231801*e^5 - 414656718034106815354362/146160698785720231801*e^4 + 158490807465955686349697/146160698785720231801*e^3 + 392902566212648723666407/146160698785720231801*e^2 - 70692939075856494487656/146160698785720231801*e - 109038985409022219646098/146160698785720231801, -1947535194208925225/146160698785720231801*e^14 - 15519371308663092628/146160698785720231801*e^13 + 28892475637217537760/146160698785720231801*e^12 + 495049918089004440867/146160698785720231801*e^11 + 429921799753081801376/146160698785720231801*e^10 - 5238512661215224915347/146160698785720231801*e^9 - 9057431085701605444955/146160698785720231801*e^8 + 23644027226914913471987/146160698785720231801*e^7 + 51615512812396661191796/146160698785720231801*e^6 - 49862642237541419765503/146160698785720231801*e^5 - 122213733422128146764972/146160698785720231801*e^4 + 52812286018560514816120/146160698785720231801*e^3 + 121480946992830841038260/146160698785720231801*e^2 - 26170048949385446377255/146160698785720231801*e - 37230520138584953551716/146160698785720231801, -986504804676367894/146160698785720231801*e^14 - 8683781488383229860/146160698785720231801*e^13 + 9344545801892814894/146160698785720231801*e^12 + 267942626689323227300/146160698785720231801*e^11 + 382541270613076271740/146160698785720231801*e^10 - 2641246143896777229428/146160698785720231801*e^9 - 6228441153172446236180/146160698785720231801*e^8 + 10152055785869644221176/146160698785720231801*e^7 + 32365992846671016331410/146160698785720231801*e^6 - 14159745152491682712272/146160698785720231801*e^5 - 68996109722674990201594/146160698785720231801*e^4 + 3277175720993429203109/146160698785720231801*e^3 + 58128469111368337140812/146160698785720231801*e^2 + 2075192052106188931813/146160698785720231801*e - 14559719251121821160054/146160698785720231801, 4428855098629900853/146160698785720231801*e^14 + 32928812812734966016/146160698785720231801*e^13 - 79558237544454451904/146160698785720231801*e^12 - 1063644529661391345894/146160698785720231801*e^11 - 519693740590160511684/146160698785720231801*e^10 + 11509778519224260709447/146160698785720231801*e^9 + 15413071018424400136239/146160698785720231801*e^8 - 53766683116105640561113/146160698785720231801*e^7 - 91045025214641197155338/146160698785720231801*e^6 + 117085255167219298829420/146160698785720231801*e^5 + 212256047409360987499069/146160698785720231801*e^4 - 118752035038241507651353/146160698785720231801*e^3 - 198817545976913469450928/146160698785720231801*e^2 + 47230739197635590490962/146160698785720231801*e + 54785534289109641771468/146160698785720231801, 5747633379080991288/146160698785720231801*e^14 + 44793952890568085106/146160698785720231801*e^13 - 91149115015206656614/146160698785720231801*e^12 - 1436738625960661319234/146160698785720231801*e^11 - 1086483251651530593491/146160698785720231801*e^10 + 15342873956856271964487/146160698785720231801*e^9 + 24890969348035962986931/146160698785720231801*e^8 - 70068733902960180651635/146160698785720231801*e^7 - 144508485111395762016158/146160698785720231801*e^6 + 148227185654310348363919/146160698785720231801*e^5 + 344561599301517029291497/146160698785720231801*e^4 - 150841530429794963182779/146160698785720231801*e^3 - 339746602917702991795484/146160698785720231801*e^2 + 68895629498096825993001/146160698785720231801*e + 99144316452903903532378/146160698785720231801, 4969554719107569182/146160698785720231801*e^14 + 37791664135209986715/146160698785720231801*e^13 - 83257609087507671881/146160698785720231801*e^12 - 1209291377587688782691/146160698785720231801*e^11 - 772861092057653320644/146160698785720231801*e^10 + 12855018416880427674937/146160698785720231801*e^9 + 19260430021927093243456/146160698785720231801*e^8 - 58182448977289662628051/146160698785720231801*e^7 - 110706784812024300963270/146160698785720231801*e^6 + 120691901537409907604553/146160698785720231801*e^5 + 255162618655425724545760/146160698785720231801*e^4 - 116659500883150409166309/146160698785720231801*e^3 - 239458227200284332316540/146160698785720231801*e^2 + 46083155043168724722406/146160698785720231801*e + 67251400396063141538048/146160698785720231801, -3444799924551777183/146160698785720231801*e^14 - 28420407960808679436/146160698785720231801*e^13 + 42900676768628598637/146160698785720231801*e^12 + 885994261411497505211/146160698785720231801*e^11 + 1005043166830770129219/146160698785720231801*e^10 - 8950651626386482768310/146160698785720231801*e^9 - 18249718776129223014208/146160698785720231801*e^8 + 36799089624783054491323/146160698785720231801*e^7 + 98212458117903938680979/146160698785720231801*e^6 - 64672669792771700348457/146160698785720231801*e^5 - 218967561806641907347035/146160698785720231801*e^4 + 51582808790386492071119/146160698785720231801*e^3 + 202274941632465538690480/146160698785720231801*e^2 - 21173447339177496177313/146160698785720231801*e - 56600421617635933537002/146160698785720231801, -3378195413026209595/146160698785720231801*e^14 - 25566993156047662788/146160698785720231801*e^13 + 57812946665568193020/146160698785720231801*e^12 + 821101808641313375177/146160698785720231801*e^11 + 487169867937811263677/146160698785720231801*e^10 - 8786856918003410163642/146160698785720231801*e^9 - 12688210132443473909385/146160698785720231801*e^8 + 40214812699449078311340/146160698785720231801*e^7 + 73233320053206129767298/146160698785720231801*e^6 - 84719550400675061193003/146160698785720231801*e^5 - 167308044242211939352015/146160698785720231801*e^4 + 83053002868328249321726/146160698785720231801*e^3 + 151412271519326692941922/146160698785720231801*e^2 - 33555890388105448544932/146160698785720231801*e - 40172434786810714389688/146160698785720231801, 340394654882952742/146160698785720231801*e^14 + 4815811032260174920/146160698785720231801*e^13 + 9036297901528354189/146160698785720231801*e^12 - 131820414668843637165/146160698785720231801*e^11 - 527964836762551065090/146160698785720231801*e^10 + 939676025027053974949/146160698785720231801*e^9 + 6425266093621929580651/146160698785720231801*e^8 - 323385310243692770941/146160698785720231801*e^7 - 30936832525261610402858/146160698785720231801*e^6 - 13289688172205046427682/146160698785720231801*e^5 + 64952884216350384232674/146160698785720231801*e^4 + 29053854122270656318920/146160698785720231801*e^3 - 54724804683911618543868/146160698785720231801*e^2 - 11591586682684830976267/146160698785720231801*e + 10064579407033773012250/146160698785720231801, -8249483605907075274/146160698785720231801*e^14 - 63194703657497039121/146160698785720231801*e^13 + 136776222359594123378/146160698785720231801*e^12 + 2026492214861917788905/146160698785720231801*e^11 + 1340777338985183806301/146160698785720231801*e^10 - 21626794528517471702814/146160698785720231801*e^9 - 32812102192118823817095/146160698785720231801*e^8 + 98542698960192333603861/146160698785720231801*e^7 + 189160488206189872429323/146160698785720231801*e^6 - 206606486997525232615195/146160698785720231801*e^5 - 438869066896864851662967/146160698785720231801*e^4 + 203480907822176388353765/146160698785720231801*e^3 + 415680382432120826779370/146160698785720231801*e^2 - 85217246257721898581016/146160698785720231801*e - 118956855619784574487528/146160698785720231801, 4944157525419426819/146160698785720231801*e^14 + 36303002971102602024/146160698785720231801*e^13 - 90823701223221979679/146160698785720231801*e^12 - 1173720955306141240626/146160698785720231801*e^11 - 517661798398098209145/146160698785720231801*e^10 + 12719288383654177306584/146160698785720231801*e^9 + 16585139460391434627540/146160698785720231801*e^8 - 59525849975268693522695/146160698785720231801*e^7 - 99317029095752053109819/146160698785720231801*e^6 + 129919013756237903223301/146160698785720231801*e^5 + 235054166043531443807504/146160698785720231801*e^4 - 132564743017010325845279/146160698785720231801*e^3 - 228385993316917858386872/146160698785720231801*e^2 + 53328872440543432892426/146160698785720231801*e + 68734968137801368298632/146160698785720231801, 9288651854028543099/146160698785720231801*e^14 + 73567467318933313770/146160698785720231801*e^13 - 138918867412781876409/146160698785720231801*e^12 - 2342266136881732627047/146160698785720231801*e^11 - 2009556447402010823025/146160698785720231801*e^10 + 24658623493835376524823/146160698785720231801*e^9 + 42604719692461367719569/146160698785720231801*e^8 - 109664085805534514594158/146160698785720231801*e^7 - 241353266611465724534991/146160698785720231801*e^6 + 221711682946717071173285/146160698785720231801*e^5 + 561048645818082742679496/146160698785720231801*e^4 - 213337057078087887205017/146160698785720231801*e^3 - 536108764405261726442313/146160698785720231801*e^2 + 95655283689264734242952/146160698785720231801*e + 152196025146868266689302/146160698785720231801, 2699343132470195457/146160698785720231801*e^14 + 22131245606233413430/146160698785720231801*e^13 - 37139049022597650296/146160698785720231801*e^12 - 705362477144542441721/146160698785720231801*e^11 - 693401981326655680107/146160698785720231801*e^10 + 7450454791188698648718/146160698785720231801*e^9 + 13669674150308974691111/146160698785720231801*e^8 - 33477625543231274616061/146160698785720231801*e^7 - 77056935141354612994047/146160698785720231801*e^6 + 69633335987592039614352/146160698785720231801*e^5 + 181215853274463861259452/146160698785720231801*e^4 - 70427843567293558927124/146160698785720231801*e^3 - 176455962905275020405070/146160698785720231801*e^2 + 31271952839296959947752/146160698785720231801*e + 49028258570850427031638/146160698785720231801, -4839920226268755114/146160698785720231801*e^14 - 37642194748533482131/146160698785720231801*e^13 + 77027597067382648517/146160698785720231801*e^12 + 1205599284757443474264/146160698785720231801*e^11 + 898317657474117666070/146160698785720231801*e^10 - 12843804997364718285332/146160698785720231801*e^9 - 20637387363404963941966/146160698785720231801*e^8 + 58478125857218288712418/146160698785720231801*e^7 + 119229633846843690055953/146160698785720231801*e^6 - 123559871854782440606562/146160698785720231801*e^5 - 283090991784256946546336/146160698785720231801*e^4 + 126649156517748240462965/146160698785720231801*e^3 + 280214365285396473015439/146160698785720231801*e^2 - 58487086864766815239598/146160698785720231801*e - 81968684229148205241504/146160698785720231801, -1267621572405201575/146160698785720231801*e^14 - 10251582298115088742/146160698785720231801*e^13 + 18787796198564563309/146160698785720231801*e^12 + 333757601896172354400/146160698785720231801*e^11 + 299574257272791133684/146160698785720231801*e^10 - 3667034303708907324176/146160698785720231801*e^9 - 6496980793839286305908/146160698785720231801*e^8 + 17639385824795540278298/146160698785720231801*e^7 + 39583982498827228820194/146160698785720231801*e^6 - 40776703076364841058504/146160698785720231801*e^5 - 103333214940389639589499/146160698785720231801*e^4 + 47206451503167883994585/146160698785720231801*e^3 + 115302124419332222233566/146160698785720231801*e^2 - 23732809811264658594242/146160698785720231801*e - 39116790338022177484920/146160698785720231801, -5792094543321919293/146160698785720231801*e^14 - 45437169711353881424/146160698785720231801*e^13 + 90193926071562597740/146160698785720231801*e^12 + 