DEGREE 3 WEIGHT 18

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 eigenvalues | standard Euler factors | spinor Euler factors | identified eigenforms | special values

DIMENSIONS
dim M183)= 8
dim S183) = 4

DETERMINING INDICES
Introduce the notation
[a b c d e f]=

 a d e d b f e f c

We use the following set of determining Fourier coefficient indices.
 t1 ½ [0 0 0 0 0 0] t2 ½ [2 0 0 0 0 0] t3 ½ [2 2 0 1 0 0] t4 ½ [2 2 0 0 0 0] t5 ½ [2 2 2 1 1 1] t6 ½ [2 2 2 1 0 0] t7 ½ [2 2 2 0 0 0] t8 ½ [4 4 4 2 2 2]

PULLBACK OF EISENSTEIN SERIES
Let E(6)18 denote the monic Eisenstein series of degree 6 and weight 18.
The rescaled Eisenstein series
E(6)18 = -88361515511741542241620438735422234638389/1933845185986560 E(6)18
has rational Fourier coefficients that are near-integers in that their denominator prime factors are at most 35.
Consider the Witt map W3,3 and the pullback W*3,3E(6)18 ∈ M183) ⊗ M183).
The columns of the 8 x 8 matrix [a(ti x tj; W*3,3E(6)18)] are determining truncations of an M183)-basis gt1,...,gt8. Each gt is the cofficient function of e(tr(t,z)) in the Fourier expansion of W*3,3E(6)18(w,z). For convenience let gj = gtj for j=1,...,8. The basis elements g1,...,g8 are not Hecke eigenforms. The matrix [a(ti x tj; W*3,3E(6)18)] is as follows (switch to factored form).
 t1 t2 t3 t4 t5 t6 t7 t8 t1 -88361515511741542241620438735422234638389/1933845185986560 2014304956157055240650612960435457967/67315691520 -1676966135848108719283695971538017/8414461440 -3030655468563872673655395910067629/131991552 3414105522856211405374241569/10999296 105119910515024127823838029321/515592 223750233651427526874011669707553/10999296 961029263619615285198271191047877597281057/10999296 t2 2014304956157055240650612960435457967/67315691520 1624433971675241850680181793116281/44520960 -5509635668739119404276766813431/5565120 -6170510849871612808924851519947/87296 71581889083002258925480101/21824 472528535444824419918533903/341 2185228922458697085918771459237/21824 -1335024185923399801529550660511398515547/21824 t3 -1676966135848108719283695971538017/8414461440 -5509635668739119404276766813431/5565120 -1657797180436310610022852866919/695640 24132153334864745357813796997/10912 40608413339658966590197749/2728 824659028463571537981469176/341 -10856459316476224278615179787/2728 1289552554921151219361278218930692597/2728 t4 -3030655468563872673655395910067629/131991552 -6170510849871612808924851519947/87296 24132153334864745357813796997/10912 -1750602966372722478880125778305/43648 -27052707731868889355227185/10912 458695705235266432284820890/341 2813162253375958988076561224655/10912 545646506567655785425943088972619807695/10912 t5 3414105522856211405374241569/10999296 71581889083002258925480101/21824 40608413339658966590197749/2728 -27052707731868889355227185/10912 40478365588210294777147935/2728 -7216336328070128002646040/341 -20570036933559517999799265/2728 -2522480163293255673384621072265185/2728 t6 105119910515024127823838029321/515592 472528535444824419918533903/341 824659028463571537981469176/341 458695705235266432284820890/341 -7216336328070128002646040/341 657320517748565276612851200/341 -3353430442644761020685031960/341 -174448011704278127472905882404348440/341 t7 223750233651427526874011669707553/10999296 2185228922458697085918771459237/21824 -10856459316476224278615179787/2728 2813162253375958988076561224655/10912 -20570036933559517999799265/2728 -3353430442644761020685031960/341 -298097086009144631006254913505/2728 -128321399478199872671629989808743141345/2728 t8 961029263619615285198271191047877597281057/10999296 -1335024185923399801529550660511398515547/21824 1289552554921151219361278218930692597/2728 545646506567655785425943088972619807695/10912 -2522480163293255673384621072265185/2728 -174448011704278127472905882404348440/341 -128321399478199872671629989808743141345/2728 -455010527897205370786515640340014845315544846305/2728

