{ "generated_at_utc": "2026-10-09T01:43:10.017322+00:00", "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb", "source_hashes": [ { "path": "preprints/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026/The-maximum-number-of-mutually-unbiased-bases-in-dimension-six-September-24-2026.pdf", "bytes": 817737, "sha256": "b4cc74c840c902494d589b51c8e9706490f37cf2735e69a0486122131c6b7446" }, { "path": "preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026.pdf", "bytes": 396915, "sha256": "6bc2448ff13557610112e91ae6e713d0b469588cd9e1e3f9b44c04fc422fd612" }, { "path": "lean/docs/266.md", "bytes": 2093, "sha256": "3141714e25026b26a4028e27ee001e70295310bad4290b5a8f7c9fd546e8a174" }, { "path": "lean/ComparatorChallenges/MUBSix.lean", "bytes": 1924, "sha256": "7a634ee492b54abe357901a69272c42aa8dfc85b7a3401eef723468bb0c6c355" }, { "path": "lean/ComparatorChallenges/MUBSix.json", "bytes": 318, "sha256": "44b6a812682454988656f7c4cc85629d1cba5b3725f8cf3c03677c4f2535358f" }, { "path": "lean/ComparatorChallenges/HadamardCubeFiber.lean", "bytes": 1084, "sha256": "9f412781be8b38c88a6efb3a4528d4c990071a233cd931612d4710213d6366a1" }, { "path": "lean/ComparatorChallenges/HadamardCubeFiber.json", "bytes": 336, "sha256": "bcb65530d2cee7c6377770c945ff888b1b3534a42195091a9abbb92976178698" }, { "path": "preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/verification/run.py", "bytes": 663, "sha256": "670e627fc97030104873c26572c0d1f6d1cb3d969cc99c95d2de9e26619a495e" }, { "path": "preprints/Exact-Fourier-certificates-for-complex-Hadamard-matrices-of-order-six-September-24-2026/verification/verify.py", "bytes": 30160, "sha256": "104a7306205b8544c8f913f6afdb59603f2e04a207c9ac592c383b80eb0e2aa9" }, { "path": "lean/OAI/Analysis/MutuallyUnbiased/Main.lean", "bytes": 1372, "sha256": "13495f1c2248552ad2766a12b80e5593cf682dab271a24c7b9f7df7052f724d4" }, { "path": "lean/OAI/LinearAlgebra/Hadamard/Main.lean", "bytes": 4288, "sha256": "e12766697f77067f7f923650162d19a0c38d58e021c11190042210c26bc80be2" } ], "python": "3.10.19 (main, Oct 9 2025, 15:25:03) [Clang 17.0.0 (clang-1700.0.13.3)]", "blocks": [ { "shape": [ 1, 1, 1, 2 ], "dimension": 5, "decimal_scale_exponent": 14, "forward": { "positive_definite": true, "pivots": [ "7856995", "35303779555791/7856995", "943079354773586510078/35303779555791", "2030112517929471051191251127/471539677386793255039", "43674396936336248004625370017787053/4060225035858942102382502254" ], "L": [ [ "1", "0", "0", "0", "0" ], [ "-2793048/7856995", "1", "0", "0", "0" ], [ "8971673/7856995", "11750638045984/35303779555791", "1", "0", "0" ], [ "815225/1571399", "-11929570621295/35303779555791", "-77521805171492443466/471539677386793255039", "1", "0" ], [ "-4716392/1571399", "5231867265260/35303779555791", "-395021546636241600527/943079354773586510078", "643884970294043294385851720/2030112517929471051191251127", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "86753990", "289232108352073/43376995", "10498497986720793362367/578464216704146", "40829555837800662670634310286/10498497986720793362367", "43674396936336248004625370017787053/40829555837800662670634310286" ], "L": [ [ "1", "0", "0", "0", "0" ], [ "-4627031/43376995", "1", "0", "0", "0" ], [ "-37895129/86753990", "-185867841615694/289232108352073", "1", "0", "0" ], [ "4524466/43376995", "-86844646839403/289232108352073", "562467881435179530688/10498497986720793362367", "1", "0" ], [ "-2358196/8675399", "67695593783615/289232108352073", "-62916225621601789934/3499499328906931120789", "1603752121147568130199833465/40829555837800662670634310286", "1" ] ], "reconstruction_exact": true } }, { "shape": [ 1, 1, 3 ], "dimension": 21, "decimal_scale_exponent": 13, "forward": { "positive_definite": true, "pivots": [ "8281974", "1816199713907/2760658", "26786295311952885193/5448599141721", "5086074138066001670219676/26786295311952885193", "474341416774905918211541339763/565119348674000185579964", "18211811164814109945759973502762004109/4269072750974153263903872057867", "9278499669053255034362421332438328633797472/18211811164814109945759973502762004109", "585919671689705953549737557907804094662087418491/1030944407672583892706935703604258737088608", "5103215492599909841832923320179861341607448134228925/65102185743300661505526395323089343851343046499", "926447788313449370722641888802352821928202480260357980235341/413360454900592697188466788934568768670203298872542925", "363554624784580111036241