(* -*- text -*- Ramanujan型級数一覧 松元隆二 (matumoto@pluto.ai.kyutech.ac.jp) 1999/05/19 インドの天才数学者Srinivasa Ramanujan (1887-1920)の6番目の論文「Modular Equations and Approximations to π」[1]から始まる，楕円積分に由来する 円周率の無限級数がいくつも知られています[2]． 代表的な公式を一つ挙げるとすると，1996年の円周率80億桁の記録更新に使わ れた，次のChudnovsky兄弟の式があります． 1 ∞ (-1)^n (6n)! 13591409+545140134n ---- = Σ ---------------・---------------------. Type F-2, N=163 12π n=0 (3n)!(n!)^3 (640320^3)^(n+1/2) この公式は，知られているRamanujan型級数としては最良です．この公式は1項 を計算するごとに約14桁の精度で円周率の値を与えます． 近年の円周率の記録更新では，E.SalaminとR.P.Breantの公式などの反復公式 が主に用いられます．しかし，Chudnovsky兄弟の式を (拡張された) Binary splittingアルゴリズム[3,4]を用いて計算すると，1億桁程度の桁数までは E.SalaminとR.P.Breantの公式より高速に計算出来るそうです[4]． このファイルでは，既知のRamanujan型級数に加えて，私が計算機を使い探索 したRamanujan型級数を，数式処理ソフトMathematica 3.0の書式で掲載してい ます． 探索アルゴリズムについては参考文献[5]をごらんください． 具体的なRamanujan型級数の形式およびType A〜G6については私の書いた「円 周率の公式集」の「Ramanujan型級数」の章をごらんください．探索アルゴリ ズムについても記述しています． http://www.pluto.ai.kyutech.ac.jp/plt/matumoto/syumi.html 参考文献： [1] Srinivasa Ramanujan, 「Modular Equations and Approximations to π」, 1914. 今世紀はじめの頃の論文なので探すのが大変ですが，次の書籍に再掲載されて います。 Lennart Berggren, Jonathan Borwein, Peter Borwein,「PI: A Source Book」, Springer, 1996, ISBN 0-387-94924-0. [2] Jonathan M.Borwein and Peter B.Borwein, 「Pi and AGM - A Study in Analytic Number Theory and Computational Complexity」, Wiley, New York, 1987, ISBN 0-471-83138-7. [3] Bruno Haible, Thomas Papanikolaou, 「Fast multiprecision evaluation of series of rational numbers」, Technical Report No. TI-7/97, Darmstadt University of Technology, 1997. (http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/papanik/) [4] 右田剛史・天野晃・浅田尚紀・藤野清次, 「級数の集約による多倍長数の 計算法とπ計算への応用」,情報処理学会研究報告 98-HPC-74, pp.31-36 (1998). [5] Jorg Arndt, 「remarks on arithmetical algorithms and the computation of π」, 1997, (http://www.jjj.de/hfloat/) 更新歴： 1999/5/24: 参考文献[1]の年号のミス 1994 -> 1914. *) (***********************************************************************) (***********************************************************************) (* 本ファイルは数式処理ソフトであるMathematica 3.0で読み込み可能な形式に なっています． Sun SPARC Station 版 Mathematica Ver.3.0をUNIX Shell インターフェース で動作させて確認しています． *) (* 作業用関数 *) poch[a_,n_] := Pochhammer[a,n]; ncr[n_,m_] := Binomial[n,m]; r[n_, 0] := (ncr[2n,n]/2^(2n))^3; r[n_, 1/6] := ((2n)! * (3n)!) / ((2^(2n) * 3^(3n) * (n!)^5)); r[n_, 1/4] := ((4n)! / (4^n * n!)^4); r[n_, 1/3] := ((6n)!)/((3n)! (12^n * n!)^3); r[n_, s_] := (poch[1/2,n] * poch[1/2+s,n] * poch[1/2-s,n]) / ((n!)^3); termp[n_, s_, x_, y_, z2_] := If[x > 0 && y > 0 && (z2 > 0 || z2 < 0), r[n, s] * (x + n * y) * z2^n, 0 ]; termm[n_, s_, x_, y_, z2_] := If[x > 0 && y > 0 && z2 > 0, (-1)^n * r[n, s] * (x + n * y) * z2^n, 0]; (***********************************************************************) (***********************************************************************) (* Ramanujan 型級数 Type A (sumA[t]) 〜 Type G-6 (sumG6[t]) 全ての級数の値は1/πです．但し一部の級数はMathematica 3.0が計算ミスを するため1/πにならない級数があります． 読み方： sumA, sumB,… sumG6はそれぞれ, Type A, Type B,… Type G-6 に対応します。 以下，Type Aについて説明します． AX[N] : Type A の係数 X_N AY[N] : Type A の係数 Y_N AZ2[N] : Type A の係数Z_Nの自乗． (Z_N)^2． pAX[N] : AX[N] を求めるのに使用した最小多項式． pAY[N] : AY[N] 〃 pAZ2[N] : AZ2[N] 〃 1 / π = sumA[N] Nが2 〜163の範囲で掲載されていて，それぞれのNが上記の式を満たし ます． 各AX[N]，BX[N]，Z2X[N]は見つける事が出来たNに対してのみこのファ イルに掲載されています．公式として成り立つためには，特定のNに対 してAX[N]，BX[N]，Z2X[N]がすべて掲載されている必要があります． すべてが存在しないNはsumA[N]が値として0を返します． Type B〜G-6も同様です． *) (* Type A, N=2〜163 *) sumA[t_, limit_:Infinity] := Sum[termp[n, 0, AX[t], AY[t], AZ2[t]], {n, 0, limit}]; AX[2]:= 3 - 2*Sqrt[2] AX[3]:= 1/4 AX[4]:= 4*(-7 + 5*Sqrt[2]) AX[5]:= Sqrt[(-11 + 5*Sqrt[5])/2] AX[6]:= 73 + 52*Sqrt[2] - 6*Sqrt[3*(99 + 70*Sqrt[2])] AX[7]:= 5/16 AX[8]:= 4*(-71 - 50*Sqrt[2] + 2*Sqrt[2513 + 1777*Sqrt[2]]) AX[9]:= 3/Sqrt[45 + 26*Sqrt[3]] AX[10]:= 917 - 290*Sqrt[10] + 2*Sqrt[420077 - 132840*Sqrt[10]] AX[11]:= -3/4 + (63 + 11*Sqrt[33])^(1/3)/(2*3^(2/3)) - (3*(63 + 11*Sqrt[33]))^(-1/3) AX[12]:= 4*(-654 + 463*Sqrt[2] - 3*Sqrt[6*(15859 - 11214*Sqrt[2])]) AX[13]:= 17*Sqrt[2/(2859 + 793*Sqrt[13])] AX[15]:= (-1 + 5*Sqrt[5])/32 AX[16]:= 16*(-1031 - 729*Sqrt[2] + Sqrt[2125884 + 1503227*Sqrt[2]]) AX[18]:= 3*(12561 - 8882*Sqrt[2] + 4*Sqrt[3*(6574017 - 4648532*Sqrt[2])]) AX[19]:= 35/12 - 73/(3*(-5309 + 741*Sqrt[57])^(1/3)) + (-5309 + 741*Sqrt[57])^(1/3)/6 AX[22]:= 171397 - 36542*Sqrt[22] + 2*Sqrt[14688428339 - 3131583444*Sqrt[22]] AX[23]:= -5/8 + (262504710144 - 24888999936*Sqrt[69])^(1/3)/12288 + ((10431 + 989*Sqrt[69])/2)^(1/3)/(16*3^(2/3)) AX[25]:= 10*Sqrt[10/(4935 + 2207*Sqrt[5])] AX[27]:= -27/4 + 15/2^(2/3) - 3/2^(1/3) AX[28]:= 16*(-80526 - 30436*Sqrt[7] + Sqrt[12968890552 + 4901779883*Sqrt[7]]) AX[31]:= 29/48 + (5*((-457 + 93*Sqrt[93])/2)^(1/3))/48 - 265/(24*2^(2/3)*(-457 + 93*Sqrt[93])^(1/3)) AX[37]:= 1529*Sqrt[2/(23073603 + 3793277*Sqrt[37])] AX[39]:= 19/16 - (13*Sqrt[13])/32 + Sqrt[-293/256 + (91*Sqrt[13])/128]/2 AX[43]:= -107/4 + (219825 + 20081*Sqrt[129])^(1/3)/3^(2/3) - 1072/(3*(219825 + 20081*Sqrt[129]))^(1/3) AX[55]:= -149/64 + (85*Sqrt[5])/64 - Sqrt[-4381/512 + (2055*Sqrt[5])/512]/2 AX[58]:= 2803965609 - 368178722*Sqrt[58] + 6*Sqrt[436790174173009733 - 57353359678834824*Sqrt[58]] AX[63]:= 93/64 - (21*Sqrt[21])/64 + Sqrt[-48897/512 + (10731*Sqrt[21])/512]/2 AX[67]:= 505/4 + (-180277569 + 13219033*Sqrt[201])^(1/3)/(2*3^(2/3)) - 47813/(3*(-180277569 + 13219033*Sqrt[201]))^(1/3) AX[163]:= 91987/12 - 264425240/(3*(-15201166943987 + 714392324511*Sqrt[489])^(1/3)) + (-15201166943987 + 714392324511*Sqrt[489])^(1/3)/3 AY[2]:= 8 - 5*Sqrt[2] AY[3]:= 3/2 AY[4]:= 6*(-11 + 8*Sqrt[2]) AY[5]:= 2*Sqrt[5*(-2 + Sqrt[5])] AY[6]:= 3*(56 + 40*Sqrt[2] - Sqrt[6*(1041 + 736*Sqrt[2])]) AY[7]:= 21/8 AY[8]:= 2*(-320 - 225*Sqrt[2] + 16*Sqrt[799 + 565*Sqrt[2]]) AY[9]:= 6*Sqrt[2*(-12 + 7*Sqrt[3])] AY[10]:= 3*(680 - 215*Sqrt[10] + 16*Sqrt[5*(721 - 228*Sqrt[10])]) AY[11]:= -11/6 + (681472 - 118272*Sqrt[33])^(1/3)/24 + (11*(121 + 21*Sqrt[33]))^(1/3)/3 AY[12]:= 6*(-960 + 680*Sqrt[2] - Sqrt[3*(615353 - 435120*Sqrt[2])]) AY[13]:= 6*Sqrt[13/(18 + 5*Sqrt[13])] AY[15]:= (3*(5 + 7*Sqrt[5]))/16 AY[16]:= 12*(-2987 - 2112*Sqrt[2] + 16*Sqrt[69708 + 49291*Sqrt[2]]) AY[18]:= 3*(27160 - 19205*Sqrt[2] + 112*Sqrt[6*(19601 - 13860*Sqrt[2])]) AY[19]:= 19/2 - (2*19^(2/3))/(-19 + 3*Sqrt[57])^(1/3) + (19*(-19 + 3*Sqrt[57]))^(1/3) AY[22]:= 3*(122584 + 86680*Sqrt[2] - 5*Sqrt[22*(54642361 + 38637984*Sqrt[2])]) AY[23]:= -23/12 + (147341312000 - 7913472000*Sqrt[69])^(1/3)/1536 + (5*((23*(391 + 21*Sqrt[69]))/2)^(1/3))/24 AY[25]:= 60*Sqrt[5/(360 + 161*Sqrt[5])] AY[27]:= -33/2 + 21*2^(1/3) - 3*2^(2/3) AY[28]:= 6*(-456960 + 122128*Sqrt[14] - 5*Sqrt[7*(2386436385 - 637801952*Sqrt[14])]) AY[31]:= 31/8 - (11*31^(2/3))/(4*2^(2/3)*(527 + 69*Sqrt[93])^(1/3)) + ((31*(527 + 69*Sqrt[93]))/2)^(1/3)/8 AY[37]:= 42*Sqrt[37/(882 + 145*Sqrt[37])] AY[39]:= 39/8 - (21*Sqrt[13])/16 + Sqrt[3627/64 + (819*Sqrt[13])/32]/2 AY[43]:= -129/2 - (8*129^(2/3))/(387 + 35*Sqrt[129])^(1/3) + 2*(129*(387 + 35*Sqrt[129]))^(1/3) AY[55]:= -165/32 + (165*Sqrt[5])/32 + Sqrt[-9405/128 + (4455*Sqrt[5])/128]/2 AY[58]:= 3*(1950848328 - 256158935*Sqrt[58] + 18480*Sqrt[29*(768555217 - 100916244*Sqrt[58])]) AY[63]:= 189/32 - (21*Sqrt[21])/32 + Sqrt[-94689/128 + (23499*Sqrt[21])/128]/2 AY[67]:= 603/2 - (226*201^(2/3))/(-162207 + 11935*Sqrt[201])^(1/3) + (201*(-162207 + 11935*Sqrt[201]))^(1/3) AY[163]:= 34067/2 - (89000*163^(2/3))/(-37848437 + 1778889*Sqrt[489])^(1/3) + 10*(163*(-37848437 + 1778889*Sqrt[489]))^(1/3) AZ2[2]:= 8*(-7 + 5*Sqrt[2]) AZ2[3]:= 1/4 AZ2[4]:= 32/(140 + 99*Sqrt[2]) AZ2[5]:= (9 + 4*Sqrt[5])^(-1) AZ2[6]:= 8*(-2359 + 1362*Sqrt[3] - 3*Sqrt[2*(618259 - 356952*Sqrt[3])]) AZ2[7]:= 1/64 AZ2[8]:= 16*(-12756 - 9020*Sqrt[2] + 5*Sqrt[2*(6508727 + 4602365*Sqrt[2])]) AZ2[9]:= (97 + 56*Sqrt[3])^(-1) AZ2[10]:= 8*(-207847 + 65727*Sqrt[10] - 18*Sqrt[10*(26666893 - 8432812*Sqrt[10])]) AZ2[11]:= 1/4 + (-9 + 7*Sqrt[33])^(1/3)/3^(2/3) - 8/(3*(-9 + 7*Sqrt[33]))^(1/3) AZ2[12]:= 16*(-692336 + 282645*Sqrt[6] - 15*Sqrt[6*(710115875 - 289903592*Sqrt[6])]) AZ2[13]:= (649 + 180*Sqrt[13])^(-1) AZ2[15]:= 1/(32*(47 + 21*Sqrt[5])) AZ2[16]:= 32*(-10037392 - 7097508*Sqrt[2] + 9*Sqrt[2487635528172 + 1759023951091*Sqrt[2]]) AZ2[17]:= 1649 + 400*Sqrt[17] - 20*Sqrt[2*(6799 + 1649*Sqrt[17])] AZ2[18]:= 8*(-184411207 + 130398415*Sqrt[2] - 140*Sqrt[3*(1156717458033 - 817922758492*Sqrt[2])]) AZ2[19]:= 1/4 - 24/(-1 + 3*Sqrt[57])^(1/3) + 3*(-1 + 3*Sqrt[57])^(1/3) AZ2[21]:= 6985 - 2640*Sqrt[7] - 12*Sqrt[21*(32257 - 12192*Sqrt[7])] AZ2[22]:= 8*(-3073652407 + 926741070*Sqrt[11] - 315*Sqrt[22*(8655570781785 - 2609752784504*Sqrt[11])]) AZ2[23]:= -11/96 + (5*((1181 + 231*Sqrt[69])/2)^(1/3))/192 - 415/(96*2^(2/3)*(1181 + 231*Sqrt[69])^(1/3)) AZ2[25]:= (51841 + 23184*Sqrt[5])^(-1) AZ2[27]:= 1/4 + 25*2^(1/3) - 20*2^(2/3) AZ2[28]:= 32*(-33559243648 + 23729968755*Sqrt[2] - 45*Sqrt[14*(79451346329781561 - 56180585764189456*Sqrt[2])]) AZ2[31]:= 55/64 - (21*3^(2/3))/(32*2^(2/3)*(-2439 + 253*Sqrt[93])^(1/3)) + (3*((3*(-2439 + 253*Sqrt[93]))/2)^(1/3))/64 AZ2[33]:= 268849 - 155220*Sqrt[3] - 60*Sqrt[11*(3650401 - 2107560*Sqrt[3])] AZ2[37]:= (1555849 + 255780*Sqrt[37])^(-1) AZ2[39]:= -35/64 + (21*Sqrt[13])/128 - Sqrt[-17685/4096 + (2457*Sqrt[13])/2048]/2 AZ2[43]:= 1/4 - 2400/(-1 + 63*Sqrt[129])^(1/3) + 30*(-1 + 63*Sqrt[129])^(1/3) AZ2[45]:= 5549769 - 2481932*Sqrt[5] - 496*Sqrt[15*(16692641 - 7465176*Sqrt[5])] AZ2[49]:= 13880161 + 5246208*Sqrt[7] - 72*Sqrt[74328271227 + 28093445864*Sqrt[7]] AZ2[55]:= -401/256 + (207*Sqrt[5])/256 - Sqrt[-227205/8192 + (102465*Sqrt[5])/8192]/2 AZ2[57]:= 78086449 - 17914260*Sqrt[19] - 780*Sqrt[3*(6681448801 - 1532829480*Sqrt[19])] AZ2[58]:= 8*(-295278299719384807 + 38771940237036435*Sqrt[58] - 20790*Sqrt[2*(201722380323473045099321281 - 26487446188247531945252652*Sqrt[58])]) AZ2[63]:= 829/256 - (155*Sqrt[21])/256 - Sqrt[-515025/8192 + (113925*Sqrt[21])/8192]/2 AZ2[67]:= 1/4 - 72600/(-1 + 651*Sqrt[201])^(1/3) + 165*(-1 + 651*Sqrt[201])^(1/3) AZ2[73]:= 1774176049 + 207651600*Sqrt[73] - 180*Sqrt[2*(97151254669323 + 11370694298041*Sqrt[73])] AZ2[85]:= 14814550729 - 1606863636*Sqrt[85] - 23184*Sqrt[5*(163327842721 - 17715391848*Sqrt[85])] AZ2[93]:= 56147328649 - 10084357920*Sqrt[31] - 1260*Sqrt[93*(42703566796801 - 7669787012160*Sqrt[31])] AZ2[97]:= 106981512049 + 10862326800*Sqrt[97] - 180*Sqrt[2*(353242096308027183 + 35866300785011593*Sqrt[97])] AZ2[133]:= 21208782485449 - 8016166295280*Sqrt[7] - 224460*Sqrt[133*(134255446617601 - 50743789129440*Sqrt[7])] AZ2[163]:= 1/4 - 1067733600/(-1 + 557403*Sqrt[489])^(1/3) + 20010*(-1 + 557403*Sqrt[489])^(1/3) AZ2[177]:= 5541238229049649 - 3199235383185660*Sqrt[3] - 73140*Sqrt[59*(194572614913330773601 - 112336551597140914680*Sqrt[3])] AZ2[193]:= 35178888293102449 + 2532231788720400*Sqrt[193] - 16380*Sqrt[2*(4612500508894302559152327 + 332015051663848798695809*Sqrt[193])] AZ2[253]:= 19655969242251327049 - 4098552909271919280*Sqrt[23] - 202604220*Sqrt[253*(74404881332329766401 - 15514490233996921440*Sqrt[23])] pAX[2] := x^2 - 6*x + 1 pAX[3] := 4*x - 1 pAX[4] := x^2 + 56*x - 16 pAX[5] := x^4 + 11*x^2 - 1 pAX[6] := x^4 - 292*x^3 - 226*x^2 + 172*x - 23 pAX[7] := 16*x - 5 pAX[8] := x^4 + 1136*x^3 + 2272*x^2 + 4864*x - 1792 pAX[9] := x^4 + 270*x^2 - 27 pAX[10] := x^4 - 3668*x^3 + 2718*x^2 + 892*x - 439 pAX[11] := 64*x^3 + 144*x^2 + 140*x - 61 pAX[12] := x^4 + 10464*x^3 - 63232*x^2 + 6144*x + 4096 pAX[13] := x^4 + 2859*x^2 - 289 pAX[15] := 256*x^2 + 16*x - 31 pAX[16] := x^4 + 65984*x^3 + 59904*x^2 + 180224*x - 65536 pAX[18] := x^4 - 150732*x^3 + 62982*x^2 + 56052*x - 19359 pAX[19] := 64*x^3 - 560*x^2 + 2412*x - 713 pAX[22] := x^4 - 685588*x^3 + 181326*x^2 + 289244*x - 88327 pAX[23] := 4096*x^3 + 7680*x^2 + 2384*x - 1669 pAX[25] := x^4 + 493500*x^2 - 50000 pAX[27] := 64*x^3 + 1296*x^2 + 13068*x - 4293 pAX[28] := x^4 + 5153664*x^3 - 15972352*x^2 + 10944512*x - 2031616 pAX[31] := 4096*x^3 - 7424*x^2 + 11552*x - 3057 pAX[37] := x^4 + 23073603*x^2 - 2337841 pAX[39] := 65536*x^4 - 311296*x^3 + 310784*x^2 + 385904*x - 144959 pAX[43] := 64*x^3 + 5136*x^2 + 205996*x - 66093 pAX[55] := 65536*x^4 + 610304*x^3 + 1255680*x^2 - 2515888*x + 653249 pAX[58] := x^4 - 11215862436*x^3 + 3579563566*x^2 + 4542610188*x - 1446914567 pAX[63] := 65536*x^4 - 380928*x^3 + 3663360*x^2 + 426816*x - 495423 pAX[67] := 64*x^3 - 24240*x^2 + 4590316*x - 1458689 pAX[163] := 64*x^3 - 1471792*x^2 + 16923216012*x - 5386677841 pAY[2] := x^2 - 16*x + 14 pAY[3] := 2*x - 3 pAY[4] := x^2 + 132*x - 252 pAY[5] := x^4 + 80*x^2 - 400 pAY[6] := x^4 - 672*x^3 - 684*x^2 + 8640*x - 7452 pAY[7] := 8*x - 21 pAY[8] := x^4 + 2560*x^3 + 11248*x^2 + 61440*x - 319424 pAY[9] := x^4 + 1728*x^2 - 15552 pAY[10] := x^4 - 8160*x^3 + 37260*x^2 + 43200*x - 251100 pAY[11] := 8*x^3 + 44*x^2 + 22*x - 847 pAY[12] := x^4 + 23040*x^3 - 436248*x^2 + 829440*x + 1400976 pAY[13] := x^4 + 16848*x^2 - 219024 pAY[15] := 64*x^2 - 120*x - 495 pAY[16] := x^4 + 143376*x^3 + 49248*x^2 + 1900800*x - 17563392 pAY[18] := x^4 - 325920*x^3 + 1495548*x^2 + 5382720*x - 24867324 pAY[19] := 8*x^3 - 228*x^2 + 3078*x - 9747 pAY[22] := x^4 - 1471008*x^3 + 6620724*x^2 + 33663168*x - 151758684 pAY[23] := 512*x^3 + 2944*x^2 - 11224*x - 70357 pAY[25] := x^4 + 2592000*x^2 - 64800000 pAY[27] := 8*x^3 + 396*x^2 + 9558*x - 61479 pAY[28] := x^4 + 10967040*x^3 - 181436472*x^2 + 921231360*x - 1419377904 pAY[31] := 512*x^3 - 5952*x^2 + 31248*x - 77841 pAY[37] := x^4 + 115132752*x^2 - 4259911824 pAY[39] := 4096*x^4 - 79872*x^3 + 284544*x^2 + 2810808*x - 15427503 pAY[43] := 8*x^3 + 1548*x^2 + 149382*x - 1048383 pAY[55] := 4096*x^4 + 84480*x^3 - 285120*x^2 - 11107800*x + 51210225 pAY[58] := x^4 - 23410179936*x^3 + 178359381036*x^2 + 1357236264384*x - 10340623655964 pAY[63] := 4096*x^4 - 96768*x^3 + 2298240*x^2 - 10033632*x - 33018111 pAY[67] := 8*x^3 - 7236*x^2 + 3271878*x - 26301051 pAY[163] := 8*x^3 - 408804*x^2 + 10445042934*x - 133286762763 pAZ2[2] := x^2 + 112*x - 64 pAZ2[3] := 4*x - 1 pAZ2[4] := x^2 + 4480*x - 512 pAZ2[5] := x^2 - 18*x + 1 pAZ2[6] := x^4 + 75488*x^3 + 108672*x^2 - 145408*x + 4096 pAZ2[7] := 64*x - 1 pAZ2[8] := x^4 + 816384*x^3 - 5397504*x^2 + 29753344*x - 262144 pAZ2[9] := x^2 - 194*x + 1 pAZ2[10] := x^4 + 6651104*x^3 + 974976*x^2 - 1325056*x + 4096 pAZ2[11] := 64*x^3 - 48*x^2 + 524*x - 1 pAZ2[12] := x^4 + 44309504*x^3 + 923283456*x^2 - 873988096*x + 1048576 pAZ2[13] := x^2 - 1298*x + 1 pAZ2[15] := 4096*x^2 - 3008*x + 1 pAZ2[16] := x^4 + 1284786176*x^3 - 5974155264*x^2 + 9398386688*x - 2097152 pAZ2[17] := x^4 - 6596*x^3 - 3194*x^2 - 6596*x + 1 pAZ2[18] := x^4 + 5901158624*x^3 + 28889216*x^2 - 39335936*x + 4096 pAZ2[19] := 64*x^3 - 48*x^2 + 13836*x - 1 pAZ2[21] := x^4 - 27940*x^3 + 76614*x^2 - 27940*x + 1 pAZ2[22] := x^4 + 98356877024*x^3 + 117926016*x^2 - 160577536*x + 4096 pAZ2[23] := 262144*x^3 + 90112*x^2 + 54592*x - 1 pAZ2[25] := x^2 - 103682*x + 1 pAZ2[27] := 64*x^3 - 48*x^2 + 192012*x - 1 pAZ2[28] := x^4 + 4295583186944*x^3 + 3328592510976*x^2 - 4346532069376*x + 16777216 pAZ2[31] := 262144*x^3 - 675840*x^2 + 617088*x - 1 pAZ2[33] := x^4 - 1075396*x^3 + 7459206*x^2 - 1075396*x + 1 pAZ2[37] := x^2 - 3111698*x + 1 pAZ2[39] := 16777216*x^4 + 36700160*x^3 + 54583296*x^2 - 5180224*x + 1 pAZ2[43] := 64*x^3 - 48*x^2 + 13824012*x - 1 pAZ2[45] := x^4 - 22199076*x^3 + 48146246*x^2 - 22199076*x + 1 pAZ2[49] := x^4 - 55520644*x^3 - 77075706*x^2 - 55520644*x + 1 pAZ2[55] := 16777216*x^4 + 105119744*x^3 + 369954816*x^2 - 205260736*x + 1 pAZ2[57] := x^4 - 312345796*x^3 + 13370198406*x^2 - 312345796*x + 1 pAZ2[58] := x^4 + 9448905591020313824*x^3 + 1155789119616*x^2 - 1573840500736*x + 4096 pAZ2[63] := 16777216*x^4 - 217317376*x^3 + 1324670976*x^2 - 1054925056*x + 1 pAZ2[67] := 64*x^3 - 48*x^2 + 2299968012*x - 1 pAZ2[73] := x^4 - 7096704196*x^3 + 12473481606*x^2 - 7096704196*x + 1 pAZ2[85] := x^4 - 59258202916*x^3 + 337405642566*x^2 - 59258202916*x + 1 pAZ2[93] := x^4 - 224589314596*x^3 + 85407724180806*x^2 - 224589314596*x + 1 pAZ2[97] := x^4 - 427926048196*x^3 - 717988406394*x^2 - 427926048196*x + 1 pAZ2[133] := x^4 - 84835129941796*x^3 + 295314272366406*x^2 - 84835129941796*x + 1 pAZ2[163] := 64*x^3 - 48*x^2 + 4102147072512012*x - 1 pAZ2[177] := x^4 - 22164952916198596*x^3 + 389145231089134012806*x^2 - 22164952916198596*x + 1 pAZ2[193] := x^4 - 140715553172409796*x^3 + 209205120043670406*x^2 - 140715553172409796*x + 1 pAZ2[253] := x^4 - 78623876969005308196*x^3 + 190350814266009633606*x^2 - 78623876969005308196*x + 1 (* Type B, N=2〜232 *) sumB[t_, limit_:Infinity] := Sum[termm[n, 0, BX[t], BY[t], BZ2[t]], {n, 0, limit}]; BX[2]:= 1/2 BX[3]:= 2*(-5 + 3*Sqrt[3]) BX[4]:= 1/(2*Sqrt[2]) BX[5]:= 34 + 15*Sqrt[5] - Sqrt[2*(1129 + 505*Sqrt[5])] BX[6]:= (-5 + 4*Sqrt[2])/2 BX[7]:= 24/(37 + 14*Sqrt[7]) BX[8]:= Sqrt[-1 + Sqrt[2]]/2 BX[9]:= 519 + 300*Sqrt[3] - 2*Sqrt[3*(44919 + 25934*Sqrt[3])] BX[10]:= (23 - 10*Sqrt[5])/2 BX[12]:= Sqrt[38 - 21*Sqrt[3]]/4 BX[13]:= 4266 + 1183*Sqrt[13] - Sqrt[2*(18194697 + 5046301*Sqrt[13])] BX[14]:= -35/2 - 12*Sqrt[2] + Sqrt[605 + 428*Sqrt[2]] BX[15]:= 4*(-2671 + 690*Sqrt[15] - Sqrt[14273417 - 3685380*Sqrt[15]]) BX[16]:= Sqrt[(-60 + 43*Sqrt[2])/2]/2 BX[18]:= 75/(2*(59 + 24*Sqrt[6])) BX[22]:= 511/(2*(401 + 284*Sqrt[2])) BX[25]:= 5*(97081 + 43416*Sqrt[5] - 2*Sqrt[2*(2356181685 + 1053716483*Sqrt[5])]) BX[28]:= 327/(8*Sqrt[8248 + 3115*Sqrt[7]]) BX[30]:= -823/2 + 185*Sqrt[5] - 2*Sqrt[2*(42441 - 18980*Sqrt[5])] BX[34]:= 1543/2 + 187*Sqrt[17] - Sqrt[2*(594597 + 144211*Sqrt[17])] BX[37]:= 17937234 + 2948863*Sqrt[37] - Sqrt[2*(321744346442001 + 52894444726289*Sqrt[37])] BX[42]:= 4811/2 + 984*Sqrt[6] - 7*Sqrt[7*(33803 + 13800*Sqrt[6])] BX[46]:= -8131/2 - 2876*Sqrt[2] + Sqrt[33073629 + 23386588*Sqrt[2]] BX[58]:= 29031/(2*(22801 + 4234*Sqrt[29])) BX[70]:= -123205/2 + 27550*Sqrt[5] - 2*Sqrt[2*(948662841 - 424254920*Sqrt[5])] BX[78]:= -271203/2 + 26598*Sqrt[26] - Sqrt[36781299453 - 7213406200*Sqrt[26]] BX[82]:= 395889/2 + 30914*Sqrt[41] - Sqrt[2*(39182295149 + 6119246433*Sqrt[41])] BX[102]:= -2294177/2 + 811150*Sqrt[2] - 34*Sqrt[17*(133917081 - 94693676*Sqrt[2])] BX[130]:= 20184205/2 - 4513325*Sqrt[5] - 13*Sqrt[13*(92717647221 - 41464592380*Sqrt[5])] BX[142]:= -47463531/2 - 16780892*Sqrt[2] + Sqrt[1126393381486429 + 796480398332700*Sqrt[2]] BX[190]:= -1039934423/2 + 164428070*Sqrt[10] - Sqrt[540731750669102077 - 170994393528463960*Sqrt[10]] BY[2]:= 2 BY[3]:= 3*(-8 + 5*Sqrt[3]) BY[4]:= 3/Sqrt[2] BY[5]:= 80 + 35*Sqrt[5] - 8*Sqrt[5*(38 + 17*Sqrt[5])] BY[6]:= 6*(-1 + Sqrt[2]) BY[7]:= 1197/(224 + 85*Sqrt[7]) BY[8]:= Sqrt[1 + 5*Sqrt[2]] BY[9]:= 3*(387 + 224*Sqrt[3] - 8*Sqrt[2*(2340 + 1351*Sqrt[3])]) BY[10]:= 6*(5 - 2*Sqrt[5]) BY[12]:= (3*Sqrt[14 - 5*Sqrt[3]])/2 BY[13]:= 3*(3120 + 865*Sqrt[13] - 8*Sqrt[13*(23382 + 6485*Sqrt[13])]) BY[14]:= 2*(-21 - 14*Sqrt[2] + Sqrt[14*(65 + 46*Sqrt[2])]) BY[15]:= 3*(-7760 + 2005*Sqrt[15] - 112*Sqrt[5*(1921 - 496*Sqrt[15])]) BY[16]:= 3*Sqrt[(-12 + 11*Sqrt[2])/2] BY[18]:= 42*(5 - 2*Sqrt[6]) BY[22]:= 66*(-7 + 5*Sqrt[2]) BY[25]:= 15*(69121 + 30912*Sqrt[5] - 16*Sqrt[37325880 + 16692641*Sqrt[5]]) BY[28]:= (3*Sqrt[7*(232 - 85*Sqrt[7])])/4 BY[30]:= 6*(-155 + 70*Sqrt[5] - Sqrt[10*(4821 - 2156*Sqrt[5])]) BY[34]:= 6*(289 + 70*Sqrt[17] - 2*Sqrt[17*(2445 + 593*Sqrt[17])]) BY[37]:= 3*(12618480 + 2074465*Sqrt[37] - 56*Sqrt[37*(2744518518 + 451196065*Sqrt[37])]) BY[42]:= 6*(889 + 364*Sqrt[6] - 2*Sqrt[7*(56549 + 23086*Sqrt[6])]) BY[46]:= 6*(-1495 - 1058*Sqrt[2] + Sqrt[46*(97329 + 68822*Sqrt[2])]) BY[58]:= 5742/(377 + 70*Sqrt[29]) BY[70]:= 42*(-3175 + 1420*Sqrt[5] - Sqrt[10*(2016021 - 901592*Sqrt[5])]) BY[78]:= 6*(-48711 + 9555*Sqrt[26] - 10*Sqrt[13*(3651051 - 716030*Sqrt[26])]) BY[82]:= 6*(70971 + 11084*Sqrt[41] - 2*Sqrt[82*(30712579 + 4796499*Sqrt[41])]) BY[102]:= 6*(-408085 + 288575*Sqrt[2] - 14*Sqrt[34*(49982451 - 35342930*Sqrt[2])]) BY[130]:= 6*(3562975 - 1593410*Sqrt[5] - 2*Sqrt[65*(97651946961 - 43671278308*Sqrt[5])]) BY[142]:= 6*(-8357055 - 5909330*Sqrt[2] + Sqrt[142*(983667349057 + 695557852950*Sqrt[2])]) BY[190]:= 114*(-9563945 + 3024385*Sqrt[10] - 2*Sqrt[5*(9146903410259 - 2892504831398*Sqrt[10])]) BZ2[2]:= 1 BZ2[3]:= 16/(26 + 15*Sqrt[3]) BZ2[4]:= 1/8 BZ2[5]:= 8*(617 + 276*Sqrt[5] - 2*Sqrt[5*(38078 + 17029*Sqrt[5])]) BZ2[6]:= (17 + 12*Sqrt[2])^(-1) BZ2[7]:= 64/(2024 + 765*Sqrt[7]) BZ2[8]:= (-7 + 5*Sqrt[2])/8 BZ2[9]:= 8*(74977 + 43288*Sqrt[3] - 2*Sqrt[6*(468462636 + 270467029*Sqrt[3])]) BZ2[10]:= (161 + 72*Sqrt[5])^(-1) BZ2[12]:= 1/(16*(26 + 15*Sqrt[3])) BZ2[13]:= 8*(3367657 + 934020*Sqrt[13] - 90*Sqrt[2800274982 + 776656541*Sqrt[13]]) BZ2[14]:= 497 + 352*Sqrt[2] - 4*Sqrt[14*(2209 + 1562*Sqrt[2])] BZ2[15]:= 32*(4518808 - 2608935*Sqrt[3] - 3*Sqrt[5*(907538592043 - 523967650416*Sqrt[3])]) BZ2[16]:= 1/(16*(140 + 99*Sqrt[2])) BZ2[18]:= (4801 + 1960*Sqrt[6])^(-1) BZ2[20]:= 33/8 + 2*Sqrt[5] - Sqrt[295/2 + (265*Sqrt[5])/4]/2 BZ2[22]:= (19601 + 13860*Sqrt[2])^(-1) BZ2[24]:= -71/8 + (21*Sqrt[3])/4 - Sqrt[4491/8 - 324*Sqrt[3]]/2 BZ2[25]:= 8*(21499758721 + 9614984400*Sqrt[5] - 36*Sqrt[713332754724099000 + 319012106028053921*Sqrt[5]]) BZ2[28]:= 1/(64*(2024 + 765*Sqrt[7])) BZ2[30]:= 116081 - 36708*Sqrt[10] - 72*Sqrt[5*(1039681 - 328776*Sqrt[10])] BZ2[32]:= -227/8 - 20*Sqrt[2] + Sqrt[821825/128 + 581125/(64*Sqrt[2])]/2 BZ2[34]:= 352673 + 85536*Sqrt[17] - 72*Sqrt[47985565 + 11638209*Sqrt[17]] BZ2[36]:= 385/8 + 28*Sqrt[3] - Sqrt[18666 + (21567*Sqrt[3])/2]/2 BZ2[37]:= 8*(19365324218857 + 3183639690420*Sqrt[37] - 630*Sqrt[1889724273627863327046 + 310668756870772626889*Sqrt[37]]) BZ2[40]:= -647/8 + (207*Sqrt[5/2])/4 - Sqrt[102465/2 - 16200*Sqrt[10]]/2 BZ2[42]:= 2716001 - 592680*Sqrt[21] - 120*Sqrt[14*(73180801 - 15969360*Sqrt[21])] BZ2[46]:= 7005041 + 4953312*Sqrt[2] - 252*Sqrt[46*(33596377 + 23756226*Sqrt[2])] BZ2[48]:= -1667/8 + (5445*Sqrt[3/2])/32 - Sqrt[176927625/512 - 141075*Sqrt[6]]/2 BZ2[52]:= 2593/8 + 90*Sqrt[13] - Sqrt[1682775/2 + (933525*Sqrt[13])/4]/2 BZ2[58]:= (192119201 + 35675640*Sqrt[29])^(-1) BZ2[60]:= 6013/8 - (55545*Sqrt[3])/128 - Sqrt[18497118735/4096 - 2607255*Sqrt[3]]/2 BZ2[64]:= -8963/8 - 792*Sqrt[2] + Sqrt[1285001253/128 + 3634532451/(256*Sqrt[2])]/2 BZ2[70]:= 1016135441 - 454429584*Sqrt[5] - 13860*Sqrt[2*(5374978561 - 2403763488*Sqrt[5])] BZ2[72]:= -19207/8 + 13615/(4*Sqrt[2]) - (35*Sqrt[3*(12513 - 8848*Sqrt[2])])/2 BZ2[78]:= 4381327601 - 1215161640*Sqrt[13] - 1020*Sqrt[26*(1419278889601 - 393637139280*Sqrt[13])] BZ2[82]:= 8845316801 + 1381406400*Sqrt[41] - 360*Sqrt[2*(603700843481683 + 94282231781859*Sqrt[41])] BZ2[88]:= -78407/8 + (11835*Sqrt[11])/4 - Sqrt[6139546875/8 - 231392700*Sqrt[11]]/2 BZ2[100]:= 207361/8 + 11592*Sqrt[5] - (9*Sqrt[66356760 + 29675681*Sqrt[5]])/2 BZ2[102]:= 235117934801 - 40322393160*Sqrt[34] - 13860*Sqrt[2*(287769694060801 - 49352095378320*Sqrt[34])] BZ2[112]:= -518147/8 + 5862195/(64*Sqrt[2]) - Sqrt[68728761563175/2048 - 23729772150*Sqrt[2]]/2 BZ2[130]:= 14061897471041 - 6288671727576*Sqrt[5] - 233640*Sqrt[13*(557288527109761 - 249227005939632*Sqrt[5])] BZ2[142]:= 70824040716401 + 50080159461600*Sqrt[2] - 1260*Sqrt[142*(44500199995373451809 + 31466393180886138546*Sqrt[2])] BZ2[148]:= 6223393/8 + 127890*Sqrt[37] - Sqrt[9682659581175/2 + (3183638987025*Sqrt[37])/4]/2 BZ2[190]:= 25025929238011121 - 7913893695431724*Sqrt[10] - 7465176*Sqrt[5*(4495316905044313921 - 1421544022419889368*Sqrt[10])] BZ2[232]:= -768476807/8 + (100907235*Sqrt[29/2])/4 - Sqrt[147637266911390025/2 - 9692861436858600*Sqrt[58]]/2 pBX[2] := 2*x - 1 pBX[3] := x^2 + 20*x - 8 pBX[4] := 8*x^2 - 1 pBX[5] := x^4 - 136*x^3 + 170*x^2 - 128*x + 29 pBX[6] := 4*x^2 + 20*x - 7 pBX[7] := x^2 + 592*x - 192 pBX[8] := 16*x^4 + 8*x^2 - 1 pBX[9] := x^4 - 2076*x^3 - 1890*x^2 - 108*x + 297 pBX[10] := 4*x^2 - 92*x + 29 pBX[12] := 256*x^4 - 1216*x^2 + 121 pBX[13] := x^4 - 17064*x^3 + 27034*x^2 - 13952*x + 2253 pBX[14] := 16*x^4 + 1120*x^3 + 824*x^2 + 248*x - 199 pBX[15] := x^4 + 42736*x^3 - 390208*x^2 - 664576*x + 249856 pBX[16] := 32*x^4 + 480*x^2 - 49 pBX[18] := 4*x^2 - 708*x + 225 pBX[22] := 4*x^2 + 1604*x - 511 pBX[25] := x^4 - 1941620*x^3 - 1853850*x^2 - 500*x + 250625 pBX[28] := 4096*x^4 - 1055744*x^2 + 106929 pBX[30] := 16*x^4 + 26336*x^3 - 85000*x^2 - 95272*x + 38089 pBX[34] := 16*x^4 - 49376*x^3 + 63032*x^2 - 44696*x + 9433 pBX[37] := x^4 - 71748936*x^3 + 114191626*x^2 - 58158208*x + 9256317 pBX[42] := 16*x^4 - 153952*x^3 - 1429576*x^2 - 880568*x + 430105 pBX[46] := 16*x^4 + 260192*x^3 - 1008328*x^2 + 1358840*x - 338759 pBX[58] := 4*x^2 - 273612*x + 87093 pBX[70] := 16*x^4 + 3942560*x^3 + 9241304*x^2 - 40822680*x + 11930769 pBX[78] := 16*x^4 + 8678496*x^3 - 377368008*x^2 - 249346056*x + 117324793 pBX[82] := 16*x^4 - 12668448*x^3 - 38601384*x^2 - 46794696*x + 19214929 pBX[102] := 16*x^4 + 73413664*x^3 - 7393290088*x^2 - 4775734904*x + 2266892833 pBX[130] := 16*x^4 - 645894560*x^3 + 13276443416*x^2 - 24215842280*x + 6383788129 pBX[142] := 16*x^4 + 1518832992*x^3 + 867942840*x^2 + 510118584*x - 299301479 pBX[190] := 16*x^4 + 33277901536*x^3 + 1612700995832*x^2 - 3221482986536*x + 860955845641 pBY[2] := x - 2 pBY[3] := x^2 + 48*x - 99 pBY[4] := 2*x^2 - 9 pBY[5] := x^4 - 320*x^3 + 1830*x^2 - 4800*x + 5225 pBY[6] := x^2 + 12*x - 36 pBY[7] := x^2 + 1344*x - 3591 pBY[8] := x^4 - 2*x^2 - 49 pBY[9] := x^4 - 4644*x^3 - 13338*x^2 + 38556*x + 130977 pBY[10] := x^2 - 60*x + 180 pBY[12] := 16*x^4 - 1008*x^2 + 9801 pBY[13] := x^4 - 37440*x^3 + 404118*x^2 - 1460160*x + 1765881 pBY[14] := x^4 + 168*x^3 + 168*x^2 - 1568*x - 5488 pBY[15] := x^4 + 93120*x^3 - 2388510*x^2 - 8769600*x + 64397025 pBY[16] := 2*x^4 + 216*x^2 - 3969 pBY[18] := x^2 - 420*x + 1764 pBY[22] := x^2 + 924*x - 4356 pBY[25] := x^4 - 4147260*x^3 - 20734650*x^2 + 103666500*x + 518450625 pBY[28] := 256*x^4 - 467712*x^2 + 12895281 pBY[30] := x^4 + 3720*x^3 - 45720*x^2 - 151200*x + 1587600 pBY[34] := x^4 - 6936*x^3 + 72216*x^2 - 249696*x + 374544 pBY[37] := x^4 - 151421760*x^3 + 2763185382*x^2 - 16807815360*x + 34079405481 pBY[42] := x^4 - 21336*x^3 - 531720*x^2 + 804384*x + 22924944 pBY[46] := x^4 + 35880*x^3 - 776664*x^2 + 5941728*x - 15768432 pBY[58] := x^2 - 149292*x + 1136916 pBY[70] := x^4 + 533400*x^3 - 1181880*x^2 - 111132000*x + 700131600 pBY[78] := x^4 + 1169064*x^3 - 131787864*x^2 - 95056416*x + 10313621136 pBY[82] := x^4 - 1703304*x^3 - 9697320*x^2 + 100214496*x + 1152466704 pBY[102] := x^4 + 9794040*x^3 - 2448938808*x^2 - 1020008160*x + 250004000016 pBY[130] := x^4 - 85511400*x^3 + 6422509080*x^2 - 114093252000*x + 592684419600 pBY[142] := x^4 + 200569320*x^3 - 1500826968*x^2 - 8689070880*x - 22728780144 pBY[190] := x^4 + 4361158920*x^3 + 452303556840*x^2 - 15003447933600*x + 109448840768400 pBZ2[2] := x - 1 pBZ2[3] := x^2 - 832*x + 256 pBZ2[4] := 8*x - 1 pBZ2[5] := x^4 - 19744*x^3 - 47744*x^2 - 67584*x + 4096 pBZ2[6] := x^2 - 34*x + 1 pBZ2[7] := x^2 - 259072*x + 4096 pBZ2[8] := 64*x^2 + 112*x - 1 pBZ2[9] := x^4 - 2399264*x^3 - 577152*x^2 - 788480*x + 4096 pBZ2[10] := x^2 - 322*x + 1 pBZ2[12] := 256*x^2 - 832*x + 1 pBZ2[13] := x^4 - 107765024*x^3 - 3897984*x^2 - 5310464*x + 4096 pBZ2[14] := x^4 - 1988*x^3 - 3194*x^2 - 1988*x + 1 pBZ2[15] := x^4 - 578407424*x^3 + 30879707136*x^2 - 50440699904*x + 16777216 pBZ2[16] := 512*x^2 + 4480*x - 1 pBZ2[18] := x^2 - 9602*x + 1 pBZ2[20] := 4096*x^4 - 67584*x^3 - 47744*x^2 - 19744*x + 1 pBZ2[22] := x^2 - 39202*x + 1 pBZ2[24] := 4096*x^4 + 145408*x^3 + 108672*x^2 - 75488*x + 1 pBZ2[25] := x^4 - 687992279072*x^3 - 311869056*x^2 - 424675328*x + 4096 pBZ2[28] := 4096*x^2 - 259072*x + 1 pBZ2[30] := x^4 - 464324*x^3 + 2183046*x^2 - 464324*x + 1 pBZ2[32] := 262144*x^4 + 29753344*x^3 + 5397504*x^2 + 816384*x - 1 pBZ2[34] := x^4 - 1410692*x^3 - 2716410*x^2 - 1410692*x + 1 pBZ2[36] := 4096*x^4 - 788480*x^3 - 577152*x^2 - 2399264*x + 1 pBZ2[37] := x^4 - 619690375003424*x^3 - 9359981184*x^2 - 12745508864*x + 4096 pBZ2[40] := 4096*x^4 + 1325056*x^3 + 974976*x^2 - 6651104*x + 1 pBZ2[42] := x^4 - 10864004*x^3 + 147168006*x^2 - 10864004*x + 1 pBZ2[46] := x^4 - 28020164*x^3 - 508026*x^2 - 28020164*x + 1 pBZ2[48] := 1048576*x^4 + 873988096*x^3 + 923283456*x^2 - 44309504*x + 1 pBZ2[52] := 4096*x^4 - 5310464*x^3 - 3897984*x^2 - 107765024*x + 1 pBZ2[58] := x^2 - 384238402*x + 1 pBZ2[60] := 16777216*x^4 - 50440699904*x^3 + 30879707136*x^2 - 578407424*x + 1 pBZ2[64] := 2097152*x^4 + 9398386688*x^3 + 5974155264*x^2 + 1284786176*x - 1 pBZ2[70] := x^4 - 4064541764*x^3 + 12286753926*x^2 - 4064541764*x + 1 pBZ2[72] := 4096*x^4 + 39335936*x^3 + 28889216*x^2 - 5901158624*x + 1 pBZ2[78] := x^4 - 17525310404*x^3 + 2838665980806*x^2 - 17525310404*x + 1 pBZ2[82] := x^4 - 35381267204*x^3 - 41385945594*x^2 - 35381267204*x + 1 pBZ2[88] := 4096*x^4 + 160577536*x^3 + 117926016*x^2 - 98356877024*x + 1 pBZ2[100] := 4096*x^4 - 424675328*x^3 - 311869056*x^2 - 687992279072*x + 1 pBZ2[102] := x^4 - 940471739204*x^3 + 575540924918406*x^2 - 940471739204*x + 1 pBZ2[112] := 16777216*x^4 + 4346532069376*x^3 + 3328592510976*x^2 - 4295583186944*x + 1 pBZ2[130] := x^4 - 56247589884164*x^3 + 1117415611998726*x^2 - 56247589884164*x + 1 pBZ2[142] := x^4 - 283296162865604*x^3 - 565321754908794*x^2 - 283296162865604*x + 1 pBZ2[148] := 4096*x^4 - 12745508864*x^3 - 9359981184*x^2 - 619690375003424*x + 1 pBZ2[190] := x^4 - 100103716952044484*x^3 + 8991748387142847366*x^2 - 100103716952044484*x + 1 pBZ2[232] := 4096*x^4 + 1573840500736*x^3 + 1155789119616*x^2 - 9448905591020313824*x + 1 (* Type D, N=3〜190 Mathematica 3.0が計算ミスを多発する． *) sumD[t_, limit_:Infinity] := (Sum[termp[n, 1/4, DX[t], DY[t], DZ2[t]],{n, 0, limit}] * Sqrt[DZ2[t]]); DX[3]:= Sqrt[(3*(7 - 4*Sqrt[3]))/2]/2 DX[4]:= 1/(2*Sqrt[2]) DX[6]:= Sqrt[3]/2 DX[7]:= 197/(2*Sqrt[3284 + 1239*Sqrt[7]]) DX[8]:= (3*Sqrt[(1 + Sqrt[2])/2])/2 DX[10]:= 2*Sqrt[2] DX[12]:= Sqrt[(3*(7 + 4*Sqrt[3]))/2] DX[14]:= (3*Sqrt[11 + 8*Sqrt[2]])/2 DX[16]:= Sqrt[(112 + 81*Sqrt[2])/2] DX[18]:= 9*Sqrt[3] DX[22]:= (19*Sqrt[11])/2 DX[28]:= Sqrt[3284 + 1239*Sqrt[7]] DX[30]:= Sqrt[3*(7841 + 5544*Sqrt[2])]/2 DX[34]:= Sqrt[(35731 + 8667*Sqrt[17])/2] DX[42]:= Sqrt[3*(45865 + 18724*Sqrt[6])] DX[46]:= Sqrt[1419515 + 1003752*Sqrt[2]]/2 DX[58]:= 2206*Sqrt[2] DX[70]:= Sqrt[7*(29416013 + 9302160*Sqrt[10])]/2 DX[78]:= Sqrt[3*(295947553 + 209266488*Sqrt[2])]/2 DX[82]:= Sqrt[2*(224054491 + 34991433*Sqrt[41])] DX[102]:= Sqrt[3*(15881618381 + 3851858196*Sqrt[17])]/2 DX[130]:= 4*Sqrt[44524003001 + 5522522895*Sqrt[65]] DX[142]:= Sqrt[14351951271419 + 10148362067304*Sqrt[2]]/2 DX[190]:= Sqrt[19*(266911239173129 + 188734747194216*Sqrt[2])]/2 DY[3]:= (115*Sqrt[3/(266 + 153*Sqrt[3])])/8 DY[4]:= 7/(2*Sqrt[2]) DY[6]:= 4*Sqrt[3] DY[7]:= 50995/(16*Sqrt[47384 + 17901*Sqrt[7]]) DY[8]:= (5*Sqrt[17 + 13*Sqrt[2]])/2 DY[10]:= 20*Sqrt[2] DY[12]:= (5*Sqrt[3*(266 + 153*Sqrt[3])])/4 DY[14]:= 4*Sqrt[7*(31 + 22*Sqrt[2])] DY[16]:= Sqrt[(71476 + 50787*Sqrt[2])/2]/2 DY[18]:= 120*Sqrt[3] DY[22]:= 140*Sqrt[11] DY[28]:= (35*Sqrt[47384 + 17901*Sqrt[7]])/8 DY[30]:= 20*Sqrt[3*(1451 + 1026*Sqrt[2])] DY[34]:= 4*Sqrt[34*(11021 + 2673*Sqrt[17])] DY[42]:= 140*Sqrt[6*(485 + 198*Sqrt[6])] DY[46]:= 28*Sqrt[23*(8935 + 6318*Sqrt[2])] DY[58]:= 52780*Sqrt[2] DY[70]:= 20*Sqrt[7*(12701693 + 4016628*Sqrt[10])] DY[78]:= 260*Sqrt[3*(842563 + 595782*Sqrt[2])] DY[82]:= 40*Sqrt[41*(5528323 + 863379*Sqrt[41])] DY[102]:= 140*Sqrt[51*(11995813 + 2909412*Sqrt[17])] DY[130]:= 40*Sqrt[13*(43943429597 + 5450511627*Sqrt[65])] DY[142]:= 20*Sqrt[71*(177060101791 + 125200398654*Sqrt[2])] DY[190]:= 20*Sqrt[19*(312824115475139 + 221200053371154*Sqrt[2])] DZ2[3]:= (64*(746 + 425*Sqrt[3]))/131769 DZ2[4]:= 32/81 DZ2[5]:= 1391057696/1908029761 - (533370240*Sqrt[5])/1908029761 + Sqrt[-81655421523444531200/3640577568861717121 + (36587558440088780800*Sqrt[5])/3640577568861717121]/2 DZ2[6]:= 1/9 DZ2[7]:= (256*(102376 + 38675*Sqrt[7]))/855036081 DZ2[8]:= 32/(457 + 325*Sqrt[2]) DZ2[9]:= 12802208/15065589 - (17038592*Sqrt[3])/35153041 + Sqrt[-4045457244160000/1235736291547681 + 3003358134173696/(529601267806149*Sqrt[3])]/2 DZ2[10]:= 1/81 DZ2[12]:= (64*(746 - 425*Sqrt[3]))/131769 DZ2[13]:= 3485416736/22430753361 - (957104000*Sqrt[13])/22430753361 + Sqrt[-678358357709393920000/503138696342012796321 + (188144079701493760000*Sqrt[13])/503138696342012796321]/2 DZ2[14]:= (249 + 176*Sqrt[2])^(-1) DZ2[15]:= 138354567918592/547665541771887 - (143992773882880*Sqrt[5])/1277886264134403 + Sqrt[1812717941905843271123556761600/4898979912190143573296544499227 - (38603249235837712877653196800*Sqrt[5])/233284757723340170156978309487]/2 DZ2[16]:= 128/(81*(884 + 627*Sqrt[2])) DZ2[18]:= 1/2401 DZ2[20]:= 1391057696/1908029761 - (533370240*Sqrt[5])/1908029761 - Sqrt[-81655421523444531200/3640577568861717121 + (36587558440088780800*Sqrt[5])/3640577568861717121]/2 DZ2[22]:= 1/9801 DZ2[24]:= -65209376/2518569 + 12754624/(279841*Sqrt[3]) - Sqrt[11472312970846208/2114396602587 - 6622669099171840/(704798867529*Sqrt[3])]/2 DZ2[25]:= 11867821024/5890087872207 - (4088497664*Sqrt[5])/4581179456161 + Sqrt[-2714620527478908843681382400/137697053379868019524548819681 + (57810252293519439840477184*Sqrt[5])/6557002541898477120216610461]/2 DZ2[26]:= -3229/43923 - 48235168/(43923*(228753433 + 211137861*Sqrt[78])^(1/3)) + (32*(228753433 + 211137861*Sqrt[78])^(1/3))/43923 DZ2[28]:= 256/(81*(102376 + 38675*Sqrt[7])) DZ2[30]:= 1/(9*(6449 + 4560*Sqrt[2])) DZ2[32]:= -71905429355264/620512135426561 + (42963403308800*Sqrt[2])/620512135426561 + Sqrt[-437638659042945688690708480000/385035310211630778817424286721 + (309808840225982016197857280000*Sqrt[2])/385035310211630778817424286721]/2 DZ2[34]:= 1/(81*(2177 + 528*Sqrt[17])) DZ2[36]:= 12802208/15065589 - (17038592*Sqrt[3])/35153041 - Sqrt[-4045457244160000/1235736291547681 + 3003358134173696/(529601267806149*Sqrt[3])]/2 DZ2[37]:= 48533496601297231136/722602051490681073492561 - (7902503882007280000*Sqrt[37])/722602051490681073492561 + Sqrt[-343639309768459837812532831327932112015360000/522153724818540901425980539569034049238522338721 + (56493954666094459427059137283847777331200000*Sqrt[37])/522153724818540901425980539569034049238522338721]/2 DZ2[38]:= -1709197/15856203 - (8137824800*2^(2/3))/(15856203*(35037999968 + 5406965223*Sqrt[114])^(1/3)) + (800*(2*(35037999968 + 5406965223*Sqrt[114]))^(1/3))/15856203 DZ2[40]:= -18693728/24935067 + (28426720*Sqrt[10])/74805201 - Sqrt[4928951354163200/621757566294489 - (465997565132800*Sqrt[10])/207252522098163]/2 DZ2[42]:= 1/(9*(150889 + 