EIGENFORM NUMBER FIELD GENERATORS
• a = Sqrt[2356201]
• b = Sqrt[18295489]

• INDICES FOR COMPUTING HECKE ACTION
Fourier coefficients for the following indices are needed to determine the action of the Hecke operator T(2) at the determining indices t1,...,t8 and also the action of Ti(4) for i=0,1,2,3 at t5.
 u1 ½ [0 0 0 0 0 0] u2 ½ [2 0 0 0 0 0] u3 ½ [4 0 0 0 0 0] u4 ½ [2 2 0 0 0 0] u5 ½ [2 2 0 1 0 0] u6 ½ [4 4 0 0 0 0] u7 ½ [4 4 0 2 0 0] u8 ½ [2 2 2 1 1 1] u9 ½ [2 2 2 1 0 0] u10 ½ [2 2 2 0 0 0] u11 ½ [2 2 4 0 1 1] u12 ½ [2 2 4 0 0 0] u13 ½ [2 2 6 1 1 1] u14 ½ [4 4 4 2 2 2] u15 ½ [4 4 4 2 0 0] u16 ½ [2 6 6 0 0 2] u17 ½ [4 4 4 0 0 0] u18 ½ [8 8 8 4 4 4]

EIGENFORM BASIS FROM PULLBACK-GENUS BASIS
The M183) eigenform basis f1,...,f8 comprises algebraic integer linear combinations of the rational near-integer non-eigenform basis g1,...,g8 from above. Specifically fi = Σj=18 bi,jgj for each i, where the matrix (bi,j) is as follows.
 g1 g2 g3 g4 g5 g6 g7 g8 f1 -1 0 0 0 0 0 0 0 f2 28728 43867 0 0 0 0 0 0 f3 -67202900494684938176544288+37955905036352555428512*a -201526200865237315820133985+118857413553114631525765*a -671176985626006311572317321-365075163419234868705971*a -246149264514486832554912121/2+(165068985928173128799229*a)/2 0 0 0 0 f4 -67202900494684938176544288-37955905036352555428512*a -201526200865237315820133985-118857413553114631525765*a -671176985626006311572317321+365075163419234868705971*a -246149264514486832554912121/2-(165068985928173128799229*a)/2 0 0 0 0 f5 -18148524847419393399055188077280-65113969784846999719016160*b -660111424834562398043235398520-948603906535624873336440*b -51585879553605230902116523200+2668594030421019484449600*b -4312489122944918274618005148+1814735135417189226268644*b 463403724294314947933910150496+31018590135968683126262112*b -4859687800234813657721720544+2650475706009755747411232*b -293651514672119719899580808+665940241930039604789624*b -18532153914277914679169/2-(66811140722575393*b)/2 f6 -18148524847419393399055188077280+65113969784846999719016160*b -660111424834562398043235398520+948603906535624873336440*b -51585879553605230902116523200-2668594030421019484449600*b -4312489122944918274618005148-1814735135417189226268644*b 463403724294314947933910150496-31018590135968683126262112*b -4859687800234813657721720544-2650475706009755747411232*b -293651514672119719899580808-665940241930039604789624*b -18532153914277914679169/2+(66811140722575393*b)/2 f7 -20837366772937707580789429277280-1851326226135283704281909280*a -754915161542151534384468242520-66294205253652082337480520*a -255941903099833651040759179200-138562108814665629761659200*a 2421786374117932735401055092+3240113827377212055224892*a -999158411773547942293881041184-350386966180544450004530784*a -187865501178198915244904637024-127952855362729897952622624*a 4291147970447657373130841432+2636557439741971618332232*a -21278201754931208656549/2-(1890492852727583399*a)/2 f8 -20837366772937707580789429277280+1851326226135283704281909280*a -754915161542151534384468242520+66294205253652082337480520*a -255941903099833651040759179200+138562108814665629761659200*a 2421786374117932735401055092-3240113827377212055224892*a -999158411773547942293881041184+350386966180544450004530784*a -187865501178198915244904637024+127952855362729897952622624*a 4291147970447657373130841432-2636557439741971618332232*a -21278201754931208656549/2+(1890492852727583399*a)/2