1451988783374569125491/146160698785720231801*e^11 + 1134781833701879456357/146160698785720231801*e^10 - 15392800032773121251429/146160698785720231801*e^9 - 25225153145063795675339/146160698785720231801*e^8 + 69289178549228264786962/146160698785720231801*e^7 + 143770829749122002689028/146160698785720231801*e^6 - 142435994205320439185532/146160698785720231801*e^5 - 334234814603516103841765/146160698785720231801*e^4 + 137561726291217376990854/146160698785720231801*e^3 + 319721965942629146931264/146160698785720231801*e^2 - 57576693057956986473136/146160698785720231801*e - 93503339259970500652730/146160698785720231801, 433409591529324965/146160698785720231801*e^14 + 3805725713208935748/146160698785720231801*e^13 - 3466214427370516718/146160698785720231801*e^12 - 117702765081533302688/146160698785720231801*e^11 - 202051541883001768377/146160698785720231801*e^10 + 1158697740211599353485/146160698785720231801*e^9 + 3382570313844926853922/146160698785720231801*e^8 - 4334009494092303247636/146160698785720231801*e^7 - 19609715255732226031304/146160698785720231801*e^6 + 4983206124093375059843/146160698785720231801*e^5 + 50233178709953521705108/146160698785720231801*e^4 + 1894471840128380497817/146160698785720231801*e^3 - 53881220569386222174376/146160698785720231801*e^2 - 1964140563521281184345/146160698785720231801*e + 15386120601421374917908/146160698785720231801, -374455932360946057/146160698785720231801*e^14 - 5167149596354484899/146160698785720231801*e^13 - 5438016205282605651/146160698785720231801*e^12 + 158577539599349907668/146160698785720231801*e^11 + 447364186346102085499/146160698785720231801*e^10 - 1555542640735407519362/146160698785720231801*e^9 - 5867176572070034730413/146160698785720231801*e^8 + 6084117435188688977734/146160698785720231801*e^7 + 30451718588677892734413/146160698785720231801*e^6 - 10305605618337613673545/146160698785720231801*e^5 - 70980535529606788897764/146160698785720231801*e^4 + 11315815651586616120540/146160698785720231801*e^3 + 69714147969804742401432/146160698785720231801*e^2 - 12643429588216325117978/146160698785720231801*e - 18321153836885357941436/146160698785720231801, -8551562675394074360/146160698785720231801*e^14 - 64508977946836254549/146160698785720231801*e^13 + 146529448923158289592/146160698785720231801*e^12 + 2070323365042218333273/146160698785720231801*e^11 + 1228122491432623542463/146160698785720231801*e^10 - 22140678627796074406027/146160698785720231801*e^9 - 32113018567981355676824/146160698785720231801*e^8 + 101457368681685166615402/146160698785720231801*e^7 + 186277941006741220137848/146160698785720231801*e^6 - 215916155594374193552516/146160698785720231801*e^5 - 431992733514635171804228/146160698785720231801*e^4 + 219290080869314510229617/146160698785720231801*e^3 + 408897223228298420113818/146160698785720231801*e^2 - 93987562874540285279482/146160698785720231801*e - 117252742741945601771538/146160698785720231801, -4828039674772912679/146160698785720231801*e^14 - 37922186056142987519/146160698785720231801*e^13 + 72603622743016626743/146160698785720231801*e^12 + 1200793705135346933513/146160698785720231801*e^11 + 1022202287867487897217/146160698785720231801*e^10 - 12497552896762577659470/146160698785720231801*e^9 - 21727554835306321535291/146160698785720231801*e^8 + 54232545831732424651109/146160698785720231801*e^7 + 122316643758488553939286/146160698785720231801*e^6 - 104028009885801933814045/146160698785720231801*e^5 - 282314321831896385382427/146160698785720231801*e^4 + 91289653929637960881027/146160698785720231801*e^3 + 269152459109945111144176/146160698785720231801*e^2 - 38643747924876374546623/146160698785720231801*e - 76259244683278798050358/146160698785720231801, 97089469310960240/146160698785720231801*e^14 + 397980203060713311/146160698785720231801*e^13 - 3823208447755547418/146160698785720231801*e^12 - 17057835477742962641/146160698785720231801*e^11 + 50256323721478177254/146160698785720231801*e^10 + 266379525257482995855/146160698785720231801*e^9 - 228332196203662954725/146160698785720231801*e^8 - 1880433915015583879374/146160698785720231801*e^7 - 23451280882408715625/146160698785720231801*e^6 + 6287072868396815924962/146160698785720231801*e^5 + 1821857103898666931183/146160698785720231801*e^4 - 10286387845243074397381/146160698785720231801*e^3 - 1919722185214399222394/146160698785720231801*e^2 + 7304854724616190746542/146160698785720231801*e - 661911181685523350716/146160698785720231801, 12974057220601100172/146160698785720231801*e^14 + 102025614909221802068/146160698785720231801*e^13 - 199147754425306647771/146160698785720231801*e^12 - 3255429493194222079212/146160698785720231801*e^11 - 2638078252443645048024/146160698785720231801*e^10 + 34423451471485968819912/146160698785720231801*e^9 + 57623464227527158751264/146160698785720231801*e^8 - 154429308606620307747479/146160698785720231801*e^7 - 328111922675929096009405/146160698785720231801*e^6 + 317051403669326806862742/146160698785720231801*e^5 + 765388900495904155470689/146160698785720231801*e^4 - 309337028425806475042903/146160698785720231801*e^3 - 736599032537950790293614/146160698785720231801*e^2 + 135017708461086092073438/146160698785720231801*e + 212149503201147810341420/146160698785720231801, -915179220262204762/146160698785720231801*e^14 - 5992474237180380488/146160698785720231801*e^13 + 21787396669467227925/146160698785720231801*e^12 + 205672687345847792757/146160698785720231801*e^11 - 46882315198341387331/146160698785720231801*e^10 - 2464076217205501031077/146160698785720231801*e^9 - 1888969135963649425276/146160698785720231801*e^8 + 13359089068167212505274/146160698785720231801*e^7 + 15802051072005956226495/146160698785720231801*e^6 - 34662725392419218506867/146160698785720231801*e^5 - 47378802612608696119197/146160698785720231801*e^4 + 39604680788607936549413/146160698785720231801*e^3 + 55698431347896379779164/146160698785720231801*e^2 - 14295740697524811592322/146160698785720231801*e - 18219082995157423687076/146160698785720231801, 2161436308273964757/146160698785720231801*e^14 + 18024248951323890570/146160698785720231801*e^13 - 26555814513718438305/146160698785720231801*e^12 - 566389348095840631027/146160698785720231801*e^11 - 652492485526571102056/146160698785720231801*e^10 + 5822596532696498906047/146160698785720231801*e^9 + 11896391167935971486533/146160698785720231801*e^8 - 24952136604855327733143/146160698785720231801*e^7 - 65459332226752458824746/146160698785720231801*e^6 + 48959162992669282613532/146160698785720231801*e^5 + 151952939357332128564127/146160698785720231801*e^4 - 51374130637516824296765/146160698785720231801*e^3 - 149134801294103813834024/146160698785720231801*e^2 + 30031174896885141851878/146160698785720231801*e + 43880441362403268189542/146160698785720231801, -647129748823139798/146160698785720231801*e^14 - 5962917466083784237/146160698785720231801*e^13 + 3071173305885774546/146160698785720231801*e^12 + 179814774490104571332/146160698785720231801*e^11 + 357634003746876086253/146160698785720231801*e^10 - 1696804942878942868945/146160698785720231801*e^9 - 5423711315157069753983/146160698785720231801*e^8 + 6075177367318637197139/146160698785720231801*e^7 + 29280978004287647215444/146160698785720231801*e^6 - 8471142155088273606985/146160698785720231801*e^5 - 70035274280103451354474/146160698785720231801*e^4 + 7903379071761983179158/146160698785720231801*e^3 + 72007966479134369866244/146160698785720231801*e^2 - 9214707698862031553040/146160698785720231801*e - 21878958716651835976288/146160698785720231801, -2971819718039022929/146160698785720231801*e^14 - 21890638608508201923/146160698785720231801*e^13 + 54500157978484938417/146160698785720231801*e^12 + 708156519003767314684/146160698785720231801*e^11 + 315467344543754436888/146160698785720231801*e^10 - 7674168022926167910418/146160698785720231801*e^9 - 10030483319477995367186/146160698785720231801*e^8 + 35791701515982279944060/146160698785720231801*e^7 + 59917548192613716363411/146160698785720231801*e^6 - 76987704820994979687477/146160698785720231801*e^5 - 140388745367492037452180/146160698785720231801*e^4 + 75921089841282845461439/146160698785720231801*e^3 + 132059756082897318540371/146160698785720231801*e^2 - 30054727462012914492340/146160698785720231801*e - 37611182703270087119522/146160698785720231801, 1065173760970765399/146160698785720231801*e^14 + 5695946667680839286/146160698785720231801*e^13 - 33145120424734028588/146160698785720231801*e^12 - 204600161028943146845/146160698785720231801*e^11 + 325653318854376848835/146160698785720231801*e^10 + 2633717625157483317548/146160698785720231801*e^9 - 1121475874884685372313/146160698785720231801*e^8 - 15772687730520648256998/146160698785720231801*e^7 + 100860724789012529252/146160698785720231801*e^6 + 46164934163437031966802/146160698785720231801*e^5 + 6510833418889074001388/146160698785720231801*e^4 - 60091390730675925305178/146160698785720231801*e^3 - 12270306410903972890232/146160698785720231801*e^2 + 24000230623363189909360/146160698785720231801*e + 7194662039129441511876/146160698785720231801, -225735237948867600/146160698785720231801*e^14 - 3009114619388697719/146160698785720231801*e^13 - 1738848687119729913/146160698785720231801*e^12 + 102076069819244605994/146160698785720231801*e^11 + 243981947848917152758/146160698785720231801*e^10 - 1200718897861492471925/146160698785720231801*e^9 - 3746590467020871247785/146160698785720231801*e^8 + 6357741092861955269995/146160698785720231801*e^7 + 23335872182866226120754/146160698785720231801*e^6 - 16260169168210644270566/146160698785720231801*e^5 - 67126917474587072567992/146160698785720231801*e^4 + 19980822923292815601462/146160698785720231801*e^3 + 82339554541404635306992/146160698785720231801*e^2 - 10659657480024591554170/146160698785720231801*e - 29839903289857377259852/146160698785720231801, 1907208073554719151/146160698785720231801*e^14 + 15038571191434815936/146160698785720231801*e^13 - 27750000283830860221/146160698785720231801*e^12 - 471781412758760160308/146160698785720231801*e^11 - 426231431761610198412/146160698785720231801*e^10 + 4818155121741814605517/146160698785720231801*e^9 + 8662758870078945857004/146160698785720231801*e^8 - 20104670100833185301939/146160698785720231801*e^7 - 47225791916528377910642/146160698785720231801*e^6 + 35456236837251133148719/146160698785720231801*e^5 + 103480227266065874751767/146160698785720231801*e^4 - 26364733779360652630471/146160698785720231801*e^3 - 91351444845929763443367/146160698785720231801*e^2 + 10029622146591454146780/146160698785720231801*e + 25044315800778048698744/146160698785720231801, 1901913032139684345/146160698785720231801*e^14 + 17894439936811091313/146160698785720231801*e^13 - 12140314450778781173/146160698785720231801*e^12 - 557163604824254164527/146160698785720231801*e^11 - 960545680280022201872/146160698785720231801*e^10 + 5606087705345434812587/146160698785720231801*e^9 + 15100761454671381766311/146160698785720231801*e^8 - 22751669715565927595213/146160698785720231801*e^7 - 82462443223573856861388/146160698785720231801*e^6 + 38758669442725475158904/146160698785720231801*e^5 + 195454443427820334596881/146160698785720231801*e^4 - 32419585237106066688573/146160698785720231801*e^3 - 193429760175928008002764/146160698785720231801*e^2 + 