61600*Sqrt[6])) DZ2[46]:= 1/(81*(43241 + 30576*Sqrt[2])) DZ2[48]:= -1258653213377536/12289813296489 + (171421605361600*Sqrt[2/3])/1365534810721 - Sqrt[4227824857404220793330790400000/50346503620852607006575707 - (1726001689366489162168893440000*Sqrt[2/3])/16782167873617535668858569]/2 DZ2[50]:= -32503039/671898241 - (4081563782816*5^(2/3))/(671898241*(3*(3878940407693553 + 2206566231506798*Sqrt[6]))^(1/3)) + (416*(5*(3878940407693553 + 2206566231506798*Sqrt[6]))^(1/3))/(671898241*3^(2/3)) DZ2[52]:= 3485416736/22430753361 - (957104000*Sqrt[13])/22430753361 - Sqrt[-678358357709393920000/503138696342012796321 + (188144079701493760000*Sqrt[13])/503138696342012796321]/2 DZ2[54]:= -115575/130321 - (26276287712*2^(2/3))/(390963*(13663686521634 + 25436328669557*Sqrt[2])^(1/3)) + (32*(2*(13663686521634 + 25436328669557*Sqrt[2]))^(1/3))/390963 DZ2[58]:= 1/96059601 DZ2[60]:= 138354567918592/547665541771887 - (143992773882880*Sqrt[5])/1277886264134403 - Sqrt[1812717941905843271123556761600/4898979912190143573296544499227 - (38603249235837712877653196800*Sqrt[5])/233284757723340170156978309487]/2 DZ2[62]:= 11652515401/268927201 + (8245779600*Sqrt[2])/268927201 - Sqrt[1087066839563292160000/72321839437694401 + (768673064430453760000*Sqrt[2])/72321839437694401]/2 DZ2[64]:= -664758272/949132107 + (469755392*Sqrt[2])/949132107 + Sqrt[-109522299278907932672/8107665808844335041 + (8604885009323196416*Sqrt[2])/900851756538259449]/2 DZ2[66]:= 4121345/8311689 - (226936*Sqrt[11/3])/923521 - Sqrt[-28160079833600/23028058010907 + (4912315561472*Sqrt[11/3])/7676019336969]/2 DZ2[70]:= 1/(3969*(128009 + 40480*Sqrt[10])) DZ2[72]:= -758949071875521824/34700535004437432001 + (4051080881437189600*Sqrt[2])/34700535004437432001 - Sqrt[133219281202364428432379049841582080000/1204127129594187528941331872763498864001 - (24331500928441886596378427908915200000*Sqrt[2])/1204127129594187528941331872763498864001]/2 DZ2[78]:= 1/(9*(243407089 + 172114800*Sqrt[2])) DZ2[82]:= 1/(81*(54600721 + 8527200*Sqrt[41])) DZ2[88]:= -1497518432/280557433443 + (61699745600*Sqrt[11])/2525016900987 - Sqrt[1512033431590106782720000/57381393152429940254167521 - (2194937589839667200000*Sqrt[11])/2125236783423331120524723]/2 DZ2[90]:= -19390957/10256403 + (2993360*Sqrt[6])/3418801 - Sqrt[-5317346821145600/11688200277601 + (19548266867353600*Sqrt[2/3])/35064600832803]/2 DZ2[94]:= 6067/59643 + (944*Sqrt[2])/2209 - Sqrt[16603156480/32015587041 + (11134910464*Sqrt[2])/10671862347]/2 DZ2[98]:= 481784377107601/4506487876801 + (128767125364000*Sqrt[14])/4506487876801 - Sqrt[1856999205628632296912625280000/20308432983754384953993601 + (496303914989921968944673280000*Sqrt[14])/20308432983754384953993601]/2 DZ2[100]:= 11867821024/5890087872207 - (4088497664*Sqrt[5])/4581179456161 - Sqrt[-2714620527478908843681382400/137697053379868019524548819681 + (57810252293519439840477184*Sqrt[5])/6557002541898477120216610461]/2 DZ2[102]:= 1/(9*(13062107489 + 3168026400*Sqrt[17])) DZ2[106]:= 9413/83349 - 19381216/(583443*(-5818337 + 456417*Sqrt[318])^(1/3)) + (608*(-5818337 + 456417*Sqrt[318])^(1/3))/583443 DZ2[112]:= -958148985900285952/137516724173557323 + (80488958642435200*Sqrt[2])/15279636019284147 - Sqrt[10118868730537688603026974220042240000/24313949263833743572022376471762423 - (2379710532349609738193114241433600000*Sqrt[2])/8104649754611247857340792157254141]/2 DZ2[114]:= -41467583/316377369 + (1855720*Sqrt[19/3])/35153041 - Sqrt[-3356913725819392/33364879871787387 + (444690173141504*Sqrt[19/3])/11121626623929129]/2 DZ2[118]:= -125431277/68516523 - (7047405260000*2^(2/3))/(68516523*(3035372625864526 + 172884603414087*Sqrt[354])^(1/3)) + (800*(2*(3035372625864526 + 172884603414087*Sqrt[354]))^(1/3))/68516523 DZ2[126]:= 3540363801/13521270961 + (1703529968*Sqrt[2])/13521270961 - Sqrt[56416107877975953408/182824768400781863521 + (60224989372668051456*Sqrt[2])/182824768400781863521]/2 DZ2[130]:= 1/(81*(86801836241 + 10766442720*Sqrt[65])) DZ2[138]:= 5138649673769/23635028158569 - (697411972400*Sqrt[2/3])/2626114239841 - Sqrt[-703973176745842640324480000/186204852018783178336042587 + (287395948690716417660160000*Sqrt[2/3])/62068284006261059445347529]/2 DZ2[142]:= 1/(81*(437185436521 + 309136786800*Sqrt[2])) DZ2[148]:= 48533496601297231136/722602051490681073492561 - (7902503882007280000*Sqrt[37])/722602051490681073492561 - Sqrt[-343639309768459837812532831327932112015360000/522153724818540901425980539569034049238522338721 + (56493954666094459427059137283847777331200000*Sqrt[37])/522153724818540901425980539569034049238522338721]/2 DZ2[150]:= 208069199217601/620034053633289 - (21909911210704*Sqrt[10])/206678017877763 - Sqrt[-49643237619036238558566287360/128147409221642766727229652507 + (15698589354846517150032265216*Sqrt[10])/128147409221642766727229652507]/2 DZ2[154]:= 9799229329/79502005521 + (3554465264*Sqrt[22])/79502005521 - Sqrt[1346027800257820359680/6320568881861114481441 + (310603417408140752896*Sqrt[22])/6320568881861114481441]/2 DZ2[158]:= 570428209425826658601/1858108924530102184801 + (403676527599489086800*Sqrt[2])/1858108924530102184801 - Sqrt[2605189610966675604804242113245573739520000/3452568775418412976702278854578793555409601 + (1842149010729925759923138345977856942080000*Sqrt[2])/3452568775418412976702278854578793555409601]/2 DZ2[162]:= 73259319996801/35971217755201 - 10800784955253491816800/(35971217755201*(-6055854507923231142283343 + 2774715215493234368371084*Sqrt[6])^(1/3)) + (509600*(-6055854507923231142283343 + 2774715215493234368371084*Sqrt[6])^(1/3))/35971217755201 DZ2[178]:= 3431336387/686115387 + (333385400*Sqrt[89])/686115387 - Sqrt[777458435407193920000/4236788918503437921 + (9181331163884480000*Sqrt[89])/470754324278159769]/2 DZ2[190]:= 1/(29241*(427925331521 + 302588903760*Sqrt[2])) DZ2[198]:= 9918230909/20735503509 - (147851600*Sqrt[33])/48382841521 - Sqrt[-31164475294227503360000/2340899353646201593441 + (7419980378106602240000*Sqrt[11/3])/1003242580134086397189]/2 DZ2[202]:= -49635743351677/168845458495923 - 15082348229155113892000/(168845458495923*(121176392383639821373129624444741 + 4922455579364073874825114790949*Sqrt[606])^(1/3)) + (800*(121176392383639821373129624444741 + 4922455579364073874825114790949*Sqrt[606])^(1/3))/168845458495923 DZ2[210]:= 64869935911481/726705134885961 - (2109442430960*Sqrt[5/21])/11535002141047 - Sqrt[7962425817270806407727104000/176033451023207590410824964507 - (777053119404906043676672000*Sqrt[5/21])/8382545286819409067182141167]/2 DZ2[214]:= -65787892889/4657120068447 + (1984*(3062243923082141692218723 + 121284794264961615011867*Sqrt[642])^(1/3))/(10866613493043*3^(2/3)) - 5572774357399667008/(10866613493043*(3*(3062243923082141692218723 + 121284794264961615011867*Sqrt[642]))^(1/3)) DZ2[226]:= 3771042203/8448319467 + (38852752*Sqrt[113])/938702163 - Sqrt[1008828452255800483840/642366916348420476801 + (31663724988944162816*Sqrt[113])/214122305449473492267]/2 DZ2[232]:= -38059347232238774488864/69970626802003773543804341361 + (2499778969900716385824800*Sqrt[58])/23323542267334591181268113787 - Sqrt[1449725758322302540034242794616230943486672916480000/543987623896143202406056572399502262036341309896779481369 - (83759044299110439068041142569284027814297600000*Sqrt[58])/181329207965381067468685524133167420678780436632259827123]/2 DZ2[238]:= 2656006103/307419903 - (5560008400*Sqrt[2])/922259709 - Sqrt[192515285857991073280000/375098270142541224321 - (15123901969232235520000*Sqrt[2])/41677585571393469369]/2 DZ2[258]:= -7576454692988330597231/84219475763336310250569 + (222372220028111527000*Sqrt[43/3])/9357719529259590027841 - Sqrt[-42029432727033834847357272560587451821120000/2364306699283730726054133936500977261188274587 + (3700485247167862437889088341014609552320000*Sqrt[43/3])/788102233094576908684711312166992420396091529]/2 DZ2[262]:= 56294523945867923/739822699076905323 - (52403751826559129806872337600*2^(2/3))/(739822699076905323*(-15184252379256689407989890659974513350 + 577950560928753849255647530334036169*Sqrt[786])^(1/3)) + (20800*(2*(-15184252379256689407989890659974513350 + 577950560928753849255647530334036169*Sqrt[786]))^(1/3))/739822699076905323 DZ2[282]:= 2056373660116330367/3939758968403173167 - (652949332865903200*Sqrt[6])/3064256975424690241 - Sqrt[-14885345025403490289305446931778560000/253521111908849508672598541271617228187 + (289376983961461689517233803448320000*Sqrt[2/3])/4024144633473801724961881607485987749]/2 DZ2[298]:= -12006812939764477/1047760922436723 - (501261354841042753385108800*2^(2/3))/(1047760922436723*(2366758246143191796040964622662110 + 82767234116065033502438427345213*Sqrt[894])^(1/3)) + (78400*(2*(2366758246143191796040964622662110 + 82767234116065033502438427345213*Sqrt[894]))^(1/3))/1047760922436723 DZ2[310]:= -58779202080119/299230456361841 + (18777304888160*Sqrt[10])/299230456361841 - Sqrt[-1173995911866007841305704755200/89538866014515630989920909281 + (371250559662139067450483507200*Sqrt[10])/89538866014515630989920909281]/2 DZ2[322]:= 22035382843/19370043 - (9746482400*Sqrt[46])/58110129 - Sqrt[554174924484958720000/53599795117407 - (81708634869017600000*Sqrt[46])/53599795117407]/2 DZ2[330]:= 7403353326952984557769/35826425693361508150089 - (526131627009240017360*Sqrt[22])/11942141897787169383363 - Sqrt[144168651123668224375400565111139672072115200/427844259320651206667428529271978256983569307 - (30736859695409030118634237593687917597132800*Sqrt[22])/427844259320651206667428529271978256983569307]/2 DZ2[358]:= 61734456141882114323/133003126523723674923 - (17389078743088732527651076525330400*2^(2/3))/(133003126523723674923*(-2024391410266434641241025279626615750651476230 + 63074129535075978080634519512878654519518537*Sqrt[1074])^(1/3)) + (39200*(2*(-2024391410266434641241025279626615750651476230 + 63074129535075978080634519512878654519518537*Sqrt[1074]))^(1/3))/133003126523723674923 DZ2[382]:= 49147180787/2364953787 + (34339817200*Sqrt[2])/2364953787 - Sqrt[171758506806892695040000/50337057731810772321 + (40528868975122611200000*Sqrt[2])/16779019243936924107]/2 DZ2[418]:= 6673075179371358438787/49068186689483520118587 + (480725755225834522600*Sqrt[209])/49068186689483520118587 - Sqrt[3311268966445380556028220434489784021855040000/21669182504946069242531962153337679478885889121 + (77695245748678056956882824339215883974080000*Sqrt[209])/7223060834982023080843987384445893159628629707]/2 DZ2[438]:= 5300496365221380347287/11674857680699818276287 - (1447544285231063975600*Sqrt[73])/27241334588299575978003 - Sqrt[-161222217262058514221445326309849826456320000/2226270930455060485940111543706373361819604027 + (2695661894550957656438323367868354609920000*Sqrt[73])/318038704350722926562873077672339051688514861]/2 DZ2[442]:= 3350907418002587/102371336824966587 + (1417273986861200*Sqrt[17])/14624476689280941 - Sqrt[-44505200952032922825123695459840000/94319015429976840123033002997857121 + (1328335847843117671955538419200000*Sqrt[17])/4491381687141754291573000142755101]/2 DZ2[462]:= 417076667036179443360241837285169/3628022246519393000477952182813769 - (8067079443576096288608345482400*Sqrt[33])/403113582946599222275328020312641 - Sqrt[399913416199307740641701370550768764185123474547792999206383360000/4387515140413207745523722464163571883538390044496815487683378661787 - (23205330025736494405768552964840495537206929727779105556336640000*Sqrt[11/3])/487501682268134193947080273795952431504265560499646165298153184643]/2 DZ2[466]:= 17354633945222217289/570003148999409841 + (378978689935484408*Sqrt[233])/190001049666469947 - Sqrt[2409458497622864638432692908260371010048/324903589869243416023178966287645281 + (52616291496500822716494930965689967104*Sqrt[233])/108301196623081138674392988762548427]/2 DZ2[478]:= 1768399050075290874361/1007066268125221819761 + (8306194245754358800*Sqrt[2])/12432916890434837281 - Sqrt[528842917256115692912703879975470904320000/37562313644283746867164383260750235929523 + (1203049914498265174399637846254741698560000*Sqrt[2])/112686940932851240601493149782250707788569]/2 DZ2[498]:= -930576178233430005535518511/2295985643350548253027213689 + (6552541159102176037586600*Sqrt[249])/255109515927838694780801521 - Sqrt[-2465745873306087858587757946223153969887866683412160000/585727786052425662375701323797173942808223468763220969 + (156260295554472492181088661753956035201494023445440000*Sqrt[83/3])/195242595350808554125233774599057980936074489587740323]/2 DZ2[522]:= 66081930945010677634163/1313433404222168135659134963 + (1083267792824403402730800*Sqrt[6])/62544447820103244555196903 - Sqrt[-1698748641507628009036794296887735456069682555520000/191678589702959257489731279644362655591162989938779041 + (179747253108245806812530919639778431827731316480000*Sqrt[6])/27382655671851322498533039949194665084451855705539863]/2 DZ2[562]:= 59927567508016056223/122757746741933242023 + (115494409192657000*Sqrt[281])/13639749637992582447 - Sqrt[-5917031812561755351900590579780568640000/27348287217506461235109108918637598647923 + (8832190764883897272586191138443879360000*Sqrt[281])/82044861652519383705327326755912795943769]/2 DZ2[598]:= 9644744463767361032483/72361574733214076252283 + (1852674382498309814000*Sqrt[26])/72361574733214076252283 - Sqrt[6559680531077935694275377618050737745547520000/47125777480834732296707876052354025811964408801 + (428963865961566637425774147344187791651840000*Sqrt[26])/15708592493611577432235958684118008603988136267]/2 DZ2[658]:= 3658874717690818403523451129/60477903190659258224997129 - (977854721954755477675304000*Sqrt[14])/60477903190659258224997129 - Sqrt[8363327189423048945580198374849510863921557394585513600000/296263718721439016191726396455755860198306036717653921 - (745064403548913740333301967203646915340667813924797440000*Sqrt[14])/98754572907146338730575465485251953399435345572551307]/2 DZ2[742]:= -1870834771871074003452071/45070176004870138924408929 + (184458890174594604936400*Sqrt[106])/45070176004870138924408929 - Sqrt[-10911544283606133907158444928399251256896444160000/41455525818570857897119193982572468568495347243409 + (1059829213664236399683889897152941686327531520000*Sqrt[106])/41455525818570857897119193982572468568495347243409]/2 DZ2[862]:= 8845334329396117351243243907/5951936253401389479986444907 + (6930136279849699225735711600*Sqrt[2])/5951936253401389479986444907 - Sqrt[6241873793770826402252027130722844853170651140249820160000/318829906480983922837524530661883340386850464144916147841 + (1478890708362458202334793213303879758947198641253447680000*Sqrt[2])/106276635493661307612508176887294446795616821381638715947]/2 pDX[3] := 64*x^4 - 336*x^2 + 9 pDX[4] := 8*x^2 - 1 pDX[6] := 4*x^2 - 3 pDX[7] := 16*x^4 - 26272*x^2 + 38809 pDX[8] := 64*x^4 - 144*x^2 - 81 pDX[10] := x^2 - 8 pDX[12] := 4*x^4 - 84*x^2 + 9 pDX[14] := 16*x^4 - 792*x^2 - 567 pDX[16] := 2*x^4 - 224*x^2 - 289 pDX[18] := x^2 - 243 pDX[22] := 4*x^2 - 3971 pDX[28] := x^4 - 6568*x^2 + 38809 pDX[30] := 16*x^4 - 188184*x^2 + 84681 pDX[34] := x^4 - 35731*x^2 - 70688 pDX[42] := x^4 - 275190*x^2 + 622521 pDX[46] := 16*x^4 - 11356120*x^2 - 13319783 pDX[58] := x^2 - 9732872 pDX[70] := 16*x^4 - 1647296728*x^2 + 693848281 pDX[78] := 16*x^4 - 7102741272*x^2 + 253142815689 pDX[82] := x^4 - 896217964*x^2 - 3127455872 pDX[102] := 16*x^4 - 381158841144*x^2 + 52597320264801 pDX[130] := x^4 - 1424768096032*x^2 + 14364221280256 pDX[142] := 16*x^4 - 114815610171352*x^2 - 1003982645383271 pDX[190] := 16*x^4 - 40570508354315608*x^2 + 2174755978446819769 pDY[3] := 4096*x^4 - 2553600*x^2 + 2975625 pDY[4] := 8*x^2 - 49 pDY[6] := x^2 - 48 pDY[7] := 65536*x^4 - 29719244800*x^2 + 3185600280625 pDY[8] := 16*x^4 - 3400*x^2 - 30625 pDY[10] := x^2 - 800 pDY[12] := 256*x^4 - 638400*x^2 + 2975625 pDY[14] := x^4 - 6944*x^2 - 87808 pDY[16] := 32*x^4 - 571808*x^2 - 24910081 pDY[18] := x^2 - 43200 pDY[22] := x^2 - 215600 pDY[28] := 4096*x^4 - 7429811200*x^2 + 3185600280625 pDY[30] := x^4 - 3482400*x^2 + 70560000 pDY[34] := x^4 - 11990848*x^2 - 400105472 pDY[42] := x^4 - 114072000*x^2 + 13829760000 pDY[46] := x^4 - 322231840*x^2 - 7478519552 pDY[58] := x^2 - 5571456800 pDY[70] := x^4 - 71129480800*x^2 + 1273286560000 pDY[78] := x^4 - 341743552800*x^2 + 1066074740640000 pDY[82] := x^4 - 725315977600*x^2 - 47130398720000 pDY[102] := x^4 - 23982029349600*x^2 + 373022402931360000 pDY[130] := x^4 - 1828046671235200*x^2 + 1061447206543360000 pDY[142] := x^4 - 10057013781728800*x^2 - 1426494720126560000 pDY[190] := x^4 - 4754926555222112800*x^2 + 19835914275744948640000 pDZ2[3] := 1185921*x^2 - 859392*x + 4096 pDZ2[4] := 81*x - 32 pDZ2[5] := 1908029761*x^4 - 5564230784*x^3 + 25991796736*x^2 - 5182193664*x + 1048576 pDZ2[6] := 9*x - 1 pDZ2[7] := 69257922561*x^2 - 4245737472*x + 65536 pDZ2[8] := 2401*x^2 + 29248*x - 1024 pDZ2[9] := 6836598566721*x^4 - 23238004664448*x^3 + 31174019389440*x^2 - 629005221888*x + 1048576 pDZ2[10] := 81*x - 1 pDZ2[12] := 1185921*x^2 - 859392*x + 4096 pDZ2[13] := 11920621996923201*x^4 - 7409173422386304*x^3 + 9198636408723456*x^2 - 28250296418304*x + 1048576 pDZ2[14] := 49*x^2 - 498*x + 1 pDZ2[15] := 6710164160448316405761*x^4 - 6780648350290674069504*x^3 + 476025208711316176896*x^2 - 621063479255629824*x + 4294967296 pDZ2[16] := 15752961*x^2 + 9165312*x - 8192 pDZ2[18] := 2401*x - 1 pDZ2[20] := 1908029761*x^4 - 5564230784*x^3 + 25991796736*x^2 - 5182193664*x + 1048576 pDZ2[22] := 9801*x - 1 pDZ2[24] := 1836036801*x^4 + 190150540416*x^3 - 138830837760*x^2 - 19781517312*x + 1048576 pDZ2[25] := 473488614114606609692481*x^4 - 3816091203480414730368*x^3 + 4675044057591043528704*x^2 - 180353075186368512*x + 1048576 pDZ2[26] := 14641*x^3 + 3229*x^2 + 35379*x - 1 pDZ2[28] := 69257922561*x^2 - 4245737472*x + 65536 pDZ2[30] := 194481*x^2 - 116082*x + 1 pDZ2[32] := 620512135426561*x^4 + 287621717421056*x^3 + 390738946441216*x^2 + 13694880710656*x - 67108864 pDZ2[34] := 6561*x^2 - 352674*x + 1 pDZ2[36] := 6836598566721*x^4 - 23238004664448*x^3 + 31174019389440*x^2 - 629005221888*x + 1048576 pDZ2[37] := 384020356846259040377960110401*x^4 - 103170759869160007248587904*x^3 + 126372550352224149387565056*x^2 - 162448114480612245504*x + 1048576 pDZ2[38] := 5285401*x^3 + 1709197*x^2 + 1005403*x - 1 pDZ2[40] := 39754550824641*x^4 + 119215362024576*x^3 - 138330257946624*x^2 - 1743464300544*x + 1048576 pDZ2[42] := 10556001*x^2 - 2716002*x + 1 pDZ2[46] := 3470769*x^2 - 7005042*x + 1 pDZ2[48] := 8959273893140481*x^4 + 3670232770208894976*x^3 - 599665266678104064*x^2 - 2973505079476224*x + 268435456 pDZ2[50] := 671898241*x^3 + 97509117*x^2 + 17352323*x - 1 pDZ2[52] := 11920621996923201*x^4 - 7409173422386304*x^3 + 9198636408723456*x^2 - 28250296418304*x + 1048576 pDZ2[54] := 1172889*x^3 + 3120525*x^2 + 41479899*x - 1 pDZ2[58] := 96059601*x - 1 pDZ2[60] := 6710164160448316405761*x^4 - 6780648350290674069504*x^3 + 476025208711316176896*x^2 - 621063479255629824*x + 4294967296 pDZ2[62] := 268927201*x^4 - 46610061604*x^3 - 3042658394*x^2 - 216207204*x + 1 pDZ2[64] := 22155100113214361601*x^4 + 62068434767415926784*x^3 + 193140475265405288448*x^2 + 172440481085521920*x - 536870912 pDZ2[66] := 6059221281*x^4 - 12017842020*x^3 + 9960278886*x^2 - 474248484*x + 1 pDZ2[70] := 1275989841*x^2 - 1016135442*x + 1 pDZ2[72] := 34700535004437432001*x^4 + 3035796287502087296*x^3 - 3711719247391750144*x^2 - 1546950810927104*x + 1048576 pDZ2[78] := 179607287601*x^2 - 4381327602*x + 1 pDZ2[82] := 1836036801*x^2 - 8845316802*x + 1 pDZ2[88] := 9665687742038144619201*x^4 + 206368377041762925696*x^3 - 252663796166074988544*x^2 - 25783654895714304*x + 1048576 pDZ2[90] := 276922881*x^4 + 2094223356*x^3 + 66382256646*x^2 - 34306042884*x + 1 pDZ2[94] := 95090206689*x^4 - 38691030564*x^3 - 88215282522*x^2 - 66051026532*x + 1 pDZ2[98] := 4506487876801*x^4 - 1927137508430404*x^3 - 15470750769594*x^2 - 125428676804*x + 1 pDZ2[100] := 473488614114606609692481*x^4 - 3816091203480414730368*x^3 + 4675044057591043528704*x^2 - 180353075186368512*x + 1048576 pDZ2[102] := 36088866774801*x^2 - 235117934802*x + 1 pDZ2[106] := 3063651608241*x^3 - 1037978353251*x^2 + 435385886643*x - 1 pDZ2[112] := 10743057735493363161989121*x^4 + 299409397266910313570697216*x^3 - 298726429226717360893722624*x^2 - 4612347048123521040384*x + 4294967296 pDZ2[114] := 3376787092396641*x^4 + 1770381989961948*x^3 + 398741995826982*x^2 - 1443155503716*x + 1 pDZ2[118] := 149845635801*x^3 + 822954608397*x^2 + 2586311755803*x - 1 pDZ2[126] := 197964928140001*x^4 - 207337865641764*x^3 + 38319587442086*x^2 - 8069499941220*x + 1 pDZ2[130] := 76869424485441*x^2 - 14061897471042*x + 1 pDZ2[138] := 17229935527596801*x^4 - 14984302448710404*x^3 + 35836612586630406*x^2 - 41644065516804*x + 1 pDZ2[142] := 79410676401*x^2 - 70824040716402*x + 1 pDZ2[148] := 384020356846259040377960110401*x^4 - 103170759869160007248587904*x^3 + 126372550352224149387565056*x^2 - 162448114480612245504*x + 1048576 pDZ2[150] := 452004825098667681*x^4 - 606729784918524516*x^3 + 291364883707242726*x^2 - 200396187475236*x + 1 pDZ2[154] := 42250625316085761*x^4 - 20830848935332356*x^3 - 4363524253584378*x^2 - 333599442487812*x + 1 pDZ2[158] := 1858108924530102184801*x^4 - 2281712837703306634404*x^3 - 1121413573997285594*x^2 - 551702398264804*x + 1 pDZ2[162] := 35971217755201*x^3 - 219777959990403*x^2 + 906642198235203*x - 1 pDZ2[178] := 1093889542148001*x^4 - 21882634090124004*x^3 + 17818847937804006*x^2 - 6234634589828004*x + 1 pDZ2[190] := 574497238815433521*x^2 - 25025929238011122*x + 1 pDZ2[198] := 9409543401845601*x^4 - 18003136343856804*x^3 + 75545914130176806*x^2 - 61693170788165604*x + 1 pDZ2[202] := 369265017730583601*x^3 + 325660112130352797*x^2 + 96203629755063603*x - 1 pDZ2[210] := 380060362198670345990721*x^4 - 135705612385364165677764*x^3 + 3522799708579459911366*x^2 - 230914817439264324*x + 1 pDZ2[214] := 513544015673940450969*x^3 + 21763436330004480909*x^2 + 355521109200228315*x - 1 pDZ2[226] := 1755339166248224384961*x^4 - 3134094586435642102596*x^3 + 40455290156701249350*x^2 - 1267167814902334404*x + 1 pDZ2[232] := 89281808967759133485558908068332113601*x^4 + 194253361693712575736321726522496*x^3 - 237937121192996675250748964665344*x^2 - 2476973907151703357128704*x + 1048576 pDZ2[238] := 504340294048978401*x^4 - 17429332140318855204*x^3 + 23130827104122775206*x^2 - 4368509227452898404*x + 1 pDZ2[258] := 61395997831472170172664801*x^4 + 22092941884753972021525596*x^3 + 2533066810920203102954406*x^2 - 32128416105297144804*x + 1 pDZ2[262] := 1617992242881191941401*x^3 - 369348371608839442803*x^2 + 47437372559975501403*x - 1 pDZ2[282] := 48271120627843103803553601*x^4 - 100781252659857179618340804*x^3 + 54020598864990823442020806*x^2 - 318812368107627233604*x + 1 pDZ2[298] := 2291453137369113201*x^3 + 78776699697794733597*x^2 + 1394914720951012153203*x - 1 pDZ2[310] := 152821422973976810308641*x^4 + 120077633973147044565276*x^3 + 1025210533154821631879526*x^2 - 4112298460537176993444*x + 1 pDZ2[322] := 22155100113214361601*x^4 - 100814667870313163724804*x^3 + 158687985978210780364806*x^2 - 11874583392970831001604*x + 1 pDZ2[330] := 7308737335700407817824981713921*x^4 - 6041257404040651042154930869764*x^3 + 17004856974729837164989685766*x^2 - 23817015520631479569924*x + 1 pDZ2[358] := 290877837707383677056601*x^3 - 405039766746888552073203*x^2 + 255253742231069747016603*x - 1 pDZ2[382] := 21736183418874580076001*x^4 - 1806838073503244712788004*x^3 + 908001797964989685348006*x^2 - 1812385890730153952636004*x + 1 pDZ2[418] := 78230538607337434246025981601*x^4 - 42556148956803529200808824804*x^3 - 434692265143391499084295194*x^2 - 30654941290726384532861604*x + 1 pDZ2[438] := 2094305648918065081711894416428001*x^4 - 3803338690150918149354489945044004*x^3 + 1802584840478517639408138912804006*x^2 - 139972172979280152984188004*x + 1 pDZ2[442] := 391874357394739680529328001*x^4 - 51308685882034098284624004*x^3 - 30159465140293895258735994*x^2 - 188855754244350221385968004*x + 1 pDZ2[462] := 2644828217712637497348427141271237601*x^4 - 1216195561077499256838465197523552804*x^3 + 19278152239466674500216050177392806*x^2 - 827786136705898952325077604*x + 1 pDZ2[466] := 83886321929356269367936627168161*x^4 - 10216199069430421626469530126786276*x^3 + 2080306977729719901985797915366*x^2 - 1108147592376994945800599460*x + 1 pDZ2[478] := 535196304598736009115605601*x^4 - 3759199038284250630245136804*x^3 + 5178640479867717315991456806*x^2 - 2638811031444134648461925604*x + 1 pDZ2[498] := 218127840724746276385531686554679201*x^4 + 353633870448297553387065801754842396*x^3 + 602457640105757531383793431034277606*x^2 - 10941197836746434157743799204*x + 1 pDZ2[522] := 85145947295510493730374742246401*x^4 - 17135573349488828795959539204*x^3 + 70797365901632277656428339206*x^2 - 58090118215773608060811046404*x + 1 pDZ2[562] := 1096463464227303658650796018401*x^4 - 2141075085409964866552119255204*x^3 + 1642270090770435959858282455206*x^2 - 863776782386717620232159218404*x + 1 pDZ2[598] := 893533281691483389794339381377162401*x^4 - 476379913154664204919707633735087204*x^3 + 2596362911193875991261796330687206*x^2 - 9042155034248583166783972762404*x + 1 pDZ2[658] := 289263936145924321653156293096001*x^4 - 70001137398395744034728630092088004*x^3 + 152249895651492275002582071624888006*x^2 - 389112016100170047890623425896004*x + 1 pDZ2[742] := 328436741535007770525762285392657636001*x^4 + 54532813571203233257999636309575491996*x^3 + 45453197114029339276087761685788108006*x^2 - 57138803647564970053630548021236004*x + 1 pDZ2[862] := 138932971068038885009222178111501212001*x^4 - 825888266374378582805733983469842276004*x^3 - 272325161001919236719916801564003083994*x^2 - 44629983271874494134178394855255852004*x + 1 (* Type E, N=4〜793, Mathematica 3.0が計算ミスを多発する． *) sumE[t_, limit_:Infinity] := (Sum[termm[n, 1/4, EX[t], EY[t], EZ2[t]],{n, 0, limit}] * Sqrt[EZ2[t]]); EX[4]:= Sqrt[(-112 + 81*Sqrt[2])/2]/2 EX[5]:= 3/4 EX[7]:= Sqrt[7]/2 EX[9]:= 9/4 EX[13]:= 23/4 EX[15]:= Sqrt[(3*(103 + 45*Sqrt[5]))/2]/2 EX[17]:= (3*(9 + 2*Sqrt[17]))/4 EX[21]:= (51 + 32*Sqrt[3])/4 EX[25]:= 205/4 EX[29]:= 127/4 + (211940278272 - 679477248*Sqrt[87])^(1/3)/192 + 2*(3743 + 12*Sqrt[87])^(1/3) EX[33]:= (327 + 58*Sqrt[33])/4 EX[37]:= 1123/4 EX[41]:= 465/4 + 18*Sqrt[41] + 3*Sqrt[(6025 + 941*Sqrt[41])/2] EX[45]:= (9*(167 + 96*Sqrt[3]))/4 EX[49]:= (7*(339 + 128*Sqrt[7]))/4 EX[53]:= 2459/4 + (1632759422386176 - 790232039424*Sqrt[159])^(1/3)/192 + 2*(28835569 + 13956*Sqrt[159])^(1/3) EX[57]:= (5619 + 746*Sqrt[57])/4 EX[61]:= 16925/12 + (19924721522966528 - 474954596352*Sqrt[183])^(1/3)/192 + (2*(9500847589 + 226476*Sqrt[183])^(1/3))/3 EX[65]:= 6297/4 + 195*Sqrt[65] + 3*Sqrt[(1098601 + 136265*Sqrt[65])/2] EX[69]:= 9231/4 + 1332*Sqrt[3] + Sqrt[3*(3556787 + 2053512*Sqrt[3])] EX[73]:= (26819 + 3138*Sqrt[73])/4 EX[77]:= 19275/4 + 1452*Sqrt[11] + 3*Sqrt[5159153 + 1555544*Sqrt[11]] EX[81]:= 36585/4 + (5418764133973622784 - 372494863171584*Sqrt[3])^(1/3)/192 + 18*(3*(43758033 + 3008*Sqrt[3]))^(1/3) EX[85]:= (77491 + 18792*Sqrt[17])/4 EX[93]:= (150831 + 87104*Sqrt[3])/4 EX[97]:= (31*(6717 + 682*Sqrt[97]))/4 EX[105]:= 194559/4 + (9495*Sqrt[105])/2 + 16*Sqrt[6*(3080797 + 300655*Sqrt[105])] EX[109]:= 1054501/12 + (4802712098173660168192 - 10735001247154176*Sqrt[327])^(1/3)/192 + (16*(4472874196408 + 9997749*Sqrt[327])^(1/3))/3 EX[113]:= 355227/4 + (16707*Sqrt[113])/2 + 3*Sqrt[2*(876241049 + 82429825*Sqrt[113])] EX[117]:= 476127/4 + 68724*Sqrt[3] + 3*Sqrt[3*(1049514363 + 605937400*Sqrt[3])] EX[121]:= 2540131/12 + (67134559768394233544704 - 507598303219679232*Sqrt[3])^(1/3)/192 + (44*(11*(273309991609 + 2066472*Sqrt[3]))^(1/3))/3 EX[133]:= (2931819 + 672608*Sqrt[19])/4 EX[137]:= 1921077/4 + 41031*Sqrt[137] + 3*Sqrt[(102511479721 + 8758146781*Sqrt[137])/2] EX[141]:= 2507607/4 + 361944*Sqrt[3] + 2*Sqrt[3*(65504478515 + 37819028304*Sqrt[3])] EX[145]:= 3261097/4 + 67705*Sqrt[145] + Sqrt[(2658679256881 + 220791294665*Sqrt[145])/2] EX[153]:= 5456727/4 + (661725*Sqrt[17])/2 + 9*Sqrt[6*(7658381851 + 1857430429*Sqrt[17])] EX[157]:= 28092077/12 + (90805026667384127394676736 - 1969881467609677824*Sqrt[471])^(1/3)/192 + (2*(43299210866634429643 + 939312681012*Sqrt[471])^(1/3))/3 EX[165]:= 11523759/4 + 868644*Sqrt[11] + Sqrt[3*(5533248710515 + 1668337258536*Sqrt[11])] EX[169]:= 58780943/12 + (831896096040594002992431104 - 908625213186618949632*Sqrt[3])^(1/3)/192 + (26*(13*(13888833386655607 + 15169856256*Sqrt[3]))^(1/3))/3 EX[177]:= (47389527 + 3562034*Sqrt[177])/4 EX[193]:= (119404627 + 8594934*Sqrt[193])/4 EX[205]:= 116460447/4 + 4547016*Sqrt[41] + Sqrt[2*(847689367191593 + 132386837387283*Sqrt[41])] EX[213]:= 179861631/4 + 25960788*Sqrt[3] + Sqrt[3*(1347928872381971 + 778227097318200*Sqrt[3])] EX[217]:= 222838127/4 + 10005728*Sqrt[31] + (161*Sqrt[7*(136835638295 + 24576406144*Sqrt[31])])/2 EX[225]:= 340057845/4 + 21950640*Sqrt[15] + 30*Sqrt[3*(5353672940955 + 1382312409424*Sqrt[15])] EX[253]:= (2822457127 + 851002848*Sqrt[11])/4 EX[265]:= 2534831485/4 + 38928365*Sqrt[265] + Sqrt[(1606342618726429681 + 98676842664590725*Sqrt[265])/2] EX[273]:= 3718164819/4 + (112516807*Sqrt[273])/2 + 48*Sqrt[2*(375020403232679 + 22697267334897*Sqrt[273])] EX[277]:= 5991601867/4 + (23787705655540625240860778507010048 - 504464540473712990748672*Sqrt[831])^(1/3)/192 + 2*(420105998702236903876918837 + 8909164366434468*Sqrt[831])^(1/3) EX[289]:= 7869174081/4 + 477138762*Sqrt[17] + 17*Sqrt[2*(13391847019994177 + 3247999987385241*Sqrt[17])] EX[301]:= 13622369731/4 + 519347980*Sqrt[43] + Sqrt[23196119813802309209 + 3537375108868656136*Sqrt[43]] EX[313]:= 23327652377/4 + 329639218*Sqrt[313] + Sqrt[(136044841405258383697 + 7689709083721858189*Sqrt[313])/2] EX[333]:= 55910862027/4 + 8070037812*Sqrt[3] + 3*Sqrt[3*(14472335611200673107 + 8355606860929315736*Sqrt[3])] EX[337]:= 66380476219/4 + (1807987475*Sqrt[337])/2 + Sqrt[2*(275397976358884818721 + 15001883698000560089*Sqrt[337])] EX[345]:= 93285285459/4 + (2511155525*Sqrt[345])/2 + 720*Sqrt[6*(349719676635877 + 18828274469439*Sqrt[345])] EX[357]:= 154275226827/4 + 9354309786*Sqrt[17] + 8*Sqrt[6*(7747671216541578733 + 1879086281079917853*Sqrt[17])] EX[385]:= 483313301871/4 + (12315963345*Sqrt[385])/2 + 16*Sqrt[2*(57029235275886529319 + 2906478958819112985*Sqrt[385])] EX[397]:= 1037939434023/4 + (123662991699136551391359367488981486796800 - 222196427328895265326453751808*Sqrt[1191])^(1/3)/192 + 4*(272995877484781988001221567368025 + 490516263751840735644*Sqrt[1191])^(1/3) EX[445]:= 4892214629403/4 + 129643428393*Sqrt[89] + 2*Sqrt[2*(373965062167981293538373 + 39640217309450678489769*Sqrt[89])] EX[457]:= 7625137620977/4 + 89172223326*Sqrt[457] + 3*Sqrt[(1615075659420372755496073 + 75550052758992477147677*Sqrt[457])/2] EX[505]:= 42560110023709/4 + 473475009695*Sqrt[505] + Sqrt[(452840741302583945084891209 + 20151148505876498242792645*Sqrt[505])/2] EX[553]:= 219297959306027/4 + 20721709405280*Sqrt[7] + (7*Sqrt[79*(6211779250296298944112943 + 2347831870787893222811008*Sqrt[7])])/2 EX[577]:= 484677078339227/4 + (10088685390383*Sqrt[577])/2 + Sqrt[2*(14681991891712149455475398497 + 611219319911806393932412993*Sqrt[577])] EX[697]:= 20371115782852011/4 + (385805515860361*Sqrt[697])/2 + 324*Sqrt[494139563136290584244119529 + 18716870601981290877473880*Sqrt[697]] EX[793]:= 323090083874404869/4 + 2868316320866425*Sqrt[793] + 3*Sqrt[(2899644508276943204253874724383537 + 102969395631895282171240897567421*Sqrt[793])/2] EY[4]:= 4991/(4*Sqrt[71476 + 50787*Sqrt[2]]) EY[5]:= 5 EY[7]:= (65*Sqrt[7])/16 EY[9]:= 21 EY[13]:= 65 EY[15]:= (35*Sqrt[(3*(787 + 351*Sqrt[5]))/2])/16 EY[17]:= 5*(17 + 4*Sqrt[17]) EY[21]:= 7*(27 + 16*Sqrt[3]) EY[25]:= 805 EY[29]:= 1595/3 + (3975225344 - 4988928*Sqrt[87])^(1/3)/3 + (16*(58*(16733 + 21*Sqrt[87]))^(1/3))/3 EY[33]:= 5*(297 + 52*Sqrt[33]) EY[37]:= 5365 EY[41]:= 2337 + 364*Sqrt[41] + 8*Sqrt[82*(2081 + 325*Sqrt[41])] EY[45]:= 15*(527 + 304*Sqrt[3]) EY[49]:= 7*(1863 + 704*Sqrt[7]) EY[53]:= 14045 + (74634365952000 - 12536832000*Sqrt[159])^(1/3)/3 + (80*(106*(458397 + 77*Sqrt[159]))^(1/3))/3^(2/3) EY[57]:= 65*(513 + 68*Sqrt[57]) EY[61]:= 103883/3 + (1121774134206464 - 6921510912*Sqrt[183])^(1/3)/3 + (16*(122*(2244841297 + 13851*Sqrt[183]))^(1/3))/3 EY[65]:= 5*(7969 + 988*Sqrt[65] + 8*Sqrt[26*(76277 + 9461*Sqrt[65])]) EY[69]:= 60237 + 34776*Sqrt[3] + 8*Sqrt[138*(822182 + 474687*Sqrt[3])] EY[73]:= 5*(35989 + 4212*Sqrt[73]) EY[77]:= 5*(26565 + 8008*Sqrt[11] + 8*Sqrt[154*(143182 + 43171*Sqrt[11])]) EY[81]:= 258633 + (467159029453651968 - 7548758654976*Sqrt[3])^(1/3)/3 + 288*(724308397 + 11704*Sqrt[3])^(1/3) EY[85]:= 35*(16031 + 3888*Sqrt[17]) EY[93]:= 1085*(1053 + 608*Sqrt[3]) EY[97]:= 5*(322137 + 32708*Sqrt[97]) EY[105]:= 5*(313173 + 30564*Sqrt[105] + 32*Sqrt[42*(4561051 + 445113*Sqrt[105])]) EY[109]:= 8646643/3 + (646457373042995888128 - 315846088556544*Sqrt[327])^(1/3)/3 + (32*(109*(180993700791944 + 88429887*Sqrt[327]))^(1/3))/3 EY[113]:= 5*(593137 + 55796*Sqrt[113] + 64*Sqrt[113*(1520164 + 143005*Sqrt[113])]) EY[117]:= 15*(269659 + 155688*Sqrt[3] + 24*Sqrt[26*(9710994 + 5606645*Sqrt[3])]) EY[121]:= 21945319/3 + (10568882546816156434432 - 17117788792946688*Sqrt[3])^(1/3)/3 + (704*(22*(1376855657129 + 2230011*Sqrt[3]))^(1/3))/3 EY[133]:= 35*(758727 + 174064*Sqrt[19]) EY[137]:= 5*(3531997 + 301756*Sqrt[137] + 8*Sqrt[274*(1422773377 + 121555733*Sqrt[137])]) EY[141]:= 23386401 + 13502160*Sqrt[3] + 16*Sqrt[141*(30304358809 + 17496229716*Sqrt[3])] EY[145]:= 5*(6168329 + 512252*Sqrt[145] + 8*Sqrt[58*(20500135781 + 1702443613*Sqrt[145])]) EY[153]:= 15*(3534079 + 857140*Sqrt[17] + 64*Sqrt[51*(119578264 + 29001989*Sqrt[17])]) EY[157]:= 276454235/3 + (21128542078382767619072000 - 77134040957952000*Sqrt[471])^(1/3)/3 + (80*(314*(131422559703316379 + 479784789*Sqrt[471]))^(1/3))/3 EY[165]:= 5*(23251833 + 7010712*Sqrt[11] + 56*Sqrt[66*(5224268590 + 1575176247*Sqrt[11])]) EY[169]:= 600163655/3 + (216176746228249189389074432 - 48518006776311840768*Sqrt[3])^(1/3)/3 + (2912*(13*(673428530171563 + 151142112*Sqrt[3]))^(1/3))/3 EY[177]:= 265*(1868589 + 140452*Sqrt[177]) EY[193]:= 65*(20043629 + 1442772*Sqrt[193]) EY[205]:= 35*(37417707 + 5843664*Sqrt[41] + 16*Sqrt[41*(266784431246 + 41664728241*Sqrt[41])]) EY[213]:= 5*(412333281 + 238060728*Sqrt[3] + 8*Sqrt[426*(12472042938842 + 7200737348085*Sqrt[3])]) EY[217]:= 35*(73661611 + 13230016*Sqrt[31] + 4*Sqrt[217*(3125595020465 + 561373437664*Sqrt[31])]) EY[225]:= 15*(267080807 + 68959968*Sqrt[15] + 96*Sqrt[2*(7740034431000 + 1998468296689*Sqrt[15])]) EY[253]:= 1495*(23585023 + 7111152*Sqrt[11]) EY[265]:= 5*(6481744445 + 398170396*Sqrt[265] + 88*Sqrt[106*(102362902547453 + 6288103117985*Sqrt[265])]) EY[273]:= 5*(9650056689 + 584048036*Sqrt[273] + 9504*Sqrt[182*(11329363421 + 685684267*Sqrt[273])]) EY[277]:= 78320006285 + (12971252254796864403384429259776000 - 33523828097392475136000*Sqrt[831])^(1/3)/3 + 2160*(554*(86049256637445881807 + 222391827*Sqrt[831]))^(1/3) EY[289]:= 17*(6180434865 + 1498975632*Sqrt[17] + 32*Sqrt[2*(37302514746963617 + 9047188729581849*Sqrt[17])]) EY[301]:= 185620438297 + 28306851496*Sqrt[43] + 184*Sqrt[602*(3381033287918710 + 515602742654549*Sqrt[43])] EY[313]:= 5*(64828068277 + 3664299068*Sqrt[313] + 8*Sqrt[626*(209798244651342889 + 11858497911277477*Sqrt[313])]) EY[333]:= 105*(7631657777 + 4406139672*Sqrt[3] + 24*Sqrt[74*(2732835980861526 + 1577803589201497*Sqrt[3])]) EY[337]:= 5*(191414657729 + 10427020820*Sqrt[337] + 32*Sqrt[674*(106174573420683037 + 5783697553631357*Sqrt[337])]) EY[345]:= 5*(272171453373 + 14653218580*Sqrt[345] + 864*Sqrt[690*(287632905141079 + 15485635056437*Sqrt[345])]) EY[357]:= 35*(65411203671 + 15864547248*Sqrt[17] + 18224*Sqrt[6*(4294331986573 + 1041528492477*Sqrt[17])]) EY[385]:= 35*(212804569791 + 10845525132*Sqrt[385] + 352*Sqrt[2*(365490903609023471 + 18627141252033873*Sqrt[385])]) EY[397]:= 16242659756065 + (115700491847968452494454961970597928960000 - 30138614987027182035738624000*Sqrt[1191])^(1/3)/3 + 4320*(794*(66942156400731667297689565 + 17437643055261*Sqrt[1191]))^(1/3) EY[445]:= 5*(16210834966701 + 1718345069784*Sqrt[89] + 8*Sqrt[178*(46136090293968962231983 + 4890415790338910130789*Sqrt[89])]) EY[457]:= 5*(25605052075837 + 1197753816636*Sqrt[457] + 648*Sqrt[914*(3416529028697077801 + 159818487056717021*Sqrt[457])]) EY[505]:= 5*(150234026823413 + 6685326449308*Sqrt[505] + 152*Sqrt[202*(9672262321182510289901 + 430410024198126046841*Sqrt[505])]) EY[553]:= 5*(810059711578117 + 306173791992640*Sqrt[7] + 196*Sqrt[553*(61776996203552237585609 + 23349509814168652587616*Sqrt[7])]) EY[577]:= 5*(1828774952622937 + 76132897433684*Sqrt[577] + 32*Sqrt[1154*(5660369210593783480584469 + 235644253509079045169149*Sqrt[577])]) EY[697]:= 35*(12068493010227243 + 457126769205964*Sqrt[697] + 85536*Sqrt[1394*(28561133172414716689 + 1081830061210052115*Sqrt[697])]) EY[793]:= 5*(1429157523014378469 + 50750871697377020*Sqrt[793] + 648*Sqrt[1586*(6133904363958485354642138881 + 217821330655449483013747277*Sqrt[793])]) EZ2[4]:= (64*(884 + 627*Sqrt[2]))/194481 EZ2[5]:= 1/4 EZ2[6]:= 65209376/2518569 + 12754624/(279841*Sqrt[3]) - Sqrt[11472312970846208/2114396602587 + 6622669099171840/(704798867529*Sqrt[3])]/2 EZ2[7]:= 256/3969 EZ2[8]:= 71905429355264/620512135426561 - (42963403308800*Sqrt[2])/620512135426561 + Sqrt[-437638659042945688690708480000/385035310211630778817424286721 + (309808840225982016197857280000*Sqrt[2])/385035310211630778817424286721]/2 EZ2[9]:= 1/48 EZ2[10]:= 18693728/24935067 + (28426720*Sqrt[10])/74805201 - Sqrt[4928951354163200/621757566294489 + (465997565132800*Sqrt[10])/207252522098163]/2 EZ2[11]:= -140016/290521 + (64*(282619266417 + 59774986271*Sqrt[33])^(1/3))/(290521*3^(2/3)) - 1492364288/(290521*(3*(282619266417 + 59774986271*Sqrt[33]))^(1/3)) EZ2[12]:= 1258653213377536/12289813296489 + (171421605361600*Sqrt[2/3])/1365534810721 - Sqrt[4227824857404220793330790400000/50346503620852607006575707 + (1726001689366489162168893440000*Sqrt[2/3])/16782167873617535668858569]/2 EZ2[13]:= 1/324 EZ2[15]:= 512/(9*(21367 + 9555*Sqrt[5])) EZ2[16]:= 664758272/949132107 - (469755392*Sqrt[2])/949132107 + Sqrt[-109522299278907932672/8107665808844335041 + (8604885009323196416*Sqrt[2])/900851756538259449]/2 EZ2[17]:= 1/(8*(103 + 25*Sqrt[17])) EZ2[18]:= 758949071875521824/34700535004437432001 + (4051080881437189600*Sqrt[2])/34700535004437432001 - Sqrt[133219281202364428432379049841582080000/1204127129594187528941331872763498864001 + (24331500928441886596378427908915200000*Sqrt[2])/1204127129594187528941331872763498864001]/2 EZ2[19]:= -1744/87723 - 2911232/(87723*(1896929 + 1309347*Sqrt[57])^(1/3)) + (64*(1896929 + 1309347*Sqrt[57])^(1/3))/87723 EZ2[21]:= 1/(36*(97 + 56*Sqrt[3])) EZ2[22]:= 1497518432/280557433443 + (61699745600*Sqrt[11])/2525016900987 - Sqrt[1512033431590106782720000/57381393152429940254167521 + (2194937589839667200000*Sqrt[11])/2125236783423331120524723]/2 EZ2[23]:= -343131204352/496573444227 + (18122107374498035944742322176000000 - 2181424841154469445724930048000000*Sqrt[69])^(1/3)/496573444227 + (35200*2^(2/3)*(103877315475372359993 + 12504095231733139839*Sqrt[69])^(1/3))/496573444227 EZ2[25]:= 1/25920 EZ2[27]:= -5887856/4097152081 - (403998400*2^(1/3))/12291456243 + (331942400*2^(2/3))/12291456243 EZ2[28]:= 958148985900285952/137516724173557323 + (80488958642435200*Sqrt[2])/15279636019284147 - Sqrt[10118868730537688603026974220042240000/24313949263833743572022376471762423 + (2379710532349609738193114241433600000*Sqrt[2])/8104649754611247857340792157254141]/2 EZ2[29]:= -10685/28812 - (661862*2^(2/3))/(7203*(1258728979 + 138002277*Sqrt[87])^(1/3)) + (2*(2*(1258728979 + 138002277*Sqrt[87]))^(1/3))/7203 EZ2[31]:= -32216576/18915363 - (2281246114048*(2/(29301543701107 + 5665538633157*Sqrt[93]))^(1/3))/18915363 + (1408*2^(2/3)*(29301543701107 + 5665538633157*Sqrt[93])^(1/3))/18915363 EZ2[33]:= 1/(72*(1867 + 325*Sqrt[33])) EZ2[37]:= 1/777924 EZ2[39]:= -363732800/863869167 + (355812544*Sqrt[13])/2015694723 - Sqrt[-1343340125073276928/12189075648990140187 + (142858306456027136*Sqrt[13])/1741296521284305741]/2 EZ2[41]:= -1593/1024 - (221*Sqrt[41])/1024 + Sqrt[2247425/131072 + (355589*Sqrt[41])/131072]/2 EZ2[43]:= -1744592/87381674667 - 58915182899200/(87381674667*(15274386853685 + 219952620570123*Sqrt[129])^(1/3)) + (3200*(15274386853685 + 219952620570123*Sqrt[129])^(1/3))/87381674667 EZ2[45]:= 1/(4*(693721 + 400520*Sqrt[3])) EZ2[49]:= 1/(1296*(5355 + 2024*Sqrt[7])) EZ2[53]:= -18433117/421836492 - (339046664750*2^(2/3))/(105459123*(1133179095206057 + 109535434481319*Sqrt[159])^(1/3)) + (50*(2*(1133179095206057 + 109535434481319*Sqrt[159]))^(1/3))/105459123 EZ2[55]:= 662256448/425758707 + (131103680*Sqrt[5])/141919569 - Sqrt[42424908375735500800/1631434289276806641 + (6431565230914764800*Sqrt[5])/543811429758935547]/2 EZ2[57]:= 1/(72*(542267 + 71825*Sqrt[57])) EZ2[58]:= 38059347232238774488864/69970626802003773543804341361 + (2499778969900716385824800*Sqrt[58])/23323542267334591181268113787 - Sqrt[1449725758322302540034242794616230943486672916480000/543987623896143202406056572399502262036341309896779481369 + (83759044299110439068041142569284027814297600000*Sqrt[58])/181329207965381067468685524133167420678780436632259827123]/2 EZ2[61]:= -637/972 - (19262*2^(2/3))/(243*(1276511 + 136629*Sqrt[183])^(1/3)) + (2*(2*(1276511 + 136629*Sqrt[183]))^(1/3))/243 EZ2[63]:= 31197244714922752/177386568725523 + (2264813310032000*Sqrt[21])/59128856241841 - Sqrt[863429100696996683791636029440000/3496221640468299386279069281 + (1695747062921118759923028869120000*Sqrt[7/3])/10488664921404898158837207843]/2 EZ2[65]:= 7875789/9834496 + (1011245*Sqrt[65])/9834496 - Sqrt[64177137301225/12089663946752 + (7973273210825*Sqrt[65])/12089663946752]/2 EZ2[67]:= -290256592/2418771342122667 - 49332578794023500800/(2418771342122667*(70344605314508455477 + 10467277685513608820679*Sqrt[201])^(1/3)) + (17600*(70344605314508455477 + 10467277685513608820679*Sqrt[201])^(1/3))/2418771342122667 EZ2[69]:= -215995/527076 + 10943/(14641*Sqrt[3]) - Sqrt[-918715312/5787689787 + 536729288/(1929229929*Sqrt[3])]/2 EZ2[73]:= 1/(648*(1368963 + 160225*Sqrt[73])) EZ2[77]:= 431733509/25542916 + (32568575*Sqrt[11])/6385729 - Sqrt[13324247419010000/5825362123063 + (4017415281605000*Sqrt[11])/5825362123063]/2 EZ2[81]:= -15879/614656 + (11*(19932707204391 + 170191378464352*Sqrt[3])^(1/3))/(614656*3^(2/3)) - 33730358783/(614656*(3*(19932707204391 + 170191378464352*Sqrt[3]))^(1/3)) EZ2[85]:= 1/(324*(22861961 + 5544840*Sqrt[17])) EZ2[93]:= 1/(36*(779824009 + 450231600*Sqrt[3])) EZ2[97]:= 1/(648*(82547463 + 8381425*Sqrt[97])) EZ2[105]:= 124297/56448 - 1955/(336*Sqrt[7]) - Sqrt[8145572875/265531392 - 192420875/(2370816*Sqrt[7])]/2 EZ2[109]:= -34730141/189035532 - 34820175884/(47258883*(2495264529645208 + 137991770826651*Sqrt[327])^(1/3)) + (52*(2495264529645208 + 137991770826651*Sqrt[327])^(1/3))/47258883 EZ2[113]:= -1355306033511/143986855936 - (127471048575*Sqrt[113])/143986855936 + Sqrt[1836488204261531860410625/2591526835291802304512 + (172762288068473713155625*Sqrt[113])/2591526835291802304512]/2 EZ2[117]:= 127041583/3358092 + (6324925*Sqrt[3])/279841 - Sqrt[927985084130000/78310985281 + 4823209086085000/(234932955843*Sqrt[3])]/2 EZ2[121]:= 349393/9335088 - (776702767*(11/(2*(-1583842860973 + 2519280273321*Sqrt[3])))^(1/3))/583443 + (19*((-1583842860973 + 2519280273321*Sqrt[3])/11)^(1/3))/(583443*2^(2/3)) EZ2[133]:= 1/(324*(32729602601 + 7508685800*Sqrt[19])) EZ2[137]:= -626369238269/575947423744 - (53484396225*Sqrt[137])/575947423744 + Sqrt[392118862514451132495625/41464429364668836872192 + (33500990998845323208125*Sqrt[137])/41464429364668836872192]/2 EZ2[141]:= 66747215/3455476668 - (7295618*Sqrt[3])/671898241 - Sqrt[-170889447927292336/4063025216330046729 + 14095071897852352/(193477391253811749*Sqrt[3])]/2 EZ2[145]:= -10379/36864 + (9685*Sqrt[145])/331776 - Sqrt[-645162325/509607936 + (163219225*Sqrt[145])/1528823808]/2 EZ2[153]:= 8505734611/2135179264 + (2409525925*Sqrt[17])/2135179264 - Sqrt[84968882649363635625/569873811176947712 + (20629227261902829375*Sqrt[17])/569873811176947712]/2 EZ2[157]:= 2850472003/10260432972 - (2241737944060450*2^(2/3))/(2565108243*(-8465280388610221741 + 663077216762762787*Sqrt[471])^(1/3)) + (550*(2*(-8465280388610221741 + 663077216762762787*Sqrt[471]))^(1/3))/2565108243 EZ2[163]:= -517692085968592/7694380706227248880627370667 - 2308017004855871751481902727299788800/(7694380706227248880627370667*(399115977617490956505931934002701852469 + 50849929890726229380141492926956988287108311*Sqrt[489])^(1/3)) + (2134400*(399115977617490956505931934002701852469 + 50849929890726229380141492926956988287108311*Sqrt[489])^(1/3))/7694380706227248880627370667 EZ2[165]:= 113428027/1494108 - 11518055/(26411*Sqrt[33]) - Sqrt[104957041251044200/2278866188907 - 2610096530996200/(9865221597*Sqrt[33])]/2 EZ2[169]:= -5874761/151797888 - (17501786141*(13/(17691809097613 + 10232674195656*Sqrt[3]))^(1/3))/303595776 + (931*((17691809097613 + 10232674195656*Sqrt[3])/13)^(1/3))/303595776 EZ2[177]:= 1/(72*(38480821035067 + 2892395628525*Sqrt[177])) EZ2[193]:= 1/(648*(27144203929863 + 1953882553025*Sqrt[193])) EZ2[205]:= -298634453/99740268 + (11722270*Sqrt[41])/24935067 - Sqrt[-4178573951079533600/5595818096650401 + (72509390583523600*Sqrt[41])/621757566294489]/2 EZ2[213]:= 76121787472374029/719740625895581796 - 3661389839761025/(19992795163766161*Sqrt[3]) - Sqrt[-2513533108042751819161981593730000/10792220178428413103862328194303867 + 1451189038227853461253919828215000/(3597406726142804367954109398101289*Sqrt[3])]/2 EZ2[217]:= -28461983/839808 + (1352575*Sqrt[7])/104976 - Sqrt[1510565888260625/176319369216 - (35683109065625*Sqrt[7])/11019960576]/2 EZ2[225]:= 318263221/1687345968 + (37565831*Sqrt[15])/140612164 - Sqrt[2894638208857060/1235736291547681 + (20925944252637841*Sqrt[5/3])/7414417749286086]/2 EZ2[253]:= 1/(777924*(12633605109401 + 3809175263400*Sqrt[11])) EZ2[265]:= -8596013080531/120326507790336 + (562364627825*Sqrt[265])/120326507790336 - Sqrt[-15534812587913818596068375/1809808559627223762166874112 + (963880677890112055484125*Sqrt[265])/1809808559627223762166874112]/2 EZ2[273]:= 90978561713844257/6793752766243968 - 716388626635825/(20219502280488*Sqrt[7]) - Sqrt[5450648688450021595220326422366875/3846256387403963942140874698752 - 64379736221511212881579707918125/(17170787443767696170271762048*Sqrt[7])]/2 EZ2[277]:= -3009262289513597/3809277878631372 + (6239719223945683240782978477056250482571918928256237568000000 - 192576043100921965211663486707672206192733158739083264000000*Sqrt[831])^(1/3)/399882754587206907072 + (50*(2*(337112614472666952110830440753085329073 + 10404284398793955709426381000645603629*Sqrt[831]))^(1/3))/952319469657843 EZ2[289]:= -37243691/37933056 - (62924389*Sqrt[17])/265531392 + Sqrt[608748560109978497/79320285154639872 + 39840478057840471/(1259052145311744*Sqrt[17])]/2 EZ2[301]:= 862928158429/30291880485636 + (10407502829*Sqrt[43])/2524323373803 - Sqrt[619532968937388291088/101146166595685086772743 + (861521730584371754552*Sqrt[43])/910315499361165780954687]/2 EZ2[313]:= -77282493952409/158259620496384 - (4159962443125*Sqrt[313])/158259620496384 + Sqrt[5643372243377304548724210625/3130763434957435834319634432 + (324386108657966198859128125*Sqrt[313])/3130763434957435834319634432]/2 EZ2[333]:= 1316873314217603983/211883798992451114892 + (2615030721359132825*Sqrt[3])/17656983249370926241 - Sqrt[-17883348752889305081577520898595610000/311769057468565472849040660294262390081 + 540236426172956964946931762816670425000/(935307172405696418547121980882787170243*Sqrt[3])]/2 EZ2[337]:= 435269210429/1032386052096 - (52518135275*Sqrt[337])/1032386052096 + Sqrt[-698806456123583995424375/133227620070295603249152 + (45683631770569819450625*Sqrt[337])/133227620070295603249152]/2 EZ2[345]:= 46795449081941826653/2215180831773837312 - (503438864035406195*Sqrt[5/3])/30766400441303296 - Sqrt[1459724752325146351277566126781181311875/408918843121519143442396394120282112 - (23556206899175153476614711211653394375*Sqrt[5/3])/8519142565031648821716591544172544]/2 EZ2[357]:= 35468407180960542158250929/101021624635973177122596 - 1706474534549945821626350/(2806156239888143808961*Sqrt[3]) - Sqrt[209635551122220092461072945583266264302681714680000/212611846751905473983134834400351338125287067 - 121033141872129323857042489837261782775431021860000/(70870615583968491327711611466783779375095689*Sqrt[3])]/2 EZ2[385]:= 771240933665935963/2136219299210322432 - (39244400210646085*Sqrt[385])/2136219299210322432 - Sqrt[8304344773218275248948496487292975/8912954871716095854582550510551552 - (423228015901120460195597824817425*Sqrt[385])/8912954871716095854582550510551552]/2 EZ2[397]:= -803894147252244903197/153498526877774106965772 - (6473122211610779480259083334288740500*2^(2/3))/(38374631719443526741443*(1310359622078022628241676192552769975088197927073 + 95190505027137284558312360480363428954129049313*Sqrt[1191])^(1/3)) + (39100*(2*(1310359622078022628241676192552769975088197927073 + 95190505027137284558312360480363428954129049313*Sqrt[1191]))^(1/3))/38374631719443526741443 EZ2[445]:= -651526277/1627083612 + (40308535*Sqrt[89])/949132107 - Sqrt[-3600535832912347400/900851756538259449 + (6058032606464600*Sqrt[89])/14299234230766023]/2 EZ2[457]:= -162620540661648809/78714290673091584 - (8096001844640125*Sqrt[457])/78714290673091584 + Sqrt[27591597292225267400775553238310625/774492444520994091515375056453632 + (1345027131651382906927471199703125*Sqrt[457])/774492444520994091515375056453632]/2 EZ2[505]:= -10295778868309411/59589387451109376 + (458406559732745*Sqrt[505])/59589387451109376 - Sqrt[-6309037292396009698081619878775/443861887099803946885586639388672 + (280749179292638909491730769925*Sqrt[505])/443861887099803946885586639388672]/2 EZ2[553]:= -958604741365339/284935187787264 + (47231979605525*Sqrt[79])/124659144656928 - Sqrt[7949530675677082068189949139375/142079107168885949538911059968 - (27949730034943191955140464375*Sqrt[79])/4439972099027685923090970624]/2 EZ2[577]:= -2325997465520284844010871/9233809203722754410090496 - (98107818279333735988375*Sqrt[577])/9233809203722754410090496 + Sqrt[5481380096241442874111065698955414819331979750625/10657904051344380982040911249071829608272863690752 + (228223767054180855716352063485654557273530930625*Sqrt[577])/10657904051344380982040911249071829608272863690752]/2 EZ2[697]:= -4599554209541892166451/219910931627182718976 + (64457014085228239475*Sqrt[697])/73303643875727572992 - Sqrt[2467014963292338263035282253706603369510625/671678025682436564827850226307335979008 - (30968983883182789741671474253522975230625*Sqrt[697])/223892675227478854942616742102445326336]/2 EZ2[793]:= -19359497172023980239251/24006358164176378597376 + (823316262125539457225*Sqrt[793])/24006358164176378597376 - Sqrt[-152614793117352117469328141011203157323164375/72038154038339733307271940320617540639260672 + (5679325223622782805028399861195858481943125*Sqrt[793])/72038154038339733307271940320617540639260672]/2 pEX[4] := 32*x^4 + 896*x^2 - 289 pEX[5] := 4*x - 3 pEX[7] := 4*x^2 - 7 pEX[9] := 4*x - 9 pEX[13] := 4*x - 23 pEX[15] := 16*x^4 - 1236*x^2 + 1089 pEX[17] := 16*x^2 - 216*x + 117 pEX[21] := 16*x^2 - 408*x - 471 pEX[25] := 4*x - 205 pEX[29] := 64*x^3 - 6096*x^2 + 8460*x - 4671 pEX[33] := 16*x^2 - 2616*x - 4083 pEX[37] := 4*x - 1123 pEX[41] := 256*x^4 - 119040*x^3 + 74592*x^2 + 22896*x - 406863 pEX[45] := 16*x^2 - 12024*x + 19521 pEX[49] := 16*x^2 - 18984*x + 11417 pEX[53] := 64*x^3 - 118032*x^2 + 342828*x - 799011 pEX[57] := 16*x^2 - 44952*x - 148251 pEX[61] := 64*x^3 - 270800*x^2 - 848884*x - 683743 pEX[65] := 256*x^4 - 1612032*x^3 + 9963360*x^2 - 39012624*x + 50385969 pEX[69] := 256*x^4 - 2363136*x^3 - 8142240*x^2 + 12956688*x - 8859231 pEX[73] := 16*x^2 - 214552*x + 424549 pEX[77] := 256*x^4 - 4934400*x^3 + 19114848*x^2 - 104893488*x - 362449647 pEX[81] := 64*x^3 - 1756080*x^2 - 6593076*x - 6882489 pEX[85] := 16*x^2 - 619928*x + 1487593 pEX[93] := 16*x^2 - 1206648*x - 11329887 pEX[97] := 16*x^2 - 1665816*x + 1019621 pEX[105] := 256*x^4 - 49807104*x^3 - 613252128*x^2 + 696893904*x + 4712254281 pEX[109] := 64*x^3 - 16872016*x^2 + 32733644*x - 86825063 pEX[113] := 256*x^4 - 90938112*x^3 + 1192407264*x^2 - 18432433008*x - 56046143943 pEX[117] := 256*x^4 - 121888512*x^3 - 92060064*x^2 + 733723920*x + 1003437153 pEX[121] := 64*x^3 - 40642096*x^2 - 235776244*x - 446059361 pEX[133] := 16*x^2 - 23454552*x - 66262855 pEX[137] := 256*x^4 - 491795712*x^3 + 14649899616*x^2 - 400236449616*x + 873735365889 pEX[141] := 256*x^4 - 641947392*x^3 - 23914049952*x^2 - 152015673456*x - 351261727839 pEX[145] := 256*x^4 - 834840832*x^3 + 748069728*x^2 + 11338655728*x + 17527070321 pEX[153] := 256*x^4 - 1396922112*x^3 + 6177334752*x^2 - 8947909296*x + 8890266537 pEX[157] := 64*x^3 - 449473232*x^2 + 2597413772*x - 3934480495 pEX[165] := 256*x^4 - 2950082304*x^3 - 138745984416*x^2 + 458015315472*x + 2759827167009 pEX[169] := 64*x^3 - 940495088*x^2 + 3598020140*x - 30362630077 pEX[177] := 16*x^2 - 379116216*x - 23991152883 pEX[193] := 16*x^2 - 955237016*x - 2910611579 pEX[205] := 256*x^4 - 29813874432*x^3 + 474924688480*x^2 - 2193035198448*x + 3138535421761 pEX[213] := 256*x^4 - 46044577536*x^3 - 5363464941984*x^2 + 44205274005264*x - 98205142134303 pEX[217] := 256*x^4 - 57046560512*x^3 - 311871972384*x^2 + 278083276496*x + 2383311785033 pEX[225] := 256*x^4 - 87054808320*x^3 - 11181693600*x^2 + 817703262000*x + 1505316200625 pEX[253] := 16*x^2 - 22579657016*x - 86592128015 pEX[265] := 256*x^4 - 648916860160*x^3 + 12529920135264*x^2 - 44048299021520*x + 259738193117729 pEX[273] := 256*x^4 - 951850193664*x^3 - 326852928669984*x^2 - 674549317952496*x + 8111655856070361 pEX[277] := 64*x^3 - 287596889616*x^2 - 1036613914452*x - 1014479555891 pEX[289] := 256*x^4 - 2014508564736*x^3 + 19172916339808*x^2 - 772773966063120*x - 2906562230539199 pEX[301] := 256*x^4 - 3487326651136*x^3 - 156663591214752*x^2 - 2832128856316592*x - 13663630205324239 pEX[313] := 256*x^4 - 5971879008512*x^3 - 41798804844192*x^2 - 158840078773264*x + 870062415750737 pEX[333] := 256*x^4 - 14313180678912*x^3 - 424544273568*x^2 + 171903081022416*x + 1172551809705489 pEX[337] := 256*x^4 - 16993401912064*x^3 + 158306914121952*x^2 - 416252280742256*x + 201242345772473 pEX[345] := 256*x^4 - 23881033077504*x^3 - 23150362687144224*x^2 + 708715457556561936*x + 3706431275590435161 pEX[357] := 256*x^4 - 39494458067712*x^3 - 46866317368584864*x^2 - 246270659177073456*x + 2195705355362994609 pEX[385] := 256*x^4 - 123728205278976*x^3 + 3794942112709600*x^2 + 90491392970899152*x + 341604126501413449 pEX[397] := 64*x^3 - 49821092833104*x^2 - 775118555673780*x - 7314375832066231 pEX[445] := 256*x^4 - 1252406945127168*x^3 + 84272777298243424*x^2 + 721837004759604432*x + 1556569122001225681 pEX[457] := 256*x^4 - 1952035230970112*x^3 - 28481528097784992*x^2 - 145244811412075664*x - 256360985615776463 pEX[505] := 256*x^4 - 10895388166069504*x^3 + 1282468783474507872*x^2 - 2564631969666278096*x + 23887316639122850081 pEX[553] := 256*x^4 - 56140277582342912*x^3 - 1077345312627712800*x^2 + 11809846591247512976*x - 23770871999534093959 pEX[577] := 256*x^4 - 124077332054842112*x^3 + 6936696670004559072*x^2 - 120639207284204764528*x + 72293944808053759481 pEX[697] := 256*x^4 - 5215005640410114816*x^3 + 15085291327523729632*x^2 + 214567892725515870096*x - 627433721613335417927 pEX[793] := 256*x^4 - 82711061471847646464*x^3 + 1541725810143377178208*x^2 - 9163750920737146705488*x + 17783404885341091924417 pEY[4] := 512*x^4 + 2287232*x^2 - 24910081 pEY[5] := x - 5 pEY[7] := 256*x^2 - 29575 pEY[9] := x - 21 pEY[13] := x - 65 pEY[15] := 65536*x^4 - 740409600*x^2 + 11358230625 pEY[17] := x^2 - 170*x + 425 pEY[21] := x^2 - 378*x - 1911 pEY[25] := x - 805 pEY[29] := x^3 - 1595*x^2 + 11571*x - 41209 pEY[33] := x^2 - 2970*x - 25575 pEY[37] := x - 5365 pEY[41] := x^4 - 9348*x^3 + 62566*x^2 - 437060*x - 6534047 pEY[45] := x^2 - 15810*x + 108225 pEY[49] := x^2 - 26082*x + 71393 pEY[53] := x^3 - 42135*x^2 + 899675*x - 17205125 pEY[57] := x^2 - 66690*x - 1685775 pEY[61] := x^3 - 103883*x^2 - 1502125*x - 5719177 pEY[65] := x^4 - 159380*x^3 + 7029750*x^2 - 236008500*x + 1702780625 pEY[69] := x^4 - 240948*x^3 - 8266890*x^2 + 56732076*x - 247148271 pEY[73] := x^2 - 359890*x + 2980225 pEY[77] := x^4 - 531300*x^3 + 24358950*x^2 - 1295486500*x - 13721929375 pEY[81] := x^3 - 775899*x^2 - 15147405*x - 87480729 pEY[85] := x^2 - 1122170*x + 14348425 pEY[93] := x^2 - 2285010*x - 215432175 pEY[97] := x^2 - 3221370*x + 9004025 pEY[105] := x^4 - 6263460*x^3 - 814885050*x^2 + 7308913500*x + 167128250625 pEY[109] := x^3 - 8646643*x^2 + 102981347*x - 2175565553 pEY[113] := x^4 - 11862740*x^3 + 1937831350*x^2 - 335677856500*x - 3747438139375 pEY[117] := x^4 - 16179540*x^3 - 79799850*x^2 + 1654087500*x + 12123320625 pEY[121] := x^3 - 21945319*x^2 - 832183429*x - 10969770581 pEY[133] := x^2 - 53110890*x - 716986375 pEY[137] := x^4 - 70639940*x^3 + 24442026150*x^2 - 8197445210500*x + 81695838030625 pEY[141] := x^4 - 93545604*x^3 - 39708736122*x^2 - 1912015969668*x - 34320822371199 pEY[145] := x^4 - 123366580*x^3 + 1888478550*x^2 + 65395739500*x + 530230000625 pEY[153] := x^4 - 212044740*x^3 + 4250240550*x^2 - 37637770500*x + 227550110625 pEY[157] := x^3 - 276454235*x^2 + 8257097075*x - 66567705625 pEY[165] := x^4 - 465036660*x^3 - 295616027850*x^2 + 10743616075500*x + 186178163180625 pEY[169] := x^3 - 600163655*x^2 + 18285930299*x - 1349198793397 pEY[177] := x^2 - 990352170*x - 872959039575 pEY[193] := x^2 - 2605671770*x - 33796919975 pEY[205] := x^4 - 5238478980*x^3 + 574071247750*x^2 - 13146957274500*x + 85971047850625 pEY[213] := x^4 - 8246665620*x^3 - 15273579167850*x^2 + 749383160719500*x - 10464421296639375 pEY[217] := x^4 - 10312625540*x^3 - 318197309850*x^2 + 816970605500*x + 47925330070625 pEY[225] := x^4 - 16024848420*x^3 - 12282125850*x^2 + 3210470329500*x + 37164249950625 pEY[253] := x^2 - 70519218770*x - 1179232715375 pEY[265] := x^4 - 129634888900*x^3 + 24384572922150*x^2 - 586293307242500*x + 30871358528830625 pEY[273] := x^4 - 193001133780*x^3 - 1144793998379850*x^2 - 31000521226720500*x + 836262547960100625 pEY[277] := x^3 - 234960018855*x^2 - 3898365656325*x - 18836672175125 pEY[289] := x^4 - 420269570820*x^3 + 51519814319878*x^2 - 19752332388945156*x - 302199612764993279 pEY[301] := x^4 - 742481753188*x^3 - 344519192403162*x^2 - 64050851032779044*x - 2600143057512490399 pEY[313] := x^4 - 1296561365540*x^3 - 81483726901050*x^2 - 3213907383134500*x + 53693303630410625 pEY[333] := x^4 - 3205296266340*x^3 - 545556447450*x^2 + 950613269665500*x + 67313429334230625 pEY[337] := x^4 - 3828293154580*x^3 + 171844118450550*x^2 - 2180990943960500*x + 4893592883020625 pEY[345] := x^4 - 5443429067460*x^3 - 103706744388178650*x^2 + 40102513795552981500*x + 785432583794220350625 pEY[357] := x^4 - 9157568513940*x^3 - 214639826561135850*x^2 - 13758789096248080500*x + 336800025452018480625 pEY[385] := x^4 - 29792639770740*x^3 + 13592816436025750*x^2 + 2129395212399955500*x + 45207637463243880625 pEY[397] := x^3 - 48727979268195*x^2 - 6683451247672125*x - 575478342761622625 pEY[445] := x^4 - 324216699334020*x^3 + 310790636846374150*x^2 + 11964368702022565500*x + 126256980497756250625 pEY[457] := x^4 - 512101041516740*x^3 - 38804704423801050*x^2 - 1053752201309034500*x - 9659818233599489375 pEY[505] := x^4 - 3004680536468260*x^3 + 4947222754839658950*x^2 - 57740983488110526500*x + 4601415583602279850625 pEY[553] := x^4 - 16201194231562340*x^3 - 4095129050054768250*x^2 + 161270143251863145500*x - 1370085110339732749375 pEY[577] := x^4 - 36575499052458740*x^3 + 21833313597669878550*x^2 - 4032867190957951196500*x + 11300735425476940600625 pEY[697] := x^4 - 1689589021431814020*x^3 + 27287514171679752550*x^2 + 1227300643761425005500*x - 17141546054219486729375 pEY[793] := x^4 - 28583150460287569380*x^3 + 2890143760105117010950*x^2 - 86061612078955408486500*x + 818941280835129819810625 pEZ2[4] := 15752961*x^2 - 9165312*x - 8192 pEZ2[5] := 4*x - 1 pEZ2[6] := 1836036801*x^4 - 190150540416*x^3 - 138830837760*x^2 + 19781517312*x + 1048576 pEZ2[7] := 3969*x - 256 pEZ2[8] := 620512135426561*x^4 - 287621717421056*x^3 + 390738946441216*x^2 - 13694880710656*x - 67108864 pEZ2[9] := 48*x - 1 pEZ2[10] := 39754550824641*x^4 - 119215362024576*x^3 - 138330257946624*x^2 + 1743464300544*x + 1048576 pEZ2[11] := 290521*x^3 + 420048*x^2 + 531200*x - 4096 pEZ2[12] := 8959273893140481*x^4 - 3670232770208894976*x^3 - 599665266678104064*x^2 + 2973505079476224*x + 268435456 pEZ2[13] := 324*x - 1 pEZ2[15] := 1185921*x^2 - 49229568*x + 65536 pEZ2[16] := 22155100113214361601*x^4 - 62068434767415926784*x^3 + 193140475265405288448*x^2 - 172440481085521920*x - 536870912 pEZ2[17] := 1024*x^2 + 1648*x - 1 pEZ2[18] := 34700535004437432001*x^4 - 3035796287502087296*x^3 - 3711719247391750144*x^2 + 1546950810927104*x + 1048576 pEZ2[19] := 191850201*x^3 + 11442384*x^2 + 14162688*x - 4096 pEZ2[21] := 1296*x^2 - 6984*x + 1 pEZ2[22] := 9665687742038144619201*x^4 - 206368377041762925696*x^3 - 252663796166074988544*x^2 + 25783654895714304*x + 1048576 pEZ2[23] := 165524481409*x^3 + 343131204352*x^2 + 228948836352*x - 16777216 pEZ2[25] := 25920*x - 1 pEZ2[27] := 36874368729*x^3 + 158972112*x^2 + 196614912*x - 4096 pEZ2[28] := 10743057735493363161989121*x^4 - 299409397266910313570697216*x^3 - 298726429226717360893722624*x^2 + 4612347048123521040384*x + 4294967296 pEZ2[29] := 153664*x^3 + 170960*x^2 + 86924*x - 1 pEZ2[31] := 41367898881*x^3 + 211372955136*x^2 + 2588240314368*x - 16777216 pEZ2[33] := 331776*x^2 - 268848*x + 1 pEZ2[37] := 777924*x - 1 pEZ2[39] := 10584386786441601*x^4 + 17826257906553600*x^3 + 3266926173093888*x^2 - 5562212227743744*x + 4294967296 pEZ2[41] := 4194304*x^4 + 26099712*x^3 + 8924928*x^2 + 2128288*x - 1 pEZ2[43] := 191103722496729*x^3 + 11446268112*x^2 + 14155782912*x - 4096 pEZ2[45] := 234256*x^2 - 5549768*x + 1 pEZ2[49] := 11757312*x^2 + 13880160*x - 1 pEZ2[53] := 2249794624*x^3 + 294929872*x^2 + 33463372*x - 1 pEZ2[55] := 82134424781463681*x^4 - 511031732481236736*x^3 - 576517840835641344*x^2 - 220397021750624256*x + 4294967296 pEZ2[57] := 796594176*x^2 - 78086448*x + 1 pEZ2[58] := 89281808967759133485558908068332113601*x^4 - 194253361693712575736321726522496*x^3 - 237937121192996675250748964665344*x^2 + 2476973907151703357128704*x + 1048576 pEZ2[61] := 34012224*x^3 + 66869712*x^2 + 176961996*x - 1 pEZ2[63] := 4789437355589121*x^4 - 3369302429211657216*x^3 + 2324569653219557376*x^2 - 1132717159131119616*x + 4294967296 pEZ2[65] := 40282095616*x^4 - 129036926976*x^3 - 7280455424*x^2 - 390583456*x + 1 pEZ2[67] := 5289852925222272729*x^3 + 1904373500112*x^2 + 2355167238912*x - 4096 pEZ2[69] := 24591257856*x^4 + 40309850880*x^3 + 17571714912*x^2 - 841630032*x + 1 pEZ2[73] := 107495424*x^2 + 1774176048*x - 1 pEZ2[77] := 80102584576*x^4 - 5415665136896*x^3 - 143101418144*x^2 - 3665337296*x + 1 pEZ2[81] := 7552892928*x^3 + 585363456*x^2 + 7432710528*x - 1 pEZ2[85] := 13680577296*x^2 - 14814550728*x + 1 pEZ2[93] := 5309909096976*x^2 - 56147328648*x + 1 pEZ2[97] := 98365031424*x^2 + 106981512048*x - 1 pEZ2[105] := 16518176833536*x^4 - 145490350473216*x^3 + 67413868206336*x^2 - 373643437536*x + 1 pEZ2[109] := 6614731335744*x^3 + 3645831281616*x^2 + 685910359692*x - 1 pEZ2[113] := 2359080647655424*x^4 + 88821336212176896*x^3 + 333357330278144*x^2 + 1245316147296*x - 1 pEZ2[117] := 5802782976*x^4 - 878111421696*x^3 - 2336998582944*x^2 - 2237416018896*x + 1 pEZ2[121] := 57490998276096*x^3 - 6455306803968*x^2 + 3980154465936*x - 1 pEZ2[133] := 7852750780176*x^2 - 21208782485448*x + 1 pEZ2[137] := 5664152635020673024*x^4 + 24640103073118109696*x^3 + 29984130231090944*x^2 + 36423009044896*x - 1 pEZ2[141] := 2709603017329049856*x^4 - 209358618262053120*x^3 + 61131767252109408*x^2 - 62062832944656*x + 1 pEZ2[145] := 722204136308736*x^4 + 813341659152384*x^3 + 622175991111936*x^2 - 104960753682336*x + 1 pEZ2[153] := 34982777061376*x^4 - 557431823466496*x^3 - 791799627007744*x^2 - 293875576870496*x + 1 pEZ2[157] := 359033070556224*x^3 - 299231148986928*x^2 + 486795716784972*x - 1 pEZ2[163] := 16827610604518993301932059648729*x^3 + 3396577776039932112*x^2 + 4200598602252294912*x - 4096 pEZ2[165] := 141763707879526656*x^4 - 43049037111049702656*x^3 + 3572971108229856096*x^2 - 1310664765915216*x + 1 pEZ2[169] := 424257036654477312*x^3 + 49257774118305792*x^2 + 2131339504207680*x - 1 pEZ2[177] := 24318806323956350976*x^2 - 5541238229049648*x + 1 pEZ2[193] := 4514124143821824*x^2 + 35178888293102448*x - 1 pEZ2[205] := 10177165011108096*x^4 + 121886662914641664*x^3 + 4162785426763576416*x^2 - 133861760369557776*x + 1 pEZ2[213] := 33580218641784264274176*x^4 - 14206152465244330788096*x^3 + 5413356883841146210656*x^2 - 319284152090367696*x + 1 pEZ2[217] := 3656158440062976*x^4 + 495644334735458304*x^3 + 1037731565797837056*x^2 - 490093300297948896*x + 1 pEZ2[225] := 448043323668627456*x^4 - 338035504378134528*x^3 - 1388477850849409536*x^2 - 1141314519593514432*x + 1 pEZ2[253] := 2068941270499938576*x^2 - 19655969242251327048*x + 1 pEZ2[265] := 261924616710569796304896*x^4 + 74846597734899305201664*x^3 + 6112340671951347446016*x^2 - 63415865552249801376*x + 1 pEZ2[273] := 1988031631876102397362176*x^4 - 106490927611256199718404096*x^3 + 17423506553795675130214656*x^2 - 136444834908254409696*x + 1 pEZ2[277] := 133294251529068969024*x^3 + 315900318103979358672*x^2 + 199300398801944717772*x - 1 pEZ2[289] := 4529739082390050510471168*x^4 + 17789676918744282842529792*x^3 + 168837207775201512124416*x^2 + 611164401571582584192*x - 1 pEZ2[301] := 739142349274677457460203776*x^4 - 84224120266013981947981056*x^3 + 254770836043809608663904*x^2 - 1831492207661676189264*x + 1 pEZ2[313] := 344496746398592243073024*x^4 + 672908670870522943389696*x^3 + 33408369605817478450944*x^2 + 5370835063175453524896*x - 1 pEZ2[333] := 366135204658955526533376*x^4 - 9102228347872078730496*x^3 - 37599385609961912451744*x^2 - 30852625090132838828496*x + 1 pEZ2[337] := 8989118888541394305024*x^4 - 15159781258664226914304*x^3 + 17483529362603588146944*x^2 + 43489105273176259756896*x - 1 pEZ2[345] := 508204843020827870950280134656*x^4 - 42943083496680275576733741613056*x^3 + 94027713019449902995529431296*x^2 - 85886725275020098571616*x + 1 pEZ2[357] := 4713264919015964551831838976*x^4 - 6619256021739580219741421373696*x^3 + 359502006476024001998122345056*x^2 - 234904934220686031082896*x + 1 pEZ2[385] := 37200675490746628950737289216*x^4 - 53722356518533028133297586176*x^3 + 2095598502611881454014085376*x^2 - 2305458141511410719189856*x + 1 pEZ2[397] := 5371220452507071550946293824*x^3 + 84389592001951660958008272*x^2 + 5980896633690198061042572*x - 1 pEZ2[445] := 199377700515565848358087332096*x^4 + 319343910726396272569897169664*x^3 + 526239544132287900165540760416*x^2 - 236216782306572457163677776*x + 1 pEZ2[457] := 171343877527955310561460224*x^4 + 1415958081532187520266551296*x^3 - 320847096466933178286387456*x^2 + 573845682106362088683912096*x - 1 pEZ2[505] := 747770358573823195308007291355136*x^4 + 516795260731225374047362351939584*x^3 + 94556804188807240165213059707136*x^2 - 17877435893507517358978827936*x + 1 pEZ2[553] := 4086366892892874790746955186176*x^4 + 54990901038310428049111378427904*x^3 + 70502070284163622586233026406656*x^2 - 474645017231133871152147225696*x + 1 pEZ2[577] := 80399971074631668964604367417114624*x^4 + 81011043144405201570102070156394496*x^3 - 538762461387853321765334545664256*x^2 + 2318487228659214074431965446496*x - 1 pEZ2[697] := 7659171703349681281782540926976*x^4 + 640782614835534945276627751010304*x^3 - 2217589653973904807609088665650944*x^2 - 4095711709243780260004567926124896*x + 1 pEZ2[793] := 765089120763182731906249255997669376*x^4 + 2467969621791955423090461630577557504*x^3 + 2368569068232706619878887297545216256*x^2 - 1030260391217449537871693575710062496*x + 1 (* Type F1, N=2〜190 *) sumF1[t_, limit_:Infinity] := (Sum[termp[n, 1/3, F1X[t], F1Y[t], F1Z2[t]], {n, 0, limit}] * Sqrt[F1Z2[t]] / Sqrt[3]); F1X[2]:= 1 F1X[3]:= 3 F1X[4]:= 5*Sqrt[2] F1X[5]:= Sqrt[10*(11 + 5*Sqrt[5])] F1X[6]:= 5*(3 + 2*Sqrt[2]) F1X[7]:= 54 F1X[8]:= Sqrt[2*(2297 + 1625*Sqrt[2])] F1X[9]:= 10*Sqrt[3*(45 + 26*Sqrt[3])] F1X[10]:= 135 + 62*Sqrt[5] F1X[11]:= 445/3 + (87589000 - 309000*Sqrt[33])^(1/3)/3 + (10*(87589 + 309*Sqrt[33])^(1/3))/3 F1X[12]:= 2*Sqrt[2*(31177 + 18000*Sqrt[3])] F1X[13]:= Sqrt[2*(303287 + 84125*Sqrt[13])] F1X[14]:= 5*(85 + 60*Sqrt[2] + 2*Sqrt[3527 + 2494*Sqrt[2]]) F1X[15]:= 1275 + 571*Sqrt[5] F1X[16]:= 10*Sqrt[2*(36160 + 25569*Sqrt[2])] F1X[18]:= 3*(1355 + 556*Sqrt[6]) F1X[19]:= 3915 + (1619568999000 - 177717000*Sqrt[57])^(1/3)/3 + (10*(539856333 + 59239*Sqrt[57])^(1/3))/3^(2/3) F1X[22]:= 16659 + 11750*Sqrt[2] F1X[23]:= 46346/3 + (99493044015500 - 7313662500*Sqrt[69])^(1/3)/3 + (5*2^(2/3)*(198986088031 + 14627325*Sqrt[69])^(1/3))/3 F1X[25]:= 50*Sqrt[2*(774535 + 346383*Sqrt[5])] F1X[27]:= 3*(18109 + 14374*2^(1/3) + 11408*2^(2/3)) F1X[28]:= 4*Sqrt[1511227684 + 571190375*Sqrt[7]] F1X[30]:= 98565 + 69700*Sqrt[2] + 2*Sqrt[5*(970137283 + 685990650*Sqrt[2])] F1X[31]:= 174600 + (143712295381345500 - 470757070500*Sqrt[93])^(1/3)/3 + 5*(2/3)^(2/3)*(95808196920897 + 313838047*Sqrt[93])^(1/3) F1X[34]:= 5*(59859 + 14518*Sqrt[17] + 2*Sqrt[2*(896533171 + 217441233*Sqrt[17])]) F1X[37]:= Sqrt[2*(1744104472943 + 286729020625*Sqrt[37])] F1X[39]:= 2198535/2 + (609765*Sqrt[13])/2 + 5*Sqrt[(193347425495 + 53624927431*Sqrt[13])/2] F1X[42]:= 2305227 + 616196*Sqrt[14] + 54*Sqrt[3*(1215115791 + 324753352*Sqrt[14])] F1X[43]:= 3911391 + (1615695607872076757184 - 421047715416000*Sqrt[129])^(1/3)/3 + (4*(8415081291000399777 + 2192956851125*Sqrt[129])^(1/3))/3^(2/3) F1X[46]:= 5*(1189269 + 840940*Sqrt[2] + 10*Sqrt[28281865871 + 19998299142*Sqrt[2]]) F1X[55]:= 87115365/2 + (38959175*Sqrt[5])/2 + 3*Sqrt[(5*(168646346135651 + 75420938823255*Sqrt[5]))/2] F1X[58]:= 3*(54357921 + 10094270*Sqrt[29]) F1X[63]:= 223862049 + 48850704*Sqrt[21] + Sqrt[3*(33409478207908629 + 7290545848415186*Sqrt[21])] F1X[67]:= 650757843 + (7440839737719810251863585608 - 32567423497198431000*Sqrt[201])^(1/3)/3 + (2*(310034989071658760494316067 + 1356975979049934625*Sqrt[201])^(1/3))/3^(2/3) F1X[70]:= 862525935 + 272754648*Sqrt[10] + 50*Sqrt[2*(297575726104859 + 94101707086978*Sqrt[10])] F1X[78]:= 3718993257 + 2629725500*Sqrt[2] + 30*Sqrt[13*(2364240538839507 + 1671770517369550*Sqrt[2])] F1X[82]:= 7508128113 + 1172572612*Sqrt[41] + 6*Sqrt[2*(1565896873552862629 + 244552005472357449*Sqrt[41])] F1X[102]:= 199574352435 + 48403890500*Sqrt[17] + 2*Sqrt[2*(9957470308969564032157 + 2415041285166660805500*Sqrt[17])] F1X[130]:= 11936108891565 + 5337990529550*Sqrt[5] + 2*Sqrt[65*(1095928499758003812605761 + 490114124787650580212580*Sqrt[5])] F1X[142]:= 60117313798305 + 42509360253500*Sqrt[2] + 6*Sqrt[200782844644482158176274471 + 141974910994038410890545750*Sqrt[2]] F1X[163]:= 1160670193565427 + (42217281020446354127659865246120402012104776000 - 2419196418853322016934861015800000*Sqrt[489])^(1/3)/3 + (20*(1759053375851931421985827718588350083837699 + 100799850785555084038952542325*Sqrt[489])^(1/3))/3^(2/3) F1X[190]:= 21242668516504965 + 15020834958518500*Sqrt[2] + 2*Sqrt[5*(45125096427586568251645610141659 + 31908261685643312902173585434250*Sqrt[2])] F1Y[2]:= 28/3 F1Y[3]:= 33 F1Y[4]:= 63*Sqrt[2] F1Y[5]:= (4*Sqrt[5*(2462 + 1105*Sqrt[5])])/3 F1Y[6]:= 12*(19 + 13*Sqrt[2]) F1Y[7]:= 3591/4 F1Y[8]:= (14*Sqrt[66641 + 47125*Sqrt[2]])/3 F1Y[9]:= 28*Sqrt[6*(1020 + 589*Sqrt[3])] F1Y[10]:= 36*(75 + 34*Sqrt[5]) F1Y[11]:= 27797/9 + (15619210621655256 - 17346014437752*Sqrt[33])^(1/3)/81 + (14*(11*(709830671 + 788307*Sqrt[33]))^(1/3))/9 F1Y[12]:= 3*Sqrt[13128734 + 7579875*Sqrt[3]] F1Y[13]:= 36*Sqrt[13*(18478 + 5125*Sqrt[13])] F1Y[14]:= 29876/3 + (21112*Sqrt[2])/3 + Sqrt[7056796544/9 + (4989915392*Sqrt[2])/9]/2 F1Y[15]:= (231*(1075 + 481*Sqrt[5]))/8 F1Y[16]:= 693*Sqrt[2*(4756 + 3363*Sqrt[2])] F1Y[18]:= 28*(3875 + 1586*Sqrt[6]) F1Y[19]:= 107217 + (33274118060107704 - 868368942792*Sqrt[57])^(1/3)/3 + 78*(57*(45560043 + 1189*Sqrt[57]))^(1/3) F1Y[22]:= 2772*(177 + 125*Sqrt[2]) F1Y[23]:= 2792867/6 + (14047819816799740356000000000 - 337578953914188000000000*Sqrt[69])^(1/3)/5184 + (875*((23*(203553323523 + 4891529*Sqrt[69]))/2)^(1/3))/(12*3^(2/3)) F1Y[25]:= 2520*Sqrt[601880 + 269169*Sqrt[5]] F1Y[27]:= 3*(591239 + 469274*2^(1/3) + 372458*2^(2/3)) F1Y[28]:= (63*Sqrt[26936833624 + 10181166125*Sqrt[7]])/2 F1Y[30]:= 84*(40375 + 28550*Sqrt[2] + Sqrt[10*(325795419 + 230372150*Sqrt[2])]) F1Y[31]:= 24432309/4 + (1612934175787549102009387008 - 995270089684374706176*Sqrt[93])^(1/3)/192 + (39*((93*(5287448593046169 + 3262649843*Sqrt[93]))/2)^(1/3))/4 F1Y[34]:= 36*(304623 + 73882*Sqrt[17] + 2*Sqrt[17*(2730421549 + 662224497*Sqrt[17])]) F1Y[37]:= 252*Sqrt[37*(2168508622 + 356500625*Sqrt[37])] F1Y[39]:= 172535181/4 + (95705337*Sqrt[13])/8 + Sqrt[238149191218944915/16 + (33025350775010139*Sqrt[13])/8]/2 F1Y[42]:= 84*(1117523 + 298694*Sqrt[14] + 18*Sqrt[3*(2569867239 + 686825908*Sqrt[14])]) F1Y[43]:= 161155701 + (113005951102647032576981184 - 7244334224838648000*Sqrt[129])^(1/3)/3 + 84*(129*(54740654058707037 + 3509192125*Sqrt[129]))^(1/3) F1Y[46]:= 252*(1005537 + 711022*Sqrt[2] + Sqrt[46*(43956917921 + 31082234742*Sqrt[2])]) F1Y[55]:= 32474759625/16 + (14523153975*Sqrt[5])/16 + Sqrt[1054609977394072252395/32 + (471635919840532424175*Sqrt[5])/32]/2 F1Y[58]:= 8316*(938353 + 174250*Sqrt[29]) F1Y[63]:= 178628438079/16 + (38979920889*Sqrt[21])/16 + Sqrt[31908118925896545077991/32 + (6962922393408283412019*Sqrt[21])/32]/2 F1Y[67]:= 33468532713 + (1012217336778159291698695663935048 - 1105281594332691979203000*Sqrt[201])^(1/3)/3 + 6006*(201*(860910423845138289 + 940063375*Sqrt[201]))^(1/3) F1Y[70]:= 252*(179928375 + 56898348*Sqrt[10] + 325*Sqrt[2*(306499088201 + 96923521948*Sqrt[10])]) F1Y[78]:= 84*(2456817363 + 1737232250*Sqrt[2] + 125*Sqrt[26*(29715342133067 + 21011919927570*Sqrt[2])]) F1Y[82]:= 36*(11866325493 + 1853208692*Sqrt[41] + 6*Sqrt[82*(95399766260229899 + 14898940380153819*Sqrt[41])]) F1Y[102]:= 84*(150766669625 + 36566288500*Sqrt[17] + 13*Sqrt[34*(7911791500208394501 + 1918891296660189500*Sqrt[17])]) F1Y[130]:= 252*(3393233790375 + 1517500334350*Sqrt[5] + 82*Sqrt[65*(52688582528420466481 + 23563050434331168540*Sqrt[5])]) F1Y[142]:= 252*(17861711213625 + 12630137122750*Sqrt[2] + 57*Sqrt[142*(1383050550771387306753 + 977964423174237401750*Sqrt[2])]) F1Y[163]:= 93107036194678737 + (21792711576642603490625597265327925547588779125000000 - 312198449690093633771532683448375000000*Sqrt[489])^(1/3)/3 + 10500*(489*(1425839857142773951339723004243900751 + 20426324247939130348789*Sqrt[489]))^(1/3) F1Y[190]:= 4788*(384247985318175 + 271704356075750*Sqrt[2] + 5083*Sqrt[10*(1142912476713024496667 + 808161162586491705750*Sqrt[2])]) F1Z2[2]:= 27/125 F1Z2[3]:= 4/125 F1Z2[4]:= 8/1331 F1Z2[5]:= 27/(5*(1975 + 884*Sqrt[5])) F1Z2[6]:= (1399 + 988*Sqrt[2])^(-1) F1Z2[7]:= 64/614125 F1Z2[8]:= 216/(125*(26125 + 18473*Sqrt[2])) F1Z2[9]:= 9/(399849 + 230888*Sqrt[3]) F1Z2[10]:= 1/(5*(24635 + 11016*Sqrt[5])) F1Z2[11]:= 28570212/119823157 + (91728*(3*(-71585567332587 + 46017723976379*Sqrt[33]))^(1/3))/(1318054727*11^(2/3)) - (114840105359616*3^(2/3))/(1318054727*(11*(-71585567332587 + 46017723976379*Sqrt[33]))^(1/3)) F1Z2[12]:= 16/(375*(35010 + 20213*Sqrt[3])) F1Z2[13]:= 1/(125*(15965 + 4428*Sqrt[13])) F1Z2[14]:= -32816097/338608873 + (33034557024*Sqrt[2])/450688409963 - Sqrt[-234086514997407362833536/203120042874977157661369 + (124380387103174449408*Sqrt[2])/152607094571733401699]/2 F1Z2[15]:= 128/(5*(274207975 + 122629507*Sqrt[5])) F1Z2[16]:= 32/(761354780 + 538359129*Sqrt[2]) F1Z2[17]:= -170937/2595575 + 58042224/(220623875*Sqrt[17]) + Sqrt[-149795884519208064/827473201740265625 + 427461329642112/(572645814353125*Sqrt[17])]/2 F1Z2[18]:= 27/(125*(23604673 + 9636536*Sqrt[6])) F1Z2[19]:= 8063833636/10260751717 - 18321559428047616/(10260751717*(-103203545922327192481 + 14258557693188780003*Sqrt[57])^(1/3)) + (1872*(-103203545922327192481 + 14258557693188780003*Sqrt[57])^(1/3))/10260751717 F1Z2[20]:= 47893464/273359449 + 3664064143584/(6715074864685*Sqrt[5]) - Sqrt[14177834733024632366880768/45092230438324271060149225 + 1594951203089817510912/(1835629165004041158565*Sqrt[5])]/2 F1Z2[21]:= 159390302261/21323063917 - 828269868608/(63969191751*Sqrt[3]) + Sqrt[5406293834462884689167296/12276172479828619338003 - (115604636815540627862016*Sqrt[3])/454673054808467382889]/2 F1Z2[22]:= 1/(125*(14571395 + 10303524*Sqrt[2])) F1Z2[23]:= -449856/18609625 - (21070457394340032*(2/(23*(99477707703247841 + 16010443391767401*Sqrt[69])))^(1/3))/569696450125 + (239904*(2/23)^(2/3)*(99477707703247841 + 16010443391767401*Sqrt[69])^(1/3))/569696450125 F1Z2[24]:= 88870583933464/452118343792751 - (242296453384544*Sqrt[2])/452118343792751 + Sqrt[456691760418254520786177028608/204410996793900186691640148001 - (140755021909125632434336914432*Sqrt[2])/204410996793900186691640148001]/2 F1Z2[25]:= (12740595841 + 5697769392*Sqrt[5])^(-1) F1Z2[27]:= 56143116/817400375 + (31411728*2^(1/3))/163480075 - (160025472*2^(2/3))/817400375 F1Z2[28]:= 64/(125*(40728492440 + 15393923181*Sqrt[7])) F1Z2[30]:= 11010382727/48587168449 - (1050909850592*Sqrt[2])/6559267740615 - Sqrt[81532128534047880889938304/215119966465363034602891125 - (15816713431186242063104*Sqrt[2])/59017823447287526640025]/2 F1Z2[31]:= -19218839489920/22884533780471 - (7751492949727752518592*(2/(31022050996275055301273389 + 4478794001981733908757861*Sqrt[93]))^(1/3))/22884533780471 + (63648*2^(2/3)*(31022050996275055301273389 + 4478794001981733908757861*Sqrt[93])^(1/3))/22884533780471 F1Z2[32]:= -322459354944/4644924219125 - (5068462103070912*Sqrt[2])/113285056780239625 + Sqrt[448968874257596741520560641652736/12833504089702115831861872420140625 + (13189349118893836558493730816*Sqrt[2])/526200503903485826883507828125]/2 F1Z2[33]:= -1024805137/71473375 + (591882876*Sqrt[3])/71473375 - Sqrt[11186777655879630196288/6799338077408421875 - (6458688679059088602624*Sqrt[3])/6799338077408421875]/2 F1Z2[34]:= 66784212820781/204159590351387 - (16197076947168*Sqrt[17])/204159590351387 - Sqrt[-3629955995503387200453613824/3789194393858741075102983979 + (9684330112164917173409632512*Sqrt[17])/41681138332446151826132823769]/2 F1Z2[36]:= -70956865866153181032/191478360645378085609 + (48229558361525739072*Sqrt[3])/191478360645378085609 - Sqrt[-70701086268051798135142619265675665793024/36663962595441475241214715864337732900881 + (41184721024494941972039668068463176628224*Sqrt[3])/36663962595441475241214715864337732900881]/2 F1Z2[37]:= 1/(125*(91805981021 + 15092810460*Sqrt[37])) F1Z2[39]:= 183978994354870920080/1087361181471083323897 - (50483479666655360304*Sqrt[13])/1087361181471083323897 - Sqrt[-449030461857837054776229737980936858448660480/861936313109268655848124485037759596413357961 + (124541743915853300811195168123796257076348928*Sqrt[13])/861936313109268655848124485037759596413357961]/2 F1Z2[40]:= 170732539832/8792083715 - 382623248448/(8792083715*Sqrt[5]) + Sqrt[45610927936622638852608/15460147210313640245 - 20397774929706015934464/(3092029442062728049*Sqrt[5])]/2 F1Z2[42]:= 4933330105577/21427041109375 - (2014012711872*Sqrt[6])/21427041109375 - Sqrt[17531384331169819502893312/41738008245713293701171875 - (78728734508157665110513152*Sqrt[6])/459118090702846230712890625]/2 F1Z2[43]:= 532559450116/549856483328125 - 24078061275070621658112/(549856483328125*(-96610549331103309238603193 + 196409380126722630910986375*Sqrt[129])^(1/3)) + (14112*(-96610549331103309238603193 + 196409380126722630910986375*Sqrt[129])^(1/3))/549856483328125 F1Z2[45]:= 5588360415766688607/5261550616923712903 - (16132216188673406016*Sqrt[3])/26307753084618564515 + Sqrt[22484005135147808092303312484441778513984/3460489361806287980553355252896085926125 - (2596229283447111898229891645302631640576*Sqrt[3])/692097872361257596110671050579217185225]/2 F1Z2[46]:= -1875342387062937871385/12850316252289637351777 + (1326071696797345758624*Sqrt[2])/12850316252289637351777 - Sqrt[-21501971610841264716708279216483262279496832/165130627783859190641536338155152393645057729 + (15204189935014908233647605426655173446471424*Sqrt[2])/165130627783859190641536338155152393645057729]/2 F1Z2[48]:= 3287080115456/9945310362625 - (1992270745728*Sqrt[3])/9945310362625 + Sqrt[90618345589392096373481472/98909198208936208996890625 - (52256689468658884620619776*Sqrt[3])/98909198208936208996890625]/2 F1Z2[49]:= 9131582758383369829/177631422362629154821 - (3451430189897485056*Sqrt[7])/177631422362629154821 + Sqrt[-303937231089076499724354390410907713280/2868447473688249908229515895472071594731 + (1263652229143952035500430261726719141888*Sqrt[7])/31552922210570748990524674850192787542041]/2 F1Z2[52]:= 397161865049912/344251017864125 - (109168411726368*Sqrt[13])/344251017864125 - Sqrt[-676753872873458025123440142336/118508763300486109876962015625 + (187711730783850973797912941568*Sqrt[13])/118508763300486109876962015625]/2 F1Z2[55]:= 25721293723649360/41467364539950383 - 253953790163582256/(207336822699751915*Sqrt[5]) - Sqrt[-8246516021557854594030525452101632/42988558047228360978681002546167225 + 4092320405185530239071469079595008/(8597711609445672195736200509233445*Sqrt[5])]/2 F1Z2[57]:= -54050005549505898841/255261787238467012375 + (12406790293101290268*Sqrt[19])/255261787238467012375 - Sqrt[631372447021191975919242073675499356202048/1759281660652762813382651094508576884796875 - (144846751069582371579386605396530504951296*Sqrt[19])/1759281660652762813382651094508576884796875]/2 F1Z2[58]:= 1/(125*(1399837865393267 + 259943365786104*Sqrt[29])) F1Z2[60]:= 471793406023940515072/17622887736823226676005 - (54319731503287277664*Sqrt[3])/3524577547364645335201 - Sqrt[6155221780067507644652772052363335947628544/1552830860923372341408554110547231206213800125 - (710739451181119346096260637041354322804736*Sqrt[3])/310566172184674468281710822109446241242760025]/2 F1Z2[63]:= 741398652077581283904/280204508921449203125 - (137315717495979850464*Sqrt[21])/280204508921449203125 - Sqrt[-7783101638367743059563976847381913970102272/78514566819910506066334008939697509765625 + (1709388511053981428614763002638707203940352*Sqrt[21])/78514566819910506066334008939697509765625]/2 F1Z2[64]:= 2055542283332289997922816/188098843288735029296706731 - (1855284887071024010614656*Sqrt[2])/188098843288735029296706731 + Sqrt[-30857176311065045336037405283585071136383789416448/3216470440596372633811926978708596386145025656427851 + (240925752034582851860968213889508912414491909369856*Sqrt[2])/35381174846560098971931196765794560247595282220706361]/2 F1Z2[67]:= 14742040586583556/2531829841056471296125 - 781040460528238579126700546304/(506365968211294259225*(-701000833994004337491643981733143 + 14721049871139742945240761480812157*Sqrt[201])^(1/3)) + (11099088*(-701000833994004337491643981733143 + 14721049871139742945240761480812157*Sqrt[201])^(1/3))/2531829841056471296125 F1Z2[70]:= 135675439878801187/786834064508766373 - (214521702148982592*Sqrt[2/5])/786834064508766373 - Sqrt[1256822449481043886723798202127552384/7035316421265744568717079162449717375 - (4371863710271206181153325373929457152*Sqrt[2/5])/15477696126784638051177574157389378225]/2 F1Z2[72]:= -7369819724411501008134456/5124324337526057019174125 + (6935268358486006105294728*Sqrt[2])/5124324337526057019174125 - Sqrt[601049735104313091605767287326871066052468062990336/26258699916161863141284024743782615717897069515625 - (408192809316622529337491612612583235026348521865216*Sqrt[2])/26258699916161863141284024743782615717897069515625]/2 F1Z2[73]:= 9424429106743/182236043902375 - (1103046034896*Sqrt[73])/182236043902375 + Sqrt[-48156480942020934252142119552/33209975697188348418530640625 + (5636289774382728463835524224*Sqrt[73])/33209975697188348418530640625]/2 F1Z2[78]:= 23526241854944581/607324998369091475 - (408652649819499574944*Sqrt[2])/14918938584936732083375 - Sqrt[242804352793132840847428862640569787344512/20234066227374001990904131988911278904671875 - (76880710277955848915548327801881199872*Sqrt[2])/9060644351765276690410968934582701728125]/2 F1Z2[82]:= -207898649552319463/781166344651859375 + (32468314238695872*Sqrt[41])/781166344651859375 - Sqrt[-11807211404018929750050903521914368/55474623456067958724242785888671875 + (20283742846176550948262826590234112*Sqrt[41])/610220858016747545966670644775390625]/2 F1Z2[85]:= -91577309554356391847148115099/1544688837889421363183784605 + (9934290661787833678834674996*Sqrt[17/5])/308937767577884272636756921 - Sqrt[335501295121614412725028946183455553392853500755194788537344/11930318029500855359948500393998052233944050055175030125 - (7278044889044040540097399561787963133670918858611883302912*Sqrt[17/5])/477212721180034214397940015759922089357762002207001205]/2 F1Z2[88]:= -94439944292144168/341478721288090375 + 710827748239673232/(341478721288090375*Sqrt[11]) - Sqrt[2410341197874988850835810860023865856/1282684888018042373235984955844046875 - 536080968516720280480169486650085376/(116607717092549306657816814167640625*Sqrt[11])]/2 F1Z2[93]:= -442507444851094956402210341/24152505391982290294853336675 + (79483023173114819351978976*Sqrt[31])/24152505391982290294853336675 - Sqrt[30835932336783908190447477886272480907726845788058402063296/11481950439397686570163592386148802934138985625081255794866875 - (138457423075141975830610564728932123462710938908156313276416*Sqrt[31])/287048760984942164254089809653720073353474640627031394871671875]/2 F1Z2[97]:= 74947690687163772053051/934581784125513804792875 - (7609785035476857691536*Sqrt[97])/934581784125513804792875 + Sqrt[-50589347723149312814396663830359076190674754688/873443111219228487215659451171583931321650765625 + (5136570020731083674500680640977648938373929088*Sqrt[97])/873443111219228487215659451171583931321650765625]/2 F1Z2[100]:= 311136656181262515239249384/3301837593032135891442032423 - (138952298175203782646100864*Sqrt[5])/3301837593032135891442032423 - Sqrt[-382864631054755615792849378416507741489383534655406080/474005716989576027734642260203970859596668715173184823 + (3938112500168557184997126812896091225958534105139482624*Sqrt[5])/10902131490760248637896771984691329770723380448983250929]/2 F1Z2[102]:= 22260577647066982332763/2057969649376599201414125 - 3298395350048828231862097984/(73957255289646845501219410125*Sqrt[17]) - Sqrt[87026242464640364420432905194434523108324245461371943552/92984485369625937257315765518906570066643641712900192765625 - 21753051493122236887049891481623607087137113242112/(5637103212492227972257900461543998903591066605296875*Sqrt[17])]/2 F1Z2[112]:= 884790342267645663686656/1002480017341979807967799 - (41804882564758852745396736*Sqrt[7])/125310002167747475995974875 + Sqrt[84754041942466994601039167767207803116097366049554432/15702596643280877133240342859419666881347201631265625 - (6406803346743618513902909263024796975589881800409088*Sqrt[7])/3140519328656175426648068571883933376269440326253125]/2 F1Z2[130]:= 3362809364096469028732769269055/17115748388664878729059187962937 - (22940784182211547905764207984448*Sqrt[13/5])/188273232275313666019651067592307 - Sqrt[1361129964126232861165381226860368808280489728918230295285610985984/4430851248924276438296772339111020671517228949055177304245697781125 - (15347944894710556381256590814272591051670557886130597511174651392*Sqrt[13/5])/80560931798623207969032224347473103118495071801003223713558141475]/2 F1Z2[133]:= 322307732878539079499171/2773715363974498488875 - (73942465070487133253952*Sqrt[19])/2773715363974498488875 + Sqrt[3283291428937358147476933462212073563205849152/30409078736554089444962021652449243078125 - (190569394308189121957215665955489972744287589888*Sqrt[19])/7693496920348184629575391478069658498765625]/2 F1Z2[142]:= 20592049093350626979466807278367/42154598784281913066313347531625 - (14560777552433105688013641605472*Sqrt[2])/42154598784281913066313347531625 - Sqrt[-140592123491809138061739811194705859708201125772223330784523392/1777010198663782143060892177416175446970826058100075480375140625 + (99413643902474752068876217611026768721260383441946466850152192*Sqrt[2])/1777010198663782143060892177416175446970826058100075480375140625]/2 F1Z2[148]:= 9645224515860105309415437496/2988975514315424180732263874125 - (316706658931855161807391008*Sqrt[37])/597795102863084836146452774825 - Sqrt[-266949412541549127599623408406357770405635164050251157776384/8933974625177154501563987032883426215115213066348553844515625 + (8777242638833979872439234613244413144953936247588093080576*Sqrt[37])/1786794925035430900312797406576685243023042613269710768903125]/2 F1Z2[163]:= 35233719653329995065411564/10792555251621895860488211571345343375 - 721765008917706076738535709528456446423850681988475904/(2158511050324379172097642314269068675*(-12737965652562547164590026038483234248161827096523072256574968383 + 229038073182066825378006485964950394558349727761749294205546402325349*Sqrt[489])^(1/3)) + (122365152*(-12737965652562547164590026038483234248161827096523072256574968383 + 229038073182066825378006485964950394558349727761749294205546402325349*Sqrt[489])^(1/3))/10792555251621895860488211571345343375 F1Z2[177]:= -119704396734808530595233033276109/311139207533976613448431110735832675 + (345557443066701312797921929958964*Sqrt[3])/1555696037669883067242155553679163375 - Sqrt[87131265907878508598645685509309892750525472432209036909316776673477691644376128/73582161661375545110226708181307322610255894994916687888267475478423336935545653421875 - (2012210393066677320346274050899655006334833739050814514596642619447652394623488*Sqrt[3])/2943286466455021804409068327252292904410235799796667515530699019136933477421826136875]/2 F1Z2[190]:= 102074768169040202948138466868949001048768352681/1547535782386692158683406897835240469412324669455 - (14435552152074585899633463828910110013256981088*Sqrt[2])/309507156477338431736681379567048093882464933891 - Sqrt[37858425246919617396548186027808792085774366401537237658691591855523073842454246502346064347264/1088575908075996103869235997144790488490514633957557417579003791518956783650790900832352277271375 - (58893888277709883927214549389253309863440635771240008653488465689736999167090286186296859540224*Sqrt[2])/2394866997767191428512319193718539074679132194706626318673808341341704924031739981831175009997025]/2 F1Z2[193]:= -8352665866066377773384459744309713654381/47220156796596840985156450723020842799875 + (601238045113556128502834768619399500016*Sqrt[193])/47220156796596840985156450723020842799875 + Sqrt[-1849325390168829621242885718760361924096943807305190734073442943674627725257245824/2229743207895190835419089642625346050204618219214148850224970010541556629300015625 + (133117354410299853185790637734419490823167258261956070323343271703015516029511808*Sqrt[193])/2229743207895190835419089642625346050204618219214148850224970010541556629300015625]/2 F1Z2[232]:= -117450988032190678500667097512/4490096163237419343427303443542375 + (3248423924546340779664287097144*Sqrt[58])/4490096163237419343427303443542375 - Sqrt[2448147663082621180231282351051287162957249648095532725200816128/20160963555119393934946196867206062085651774763182421659088420640625 - (3048125665442332068305398652484909102534212470834981068251136*Sqrt[58])/20160963555119393934946196867206062085651774763182421659088420640625]/2 F1Z2[253]:= 254942344478178099492506992890259767305189751748579/96977759394434898761111465213728431807061981808875 - 845548099807651569627713349319558464492321957799872/(96977759394434898761111465213728431807061981808875*Sqrt[11]) + Sqrt[42675238193874120764908588827262302955037187568317241460518926934116425358555047107470685177695223488/827612351910511751061968322972121802879143886443168498972339630976814477798721368373661564698531375 - 64335342240056594674271029521348556322731103718792642468260655813690042225587693723715175244061209088/(376187432686596250482712874078237183126883584746894772260154377716733853544873349260755256681150625*Sqrt[11])]/2 pF1X[2] := x - 1 pF1X[3] := x - 3 pF1X[4] := x^2 - 50 pF1X[5] := x^4 - 220*x^2 - 400 pF1X[6] := x^2 - 30*x + 25 pF1X[7] := x - 54 pF1X[8] := x^4 - 9188*x^2 - 20164 pF1X[9] := x^4 - 27000*x^2 - 270000 pF1X[10] := x^2 - 270*x - 995 pF1X[11] := x^3 - 445*x^2 + 275*x - 1375 pF1X[12] := x^4 - 498832*x^2 + 341056 pF1X[13] := x^4 - 1213148*x^2 - 72795024 pF1X[14] := x^4 - 1700*x^3 + 18350*x^2 - 32500*x + 85625 pF1X[15] := x^2 - 2550*x - 4580 pF1X[16] := x^4 - 14464000*x^2 - 76880000 pF1X[18] := x^2 - 8130*x - 169119 pF1X[19] := x^3 - 11745*x^2 + 11275*x - 43875 pF1X[22] := x^2 - 33318*x + 1397281 pF1X[23] := x^3 - 46346*x^2 + 268272*x - 1762168 pF1X[25] := x^4 - 7745350000*x^2 - 36180500000000 pF1X[27] := x^3 - 162981*x^2 - 575181*x - 1683639 pF1X[28] := x^4 - 48359285888*x^2 + 368516987136 pF1X[30] := x^4 - 394260*x^3 + 52504030*x^2 + 651863100*x - 561590775 pF1X[31] := x^3 - 523800*x^2 + 358900*x - 5373000 pF1X[34] := x^4 - 1197180*x^3 - 304761650*x^2 - 754339500*x - 1882974375 pF1X[37] := x^4 - 6976417891772*x^2 - 977589488681487504 pF1X[39] := x^4 - 4397070*x^3 - 138227000*x^2 - 524982000*x - 1240290000 pF1X[42] := x^4 - 9220908*x^3 - 6767041810*x^2 - 221500374492*x + 182882736409 pF1X[43] := x^3 - 11734173*x^2 - 146816669*x - 983476863 pF1X[46] := x^4 - 23785380*x^3 + 26775439150*x^2 - 66620704500*x + 750712325625 pF1X[55] := x^4 - 174230730*x^3 + 1360818980*x^2 - 2293666200*x + 4983463600 pF1X[58] := x^2 - 326147526*x - 1356684406731 pF1X[63] := x^4 - 895448196*x^3 - 1166997240*x^2 - 16122199176*x - 27241484976 pF1X[67] := x^3 - 1952273529*x^2 + 90420390379*x - 2108115753291 pF1X[70] := x^4 - 3450103740*x^3 + 46710125077270*x^2 - 459419682591900*x - 1461672781865775 pF1X[78] := x^4 - 14875973028*x^3 + 411643423344494*x^2 + 175823511727410828*x + 1285268729669350201 pF1X[82] := x^4 - 30032512452*x^3 - 1198718111782570*x^2 + 2283270117899292*x - 49954778539492271 pF1X[102] := x^4 - 798297409740*x^3 + 163027360849560838*x^2 + 258673394322643421940*x + 3930779638821936836961 pF1X[130] := x^4 - 47744435566260*x^3 - 75982034559218125370*x^2 + 6317226333136078505100*x + 16036227668571354288225 pF1X[142] := x^4 - 240469255193220*x^3 + 858893138751584476238*x^2 - 2594191121144788572180*x + 5703586127760905900761 pF1X[163] := x^3 - 3482010580696281*x^2 + 5913436467819477787*x - 5021384073173897227083 pF1X[190] := x^4 - 84970674066019860*x^3 + 5704998902295029443240990*x^2 - 2233154457185835655186373700*x + 18983882886895192207942622025 pF1Y[2] := 3*x - 28 pF1Y[3] := x - 33 pF1Y[4] := x^2 - 7938 pF1Y[5] := 81*x^4 - 3545280*x^2 - 279558400 pF1Y[6] := x^2 - 456*x + 3312 pF1Y[7] := 4*x - 3591 pF1Y[8] := 81*x^4 - 235109448*x^2 - 19529503504 pF1Y[9] := x^4 - 9596160*x^2 - 8032324608 pF1Y[10] := x^2 - 5400*x - 200880 pF1Y[11] := 27*x^3 - 250173*x^2 + 1269345*x - 33907951 pF1Y[12] := x^4 - 236317212*x^2 + 11453066361 pF1Y[13] := x^4 - 622634688*x^2 - 4723632785664 pF1Y[14] := 81*x^4 - 3226608*x^3 + 397690272*x^2 - 5525845248*x + 108362008832 pF1Y[15] := 16*x^2 - 993300*x - 15741495 pF1Y[16] := x^4 - 9136256976*x^2 - 1845112816008 pF1Y[18] := x^2 - 217000*x - 60172784 pF1Y[19] := x^3 - 321651*x^2 + 2550123*x - 52896969 pF1Y[22] := x^2 - 981288*x + 607034736 pF1Y[23] := 1728*x^3 - 2413037088*x^2 + 143222662716*x - 9068123555029 pF1Y[25] := x^4 - 7644357504000*x^2 - 8807745144844800000 pF1Y[27] := x^3 - 5321151*x^2 - 166208301*x - 3579300549 pF1Y[28] := 16*x^4 - 855298341229248*x^2 + 521806814257556961 pF1Y[30] := x^4 - 13566000*x^3 + 31931010720*x^2 + 4532703840000*x - 31902352070400 pF1Y[31] := 64*x^3 - 1172750832*x^2 + 6653607624*x - 525882820419 pF1Y[34] := x^4 - 43865712*x^3 - 203465916576*x^2 - 4241342248704*x - 67133524246272 pF1Y[37] := x^4 - 10190463893330112*x^2 - 521450030175393048516864 pF1Y[39] := 256*x^4 - 44169006336*x^3 - 17415361585440*x^2 - 576159438021804*x - 10182869559447039 pF1Y[42] := x^4 - 375487728*x^3 - 5524405236000*x^2 - 2519928963078912*x + 17069627565897984 pF1Y[43] := x^3 - 483467103*x^2 - 63373265109*x - 4295572165773 pF1Y[46] := x^4 - 1013581296*x^3 + 24281614625184*x^2 - 545421111895296*x + 45484707405682944 pF1Y[55] := 256*x^4 - 2078384616000*x^3 + 152817308827920*x^2 - 1853200743322500*x + 25426421640504225 pF1Y[58] := x^2 - 15606687096*x - 1553232987771696 pF1Y[63] := 256*x^4 - 11432220037056*x^3 - 125860696164000*x^2 - 7683980933328336*x - 111366548601024591 pF1Y[67] := x^3 - 100405598139*x^2 + 59916619711179*x - 17923464833770881 pF1Y[70] := x^4 - 181367802000*x^3 + 64514560690651680*x^2 - 7121831812714080000*x - 183549883280689094400 pF1Y[78] := x^4 - 825490633968*x^3 + 637057680523284384*x^2 + 4965690993111074274048*x + 351552303249246399396096 pF1Y[82] := x^4 - 1708750870992*x^3 - 1940327167021380000*x^2 + 32627249255870767872*x - 4791292839128230592256 pF1Y[102] := x^4 - 50657600994000*x^3 + 329090927092873148448*x^2 + 10964028581076624397344000*x + 1794871872686635262469202176 pF1Y[130] := x^4 - 3420379660698000*x^3 - 194983340733655928606880*x^2 + 235258740270875371770720000*x + 4948209820302547908543033600 pF1Y[142] := x^4 - 18004604903334000*x^3 + 2407448097258683102997408*x^2 - 60228835748842209263136000*x + 823823872182122958433679616 pF1Y[163] := x^3 - 279321108584036211*x^2 + 9513245277883088745507*x - 162003527014352783191061553 pF1Y[190] := x^4 - 7359117414813687600*x^3 + 21396235898865291113024998560*x^2 - 143564046791790430632439232928000*x + 11316047287507303785105891917318400 pF1Z2[2] := 125*x - 27 pF1Z2[3] := 125*x - 4 pF1Z2[4] := 1331*x - 8 pF1Z2[5] := 166375*x^2 + 533250*x - 729 pF1Z2[6] := 4913*x^2 - 2798*x + 1 pF1Z2[7] := 614125*x - 64 pF1Z2[8] := 190109375*x^2 - 1410750000*x + 46656 pF1Z2[9] := 16194277*x^2 + 2399094*x - 27 pF1Z2[10] := 3048625*x^2 - 246350*x + 1 pF1Z2[11] := 159484621967*x^3 - 114080856516*x^2 + 818421041232*x - 1259712 pF1Z2[12] := 561515625*x^2 - 420120000*x + 256 pF1Z2[13] := 190109375*x^2 + 3991250*x - 1 pF1Z2[14] := 599866273660753*x^4 + 232542870469668*x^3 + 366572950847046*x^2 - 4988528567964*x + 531441 pF1Z2[15] := 210114283625*x^2 - 87746552000*x + 4096 pF1Z2[16] := 1263214441*x^2 + 24363352960*x - 512 pF1Z2[17] := 124531835693359375*x^4 + 32805214101562500*x^3 + 13498547750156250*x^2 + 54808248442500*x - 531441 pF1Z2[18] := 56733768015625*x^2 - 159331542750*x + 729 pF1Z2[19] := 10260751717*x^3 - 24191500908*x^2 + 29039794032*x - 64 pF1Z2[20] := 103097383781866890625*x^4 - 72251986996813500000*x^3 - 9497816769831696000*x^2 - 2011983249694464000*x + 2176782336 pF1Z2[21] := 575722725759*x^4 - 17214152644188*x^3 + 1896754712378*x^2 + 1850000548*x - 1 pF1Z2[22] := 5290763640625*x^2 - 3642848750*x + 1 pF1Z2[23] := 6267542200571287109375*x^3 + 454521485120769000000*x^2 + 36452366690171904000*x - 5159780352 pF1Z2[24] := 452118343792751*x^4 - 355482335733856*x^3 - 919644794502272*x^2 + 55324786481152*x - 4096 pF1Z2[25] := 97838353751039*x^2 + 25481191682*x - 1 pF1Z2[27] := 16999373423828125*x^3 - 3502804096687500*x^2 + 4077357175062000*x - 46656 pF1Z2[28] := 1834891285515625*x^2 - 651655879040000*x + 4096 pF1Z2[30] := 553438215614390625*x^4 - 501660562998937500*x^3 + 8817665066947750*x^2 - 511034705500*x + 1 pF1Z2[31] := 30459314461806901*x^3 + 76740826083250560*x^2 + 236618264481632256*x - 262144 pF1Z2[32] := 5396307128541531668212890625*x^4 + 1498487065588342570500000000*x^3 + 18441177741337842576000000*x^2 + 220093689501926866944000*x - 139314069504 pF1Z2[33] := 185802855712890625*x^4 + 10656372166773437500*x^3 - 108912710344656250*x^2 - 2741240450500*x + 1 pF1Z2[34] := 271736414757696097*x^4 - 355559149057838044*x^3 + 246471524163920166*x^2 - 4717175541916*x + 1 pF1Z2[36] := 191478360645378085609*x^4 + 283827463464612724128*x^3 + 269499185406087942528*x^2 - 40743654857689651200*x + 2985984 pF1Z2[37] := 2645105437918109375*x^2 + 22951495255250*x - 1 pF1Z2[39] := 792686301292419743120913*x^4 - 536482747538803602953280*x^3 + 298209788172578527633408*x^2 - 1067164464888813715456*x + 16777216 pF1Z2[40] := 134985960286859375*x^4 - 10485112102432700000*x^3 + 4033930575960624000*x^2 + 429500491436185600*x - 4096 pF1Z2[42] := 55701936946441650390625*x^4 - 51298924769710835937500*x^3 + 112697080651205843750*x^2 - 279766037081500*x + 1 pF1Z2[43] := 8591507552001953125*x^3 - 24963724224187500*x^2 + 28991078006790000*x - 64 pF1Z2[45] := 403906221577284398319359375*x^4 - 1715975920166358820386937500*x^3 + 510399269097896172328292250*x^2 + 620784640003801702500*x - 531441 pF1Z2[46] := 12850316252289637351777*x^4 + 7501369548251751485540*x^3 + 1931359131577797616806*x^2 - 1861047971688028*x + 1 pF1Z2[48] := 127020319060954077880859375*x^4 - 167928782439298606000000000*x^3 - 5515244909180922048000000*x^2 + 4879884007274381312000*x - 1048576 pF1Z2[49] := 236427423164659405066751*x^4 - 48616546605633060969596*x^3 + 15025024196814134539002*x^2 + 7306766273939332*x - 1 pF1Z2[52] := 672365269265869140625*x^4 - 3102827070702437500000*x^3 + 5531375051003094000000*x^2 - 112753964544118528000*x + 4096 pF1Z2[55] := 7883334755587129843140625*x^4 - 19559436295977610195000000*x^3 + 14223852181012485364224000*x^2 - 1675513225224923348992000*x + 16777216 pF1Z2[57] := 13461070811403533855712890625*x^4 + 11401173045598900536773437500*x^3 - 2674232861134373288656250*x^2 - 231253023524354500*x + 1 pF1Z2[58] := 4980291492907241681640625*x^2 - 349959466348316750*x + 1 pF1Z2[60] := 97562564443544663354281543140625*x^4 - 10447634977114726035268342400000*x^3 + 87148926763262109241058816000*x^2 - 13304658857139055152332800*x + 16777216 pF1Z2[63] := 547274431487205474853515625*x^4 - 5792176969356103780500000000*x^3 + 44593873904366069897088000000*x^2 - 32263155987043153366646784000*x + 12230590464 pF1Z2[64] := 250359560417306323993916658961*x^4 - 10943707116461111948941072384*x^3 + 1282874415411766922994425856*x^2 + 8205552571468594788958208*x - 2097152 pF1Z2[67] := 39559841266507364001953125*x^3 - 691033152496104187500*x^2 + 802490270074994694000*x - 64 pF1Z2[70] := 199097012401419243322614390625*x^4 - 137322853468384553137924937500*x^3 + 5895047168419076051452707750*x^2 - 39159703063321217500*x + 1 pF1Z2[72] := 10008445971730580115574462890625*x^4 + 57576716596964851626050437500000*x^3 - 63663576018591485966561694000000*x^2 - 179682504297333484641617664000*x + 2176782336 pF1Z2[73] := 42648629100728852144287109375*x^4 - 8822381628848720684773437500*x^3 + 31377804607100720820840656250*x^2 + 119379461724784898500*x - 1 pF1Z2[78] := 190542906155144596191019629150390625*x^4 - 29524610421029431908188943710937500*x^3 + 472597469957470843560779843750*x^2 - 728027257108471697500*x + 1 pF1Z2[82] := 9976963485247017149566650390625*x^4 + 10621027131628719448499914062500*x^3 + 3888414868982708122391625843750*x^2 - 