EIGENVALUES
The T(2) and Ti(4) (i=0,1,2,3) eigenvalues of the eigenforms are shown in the following table.
 f λ2(f) λ0,4(f) λ1,4(f) λ2,4(f) λ3,4(f) f1 281490009325569 79230278295859274766069383169 2115644397278092366823424 8070481320452554752 4398046511104 f2 -1133923271184 378999337546248301396224 302243588265370261192704 3458799768522719232 4398046511104 f3 4448981592-2359368*a 24503174988911586432+1806864483987072*a -2962603862614867968-7599854784872448*a 1152903297166737408-57982058496*a 4398046511104 f4 4448981592+2359368*a 24503174988911586432-1806864483987072*a -2962603862614867968+7599854784872448*a 1152903297166737408+57982058496*a 4398046511104 f5 -62453952+6336*b 946120373379072-203838529536*b 694537653583872-99222552576*b 67433134030848-19327352832*b 4398046511104 f6 -62453952-6336*b 946120373379072+203838529536*b 694537653583872+99222552576*b 67433134030848+19327352832*b 4398046511104 f7 29325888-15552*a -192598426902528-352093298688*a 535321034883072+103223918592*a -38480759488512-57982058496*a 4398046511104 f8 29325888+15552*a -192598426902528+352093298688*a 535321034883072-103223918592*a -38480759488512+57982058496*a 4398046511104