22367631267507899847374/146160698785720231801*e + 53247633966898024080376/146160698785720231801, -6582280919147538863/146160698785720231801*e^14 - 52251981359589280295/146160698785720231801*e^13 + 96575386464147173279/146160698785720231801*e^12 + 1654045953879659454295/146160698785720231801*e^11 + 1468186162094653521847/146160698785720231801*e^10 - 17218422176014168166512/146160698785720231801*e^9 - 30361329479689478343118/146160698785720231801*e^8 + 74961539226602395966942/146160698785720231801*e^7 + 169626357071081229553965/146160698785720231801*e^6 - 145982649518011284351134/146160698785720231801*e^5 - 388878787152093574731516/146160698785720231801*e^4 + 133957561525535112099223/146160698785720231801*e^3 + 366503054739159577649660/146160698785720231801*e^2 - 60003380593243032110244/146160698785720231801*e - 99998847772969029154836/146160698785720231801, 54681425735391447/146160698785720231801*e^14 + 976944676804957485/146160698785720231801*e^13 + 2032851154044159716/146160698785720231801*e^12 - 28912383484377432427/146160698785720231801*e^11 - 102577741953525417834/146160698785720231801*e^10 + 274309643042830339734/146160698785720231801*e^9 + 1218708403576073000284/146160698785720231801*e^8 - 1199127942502839908638/146160698785720231801*e^7 - 6025015491548484396003/146160698785720231801*e^6 + 3806709265116464892005/146160698785720231801*e^5 + 14633099113286484683751/146160698785720231801*e^4 - 8755640470129870153846/146160698785720231801*e^3 - 17281988240709730806184/146160698785720231801*e^2 + 6825229165830442388569/146160698785720231801*e + 5542413464520460457074/146160698785720231801, -799188704667288320/146160698785720231801*e^14 - 4421162540791976081/146160698785720231801*e^13 + 24765607795835734507/146160698785720231801*e^12 + 167562496465608857587/146160698785720231801*e^11 - 210156750523954926011/146160698785720231801*e^10 - 2308223498995459161818/146160698785720231801*e^9 - 137773189493435622403/146160698785720231801*e^8 + 14760165857812424612770/146160698785720231801*e^7 + 9177957037589395842771/146160698785720231801*e^6 - 45378340242975315808299/146160698785720231801*e^5 - 38216281409307582501190/146160698785720231801*e^4 + 62430639528024368883836/146160698785720231801*e^3 + 49690380367957966915511/146160698785720231801*e^2 - 30223041239399875119678/146160698785720231801*e - 15713429417331754167464/146160698785720231801, -859869445006450393/146160698785720231801*e^14 - 4203620610156905363/146160698785720231801*e^13 + 31140274868161836216/146160698785720231801*e^12 + 170526124641511097596/146160698785720231801*e^11 - 372239349198990595318/146160698785720231801*e^10 - 2547111386921017435231/146160698785720231801*e^9 + 1443491925967856209658/146160698785720231801*e^8 + 17627177950767363136806/146160698785720231801*e^7 + 2524528339682555090565/146160698785720231801*e^6 - 57751152849249271362120/146160698785720231801*e^5 - 26722331622383240559273/146160698785720231801*e^4 + 81941202777844191156522/146160698785720231801*e^3 + 45109762524309703546270/146160698785720231801*e^2 - 38010248736421303462830/146160698785720231801*e - 19818562853492773644158/146160698785720231801, -7995570245524865923/146160698785720231801*e^14 - 64601947684619762027/146160698785720231801*e^13 + 110549056966881957651/146160698785720231801*e^12 + 2040109593512402188719/146160698785720231801*e^11 + 2011307879896725604949/146160698785720231801*e^10 - 21140649156905941402905/146160698785720231801*e^9 - 39521190648254888195375/146160698785720231801*e^8 + 91283878288166287790554/146160698785720231801*e^7 + 219528330489247353912719/146160698785720231801*e^6 - 175543850088993468578543/146160698785720231801*e^5 - 503601268295496345837962/146160698785720231801*e^4 + 159697578588984911123653/146160698785720231801*e^3 + 474904230096116390079529/146160698785720231801*e^2 - 73022539869317000769178/146160698785720231801*e - 131408763673005668556796/146160698785720231801, 2246532281694260654/146160698785720231801*e^14 + 18756515824777014893/146160698785720231801*e^13 - 27981757659105002093/146160698785720231801*e^12 - 594183735174213743270/146160698785720231801*e^11 - 681228593806171818227/146160698785720231801*e^10 + 6192350871605057159566/146160698785720231801*e^9 + 12684546158849361992984/146160698785720231801*e^8 - 26991336188060115921615/146160698785720231801*e^7 - 71487395545486557531062/146160698785720231801*e^6 + 52612773720002938168500/146160698785720231801*e^5 + 169331260242659472910104/146160698785720231801*e^4 - 48412325485249145834238/146160698785720231801*e^3 - 163731790894179017936938/146160698785720231801*e^2 + 21836366234593424298194/146160698785720231801*e + 43714773894964968196390/146160698785720231801, -5404465305881526421/146160698785720231801*e^14 - 43931439162965980433/146160698785720231801*e^13 + 73867730253870568190/146160698785720231801*e^12 + 1393538412609102670343/146160698785720231801*e^11 + 1411563343335252673551/146160698785720231801*e^10 - 14554752171117023968659/146160698785720231801*e^9 - 27757401246003725721537/146160698785720231801*e^8 + 63600371018444644372014/146160698785720231801*e^7 + 156968431349392765869272/146160698785720231801*e^6 - 123668132291275878927703/146160698785720231801*e^5 - 370150957626418801489757/146160698785720231801*e^4 + 111038870077831957929767/146160698785720231801*e^3 + 361170958351912823132986/146160698785720231801*e^2 - 48353331353087506761492/146160698785720231801*e - 105628344905210029559302/146160698785720231801, 10366697332424992134/146160698785720231801*e^14 + 81701318120109997701/146160698785720231801*e^13 - 155906024715806096068/146160698785720231801*e^12 - 2594542065737305536462/146160698785720231801*e^11 - 2197025125602858143352/146160698785720231801*e^10 + 27184802789628076065627/146160698785720231801*e^9 + 46712597661380908916480/146160698785720231801*e^8 - 119928975562376653116821/146160698785720231801*e^7 - 262951297435801196587219/146160698785720231801*e^6 + 239684577219882410252090/146160698785720231801*e^5 + 605480252809566579621516/146160698785720231801*e^4 - 227472242254125864730548/146160698785720231801*e^3 - 573445846729481732949880/146160698785720231801*e^2 + 97817310712611191980242/146160698785720231801*e + 162423602719932010975708/146160698785720231801, -7816957108879219364/146160698785720231801*e^14 - 61340833733450103796/146160698785720231801*e^13 + 120631691065430749781/146160698785720231801*e^12 + 1962789947693588104750/146160698785720231801*e^11 + 1586149327822422918881/146160698785720231801*e^10 - 20873890477841149017086/146160698785720231801*e^9 - 35042378007529956647158/146160698785720231801*e^8 + 94758314195900110716864/146160698785720231801*e^7 + 202177788766297380713319/146160698785720231801*e^6 - 199515830629101310336882/146160698785720231801*e^5 - 480631545702233930485002/146160698785720231801*e^4 + 204519199852255713630108/146160698785720231801*e^3 + 471871500336600415804554/146160698785720231801*e^2 - 95413790141843681599106/146160698785720231801*e - 136423640404093227953774/146160698785720231801, -2878741556449970210/146160698785720231801*e^14 - 24267716106457010912/146160698785720231801*e^13 + 33494161821353300634/146160698785720231801*e^12 + 759878213960994414345/146160698785720231801*e^11 + 936494101376649124375/146160698785720231801*e^10 - 7739308020104722226372/146160698785720231801*e^9 - 16703009684261276775557/146160698785720231801*e^8 + 32279252739882323012778/146160698785720231801*e^7 + 92059266068719695609134/146160698785720231801*e^6 - 58388281791925546714815/146160698785720231801*e^5 - 214449005216618387496802/146160698785720231801*e^4 + 51378579322499914145512/146160698785720231801*e^3 + 208275143118812131113776/146160698785720231801*e^2 - 29014309876903587899172/146160698785720231801*e - 59356486319908400841010/146160698785720231801, 1219095490120669107/146160698785720231801*e^14 + 10394678094435546767/146160698785720231801*e^13 - 11562575047689642862/146160698785720231801*e^12 - 311902864452647904172/146160698785720231801*e^11 - 460184602375196385812/146160698785720231801*e^10 + 2882644283157633005563/146160698785720231801*e^9 + 7339966308957041718574/146160698785720231801*e^8 - 9280613989654839241471/146160698785720231801*e^7 - 36871099808831816070272/146160698785720231801*e^6 + 4982217603712928116428/146160698785720231801*e^5 + 75538287904632688572012/146160698785720231801*e^4 + 16151408547480701232874/146160698785720231801*e^3 - 61648008019470273464972/146160698785720231801*e^2 - 13177163549868375887579/146160698785720231801*e + 14608865369140638471786/146160698785720231801, 9022856484431750645/146160698785720231801*e^14 + 70865751879673133083/146160698785720231801*e^13 - 138682428991367132373/146160698785720231801*e^12 - 2267556141569322314793/146160698785720231801*e^11 - 1854111873465340568084/146160698785720231801*e^10 + 24110255408651955494782/146160698785720231801*e^9 + 40801994579738772501847/146160698785720231801*e^8 - 109338526775618875001520/146160698785720231801*e^7 - 235768028943046150463259/146160698785720231801*e^6 + 229369527295219913712899/146160698785720231801*e^5 + 561802454125563502039825/146160698785720231801*e^4 - 233376017699268795515779/146160698785720231801*e^3 - 552279170105285357842662/146160698785720231801*e^2 + 109889070900843496597408/146160698785720231801*e + 159317470234826926238524/146160698785720231801, 5832016736230098336/146160698785720231801*e^14 + 46642122111136995167/146160698785720231801*e^13 - 84655057804276411461/146160698785720231801*e^12 - 1481580068320873564843/146160698785720231801*e^11 - 1342497108589131374013/146160698785720231801*e^10 + 15528365354391175905502/146160698785720231801*e^9 + 27576231799566988812291/146160698785720231801*e^8 - 68487689490154205165277/146160698785720231801*e^7 - 154989967571986588412841/146160698785720231801*e^6 + 136400863207187588478240/146160698785720231801*e^5 + 358684449157474611332712/146160698785720231801*e^4 - 127585945194196937746655/146160698785720231801*e^3 - 343246026329155969022908/146160698785720231801*e^2 + 53621824173312249293664/146160698785720231801*e + 98656675951697103052812/146160698785720231801, -7433418098089181634/146160698785720231801*e^14 - 58111190816196419674/146160698785720231801*e^13 + 114626986612472114714/146160698785720231801*e^12 + 1850241243780586835462/146160698785720231801*e^11 + 1492696521642724130914/146160698785720231801*e^10 - 19468375432700697181701/146160698785720231801*e^9 - 32760168988823473776092/146160698785720231801*e^8 + 86307373653868001068677/146160698785720231801*e^7 + 186109486263199551222487/146160698785720231801*e^6 - 172264313749980508817512/146160698785720231801*e^5 - 430353614092908011979104/146160698785720231801*e^4 + 159159523593779907158004/146160698785720231801*e^3 + 405150952415590300170574/146160698785720231801*e^2 - 65287643411916537497708/146160698785720231801*e - 114176137806217852611980/146160698785720231801, 10824750083956394170/146160698785720231801*e^14 + 85320246477904572065/146160698785720231801*e^13 - 164748234935402496910/146160698785720231801*e^12 - 2723290980301539037475/146160698785720231801*e^11 - 2261254155660671357435/146160698785720231801*e^10 + 28808254467345621451160/146160698785720231801*e^9 + 49023088443406053962913/146160698785720231801*e^8 - 129254749739070005236464/146160698785720231801*e^7 - 280497813411104410026840/146160698785720231801*e^6 + 265262437889061925031579/146160698785720231801*e^5 + 660265060762883860045937/146160698785720231801*e^4 - 260542962815546767575080/146160698785720231801*e^3 - 641150138722836854834448/146160698785720231801*e^2 + 119693719391689691990896/146160698785720231801*e + 183605492775334060201744/146160698785720231801, 2156404392272586798/146160698785720231801*e^14 + 17578399667152994201/146160698785720231801*e^13 - 28153172503813675058/146160698785720231801*e^12 - 549122760403101786660/146160698785720231801*e^11 - 591410880646823030610/146160698785720231801*e^10 + 5551562228401178288570/146160698785720231801*e^9 + 11083351688543035027969/146160698785720231801*e^8 - 22551322260628814794758/146160698785720231801*e^7 - 60190483818537303511541/146160698785720231801*e^6 + 36700547543373971329739/146160698785720231801*e^5 + 133866809338872225330550/146160698785720231801*e^4 - 21637687239755981619399/146160698785720231801*e^3 - 119913148571558141031866/146160698785720231801*e^2 + 7231261004248082243950/146160698785720231801*e + 29143290825531263089526/146160698785720231801, -7662666923078719241/146160698785720231801*e^14 - 58728682941403080326/146160698785720231801*e^13 + 129467623608746338335/146160698785720231801*e^12 + 1904977055760644759543/146160698785720231801*e^11 + 1216479898576429222258/146160698785720231801*e^10 - 20772804898925823992912/146160698785720231801*e^9 - 31159841472884668933273/146160698785720231801*e^8 + 98351471774444854890644/146160698785720231801*e^7 + 186928385422878468126766/146160698785720231801*e^6 - 219500932426091458458838/146160698785720231801*e^5 - 457932431144237963099856/146160698785720231801*e^4 + 235681849582375443352630/146160698785720231801*e^3 + 461623354559401895293371/146160698785720231801*e^2 - 109373576434516653726570/146160698785720231801*e - 135912898999527829734508/146160698785720231801, -490772055746172950/146160698785720231801*e^14 - 1778801343773519763/146160698785720231801*e^13 + 19915989437860930200/146160698785720231801*e^12 + 74789040701670066264/146160698785720231801*e^11 - 285066214218218750686/146160698785720231801*e^10 - 1143927044922050818835/146160698785720231801*e^9 + 1675855728945094721584/146160698785720231801*e^8 + 7829786273582092770190/146160698785720231801*e^7 - 3050929796891569854023/146160698785720231801*e^6 - 23844084115643735628755/146160698785720231801*e^5 - 4042194490897315139915/146160698785720231801*e^4 + 28402542598297385262879/146160698785720231801*e^3 + 14133132499271209103276/146160698785720231801*e^2 - 9564396199626034909600/146160698785720231801*e - 5607888241335671721414/146160698785720231801, -9715679609636504609/146160698785720231801*e^14 - 75066349459657034398/146160698785720231801*e^13 + 154993955457855754671/146160698785720231801*e^12 + 2388519290996721671465/146160698785720231801*e^11 + 1751809514091021702573/146160698785720231801*e^10 - 25124628169460991448101/146160698785720231801*e^9 - 40059590388534049619602/146160698785720231801*e^8 + 111683401620163680740936/146160698785720231801*e^7 + 226188036011951591437609/146160698785720231801*e^6 - 225974146864816552957662/146160698785720231801*e^5 - 516349516601882036255840/146160698785720231801*e^4 + 215765435811606130478291/146160698785720231801*e^3 + 485130760006548281773806/146160698785720231801*e^2 - 89638026866628391352852/146160698785720231801*e - 139726323647146358412870/146160698785720231801, 7272518338363064824/146160698785720231801*e^14 + 56282139601323576969/146160698785720231801*e^13 - 118010986814665180936/146160698785720231801*e^12 - 1807780845202124325830/146160698785720231801*e^11 - 1280485992075509811698/146160698785720231801*e^10 + 19361623542048086764664/146160698785720231801*e^9 + 30320672022049857282848/146160698785720231801*e^8 - 88948327149829077651843/146160698785720231801*e^7 - 176147561923914175634467/146160698785720231801*e^6 + 190257994416550521607439/146160698785720231801*e^5 + 417838540661381348879206/146160698785720231801*e^4 - 196235472819699207564007/146160698785720231801*e^3 - 409852801371521238352171/146160698785720231801*e^2 + 88278570379395686182188/146160698785720231801*e + 120342368001367394757394/146160698785720231801, 222604915669620983/146160698785720231801*e^14 + 1755725172074594949/146160698785720231801*e^13 - 5406413170502605626/146160698785720231801*e^12 - 72976744323414023770/146160698785720231801*e^11 - 18650735156721435811/146160698785720231801*e^10 + 1118649700108051933735/146160698785720231801*e^9 + 1453467260421462335988/146160698785720231801*e^8 - 7935055353503096501837/146160698785720231801*e^7 - 13771866121164767557374/146160698785720231801*e^6 + 26841976889047231934746/146160698785720231801*e^5 + 49433759031810959551348/146160698785720231801*e^4 - 40850790519521960890951/146160698785720231801*e^3 - 66038043434533431966110/146160698785720231801*e^2 + 22788362316500233169868/146160698785720231801*e + 23023801456751963765138/146160698785720231801, 4872326640436230975/146160698785720231801*e^14 + 40536398549602046074/146160698785720231801*e^13 - 63220699052616992473/146160698785720231801*e^12 - 1291300015263445226097/146160698785720231801*e^11 - 1397564020831803560768/146160698785720231801*e^10 + 13604029200309939827368/146160698785720231801*e^9 + 26690364457462385707311/146160698785720231801*e^8 - 60517891122896784896941/146160698785720231801*e^7 - 151714521379852218634123/146160698785720231801*e^6 + 122200981659525413216983/146160698785720231801*e^5 + 363072693202708342983044/146160698785720231801*e^4 - 118190420725825664817065/146160698785720231801*e^3 - 359278908208516466657948/146160698785720231801*e^2 + 56820048668589629127404/146160698785720231801*e + 101763087882905842767660/146160698785720231801, -3664570197016226540/146160698785720231801*e^14 - 28161512156645317483/146160698785720231801*e^13 + 60082461190311870437/146160698785720231801*e^12 + 902988958282081896612/146160698785720231801*e^11 + 619210567342868313306/146160698785720231801*e^10 - 9648002540221244861848/146160698785720231801*e^9 - 14895584178431452005694/146160698785720231801*e^8 + 44259147365320997168375/146160698785720231801*e^7 + 86482653054230776708811/146160698785720231801*e^6 - 95128712329552221904326/146160698785720231801*e^5 - 206137947037646272850044/146160698785720231801*e^4 + 99749331750210804704795/146160698785720231801*e^3 + 208265469903355393499209/146160698785720231801*e^2 - 45757650212526839930322/146160698785720231801*e - 65685785207601730312736/146160698785720231801, -9348634903058809482/146160698785720231801*e^14 - 74463499607329684707/146160698785720231801*e^13 + 136831931509868824288/146160698785720231801*e^12 + 2365652576217600689148/146160698785720231801*e^11 + 2122305321377604155590/146160698785720231801*e^10 - 24786824681126920073383/146160698785720231801*e^9 - 44033533766336666960816/146160698785720231801*e^8 + 109046294196127377799993/146160698785720231801*e^7 + 249007652639151090578278/146160698785720231801*e^6 - 215045407515535158007345/146160698785720231801*e^5 - 581017543284026194317277/146160698785720231801*e^4 + 197733022143346183687568/146160698785720231801*e^3 + 561125392362140617952097/146160698785720231801*e^2 - 88307153076974524431802/146160698785720231801*e - 162251143405657721048354/146160698785720231801, -3240200739749766480/146160698785720231801*e^14 - 27402911135282708610/146160698785720231801*e^13 + 38880452837967912123/146160698785720231801*e^12 + 865136164837399337713/146160698785720231801*e^11 + 1019821899585156578797/146160698785720231801*e^10 - 8955974421487016007120/146160698785720231801*e^9 - 18478552940603680251704/146160698785720231801*e^8 + 38526218685656567507482/146160698785720231801*e^7 + 102101670653545872455366/146160698785720231801*e^6 - 73129051852705721707001/146160698785720231801*e^5 - 236031064068937558203194/146160698785720231801*e^4 + 64240582569164816447536/146160698785720231801*e^3 + 224721275420810113303432/146160698785720231801*e^2 - 28135581680291753270557/146160698785720231801*e - 64433932253662683936434/146160698785720231801, 5489305329174295044/146160698785720231801*e^14 + 43103988461291327721/146160698785720231801*e^13 - 83516012881982690945/146160698785720231801*e^12 - 1373061079902699266206/146160698785720231801*e^11 - 1142632987676761676955/146160698785720231801*e^10 + 14473341431678888658634/146160698785720231801*e^9 + 24717991955088581796910/146160698785720231801*e^8 - 64580716783787635536947/146160698785720231801*e^7 - 140776559534916231072429/146160698785720231801*e^6 + 131632389231820393066456/146160698785720231801*e^5 + 328552133223100037127403/146160698785720231801*e^4 - 128174210029166154289968/146160698785720231801*e^3 - 313464052515629968639714/146160698785720231801*e^2 + 57159827558801740383622/146160698785720231801*e + 86775193772505100073738/146160698785720231801, -4684583919985936971/146160698785720231801*e^14 - 36230712386331507523/146160698785720231801*e^13 + 73216511450006282669/146160698785720231801*e^12 + 1148146373349264504954/146160698785720231801*e^11 + 896712742964054227691/146160698785720231801*e^10 - 11965520021333509884134/146160698785720231801*e^9 - 19932552213868354763958/146160698785720231801*e^8 + 52004302517918135263429/146160698785720231801*e^7 + 112255445514508750411040/146160698785720231801*e^6 - 99518213773953879327834/146160698785720231801*e^5 - 256343918030820996477464/146160698785720231801*e^4 + 84795064190914387036415/146160698785720231801*e^3 + 241434225033964913865603/146160698785720231801*e^2 - 32711764673772985762474/146160698785720231801*e - 70786474040563100204080/146160698785720231801, -9983750087295828195/146160698785720231801*e^14 - 78108134007047023422/146160698785720231801*e^13 + 152435883033673975016/146160698785720231801*e^12 + 2471677012915737098956/146160698785720231801*e^11 + 2010985187945167987980/146160698785720231801*e^10 - 25711859199979382728550/146160698785720231801*e^9 - 43226897054409315636994/146160698785720231801*e^8 + 111765824368713463505610/146160698785720231801*e^7 + 239994498306058745916807/146160698785720231801*e^6 - 216680958351154349696358/146160698785720231801*e^5 - 538485269395119515575387/146160698785720231801*e^4 + 194962247773707495227591/146160698785720231801*e^3 + 492154782923963883706696/146160698785720231801*e^2 - 79926365873954711691352/146160698785720231801*e - 133303341173250226086624/146160698785720231801, 11648514029987249017/146160698785720231801*e^14 + 90471240912208268308/146160698785720231801*e^13 - 183782430747775081237/146160698785720231801*e^12 - 2881072797418734960600/146160698785720231801*e^11 - 2182710076806259891615/146160698785720231801*e^10 + 30333387494525734848716/146160698785720231801*e^9 + 49224848774080003861548/146160698785720231801*e^8 - 134721529798481423004733/146160698785720231801*e^7 - 278850754849019239816653/146160698785720231801*e^6 + 269942888930695705498274/146160698785720231801*e^5 + 640198292190054694344068/146160698785720231801*e^4 - 249873689013931905236032/146160698785720231801*e^3 - 602436599628979555124632/146160698785720231801*e^2 + 101752169548175382509469/146160698785720231801*e + 