2967310385945378729500*x + 1 pF1Z2[85] := 4827152618404441759949326890625*x^4 + 1144716369429454898089351438737500*x^3 - 18268288578378644515592685800250*x^2 - 8323637599084207540900*x + 1 pF1Z2[88] := 107413065512047349578369140625*x^4 + 118825370845266487504437500000*x^3 - 136252585169027771671326000000*x^2 - 93925954978887091042048000*x + 4096 pF1Z2[93] := 4642517222953002147203107673574462890625*x^4 + 340229454570472735424402583668085937500*x^3 - 994493276046683059398831647656250*x^2 - 119562334956358303022500*x + 1 pF1Z2[97] := 125805295202567454961190894287109375*x^4 - 40355232733203236981783812273437500*x^3 + 6879527561430205965938321520656250*x^2 + 434063887942527195938500*x - 1 pF1Z2[100] := 40173457994421997391175208490641*x^4 - 15142398783029684091663789020512*x^3 + 17653342747821487221723291417984*x^2 - 4595611279063401997855725568*x + 4096 pF1Z2[102] := 1500204578684428086872355549102254150390625*x^4 - 64909451935612890662444677180095960937500*x^3 + 73029911755739899454018063743843750*x^2 - 2096561993697267648929500*x + 1 pF1Z2[112] := 16868145819147116783434735077880859375*x^4 - 59551401542410553502878924000000000000*x^3 + 7034531502800645366539293373440000000*x^2 + 733804504709872698810239549440000*x - 16777216 pF1Z2[130] := 19236826333037936730885942502387761114390625*x^4 - 15118188993962809261441282564227180925937500*x^3 + 15622991663433664722390303556497775347750*x^2 - 7499357316207209662281449500*x + 1 pF1Z2[133] := 2139673403644138632031271784175537109375*x^4 - 994526392702189382279906817825521585937500*x^3 + 53601832072238278495073633108346759656250*x^2 + 17059553830496608260519374500*x - 1 pF1Z2[142] := 2008024433105178862840461392478129150390625*x^4 - 3923589729201003448454812208688224710937500*x^3 + 1996064277164517601938808163181903387843750*x^2 - 190238141379262042820979665500*x + 1 pF1Z2[148] := 28681321683264998046753149245265869140625*x^4 - 370210844112661698321547222014437500000*x^3 + 429698809548865498425463990020822000000*x^2 - 3728427128725901871235804909312000*x + 4096 pF1Z2[163] := 224451422498574115473590775022822688001953125*x^3 - 2198253790246041723377943360187500*x^2 + 2552810853189232588558727380998000*x - 64 pF1Z2[177] := 453862812208398970976788666031391041820019781421855712890625*x^4 + 698457446959169058204847636214112364135655147512773437500*x^3 - 955988126716674918584499441060400215841192656250*x^2 - 1164527733988793689131688220162500*x + 1 pF1Z2[190] := 6436781644864647697523795565683453327461887922014390625*x^4 - 1698268955412406376549653742532139004948883467730137500*x^3 + 88064942603596954678608650784469580855415391299750*x^2 - 23752898720272640689632999159799900*x + 1 pF1Z2[193] := 453110606136094296406393832816799610694894287109375*x^4 + 320598807812375890629983208779637681124795726562500*x^3 + 244612559870637809842371050014562021301625968656250*x^2 + 46935388218352090256815237384994500*x - 1 pF1Z2[232] := 101593661267122957308468060913151353430146078369140625*x^4 + 10629862221060282813907580605122243739555437500000*x^3 - 12336050585549692139911996453885393153159998000000*x^2 - 866840466705515186297226740329752000256000*x + 4096 pF1Z2[253] := 22918572044387935058778295489963164548153319919675537109375*x^4 - 241000185014527734676510516716573686280687187199828585937500*x^3 + 42669328796600344303048307450894780819546428170306519656250*x^2 + 14652951773955041963658819957780221198500*x - 1 (* Type F2' N=7〜1555 著者が N=7〜10,000 までを探索してみたが、1555以上では4次方程式で解け る最小多項式を発見する事はできなかった． *) sumF2D[t_, limit_:Infinity] := (Sum[termp[n, 1/3, F2DX[t], F2DY[t], F2DZ2[t]], {n, 0, limit}] * Sqrt[F2DZ2[t]/ -1728]); F2DX[7]:= 24 F2DX[9]:= 360/Sqrt[45 + 26*Sqrt[3]] F2DX[11]:= 60 F2DX[13]:= 51192*Sqrt[2/(303287 + 84125*Sqrt[13])] F2DX[15]:= 12*(5 + 3*Sqrt[5]) F2DX[19]:= 300 F2DX[23]:= 216 + (184944384 - 2592000*Sqrt[69])^(1/3)/3 + 4*2^(2/3)*(3*(8919 + 125*Sqrt[69]))^(1/3) F2DX[25]:= 322800*Sqrt[10/(774535 + 346383*Sqrt[5])] F2DX[27]:= 1116 F2DX[31]:= 640 + (8516448000 - 69984000*Sqrt[93])^(1/3)/3 + 20*2^(2/3)*(9857 + 81*Sqrt[93])^(1/3) F2DX[35]:= 12*(145 + 64*Sqrt[5]) F2DX[37]:= 5932387512*Sqrt[2/(1744104472943 + 286729020625*Sqrt[37])] F2DX[39]:= 30*(49 + 13*Sqrt[13] + 3*Sqrt[2*(263 + 73*Sqrt[13])]) F2DX[43]:= 9468 F2DX[51]:= 60*(197 + 48*Sqrt[17]) F2DX[55]:= 6*(1535 + 675*Sqrt[5] + Sqrt[10*(460891 + 206145*Sqrt[5])]) F2DX[59]:= 18460 + (168942108672000 - 42467328000*Sqrt[177])^(1/3)/3 + 640*(23869 + 6*Sqrt[177])^(1/3) F2DX[63]:= 12*(1713 + 378*Sqrt[21] + Sqrt[3*(1980441 + 432194*Sqrt[21])]) F2DX[67]:= 122124 F2DX[75]:= 900*(143 + 64*Sqrt[5]) F2DX[83]:= 174124 + (142393828951719936 - 8196194304000*Sqrt[249])^(1/3)/3 + 128*(2514765509 + 144750*Sqrt[249])^(1/3) F2DX[91]:= 60*(8537 + 2368*Sqrt[13]) F2DX[99]:= 180*(5423 + 944*Sqrt[33]) F2DX[107]:= 1208828 + (47680314144769179648 - 694935355392000*Sqrt[321])^(1/3)/3 + 256*(105258081014 + 1534125*Sqrt[321])^(1/3) F2DX[115]:= 12*(274345 + 122688*Sqrt[5]) F2DX[123]:= 12*(488045 + 76224*Sqrt[41]) F2DX[139]:= 11711420 + (43369988405428224000000 - 11752833024000000*Sqrt[417])^(1/3)/3 + 3200*(49020259609 + 13284*Sqrt[417])^(1/3) F2DX[147]:= 84*(353695 + 77184*Sqrt[21]) F2DX[155]:= 12*(2064365 + 923200*Sqrt[5] + 16*Sqrt[5*(6658640053 + 2977834360*Sqrt[5])]) F2DX[163]:= 163096908 F2DX[171]:= 60*(1105113 + 146376*Sqrt[57] + 8*Sqrt[6*(6360806835 + 842509447*Sqrt[57])]) F2DX[187]:= 12*(28276253 + 6858000*Sqrt[17]) F2DX[195]:= 12*(22276545 + 9962400*Sqrt[5] + 32*Sqrt[65*(14911222841 + 6668501580*Sqrt[5])]) F2DX[203]:= 12*(34777205 + 6457952*Sqrt[29] + 80*Sqrt[377953708933 + 70184241796*Sqrt[29]]) F2DX[211]:= 861161260 + (17243182379284687419604992000 - 112409083975827456000*Sqrt[633])^(1/3)/3 + 640*(2436204469367795509 + 15881726862*Sqrt[633])^(1/3) F2DX[219]:= 60*(16523489 + 1933928*Sqrt[73] + 120*Sqrt[2*(18960158561 + 2219118709*Sqrt[73])]) F2DX[235]:= 36*(126842375 + 56725632*Sqrt[5]) F2DX[243]:= 108*(42322017 + 29344448*3^(1/3) + 20346304*3^(2/3)) F2DX[259]:= 60*(126304429 + 20764320*Sqrt[37] + 32*Sqrt[31157829815957 + 5122315668376*Sqrt[37]]) F2DX[267]:= 12*(1860739157 + 197238000*Sqrt[89]) F2DX[275]:= 300*(54510481 + 24377824*Sqrt[5] + 16*Sqrt[23214000367045 + 10381616570084*Sqrt[5]]) F2DX[283]:= 31762181212 + (865156583438085986615486840832000 - 45693131706807091200000*Sqrt[849])^(1/3)/3 + 1280*(15279215061012656364008 + 806969743425*Sqrt[849])^(1/3) F2DX[291]:= 60*(575304005 + 58413272*Sqrt[97] + 24*Sqrt[2*(574608975983921 + 58342702021663*Sqrt[97])]) F2DX[307]:= 95198772332 + (23294736765204945745579410815188992 - 1131467934282144546816000*Sqrt[921])^(1/3)/3 + 128*(411399854822599371196241923 + 19982442754854000*Sqrt[921])^(1/3) F2DX[315]:= 36*(2832218015 + 618040640*Sqrt[21] + 16*Sqrt[5*(12533529456159541 + 2735040355133800*Sqrt[21])]) F2DX[323]:= 12*(12079021865 + 2929593000*Sqrt[17] + 8*Sqrt[2*(2279730676891017097 + 552915904634266625*Sqrt[17])]) F2DX[331]:= 273561472700 + (552749763243324484058872132141056000 - 31157134293522746179584000*Sqrt[993])^(1/3)/3 + 1280*(9761912085273963152194414 + 550254791639871*Sqrt[993])^(1/3) F2DX[355]:= 12*(47317196545 + 21160893600*Sqrt[5] + 16*Sqrt[5*(3498307948375615073 + 1564490875759140060*Sqrt[5])]) F2DX[363]:= 396*(1997677405 + 347751000*Sqrt[33] + 8*Sqrt[2*(62354923715958313 + 10854598957770375*Sqrt[33])]) F2DX[379]:= 2025421044380 + (224341551034589411664786796183289856000 - 3878628492590642480283648000*Sqrt[1137])^(1/3)/3 + 640*(31696114862878504387860728537 + 547992352039286646*Sqrt[1137])^(1/3) F2DX[387]:= 12*(174513884841 + 15365090808*Sqrt[129] + 8*Sqrt[6*(158620291673554596123 + 13965737956561594501*Sqrt[129])]) F2DX[403]:= 12*(656857196889 + 182179408000*Sqrt[13]) F2DX[427]:= 12*(1657145277365 + 212175710912*Sqrt[61]) F2DX[435]:= 12*(1121428000265 + 208243952160*Sqrt[29] + 32*Sqrt[5*(491250297713786535089 + 91222890163538998200*Sqrt[29])]) F2DX[475]:= 300*(195711118805 + 87524673120*Sqrt[5] + 16*Sqrt[299240953311759204685 + 133824622651386880068*Sqrt[5]]) F2DX[483]:= 12*(6519833252657 + 784895688576*Sqrt[69] + 1344*Sqrt[7*(6723670088957005259 + 809434759526358768*Sqrt[69])]) F2DX[499]:= 183932475905900 + (168011502190900244037290865622336880246784000 - 69014959816438443775407685632000*Sqrt[1497])^(1/3)/3 + 640*(23737519185228735469859210208233993 + 9750784388851369755414*Sqrt[1497])^(1/3) F2DX[507]:= 156*(1170213525105 + 324558836000*Sqrt[13] + 144*Sqrt[3*(44026481972767522007 + 12210749094700328500*Sqrt[13])]) F2DX[547]:= 956681088341708 + (23640972125164858617156883456316114331676704768 - 26156173047771848258334228480000*Sqrt[1641])^(1/3)/3 + 512*2^(2/3)*(1630916372297873832089266529811485107 + 1804432179625101129375*Sqrt[1641])^(1/3) F2DX[555]:= 12*(78144199334725 + 34947148356000*Sqrt[5] + 48*Sqrt[185*(28652946182227464928221 + 12813987083820737625820*Sqrt[5])]) F2DX[595]:= 12*(289712417482185 + 129563331883200*Sqrt[5] + 16*Sqrt[85*(7714456327508702771311141 + 3450009751552568048325480*Sqrt[5])]) F2DX[603]:= 12*(374508384059013 + 26415784679832*Sqrt[201] + 104*Sqrt[6*(4322501532621100481161203 + 304885750557636501367153*Sqrt[201])]) F2DX[627]:= 12*(800901385316545 + 55399507236744*Sqrt[209] + 27000*Sqrt[6*(293298138554059466259 + 20287856466283892453*Sqrt[209])]) F2DX[643]:= 21099774836356492 + (253628017233079601646769799959458148645292998656000 - 300882483171393370323565097779200000*Sqrt[1929])^(1/3)/3 + 2560*(559903995269050425173551506376836363133 + 664221982539568499996850*Sqrt[1929])^(1/3) F2DX[667]:= 12*(2754449619866205 + 511488453652704*Sqrt[29] + 160*Sqrt[592733805342269896592604577 + 110067904432003638720797676*Sqrt[29]]) F2DX[715]:= 12*(11560288517735525 + 1433877318072000*Sqrt[65] + 32*Sqrt[10*(26101615354156447486813747573 + 3237506932802403245306303475*Sqrt[65])]) F2DX[723]:= 12*(14612831313525313 + 941295212108488*Sqrt[241] + 24*Sqrt[2*(370720206595588481320222462649 + 23880187761923332188481798081*Sqrt[241])]) F2DX[763]:= 12*(46272275676974397 + 4432080192040544*Sqrt[109] + 48*Sqrt[1858614146116251186769192158677 + 178022948323401115914087866116*Sqrt[109]]) F2DX[795]:= 12*(113870789468214365 + 50924565180544800*Sqrt[5] + 32*Sqrt[265*(95567192615904946884990197341 + 42738947821595882157918510480*Sqrt[5])]) F2DX[883]:= 19822848604593634796 + (210310984522394623277496073918123039338330782469254780289024 - 27897024322913966002843509606013992960000*Sqrt[2649])^(1/3)/3 + 256*(464278204622963232635339264335727336976993486769232 + 61584897224359967096742677701875*Sqrt[2649])^(1/3) F2DX[907]:= 37222766169818947772 + (1392482341707418293002650780718653262569418401261721015549952 - 53832758926594906124559583644009627648000*Sqrt[2721])^(1/3)/3 + 27136*(2581002591670714650084289323501202067163298721 + 99780432501542041707016500*Sqrt[2721])^(1/3) F2DX[955]:= 12*(8004252765996083725 + 3579610658771592000*Sqrt[5] + 192*Sqrt[5*(695182968120181621073378122009757 + 310895274703359058978348603040940*Sqrt[5])]) F2DX[1003]:= 12*(26707178098931898365 + 6477442133181111000*Sqrt[17] + 8*Sqrt[2*(11144896281376057010188950901187788937 + 2703034385568645068464003957131525375*Sqrt[17])]) F2DX[1027]:= 12*(48259713058926806497 + 13384836151779976000*Sqrt[13] + 640*Sqrt[11372069846337649164891747991397669 + 3154044687625252590483288020269700*Sqrt[13]]) F2DX[1227]:= 12*(5220092801775318979669 + 258116976851086836688*Sqrt[409] + 96*Sqrt[2*(2956745752945587891226812389602872762761 + 146201668063841898100403344761818961013*Sqrt[409])]) F2DX[1243]:= 12*(7464061190103130352365 + 702159812442212346000*Sqrt[113] + 32*Sqrt[2*(54406454540628670528958351297130845339777 + 5118128716113291287523348973628897808375*Sqrt[113])]) F2DX[1387]:= 12*(169031329918875472759133 + 19783620765792812343000*Sqrt[73] + 40*Sqrt[2*(17857244058839829085187791612599757099074457 + 2090032330407900433150368219958545404859475*Sqrt[73])]) F2DX[1411]:= 60*(55958278885801955996693 + 13571876145525411689496*Sqrt[17] + 8*Sqrt[2*(48927015247831078094038063038387306833027225 + 11866544224294904369319909645909830338755183*Sqrt[17])]) F2DX[1435]:= 12*(461156038220802318974045 + 72020473306588499307840*Sqrt[41] + 128*Sqrt[5*(5192013954773097881799728815805540263756829 + 810856351095053690318956989912231357734100*Sqrt[41])]) F2DX[1467]:= 12*(892063338250599020584821 + 40340498597535404203272*Sqrt[489] + 8*Sqrt[6*(4144671872139597092018576817251797593886187763 + 187428540862557503568687737562893875775186239*Sqrt[489])]) F2DX[1507]:= 36*(671582608538127180626171 + 57377174439394672632000*Sqrt[137] + 160*Sqrt[2*(17618093753549819339485106613861382321515053 + 1505215331271712082065378625373332043551025*Sqrt[137])]) F2DX[1555]:= 12*(5280419026080999965452185 + 2361475178400070170568800*Sqrt[5] + 32*Sqrt[5*(10891728551171178200467436212395209160385656017 + 4870929086578810225077338534541688721351255040*Sqrt[5])]) F2DY[7]:= 189 F2DY[9]:= 11088*Sqrt[2/(1020 + 589*Sqrt[3])] F2DY[11]:= 616 F2DY[13]:= 55728*Sqrt[13/(18478 + 5125*Sqrt[13])] F2DY[15]:= (63*(25 + 13*Sqrt[5]))/2 F2DY[19]:= 4104 F2DY[23]:= 9338/3 + (1355347216573/2 - (10511106375*Sqrt[69])/2)^(1/3)/3 + (7*((23*(171802157 + 1332375*Sqrt[69]))/2)^(1/3))/3 F2DY[25]:= 6320160*Sqrt[5/(601880 + 269169*Sqrt[5])] F2DY[27]:= 18216 F2DY[31]:= 11439 + (88229746029987/2 - (387149276943*Sqrt[93])/2)^(1/3)/3 + 9*((31*(144597919 + 634491*Sqrt[93]))/2)^(1/3) F2DY[35]:= 56*(575 + 256*Sqrt[5]) F2DY[37]:= 929362896*Sqrt[37/(2168508622 + 356500625*Sqrt[37])] F2DY[39]:= 28665 + (15561*Sqrt[13])/2 + (63*Sqrt[13*(125887 + 34922*Sqrt[13])])/2 F2DY[43]:= 195048 F2DY[51]:= 504*(527 + 128*Sqrt[17]) F2DY[55]:= 853875/4 + (378675*Sqrt[5])/4 + Sqrt[721997922195/2 + (322898466825*Sqrt[5])/2]/2 F2DY[59]:= 445096 + (2376815385275006976 - 217419834458112*Sqrt[177])^(1/3)/3 + (2048*(59*(1563264 + 143*Sqrt[177]))^(1/3))/3^(2/3) F2DY[63]:= 2056509/4 + (451269*Sqrt[21])/4 + Sqrt[4254042462831/2 + (928322405829*Sqrt[21])/2]/2 F2DY[67]:= 3140424 F2DY[75]:= 360*(9729 + 4352*Sqrt[5]) F2DY[83]:= 14948632/3 + (3339326453917476192256 - 66038343401472000*Sqrt[249])^(1/3)/3 + (2048*(83*(4683720046 + 92625*Sqrt[249]))^(1/3))/3 F2DY[91]:= 16632*(923 + 256*Sqrt[13]) F2DY[99]:= 3192*(9559 + 1664*Sqrt[33]) F2DY[107]:= 117844664/3 + (1636404980638620160360448 - 8039109331255296000*Sqrt[321])^(1/3)/3 + (14336*2^(2/3)*(107*(1297666361 + 6375*Sqrt[321]))^(1/3))/3 F2DY[115]:= 4968*(22325 + 9984*Sqrt[5]) F2DY[123]:= 504*(404875 + 63232*Sqrt[41]) F2DY[139]:= 433776744 + (2203748202570798477682409472 - 136637836569719341056*Sqrt[417])^(1/3)/3 + 18432*(139*(93770454593 + 5814*Sqrt[417]))^(1/3) F2DY[147]:= 5544*(204125 + 44544*Sqrt[21]) F2DY[155]:= 56*(17301875 + 7737600*Sqrt[5] + 128*Sqrt[155*(235755847 + 105433220*Sqrt[5])]) F2DY[163]:= 6541681608 F2DY[171]:= 24*(113499711 + 15033408*Sqrt[57] + 64*Sqrt[114*(55176575325 + 7308315937*Sqrt[57])]) F2DY[187]:= 2376*(6135181 + 1488000*Sqrt[17]) F2DY[195]:= 72*(162878625 + 72841600*Sqrt[5] + 2432*Sqrt[130*(69006187 + 30860505*Sqrt[5])]) F2DY[203]:= 56*(333568875 + 61942144*Sqrt[29] + 16000*Sqrt[29*(29975249 + 5566264*Sqrt[29])]) F2DY[211]:= 39298468104 + (1638666849179005458750125786529792 - 2226029985548219266891776*Sqrt[633])^(1/3)/3 + 129024*(211*(133916146295164 + 181917*Sqrt[633]))^(1/3) F2DY[219]:= 504*(91452283 + 10703680*Sqrt[73] + 64*Sqrt[146*(27970911149 + 3273747529*Sqrt[73])]) F2DY[235]:= 213192*(1031525 + 461312*Sqrt[5]) F2DY[243]:= 72*(3108927753 + 2155610112*3^(1/3) + 1494616576*3^(2/3)) F2DY[259]:= 1512*(253406525 + 41659776*Sqrt[37] + 128*Sqrt[74*(105928768531 + 17414582273*Sqrt[37])]) F2DY[267]:= 504*(2274268531 + 241072000*Sqrt[89]) F2DY[275]:= 280*(3042702091 + 1360737664*Sqrt[5] + 128*Sqrt[11*(102739207765655 + 45946370503696*Sqrt[5])]) F2DY[283]:= 1678623925032 + (127709730865545415768928157696000000000 - 1086682434499510272000000000*Sqrt[849])^(1/3)/3 + 2304000*2^(2/3)*(283*(341638160183501 + 2907*Sqrt[849]))^(1/3) F2DY[291]:= 504*(3670409287 + 372673600*Sqrt[97] + 832*Sqrt[194*(200636819309 + 20371582507*Sqrt[97])]) F2DY[307]:= 5240230712712 + (3885214390268711910575572620712819556352 - 29790863328777377685700608000*Sqrt[921])^(1/3)/3 + 18432*(307*(74850630640566730935101 + 573936129000*Sqrt[921]))^(1/3) F2DY[315]:= 168*(33839586625 + 7384403200*Sqrt[21] + 5504*Sqrt[5*(15120050402521 + 3299465499100*Sqrt[21])]) F2DY[323]:= 56*(146142359375 + 35444728000*Sqrt[17] + 1472*Sqrt[646*(30516454942511 + 7401327473375*Sqrt[17])]) F2DY[331]:= 15635753063784 + (103209618673314620073229670718766206418944 - 1171554164948609939875829907456*Sqrt[993])^(1/3)/3 + 1677312*2^(2/3)*(331*(611824497271160651 + 6944949*Sqrt[993]))^(1/3) F2DY[355]:= 216*(155600342875 + 69586588800*Sqrt[5] + 128*Sqrt[355*(8325355791425107 + 3723212297299620*Sqrt[5])]) F2DY[363]:= 792*(59785869375 + 10407384000*Sqrt[33] + 64*Sqrt[2*(872644093707005653 + 151907838316099875*Sqrt[33])]) F2DY[379]:= 123875321800104 + (51323722862646336915555142473346932893810688 - 178096184148367407793508689379328*Sqrt[1137])^(1/3)/3 + 129024*(379*(2335090257174672939642164 + 8102893579209*Sqrt[1137]))^(1/3) F2DY[387]:= 168*(770384091429 + 67828537152*Sqrt[129] + 64*Sqrt[258*(1123220325227312949 + 98894035334974963*Sqrt[129])]) F2DY[403]:= 46872*(10605743499 + 2941504000*Sqrt[13]) F2DY[427]:= 34776*(37121542375 + 4752926464*Sqrt[61]) F2DY[435]:= 504*(1749510714575 + 324875984000*Sqrt[29] + 31616*Sqrt[290*(21117930944427 + 3921501328325*Sqrt[29])]) F2DY[475]:= 1080*(3722285464339 + 1664656665984*Sqrt[5] + 128*Sqrt[19*(89017585051068119935 + 39809874273411480888*Sqrt[5])]) F2DY[483]:= 504*(10717923092071 + 1290286315008*Sqrt[69] + 76544*Sqrt[14*(2800921424641633 + 337191315131691*Sqrt[69])]) F2DY[499]:= 12907988279996040 + (58068345395068528442703981895852439874659225174016 - 4774211117672768834218053494139518976*Sqrt[1497])^(1/3)/3 + 18450432*(499*(686207600339595812898244 + 56418000759*Sqrt[1497]))^(1/3) F2DY[507]:= 936*(13796461562625 + 3826449968000*Sqrt[13] + 384*Sqrt[3*(860561124189422685107 + 238676712225838265500*Sqrt[13])]) F2DY[547]:= 70292780852800968 + (9377691434064534135245377069063317219159350483877888 - 1161425406897297293357832669757440000*Sqrt[1641])^(1/3)/3 + 258048*(547*(36952460016205849031198818739056 + 4576555564014375*Sqrt[1641]))^(1/3) F2DY[555]:= 504*(137703132447875 + 61582712976000*Sqrt[5] + 1281664*Sqrt[185*(124795100437069 + 55810065567240*Sqrt[5])]) F2DY[595]:= 16632*(16018145541375 + 7163532460800*Sqrt[5] + 3712*Sqrt[85*(438146761053974641 + 195945188367608940*Sqrt[5])]) F2DY[603]:= 168*(2063678491084977 + 145560657622848*Sqrt[201] + 64*Sqrt[402*(5172828380760693056173449 + 364863181995848670407299*Sqrt[201])]) F2DY[627]:= 5544*(136370587790125 + 9432950802112*Sqrt[209] + 72000*Sqrt[114*(62936353470788841 + 4353398599873247*Sqrt[209])]) F2DY[643]:= 1680866338450798152 + (128222223596479529604369269541711251027269779456000000000 - 21886507431490347033527976984576000000000*Sqrt[1929])^(1/3)/3 + 59904000*(643*(34357463895158903488208076439 + 5864544131094*Sqrt[1929]))^(1/3) F2DY[667]:= 1512*(1773687387743625 + 329365479287424*Sqrt[29] + 16000*Sqrt[1334*(18424188000379517393 + 3421285821368055423*Sqrt[29])]) F2DY[715]:= 16632*(700661632306675 + 86906379600000*Sqrt[65] + 1664*Sqrt[10*(35460105615136807693213 + 4398284788478794401675*Sqrt[65])]) F2DY[723]:= 504*(29390305600339039 + 1893196010440384*Sqrt[241] + 832*Sqrt[482*(5177790908659412629340069 + 333530832393093980589061*Sqrt[241])]) F2DY[763]:= 1512*(31868561114053017 + 3052454550721664*Sqrt[109] + 384*Sqrt[109*(126376394100225125079424857 + 12104663210066286477036056*Sqrt[109])]) F2DY[795]:= 504*(240157679314566875 + 107401779253225600*Sqrt[5] + 31616*Sqrt[530*(217737502303113698723127 + 97375171280155849855555*Sqrt[5])]) F2DY[883]:= 1850530675332332165256 + (171101032346556323614577355518175681552650310335964983885083705344 - 2040406015698800156751780979167714795847680000*Sqrt[2649])^(1/3)/3 + 129024*2^(2/3)*(883*(835327281508916099554861447582907918375537729 + 9961405766482632088708125*Sqrt[2649]))^(1/3) F2DY[907]:= 3521779493604002065512 + (1179370458654051983944161374565147690752331177374452150119539146752 - 4045193340585609701885770999491657228877824000*Sqrt[2721])^(1/3)/3 + 193019904*(907*(6696886031513505648275135384091973612 + 22970050316722125*Sqrt[2721]))^(1/3) F2DY[955]:= 216*(43171769350445071375 + 19307002195307424000*Sqrt[5] + 768*Sqrt[1910*(3308825656694303897818070623781 + 1479751818812769118929479747385*Sqrt[5])]) F2DY[1003]:= 1512*(21089087883959062625 + 5114855111382168000*Sqrt[17] + 64*Sqrt[2006*(108256682047935522937348761329711 + 26256102044855609177404035614625*Sqrt[17])]) F2DY[1027]:= 216*(269927619562104483499 + 74864451768854176000*Sqrt[13] + 64000*Sqrt[1027*(34641305742256064323337778191 + 9607769546363797620120673100*Sqrt[13])]) F2DY[1227]:= 504*(13677322505772780988627 + 676300071793120912384*Sqrt[409] + 128*Sqrt[818*(27916368842003217464639844506364074009 + 1380375599396842010752270328864595397*Sqrt[409])]) F2DY[1243]:= 1512*(6561302835408690939625 + 617235450105342288000*Sqrt[113] + 1024*Sqrt[1243*(66060083712967003750660681813981237 + 6214409931595545189436969768793250*Sqrt[113])]) F2DY[1387]:= 16632*(14268952144500366465283 + 1670054528279010264000*Sqrt[73] + 8000*Sqrt[2774*(2293653065316798925642414008151027 + 268451786034599533816756041909649*Sqrt[73])]) F2DY[1411]:= 16632*(23822344568065528870487 + 5777767229646664699968*Sqrt[17] + 3904*Sqrt[2822*(26388965922292547767501447108379495 + 6400264344025714105679298344612841*Sqrt[17])]) F2DY[1435]:= 1512*(435565203642581990719625 + 68023856400638811129600*Sqrt[41] + 1588736*Sqrt[205*(733295494707289677769556111214829 + 114521515984403847512144949983700*Sqrt[41])]) F2DY[1467]:= 168*(7667125730732233862047809 + 346719410523340828678848*Sqrt[489] + 64*Sqrt[978*(29349206453528551506534141878018145115085949 + 1327216993469522326204576718165788484370697*Sqrt[489])]) F2DY[1507]:= 4536*(650032984842464283255151 + 55536065836864256336000*Sqrt[137] + 368000*Sqrt[3014*(2070436426359582545088899392281203 + 176889321567603397681369231438455*Sqrt[137])]) F2DY[1555]:= 1512*(5191739717921049742255125 + 2321816586151410072067200*Sqrt[5] + 1664*Sqrt[3110*(6260208323789001636993322654444020882161 + 2799650273060444296577206890718825190235*Sqrt[5])]) F2DZ2[7]:= -64/125 F2DZ2[9]:= (3*(-399849 - 230888*Sqrt[3]))/16194277 F2DZ2[11]:= -27/512 F2DZ2[13]:= (-15965 - 4428*Sqrt[13])/1520875 F2DZ2[15]:= (32*(1415 - 637*Sqrt[5]))/33275 F2DZ2[19]:= -1/512 F2DZ2[23]:= 189897408/817400375 - (5164103423808*(2/(-4007553325387 + 766715012547*Sqrt[69]))^(1/3))/817400375 + (14112*2^(2/3)*(-4007553325387 + 766715012547*Sqrt[69])^(1/3))/817400375 F2DZ2[25]:= (-12740595841 - 5697769392*Sqrt[5])/97838353751039 F2DZ2[27]:= -9/64000 F2DZ2[31]:= 1717278848/79562482901 - (20824871253690816*(2/(-1929445201756659679 + 982451144046124071*Sqrt[93]))^(1/3))/79562482901 + (3744*2^(2/3)*(-1929445201756659679 + 982451144046124071*Sqrt[93])^(1/3))/79562482901 F2DZ2[35]:= -27/(2560*(360 + 161*Sqrt[5])) F2DZ2[37]:= (-91805981021 - 15092810460*Sqrt[37])/21160843503344875 F2DZ2[39]:= -3307942286384/1457888351219 - (919025209872*Sqrt[13])/1457888351219 + Sqrt[2366578120373643223476316160/57386838004741466067220947 + (656942845056977340777703424*Sqrt[13])/57386838004741466067220947]/2 F2DZ2[43]:= -1/512000 F2DZ2[51]:= -1/(256*(6263 + 1519*Sqrt[17])) F2DZ2[55]:= 74200280240/18490056959 + 829564121808/(92450284795*Sqrt[5]) - Sqrt[12112161766671926168045568/94017606745442690112275 + 5416761639247009207953408/(18803521349088538022455*Sqrt[5])]/2 F2DZ2[59]:= 1180269/5451776 - 8474088987/(5451776*(-1609239075319 + 129527521464*Sqrt[177])^(1/3)) + (117*(-1609239075319 + 129527521464*Sqrt[177])^(1/3))/5451776 F2DZ2[63]:= 1383067873521216/4394423627684875 + (301791893186784*Sqrt[21])/4394423627684875 - Sqrt[15300381224823567298498322804736/19310959019555096892552303765625 + (3339562389823416712733718700032*Sqrt[21])/19310959019555096892552303765625]/2 F2DZ2[67]:= -1/85184000 F2DZ2[75]:= -1/(512*(369830 + 165393*Sqrt[5])) F2DZ2[83]:= 22257/512000 - 6685731/(512000*(-19747547 + 1521672*Sqrt[249])^(1/3)) + (117*(-19747547 + 1521672*Sqrt[249])^(1/3))/512000 F2DZ2[91]:= -1/(512*(5854330 + 1623699*Sqrt[13])) F2DZ2[99]:= -27/(2816*(104359189 + 18166603*Sqrt[33])) F2DZ2[107]:= 3628773/314432000 - (465983973*3^(2/3))/(7860800*2^(2/3)*(-153634329171 + 10845953539*Sqrt[321])^(1/3)) + (441*((3*(-153634329171 + 10845953539*Sqrt[321]))/2)^(1/3))/157216000 F2DZ2[115]:= -1/(2560*(48360710 + 21627567*Sqrt[5])) F2DZ2[123]:= -1/(64000*(6122264 + 956137*Sqrt[41])) F2DZ2[139]:= 22587569/49836032 - 21814014627/(49836032*(147094934237 - 7132587408*Sqrt[417])^(1/3)) - (2907*(147094934237 - 7132587408*Sqrt[417])^(1/3))/49836032 F2DZ2[147]:= -1/(192000*(52518123 + 11460394*Sqrt[21])) F2DZ2[155]:= -7825900563/33240841216 - 705571475679/(1329633648640*Sqrt[5]) + Sqrt[197545282192107732084237/441981409898929743462400 + (220883253334077771675*Sqrt[5])/1104953524747324358656]/2 F2DZ2[163]:= -1/151931373056000 F2DZ2[171]:= 8833415049/3196715008 + (1195010661*Sqrt[57])/3196715008 - Sqrt[79089575166271236177/1277373355296555008 + (10638738788300519949*Sqrt[57])/1277373355296555008]/2 F2DZ2[187]:= -1/(544000*(2417649815 + 586366209*Sqrt[17])) F2DZ2[195]:= 4841263/24974336 + (5335751*Sqrt[13/5])/24974336 - Sqrt[6086763759894597/9745585291264000 + (646354271024163*Sqrt[13/5])/1949117058252800]/2 F2DZ2[203]:= -108567/32000 - (858743613*Sqrt[29])/1362944000 + Sqrt[42767945116874024229/464404086784000000 + (93231218495961*Sqrt[29])/5451776000000]/2 F2DZ2[211]:= -118125334153/3926365208576 - 133312135300809296013/(3926365208576*(13851247899505968719182621 + 1385426295859493230757952*Sqrt[633])^(1/3)) + (1323*(13851247899505968719182621 + 1385426295859493230757952*Sqrt[633])^(1/3))/3926365208576 F2DZ2[219]:= 854602006709/13738996645888 - (100282157703*Sqrt[73])/13738996645888 + Sqrt[-8820861823101418191119837/637065097320560784977166336 + (1032411498068762643207103*Sqrt[73])/637065097320560784977166336]/2 F2DZ2[235]:= -1/(3407360*(69903946375 + 31261995198*Sqrt[5])) F2DZ2[243]:= 670669799751/1036433728000 + (29740610781*3^(1/3))/259108432000 - (202454180667*3^(2/3))/518216864000 F2DZ2[259]:= -3966101476643/7327319022592 - (719584622505*Sqrt[37])/7327319022592 + Sqrt[17381410094791019862634707/6711200507354822775799808 + (2864287629304925854648401*Sqrt[37])/6711200507354822775799808]/2 F2DZ2[267]:= -1/(32000*(177979346192125 + 18865772964857*Sqrt[89])) F2DZ2[275]:= 6570307239849/1183363645376 + (1847802155272643115*Sqrt[5])/744174795485732864 - Sqrt[375582686917092184816974399399505931295/1522939347149638919104620981716516864 + (2086670416675428818818944750117*Sqrt[5])/18919772239477142999925025792]/2 F2DZ2[283]:= -2475738649/9528128000 + (153*((9364144409140000195631 + 574868337021533513241*Sqrt[849])/2)^(1/3))/4764064000 - 27844590845319417/(1191016000*2^(2/3)*(9364144409140000195631 + 574868337021533513241*Sqrt[849])^(1/3)) F2DZ2[291]:= -15262747557971281/2696554264946409472 + (1545568929065889*Sqrt[97])/2696554264946409472 + Sqrt[-66270057651685895798599220845052165/24540991550327263583201179853333200896 + (6728707155984253394415351470054293*Sqrt[97])/24540991550327263583201179853333200896]/2 F2DZ2[307]:= 4329688777/13289344000 - 82093250369709891/(10631475200*(842712494655557570090554 - 26910902370745959376689*Sqrt[921])^(1/3)) - (117*(842712494655557570090554 - 26910902370745959376689*Sqrt[921])^(1/3))/53157376000 F2DZ2[315]:= -1970302565593539/289892885688320 + (858324692451807*Sqrt[21])/579785771376640 + Sqrt[137597784311487077112663938466909/420189425863506833400922112000 - (1501312028493166590199929238053*Sqrt[21])/21009471293175341670046105600]/2 F2DZ2[323]:= 130948643581479/500960614531072 + (5283904834417825161*Sqrt[17])/83347322242607104000 - Sqrt[474644573904352106379217463351363696769/868347015626623611501147863908352000000 + (5535361369763733113844870688875*Sqrt[17])/41753725770175740898627695935488]/2 F2DZ2[331]:= -157021722383303233/41531876424401606144 + (5733*((58348839397249590373429576493141323541729 + 3675691929717569487995185135363992716913*Sqrt[993])/2)^(1/3))/20765938212200803072 - 972984044587620439780005543489/(1297871138262550192*2^(2/3)*(58348839397249590373429576493141323541729 + 3675691929717569487995185135363992716913*Sqrt[993])^(1/3)) F2DZ2[355]:= 69350422069/1119680303104 - 1707781993029/(11196803031040*Sqrt[5]) + Sqrt[-6771951695955994548899607/31342099528976632800870400 + 757678802252744962926711/(1567104976448831640043520*Sqrt[5])]/2 F2DZ2[363]:= 6678884608313/49079565107200 - (5813302716621*Sqrt[33])/245397825536000 + Sqrt[-186957209147884281761866839/7527511597224636710912000000 + (14319832010346770137606773*Sqrt[3/11])/301100463888985468436480000]/2 F2DZ2[379]:= 51769011483145258847/11417667973112471257088 - 515914057473281700389808788093139/(11417667973112471257088*(-244748115312006364161080881977846868610197 + 7278909077884379250882347292145933763904*Sqrt[1137])^(1/3)) + (739557*(-244748115312006364161080881977846868610197 + 7278909077884379250882347292145933763904*Sqrt[1137])^(1/3))/11417667973112471257088 F2DZ2[387]:= -16124563449/29320069120 - (20871203619*Sqrt[129])/146600345600 + Sqrt[595165753713276290329281/67161441656373248000000 + (58663989954330187081599*Sqrt[129])/67161441656373248000000]/2 F2DZ2[403]:= -1/(64000*(11089461214325319155 + 3075663155809161078*Sqrt[13])) F2DZ2[427]:= -1/(85184000*(53028779614147702 + 6789639488444631*Sqrt[61])) F2DZ2[435]:= 16153646586748199/10914379237381120 + 976418578408772317/(294688239409290240*Sqrt[5]) - Sqrt[5523109816038698276122175399493055607/314799199367283459707037924527308800 + 3388214063392353436588875507343819/(86364663749597656984098196029440*Sqrt[5])]/2 F2DZ2[475]:= 9375616292660268227/25205714208203780096 + (6459961666619003283*Sqrt[5])/50411428416407560192 - Sqrt[549033982930194633422936422879726278225/635328028745645912986151134263525769216 + (61821703560403162619663478493738220073*Sqrt[5])/158832007186411478246537783565881442304]/2 F2DZ2[483]:= 29681222042451791911/126745058206690496000 + (1071646451391779991*Sqrt[69])/31686264551672624000 - Sqrt[214883724359728840139369372489207990363/401607744495434046246462428418150400000 + (127231113000092514711211745876941892541*Sqrt[69])/2008038722477170231232312142090752000000]/2 F2DZ2[499]:= 2582202696379099701590591/3453433627531149582753738752 - 73513594346328922848430866137205637848777/(3453433627531149582753738752*(-5399024420105348472490682093615296711129437776192519 + 139956527678747806546350613820856169905477473149896*Sqrt[1497])^(1/3)) + (13180167*(-5399024420105348472490682093615296711129437776192519 + 139956527678747806546350613820856169905477473149896*Sqrt[1497])^(1/3))/3453433627531149582753738752 F2DZ2[507]:= -180347944559/8291469824000 + (100038811779*Sqrt[13])/16582939648000 + Sqrt[-29925592410892136713809997/4556148724821689892864000000 + 296720209187241811795417567/(12529408993259647205376000000*Sqrt[13])]/2 F2DZ2[547]:= 3807729175546146059/3941616502257344000 - 335871833017063731752901553989021/(1970808251128672000*(-45163153419580197002809079856134208556241297678 + 1115005460049048892979339276046259313905738245*Sqrt[1641])^(1/3)) + (441*(-45163153419580197002809079856134208556241297678 + 1115005460049048892979339276046259313905738245*Sqrt[1641])^(1/3))/1970808251128672000 F2DZ2[555]:= 62866690052680341539/4020750888729321472 + (2100975557486500793*Sqrt[37/5])/365522808066301952 - Sqrt[123509442654237950460504635453689511007657/63150147301631361159745484693438464000 + (1816118963735505533592028362830384411553*Sqrt[37/5])/2526005892065254446389819387737538560]/2 F2DZ2[595]:= 2790070318353240233953/1222025081920172449792 + (3406577493614179229037*Sqrt[17])/6110125409600862248960 - Sqrt[244933239870646674177568138473355963662759777/5833380081414078854799967983047698284544000 + (11880745094119099683981639926060594904851109*Sqrt[17])/1166676016282815770959993596609539656908800]/2 F2DZ2[603]:= -1839298238700956793/585559386411907072000 - (1534901530593519543*Sqrt[201])/117111877282381414400 + Sqrt[-2032077425898499042200184799010329344911/42859974376886137563552877495451648000000 + (575078821748086171519294992859156264539*Sqrt[201])/42859974376886137563552877495451648000000]/2 F2DZ2[627]:= 6080009095213700243083/33737805968811081728000 + (3414764939932573923619*Sqrt[209])/33737805968811081728000 - Sqrt[1237017997811459785447670124255544926994233897/142279943948643081618945769872186933248000000 + (20761802250023454228289893213252752440881249*Sqrt[209])/142279943948643081618945769872186933248000000]/2 F2DZ2[643]:= 7113845582864099/603865369029824000 - 440397996755631857443683/(12077307380596480*(22646875146705935736742913128829 - 514747882435787408021711664402*Sqrt[1929])^(1/3)) - (91143*(22646875146705935736742913128829 - 514747882435787408021711664402*Sqrt[1929])^(1/3))/301932684514912000 F2DZ2[667]:= -102782438901467/450815824000000 + (69977269884879*Sqrt[29])/450815824000000 - Sqrt[-1315421859456841697171808263703/584300358110297056000000000000 + (404658584944588462942602709911*Sqrt[29])/584300358110297056000000000000]/2 F2DZ2[715]:= -179337096516065693749/57845816910931045376 + (111218579915117516919*Sqrt[13/5])/57845816910931045376 + Sqrt[2596240578209206728688068799843864811103933/52283414595202439200169735340815171584000 - (12880960439939514631021559081178840285789*Sqrt[13/5])/418267316761619513601357882726521372672]/2 F2DZ2[723]:= 477482236356302648032605271/2776166963553646690304000000 - (30757334745003200939387601*Sqrt[241])/2776166963553646690304000000 + Sqrt[-23006434329338804592902732715305804972974109341646279093/26011472657152527014284257000261434845691904000000000000 + (1481974712309914605538040201533036679648062790686780483*Sqrt[241])/26011472657152527014284257000261434845691904000000000000]/2 F2DZ2[763]:= -129495986318116861/97414207616000000 + (6185029357939131*Sqrt[109])/48707103808000000 + Sqrt[-9442868227354567440914043697210953/215671087396662554624000000000000 + (2487275446869928893817922406199209*Sqrt[109])/593095490340822025216000000000000]/2 F2DZ2[795]:= -4618781919031203897203106060623/174266824668931010328385627136 + (283729517856791822812673824875*Sqrt[265])/174266824668931010328385627136 + Sqrt[1943980402575189810192011532899753695531911275513227665518125105393/345921049771248836354241936036099809009925630167319222829056000 - (119417766852283768240711328969736473445608815774926082062340611611*Sqrt[53/5])/69184209954249767270848387207219961801985126033463844565811200]/2 F2DZ2[883]:= 3111593589072072968841613/5971933320897538447552000 - (23234967*((85649194066584136422712228483549777258126764164123 - 963883652650186364490522404971250604456942123585*Sqrt[2649])/2)^(1/3))/2985966660448769223776000 - 1551138551188614312573835498473720823887/(93311458139024038243000*2^(2/3)*(85649194066584136422712228483549777258126764164123 - 963883652650186364490522404971250604456942123585*Sqrt[2649])^(1/3)) F2DZ2[907]:= -16685278095723494595037561/110277001751083003695104000 - (8201210147364607179997684975053253792225191*3^(2/3))/(22055400350216600739020800*(166348858077805857937855353125049391749390254907335643 + 12838356952736314639594803529104985323501982340967512*Sqrt[2721])^(1/3)) + (78920919*(3*(166348858077805857937855353125049391749390254907335643 + 12838356952736314639594803529104985323501982340967512*Sqrt[2721]))^(1/3))/110277001751083003695104000 F2DZ2[955]:= -50264983497075128487746719/98179983348309821215703819648 + 2233910658023658948825667449/(1963599666966196424314076392960*Sqrt[5]) + Sqrt[-316561400984538544665542284056582963418976187858150669/96393091302743937727014122474669706357504638267369108439040 + 141572317347464112823414460866524377737802645490528399/(19278618260548787545402824494933941271500927653473821687808*Sqrt[5])]/2 F2DZ2[1003]:= -964954461393115150858917503/25739291151588556668928000 - (234880143220377635527941849*Sqrt[17])/25739291151588556668928000 + Sqrt[934496215785237429864629833576555577054181714461580033/82813888623280620965268426633099452925083648000000 + (226650129993291644445186194559018674565684612008102823*Sqrt[17])/82813888623280620965268426633099452925083648000000]/2 F2DZ2[1027]:= -457120726449253722674796647/1742529815250231433193025280 - (6344402964314368892839928073*Sqrt[13])/87126490762511571659651264000 + Sqrt[23765081542107542572942164042933740825525639918804920527/43130826094261444475009519475217072072109534640896000000 + (3625210252298033620597180258499971101526958938677961419*Sqrt[13])/23721954351843794461255235711369389639660244052492800000]/2 F2DZ2[1227]:= -1193322209532588715350779719979109043747/77792734703601857902244123430879571000000 + (921968526315703106599227486571580991*Sqrt[409])/1215511479743779029722564428607493296875 + Sqrt[-3570097713426435434424782580595939193923770406363286690274019910911426201193564920313/334635332530082780663878789568078158952088992387152898888399071311644891136000000000000 + (176529970604969374314189983687503128505092903818623203561996881243973639013292189221*Sqrt[409])/334635332530082780663878789568078158952088992387152898888399071311644891136000000000000]/2 F2DZ2[1243]:= 41751269770859103884266143773/53993684069110081814921216000 - (4119537385711240313419615653*Sqrt[113])/53993684069110081814921216000 + Sqrt[-2573891457013090142295587230240889629586569751687930200797/4008562139112948783072036896038814215673672894513152000000 + (244284565956742686785796917980822786160328051818955724389*Sqrt[113])/4008562139112948783072036896038814215673672894513152000000]/2 F2DZ2[1387]:= -5520619083263760990976283255353/715037311125467405891004416000 - (629397137184557389659932375763*Sqrt[73])/715037311125467405891004416000 + Sqrt[29690907207398173961945957052864071530004305525447898591624433/63909794537692309258580097919068600204001228666437632000000 + (3475463335918706320409635145986555979055506807923227833568411*Sqrt[73])/63909794537692309258580097919068600204001228666437632000000]/2 F2DZ2[1411]:= -7832431771048299068863787370892031302992144795941/8367305819873682422601034351384217271715445997568 - (1899643674220419337474793871877856058652048449315*Sqrt[17])/8367305819873682422601034351384217271715445997568 + Sqrt[61346985480611296926250982598856330490334264440365950630102385226612371915274189903774940204880473/8751475835411499599867328082884264518097034637982373145319927886865515221964345271161508832739328 + (14878829467634977164075441620320113242639390092746460081892321311029708184083653559902692339643919*Sqrt[17])/8751475835411499599867328082884264518097034637982373145319927886865515221964345271161508832739328]/2 F2DZ2[1435]:= 834132612043742904834745903492910107/3048221975187569079064498793067997840 + 14923368233157611250712220623529279751/(24385775801500552632515990344543982720*Sqrt[5]) - Sqrt[58430658399627328201178211969407864675979318101120172135081025264250625896829/97525234076332186904193463535184605275675949794013463596782427083784010137600 + 6532746152026552100086692848936489981385627200259940064507448027256339190547/(4876261703816609345209673176759230263783797489700673179839121354189200506880*Sqrt[5])]/2 F2DZ2[1467]:= -7840032401664094591378406566664523/4453068677154427064304524664981734144000000 - (272035619342637175799916390296922210519*Sqrt[489])/4453068677154427064304524664981734144000000 + Sqrt[-17967977114975949658516768943262447951580490454125039422679254940561401450170471/2478727580431734871861866858524733997940721985319397981205207145186926592000000000000 + (1630773238703981630496970977429456349892555267156423282459287114390266655873437*Sqrt[489])/2478727580431734871861866858524733997940721985319397981205207145186926592000000000000]/2 F2DZ2[1507]:= 80487467076417574820260335823514557/1339053100157246371972739891545369600 - (42035970412680968572110447435739881*Sqrt[137])/6695265500786231859863699457726848000 + Sqrt[-95221072876463060361043866796613073816267644029700977950405488619123621/61636547673275179128302190363654009475527864983195458531135647520768000000 + (2381219716108039924078029856726653744382440798474497221791191109616563*Sqrt[137])/12327309534655035825660438072730801895105572996639091706227129504153600000]/2 F2DZ2[1555]:= 5339410210363231261289678723546473229372525/14406967931020738356232694565435044690822144 - 59696423366757871829536330962452073336863817/(72034839655103691781163472827175223454110720*Sqrt[5]) + Sqrt[-76363632013494435530071255664849989443488510334176513099982176103887136853600042295601/648627265517062420085539372610314293718692307904560910641476963949710171449708252364800 + 34150854438190800189305504229029951718287001026527721727397098496761053869791400409061/(129725453103412484017107874522062858743738461580912182128295392789942034289941650472960*Sqrt[5])]/2 pF2DX[7] := x - 24 pF2DX[9] := x^4 + 3888000*x^2 - 5598720000 pF2DX[11] := x - 60 pF2DX[13] := x^4 + 174693312*x^2 - 1509477617664 pF2DX[15] := x^2 - 120*x - 2880 pF2DX[19] := x - 300 pF2DX[23] := x^3 - 648*x^2 + 32256*x - 511488 pF2DX[25] := x^4 + 1115330400000*x^2 - 750238848000000000 pF2DX[27] := x - 1116 pF2DX[31] := x^3 - 1920*x^2 - 158400*x - 5184000 pF2DX[35] := x^2 - 3480*x + 78480 pF2DX[37] := x^4 + 1004604176415168*x^2 - 20271295637299324882944 pF2DX[39] := x^4 - 5880*x^3 + 489600*x^2 - 10368000*x - 1866240000 pF2DX[43] := x - 9468 pF2DX[51] := x^2 - 23640*x - 1292400 pF2DX[55] := x^4 - 36840*x^3 + 13078080*x^2 - 2246745600*x + 82935705600 pF2DX[59] := x^3 - 55380*x^2 + 3639600*x - 129816000 pF2DX[63] := x^4 - 82224*x^3 - 39968640*x^2 - 9604790784*x - 204895236096 pF2DX[67] := x - 122124 pF2DX[75] := x^2 - 257400*x - 25110000 pF2DX[83] := x^3 - 522372*x^2 + 62625456*x - 6228004032 pF2DX[91] := x^2 - 1024440*x - 58114800 pF2DX[99] := x^2 - 1952280*x + 46688400 pF2DX[107] := x^3 - 3626484*x^2 + 795365424*x - 164029358016 pF2DX[115] := x^2 - 6584280*x + 497131920 pF2DX[123] := x^2 - 11713080*x - 3758859504 pF2DX[139] := x^3 - 35134260*x^2 + 1974769200*x - 76937688000 pF2DX[147] := x^2 - 59420760*x - 32556038256 pF2DX[155] := x^4 - 99089520*x^3 + 74330448480*x^2 - 47887065388800*x + 4183993921593600 pF2DX[163] := x - 163096908 pF2DX[171] := x^4 - 265227120*x^3 - 27351108000*x^2 + 1324773792000*x + 245286571680000 pF2DX[187] := x^2 - 678630072*x - 43816318704 pF2DX[195] := x^4 - 1069274160*x^3 - 1350629534880*x^2 + 253342941062400*x - 5336077736390400 pF2DX[203] := x^4 - 1669305840*x^3 + 2606016976992*x^2 - 4318755978551040*x - 453665520466493184 pF2DX[211] := x^3 - 2583483780*x^2 - 696663896400*x - 64145792376000 pF2DX[219] := x^4 - 3965637360*x^3 - 8341400656800*x^2 + 878246045856000*x - 213284291775840000 pF2DX[235] := x^2 - 9132651000*x + 1900769982480 pF2DX[243] := x^3 - 13712333508*x^2 - 1966980346704*x - 80654180683968 pF2DX[259] := x^4 - 30313062960*x^3 + 1268635356000*x^2 - 1198150511328000*x - 210442663306080000 pF2DX[267] := x^2 - 44657739768*x - 221604901826544 pF2DX[275] := x^4 - 65412577200*x^3 + 361388822940000*x^2 - 2036273117868000000*x - 229983668055900000000 pF2DX[283] := x^3 - 95286543636*x^2 + 22392564106032*x - 1391460588462528 pF2DX[291] := x^4 - 138072961200*x^3 - 1075418765028000*x^2 - 574853226833376000*x - 115894130678609760000 pF2DX[307] := x^3 - 285596316996*x^2 + 18423545571504*x - 2171781534677184 pF2DX[315] := x^4 - 407839394160*x^3 + 163460868294240*x^2 + 11920484422252800*x - 3167174143412985600 pF2DX[323] := x^4 - 579793049520*x^3 + 6775879981322592*x^2 - 79019277198385201920*x + 1924398946641043190016 pF2DX[331] := x^3 - 820684418100*x^2 - 649374037160400*x - 193046772130776000 pF2DX[355] := x^4 - 2271225434160*x^3 + 852793262678880*x^2 + 250103774726841600*x + 30289612645025337600 pF2DX[363] := x^4 - 3164321009520*x^3 - 64712650897734048*x^2 + 5277946855352244480*x - 1253806392866612961024 pF2DX[379] := x^3 - 6076263133140*x^2 + 2723906951146800*x - 3129133923190296000 pF2DX[387] := x^4 - 8376666472368*x^3 - 47416926195360*x^2 + 117922723044703488*x + 7325364519890383104 pF2DX[403] := x^2 - 15764572725336*x + 2142501016078224 pF2DX[427] := x^2 - 39771486656760*x - 9884961623974896 pF2DX[435] := x^4 - 53828544012720*x^3 - 2789219874455252640*x^2 + 2822910104785685126400*x + 407166150090466154246400 pF2DX[475] := x^4 - 234853342566000*x^3 + 16175666288700000*x^2 - 16474422613500000000*x - 1312127862169500000000 pF2DX[483] := x^4 - 312951996127536*x^3 - 29809770443886172320*x^2 - 8892307196445952002816*x + 235526888079426509017344 pF2DX[499] := x^3 - 551797427717700*x^2 + 606592414710759600*x - 1738536908186085624000 pF2DX[507] := x^4 - 730213239665520*x^3 - 91487992362507760032*x^2 + 59940385360086644824320*x - 11739713565031948386918144 pF2DX[547] := x^3 - 2870043265025124*x^2 + 641821608961316784*x - 37641143160190708416 pF2DX[555] := x^4 - 3750921568066800*x^3 - 805909468870783343520*x^2 + 1996444475641262609568000*x + 341565723587361522723897600 pF2DX[595] := x^4 - 13906196039144880*x^3 + 41770900349422420320*x^2 + 19317458283265253203200*x - 3975883046089399162310400 pF2DX[603] := x^4 - 17976402434832624*x^3 - 10360308965876640*x^2 + 343721088987749519616*x + 162738607839159718658304 pF2DX[627] := x^4 - 38443266495194160*x^3 - 18158422855170697905312*x^2 - 5848765789577150153399040*x - 462514632821832303710187264 pF2DX[643] := x^3 - 63299324509069476*x^2 + 18813175513500994992*x - 26899324789544591249088 pF2DX[667] := x^4 - 132213581753577840*x^3 + 39979388182261827168*x^2 - 1181888691268268885760*x - 333229019195103185919744 pF2DX[715] := x^4 - 554893848851305200*x^3 + 3916257301960107654240*x^2 + 115613633093426978976000*x - 153074596603778045523705600 pF2DX[723] := x^4 - 701415903049215024*x^3 - 871413061595580993152160*x^2 + 244573654906525946516464896*x - 23518288225610951370493406976 pF2DX[763] := x^4 - 2221069232494771056*x^3 - 3286217869917980545440*x^2 - 1003881142318406109325056*x - 87579648673710562221186816 pF2DX[795] := x^4 - 5465797894474289520*x^3 - 13405518730102812075096480*x^2 + 148058636349886550014362220800*x + 29338992382003061842862843961600 pF2DX[883] := x^3 - 59468545813780904388*x^2 + 3225578464047253550256*x - 406793552432356723163328 pF2DX[907] := x^3 - 111668298509456843316*x^2 + 44456371015450646847024*x - 4634375653281672773198784 pF2DX[955] := x^4 - 384204132767812018800*x^3 + 11649742807562055710390880*x^2 - 43575634093557528811186272000*x + 52807482887112444575992283193600 pF2DX[1003] := x^4 - 1281944548748731121520*x^3 - 96909095620058389707168*x^2 - 34791853848522230793496320*x + 25679269705779196231518003456 pF2DX[1027] := x^4 - 2316466226828486711856*x^3 - 7959586385882686748939424*x^2 - 18076963365997631188480555776*x + 5195426818224385993365950812416 pF2DX[1227] := x^4 - 250564454485215311024112*x^3 - 22092852266024288268564340924320*x^2 - 20186401223906419879950002627804928*x - 6215574886917580731045347358389174016 pF2DX[1243] := x^4 - 358274937124950256913520*x^3 - 312658696967692026408082848*x^2 - 71782689776687819988010571520*x - 5049809907602547959967501229824 pF2DX[1387] := x^4 - 8113503836106022692438384*x^3 - 8553537073516837798231871904*x^2 - 3003906594415293316304914892544*x - 344817420419630740818899290316544 pF2DX[1411] := x^4 - 13429986932592469439206320*x^3 - 4608809113722720368624311140000*x^2 - 603831707999417677360478117900256000*x + 162526337910499882162159615916011680000 pF2DX[1435] := x^4 - 22135489834598511310754160*x^3 + 4948103261090345741189989860960*x^2 + 57255597563534093048072129439955200*x + 4127377256561527480291978232034566400 pF2DX[1467] := x^4 - 42819040236028752988071408*x^3 - 30884019305884335660960*x^2 + 1425732196674387772983198359808*x + 515834569412758692773628138171465984 pF2DX[1507] := x^4 - 96707895629490314010168624*x^3 - 76679377769812786956042881184*x^2 - 6669177651556774369993224555264*x - 15406614399933715704793086462914304 pF2DX[1555] := x^4 - 253460113251887998341704880*x^3 + 96773086085302356739873290902880*x^2 + 15922115594542754597045825861356800*x + 1888157233232063883269357017231929600 pF2DY[7] := x - 189 pF2DY[9] := x^4 + 1381847040*x^2 - 166558283071488 pF2DY[11] := x - 616 pF2DY[13] := x^4 + 89659395072*x^2 - 97949249443528704 pF2DY[15] := x^2 - 1575*x - 218295 pF2DY[19] := x - 4104 pF2DY[23] := x^3 - 9338*x^2 + 3384381*x - 417146653 pF2DY[25] := x^4 + 1100787480576000*x^2 - 182637403323501772800000 pF2DY[27] := x - 18216 pF2DY[31] := x^3 - 34317*x^2 - 23367366*x - 6866276769 pF2DY[35] := x^2 - 64400*x + 9235520 pF2DY[37] := x^4 + 1467426800639536128*x^2 - 10812787825716950254045691904 pF2DY[39] := x^4 - 114660*x^3 + 108456894*x^2 - 42553748601*x - 22104665145927 pF2DY[43] := x - 195048 pF2DY[51] := x^2 - 531216*x - 202958784 pF2DY[55] := x^4 - 853875*x^3 + 3292240545*x^2 - 6265209616875*x + 1599649752717225 pF2DY[59] := x^3 - 1335288*x^2 + 665365184*x - 213282707968 pF2DY[63] := x^4 - 2056509*x^3 - 12114380250*x^2 - 35527500914724*x - 5051512154027871 pF2DY[67] := x - 3140424 pF2DY[75] := x^2 - 7004880*x - 5971838400 pF2DY[83] := x^3 - 14948632*x^2 + 16634384576*x - 16671685100032 pF2DY[91] := x^2 - 30702672*x - 10788313536 pF2DY[99] := x^2 - 61024656*x + 9302432832 pF2DY[107] := x^3 - 117844664*x^2 + 276956903104*x - 632259939437056 pF2DY[115] := x^2 - 221821200*x + 107239049280 pF2DY[123] := x^2 - 408114000*x - 1512197636544 pF2DY[139] := x^3 - 1301330232*x^2 + 508393029312*x - 180497249413632 pF2DY[147] := x^2 - 2263338000*x - 15707016110016 pF2DY[155] := x^4 - 3875620000*x^3 + 35613503784320*x^2 - 299930560160000000*x + 204619491573408665600 pF2DY[163] := x - 6541681608 pF2DY[171] := x^4 - 10895972256*x^3 - 10246683669120*x^2 + 644881511798784*x + 3942737995688644608 pF2DY[187] := x^2 - 29154380112*x - 11839702716864 pF2DY[195] := x^4 - 46909044000*x^3 - 917343611233920*x^2 + 1328167966544640000*x - 183578406090669158400 pF2DY[203] := x^4 - 74719428000*x^3 + 1804041147522432*x^2 - 44641879673608448000*x - 28093578245752646201344 pF2DY[211] := x^3 - 117895404312*x^2 - 280005501996864*x - 237149887414583808 pF2DY[219] := x^4 - 184367802528*x^3 - 6141364806294144*x^2 + 5911270533971712000*x - 14052577880572848304128 pF2DY[235] := x^2 - 439825755600*x + 859247919673920 pF2DY[243] := x^3 - 671528394648*x^2 - 637501682435904*x - 185523964435358208 pF2DY[259] := x^4 - 1532602663200*x^3 + 1210510810970496*x^2 - 7506880062162388992*x - 7596502014017438871552 pF2DY[267] := x^2 - 2292462679248*x - 194647152383538624 pF2DY[275] := x^4 - 3407826341920*x^3 + 331197511220822400*x^2 - 32409925434809931008000*x - 21984258188140624893440000 pF2DY[283] := x^3 - 5035871775096*x^2 + 8367427548603072*x - 3766509569857632768 pF2DY[291] := x^4 - 7399545122592*x^3 - 999406696976037504*x^2 - 5764683937213264250880*x - 12647657494065593696514048 pF2DY[307] := x^3 - 15720692138136*x^2 + 7493376156813504*x - 8684908457046188544 pF2DY[315] := x^4 - 22740202212000*x^3 + 99076037125887360*x^2 + 57735245228855040000*x - 89713095272425000857600 pF2DY[323] := x^4 - 32735888500000*x^3 + 7190232702278883712*x^2 - 1578152490169824800000000*x + 245963643172814586084724736 pF2DY[331] := x^3 - 46907259191352*x^2 - 421424462984728896*x - 1435632442845943491072 pF2DY[355] := x^4 - 134438696244000*x^3 + 706333045595253120*x^2 + 1468964323093512960000*x + 1526141399151853044633600 pF2DY[363] := x^4 - 189401634180000*x^3 - 77464782668434854528*x^2 + 51625624194174539520000*x - 121853026143243720869474304 pF2DY[379] := x^3 - 371625965400312*x^2 + 2030652587246222016*x - 28798814700595775937024 pF2DY[387] := x^4 - 517698109440288*x^3 - 23203948125456000*x^2 + 295488936142132819968*x + 137577825536800848482304 pF2DY[403] := x^2 - 994224818570256*x + 818954492129976384 pF2DY[427] := x^2 - 2581877515266000*x - 5760835354614545856 pF2DY[435] := x^4 - 3527013600583200*x^3 - 4019102115669608607360*x^2 + 56348331903433100434176000*x + 47048954882245502791946342400 pF2DY[475] := x^4 - 16080273205944480*x^3 + 14184229734477014400*x^2 - 119037956460217696512000*x - 57125430952022415767040000 pF2DY[483] := x^4 - 21607332953615136*x^3 - 47283177466621667088000*x^2 - 140119585862410258364123136*x + 23085907877172618618968346624 pF2DY[499] := x^3 - 38723964839988120*x^2 + 597035021372739778752*x - 24064382283671706510352896 pF2DY[507] := x^4 - 51653952090468000*x^3 - 153059187978010164120192*x^2 + 992600111045247163100928000*x - 1952035416113754148283364470784 pF2DY[547] := x^3 - 210878342558402904*x^2 + 303153044219253998784*x - 117693586653896166068736 pF2DY[555] := x^4 - 277609515014916000*x^3 - 1477809608113268443198080*x^2 + 55997519381862017517008640000*x + 55792887544600764862852916121600 pF2DY[595] := x^4 - 1065655186576596000*x^3 + 50105126069517151543680*x^2 + 277503176968782535330560000*x - 310547166749274220997491814400 pF2DY[603] := x^4 - 1386791946009104544*x^3 - 6015289917876624000*x^2 + 1234277981456343238711296*x + 7886620356794308922385567744 pF2DY[627] := x^4 - 3024154154833812000*x^3 - 37437019194564843811638912*x^2 - 78431556007914309808489728000*x - 39877756215405597673031339864064 pF2DY[643] := x^3 - 5042599015352394456*x^2 + 16936292323622083845312*x - 281126588715231815026487808 pF2DY[667] := x^4 - 10727261321073444000*x^3 + 22811774803232311870848*x^2 - 5786422689925336064256000*x - 8277335515228703099829940224 pF2DY[715] := x^4 - 46613617074098474400*x^3 + 5529756841065397509528960*x^2 + 1966029795081240739538688000*x - 9651188540347100853069893529600 pF2DY[723] := x^4 - 59250856090283502624*x^3 - 2073069481838183757120528000*x^2 + 4189016736074941851085166278656*x - 3231571467285931086198865494798336 pF2DY[763] := x^4 - 192741057617792646816*x^3 - 3088428592419711901584000*x^2 - 6595580594327210968572389376*x - 3819221945813263835047788343296 pF2DY[795] := x^4 - 484157881498166820000*x^3 - 35123170083275837798553467520*x^2 + 6939682669061202778252587360000000*x + 8220805469675780675809590293078937600 pF2DY[883] := x^3 - 5551592025996996495768*x^2 + 2038049808718242855082176*x - 2574302250130549079820231168 pF2DY[907] := x^3 - 10565338480812006196536*x^2 + 28694333242035085634944704*x - 20880964330119359918068345344 pF2DY[955] := x^4 - 37300408718784541668000*x^3 + 21104281335360808504995419520*x^2 - 1123225191944483849789067751680000*x + 19127605322225973887307645842498457600 pF2DY[1003] := x^4 - 127546803522184410756000*x^3 - 158662132950746110805578368*x^2 - 573550973931058215870064896000*x + 1328352414448569937055987419385856 pF2DY[1027] := x^4 - 233217463301658273743136*x^3 - 11944314289209639953929832064*x^2 - 399194641329768096704022367881216*x + 785994768805589600354555048498958336 pF2DY[1227] := x^4 - 27573482171637926473072032*x^3 - 89180837076914733093094638005904000*x^2 - 799057467166949097106554313903467767808*x - 2466290698073978392407068614446221301313536 pF2DY[1243] := x^4 - 39682759548551762802852000*x^3 - 298510515653829221637238151808*x^2 - 478599622423488344625455169792000*x - 228163176259408341183141820478582784 pF2DY[1387] := x^4 - 949284848269320380202347424*x^3 - 8047188578937476035033440211584*x^2 - 22162491055479573373010431140440064*x - 18646213690973988706556005794596450304 pF2DY[1411] := x^4 - 1584852939424263504695759136*x^3 - 12843726195758541406511479745021568*x^2 - 39752052665498841881856840767064082925568*x + 69910477819617612436685422746703847870828544 pF2DY[1435] := x^4 - 2634298351630335879872292000*x^3 + 14215539333878185574253809053664640*x^2 + 2746402500735044151232918267132911360000*x + 1268676525903635557471163591763420999782400 pF2DY[1467] := x^4 - 5152308491052061155296127648*x^3 - 26101099386993277631376000*x^2 + 11156252357178311490593052647528448*x + 148334656304938377775996516849064904167424 pF2DY[1507] := x^4 - 11794198476981671955381459744*x^3 - 105367250784488804546527810295424*x^2 - 68983756493604339751450572339431424*x - 1941224575040986530121563729236153462784 pF2DY[1555] := x^4 - 31399641813986508841158996000*x^3 + 297132449299979058782432130560065920*x^2 + 334812005428164423653134060439120640000*x + 363174036856096863603654564483253617561600 pF2DZ2[7] := 125*x + 64 pF2DZ2[9] := 16194277*x^2 + 2399094*x - 27 pF2DZ2[11] := 512*x + 27 pF2DZ2[13] := 190109375*x^2 + 3991250*x - 1 pF2DZ2[15] := 166375*x^2 - 452800*x - 4096 pF2DZ2[19] := 512*x + 1 pF2DZ2[23] := 12771880859375*x^3 - 8901441000000*x^2 + 10426309632000*x + 5159780352 pF2DZ2[25] := 97838353751039*x^2 + 25481191682*x - 1 pF2DZ2[27] := 64000*x + 9 pF2DZ2[31] := 79562482901*x^3 - 5151836544*x^2 + 5990977536*x + 262144 pF2DZ2[35] := 32768000*x^2 - 49766400*x - 729 pF2DZ2[37] := 2645105437918109375*x^2 + 22951495255250*x - 1 pF2DZ2[39] := 39362985482913*x^4 + 357257766929472*x^3 - 2415341871104*x^2 + 3218852544512*x + 16777216 pF2DZ2[43] := 512000*x + 1 pF2DZ2[51] := 2097152*x^2 + 3206656*x + 1 pF2DZ2[55] := 34957763938109375*x^4 - 561139619315000000*x^3 + 117701838336000*x^2 - 127544557568000*x - 16777216 pF2DZ2[59] := 1429150367744*x^3 - 928201310208*x^2 + 343970426880*x + 19683 pF2DZ2[63] := 8582858647822021484375*x^4 - 10805217761884500000000*x^3 + 790809975936000000*x^2 - 477865023012864000*x - 12230590464 pF2DZ2[67] := 85184000*x + 1 pF2DZ2[75] := 1744568320*x^2 + 378705920*x + 1 pF2DZ2[83] := 2097152000000000*x^3 - 273494016000000*x^2 + 30662509824000*x + 19683 pF2DZ2[91] := 1287913472*x^2 - 5994833920*x - 1 pF2DZ2[99] := 13713702649856*x^2 - 15869275716096*x - 729 pF2DZ2[107] := 1287913472000000000*x^3 - 44590362624000000*x^2 + 1478312669376000*x + 19683 pF2DZ2[115] := 43614208000*x^2 + 247606835200*x + 1 pF2DZ2[123] := 49836032000000*x^2 + 783649792000*x + 1 pF2DZ2[139] := 13064216772608*x^3 - 17763587063808*x^2 + 7050440297472*x + 1 pF2DZ2[147] := 3803369472000000*x^2 + 20166959232000*x + 1 pF2DZ2[155] := 2230755092410138624000000*x^4 + 2100749186239561728000000*x^3 - 7916105475889790976000*x^2 + 29802996904731264000*x + 531441 pF2DZ2[163] := 151931373056000*x + 1 pF2DZ2[171] := 107263956359315456*x^4 - 1185600898357788672*x^3 - 115259586802089984*x^2 - 292900243166664192*x - 729 pF2DZ2[187] := 1287913472000000*x^2 - 2630402998720000*x - 1 pF2DZ2[195] := 26187489345536000000*x^4 - 20305728765952000000*x^3 - 8489375961841664000*x^2 - 6530330732672000*x - 1 pF2DZ2[203] := 1902199139467264000000000000*x^4 + 25814506746817806336000000000*x^3 - 14781698096293564416000000*x^2 + 8458280375555317248000*x + 531441 pF2DZ2[211] := 1029273081236946944*x^3 + 92897542788612096*x^2 + 38121288940179456*x + 1 pF2DZ2[219] := 12447114174972278341632*x^4 - 3096973971487513903104*x^3 + 278313319312346841088*x^2 + 89821946589435392*x + 1 pF2DZ2[235] := 4000899258155008000*x^2 + 476375821440640000*x + 1 pF2DZ2[243] := 4245232549888000000000*x^3 - 8241190499340288000000*x^2 + 7046099782711303104000*x + 6561 pF2DZ2[259] := 491728055771739455488*x^4 + 1064642258424937054208*x^3 - 123305909241488867328*x^2 + 5248263711985894400*x + 1 pF2DZ2[267] := 177974718776999936000000*x^2 + 11390678156296000000*x + 1 pF2DZ2[275] := 237507301581003441889255425572864*x^4 - 5274780746196871268691567018246144*x^3 + 261747995454384684591381479424*x^2 - 12987737762292441373630464*x - 531441 pF2DZ2[283] := 39027212288000000000*x^3 + 30421876518912000000*x^2 + 51858404737750464000*x + 1 pF2DZ2[291] := 2442996361371265567354257408*x^4 + 55310345107248247876878336*x^3 + 3612406543818182657572864*x^2 + 108886323541285736960*x + 1 pF2DZ2[307] := 1741860896768000000000*x^3 - 1702502902136832000000*x^2 + 465866210653924416000*x + 1 pF2DZ2[315] := 972719112011250663424000000*x^4 + 26444953382653577605939200000*x^3 + 20802190592905630201184256000*x^2 + 504881443671480487533542400*x + 531441 pF2DZ2[323] := 7270254897064185392267264000000000000*x^4 - 7601635654757532261384192000000000000*x^3 + 88071969587537616522301440000000*x^2 - 1020368530531278029160000000*x - 531441 pF2DZ2[331] := 10887332213398334641012736*x^3 + 123486907177345928134656*x^2 + 3846877737369093394944*x + 1 pF2DZ2[355] := 18785118296121278464000000*x^4 - 4654028042971119616000000*x^3 + 2286995523625156706304000*x^2 + 29462967929013161216000*x + 1 pF2DZ2[363] := 176906310837600256000000000000*x^4 - 96295623971888168960000000000*x^3 + 15300866874143421542400000000*x^2 + 57189603077785604800000*x + 1 pF2DZ2[379] := 2993073153143595665218076672*x^3 - 40712807238712892205563904*x^2 + 210876969967953842024448*x + 1 pF2DZ2[387] := 48038001246208000000000000*x^4 + 105673939019366400000000000*x^3 - 376882366580487180288000000*x^2 + 292163516553155689448640000*x + 729 pF2DZ2[403] := 36451703492882432000000*x^2 - 1419451035433640851840000*x - 1 pF2DZ2[427] := 51923170459928424448000000*x^2 + 9034407125303115694336000*x + 1 pF2DZ2[435] := 1403306293805292659341787136000000*x^4 - 8307761139708899634833050828800000*x^3 - 29291978613471914389860253696000*x^2 - 16549362689890741931033600*x - 1 pF2DZ2[475] := 27064429549139442603973935104*x^4 - 40267965356820616873552904192*x^3 + 6328883616153624547580706816*x^2 - 315028248510949800730677248*x - 1 pF2DZ2[483] := 33225456538534673383424000000000000*x^4 - 31123017084385930154868736000000000*x^3 - 3200762812182691585859330048000000*x^2 - 559385828184846052676864000*x - 1 pF2DZ2[499] := 905296904855525676221396091404288*x^3 - 2030726830918808136521291661312*x^2 + 1739063141244806829112688640*x + 1 pF2DZ2[507] := 5922078143165421796196352000000000000*x^4 + 515245013638567711136022528000000000*x^3 + 30655760817105013529603469312000000*x^2 + 3045477626733236817897216000*x + 1 pF2DZ2[547] := 16144861193246081024000000000*x^3 - 46789376109111042772992000000*x^2 + 47047103900249800186132800000*x + 1 pF2DZ2[555] := 59752100629321501963779924033536000000*x^4 - 3737030116230117230577730063433728000000*x^3 - 2408255840073651895334151384694784000*x^2 - 80358528142488833904664064000*x - 1 pF2DZ2[595] := 10251089378396213973704769536000000*x^4 - 93619224772402151409840029696000000*x^3 - 2931064418010112680101968379904000*x^2 - 1104517756650228973441911680000*x - 1 pF2DZ2[603] := 38375219947890741870592000000000000*x^4 + 482160997486023617544192000000000*x^3 - 1737945383375565947500793856000000*x^2 + 1345516722142527386622948677568000*x + 729 pF2DZ2[627] := 141506614526208195336077312000000000000*x^4 - 102005625872364815137455996928000000000*x^3 - 1193528890055061407030279377780736000000*x^2 - 8441051922988549421475785024000*x - 1 pF2DZ2[643] := 59702648879791472057778176000000000*x^3 - 2109984013660906380107747328000000*x^2 + 22885170811762809085354436928000*x + 1 pF2DZ2[667] := 31258256460480512000000000000000*x^4 + 28506540043862562832384000000000*x^3 + 1251797513362901610037248000000*x^2 - 99840822167560599369043634048000*x - 1 pF2DZ2[715] := 1479332728553547776052705624064000000*x^4 + 18345266813569654922283522719744000000*x^3 + 20146249392014231135851623609532416000*x^2 + 1758635470676859749667112938368000*x + 1 pF2DZ2[723] := 4912349709333198316385599488000000000000000*x^4 - 3379565790919438236878200456347648000000000*x^3 + 2753682126531387316056224077974679552000000*x^2 + 2810005849018070101921712115776000*x + 1 pF2DZ2[763] := 135956592419821060096000000000000000*x^4 + 722926704952768376827019264000000000*x^3 + 3939933879904800636227313512448000000*x^2 + 28176055843485503636665080217088000*x + 1 pF2DZ2[795] := 177304686516700803645437111827886153662464000000*x^4 + 18797190613844604948063564784012618742366208000000*x^3 + 657241421500408290886652550505879412015104000*x^2 + 170633046687094682841073820918144000*x + 1 pF2DZ2[883] := 32557642752469498567441252352000000000*x^3 - 50891133751970969045338360664064000000*x^2 + 20199036076974432314365911465239232000*x + 1 pF2DZ2[907] := 28908454347035902920649342976000000000*x^3 + 13121836623376019301364579172352000000*x^2 + 71222268935878705089396753765531648000*x + 1 pF2DZ2[955] := 49231506617617140327724490904801868685246464000000*x^4 + 100819771333288636020749866701167544762368000000*x^3 + 132776902921317613109443310347500301123584000*x^2 + 843101906745914419152035920929810944000*x + 1 pF2DZ2[1003] := 1686850184910507649854865408000000000000*x^4 + 252957022327436778106760069906432000000000*x^3 - 68484625045287672735759388415545344000000*x^2 + 9386301217139503716701232666867695936000*x + 1 pF2DZ2[1027] := 30399623123410066310167483484471296000000000000*x^4 + 31899133511150165288820635711936921600000000000*x^3 - 13914141595110597303881296172926279680000000*x^2 + 30648410277180661325661832977232801280000*x + 1 pF2DZ2[1227] := 281911430884253259173887413402593968653336576000000000000000*x^4 + 17297819539423631927944600720759800118125294256128000000000*x^3 + 1769147654095808336211579211538737512775288458047488000000*x^2 + 358587321092186396391002914702750635846656000*x + 1 pF2DZ2[1243] := 3425297116620295975524351153799168000000000000*x^4 - 10594609827202102082920677945445974016000000000*x^3 + 8882029681444776912623908480761834246144000000*x^2 + 733143290104295213180437464841869447360128000*x + 1 pF2DZ2[1387] := 230226546495286238585979187744473088000000000000*x^4 + 7110079691115687509666425637057144815616000000000*x^3 + 2820307283308789434854916524023853282095104000000*x^2 + 375987060382831741351540064837995486044527552000*x + 1 pF2DZ2[1411] := 29149365637874555882228552892772971838064042174081745654120448*x^4 + 109144053028738917404257088453622933324280198847339957011349504*x^3 + 6553389087221930454176654856887917239657600474422181888*x^2 + 1030165941380607497744538328501771352261927129600*x + 1 pF2DZ2[1435] := 449727045360789079967069528804401072833377370411892736000000*x^4 - 492263356287137191052948349977325148809676243338474291200000*x^3 - 35218374266403250383497196740796549738035351290576896000*x^2 - 2798557799958988554658793898877114853425329766400*x - 1 pF2DZ2[1467] := 388434127047396060206813828159287338314235904000000000000000*x^4 + 2735494431143338941120422645656578978742272000000000*x^3 - 9860702243006384318202021366246547174726520832000000*x^2 + 7634092059135496744431478114751769954359558575296000*x + 729 pF2DZ2[1507] := 106184982606005410862662632654103983947776000000000000*x^4 - 25530160948829294567755613823684474036551680000000000*x^3 + 1236976379988022799900532876747581450221240320000000*x^2 + 53417046727323720145934633586920116599406152320000*x + 1 pF2DZ2[1555] := 20107151871771780319433946789675316788314005741502464000000*x^4 - 29807890881549532644094770701047088779812481898905600000000*x^3 + 12230811694410859878541593542225600675714824056718884864000*x^2 + 366923270977227721018250307833334971970207993728000*x + 1 (* Type G, s=1/3, N=2〜58 *) sumG3[t_, limit_:Infinity] := Sum[termp[n, 1/3, G3X[t], G3Y[t], G3Z2[t]], {n, 0, limit}]; G3X[2]:= 3/(5*Sqrt[5]) G3X[3]:= (2*Sqrt[3/5])/5 G3X[4]:= 20/(11*Sqrt[33]) G3X[5]:= (3*Sqrt[(2*(375 - 151*Sqrt[5]))/55])/11 G3X[6]:= (5*Sqrt[(71 - 8*Sqrt[2])/51])/17 G3X[7]:= (144*Sqrt[3/85])/85 G3X[8]:= (12*Sqrt[(-28125 + 20644*Sqrt[2])/115])/115 G3X[9]:= (30*Sqrt[(5353 - 2038*Sqrt[3])/253])/253 G3X[10]:= Sqrt[(83675 - 20844*Sqrt[5])/435]/29 G3X[12]:= (8*Sqrt[(2*(4770 - 701*Sqrt[3]))/165])/165 G3X[13]:= Sqrt[(2*(594545 - 100789*Sqrt[13]))/345]/115 G3X[15]:= (8*Sqrt[(2*(54145375 - 15288853*Sqrt[5]))/17835])/1189 G3X[16]:= 2480/Sqrt[3*(10147001 + 7132590*Sqrt[2])] G3X[18]:= (9*Sqrt[(1412999833 - 345077296*Sqrt[6])/7685])/7685 G3X[22]:= Sqrt[(32125274995 - 13618650744*Sqrt[2])/10455]/3485 G3X[25]:= (50*Sqrt[(2*(14876836745 - 3993160383*Sqrt[5]))/138237])/46079 G3X[28]:= (32*Sqrt[(21576628835 - 6508277804*Sqrt[7])/73455])/24485 G3X[37]:= Sqrt[(2*(8040312296272697 - 793101770174345*Sqrt[37]))/829785]/276595 G3X[58]:= Sqrt[(3*(3364059538285542450607 - 374814055537196859684*Sqrt[29]))/1366181]/170772625 G3Y[2]:= 28/(5*Sqrt[5]) G3Y[3]:= (22*Sqrt[3/5])/5 G3Y[4]:= (84*Sqrt[3/11])/11 G3Y[5]:= (4*Sqrt[(21650 - 5967*Sqrt[5])/55])/11 G3Y[6]:= (4*Sqrt[(3*(1757 + 494*Sqrt[2]))/17])/17 G3Y[7]:= (2394*Sqrt[3/85])/85 G3Y[8]:= (28*Sqrt[(2*(-84125 + 81432*Sqrt[2]))/115])/115 G3Y[9]:= (84*Sqrt[(2*(44372 - 1767*Sqrt[3]))/253])/253 G3Y[10]:= (12*Sqrt[(3*(10835 + 204*Sqrt[5]))/145])/29 G3Y[12]:= (4*Sqrt[(937215 + 323408*Sqrt[3])/165])/55 G3Y[13]:= (12*Sqrt[(39*(14230 - 41*Sqrt[13]))/115])/115 G3Y[15]:= (154*Sqrt[(3*(5607725 + 661856*Sqrt[5]))/5945])/1189 G3Y[16]:= (1848*Sqrt[(3*(83987 - 53808*Sqrt[2]))/1081])/1081 G3Y[18]:= (84*Sqrt[(4624824673 + 2654964*Sqrt[6])/7685])/7685 G3Y[22]:= (924*Sqrt[(3*(1453705 + 354*Sqrt[2]))/3485])/3485 G3Y[25]:= (840*Sqrt[(3*(4622595160 - 269169*Sqrt[5]))/46079])/46079 G3Y[28]:= (84*Sqrt[(3*(63875697185 + 5212757056*Sqrt[7]))/24485])/24485 G3Y[37]:= (84*Sqrt[(111*(3998665024438 - 2852005*Sqrt[37]))/276595])/276595 G3Y[58]:= (2772*Sqrt[(87*(13826969809210107 + 90211316*Sqrt[29]))/1366181])/170772625 G3Z2[2]:= 27/125 G3Z2[3]:= 4/125 G3Z2[4]:= 8/1331 G3Z2[5]:= 27/(5*(1975 + 884*Sqrt[5])) G3Z2[6]:= (1399 + 988*Sqrt[2])^(-1) G3Z2[7]:= 64/614125 G3Z2[8]:= 216/(125*(26125 + 18473*Sqrt[2])) G3Z2[9]:= 9/(399849 + 230888*Sqrt[3]) G3Z2[10]:= 1/(5*(24635 + 11016*Sqrt[5])) G3Z2[11]:= 28570212/119823157 + (91728*(3*(-71585567332587 + 46017723976379*Sqrt[33]))^(1/3))/(1318054727*11^(2/3)) - (114840105359616*3^(2/3))/(1318054727*(11*(-71585567332587 + 46017723976379*Sqrt[33]))^(1/3)) G3Z2[12]:= 16/(375*(35010 + 20213*Sqrt[3])) G3Z2[13]:= 1/(125*(15965 + 4428*Sqrt[13])) G3Z2[14]:= -32816097/338608873 + (33034557024*Sqrt[2])/450688409963 - Sqrt[-234086514997407362833536/203120042874977157661369 + (124380387103174449408*Sqrt[2])/152607094571733401699]/2 G3Z2[15]:= 128/(5*(274207975 + 122629507*Sqrt[5])) G3Z2[16]:= 32/(761354780 + 538359129*Sqrt[2]) G3Z2[17]:= -170937/2595575 + 58042224/(220623875*Sqrt[17]) + Sqrt[-149795884519208064/827473201740265625 + 427461329642112/(572645814353125*Sqrt[17])]/2 G3Z2[18]:= 27/(125*(23604673 + 9636536*Sqrt[6])) G3Z2[19]:= 8063833636/10260751717 - 18321559428047616/(10260751717*(-103203545922327192481 + 14258557693188780003*Sqrt[57])^(1/3)) + (1872*(-103203545922327192481 + 14258557693188780003*Sqrt[57])^(1/3))/10260751717 G3Z2[20]:= 47893464/273359449 + 3664064143584/(6715074864685*Sqrt[5]) - Sqrt[14177834733024632366880768/45092230438324271060149225 + 1594951203089817510912/(1835629165004041158565*Sqrt[5])]/2 G3Z2[21]:= 159390302261/21323063917 - 828269868608/(63969191751*Sqrt[3]) + Sqrt[5406293834462884689167296/12276172479828619338003 - (115604636815540627862016*Sqrt[3])/454673054808467382889]/2 G3Z2[22]:= 1/(125*(14571395 + 10303524*Sqrt[2])) G3Z2[23]:= -449856/18609625 - (21070457394340032*(2/(23*(99477707703247841 + 16010443391767401*Sqrt[69])))^(1/3))/569696450125 + (239904*(2/23)^(2/3)*(99477707703247841 + 16010443391767401*Sqrt[69])^(1/3))/569696450125 G3Z2[24]:= 88870583933464/452118343792751 - (242296453384544*Sqrt[2])/452118343792751 + Sqrt[456691760418254520786177028608/204410996793900186691640148001 - (140755021909125632434336914432*Sqrt[2])/204410996793900186691640148001]/2 G3Z2[25]:= (12740595841 + 5697769392*Sqrt[5])^(-1) G3Z2[27]:= 56143116/817400375 + (31411728*2^(1/3))/163480075 - (160025472*2^(2/3))/817400375 G3Z2[28]:= 64/(125*(40728492440 + 15393923181*Sqrt[7])) G3Z2[30]:= 11010382727/48587168449 - (1050909850592*Sqrt[2])/6559267740615 - Sqrt[81532128534047880889938304/215119966465363034602891125 - (15816713431186242063104*Sqrt[2])/59017823447287526640025]/2 G3Z2[31]:= -19218839489920/22884533780471 - (7751492949727752518592*(2/(31022050996275055301273389 + 4478794001981733908757861*Sqrt[93]))^(1/3))/22884533780471 + (63648*2^(2/3)*(31022050996275055301273389 + 4478794001981733908757861*Sqrt[93])^(1/3))/22884533780471 G3Z2[32]:= -322459354944/4644924219125 - (5068462103070912*Sqrt[2])/113285056780239625 + Sqrt[448968874257596741520560641652736/12833504089702115831861872420140625 + (13189349118893836558493730816*Sqrt[2])/526200503903485826883507828125]/2 G3Z2[33]:= -1024805137/71473375 + (591882876*Sqrt[3])/71473375 - Sqrt[11186777655879630196288/6799338077408421875 - (6458688679059088602624*Sqrt[3])/6799338077408421875]/2 G3Z2[34]:= 66784212820781/204159590351387 - (16197076947168*Sqrt[17])/204159590351387 - Sqrt[-3629955995503387200453613824/3789194393858741075102983979 + (9684330112164917173409632512*Sqrt[17])/41681138332446151826132823769]/2 G3Z2[36]:= -70956865866153181032/191478360645378085609 + (48229558361525739072*Sqrt[3])/191478360645378085609 - Sqrt[-70701086268051798135142619265675665793024/36663962595441475241214715864337732900881 + (41184721024494941972039668068463176628224*Sqrt[3])/36663962595441475241214715864337732900881]/2 G3Z2[37]:= 1/(125*(91805981021 + 15092810460*Sqrt[37])) G3Z2[39]:= 183978994354870920080/1087361181471083323897 - (50483479666655360304*Sqrt[13])/1087361181471083323897 - Sqrt[-449030461857837054776229737980936858448660480/861936313109268655848124485037759596413357961 + (124541743915853300811195168123796257076348928*Sqrt[13])/861936313109268655848124485037759596413357961]/2 G3Z2[40]:= 170732539832/8792083715 - 382623248448/(8792083715*Sqrt[5]) + Sqrt[45610927936622638852608/15460147210313640245 - 20397774929706015934464/(3092029442062728049*Sqrt[5])]/2 G3Z2[42]:= 4933330105577/21427041109375 - (2014012711872*Sqrt[6])/21427041109375 - Sqrt[17531384331169819502893312/41738008245713293701171875 - (78728734508157665110513152*Sqrt[6])/459118090702846230712890625]/2 G3Z2[43]:= 532559450116/549856483328125 - 24078061275070621658112/(549856483328125*(-96610549331103309238603193 + 196409380126722630910986375*Sqrt[129])^(1/3)) + (14112*(-96610549331103309238603193 + 196409380126722630910986375*Sqrt[129])^(1/3))/549856483328125 G3Z2[45]:= 5588360415766688607/5261550616923712903 - (16132216188673406016*Sqrt[3])/26307753084618564515 + Sqrt[22484005135147808092303312484441778513984/3460489361806287980553355252896085926125 - (2596229283447111898229891645302631640576*Sqrt[3])/692097872361257596110671050579217185225]/2 G3Z2[46]:= -1875342387062937871385/12850316252289637351777 + (1326071696797345758624*Sqrt[2])/12850316252289637351777 - Sqrt[-21501971610841264716708279216483262279496832/165130627783859190641536338155152393645057729 + (15204189935014908233647605426655173446471424*Sqrt[2])/165130627783859190641536338155152393645057729]/2 G3Z2[48]:= 3287080115456/9945310362625 - (1992270745728*Sqrt[3])/9945310362625 + Sqrt[90618345589392096373481472/98909198208936208996890625 - (52256689468658884620619776*Sqrt[3])/98909198208936208996890625]/2 G3Z2[49]:= 9131582758383369829/177631422362629154821 - (3451430189897485056*Sqrt[7])/177631422362629154821 + Sqrt[-303937231089076499724354390410907713280/2868447473688249908229515895472071594731 + (1263652229143952035500430261726719141888*Sqrt[7])/31552922210570748990524674850192787542041]/2 G3Z2[52]:= 397161865049912/344251017864125 - (109168411726368*Sqrt[13])/344251017864125 - Sqrt[-676753872873458025123440142336/118508763300486109876962015625 + (187711730783850973797912941568*Sqrt[13])/118508763300486109876962015625]/2 G3Z2[55]:= 25721293723649360/41467364539950383 - 253953790163582256/(207336822699751915*Sqrt[5]) - Sqrt[-8246516021557854594030525452101632/42988558047228360978681002546167225 + 4092320405185530239071469079595008/(8597711609445672195736200509233445*Sqrt[5])]/2 G3Z2[57]:= -54050005549505898841/255261787238467012375 + (12406790293101290268*Sqrt[19])/255261787238467012375 - Sqrt[631372447021191975919242073675499356202048/1759281660652762813382651094508576884796875 - (144846751069582371579386605396530504951296*Sqrt[19])/1759281660652762813382651094508576884796875]/2 G3Z2[58]:= 1/(125*(1399837865393267 + 259943365786104*Sqrt[29])) G3Z2[60]:= 471793406023940515072/17622887736823226676005 - (54319731503287277664*Sqrt[3])/3524577547364645335201 - Sqrt[6155221780067507644652772052363335947628544/1552830860923372341408554110547231206213800125 - (710739451181119346096260637041354322804736*Sqrt[3])/310566172184674468281710822109446241242760025]/2 G3Z2[63]:= 741398652077581283904/280204508921449203125 - (137315717495979850464*Sqrt[21])/280204508921449203125 - Sqrt[-7783101638367743059563976847381913970102272/78514566819910506066334008939697509765625 + (1709388511053981428614763002638707203940352*Sqrt[21])/78514566819910506066334008939697509765625]/2 G3Z2[64]:= 2055542283332289997922816/188098843288735029296706731 - (1855284887071024010614656*Sqrt[2])/188098843288735029296706731 + Sqrt[-30857176311065045336037405283585071136383789416448/3216470440596372633811926978708596386145025656427851 + (240925752034582851860968213889508912414491909369856*Sqrt[2])/35381174846560098971931196765794560247595282220706361]/2 G3Z2[67]:= 14742040586583556/2531829841056471296125 - 781040460528238579126700546304/(506365968211294259225*(-701000833994004337491643981733143 + 14721049871139742945240761480812157*Sqrt[201])^(1/3)) + (11099088*(-701000833994004337491643981733143 + 14721049871139742945240761480812157*Sqrt[201])^(1/3))/2531829841056471296125 G3Z2[70]:= 135675439878801187/786834064508766373 - (214521702148982592*Sqrt[2/5])/786834064508766373 - Sqrt[1256822449481043886723798202127552384/7035316421265744568717079162449717375 - (4371863710271206181153325373929457152*Sqrt[2/5])/15477696126784638051177574157389378225]/2 G3Z2[72]:= -7369819724411501008134456/5124324337526057019174125 + (6935268358486006105294728*Sqrt[2])/5124324337526057019174125 - Sqrt[601049735104313091605767287326871066052468062990336/26258699916161863141284024743782615717897069515625 - (408192809316622529337491612612583235026348521865216*Sqrt[2])/26258699916161863141284024743782615717897069515625]/2 G3Z2[73]:= 9424429106743/182236043902375 - (1103046034896*Sqrt[73])/182236043902375 + Sqrt[-48156480942020934252142119552/33209975697188348418530640625 + (5636289774382728463835524224*Sqrt[73])/33209975697188348418530640625]/2 G3Z2[78]:= 23526241854944581/607324998369091475 - (408652649819499574944*Sqrt[2])/14918938584936732083375 - Sqrt[242804352793132840847428862640569787344512/20234066227374001990904131988911278904671875 - (76880710277955848915548327801881199872*Sqrt[2])/9060644351765276690410968934582701728125]/2 G3Z2[82]:= -207898649552319463/781166344651859375 + (32468314238695872*Sqrt[41])/781166344651859375 - Sqrt[-11807211404018929750050903521914368/55474623456067958724242785888671875 + (20283742846176550948262826590234112*Sqrt[41])/610220858016747545966670644775390625]/2 G3Z2[85]:= -91577309554356391847148115099/1544688837889421363183784605 + (9934290661787833678834674996*Sqrt[17/5])/308937767577884272636756921 - Sqrt[335501295121614412725028946183455553392853500755194788537344/11930318029500855359948500393998052233944050055175030125 - (7278044889044040540097399561787963133670918858611883302912*Sqrt[17/5])/477212721180034214397940015759922089357762002207001205]/2 G3Z2[88]:= -94439944292144168/341478721288090375 + 710827748239673232/(341478721288090375*Sqrt[11]) - Sqrt[2410341197874988850835810860023865856/1282684888018042373235984955844046875 - 536080968516720280480169486650085376/(116607717092549306657816814167640625*Sqrt[11])]/2 G3Z2[93]:= -442507444851094956402210341/24152505391982290294853336675 + (79483023173114819351978976*Sqrt[31])/24152505391982290294853336675 - Sqrt[30835932336783908190447477886272480907726845788058402063296/11481950439397686570163592386148802934138985625081255794866875 - (138457423075141975830610564728932123462710938908156313276416*Sqrt[31])/287048760984942164254089809653720073353474640627031394871671875]/2 G3Z2[97]:= 74947690687163772053051/934581784125513804792875 - (7609785035476857691536*Sqrt[97])/934581784125513804792875 + Sqrt[-50589347723149312814396663830359076190674754688/873443111219228487215659451171583931321650765625 + (5136570020731083674500680640977648938373929088*Sqrt[97])/873443111219228487215659451171583931321650765625]/2 G3Z2[100]:= 311136656181262515239249384/3301837593032135891442032423 - (138952298175203782646100864*Sqrt[5])/3301837593032135891442032423 - Sqrt[-382864631054755615792849378416507741489383534655406080/474005716989576027734642260203970859596668715173184823 + (3938112500168557184997126812896091225958534105139482624*Sqrt[5])/10902131490760248637896771984691329770723380448983250929]/2 G3Z2[102]:= 22260577647066982332763/2057969649376599201414125 - 3298395350048828231862097984/(73957255289646845501219410125*Sqrt[17]) - Sqrt[87026242464640364420432905194434523108324245461371943552/92984485369625937257315765518906570066643641712900192765625 - 21753051493122236887049891481623607087137113242112/(5637103212492227972257900461543998903591066605296875*Sqrt[17])]/2 G3Z2[112]:= 884790342267645663686656/1002480017341979807967799 - (41804882564758852745396736*Sqrt[7])/125310002167747475995974875 + Sqrt[84754041942466994601039167767207803116097366049554432/15702596643280877133240342859419666881347201631265625 - (6406803346743618513902909263024796975589881800409088*Sqrt[7])/3140519328656175426648068571883933376269440326253125]/2 G3Z2[130]:= 3362809364096469028732769269055/17115748388664878729059187962937 - (22940784182211547905764207984448*Sqrt[13/5])/188273232275313666019651067592307 - Sqrt[1361129964126232861165381226860368808280489728918230295285610985984/4430851248924276438296772339111020671517228949055177304245697781125 - (15347944894710556381256590814272591051670557886130597511174651392*Sqrt[13/5])/80560931798623207969032224347473103118495071801003223713558141475]/2 G3Z2[133]:= 322307732878539079499171/2773715363974498488875 - (73942465070487133253952*Sqrt[19])/2773715363974498488875 + Sqrt[3283291428937358147476933462212073563205849152/30409078736554089444962021652449243078125 - (190569394308189121957215665955489972744287589888*Sqrt[19])/7693496920348184629575391478069658498765625]/2 G3Z2[142]:= 20592049093350626979466807278367/42154598784281913066313347531625 - (14560777552433105688013641605472*Sqrt[2])/42154598784281913066313347531625 - Sqrt[-140592123491809138061739811194705859708201125772223330784523392/1777010198663782143060892177416175446970826058100075480375140625 + (99413643902474752068876217611026768721260383441946466850152192*Sqrt[2])/1777010198663782143060892177416175446970826058100075480375140625]/2 G3Z2[148]:= 9645224515860105309415437496/2988975514315424180732263874125 - (316706658931855161807391008*Sqrt[37])/597795102863084836146452774825 - Sqrt[-266949412541549127599623408406357770405635164050251157776384/8933974625177154501563987032883426215115213066348553844515625 + (8777242638833979872439234613244413144953936247588093080576*Sqrt[37])/1786794925035430900312797406576685243023042613269710768903125]/2 G3Z2[163]:= 35233719653329995065411564/10792555251621895860488211571345343375 - 721765008917706076738535709528456446423850681988475904/(2158511050324379172097642314269068675*(-12737965652562547164590026038483234248161827096523072256574968383 + 229038073182066825378006485964950394558349727761749294205546402325349*Sqrt[489])^(1/3)) + (122365152*(-12737965652562547164590026038483234248161827096523072256574968383 + 229038073182066825378006485964950394558349727761749294205546402325349*Sqrt[489])^(1/3))/10792555251621895860488211571345343375 G3Z2[177]:= -119704396734808530595233033276109/311139207533976613448431110735832675 + (345557443066701312797921929958964*Sqrt[3])/1555696037669883067242155553679163375 - Sqrt[87131265907878508598645685509309892750525472432209036909316776673477691644376128/73582161661375545110226708181307322610255894994916687888267475478423336935545653421875 - (2012210393066677320346274050899655006334833739050814514596642619447652394623488*Sqrt[3])/2943286466455021804409068327252292904410235799796667515530699019136933477421826136875]/2 G3Z2[190]:= 102074768169040202948138466868949001048768352681/1547535782386692158683406897835240469412324669455 - (14435552152074585899633463828910110013256981088*Sqrt[2])/309507156477338431736681379567048093882464933891 - Sqrt[37858425246919617396548186027808792085774366401537237658691591855523073842454246502346064347264/1088575908075996103869235997144790488490514633957557417579003791518956783650790900832352277271375 - (58893888277709883927214549389253309863440635771240008653488465689736999167090286186296859540224*Sqrt[2])/2394866997767191428512319193718539074679132194706626318673808341341704924031739981831175009997025]/2 G3Z2[193]:= -8352665866066377773384459744309713654381/47220156796596840985156450723020842799875 + (601238045113556128502834768619399500016*Sqrt[193])/47220156796596840985156450723020842799875 + Sqrt[-1849325390168829621242885718760361924096943807305190734073442943674627725257245824/2229743207895190835419089642625346050204618219214148850224970010541556629300015625 + (133117354410299853185790637734419490823167258261956070323343271703015516029511808*Sqrt[193])/2229743207895190835419089642625346050204618219214148850224970010541556629300015625]/2 G3Z2[232]:= -117450988032190678500667097512/4490096163237419343427303443542375 + (3248423924546340779664287097144*Sqrt[58])/4490096163237419343427303443542375 - Sqrt[2448147663082621180231282351051287162957249648095532725200816128/20160963555119393934946196867206062085651774763182421659088420640625 - (3048125665442332068305398652484909102534212470834981068251136*Sqrt[58])/20160963555119393934946196867206062085651774763182421659088420640625]/2 G3Z2[253]:= 254942344478178099492506992890259767305189751748579/96977759394434898761111465213728431807061981808875 - 845548099807651569627713349319558464492321957799872/(96977759394434898761111465213728431807061981808875*Sqrt[11]) + Sqrt[42675238193874120764908588827262302955037187568317241460518926934116425358555047107470685177695223488/827612351910511751061968322972121802879143886443168498972339630976814477798721368373661564698531375 - 64335342240056594674271029521348556322731103718792642468260655813690042225587693723715175244061209088/(376187432686596250482712874078237183126883584746894772260154377716733853544873349260755256681150625*Sqrt[11])]/2 pG3X[2] := 125*x^2 - 9 pG3X[3] := 125*x^2 - 12 pG3X[4] := 3993*x^2 - 400 pG3X[5] := 6655*x^4 - 13500*x^2 + 1296 pG3X[6] := 44217*x^4 - 10650*x^2 + 625 pG3X[7] := 614125*x^2 - 62208 pG3X[8] := 190109375*x^4 + 1012500000*x^2 - 104530176 pG3X[9] := 16194277*x^4 - 9635400*x^2 + 810000 pG3X[10] := 1097505*x^4 - 502050*x^2 + 39601 pG3X[12] := 5053640625*x^4 - 1373760000*x^2 + 87310336 pG3X[13] := 570328125*x^4 - 297272500*x^2 + 24265008 pG3X[15] := 75641142105*x^4 - 41583648000*x^2 + 3436773376 pG3X[16] := 11368929969*x^4 - 389644838400*x^2 + 39362560000 pG3X[18] := 56733768015625*x^4 - 28613246618250*x^2 + 2316700129041 pG3X[22] := 47616872765625*x^4 - 24093956246250*x^2 + 1952394192961 pG3X[25] := 880545183759351*x^4 - 446305102350000*x^2 + 36180500000000 pG3X[28] := 5504673856546875*x^4 - 5523616981760000*x^2 + 503148526436352 pG3X[37] := 7935316313754328125*x^4 - 4020156148136348500*x^2 + 325863162893829168 pG3X[58] := 4980291492907241681640625*x^4 - 2523044653714156837955250*x^2 + 204510286607449493122929 pG3Y[2] := 125*x^2 - 784 pG3Y[3] := 125*x^2 - 1452 pG3Y[4] := 1331*x^2 - 21168 pG3Y[5] := 6655*x^4 - 692800*x^2 + 11182336 pG3Y[6] := 4913*x^4 - 168672*x^2 + 1218816 pG3Y[7] := 614125*x^2 - 17193708 pG3Y[8] := 190109375*x^4 + 32977000000*x^2 - 1249888224256 pG3Y[9] := 16194277*x^4 - 1252355328*x^2 + 24096973824 pG3Y[10] := 121945*x^4 - 9361440*x^2 + 179345664 pG3Y[12] := 62390625*x^4 - 3748860000*x^2 + 36197345536 pG3Y[13] := 190109375*x^4 - 19978920000*x^2 + 524848087296 pG3Y[15] := 8404571345*x^4 - 797956836600*x^2 + 17620953943824 pG3Y[16] := 1263214441*x^4 - 1720946037888*x^2 + 104966417977344 pG3Y[18] := 56733768015625*x^4 - 8158190723172000*x^2 + 293281878679163136 pG3Y[22] := 5290763640625*x^4 - 930853830060000*x^2 + 40943463412287744 pG3Y[25] := 97838353751039*x^4 - 19570218869376000*x^2 + 978638349427200000 pG3Y[28] := 1834891285515625*x^4 - 338030189503020000*x^2 + 14842504938881620224 pG3Y[37] := 2645105437918109375*x^4 - 782954606445058152000*x^2 + 57938892241710338724096 pG3Y[58] := 4980291492907241681640625*x^4 - 2310855171518363947471764000*x^2 + 268059190478021059540824301824 pG3Z2[2] := 125*x - 27 pG3Z2[3] := 125*x - 4 pG3Z2[4] := 1331*x - 8 pG3Z2[5] := 166375*x^2 + 533250*x - 729 pG3Z2[6] := 4913*x^2 - 2798*x + 1 pG3Z2[7] := 614125*x - 64 pG3Z2[8] := 190109375*x^2 - 1410750000*x + 46656 pG3Z2[9] := 16194277*x^2 + 2399094*x - 27 pG3Z2[10] := 3048625*x^2 - 246350*x + 1 pG3Z2[11] := 159484621967*x^3 - 114080856516*x^2 + 818421041232*x - 1259712 pG3Z2[12] := 561515625*x^2 - 420120000*x + 256 pG3Z2[13] := 190109375*x^2 + 3991250*x - 1 pG3Z2[14] := 599866273660753*x^4 + 232542870469668*x^3 + 366572950847046*x^2 - 4988528567964*x + 531441 pG3Z2[15] := 210114283625*x^2 - 87746552000*x + 4096 pG3Z2[16] := 1263214441*x^2 + 24363352960*x - 512 pG3Z2[17] := 124531835693359375*x^4 + 32805214101562500*x^3 + 13498547750156250*x^2 + 54808248442500*x - 531441 pG3Z2[18] := 56733768015625*x^2 - 159331542750*x + 729 pG3Z2[19] := 10260751717*x^3 - 24191500908*x^2 + 29039794032*x - 64 pG3Z2[20] := 103097383781866890625*x^4 - 72251986996813500000*x^3 - 9497816769831696000*x^2 - 2011983249694464000*x + 2176782336 pG3Z2[21] := 575722725759*x^4 - 17214152644188*x^3 + 1896754712378*x^2 + 1850000548*x - 1 pG3Z2[22] := 5290763640625*x^2 - 3642848750*x + 1 pG3Z2[23] := 6267542200571287109375*x^3 + 454521485120769000000*x^2 + 36452366690171904000*x - 5159780352 pG3Z2[24] := 452118343792751*x^4 - 355482335733856*x^3 - 919644794502272*x^2 + 55324786481152*x - 4096 pG3Z2[25] := 97838353751039*x^2 + 25481191682*x - 1 pG3Z2[27] := 16999373423828125*x^3 - 3502804096687500*x^2 + 4077357175062000*x - 46656 pG3Z2[28] := 1834891285515625*x^2 - 651655879040000*x + 4096 pG3Z2[30] := 553438215614390625*x^4 - 501660562998937500*x^3 + 8817665066947750*x^2 - 511034705500*x + 1 pG3Z2[31] := 30459314461806901*x^3 + 76740826083250560*x^2 + 236618264481632256*x - 262144 pG3Z2[32] := 5396307128541531668212890625*x^4 + 1498487065588342570500000000*x^3 + 18441177741337842576000000*x^2 + 220093689501926866944000*x - 139314069504 pG3Z2[33] := 185802855712890625*x^4 + 10656372166773437500*x^3 - 108912710344656250*x^2 - 2741240450500*x + 1 pG3Z2[34] := 271736414757696097*x^4 - 355559149057838044*x^3 + 246471524163920166*x^2 - 4717175541916*x + 1 pG3Z2[36] := 191478360645378085609*x^4 + 283827463464612724128*x^3 + 269499185406087942528*x^2 - 40743654857689651200*x + 2985984 pG3Z2[37] := 2645105437918109375*x^2 + 22951495255250*x - 1 pG3Z2[39] := 792686301292419743120913*x^4 - 536482747538803602953280*x^3 + 298209788172578527633408*x^2 - 1067164464888813715456*x + 16777216 pG3Z2[40] := 134985960286859375*x^4 - 10485112102432700000*x^3 + 4033930575960624000*x^2 + 429500491436185600*x - 4096 pG3Z2[42] := 55701936946441650390625*x^4 - 51298924769710835937500*x^3 + 112697080651205843750*x^2 - 279766037081500*x + 1 pG3Z2[43] := 8591507552001953125*x^3 - 24963724224187500*x^2 + 28991078006790000*x - 64 pG3Z2[45] := 403906221577284398319359375*x^4 - 1715975920166358820386937500*x^3 + 510399269097896172328292250*x^2 + 620784640003801702500*x - 531441 pG3Z2[46] := 12850316252289637351777*x^4 + 7501369548251751485540*x^3 + 1931359131577797616806*x^2 - 1861047971688028*x + 1 pG3Z2[48] := 127020319060954077880859375*x^4 - 167928782439298606000000000*x^3 - 5515244909180922048000000*x^2 + 4879884007274381312000*x - 1048576 pG3Z2[49] := 236427423164659405066751*x^4 - 48616546605633060969596*x^3 + 15025024196814134539002*x^2 + 7306766273939332*x - 1 pG3Z2[52] := 672365269265869140625*x^4 - 3102827070702437500000*x^3 + 5531375051003094000000*x^2 - 112753964544118528000*x + 4096 pG3Z2[55] := 7883334755587129843140625*x^4 - 19559436295977610195000000*x^3 + 14223852181012485364224000*x^2 - 1675513225224923348992000*x + 16777216 pG3Z2[57] := 13461070811403533855712890625*x^4 + 11401173045598900536773437500*x^3 - 2674232861134373288656250*x^2 - 231253023524354500*x + 1 pG3Z2[58] := 4980291492907241681640625*x^2 - 349959466348316750*x + 1 pG3Z2[60] := 97562564443544663354281543140625*x^4 - 10447634977114726035268342400000*x^3 + 87148926763262109241058816000*x^2 - 13304658857139055152332800*x + 16777216 pG3Z2[63] := 547274431487205474853515625*x^4 - 5792176969356103780500000000*x^3 + 44593873904366069897088000000*x^2 - 32263155987043153366646784000*x + 12230590464 pG3Z2[64] := 250359560417306323993916658961*x^4 - 10943707116461111948941072384*x^3 + 1282874415411766922994425856*x^2 + 8205552571468594788958208*x - 2097152 pG3Z2[67] := 39559841266507364001953125*x^3 - 691033152496104187500*x^2 + 802490270074994694000*x - 64 pG3Z2[70] := 199097012401419243322614390625*x^4 - 137322853468384553137924937500*x^3 + 5895047168419076051452707750*x^2 - 39159703063321217500*x + 1 pG3Z2[72] := 10008445971730580115574462890625*x^4 + 57576716596964851626050437500000*x^3 - 63663576018591485966561694000000*x^2 - 179682504297333484641617664000*x + 2176782336 pG3Z2[73] := 42648629100728852144287109375*x^4 - 8822381628848720684773437500*x^3 + 31377804607100720820840656250*x^2 + 119379461724784898500*x - 1 pG3Z2[78] := 190542906155144596191019629150390625*x^4 - 29524610421029431908188943710937500*x^3 + 472597469957470843560779843750*x^2 - 728027257108471697500*x + 1 pG3Z2[82] := 9976963485247017149566650390625*x^4 + 10621027131628719448499914062500*x^3 + 3888414868982708122391625843750*x^2 - 2967310385945378729500*x + 1 pG3Z2[85] := 4827152618404441759949326890625*x^4 + 1144716369429454898089351438737500*x^3 - 18268288578378644515592685800250*x^2 - 8323637599084207540900*x + 1 pG3Z2[88] := 107413065512047349578369140625*x^4 + 118825370845266487504437500000*x^3 - 136252585169027771671326000000*x^2 - 93925954978887091042048000*x + 4096 pG3Z2[93] := 4642517222953002147203107673574462890625*x^4 + 340229454570472735424402583668085937500*x^3 - 994493276046683059398831647656250*x^2 - 119562334956358303022500*x + 1 pG3Z2[97] := 125805295202567454961190894287109375*x^4 - 40355232733203236981783812273437500*x^3 + 6879527561430205965938321520656250*x^2 + 434063887942527195938500*x - 1 pG3Z2[100] := 40173457994421997391175208490641*x^4 - 15142398783029684091663789020512*x^3 + 17653342747821487221723291417984*x^2 - 4595611279063401997855725568*x + 4096 pG3Z2[102] := 1500204578684428086872355549102254150390625*x^4 - 64909451935612890662444677180095960937500*x^3 + 73029911755739899454018063743843750*x^2 - 2096561993697267648929500*x + 1 pG3Z2[112] := 16868145819147116783434735077880859375*x^4 - 59551401542410553502878924000000000000*x^3 + 7034531502800645366539293373440000000*x^2 + 733804504709872698810239549440000*x - 16777216 pG3Z2[130] := 19236826333037936730885942502387761114390625*x^4 - 15118188993962809261441282564227180925937500*x^3 + 15622991663433664722390303556497775347750*x^2 - 7499357316207209662281449500*x + 1 pG3Z2[133] := 2139673403644138632031271784175537109375*x^4 - 994526392702189382279906817825521585937500*x^3 + 53601832072238278495073633108346759656250*x^2 + 17059553830496608260519374500*x - 1 pG3Z2[142] := 2008024433105178862840461392478129150390625*x^4 - 3923589729201003448454812208688224710937500*x^3 + 1996064277164517601938808163181903387843750*x^2 - 190238141379262042820979665500*x + 1 pG3Z2[148] := 28681321683264998046753149245265869140625*x^4 - 370210844112661698321547222014437500000*x^3 + 429698809548865498425463990020822000000*x^2 - 3728427128725901871235804909312000*x + 4096 pG3Z2[163] := 224451422498574115473590775022822688001953125*x^3 - 2198253790246041723377943360187500*x^2 + 2552810853189232588558727380998000*x - 64 pG3Z2[177] := 453862812208398970976788666031391041820019781421855712890625*x^4 + 698457446959169058204847636214112364135655147512773437500*x^3 - 955988126716674918584499441060400215841192656250*x^2 - 1164527733988793689131688220162500*x + 1 pG3Z2[190] := 6436781644864647697523795565683453327461887922014390625*x^4 - 1698268955412406376549653742532139004948883467730137500*x^3 + 88064942603596954678608650784469580855415391299750*x^2 - 23752898720272640689632999159799900*x + 1 pG3Z2[193] := 453110606136094296406393832816799610694894287109375*x^4 + 320598807812375890629983208779637681124795726562500*x^3 + 244612559870637809842371050014562021301625968656250*x^2 + 46935388218352090256815237384994500*x - 1 pG3Z2[232] := 101593661267122957308468060913151353430146078369140625*x^4 + 10629862221060282813907580605122243739555437500000*x^3 - 12336050585549692139911996453885393153159998000000*x^2 - 866840466705515186297226740329752000256000*x + 4096 pG3Z2[253] := 22918572044387935058778295489963164548153319919675537109375*x^4 - 241000185014527734676510516716573686280687187199828585937500*x^3 + 42669328796600344303048307450894780819546428170306519656250*x^2 + 14652951773955041963658819957780221198500*x - 1 G(* Type G, s=1/4, N=2〜116 *) sumG4[t_, limit_:Infinity] := Sum[termp[n, 1/4, G4X[t], G4Y[t], G4Z2[t]], {n, 0, limit}]; G4X[2]:= 2/9 G4X[3]:= 1/(2*Sqrt[3]) G4X[4]:= (6*(11 - 6*Sqrt[2]))/49 G4X[5]:= (2*Sqrt[2])/9 G4X[6]:= (4*(27 + Sqrt[3]))/363 G4X[7]:= (3*Sqrt[(-11 + 8*Sqrt[2])/7])/2 G4X[8]:= (8*(-15 + 23*Sqrt[2]))/441 G4X[9]:= (9*Sqrt[3])/49 G4X[10]:= -27804/43681 + (10350*Sqrt[5])/43681 + Sqrt[-6835933152/1908029761 + (3673389600*Sqrt[5])/1908029761]/2 G4X[11]:= 19/(18*Sqrt[11]) G4X[12]:= -1530/529 + (1272*Sqrt[2])/529 - Sqrt[60430528/839523 - (14215040*Sqrt[2])/279841]/2 G4X[14]:= (16*(841 - 98*Sqrt[7]))/29241 G4X[15]:= Sqrt[(5329 - 1704*Sqrt[2])/3]/98 G4X[16]:= -16291896/24910081 + (8531568*Sqrt[2])/24910081 + Sqrt[87683441845248/620512135426561 + (355915585152000*Sqrt[2])/620512135426561]/2 G4X[17]:= 376/(9*Sqrt[8605 + 2091*Sqrt[17]]) G4X[18]:= -2610/5929 + (984*Sqrt[3])/5929 + Sqrt[-17499456/5021863 + (88737408*Sqrt[3])/35153041]/2 G4X[20]:= 7966/8649 - (2500*Sqrt[10])/8649 + Sqrt[226491712/74805201 - (62451200*Sqrt[10])/74805201]/2 G4X[21]:= Sqrt[(133585 - 38364*Sqrt[6])/3]/361 G4X[23]:= Sqrt[(-8443 + 6504*Sqrt[2])/23]/18 G4X[24]:= 9810576/1168561 + (7542504*Sqrt[2])/1168561 - Sqrt[2425414346741248/4096604432163 + (571642519168000*Sqrt[2])/1365534810721]/2 G4X[26]:= 75796/149769 - (27586*Sqrt[13])/149769 + Sqrt[-11458902496/22430753361 + (8824255648*Sqrt[13])/22430753361]/2 G4X[29]:= (2206*Sqrt[2])/9801 G4X[30]:= 1905048/20638849 + (3550200*Sqrt[5])/20638849 - Sqrt[140955118569472/182555180590629 - (127911725824000*Sqrt[5])/425962088044801]/2 G4X[32]:= 72992/53361 - (57632*Sqrt[2])/53361 + Sqrt[-1066680320/316377369 + (8627105792*Sqrt[2])/2847396321]/2 G4X[35]:= Sqrt[(40117 - 6800*Sqrt[10])/7]/162 G4X[36]:= 2288860866/5890716001 - (3017780172*Sqrt[2])/5890716001 + Sqrt[45435936531579095808/34700535004437432001 + (9883417645626190848*Sqrt[2])/34700535004437432001]/2 G4X[39]:= Sqrt[(12914758417 - 7225750968*Sqrt[2])/3]/94178 G4X[41]:= Sqrt[2*(-94693589 + 14967993*Sqrt[41])]/4761 G4X[44]:= 434846/2752281 - (421564*Sqrt[22])/2752281 + Sqrt[12569201069248/7575050702961 + (2308578660608*Sqrt[22])/7575050702961]/2 G4X[50]:= -13779110/19263321 + (4791280*Sqrt[5])/19263321 + Sqrt[851815120000/1963362624069 + (79317799408000*Sqrt[5])/371075535949041]/2 G4X[51]:= Sqrt[(2674165790509 - 517195628556*Sqrt[17])/3]/1334978 G4X[56]:= 302267456/91757241 + (646935152*Sqrt[2/7])/91757241 - Sqrt[1788318742591350784/19645246310508189 + (1432187497199878144*Sqrt[2/7])/8419391275932081]/2 G4X[65]:= (4*Sqrt[57699723241 - 6411365025*Sqrt[65]])/974169 G4X[71]:= 3760399/(18*Sqrt[215370865931 + 152294156904*Sqrt[2]]) G4X[74]:= 473489557604/850060028169 - (100082841346*Sqrt[37])/850060028169 + Sqrt[328711068737510135197472/722602051490681073492561 + (54287974723827722499872*Sqrt[37])/722602051490681073492561]/2 G4X[95]:= Sqrt[(5038734594889 - 3266585382504*Sqrt[2])/19]/466578 G4X[116]:= 21161164591954/88173205051827 - (24875782398724*Sqrt[58])/264519615155481 + Sqrt[11403291729398974172241824576/7774514089111530393756037929 + (120033615834857592068557312*Sqrt[58])/863834898790170043750670881]/2 G4Y[2]:= 14/9 G4Y[3]:= 4/Sqrt[3] G4Y[4]:= (10*(32 - 13*Sqrt[2]))/49 G4Y[5]:= (20*Sqrt[2])/9 G4Y[6]:= (10*(96 + 17*Sqrt[3]))/363 G4Y[7]:= 4*Sqrt[(-25 + 22*Sqrt[2])/7] G4Y[8]:= (4*(-57 + 352*Sqrt[2]))/441 G4Y[9]:= (120*Sqrt[3])/49 G4Y[10]:= -114560/43681 + (56030*Sqrt[5])/43681 + Sqrt[-73925427200/1908029761 + (94019993600*Sqrt[5])/1908029761]/2 G4Y[11]:= 140/(9*Sqrt[11]) G4Y[12]:= -5568/529 + (5824*Sqrt[2])/529 - Sqrt[981207328/839523 - (231256064*Sqrt[2])/279841]/2 G4Y[14]:= (70*(2176 + 13*Sqrt[7]))/29241 G4Y[15]:= (20*Sqrt[(379 + 114*Sqrt[2])/3])/49 G4Y[16]:= -81617920/24910081 + (56825340*Sqrt[2])/24910081 + Sqrt[36150554702643200/620512135426561 + (31604412809216000*Sqrt[2])/620512135426561]/2 G4Y[17]:= (4*Sqrt[34*(-131 + 33*Sqrt[17])])/9 G4Y[18]:= -10902/5929 + (6400*Sqrt[3])/5929 + Sqrt[-29491200/5021863 + (3011739648*Sqrt[3])/35153041]/2 G4Y[20]:= 53440/8649 - (10930*Sqrt[10])/8649 + Sqrt[4739891200/74805201 + (124518400*Sqrt[10])/74805201]/2 G4Y[21]:= (140*Sqrt[(2*(365 + 22*Sqrt[6]))/3])/361 G4Y[23]:= (28*Sqrt[(-1 + 78*Sqrt[2])/23])/9 G4Y[24]:= 39173120/1168561 + (33179520*Sqrt[2])/1168561 - Sqrt[36504820602395200/4096604432163 + (8603890476544000*Sqrt[2])/1365534810721]/2 G4Y[26]:= 507520/149769 - (140530*Sqrt[13])/149769 + Sqrt[1883392409600/22430753361 + (769651916800*Sqrt[13])/22430753361]/2 G4Y[29]:= (52780*Sqrt[2])/9801 G4Y[30]:= 51669120/20638849 + (48364160*Sqrt[5])/20638849 + Sqrt[8118893066945200/182555180590629 - (8472046783283200*Sqrt[5])/425962088044801]/2 G4Y[32]:= 367736/53361 - (260096*Sqrt[2])/53361 + Sqrt[52449771520/949132107 + (404401160192*Sqrt[2])/2847396321]/2 G4Y[35]:= (20*Sqrt[(4837 + 1012*Sqrt[10])/7])/81 G4Y[36]:= 29084301120/5890716001 - (17821459110*Sqrt[2])/5890716001 + Sqrt[4287909888947581747200/34700535004437432001 + (2979886171370147020800*Sqrt[2])/34700535004437432001]/2 G4Y[39]:= (260*Sqrt[(7581907 + 66198*Sqrt[2])/3])/47089 G4Y[41]:= (40*Sqrt[41*(-39917 + 10659*Sqrt[41])])/4761 G4Y[44]:= 11865920/2752281 + (9866560*Sqrt[2])/2752281 - Sqrt[446219327655200/2525016900987 - (946574136217600*Sqrt[2])/7575050702961]/2 G4Y[50]:= -96241370/19263321 + (43041280*Sqrt[5])/19263321 + Sqrt[3525262114816000/17670263616621 + (33271281354342400*Sqrt[5])/371075535949041]/2 G4Y[51]:= (140*Sqrt[(17*(407837957 + 323268*Sqrt[17]))/3])/667489 G4Y[56]:= 1280184320/91757241 + (3474832640*Sqrt[2/7])/91757241 - Sqrt[22627902772411601600/19645246310508189 + (16981694134496665600*Sqrt[2/7])/8419391275932081]/2 G4Y[65]:= (40*Sqrt[13*(5388771277 + 67290267*Sqrt[65])])/974169 G4Y[71]:= 7087220/(9*Sqrt[2181025289 + 1545683934*Sqrt[2]]) G4Y[74]:= 5170582014080/850060028169 - (850037900530*Sqrt[37])/850060028169 + Sqrt[213872473209242244480204800/722602051490681073492561 + (35166203720432085105459200*Sqrt[37])/722602051490681073492561]/2 G4Y[95]:= (20*Sqrt[(480476278339 + 7564722594*Sqrt[2])/19])/233289 