972813782906378874495126638905517637669981/926447788313449370722641888802352821928202480260357980235341", "175704531450634101430276208617288533439961921651663321690549252983032144/363554624784580111036241972813782906378874495126638905517637669981", "1295682414472242895310030624001211461145260026381228256609756034471947134132/378673559160849356530767690985535632413711038042377848471011321084121", "3830605148346250440050147358266608817076807713661147218570443170065330668944745035/37574790019695043963990888096035132373212540765055619441682924999686466889828", "2011050307128867821120872571828894975458724922969983745980121221983652810354758498944122/3830605148346250440050147358266608817076807713661147218570443170065330668944745035", "4249091799494198961749650085194917435137728184197262571724829687913855798178391469330392338827/8044201228515471284483490287315579901834899691879934983920484887934611241419033995776488", "2251121843876590431716568599201863116963596328362311450689434693648127188930965543450253007344649617/5665455732658931948999533446926556580183637578929683428966439583885141064237855292440523118436", "2264690816657077565531488026706208492504408047662740420903972582190479732250153682491150417074888787480701/6753365531629771295149705797605589350890788985086934352068304080944381566792896630350759022033948851", "1456215882540270438248690245776315230675353760385019056776761329543467901923175679970024322620742758596664175276/2264690816657077565531488026706208492504408047662740420903972582190479732250153682491150417074888787480701", "68683188369797551980584618507334108167350032435880324519725747523043596982694758978060516355262093124023656781081747/1456215882540270438248690245776315230675353760385019056776761329543467901923175679970024322620742758596664175276", "11121503413304705536715194683099986524878432107533342903136943841652720488817237844746348395940700051204490686287478809814/68683188369797551980584618507334108167350032435880324519725747523043596982694758978060516355262093124023656781081747" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "105819/2760658", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-4538959/8281974", "-789393049545/1816199713907", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "295789/4140987", "-207181373158/1816199713907", "2205343334310524245/26786295311952885193", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-594151/1380329", "28251398680/42237202649", "7878297831941953926/26786295311952885193", "35995269011025977172781/1695358046022000556739892", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1637779/8281974", "-115277248029/1816199713907", "4808009015840211550/26786295311952885193", "3603615804010932528429011/5086074138066001670219676", "-249463013623520766701075802455/1423024250324717754634624019289", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "897633/2760658", "-2995699661325/1816199713907", "-2559949711891467918/26786295311952885193", "153157918924173945113465/1271518534516500417554919", "-560304965460655600468112961092/1423024250324717754634624019289", "-6778213271942164129726509090228686009/18211811164814109945759973502762004109", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-164059/8281974", "-429896403917/1816199713907", "-10170383468850852728/26786295311952885193", "-321259427907681475696382/1271518534516500417554919", "146894958408008175336383769308/1423024250324717754634624019289", "2201088965929797357082456146513911978/18211811164814109945759973502762004109", "-572151020531836301730764882584380452311957/1030944407672583892706935703604258737088608", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "48255/2760658", "-1356159435503/1816199713907", "1695811835660592624/26786295311952885193", "1101406936326703237982039/2543037069033000835109838", "-116873084057796130906878309742/1423024250324717754634624019289", "-1087273243919130671678663306117812318/18211811164814109945759973502762004109", "87247907363950485351066236090020343269034/289953114657914219823825666638697769806171", "-5818921592980870525385370019360866614735194304/65102185743300661505526395323089343851343046499", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-6253927/8281974", "-2583283597389/1816199713907", "-23206729156012889171/26786295311952885193", "-4909139818460666646833855/2543037069033000835109838", "-919826510048365591291447157126/1423024250324717754634624019289", "-14449569112238