171782672718252254997084/146160698785720231801, 7522161657720131719/146160698785720231801*e^14 + 56059083090640868446/146160698785720231801*e^13 - 134721520250933752780/146160698785720231801*e^12 - 1814174806650857811359/146160698785720231801*e^11 - 912330026635750604170/146160698785720231801*e^10 + 19691719152454909283372/146160698785720231801*e^9 + 26848111264193653860715/146160698785720231801*e^8 - 92365555014187187666075/146160698785720231801*e^7 - 160818486660305297351064/146160698785720231801*e^6 + 201921295003386390493277/146160698785720231801*e^5 + 385463585318584803334908/146160698785720231801*e^4 - 206070579046459567179777/146160698785720231801*e^3 - 378184568503167398971480/146160698785720231801*e^2 + 86100847231294063535210/146160698785720231801*e + 109880251933981507807360/146160698785720231801, 4682279087164392021/146160698785720231801*e^14 + 37147041538643187491/146160698785720231801*e^13 - 72051653411579329256/146160698785720231801*e^12 - 1197524373202858069894/146160698785720231801*e^11 - 972485767842647773297/146160698785720231801*e^10 + 12913648380160161531456/146160698785720231801*e^9 + 21524218033854002796512/146160698785720231801*e^8 - 60035530243772427235569/146160698785720231801*e^7 - 125559269891278808498101/146160698785720231801*e^6 + 130702055068399723653078/146160698785720231801*e^5 + 301410282448965869152505/146160698785720231801*e^4 - 136946288169052575072914/146160698785720231801*e^3 - 293557740980607461364432/146160698785720231801*e^2 + 62202158672471714149099/146160698785720231801*e + 80572808699715629621240/146160698785720231801, 4552507845140205150/146160698785720231801*e^14 + 39098235688217351462/146160698785720231801*e^13 - 51088355400562598226/146160698785720231801*e^12 - 1229166661721525239881/146160698785720231801*e^11 - 1542412170807069128886/146160698785720231801*e^10 + 12625865344050898599487/146160698785720231801*e^9 + 27079445755374504711098/146160698785720231801*e^8 - 53618192939556851547011/146160698785720231801*e^7 - 148550675912046321086416/146160698785720231801*e^6 + 100306774172957843127997/146160698785720231801*e^5 + 344996752015785441189254/146160698785720231801*e^4 - 90100981484726457724750/146160698785720231801*e^3 - 336723178373616689071478/146160698785720231801*e^2 + 46403164166812546631826/146160698785720231801*e + 98559686326542943502308/146160698785720231801, 12716124320632113968/146160698785720231801*e^14 + 99312891147677449076/146160698785720231801*e^13 - 202829568191883421073/146160698785720231801*e^12 - 3196216390674452860235/146160698785720231801*e^11 - 2378843992608210059477/146160698785720231801*e^10 + 34349620104608730359133/146160698785720231801*e^9 + 55028605952000966388924/146160698785720231801*e^8 - 158605661300780545981488/146160698785720231801*e^7 - 320926805998741023069999/146160698785720231801*e^6 + 340938238251128842558641/146160698785720231801*e^5 + 767042567527739532932108/146160698785720231801*e^4 - 351721103160835833018677/146160698785720231801*e^3 - 753850587401044671800385/146160698785720231801*e^2 + 159106025935365334185180/146160698785720231801*e + 217703019371629930121990/146160698785720231801, 3365647339853969474/146160698785720231801*e^14 + 27455386994687779540/146160698785720231801*e^13 - 48436149167493720567/146160698785720231801*e^12 - 886539378424035709815/146160698785720231801*e^11 - 821876069814146296437/146160698785720231801*e^10 + 9585952049704199532068/146160698785720231801*e^9 + 17105281709770410639038/146160698785720231801*e^8 - 44709392723935286257634/146160698785720231801*e^7 - 100569008588063895647350/146160698785720231801*e^6 + 97293616279076907652250/146160698785720231801*e^5 + 249527595330834166626477/146160698785720231801*e^4 - 100426547032002976990622/146160698785720231801*e^3 - 259316103575613626020718/146160698785720231801*e^2 + 43794667794097496907853/146160698785720231801*e + 79248178897333378152890/146160698785720231801, -5666703563035524975/146160698785720231801*e^14 - 42278610207940753898/146160698785720231801*e^13 + 97628467476588892494/146160698785720231801*e^12 + 1344286117614961664113/146160698785720231801*e^11 + 768403796983991465648/146160698785720231801*e^10 - 14115403154241936758123/146160698785720231801*e^9 - 20239260630855935359950/146160698785720231801*e^8 + 62443244945874122947455/146160698785720231801*e^7 + 114475736228146432393999/146160698785720231801*e^6 - 124504167283691443258710/146160698785720231801*e^5 - 255652005710669297561336/146160698785720231801*e^4 + 113853061345059742445680/146160698785720231801*e^3 + 234325726514503936951670/146160698785720231801*e^2 - 43952524184565602279138/146160698785720231801*e - 70246541008106116930386/146160698785720231801, -1056300716876871494/146160698785720231801*e^14 - 8852997000707230213/146160698785720231801*e^13 + 10657179394375485639/146160698785720231801*e^12 + 267494720352291328335/146160698785720231801*e^11 + 384160088746026250885/146160698785720231801*e^10 - 2516276024454542971134/146160698785720231801*e^9 - 6324712615919294844589/146160698785720231801*e^8 + 8603162688475993450346/146160698785720231801*e^7 + 32767383648428762647709/146160698785720231801*e^6 - 7889337375121990468637/146160698785720231801*e^5 - 70484286620353256631007/146160698785720231801*e^4 - 4754184835784136169178/146160698785720231801*e^3 + 63627755607847920185026/146160698785720231801*e^2 + 4735298344975836083408/146160698785720231801*e - 19432730566111338846842/146160698785720231801, -7523896020138920708/146160698785720231801*e^14 - 58236449740272416252/146160698785720231801*e^13 + 121445442498250908113/146160698785720231801*e^12 + 1869767580093077520560/146160698785720231801*e^11 + 1350520552594518709287/146160698785720231801*e^10 - 20003958910679836938559/146160698785720231801*e^9 - 31727749179833978091620/146160698785720231801*e^8 + 91635543001019499617581/146160698785720231801*e^7 + 184233609415356386516266/146160698785720231801*e^6 - 194526201982215465662599/146160698785720231801*e^5 - 435518234245560438591885/146160698785720231801*e^4 + 196903639662501904254824/146160698785720231801*e^3 + 421572959115986485426824/146160698785720231801*e^2 - 84849090552271168668128/146160698785720231801*e - 123391818607781935666064/146160698785720231801, -1075845581075514801/146160698785720231801*e^14 - 9615085498295881696/146160698785720231801*e^13 + 8787649740598000826/146160698785720231801*e^12 + 299718698208356201529/146160698785720231801*e^11 + 486558923196734394707/146160698785720231801*e^10 - 3021737614770967207026/146160698785720231801*e^9 - 8060644407228596103981/146160698785720231801*e^8 + 12298632781576476293178/146160698785720231801*e^7 + 45861449742127405207778/146160698785720231801*e^6 - 20909534590460667313172/146160698785720231801*e^5 - 115725239333540123519428/146160698785720231801*e^4 + 16328998260009287007803/146160698785720231801*e^3 + 125802708379165402282268/146160698785720231801*e^2 - 9486705642160207104543/146160698785720231801*e - 38735557981920044243958/146160698785720231801, -8674024745672114408/146160698785720231801*e^14 - 69873465296828214994/146160698785720231801*e^13 + 121203749116776022227/146160698785720231801*e^12 + 2208469188099281601076/146160698785720231801*e^11 + 2145858894294001264290/146160698785720231801*e^10 - 22907871518489517474285/146160698785720231801*e^9 - 42576144006524654234148/146160698785720231801*e^8 + 98848796042673639318313/146160698785720231801*e^7 + 237395635603083017971529/146160698785720231801*e^6 - 188214541750325113425201/146160698785720231801*e^5 - 546537653563288419524753/146160698785720231801*e^4 + 164987522729413508108010/146160698785720231801*e^3 + 518585726795699525790980/146160698785720231801*e^2 - 72884497629607234868357/146160698785720231801*e - 146057596932749229804830/146160698785720231801, 541509736268351437/146160698785720231801*e^14 + 3195085487457048579/146160698785720231801*e^13 - 16544191508798635350/146160698785720231801*e^12 - 121155585538581611831/146160698785720231801*e^11 + 139001433819619330590/146160698785720231801*e^10 + 1676227860185296611894/146160698785720231801*e^9 + 48163237772857744991/146160698785720231801*e^8 - 10836307418499986833277/146160698785720231801*e^7 - 5456399677373868692144/146160698785720231801*e^6 + 33710138468078907657054/146160698785720231801*e^5 + 23714062424225992071093/146160698785720231801*e^4 - 45232401964079903644170/146160698785720231801*e^3 - 36263286130333735896424/146160698785720231801*e^2 + 19410012925239995102452/146160698785720231801*e + 18972203032692250085476/146160698785720231801, 2118077376630085344/146160698785720231801*e^14 + 15392273570019095593/146160698785720231801*e^13 - 37432578875400501938/146160698785720231801*e^12 - 490752913309346800374/146160698785720231801*e^11 - 272987286791194308284/146160698785720231801*e^10 + 5174847585008094976968/146160698785720231801*e^9 + 7757828554896798784675/146160698785720231801*e^8 - 22994616798843900212607/146160698785720231801*e^7 - 46735673476222004983438/146160698785720231801*e^6 + 45751780660324284208779/146160698785720231801*e^5 + 114836378788856874439033/146160698785720231801*e^4 - 40789440040754790281595/146160698785720231801*e^3 - 117280205933637412665970/146160698785720231801*e^2 + 15524710066586786919504/146160698785720231801*e + 34230212354121694367554/146160698785720231801, 1878553226417324649/146160698785720231801*e^14 + 17456103595789701071/146160698785720231801*e^13 - 13882545881710475311/146160698785720231801*e^12 - 544166951530479799312/146160698785720231801*e^11 - 875287717469267459990/146160698785720231801*e^10 + 5498254741866678415808/146160698785720231801*e^9 + 13872031627063960370237/146160698785720231801*e^8 - 22652574724059294243657/146160698785720231801*e^7 - 74616750518568145634441/146160698785720231801*e^6 + 40658772056649647606787/146160698785720231801*e^5 + 172302004575339970649079/146160698785720231801*e^4 - 37826386292704170731519/146160698785720231801*e^3 - 165482418354607263625386/146160698785720231801*e^2 + 24370403782388506003387/146160698785720231801*e + 44167863928499899917482/146160698785720231801, 2657419195991915807/146160698785720231801*e^14 + 18895612829929792360/146160698785720231801*e^13 - 52621896761601579214/146160698785720231801*e^12 - 611870950363479624292/146160698785720231801*e^11 - 137818043191487501738/146160698785720231801*e^10 + 6652487554636117906519/146160698785720231801*e^9 + 7039977800423993241620/146160698785720231801*e^8 - 31333472900564757213522/146160698785720231801*e^7 - 41723962851107697065221/146160698785720231801*e^6 + 68951781290010464783133/146160698785720231801*e^5 + 91219321437571136280918/146160698785720231801*e^4 - 69622023100768432476384/146160698785720231801*e^3 - 76041724222287879738034/146160698785720231801*e^2 + 26029466244420409855806/146160698785720231801*e + 19758766766399004734774/146160698785720231801, 2434279572199077535/146160698785720231801*e^14 + 18357867951723159365/146160698785720231801*e^13 - 44505518603075268052/146160698785720231801*e^12 - 603877578281214024246/146160698785720231801*e^11 - 277493668337148049002/146160698785720231801*e^10 + 6755285489032905618144/146160698785720231801*e^9 + 8714133693739536206845/146160698785720231801*e^8 - 33378335019794200461634/146160698785720231801*e^7 - 53744621738344669992741/146160698785720231801*e^6 + 79150823114670581690518/146160698785720231801*e^5 + 133214458296067529903729/146160698785720231801*e^4 - 89680341619992118019897/146160698785720231801*e^3 - 137670518443829507118908/146160698785720231801*e^2 + 39317773084839474158048/146160698785720231801*e + 45968090067981841895006/146160698785720231801, 1674653178122651834/146160698785720231801*e^14 + 15697300555044563832/146160698785720231801*e^13 - 11288037285733661870/146160698785720231801*e^12 - 484047464938303565284/146160698785720231801*e^11 - 802643295794028327274/146160698785720231801*e^10 + 4781045750434247461981/146160698785720231801*e^9 + 12358747498483469528203/146160698785720231801*e^8 - 18726756530511421148725/146160698785720231801*e^7 - 64591551661185130332825/146160698785720231801*e^6 + 29478378349222910674806/146160698785720231801*e^5 + 143909983242453503045396/146160698785720231801*e^4 - 19014098425664867596854/146160698785720231801*e^3 - 132604122575582580803697/146160698785720231801*e^2 + 8411647532045171898626/146160698785720231801*e + 33993160628568986905628/146160698785720231801, 6762857618296161656/146160698785720231801*e^14 + 54966105978075940238/146160698785720231801*e^13 - 92150182252456787699/146160698785720231801*e^12 - 1733327547607382043134/146160698785720231801*e^11 - 1736630373737712997564/146160698785720231801*e^10 + 17909290865296387021444/146160698785720231801*e^9 + 33637036124795482135200/146160698785720231801*e^8 - 76870802305037711118500/146160698785720231801*e^7 - 185204786989059372084037/146160698785720231801*e^6 + 146134095424391059558472/146160698785720231801*e^5 + 420296450589637189989259/146160698785720231801*e^4 - 131164503488887433964913/146160698785720231801*e^3 - 392414327419726954992930/146160698785720231801*e^2 + 58554553398447377796295/146160698785720231801*e + 108321393335484919325938/146160698785720231801, -42366904121723990/146160698785720231801*e^14 - 735727241624011798/146160698785720231801*e^13 - 756928177246073548/146160698785720231801*e^12 + 28967229949004584822/146160698785720231801*e^11 + 73000191499649939893/146160698785720231801*e^10 - 412070310411912906049/146160698785720231801*e^9 - 1248189671356822730496/146160698785720231801*e^8 + 2639438823729250411374/146160698785720231801*e^7 + 8701546211507963222328/146160698785720231801*e^6 - 7784147092653384140447/146160698785720231801*e^5 - 26567884763249503606721/146160698785720231801*e^4 + 10705552606936620607054/146160698785720231801*e^3 + 32389838769773565090184/146160698785720231801*e^2 - 7569248075940385557746/146160698785720231801*e - 10161279156328613869018/146160698785720231801, -576893530009022219/146160698785720231801*e^14 - 3881447063503832685/146160698785720231801*e^13 + 14794364452235964398/146160698785720231801*e^12 + 142697215910106587779/146160698785720231801*e^11 - 43700460644795428972/146160698785720231801*e^10 - 1871707060249498582086/146160698785720231801*e^9 - 1415684169722934843033/146160698785720231801*e^8 + 11046740957851742111289/146160698785720231801*e^7 + 13655596918665927162100/146160698785720231801*e^6 - 29303503972618692666660/146160698785720231801*e^5 - 44194930155317723396075/146160698785720231801*e^4 + 29481543410558404838184/146160698785720231801*e^3 + 51558996150608718057816/146160698785720231801*e^2 - 7805593627988710261898/146160698785720231801*e - 13727537932577378240204/146160698785720231801, 2484441450119152592/146160698785720231801*e^14 + 19267872123825047765/146160698785720231801*e^13 - 37598073211978413091/146160698785720231801*e^12 - 604650900642332289559/146160698785720231801*e^11 - 500259374854434783542/146160698785720231801*e^10 + 6198728949249025133054/146160698785720231801*e^9 + 10542216496506134361520/146160698785720231801*e^8 - 26416507421970865697557/146160698785720231801*e^7 - 57095338681627315489906/146160698785720231801*e^6 + 51257969944114617235052/146160698785720231801*e^5 + 123452991039293521534285/146160698785720231801*e^4 - 52702165476959028333769/146160698785720231801*e^3 - 108355891176612954142122/146160698785720231801*e^2 + 29230474453822111922717/146160698785720231801*e + 30884480390169484809418/146160698785720231801, 8568683993900910249/146160698785720231801*e^14 + 65568250242317249153/146160698785720231801*e^13 - 140373171022842366297/146160698785720231801*e^12 - 2098132597356433887202/146160698785720231801*e^11 - 1458062613290233242288/146160698785720231801*e^10 + 22300484543088752260209/146160698785720231801*e^9 + 35038616854124188587181/146160698785720231801*e^8 - 100880554747973212257793/146160698785720231801*e^7 - 203435187391773205885181/146160698785720231801*e^6 + 209256788720247476108746/146160698785720231801*e^5 + 481390360068122115043821/146160698785720231801*e^4 - 204746409025807314161185/146160698785720231801*e^3 - 471394022209622665293242/146160698785720231801*e^2 + 88882089354231829565721/146160698785720231801*e + 138956428164335698022118/146160698785720231801, 256672712308684974/146160698785720231801*e^14 + 2655790734161928831/146160698785720231801*e^13 + 1609690238580434776/146160698785720231801*e^12 - 64838424339410760801/146160698785720231801*e^11 - 194417784337422846314/146160698785720231801*e^10 + 289261254893856236142/146160698785720231801*e^9 + 1940301994845571130207/146160698785720231801*e^8 + 1838677464798139499532/146160698785720231801*e^7 - 4402789070933206770690/146160698785720231801*e^6 - 13629702509058141932522/146160698785720231801*e^5 - 7249813269109002102065/146160698785720231801*e^4 + 22784339435205152452300/146160698785720231801*e^3 + 23359959837494644005222/146160698785720231801*e^2 - 9262268956525733320654/146160698785720231801*e - 11867172480970179992814/146160698785720231801, 8404542631211848128/146160698785720231801*e^14 + 66118154247211346329/146160698785720231801*e^13 - 126382905528714588925/146160698785720231801*e^12 - 2099251792791459193301/146160698785720231801*e^11 - 1785703744558425434357/146160698785720231801*e^10 + 21988637037075002940160/146160698785720231801*e^9 + 38012452571996115951435/146160698785720231801*e^8 - 96995686022875356672644/146160698785720231801*e^7 - 214728336919679014589419/146160698785720231801*e^6 + 194288352606122673209454/146160698785720231801*e^5 + 497823161727179349324952/146160698785720231801*e^4 - 187422142954173166795149/146160698785720231801*e^3 - 476255831054614457783290/146160698785720231801*e^2 + 87903545762751378728066/146160698785720231801*e + 133939871692746120509452/146160698785720231801, 369347217782732791/146160698785720231801*e^14 + 4576801687662832545/146160698785720231801*e^13 + 4311541127084327732/146160698785720231801*e^12 - 134556744922549176327/146160698785720231801*e^11 - 403264927822708136431/146160698785720231801*e^10 + 1183488748581739868043/146160698785720231801*e^9 + 5300860746698064513957/146160698785720231801*e^8 - 3249042040432652421999/146160698785720231801*e^7 - 27250376937388392150703/146160698785720231801*e^6 - 737095173527818233337/146160698785720231801*e^5 + 63085876850494463737202/146160698785720231801*e^4 + 9573497945201212617224/146160698785720231801*e^3 - 63885128865079469987864/146160698785720231801*e^2 - 6375266174312191642508/146160698785720231801*e + 18731471119874312157606/146160698785720231801, -4343226551034089971/146160698785720231801*e^14 - 31835651850360336949/146160698785720231801*e^13 + 80887632395861895597/146160698785720231801*e^12 + 1034772797979108980705/146160698785720231801*e^11 + 429348094655183580251/146160698785720231801*e^10 - 11317617830462058882643/146160698785720231801*e^9 - 14512637795206066183962/146160698785720231801*e^8 + 53670467276301851612861/146160698785720231801*e^7 + 88909959768921861435992/146160698785720231801*e^6 - 118114391054009723581288/146160698785720231801*e^5 - 217152561469926797273173/146160698785720231801*e^4 + 116533390230571467373689/146160698785720231801*e^3 + 218450039335504851360164/146160698785720231801*e^2 - 41545625126093161046597/146160698785720231801*e - 65458251773571109739638/146160698785720231801, 1915297347814376856/146160698785720231801*e^14 + 15554902410772005806/146160698785720231801*e^13 - 24049915758663089955/146160698785720231801*e^12 - 479038274979761287668/146160698785720231801*e^11 - 540843471502255301106/146160698785720231801*e^10 + 4727426690924956097700/146160698785720231801*e^9 + 9741063458472799538074/146160698785720231801*e^8 - 18657038733587267300765/146160698785720231801*e^7 - 51320100060379176333658/146160698785720231801*e^6 + 31429710634881946800914/146160698785720231801*e^5 + 111703788279283974091103/146160698785720231801*e^4 - 28748069407873145551166/146160698785720231801*e^3 - 102225639306923518648956/146160698785720231801*e^2 + 19367108630079838752534/146160698785720231801*e + 28908383836175064407602/146160698785720231801, -6677170790785486393/146160698785720231801*e^14 - 53122588023489784135/146160698785720231801*e^13 + 98587241654609273253/146160698785720231801*e^12 + 1692539273272344668672/146160698785720231801*e^11 + 1491680890260504793329/146160698785720231801*e^10 - 17847230082761818696316/146160698785720231801*e^9 - 31244026622565462613983/146160698785720231801*e^8 + 79673476554698548240609/146160698785720231801*e^7 + 177027514563700571571932/146160698785720231801*e^6 - 162429829645036223988611/146160698785720231801*e^5 - 411171241990697237272380/146160698785720231801*e^4 + 157758392632992733956911/146160698785720231801*e^3 + 386430889413842783959602/146160698785720231801*e^2 - 69321499706568549259555/146160698785720231801*e - 103513916335006620679336/146160698785720231801, 7670760001871142046/146160698785720231801*e^14 + 58864613459125762982/146160698785720231801*e^13 - 127192830359715428525/146160698785720231801*e^12 - 1889763536118640559702/146160698785720231801*e^11 - 1243475646591444993333/146160698785720231801*e^10 + 20229231998214267339699/146160698785720231801*e^9 + 30419782559516115687750/146160698785720231801*e^8 - 92974081387221270629345/146160698785720231801*e^7 - 175043225895201853821179/146160698785720231801*e^6 + 199492781856695386657772/146160698785720231801*e^5 + 404830574375553451170745/146160698785720231801*e^4 - 205707013587312240635137/146160698785720231801*e^3 - 380768909192810761578702/146160698785720231801*e^2 + 88285329979063073315230/146160698785720231801*e + 106027409767950369345326/146160698785720231801, 533151703462493198/146160698785720231801*e^14 + 4813388663229204592/146160698785720231801*e^13 - 6759197438390537083/146160698785720231801*e^12 - 164832518037414718580/146160698785720231801*e^11 - 186751377778300714848/146160698785720231801*e^10 + 1958021752597061416860/146160698785720231801*e^9 + 3839534752206846852423/146160698785720231801*e^8 - 10353429883819412599143/146160698785720231801*e^7 - 24969583949944331819947/146160698785720231801*e^6 + 25540370276356546796844/146160698785720231801*e^5 + 68723286826858654523883/146160698785720231801*e^4 - 28925769506103297086283/146160698785720231801*e^3 - 72774563764703317173316/146160698785720231801*e^2 + 15262983342209616651192/146160698785720231801*e + 16865929485854362306350/146160698785720231801, 7133145472554893315/146160698785720231801*e^14 + 57157898785976690833/146160698785720231801*e^13 - 