EIGENFORM FOURIER COEFFICIENTS
The eigenform Fourier coefficients at the indices ui are as follows (switch to factored denominator form).
 u a(u; f1) a(u; f2) a(u; f3) a(u; f4) a(u; f5) a(u; f6) a(u; f7) a(u; f8) u1 88361515511741542241620438735422234638389/1933845185986560 0 0 0 0 0 0 0 u2 -2014304956157055240650612960435457967/67315691520 1296529820104899193136235570157500/527 0 0 0 0 0 0 u3 -88006997839457900519265930854385594036197/22438563840 -684567745015386773975932381043160000/527 0 0 0 0 0 0 u4 3030655468563872673655395910067629/131991552 -116571112696744183199062139175000/31 19239773718219724700714365411918600771317504000000000-13390539062068831545090199005730214204160000000000*a 19239773718219724700714365411918600771317504000000000+13390539062068831545090199005730214204160000000000*a 0 0 0 0 u5 1676966135848108719283695971538017/8414461440 -25904691710387596266458253150000/527 26183849574890555482242231773164483214611219200000000/17+(15764269822595704935234115823179464690643200000000*a)/17 26183849574890555482242231773164483214611219200000000/17-(15764269822595704935234115823179464690643200000000*a)/17 0 0 0 0 u6 26033529482955009513398966449053367700858285/131991552 4041412299203538252909475635532095600000/31 3622905497836173997967432494709905792911202664448000000000-2325708047119038355526209166228583659521425408000000000*a 3622905497836173997967432494709905792911202664448000000000+2325708047119038355526209166228583659521425408000000000*a 0 0 0 0 u7 4801786375523081102119675711902242596456139/2804820480 896393932169298761359853755373138400000/527 880576130024313712097607079937223549465145717555200000000/17+(255046215882053672925424749413586770667238195200000000*a)/17 880576130024313712097607079937223549465145717555200000000/17-(255046215882053672925424749413586770667238195200000000*a)/17 0 0 0 0 u8 -3414105522856211405374241569/10999296 4736770942055204747713590000/31 -10367728895481441866995206852553536717315840000000-5237417334574675405008218617941452924160000000*a -10367728895481441866995206852553536717315840000000+5237417334574675405008218617941452924160000000*a 6993566905565904068126239947857906803880755200000000+441937405143396528262704150406732814745600000000*b 6993566905565904068126239947857906803880755200000000-441937405143396528262704150406732814745600000000*b -13804504127284323538703609751622976431718400000000000-4499872614502271909480909851173951897600000000000*a -13804504127284323538703609751622976431718400000000000+4499872614502271909480909851173951897600000000000*a u9 -105119910515024127823838029321/515592 2065971596740324659747204480000/31 -2081657021577790679137863827252467081406760960000000-599419224945384488224625329363703984855040000000*a -2081657021577790679137863827252467081406760960000000+599419224945384488224625329363703984855040000000*a -21404355235619786050719538075403551318946611200000000+9297959276185087539925196250459989763686400000000*b -21404355235619786050719538075403551318946611200000000-9297959276185087539925196250459989763686400000000*b -850622980325563673860309394489694304704921600000000000-581642208433201128311316974239141488230400000000000*a -850622980325563673860309394489694304704921600000000000+581642208433201128311316974239141488230400000000000*a u10 -223750233651427526874011669707553/10999296 154280114289242946164513370420000/31 -50603945630577723561028289375986729474132684800000000+35403884201959915423341002238840570811084800000000*a -50603945630577723561028289375986729474132684800000000-35403884201959915423341002238840570811084800000000*a -244694430578264573266186711101724675817865216000000000+509964063288431649248116696469873834852352000000000*b -244694430578264573266186711101724675817865216000000000-509964063288431649248116696469873834852352000000000*b 4009890102902764931144196407030188181815296000000000000+2524563228770904477262427930408219836416000000000000*a 4009890102902764931144196407030188181815296000000000000-2524563228770904477262427930408219836416000000000000*a u11 -6889243575423136265190872927610377/515592 67290504797182584578438666528640000/31 -10914929441026156725136156596430283656615540531200000000+7464492475988843851205810552434245283579699200000000*a -10914929441026156725136156596430283656615540531200000000-7464492475988843851205810552434245283579699200000000*a 895072008925181781408071061400509772229246976000000000-5566925356679100255135407396048093023567872000000000*b 895072008925181781408071061400509772229246976000000000+5566925356679100255135407396048093023567872000000000*b -101233319579449959241074611595546887945453568000000000000-67087872313983507835763254170490993901568000000000000*a -101233319579449959241074611595546887945453568000000000000+67087872313983507835763254170490993901568000000000000*a u12 -698271205523526663051020961491830237/523776 6754272131299679008849782086866020000/31 -1104987368912533172838826408439656811903562857717760000000+773788294593053041360328986547744247485476085760000000*a -1104987368912533172838826408439656811903562857717760000000-773788294593053041360328986547744247485476085760000000*a 71536843487995970238542434107205055666698636492800000000-139815604146781161056219238878143368272648601600000000*b 71536843487995970238542434107205055666698636492800000000+139815604146781161056219238878143368272648601600000000*b 1111842023019233053259053390909163059458500198400000000000+786102620619940083978949107799542835288473600000000000*a 1111842023019233053259053390909163059458500198400000000000-786102620619940083978949107799542835288473600000000000*a u13 -14663471569174514019400777585032968993/10999296 10192755648940521567031330531895430000/31 -10302893751766345971930722811337478647140512015435520000000-6203433856881133723322344236514176090367715892480000000*a -10302893751766345971930722811337478647140512015435520000000+6203433856881133723322344236514176090367715892480000000*a 383247309592530662024349817664725339404664150425600000000+15782929785051947232666637151338726012275916800000000*b 383247309592530662024349817664725339404664150425600000000-15782929785051947232666637151338726012275916800000000*b -49331307752797299965775223915167124261385011200000000000+224975301021924300091590909232313154089779200000000000*a -49331307752797299965775223915167124261385011200000000000-224975301021924300091590909232313154089779200000000000*a u14 -961029263619615285198271191047877597281057/10999296 -5376190252249584996300200191654113120000/31 -15352081265956541816067216170114047654230428565504000000000 -15352081265956541816067216170114047654230428565504000000000 -377528264246887113990326142518103581896131949363200000000000 -377528264246887113990326142518103581896131949363200000000000 -371333717908254700983040575795399935896219287552000000000000 -371333717908254700983040575795399935896219287552000000000000 u15 -1409025111951270577467990201715114354595621/24552 -2349268196932602886377130709135371130880000/31 -4856014014386640969374855724476306822184717715655884800000000+1510800397653418739633508650394446603010368294092800000000*a -4856014014386640969374855724476306822184717715655884800000000-1510800397653418739633508650394446603010368294092800000000*a 2326618884788042914359847643986874335877937311514624000000000-169061266842722893270814194801453343189791408128000000000*b 2326618884788042914359847643986874335877937311514624000000000+169061266842722893270814194801453343189791408128000000000*b 6319852500112508278976434018467260300592710418432000000000000+2766720529392289239831091922043723991272652800000000000000*a 6319852500112508278976434018467260300592710418432000000000000-2766720529392289239831091922043723991272652800000000000000*a u16 -62980091850030039985905547209991617392064674593/10999296 14593241820300705970247869090731758778526980000/31 972051282886358186814942285720400311045662264317036462080000000+728958876074487988954751515719507335303657182296145920000000*a 972051282886358186814942285720400311045662264317036462080000000-728958876074487988954751515719507335303657182296145920000000*a 43166744659199577029498774831135805462536514036144537600000000-1288861663971896832952253017343032038219534512947200000000*b 43166744659199577029498774831135805462536514036144537600000000+1288861663971896832952253017343032038219534512947200000000*b -64779191195666637384422335529154309085108901196595200000000000-14254043120572165990535648695968466813045230796800000000000*a -64779191195666637384422335529154309085108901196595200000000000+14254043120572165990535648695968466813045230796800000000000*a u17 -62982013849902497959327915101800375192693979937/10999296 -175605794013233168688156285189318693583680000/31 -313304414124269142332000637594825859272709986012282224640000000+200849321850752441205638581381073732831978023271792640000000*a -313304414124269142332000637594825859272709986012282224640000000-200849321850752441205638581381073732831978023271792640000000*a 52346351332451441769723899263616147835065794894705459200000000-20604275243424376596790826205851783068003454051942400000000*b 52346351332451441769723899263616147835065794894705459200000000+20604275243424376596790826205851783068003454051942400000000*b -54569164240769304976788296971552430060417313039974400000000000-55940381544185831281264657446478320978041084313600000000000*a -54569164240769304976788296971552430060417313039974400000000000+55940381544185831281264657446478320978041084313600000000000*a u18 -270505689973472570836031250773878273643077550221421656865/10999296 3232662329686440506182212534186193826012466624000000/31 -153524897924619349956420176203563486051674348358705570565324800000000-65375895863988699841577683977056500057966378802877117235200000000*a -153524897924619349956420176203563486051674348358705570565324800000000+65375895863988699841577683977056500057966378802877117235200000000*a 7654463510812314835533253785503673257501237486147447291904000000000-822671161484229612769587806556610632118260410181746688000000000*b 7654463510812314835533253785503673257501237486147447291904000000000+822671161484229612769587806556610632118260410181746688000000000*b 780926068322816387781391705517087920836709953312915456000000000000+4680146161678809195562534492516145472978555884273664000000000000*a 780926068322816387781391705517087920836709953312915456000000000000-4680146161678809195562534492516145472978555884273664000000000000*a