252779827146069317853048/18211811164814109945759973502762004109", "2712245272445275735231852801133660303527255/3092833223017751678120807110812776211265824", "-297127730060666468809224887932063054485834512915/585919671689705953549737557907804094662087418491", "-9640789554654986527115359238746612335949876774435931/5103215492599909841832923320179861341607448134228925", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1632149/8281974", "600561912529/1816199713907", "-1188458891197942150/26786295311952885193", "2402702929858922888763463/5086074138066001670219676", "83933797184026544902811241653/1423024250324717754634624019289", "2846871483320473576664717793220981124/18211811164814109945759973502762004109", "-402308546003623373465076760093395032761909/4639249834526627517181210666219164316898736", "-81359928318326393599878715120834967658006722206/195306557229901984516579185969268031554029139497", "1146923947516143153969978315247298414258774853396691/5103215492599909841832923320179861341607448134228925", "105674899295162905088988264769221956581043349425312911158099/926447788313449370722641888802352821928202480260357980235341", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-601690/4140987", "1286615300186/1816199713907", "-1626859753431039028/26786295311952885193", "2902543570174536716289169/5086074138066001670219676", "-181570818276107750621031498901/1423024250324717754634624019289", "6170287336386219142360189820403204596/18211811164814109945759973502762004109", "691192546216393034638469638671996716347025/9278499669053255034362421332438328633797472", "-110075040524872038795728961555764295126815494381/195306557229901984516579185969268031554029139497", "270805265166752861833144202036065565301838854423974/5103215492599909841832923320179861341607448134228925", "43647661270971297734050242559364170674643312865003076328386/926447788313449370722641888802352821928202480260357980235341", "164963758074575613483015864779665718916922142360409783744279999928/363554624784580111036241972813782906378874495126638905517637669981", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "208493/8281974", "9324694509175/1816199713907", "-4147583420821285289/26786295311952885193", "-7815265118472940637866459/5086074138066001670219676", "3145340409989006278513399644439/1423024250324717754634624019289", "9121532178072501636962257287661969459/18211811164814109945759973502762004109", "-69785459199930842211419242258843883527817/27614582348372782840364349203685501886302", "403418496866833760298520130242360605673122492880/585919671689705953549737557907804094662087418491", "15854624488609388581353593475473677871614662773797987/5103215492599909841832923320179861341607448134228925", "-514097971955504625546819013204549582640529147588943517622557/926447788313449370722641888802352821928202480260357980235341", "588835174857970459608747968875236883480919246016540069637349231463/363554624784580111036241972813782906378874495126638905517637669981", "648892827758213225930673155497719640062713434158352149466094778137710/378673559160849356530767690985535632413711038042377848471011321084121", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1265023/8281974", "-279223155169/1816199713907", "-2487932287145545849/26786295311952885193", "-169794136076511268296001/847679023011000278369946", "41830517444671261009251156706/474341416774905918211541339763", "-7204462392812738955073321638283124622/18211811164814109945759973502762004109", "-13160161931557510024950149037162436771477/1546416611508875839060403555406388105632912", "-41588488630223754591049767462822692523614734522/195306557229901984516579185969268031554029139497", "244175383505436029116479352325998086786206265052161/1020643098519981968366584664035972268321489626845785", "111672570382639575409812158613162086122414912597586226418470/926447788313449370722641888802352821928202480260357980235341", "102172076124283087168477183307129525287502861023838219643986689070/363554624784580111036241972813782906378874495126638905517637669981", "16746066177806895718492446654504567103200255757857221907859660418337205/87852265725317050715138104308644266719980960825831660845274626491516072", "74463845408875776836950021481991140868119885830792008297470532934008706297/647841207236121447655015312000605730572630013190614128304878017235973567066", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "-3980129/8281974", "220100745221/1816199713907", "-3198703660