106383855602171356619/146160698785720231801*e^12 - 1839539892389442357546/146160698785720231801*e^11 - 1599666141199904657749/146160698785720231801*e^10 + 19759142978556368900648/146160698785720231801*e^9 + 34247138586674407299994/146160698785720231801*e^8 - 90982377654234767876309/146160698785720231801*e^7 - 199574910596769105624231/146160698785720231801*e^6 + 193631093134042054900667/146160698785720231801*e^5 + 483326109501071887939441/146160698785720231801*e^4 - 194667082541485645278178/146160698785720231801*e^3 - 484717097561345696164740/146160698785720231801*e^2 + 85572042267922853491199/146160698785720231801*e + 144640987413489725176872/146160698785720231801, -9145573327878469540/146160698785720231801*e^14 - 70351221083128849595/146160698785720231801*e^13 + 149626541081405328342/146160698785720231801*e^12 + 2257538683045671784442/146160698785720231801*e^11 + 1569136097169875145713/146160698785720231801*e^10 - 24126982022732354283227/146160698785720231801*e^9 - 37641790772721836937867/146160698785720231801*e^8 + 110290484915335198512318/146160698785720231801*e^7 + 218690184672444459972561/146160698785720231801*e^6 - 233273323268228329533430/146160698785720231801*e^5 - 515794538538399856155986/146160698785720231801*e^4 + 236147163726097476180906/146160698785720231801*e^3 + 497486847741222110176432/146160698785720231801*e^2 - 105724726307432681544610/146160698785720231801*e - 143461707796613465759896/146160698785720231801, -711583790609829931/146160698785720231801*e^14 - 8873727386160007868/146160698785720231801*e^13 - 11028326498900220976/146160698785720231801*e^12 + 244621048808822142379/146160698785720231801*e^11 + 828711589520257255419/146160698785720231801*e^10 - 1802566181051474849167/146160698785720231801*e^9 - 10040117983193978170983/146160698785720231801*e^8 + 1612791459469075399106/146160698785720231801*e^7 + 45604978346771018382527/146160698785720231801*e^6 + 18663826088231916982961/146160698785720231801*e^5 - 84856472805609220345175/146160698785720231801*e^4 - 42368252070506769976198/146160698785720231801*e^3 + 57254727465615559083748/146160698785720231801*e^2 + 18259558782157250765560/146160698785720231801*e - 4881606447846865450808/146160698785720231801, -7259184804204236443/146160698785720231801*e^14 - 56671052216958025560/146160698785720231801*e^13 + 113127111826117732867/146160698785720231801*e^12 + 1806558568369727341123/146160698785720231801*e^11 + 1412756364886767462177/146160698785720231801*e^10 - 19070516087461667644440/146160698785720231801*e^9 - 31388168759545494349410/146160698785720231801*e^8 + 85333723084801757787951/146160698785720231801*e^7 + 178260096387264827437250/146160698785720231801*e^6 - 174875191144567936712956/146160698785720231801*e^5 - 412711494594856907931895/146160698785720231801*e^4 + 171667731998582343180996/146160698785720231801*e^3 + 394870747997580012412928/146160698785720231801*e^2 - 75618598286245846938748/146160698785720231801*e - 116585293426417240592696/146160698785720231801, -17467166551574799115/146160698785720231801*e^14 - 131796405198164441022/146160698785720231801*e^13 + 299359438418866170986/146160698785720231801*e^12 + 4230742861636751266833/146160698785720231801*e^11 + 2509581302376013166635/146160698785720231801*e^10 - 45256141268543508583786/146160698785720231801*e^9 - 65672600553321639285741/146160698785720231801*e^8 + 207346077475240455659963/146160698785720231801*e^7 + 381533267276141251520655/146160698785720231801*e^6 - 440158959125475082387335/146160698785720231801*e^5 - 888054554983521903182856/146160698785720231801*e^4 + 442238314647853401464674/146160698785720231801*e^3 + 848040924750698896004762/146160698785720231801*e^2 - 183887586841794834702988/146160698785720231801*e - 246971960933546335044766/146160698785720231801, 4357189549266904728/146160698785720231801*e^14 + 34774928602553461465/146160698785720231801*e^13 - 62864194369338424709/146160698785720231801*e^12 - 1096622405740788560043/146160698785720231801*e^11 - 989154972021791063458/146160698785720231801*e^10 + 11340047608747485040352/146160698785720231801*e^9 + 19920760264942597597076/146160698785720231801*e^8 - 48896131517602221285065/146160698785720231801*e^7 - 108229071487374283898135/146160698785720231801*e^6 + 94597787424639433912959/146160698785720231801*e^5 + 236569061256028664020985/146160698785720231801*e^4 - 88682148750874949872163/146160698785720231801*e^3 - 207471540097942637087717/146160698785720231801*e^2 + 41222799792388085585868/146160698785720231801*e + 53899410212293890484032/146160698785720231801, 5293589063307051063/146160698785720231801*e^14 + 43411617677969648471/146160698785720231801*e^13 - 69756213441304627991/146160698785720231801*e^12 - 1369731588597649883915/146160698785720231801*e^11 - 1451662117744393354493/146160698785720231801*e^10 + 14165591396193651769287/146160698785720231801*e^9 + 27650507844829344288974/146160698785720231801*e^8 - 60870075466023135607519/146160698785720231801*e^7 - 153804187833906493344989/146160698785720231801*e^6 + 115705071320347890919756/146160698785720231801*e^5 + 356695963130511962360530/146160698785720231801*e^4 - 103496507219143215696242/146160698785720231801*e^3 - 341339912759891015295354/146160698785720231801*e^2 + 48744307181168724984391/146160698785720231801*e + 94687776725324590289234/146160698785720231801, -1100521243542584116/146160698785720231801*e^14 - 6266974349814320004/146160698785720231801*e^13 + 34055506905603516926/146160698785720231801*e^12 + 228194668636461586998/146160698785720231801*e^11 - 327122001662229216302/146160698785720231801*e^10 - 2994386121817897385962/146160698785720231801*e^9 + 996560427573578295245/146160698785720231801*e^8 + 18311255420168554218816/146160698785720231801*e^7 + 1104529702024904647338/146160698785720231801*e^6 - 54372526546613803895001/146160698785720231801*e^5 - 10393638792551724735963/146160698785720231801*e^4 + 71136184321396916940773/146160698785720231801*e^3 + 16160676774822575138948/146160698785720231801*e^2 - 30553240033309046884266/146160698785720231801*e - 10102559781937034430148/146160698785720231801, -10420300650354640835/146160698785720231801*e^14 - 80312747199519115948/146160698785720231801*e^13 + 171079372168211932521/146160698785720231801*e^12 + 2580888652802580710127/146160698785720231801*e^11 + 1767479729325680518150/146160698785720231801*e^10 - 27663536588808688216877/146160698785720231801*e^9 - 42658879775172701710328/146160698785720231801*e^8 + 127190707523368521463833/146160698785720231801*e^7 + 248301697147990396483800/146160698785720231801*e^6 - 271654438755204913123337/146160698785720231801*e^5 - 588855941753373135001587/146160698785720231801*e^4 + 276433852404260864055765/146160698785720231801*e^3 + 578305631164652765440762/146160698785720231801*e^2 - 118098938124470565776796/146160698785720231801*e - 171055950777673790968288/146160698785720231801, 5150909555342135448/146160698785720231801*e^14 + 39395235337247126535/146160698785720231801*e^13 - 90186160386861407042/146160698785720231801*e^12 - 1286611031754962647309/146160698785720231801*e^11 - 710162537180092439618/146160698785720231801*e^10 + 14205930926785372376973/146160698785720231801*e^9 + 19644608157569218235594/146160698785720231801*e^8 - 68652244508816520360590/146160698785720231801*e^7 - 118158345683748176572371/146160698785720231801*e^6 + 157249718572220515561642/146160698785720231801*e^5 + 285659314775612164080916/146160698785720231801*e^4 - 170074754493834205184126/146160698785720231801*e^3 - 281698196937512736227379/146160698785720231801*e^2 + 72832622725997221545754/146160698785720231801*e + 82588180777739610819108/146160698785720231801, -2579960980603178413/146160698785720231801*e^14 - 20608547426308904255/146160698785720231801*e^13 + 37956384972444151673/146160698785720231801*e^12 + 658217101513907065111/146160698785720231801*e^11 + 585564168993250894986/146160698785720231801*e^10 - 6970739189678647793280/146160698785720231801*e^9 - 12268932258476478484895/146160698785720231801*e^8 + 31307796999171966737943/146160698785720231801*e^7 + 70109885061778380912433/146160698785720231801*e^6 - 63949249055639782657568/146160698785720231801*e^5 - 165098515392690230326957/146160698785720231801*e^4 + 61069577275726103969944/146160698785720231801*e^3 + 157650887396452474772314/146160698785720231801*e^2 - 28930258214000983368563/146160698785720231801*e - 40452720863312063952102/146160698785720231801, 7946237949617783580/146160698785720231801*e^14 + 59697766989653098871/146160698785720231801*e^13 - 132488676238842831468/146160698785720231801*e^12 - 1886240058905721188944/146160698785720231801*e^11 - 1211795281462516141249/146160698785720231801*e^10 + 19544812636193156924750/146160698785720231801*e^9 + 29628805014043399610868/146160698785720231801*e^8 - 84002888260095458481575/146160698785720231801*e^7 - 164063860624775867354475/146160698785720231801*e^6 + 157042411107116720977183/146160698785720231801*e^5 + 354811653037668443637007/146160698785720231801*e^4 - 125268308197214769779367/146160698785720231801*e^3 - 304932449937061845770376/146160698785720231801*e^2 + 36793525895785029328547/146160698785720231801*e + 80497736482901953773476/146160698785720231801, -11737361591307028745/146160698785720231801*e^14 - 91492427914757874786/146160698785720231801*e^13 + 185011959951201972494/146160698785720231801*e^12 + 2927653536369543087722/146160698785720231801*e^11 + 2242167148812937940026/146160698785720231801*e^10 - 31115518647142596245613/146160698785720231801*e^9 - 50807827685620870276133/146160698785720231801*e^8 + 140712747282117357362165/146160698785720231801*e^7 + 292518429151685730024437/146160698785720231801*e^6 - 291504977053668792952290/146160698785720231801*e^5 - 688428027440446376895174/146160698785720231801*e^4 + 284086862602759130216301/146160698785720231801*e^3 + 665875554510671391353962/146160698785720231801*e^2 - 120022024679014838550978/146160698785720231801*e - 192673595290980671773400/146160698785720231801, -12803186667489419647/146160698785720231801*e^14 - 102356795505564881674/146160698785720231801*e^13 + 183879291432289180363/146160698785720231801*e^12 + 3236515597330508796300/146160698785720231801*e^11 + 2979995660094987727321/146160698785720231801*e^10 - 33619456231742254514088/146160698785720231801*e^9 - 60297489296862382487716/146160698785720231801*e^8 + 145761443485455494370885/146160698785720231801*e^7 + 334620307752373126489512/146160698785720231801*e^6 - 281370261264863751851188/146160698785720231801*e^5 - 762138949379536462031335/146160698785720231801*e^4 + 251831453071769664724954/146160698785720231801*e^3 + 717456775467162432794474/146160698785720231801*e^2 - 104960163385359860951426/146160698785720231801*e - 204153474264725499688662/146160698785720231801, -6030463778843299758/146160698785720231801*e^14 - 46154793108155025207/146160698785720231801*e^13 + 96039814443261973773/146160698785720231801*e^12 + 1456572645574472551346/146160698785720231801*e^11 + 1070495919682253330253/146160698785720231801*e^10 - 15068946562662908517468/146160698785720231801*e^9 - 24225091739848314042073/146160698785720231801*e^8 + 64787790456056606679172/146160698785720231801*e^7 + 133468817766473767992426/146160698785720231801*e^6 - 122992537032057835289327/146160698785720231801*e^5 - 290649361735459375014110/146160698785720231801*e^4 + 106916332867894087637273/146160698785720231801*e^3 + 249701997680501529714396/146160698785720231801*e^2 - 40950253903721179231120/146160698785720231801*e - 60105171241087652557176/146160698785720231801, -14708039820347016620/146160698785720231801*e^14 - 114532491764367508717/146160698785720231801*e^13 + 234562338822975796395/146160698785720231801*e^12 + 3675378582886754949271/146160698785720231801*e^11 + 2732756069219317341847/146160698785720231801*e^10 - 39275939478129880692750/146160698785720231801*e^9 - 63050146807960369947704/146160698785720231801*e^8 + 179407251611940506033731/146160698785720231801*e^7 + 365304253206839810640257/146160698785720231801*e^6 - 378337241830795366910350/146160698785720231801*e^5 - 864805449024299032060211/146160698785720231801*e^4 + 380095004258214851804134/146160698785720231801*e^3 + 840781631367966331944281/146160698785720231801*e^2 - 169192252019204363857538/146160698785720231801*e - 240564140991038689565070/146160698785720231801, 6467264947016543465/146160698785720231801*e^14 + 51451080722451794267/146160698785720231801*e^13 - 96257844380811815312/146160698785720231801*e^12 - 1635192852773540070107/146160698785720231801*e^11 - 1396880938008493269654/146160698785720231801*e^10 + 17161298799535566417599/146160698785720231801*e^9 + 29297489441249330769906/146160698785720231801*e^8 - 75932200656668370848868/146160698785720231801*e^7 - 163738342491209644021438/146160698785720231801*e^6 + 151968902267559301133082/146160698785720231801*e^5 + 374183943969777035460305/146160698785720231801*e^4 - 140752877462540633461944/146160698785720231801*e^3 - 353328709578047278611833/146160698785720231801*e^2 + 53750021914398550089510/146160698785720231801*e + 101115235448007212266182/146160698785720231801, -6013926369481638655/146160698785720231801*e^14 - 47013334939630253011/146160698785720231801*e^13 + 95000731772749266220/146160698785720231801*e^12 + 1505871184066969467845/146160698785720231801*e^11 + 1133862088912330649751/146160698785720231801*e^10 - 16056687891743376701562/146160698785720231801*e^9 - 25728928848833091027389/146160698785720231801*e^8 + 73363853146555314010148/146160698785720231801*e^7 + 147720531320000436557606/146160698785720231801*e^6 - 156347205594783715742470/146160698785720231801*e^5 - 348040705424291438354731/146160698785720231801*e^4 + 160473033953594039043469/146160698785720231801*e^3 + 341404192879900200132456/146160698785720231801*e^2 - 68108761645584741294767/146160698785720231801*e - 101502513909392245316836/146160698785720231801, 7630540403289830618/146160698785720231801*e^14 + 59940821272911892124/146160698785720231801*e^13 - 122517918662275272025/146160698785720231801*e^12 - 1943740094582793766796/146160698785720231801*e^11 - 1423978817075204824314/146160698785720231801*e^10 + 21199976380706915278406/146160698785720231801*e^9 + 33429339654504938303239/146160698785720231801*e^8 - 100638624576776643606818/146160698785720231801*e^7 - 197924567121333966180227/146160698785720231801*e^6 + 226731405078737021373759/146160698785720231801*e^5 + 481630121963449961871221/146160698785720231801*e^4 - 247648319454591674010353/146160698785720231801*e^3 - 479150865394723604176168/146160698785720231801*e^2 + 114213865936026009502042/146160698785720231801*e + 138565506069123715201948/146160698785720231801, -3230596704634345581/146160698785720231801*e^14 - 25016410643190970869/146160698785720231801*e^13 + 48350416360751134181/146160698785720231801*e^12 + 779579846855935330955/146160698785720231801*e^11 + 664046117463001740562/146160698785720231801*e^10 - 7856936009551115017230/146160698785720231801*e^9 - 13771202169074671649396/146160698785720231801*e^8 + 31951654259773832493524/146160698785720231801*e^7 + 73815788119006054067769/146160698785720231801*e^6 - 53727512215133462050612/146160698785720231801*e^5 - 157095636465630096481778/146160698785720231801*e^4 + 37453059020670109510989/146160698785720231801*e^3 + 133415424001996853301430/146160698785720231801*e^2 - 13548812873240970359532/146160698785720231801*e - 31330555138216610489766/146160698785720231801, 7108086207073694326/146160698785720231801*e^14 + 56442605750082462263/146160698785720231801*e^13 - 107140004522878238841/146160698785720231801*e^12 - 1799399301475989842948/146160698785720231801*e^11 - 1498029206943027815479/146160698785720231801*e^10 + 19004910611477953672351/146160698785720231801*e^9 + 31910147680266329679369/146160698785720231801*e^8 - 85222192826295826980984/146160698785720231801*e^7 - 179319239126535356629717/146160698785720231801*e^6 + 175720366049883263072534/146160698785720231801*e^5 + 410674331065611398614427/146160698785720231801*e^4 - 173988251868679194310847/146160698785720231801*e^3 - 383421682045050848629488/146160698785720231801*e^2 + 74760084931143593891773/146160698785720231801*e + 104756223147999250911588/146160698785720231801, 4464485200263641721/146160698785720231801*e^14 + 36116204854875398837/146160698785720231801*e^13 - 59557120980587582497/146160698785720231801*e^12 - 1133795595571569783914/146160698785720231801*e^11 - 1196586227989305639534/146160698785720231801*e^10 + 11606494897114031584995/146160698785720231801*e^9 + 22953373178169272749641/146160698785720231801*e^8 - 48871521714307908709232/146160698785720231801*e^7 - 127762524260656758584191/146160698785720231801*e^6 + 89410297599002906850868/146160698785720231801*e^5 + 297893383032759071799762/146160698785720231801*e^4 - 75185473744842227607427/146160698785720231801*e^3 - 292942573586300334277458/146160698785720231801*e^2 + 31210317013873423379287/146160698785720231801*e + 86689304071214611537816/146160698785720231801, 2086310364745283781/146160698785720231801*e^14 + 15810784693368869711/146160698785720231801*e^13 - 33953838398685188006/146160698785720231801*e^12 - 501116445282053043464/146160698785720231801*e^11 - 351700073720541267507/146160698785720231801*e^10 + 5240728703888483772534/146160698785720231801*e^9 + 8290513649078066028826/146160698785720231801*e^8 - 23208567436952488982748/146160698785720231801*e^7 - 46811816441482097206221/146160698785720231801*e^6 + 47819349078917605905174/146160698785720231801*e^5 + 105850224259030820456516/146160698785720231801*e^4 - 49649402687234941549519/146160698785720231801*e^3 - 95311227731568130833674/146160698785720231801*e^2 + 23222876942424524920197/146160698785720231801*e + 21337241920383712680180/146160698785720231801, -3631747657767768820/146160698785720231801*e^14 - 26157843438904334040/146160698785720231801*e^13 + 72863400170328162303/146160698785720231801*e^12 + 860759723631757711626/146160698785720231801*e^11 + 178651115154789538879/146160698785720231801*e^10 - 9648549611413410047344/146160698785720231801*e^9 - 9938006726542624431207/146160698785720231801*e^8 + 48017623742208565194558/146160698785720231801*e^7 + 61939893950184464639954/146160698785720231801*e^6 - 115833842403721536317855/146160698785720231801*e^5 - 146899260575390560645266/146160698785720231801*e^4 + 134010747884779941554618/146160698785720231801*e^3 + 139494198881170956425252/146160698785720231801*e^2 - 58712006706405833153283/146160698785720231801*e - 40627490212882275632714/146160698785720231801, 3520030578399562448/146160698785720231801*e^14 + 29063984758492670959/146160698785720231801*e^13 - 43227089771890583003/146160698785720231801*e^12 - 907233886995734757820/146160698785720231801*e^11 - 1063687857607949560048/146160698785720231801*e^10 + 9169210798670972801572/146160698785720231801*e^9 + 19371932215303512839224/146160698785720231801*e^8 - 37421314490528341890025/146160698785720231801*e^7 - 106141532806868375889246/146160698785720231801*e^6 + 62937249500035630606634/146160698785720231801*e^5 + 242715878243264564091399/146160698785720231801*e^4 - 42982861366434412943718/146160698785720231801*e^3 - 228709366555017915444358/146160698785720231801*e^2 + 16149886013808331641723/146160698785720231801*e + 61923957319159152657662/146160698785720231801, -8054259958557639259/146160698785720231801*e^14 - 63282265590837413649/146160698785720231801*e^13 + 124676186125210199788/146160698785720231801*e^12 + 2030601047682256805486/146160698785720231801*e^11 + 1636056104698502265209/146160698785720231801*e^10 - 21703602308546799585557/146160698785720231801*e^9 - 36404414506314507738120/146160698785720231801*e^8 + 99296185909930643005254/146160698785720231801*e^7 + 211876369589759702400847/146160698785720231801*e^6 - 210766245679803249592991/146160698785720231801*e^5 - 509374714731439331714583/146160698785720231801*e^4 + 215184327641530034114997/146160698785720231801*e^3 + 505286208783698429614734/146160698785720231801*e^2 - 97556680331607653998246/146160698785720231801*e - 146751067300592129378892/146160698785720231801, 5181991935338192107/146160698785720231801*e^14 + 42951098745543016978/146160698785720231801*e^13 - 64203621371979606346/146160698785720231801*e^12 - 1348608247524025551085/146160698785720231801*e^11 - 1556738735435381694000/146160698785720231801*e^10 + 13816202668546272115598/146160698785720231801*e^9 + 28639204673750819497794/146160698785720231801*e^8 - 58364069791307290433845/146160698785720231801*e^7 - 159135724014459866426860/146160698785720231801*e^6 + 108254529353021507431801/146160698785720231801*e^5 + 374364636688111171619724/146160698785720231801*e^4 - 96582479828287557732398/146160698785720231801*e^3 - 371526367824076414961536/146160698785720231801*e^2 + 48012292131347218509957/146160698785720231801*e + 107428440414508007249636/146160698785720231801, -1734503597695467771/146160698785720231801*e^14 - 11719168384573158847/146160698785720231801*e^13 + 37957872670288009262/146160698785720231801*e^12 + 383080938594590164299/146160698785720231801*e^11 - 29803136080445522627/146160698785720231801*e^10 - 4231709566882776078217/146160698785720231801*e^9 - 3228413460960775776138/146160698785720231801*e^8 + 20380318102915116728417/146160698785720231801*e^7 + 20193584161195494862501/146160698785720231801*e^6 - 45754624727238948243818/146160698785720231801*e^5 - 42066236578743311832849/146160698785720231801*e^4 + 46067877500312488415518/146160698785720231801*e^3 + 31615778195004278532642/146160698785720231801*e^2 - 16377707766165817060209/146160698785720231801*e - 10174613162165190409792/146160698785720231801, 10531467623591147693/146160698785720231801*e^14 + 86515336218834176625/146160698785720231801*e^13 - 137692827081836422161/146160698785720231801*e^12 - 2728107023421800623675/146160698785720231801*e^11 - 2919704842537394884367/146160698785720231801*e^10 + 28185238016517369069771/146160698785720231801*e^9 + 55283566619310566226071/146160698785720231801*e^8 - 120966370174740328636348/146160698785720231801*e^7 - 306768469748327105728785/146160698785720231801*e^6 + 230092418554272511570049/146160698785720231801*e^5 + 711097247529993543009038/146160698785720231801*e^4 - 207642466876833901913633/146160698785720231801*e^3 - 687922265115871380892774/146160698785720231801*e^2 + 96384569812988049391195/146160698785720231801*e + 200045243159788319480844/146160698785720231801]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1])] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]