STANDARD EULER FACTORS
The standard 2-Euler factors Q2(f,  x,   st) are given by the following table (switch to expanded form).
 f Q2(f,  x,   st)/(1-x) f1 (1-131072*x)*(1-65536*x)*(1-32768*x)*(1-x/32768)*(1-x/65536)*(1-x/131072) f2 (1-65536*x)*(1-32768*x)*(1-x/32768)*(1-x/65536)*(1-(65*x)/512+x^2) f3 (1-32768*x)*(1-x/32768)*(1+(7605/16384+(9*a)/16384)*x+x^2/2)*(1+(7605/8192+(9*a)/8192)*x+2*x^2) f4 (1-32768*x)*(1-x/32768)*(1+(7605/16384-(9*a)/16384)*x+x^2/2)*(1+(7605/8192-(9*a)/8192)*x+2*x^2) f5 (1+(-4995/16384+(3*b)/16384)*x+x^2/2)*(1-(65*x)/512+x^2)*(1+(-4995/8192+(3*b)/8192)*x+2*x^2) f6 (1+(-4995/16384-(3*b)/16384)*x+x^2/2)*(1-(65*x)/512+x^2)*(1+(-4995/8192-(3*b)/8192)*x+2*x^2) f7 (1+(7605/16384+(9*a)/16384)*x+x^2/2)*(1+(295*x)/512+x^2)*(1+(7605/8192+(9*a)/8192)*x+2*x^2) f8 (1+(7605/16384-(9*a)/16384)*x+x^2/2)*(1+(295*x)/512+x^2)*(1+(7605/8192-(9*a)/8192)*x+2*x^2)