G4Y[116]:= 672055238620480/88173205051827 - (264519670917970*Sqrt[58])/264519615155481 + Sqrt[3604431994875730750832805478400/7774514089111530393756037929 + (52587216651282574559195955200*Sqrt[58])/863834898790170043750670881]/2 G4Z2[2]:= 32/81 G4Z2[3]:= 1/9 G4Z2[4]:= 32/(457 + 325*Sqrt[2]) G4Z2[5]:= 1/81 G4Z2[6]:= (64*(746 - 425*Sqrt[3]))/131769 G4Z2[7]:= (249 + 176*Sqrt[2])^(-1) G4Z2[8]:= 128/(81*(884 + 627*Sqrt[2])) G4Z2[9]:= 1/2401 G4Z2[10]:= 1391057696/1908029761 - (533370240*Sqrt[5])/1908029761 - Sqrt[-81655421523444531200/3640577568861717121 + (36587558440088780800*Sqrt[5])/3640577568861717121]/2 G4Z2[11]:= 1/9801 G4Z2[12]:= -65209376/2518569 + 12754624/(279841*Sqrt[3]) - Sqrt[11472312970846208/2114396602587 - 6622669099171840/(704798867529*Sqrt[3])]/2 G4Z2[13]:= -3229/43923 - 48235168/(43923*(228753433 + 211137861*Sqrt[78])^(1/3)) + (32*(228753433 + 211137861*Sqrt[78])^(1/3))/43923 G4Z2[14]:= 256/(81*(102376 + 38675*Sqrt[7])) G4Z2[15]:= 1/(9*(6449 + 4560*Sqrt[2])) G4Z2[16]:= -71905429355264/620512135426561 + (42963403308800*Sqrt[2])/620512135426561 + Sqrt[-437638659042945688690708480000/385035310211630778817424286721 + (309808840225982016197857280000*Sqrt[2])/385035310211630778817424286721]/2 G4Z2[17]:= 1/(81*(2177 + 528*Sqrt[17])) G4Z2[18]:= 12802208/15065589 - (17038592*Sqrt[3])/35153041 - Sqrt[-4045457244160000/1235736291547681 + 3003358134173696/(529601267806149*Sqrt[3])]/2 G4Z2[19]:= -1709197/15856203 - (8137824800*2^(2/3))/(15856203*(35037999968 + 5406965223*Sqrt[114])^(1/3)) + (800*(2*(35037999968 + 5406965223*Sqrt[114]))^(1/3))/15856203 G4Z2[20]:= -18693728/24935067 + (28426720*Sqrt[10])/74805201 - Sqrt[4928951354163200/621757566294489 - (465997565132800*Sqrt[10])/207252522098163]/2 G4Z2[21]:= 1/(9*(150889 + 61600*Sqrt[6])) G4Z2[23]:= 1/(81*(43241 + 30576*Sqrt[2])) G4Z2[24]:= -1258653213377536/12289813296489 + (171421605361600*Sqrt[2/3])/1365534810721 - Sqrt[4227824857404220793330790400000/50346503620852607006575707 - (1726001689366489162168893440000*Sqrt[2/3])/16782167873617535668858569]/2 G4Z2[25]:= -32503039/671898241 - (4081563782816*5^(2/3))/(671898241*(3*(3878940407693553 + 2206566231506798*Sqrt[6]))^(1/3)) + (416*(5*(3878940407693553 + 2206566231506798*Sqrt[6]))^(1/3))/(671898241*3^(2/3)) G4Z2[26]:= 3485416736/22430753361 - (957104000*Sqrt[13])/22430753361 - Sqrt[-678358357709393920000/503138696342012796321 + (188144079701493760000*Sqrt[13])/503138696342012796321]/2 G4Z2[27]:= -115575/130321 - (26276287712*2^(2/3))/(390963*(13663686521634 + 25436328669557*Sqrt[2])^(1/3)) + (32*(2*(13663686521634 + 25436328669557*Sqrt[2]))^(1/3))/390963 G4Z2[29]:= 1/96059601 G4Z2[30]:= 138354567918592/547665541771887 - (143992773882880*Sqrt[5])/1277886264134403 - Sqrt[1812717941905843271123556761600/4898979912190143573296544499227 - (38603249235837712877653196800*Sqrt[5])/233284757723340170156978309487]/2 G4Z2[31]:= 11652515401/268927201 + (8245779600*Sqrt[2])/268927201 - Sqrt[1087066839563292160000/72321839437694401 + (768673064430453760000*Sqrt[2])/72321839437694401]/2 G4Z2[32]:= -664758272/949132107 + (469755392*Sqrt[2])/949132107 + Sqrt[-109522299278907932672/8107665808844335041 + (8604885009323196416*Sqrt[2])/900851756538259449]/2 G4Z2[33]:= 4121345/8311689 - (226936*Sqrt[11/3])/923521 - Sqrt[-28160079833600/23028058010907 + (4912315561472*Sqrt[11/3])/7676019336969]/2 G4Z2[35]:= 1/(3969*(128009 + 40480*Sqrt[10])) G4Z2[36]:= -758949071875521824/34700535004437432001 + (4051080881437189600*Sqrt[2])/34700535004437432001 - Sqrt[133219281202364428432379049841582080000/1204127129594187528941331872763498864001 - (24331500928441886596378427908915200000*Sqrt[2])/1204127129594187528941331872763498864001]/2 G4Z2[39]:= 1/(9*(243407089 + 172114800*Sqrt[2])) G4Z2[41]:= 1/(81*(54600721 + 8527200*Sqrt[41])) G4Z2[44]:= -1497518432/280557433443 + (61699745600*Sqrt[11])/2525016900987 - Sqrt[1512033431590106782720000/57381393152429940254167521 - (2194937589839667200000*Sqrt[11])/2125236783423331120524723]/2 G4Z2[45]:= -19390957/10256403 + (2993360*Sqrt[6])/3418801 - Sqrt[-5317346821145600/11688200277601 + (19548266867353600*Sqrt[2/3])/35064600832803]/2 G4Z2[47]:= 6067/59643 + (944*Sqrt[2])/2209 - Sqrt[16603156480/32015587041 + (11134910464*Sqrt[2])/10671862347]/2 G4Z2[49]:= 481784377107601/4506487876801 + (128767125364000*Sqrt[14])/4506487876801 - Sqrt[1856999205628632296912625280000/20308432983754384953993601 + (496303914989921968944673280000*Sqrt[14])/20308432983754384953993601]/2 G4Z2[50]:= 11867821024/5890087872207 - (4088497664*Sqrt[5])/4581179456161 - Sqrt[-2714620527478908843681382400/137697053379868019524548819681 + (57810252293519439840477184*Sqrt[5])/6557002541898477120216610461]/2 G4Z2[51]:= 1/(9*(13062107489 + 3168026400*Sqrt[17])) G4Z2[53]:= 9413/83349 - 19381216/(583443*(-5818337 + 456417*Sqrt[318])^(1/3)) + (608*(-5818337 + 456417*Sqrt[318])^(1/3))/583443 G4Z2[56]:= -958148985900285952/137516724173557323 + (80488958642435200*Sqrt[2])/15279636019284147 - Sqrt[10118868730537688603026974220042240000/24313949263833743572022376471762423 - (2379710532349609738193114241433600000*Sqrt[2])/8104649754611247857340792157254141]/2 G4Z2[57]:= -41467583/316377369 + (1855720*Sqrt[19/3])/35153041 - Sqrt[-3356913725819392/33364879871787387 + (444690173141504*Sqrt[19/3])/11121626623929129]/2 G4Z2[59]:= -125431277/68516523 - (7047405260000*2^(2/3))/(68516523*(3035372625864526 + 172884603414087*Sqrt[354])^(1/3)) + (800*(2*(3035372625864526 + 172884603414087*Sqrt[354]))^(1/3))/68516523 G4Z2[63]:= 3540363801/13521270961 + (1703529968*Sqrt[2])/13521270961 - Sqrt[56416107877975953408/182824768400781863521 + (60224989372668051456*Sqrt[2])/182824768400781863521]/2 G4Z2[65]:= 1/(81*(86801836241 + 10766442720*Sqrt[65])) G4Z2[69]:= 5138649673769/23635028158569 - (697411972400*Sqrt[2/3])/2626114239841 - Sqrt[-703973176745842640324480000/186204852018783178336042587 + (287395948690716417660160000*Sqrt[2/3])/62068284006261059445347529]/2 G4Z2[71]:= 1/(81*(437185436521 + 309136786800*Sqrt[2])) G4Z2[74]:= 48533496601297231136/722602051490681073492561 - (7902503882007280000*Sqrt[37])/722602051490681073492561 - Sqrt[-343639309768459837812532831327932112015360000/522153724818540901425980539569034049238522338721 + (56493954666094459427059137283847777331200000*Sqrt[37])/522153724818540901425980539569034049238522338721]/2 G4Z2[75]:= 208069199217601/620034053633289 - (21909911210704*Sqrt[10])/206678017877763 - Sqrt[-49643237619036238558566287360/128147409221642766727229652507 + (15698589354846517150032265216*Sqrt[10])/128147409221642766727229652507]/2 G4Z2[77]:= 9799229329/79502005521 + (3554465264*Sqrt[22])/79502005521 - Sqrt[1346027800257820359680/6320568881861114481441 + (310603417408140752896*Sqrt[22])/6320568881861114481441]/2 G4Z2[79]:= 570428209425826658601/1858108924530102184801 + (403676527599489086800*Sqrt[2])/1858108924530102184801 - Sqrt[2605189610966675604804242113245573739520000/3452568775418412976702278854578793555409601 + (1842149010729925759923138345977856942080000*Sqrt[2])/3452568775418412976702278854578793555409601]/2 G4Z2[81]:= 73259319996801/35971217755201 - 10800784955253491816800/(35971217755201*(-6055854507923231142283343 + 2774715215493234368371084*Sqrt[6])^(1/3)) + (509600*(-6055854507923231142283343 + 2774715215493234368371084*Sqrt[6])^(1/3))/35971217755201 G4Z2[89]:= 3431336387/686115387 + (333385400*Sqrt[89])/686115387 - Sqrt[777458435407193920000/4236788918503437921 + (9181331163884480000*Sqrt[89])/470754324278159769]/2 G4Z2[95]:= 1/(29241*(427925331521 + 302588903760*Sqrt[2])) G4Z2[99]:= 9918230909/20735503509 - (147851600*Sqrt[33])/48382841521 - Sqrt[-31164475294227503360000/2340899353646201593441 + (7419980378106602240000*Sqrt[11/3])/1003242580134086397189]/2 G4Z2[101]:= -49635743351677/168845458495923 - 15082348229155113892000/(168845458495923*(121176392383639821373129624444741 + 4922455579364073874825114790949*Sqrt[606])^(1/3)) + (800*(121176392383639821373129624444741 + 4922455579364073874825114790949*Sqrt[606])^(1/3))/168845458495923 G4Z2[105]:= 64869935911481/726705134885961 - (2109442430960*Sqrt[5/21])/11535002141047 - Sqrt[7962425817270806407727104000/176033451023207590410824964507 - (777053119404906043676672000*Sqrt[5/21])/8382545286819409067182141167]/2 G4Z2[107]:= -65787892889/4657120068447 + (1984*(3062243923082141692218723 + 121284794264961615011867*Sqrt[642])^(1/3))/(10866613493043*3^(2/3)) - 5572774357399667008/(10866613493043*(3*(3062243923082141692218723 + 121284794264961615011867*Sqrt[642]))^(1/3)) G4Z2[113]:= 3771042203/8448319467 + (38852752*Sqrt[113])/938702163 - Sqrt[1008828452255800483840/642366916348420476801 + (31663724988944162816*Sqrt[113])/214122305449473492267]/2 G4Z2[116]:= -38059347232238774488864/69970626802003773543804341361 + (2499778969900716385824800*Sqrt[58])/23323542267334591181268113787 - Sqrt[1449725758322302540034242794616230943486672916480000/543987623896143202406056572399502262036341309896779481369 - (83759044299110439068041142569284027814297600000*Sqrt[58])/181329207965381067468685524133167420678780436632259827123]/2 G4Z2[119]:= 2656006103/307419903 - (5560008400*Sqrt[2])/922259709 - Sqrt[192515285857991073280000/375098270142541224321 - (15123901969232235520000*Sqrt[2])/41677585571393469369]/2 G4Z2[129]:= -7576454692988330597231/84219475763336310250569 + (222372220028111527000*Sqrt[43/3])/9357719529259590027841 - Sqrt[-42029432727033834847357272560587451821120000/2364306699283730726054133936500977261188274587 + (3700485247167862437889088341014609552320000*Sqrt[43/3])/788102233094576908684711312166992420396091529]/2 G4Z2[131]:= 56294523945867923/739822699076905323 - (52403751826559129806872337600*2^(2/3))/(739822699076905323*(-15184252379256689407989890659974513350 + 577950560928753849255647530334036169*Sqrt[786])^(1/3)) + (20800*(2*(-15184252379256689407989890659974513350 + 577950560928753849255647530334036169*Sqrt[786]))^(1/3))/739822699076905323 G4Z2[141]:= 2056373660116330367/3939758968403173167 - (652949332865903200*Sqrt[6])/3064256975424690241 - Sqrt[-14885345025403490289305446931778560000/253521111908849508672598541271617228187 + (289376983961461689517233803448320000*Sqrt[2/3])/4024144633473801724961881607485987749]/2 G4Z2[149]:= -12006812939764477/1047760922436723 - (501261354841042753385108800*2^(2/3))/(1047760922436723*(2366758246143191796040964622662110 + 82767234116065033502438427345213*Sqrt[894])^(1/3)) + (78400*(2*(2366758246143191796040964622662110 + 82767234116065033502438427345213*Sqrt[894]))^(1/3))/1047760922436723 G4Z2[155]:= -58779202080119/299230456361841 + (18777304888160*Sqrt[10])/299230456361841 - Sqrt[-1173995911866007841305704755200/89538866014515630989920909281 + (371250559662139067450483507200*Sqrt[10])/89538866014515630989920909281]/2 G4Z2[161]:= 22035382843/19370043 - (9746482400*Sqrt[46])/58110129 - Sqrt[554174924484958720000/53599795117407 - (81708634869017600000*Sqrt[46])/53599795117407]/2 G4Z2[165]:= 7403353326952984557769/35826425693361508150089 - (526131627009240017360*Sqrt[22])/11942141897787169383363 - Sqrt[144168651123668224375400565111139672072115200/427844259320651206667428529271978256983569307 - (30736859695409030118634237593687917597132800*Sqrt[22])/427844259320651206667428529271978256983569307]/2 G4Z2[179]:= 61734456141882114323/133003126523723674923 - (17389078743088732527651076525330400*2^(2/3))/(133003126523723674923*(-2024391410266434641241025279626615750651476230 + 63074129535075978080634519512878654519518537*Sqrt[1074])^(1/3)) + (39200*(2*(-2024391410266434641241025279626615750651476230 + 63074129535075978080634519512878654519518537*Sqrt[1074]))^(1/3))/133003126523723674923 G4Z2[191]:= 49147180787/2364953787 + (34339817200*Sqrt[2])/2364953787 - Sqrt[171758506806892695040000/50337057731810772321 + (40528868975122611200000*Sqrt[2])/16779019243936924107]/2 G4Z2[209]:= 6673075179371358438787/49068186689483520118587 + (480725755225834522600*Sqrt[209])/49068186689483520118587 - Sqrt[3311268966445380556028220434489784021855040000/21669182504946069242531962153337679478885889121 + (77695245748678056956882824339215883974080000*Sqrt[209])/7223060834982023080843987384445893159628629707]/2 G4Z2[219]:= 5300496365221380347287/11674857680699818276287 - (1447544285231063975600*Sqrt[73])/27241334588299575978003 - Sqrt[-161222217262058514221445326309849826456320000/2226270930455060485940111543706373361819604027 + (2695661894550957656438323367868354609920000*Sqrt[73])/318038704350722926562873077672339051688514861]/2 G4Z2[221]:= 3350907418002587/102371336824966587 + (1417273986861200*Sqrt[17])/14624476689280941 - Sqrt[-44505200952032922825123695459840000/94319015429976840123033002997857121 + (1328335847843117671955538419200000*Sqrt[17])/4491381687141754291573000142755101]/2 G4Z2[231]:= 417076667036179443360241837285169/3628022246519393000477952182813769 - (8067079443576096288608345482400*Sqrt[33])/403113582946599222275328020312641 - Sqrt[399913416199307740641701370550768764185123474547792999206383360000/4387515140413207745523722464163571883538390044496815487683378661787 - (23205330025736494405768552964840495537206929727779105556336640000*Sqrt[11/3])/487501682268134193947080273795952431504265560499646165298153184643]/2 G4Z2[233]:= 17354633945222217289/570003148999409841 + (378978689935484408*Sqrt[233])/190001049666469947 - Sqrt[2409458497622864638432692908260371010048/324903589869243416023178966287645281 + (52616291496500822716494930965689967104*Sqrt[233])/108301196623081138674392988762548427]/2 G4Z2[239]:= 1768399050075290874361/1007066268125221819761 + (8306194245754358800*Sqrt[2])/12432916890434837281 - Sqrt[528842917256115692912703879975470904320000/37562313644283746867164383260750235929523 + (1203049914498265174399637846254741698560000*Sqrt[2])/112686940932851240601493149782250707788569]/2 G4Z2[249]:= -930576178233430005535518511/2295985643350548253027213689 + (6552541159102176037586600*Sqrt[249])/255109515927838694780801521 - Sqrt[-2465745873306087858587757946223153969887866683412160000/585727786052425662375701323797173942808223468763220969 + (156260295554472492181088661753956035201494023445440000*Sqrt[83/3])/195242595350808554125233774599057980936074489587740323]/2 G4Z2[261]:= 66081930945010677634163/1313433404222168135659134963 + (1083267792824403402730800*Sqrt[6])/62544447820103244555196903 - Sqrt[-1698748641507628009036794296887735456069682555520000/191678589702959257489731279644362655591162989938779041 + (179747253108245806812530919639778431827731316480000*Sqrt[6])/27382655671851322498533039949194665084451855705539863]/2 G4Z2[281]:= 59927567508016056223/122757746741933242023 + (115494409192657000*Sqrt[281])/13639749637992582447 - Sqrt[-5917031812561755351900590579780568640000/27348287217506461235109108918637598647923 + (8832190764883897272586191138443879360000*Sqrt[281])/82044861652519383705327326755912795943769]/2 G4Z2[299]:= 9644744463767361032483/72361574733214076252283 + (1852674382498309814000*Sqrt[26])/72361574733214076252283 - Sqrt[6559680531077935694275377618050737745547520000/47125777480834732296707876052354025811964408801 + (428963865961566637425774147344187791651840000*Sqrt[26])/15708592493611577432235958684118008603988136267]/2 G4Z2[329]:= 3658874717690818403523451129/60477903190659258224997129 - (977854721954755477675304000*Sqrt[14])/60477903190659258224997129 - Sqrt[8363327189423048945580198374849510863921557394585513600000/296263718721439016191726396455755860198306036717653921 - (745064403548913740333301967203646915340667813924797440000*Sqrt[14])/98754572907146338730575465485251953399435345572551307]/2 G4Z2[371]:= -1870834771871074003452071/45070176004870138924408929 + (184458890174594604936400*Sqrt[106])/45070176004870138924408929 - Sqrt[-10911544283606133907158444928399251256896444160000/41455525818570857897119193982572468568495347243409 + (1059829213664236399683889897152941686327531520000*Sqrt[106])/41455525818570857897119193982572468568495347243409]/2 G4Z2[431]:= 8845334329396117351243243907/5951936253401389479986444907 + (6930136279849699225735711600*Sqrt[2])/5951936253401389479986444907 - Sqrt[6241873793770826402252027130722844853170651140249820160000/318829906480983922837524530661883340386850464144916147841 + (1478890708362458202334793213303879758947198641253447680000*Sqrt[2])/106276635493661307612508176887294446795616821381638715947]/2 pG4X[2] := 9*x - 2 pG4X[3] := 12*x^2 - 1 pG4X[4] := 49*x^2 - 132*x + 36 pG4X[5] := 81*x^2 - 8 pG4X[6] := 363*x^2 - 216*x + 32 pG4X[7] := 112*x^4 + 792*x^2 - 81 pG4X[8] := 3969*x^2 + 2160*x - 1088 pG4X[9] := 2401*x^2 - 243 pG4X[10] := 43681*x^4 + 111216*x^3 + 159912*x^2 + 13824*x - 24624 pG4X[11] := 3564*x^2 - 361 pG4X[12] := 4761*x^4 + 55080*x^3 - 42504*x^2 - 4320*x + 3856 pG4X[14] := 263169*x^2 - 242208*x + 50432 pG4X[15] := 345744*x^4 - 127896*x^2 + 9409 pG4X[16] := 24910081*x^4 + 65167584*x^3 + 50484096*x^2 + 497664*x - 7630848 pG4X[17] := 6561*x^4 + 697005*x^2 - 70688 pG4X[18] := 290521*x^4 + 511560*x^3 + 795960*x^2 + 137376*x - 143856 pG4X[20] := 6305121*x^4 - 23228856*x^3 + 12010680*x^2 + 2070432*x - 1191536 pG4X[21] := 1172889*x^4 - 801510*x^2 + 69169 pG4X[23] := 2414448*x^4 + 5471064*x^2 - 579121 pG4X[24] := 10517049*x^4 - 353180736*x^3 - 418274304*x^2 - 24330240*x + 61407232 pG4X[26] := 109181601*x^4 - 221021136*x^3 + 99364968*x^2 + 115490304*x - 40822064 pG4X[29] := 96059601*x^2 - 9732872 pG4X[30] := 9101732409*x^4 - 3360504672*x^3 - 5741687040*x^2 + 3467943936*x - 507183104 pG4X[32] := 4706920449*x^4 - 25754205312*x^3 + 38815967232*x^2 + 20991836160*x - 9832497152 pG4X[35] := 416649744*x^4 - 181970712*x^2 + 14160169 pG4X[36] := 5890716001*x^4 - 9155443464*x^3 - 4704462504*x^2 + 8139395808*x - 1879385328 pG4X[39] := 319301844624*x^4 - 309954202008*x^2 + 28126979521 pG4X[41] := 1836036801*x^4 + 30680722836*x^2 - 3127455872 pG4X[44] := 98314229601*x^4 - 62132535864*x^3 - 168327985032*x^2 + 157256385696*x - 32006494064 pG4X[50] := 688105089441*x^4 + 1968814353240*x^3 + 1537486968600*x^2 + 1900764000*x - 226946390000 pG4X[51] := 64157985377424*x^4 - 64179978972216*x^2 + 5844146696089 pG4X[56] := 468237200823*x^4 - 6169883311872*x^3 - 4125160120320*x^2 + 637882859520*x + 409102974976 pG4X[65] := 76869424485441*x^4 - 149557682640672*x^2 + 14364221280256 pG4X[71] := 17895363696*x^4 + 139560321123288*x^2 - 14140600639201 pG4X[74] := 619693760535201*x^4 - 1380695549973264*x^3 + 376971073189416*x^2 + 639601627203072*x - 203618891569712 pG4X[95] := 25462481498744976*x^4 - 62036900332273368*x^2 + 6024254787941329 pG4X[116] := 9448905172968936801*x^4 - 9070775524670266008*x^3 - 13357612262919114504*x^2 + 14617886926543174944*x - 3104064702383276912 pG4Y[2] := 9*x - 14 pG4Y[3] := 3*x^2 - 16 pG4Y[4] := 49*x^2 - 640*x + 1400 pG4Y[5] := 81*x^2 - 800 pG4Y[6] := 363*x^2 - 1920*x + 2300 pG4Y[7] := 7*x^4 + 800*x^2 - 12544 pG4Y[8] := 3969*x^2 + 4104*x - 79856 pG4Y[9] := 2401*x^2 - 43200 pG4Y[10] := 43681*x^4 + 458240*x^3 + 1930200*x^2 - 9984000*x - 52390000 pG4Y[11] := 891*x^2 - 19600 pG4Y[12] := 4761*x^4 + 200448*x^3 - 1925808*x^2 + 1677312*x + 11692096 pG4Y[14] := 263169*x^2 - 2741760*x + 7139300 pG4Y[15] := 21609*x^4 - 909600*x^2 + 7840000 pG4Y[16] := 24910081*x^4 + 326471680*x^3 + 360382400*x^2 - 10436608000*x - 37098880000 pG4Y[17] := 6561*x^4 + 11544768*x^2 - 400105472 pG4Y[18] := 290521*x^4 + 2136792*x^3 + 4715544*x^2 - 77710752*x - 541555056 pG4Y[20] := 6305121*x^4 - 155831040*x^3 + 1043118000*x^2 - 859392000*x - 6955160000 pG4Y[21] := 1172889*x^4 - 85848000*x^2 + 1536640000 pG4Y[23] := 150903*x^4 + 127008*x^2 - 325153024 pG4Y[24] := 10517049*x^4 - 1410232320*x^3 - 9861813600*x^2 + 67706880000*x + 449026720000 pG4Y[26] := 109181601*x^4 - 1479928320*x^3 + 439522200*x^2 + 76707072000*x - 316285190000 pG4Y[29] := 96059601*x^2 - 5571456800 pG4Y[30] := 9101732409*x^4 - 91144327680*x^3 - 359930211000*x^2 + 5065691904000*x - 8049049190000 pG4Y[32] := 4706920449*x^4 - 129750499296*x^3 + 763886567808*x^2 + 8312621893632*x - 68237005942784 pG4Y[35] := 26040609*x^4 - 2194063200*x^2 + 25985440000 pG4Y[36] := 5890716001*x^4 - 116337204480*x^3 + 281970284400*x^2 + 5948377344000*x - 30237905880000 pG4Y[39] := 19956365289*x^4 - 3075221479200*x^2 + 118452748960000 pG4Y[41] := 1836036801*x^4 + 424205942400*x^2 - 47130398720000 pG4Y[44] := 98314229601*x^4 - 1695450113280*x^3 - 2776461850800*x^2 + 175050425088000*x - 759518892440000 pG4Y[50] := 688105089441*x^4 + 13751351911080*x^3 + 62376269400*x^2 - 1375135223868000*x - 6887288193590000 pG4Y[51] := 4009874086089*x^4 - 815349643634400*x^2 + 41446933659040000 pG4Y[56] := 468237200823*x^4 - 26131122339840*x^3 - 106517619540000*x^2 + 2926708162560000*x + 6056168241760000 pG4Y[65] := 76869424485441*x^4 - 18158003694979200*x^2 + 1061447206543360000 pG4Y[71] := 1118460231*x^4 + 141330438727200*x^2 - 20091474931360000 pG4Y[74] := 619693760535201*x^4 - 15077417153057280*x^3 + 3006345245400*x^2 + 2231454870118656000*x - 13574182172639270000 pG4Y[95] := 1591405093671561*x^4 - 591562393890976800*x^2 + 54947130957742240000 pG4Y[116] := 9448905172968936801*x^4 - 288077822145145992960*x^3 + 7157856945000740400*x^2 + 66725021340371826432000*x - 508577747611492464920000 pG4Z2[2] := 81*x - 32 pG4Z2[3] := 9*x - 1 pG4Z2[4] := 2401*x^2 + 29248*x - 1024 pG4Z2[5] := 81*x - 1 pG4Z2[6] := 1185921*x^2 - 859392*x + 4096 pG4Z2[7] := 49*x^2 - 498*x + 1 pG4Z2[8] := 15752961*x^2 + 9165312*x - 8192 pG4Z2[9] := 2401*x - 1 pG4Z2[10] := 1908029761*x^4 - 5564230784*x^3 + 25991796736*x^2 - 5182193664*x + 1048576 pG4Z2[11] := 9801*x - 1 pG4Z2[12] := 1836036801*x^4 + 190150540416*x^3 - 138830837760*x^2 - 19781517312*x + 1048576 pG4Z2[13] := 14641*x^3 + 3229*x^2 + 35379*x - 1 pG4Z2[14] := 69257922561*x^2 - 4245737472*x + 65536 pG4Z2[15] := 194481*x^2 - 116082*x + 1 pG4Z2[16] := 620512135426561*x^4 + 287621717421056*x^3 + 390738946441216*x^2 + 13694880710656*x - 67108864 pG4Z2[17] := 6561*x^2 - 352674*x + 1 pG4Z2[18] := 6836598566721*x^4 - 23238004664448*x^3 + 31174019389440*x^2 - 629005221888*x + 1048576 pG4Z2[19] := 5285401*x^3 + 1709197*x^2 + 1005403*x - 1 pG4Z2[20] := 39754550824641*x^4 + 119215362024576*x^3 - 138330257946624*x^2 - 1743464300544*x + 1048576 pG4Z2[21] := 10556001*x^2 - 2716002*x + 1 pG4Z2[23] := 3470769*x^2 - 7005042*x + 1 pG4Z2[24] := 8959273893140481*x^4 + 3670232770208894976*x^3 - 599665266678104064*x^2 - 2973505079476224*x + 268435456 pG4Z2[25] := 671898241*x^3 + 97509117*x^2 + 17352323*x - 1 pG4Z2[26] := 11920621996923201*x^4 - 7409173422386304*x^3 + 9198636408723456*x^2 - 28250296418304*x + 1048576 pG4Z2[27] := 1172889*x^3 + 3120525*x^2 + 41479899*x - 1 pG4Z2[29] := 96059601*x - 1 pG4Z2[30] := 6710164160448316405761*x^4 - 6780648350290674069504*x^3 + 476025208711316176896*x^2 - 621063479255629824*x + 4294967296 pG4Z2[31] := 268927201*x^4 - 46610061604*x^3 - 3042658394*x^2 - 216207204*x + 1 pG4Z2[32] := 22155100113214361601*x^4 + 62068434767415926784*x^3 + 193140475265405288448*x^2 + 172440481085521920*x - 536870912 pG4Z2[33] := 6059221281*x^4 - 12017842020*x^3 + 9960278886*x^2 - 474248484*x + 1 pG4Z2[35] := 1275989841*x^2 - 1016135442*x + 1 pG4Z2[36] := 34700535004437432001*x^4 + 3035796287502087296*x^3 - 3711719247391750144*x^2 - 1546950810927104*x + 1048576 pG4Z2[39] := 179607287601*x^2 - 4381327602*x + 1 pG4Z2[41] := 1836036801*x^2 - 8845316802*x + 1 pG4Z2[44] := 9665687742038144619201*x^4 + 206368377041762925696*x^3 - 252663796166074988544*x^2 - 25783654895714304*x + 1048576 pG4Z2[45] := 276922881*x^4 + 2094223356*x^3 + 66382256646*x^2 - 34306042884*x + 1 pG4Z2[47] := 95090206689*x^4 - 38691030564*x^3 - 88215282522*x^2 - 66051026532*x + 1 pG4Z2[49] := 4506487876801*x^4 - 1927137508430404*x^3 - 15470750769594*x^2 - 125428676804*x + 1 pG4Z2[50] := 473488614114606609692481*x^4 - 3816091203480414730368*x^3 + 4675044057591043528704*x^2 - 180353075186368512*x + 1048576 pG4Z2[51] := 36088866774801*x^2 - 235117934802*x + 1 pG4Z2[53] := 3063651608241*x^3 - 1037978353251*x^2 + 435385886643*x - 1 pG4Z2[56] := 10743057735493363161989121*x^4 + 299409397266910313570697216*x^3 - 298726429226717360893722624*x^2 - 4612347048123521040384*x + 4294967296 pG4Z2[57] := 3376787092396641*x^4 + 1770381989961948*x^3 + 398741995826982*x^2 - 1443155503716*x + 1 pG4Z2[59] := 149845635801*x^3 + 822954608397*x^2 + 2586311755803*x - 1 pG4Z2[63] := 197964928140001*x^4 - 207337865641764*x^3 + 38319587442086*x^2 - 8069499941220*x + 1 pG4Z2[65] := 76869424485441*x^2 - 14061897471042*x + 1 pG4Z2[69] := 17229935527596801*x^4 - 14984302448710404*x^3 + 35836612586630406*x^2 - 41644065516804*x + 1 pG4Z2[71] := 79410676401*x^2 - 70824040716402*x + 1 pG4Z2[74] := 384020356846259040377960110401*x^4 - 103170759869160007248587904*x^3 + 126372550352224149387565056*x^2 - 162448114480612245504*x + 1048576 pG4Z2[75] := 452004825098667681*x^4 - 606729784918524516*x^3 + 291364883707242726*x^2 - 200396187475236*x + 1 pG4Z2[77] := 42250625316085761*x^4 - 20830848935332356*x^3 - 4363524253584378*x^2 - 333599442487812*x + 1 pG4Z2[79] := 1858108924530102184801*x^4 - 2281712837703306634404*x^3 - 1121413573997285594*x^2 - 551702398264804*x + 1 pG4Z2[81] := 35971217755201*x^3 - 219777959990403*x^2 + 906642198235203*x - 1 pG4Z2[89] := 1093889542148001*x^4 - 21882634090124004*x^3 + 17818847937804006*x^2 - 6234634589828004*x + 1 pG4Z2[95] := 574497238815433521*x^2 - 25025929238011122*x + 1 pG4Z2[99] := 9409543401845601*x^4 - 18003136343856804*x^3 + 75545914130176806*x^2 - 61693170788165604*x + 1 pG4Z2[101] := 369265017730583601*x^3 + 325660112130352797*x^2 + 96203629755063603*x - 1 pG4Z2[105] := 380060362198670345990721*x^4 - 135705612385364165677764*x^3 + 3522799708579459911366*x^2 - 230914817439264324*x + 1 pG4Z2[107] := 513544015673940450969*x^3 + 21763436330004480909*x^2 + 355521109200228315*x - 1 pG4Z2[113] := 1755339166248224384961*x^4 - 3134094586435642102596*x^3 + 40455290156701249350*x^2 - 1267167814902334404*x + 1 pG4Z2[116] := 89281808967759133485558908068332113601*x^4 + 194253361693712575736321726522496*x^3 - 237937121192996675250748964665344*x^2 - 2476973907151703357128704*x + 1048576 pG4Z2[119] := 504340294048978401*x^4 - 17429332140318855204*x^3 + 23130827104122775206*x^2 - 4368509227452898404*x + 1 pG4Z2[129] := 61395997831472170172664801*x^4 + 22092941884753972021525596*x^3 + 2533066810920203102954406*x^2 - 32128416105297144804*x + 1 pG4Z2[131] := 1617992242881191941401*x^3 - 369348371608839442803*x^2 + 47437372559975501403*x - 1 pG4Z2[141] := 48271120627843103803553601*x^4 - 100781252659857179618340804*x^3 + 54020598864990823442020806*x^2 - 318812368107627233604*x + 1 pG4Z2[149] := 2291453137369113201*x^3 + 78776699697794733597*x^2 + 1394914720951012153203*x - 1 pG4Z2[155] := 152821422973976810308641*x^4 + 120077633973147044565276*x^3 + 1025210533154821631879526*x^2 - 4112298460537176993444*x + 1 pG4Z2[161] := 22155100113214361601*x^4 - 100814667870313163724804*x^3 + 158687985978210780364806*x^2 - 11874583392970831001604*x + 1 pG4Z2[165] := 7308737335700407817824981713921*x^4 - 6041257404040651042154930869764*x^3 + 17004856974729837164989685766*x^2 - 23817015520631479569924*x + 1 pG4Z2[179] := 290877837707383677056601*x^3 - 405039766746888552073203*x^2 + 255253742231069747016603*x - 1 pG4Z2[191] := 21736183418874580076001*x^4 - 1806838073503244712788004*x^3 + 908001797964989685348006*x^2 - 1812385890730153952636004*x + 1 pG4Z2[209] := 78230538607337434246025981601*x^4 - 42556148956803529200808824804*x^3 - 434692265143391499084295194*x^2 - 30654941290726384532861604*x + 1 pG4Z2[219] := 2094305648918065081711894416428001*x^4 - 3803338690150918149354489945044004*x^3 + 1802584840478517639408138912804006*x^2 - 139972172979280152984188004*x + 1 pG4Z2[221] := 391874357394739680529328001*x^4 - 51308685882034098284624004*x^3 - 30159465140293895258735994*x^2 - 188855754244350221385968004*x + 1 pG4Z2[231] := 2644828217712637497348427141271237601*x^4 - 1216195561077499256838465197523552804*x^3 + 19278152239466674500216050177392806*x^2 - 827786136705898952325077604*x + 1 pG4Z2[233] := 83886321929356269367936627168161*x^4 - 10216199069430421626469530126786276*x^3 + 2080306977729719901985797915366*x^2 - 1108147592376994945800599460*x + 1 pG4Z2[239] := 535196304598736009115605601*x^4 - 3759199038284250630245136804*x^3 + 5178640479867717315991456806*x^2 - 2638811031444134648461925604*x + 1 pG4Z2[249] := 218127840724746276385531686554679201*x^4 + 353633870448297553387065801754842396*x^3 + 602457640105757531383793431034277606*x^2 - 10941197836746434157743799204*x + 1 pG4Z2[261] := 85145947295510493730374742246401*x^4 - 17135573349488828795959539204*x^3 + 70797365901632277656428339206*x^2 - 58090118215773608060811046404*x + 1 pG4Z2[281] := 1096463464227303658650796018401*x^4 - 2141075085409964866552119255204*x^3 + 1642270090770435959858282455206*x^2 - 863776782386717620232159218404*x + 1 pG4Z2[299] := 893533281691483389794339381377162401*x^4 - 476379913154664204919707633735087204*x^3 + 2596362911193875991261796330687206*x^2 - 9042155034248583166783972762404*x + 1 pG4Z2[329] := 289263936145924321653156293096001*x^4 - 70001137398395744034728630092088004*x^3 + 152249895651492275002582071624888006*x^2 - 389112016100170047890623425896004*x + 1 pG4Z2[371] := 328436741535007770525762285392657636001*x^4 + 54532813571203233257999636309575491996*x^3 + 45453197114029339276087761685788108006*x^2 - 57138803647564970053630548021236004*x + 1 pG4Z2[431] := 138932971068038885009222178111501212001*x^4 - 825888266374378582805733983469842276004*x^3 - 272325161001919236719916801564003083994*x^2 - 44629983271874494134178394855255852004*x + 1 (* Type G, s=1/6 , N=2〜6 非常に計算機パワーを要する．N=6以上は探索していない． *) sumG6[t_, limit_:Infinity] := Sum[termp[n, 1/6, G6X[t], G6Y[t], G6Z2[t]], {n, 0, limit}]; G6X[2]:= 1/(3 * Sqrt[3]) G6X[3]:= 2-Sqrt[3] G6X[4]:= 8/27 G6X[5]:= 8/(15 * Sqrt[3]) G6X[6]:= (3 Sqrt[131 + 16 Sqrt[6]]) / 125 G6Y[2]:= 6/(3*Sqrt[3]) (*2/Sqrt[3]*) G6Y[3]:= (14-3*Sqrt[12])/2 G6Y[4]:= 60/27 (*20/9*) G6Y[5]:= 66/(15 * Sqrt[3]) (*22/(Sqrt[3]*5)*) G6Y[6]:= 2 Sqrt[18749 + 4914 Sqrt[6]] / 125 G6Z2[2]:= 1/2 G6Z2[3]:= (-36+21 * Sqrt[3])/2 G6Z2[4]:= 2/27 G6Z2[5]:= 4/125 G6Z2[6]:= 27 (463 - 182 Sqrt[6]) / 31250 pA6X[2]:=27 * x^2 + -1 pA6X[3]:=x^2 + -4 * x + 1 pA6X[4]:=27 * x+ -8 pA6X[5]:=675 * x^2 + -64 pA6Y[2]:=3 * x^2 + -4 pA6Y[3]:=x^2 + -14 * x + 22 pA6Y[4]:=9 * x+ -20 pA6Y[5]:=75 * x^2 + -484 pA6Z[2]:=2 * x+ -1 pA6Z[3]:=4 * x^2 + 144 * x + -27 pA6Z[4]:=27 * x+ -2 pA6Z[5]:=125 * x+ -4 (***********************************************************************) (***********************************************************************) (* 検査用のプログラム 関数 checkall[] で本ファイルに掲載されている全Ramanujan型級数の検査が 出来ます．しかし，Mathematica 3.0 は計算ミスしますので，別ファイルの C++言語のプログラム「rama_check.cc」を使用してください． *) AX[n_]:= 0;AY[n_]:= 0;AZ2[n_]:= 0; BX[n_]:= 0;BY[n_]:= 0;BZ2[n_]:= 0; DX[n_]:= 0;DY[n_]:= 0;DZ2[n_]:= 0; EX[n_]:= 0;EY[n_]:= 0;EZ2[n_]:= 0; F1X[n_]:= 0;F1Y[n_]:= 0;F1Z2[n_]:= 0; F2DX[n_]:= 0;F2DY[n_]:= 0;F2DZ2[n_]:= 0; G3X[n_]:= 0;G3Y[n_]:= 0;G3Z2[n_]:= 0; G4X[n_]:= 0;G4Y[n_]:= 0;G4Z2[n_]:= 0; G6X[n_]:= 0;G6Y[n_]:= 0;G6Z2[n_]:= 0; check[sum_, str_, u_] := Block[{diff}, diff := sum - 1/Pi; If[sum == 0, Print[str, ", N=", u, ", No Exist"], Print[str, ", N=", u, ", Diff=", diff] ] ]; checkall[seido_:1000, limit_:Infinity] := Block[{u}, Do[check[N[sumA[u, limit],seido], "Type A", u], {u, 2, 163}]; Do[check[N[sumB[u, limit],seido], "Type B", u], {u, 2, 190}]; (* Type D, N=8, 12では値が変だが，多分Mathematica 3.0のバグ *) Do[check[N[sumD[u, limit],seido], "Type D", u], {u, 3, 190}]; (* Type E, ほとんどのNでは値が変だが，多分Mathematica 3.0のバグ *) Do[check[N[sumE[u, limit, seido],seido], "Type E", u], {u, 4, 793}]; Do[check[N[sumF1[u, limit],seido], "Type F-1", u], {u, 2, 190}]; Do[check[N[sumF2D[u, limit],seido], "Type F-2'", u], {u, 7, 1555}]; Do[check[N[sumG3[u, limit],seido], "Type G s=1/3", u], {u, 2, 58}]; Do[check[N[sumG4[u, limit],seido], "Type G s=1/4", u], {u, 2, 116}]; Do[check[N[sumG6[u, limit],seido], "Type G s=1/6", u], {u, 2, 6}]; ]; (***********************************************************************) (***********************************************************************) (* 別の検査用プログラム「rama_check.cc」で処理を行なうための テーブル作りの関数． 関数「printnum[]」で作成出来ます．作成するには，Mathematica 3.0をUNIX Shellインターフェースで使用し，UNIXの「script」等のログを取るプログラ ムで出力をファイルにセーブしてください．ファイル名は 「rama_check_init.cc」です． *) (* printnumaux[num_, str_, u_,seido_]:= If[Abs[num] > 0, Print[str,"[",u,"]=\"",CForm[N[num,seido]], "\";"] ]; *) printnumaux[num_, str_, u_,seido_]:= If[Abs[num] > 0, Print["string_to_bigfloat(\"",CForm[N[num,seido]],"\", ", str,"[",u,"]);"]; ]; (* 引数は有効精度． 有効精度はC++のプログラムに合わせてください*) printnum[seido_] := Block[{u}, SetOptions[$Output,PageWidth -> (seido + 50)]; Do[printnumaux[AX[u], "AX", u, seido], {u, 2, 163}]; Do[printnumaux[AY[u], "AY", u, seido], {u, 2, 163}]; Do[printnumaux[AZ2[u], "AZ2", u, seido], {u, 2, 163}]; Do[printnumaux[BX[u], "BX", u, seido], {u, 2, 190}]; Do[printnumaux[BY[u], "BY", u, seido], {u, 2, 190}]; Do[printnumaux[BZ2[u], "BZ2", u, seido], {u, 2, 190}]; Do[printnumaux[DX[u], "DX", u, seido], {u, 3, 190}]; Do[printnumaux[DY[u], "DY", u, seido], {u, 3, 190}]; Do[printnumaux[DZ2[u], "DZ2", u, seido], {u, 3, 190}]; Do[printnumaux[EX[u], "EX", u, seido], {u, 4, 793}]; Do[printnumaux[EY[u], "EY", u, seido], {u, 4, 793}]; Do[printnumaux[EZ2[u], "EZ2", u, seido], {u, 4, 793}]; Do[printnumaux[F1X[u], "F1X", u, seido], {u, 2, 190}]; Do[printnumaux[F1Y[u], "F1Y", u, seido], {u, 2, 190}]; Do[printnumaux[F1Z2[u], "F1Z2", u, seido], {u, 2, 190}]; Do[printnumaux[F2DX[u], "F2DX", u, seido], {u, 7, 1555}]; Do[printnumaux[F2DY[u], "F2DY", u, seido], {u, 7, 1555}]; Do[printnumaux[F2DZ2[u], "F2DZ2", u, seido], {u, 7, 1555}]; Do[printnumaux[G3X[u], "G3X", u, seido], {u, 2, 58}]; Do[printnumaux[G3Y[u], "G3Y", u, seido], {u, 2, 58}]; Do[printnumaux[G3Z2[u], "G3Z2", u, seido], {u, 2, 58}]; Do[printnumaux[G4X[u], "G4X", u, seido], {u, 2, 116}]; Do[printnumaux[G4Y[u], "G4Y", u, seido], {u, 2, 116}]; Do[printnumaux[G4Z2[u], "G4Z2", u, seido], {u, 2, 116}]; Do[printnumaux[G6X[u], "G6X", u, seido], {u, 2, 6}]; Do[printnumaux[G6Y[u], "G6Y", u, seido], {u, 2, 6}]; Do[printnumaux[G6Z2[u], "G6Z2", u, seido], {u, 2, 6}]; ]; (* EOF *)