SPINOR EULER FACTORS
The spinor 2-Euler factors Q2(f,  x,   spin) are given by the following table (switch to expanded form).
 f Q2(f,  x,  spin) f1 (1-281474976710656*x)*(1-8589934592*x)*(1-4294967296*x)*(1-2147483648*x)*(1-131072*x)*(1-65536*x)*(1-32768*x)*(1-x) f2 (1+528*x+131072*x^2)*(1+17301504*x+140737488355328*x^2)*(1+34603008*x+562949953421312*x^2)*(1+1133871366144*x+604462909807314587353088*x^2) f3 (1-4294967296*x)*(1-2147483648*x)*(1-131072*x)*(1-65536*x)*(1+(60840+72*a)*x+8589934592*x^2)*(1+(1993605120+2359296*a)*x+9223372036854775808*x^2) f4 (1-4294967296*x)*(1-2147483648*x)*(1-131072*x)*(1-65536*x)*(1+(60840-72*a)*x+8589934592*x^2)*(1+(1993605120-2359296*a)*x+9223372036854775808*x^2) f5 (1+17301504*x+140737488355328*x^2)*(1+34603008*x+562949953421312*x^2)*(1+(10549440-6336*b)*x+(433373914857472-62851645440*b)*x^2+(2969403378310462832640-1783425452438716416*b)*x^3+79228162514264337593543950336*x^4) f6 (1+17301504*x+140737488355328*x^2)*(1+34603008*x+562949953421312*x^2)*(1+(10549440+6336*b)*x+(433373914857472+62851645440*b)*x^2+(2969403378310462832640+1783425452438716416*b)*x^3+79228162514264337593543950336*x^4) f7 (1-14155776*x+140737488355328*x^2)*(1-28311552*x+562949953421312*x^2)*(1+(13141440+15552*a)*x+(359359213207552+287079137280*a)*x^2+(3698986517944483184640+4377498837804122112*a)*x^3+79228162514264337593543950336*x^4) f8 (1-14155776*x+140737488355328*x^2)*(1-28311552*x+562949953421312*x^2)*(1+(13141440-15552*a)*x+(359359213207552-287079137280*a)*x^2+(3698986517944483184640-4377498837804122112*a)*x^3+79228162514264337593543950336*x^4)

IDENTIFIED EIGENFORMS
Based on matching standard and spinor 2-Euler factors we identify the following eigenforms.
• f1 = E 18 : Basic Siegel Eisenstein series
• f2 = K1 18 1 : Klingen lift from degree 1
• f3 = K2 18 1 li : Klingen lift of degree 2 lift
• f4 = K2 18 2 li : Klingen lift of degree 2 lift
• f5 = M1 18 1 1 : Miyawaki lift of type 1
• f6 = M1 18 2 1 : Miyawaki lift of type 1
• f7 = M2 18 1 1 : Conjectural Miyawaki lift of type 2
• f8 = M2 18 2 1 : Conjectural Miyawaki lift of type 2

• SPECIAL VALUES
The special values ci such that W*3,3E(6)18i=18 ci fi⊗fi are given in the following table (switch to factored denominator form).
 c1 -1933845185986560/88361515511741542241620438735422234638389 c2 527/56874873618541612905307245756099052500 c3 -260516305465134039321405658307269/1392747843306888023205107560193427337095935802143179698609472356021139028298349775015788670767595520000000000000-(185075913360897737242322869336210081*a)/3281593861147532867163897638435313685092781032945562149043337374729363799615600038241976281851279331819520000000000000 c4 -260516305465134039321405658307269/1392747843306888023205107560193427337095935802143179698609472356021139028298349775015788670767595520000000000000+(185075913360897737242322869336210081*a)/3281593861147532867163897638435313685092781032945562149043337374729363799615600038241976281851279331819520000000000000 c5 47241888338514346677413/653323864632863892193806880848740218573616084637454626656661394595253675687526953488744448000000000000000-(1232243313434233045361029*b)/11952879578828050378128979656692437332771188766707620109996055321542123075750716814756835672195072000000000000000 c6 47241888338514346677413/653323864632863892193806880848740218573616084637454626656661394595253675687526953488744448000000000000000+(1232243313434233045361029*b)/11952879578828050378128979656692437332771188766707620109996055321542123075750716814756835672195072000000000000000 c7 4565530545101801323753/63225954154553014157699575735615462447886234204780836214024426744406878577583907143680000000000000000000-(6882343785622625101761803*a)/148973056404911966511385898047832888235171992919538811068320568319598231711381779595845959680000000000000000000 c8 4565530545101801323753/63225954154553014157699575735615462447886234204780836214024426744406878577583907143680000000000000000000+(6882343785622625101761803*a)/148973056404911966511385898047832888235171992919538811068320568319598231711381779595845959680000000000000000000

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