865177020/26786295311952885193", "1167024213979630234341320/1271518534516500417554919", "517365475189455020132046262228/1423024250324717754634624019289", "5962468424869206611579477042037769996/18211811164814109945759973502762004109", "-392721783875685023128861916666727167727931/1159812458631656879295302666554791079224684", "-200980790517144647445693056114866325802344457208/585919671689705953549737557907804094662087418491", "1005266215060615876199757014510084437395285094072944/5103215492599909841832923320179861341607448134228925", "166967970134874634174223783935175775322847145681870642197891/926447788313449370722641888802352821928202480260357980235341", "432011539076512295684763348310010792578217703771740887238780722772/363554624784580111036241972813782906378874495126638905517637669981", "89137106031814681041392461013924749105170658866690152011700856757651601/175704531450634101430276208617288533439961921651663321690549252983032144", "130811994236056460498115420302435180439798989184799245710665196043207382211/1295682414472242895310030624001211461145260026381228256609756034471947134132", "2107948368235546825639090074096535988230284812177800521459039007935939806478331711/7661210296692500880100294716533217634153615427322294437140886340130661337889490070", "1", "0", "0", "0", "0", "0", "0" ], [ "1656215/2760658", "-5158645875/2190831983", "-2763601591816753425/26786295311952885193", "808307579020158145302250/1271518534516500417554919", "-1160579191024273750016551021912/1423024250324717754634624019289", "-12571582931426476870715470160335684318/18211811164814109945759973502762004109", "516437575814927691181095822706342187388521/421749984956966137925564606019924028808976", "-30111351322988130755997742999886319533435664074/585919671689705953549737557907804094662087418491", "-287468244336262496052351510190038037453321015356762/204128619703996393673316932807194453664297925369157", "190406016743167821607333587044182436630523716786635929477550/926447788313449370722641888802352821928202480260357980235341", "-378956141197558551181494504179058035463214151406451553000888433364/363554624784580111036241972813782906378874495126638905517637669981", "-192323180623331989891203318357020031251917503867257609901573642013716935/175704531450634101430276208617288533439961921651663321690549252983032144", "-153298930773230753753754498972293019790840531120046117400470966180486838725/323920603618060723827507656000302865286315006595307064152439008617986783533", "109042672677081048182898732353149048277549724391466520043840634524102544392469997/510747353112833392006686314435547842276907695154819629142725756008710755859299338", "335776864516957850459495957173860210803234965479587682372030110459885611142478451974735/4022100614257735642241745143657789950917449845939967491960242443967305620709516997888244", "1", "0", "0", "0", "0", "0" ], [ "-2659420/4140987", "-3037737302592/1816199713907", "-13366065886898927551/26786295311952885193", "-3268971958919087345337131/5086074138066001670219676", "-1941918137458539014719433629189/1423024250324717754634624019289", "-3985562737459735261301161561300685374/18211811164814109945759973502762004109", "917774433827533535313133590797880742763045/773208305754437919530201777703194052816456", "75026710907879751785146255525366285530852800788/195306557229901984516579185969268031554029139497", "-9189590876239128852528918075476782170967540064933268/5103215492599909841832923320179861341607448134228925", "513954568163402657811786163053023825063109088601930666708073/926447788313449370722641888802352821928202480260357980235341", "-291484018064276574575893394326188469104412986534731688326410907382/363554624784580111036241972813782906378874495126638905517637669981", "-1713775770696166711655691162483850249727155883195157509418196081513615/1689466648563789436829578929012389744615018477419839631639896663298386", "-322201652997244329992762372807498282423267579694020888415601991048808877333/647841207236121447655015312000605730572630013190614128304878017235973567066", "-962100425129512839349257587832399951991100654381588958946004460580714569248339036/766121029669250088010029471653321763415361542732229443714088634013066133788949007", "389372214846567278561798409269468403257663812516441652325352118618977383138025206449125/4022100614257735642241745143657789950917449845939967491960242443967305620709516997888244", "-9106993295298930866259113826976479589278764900428786438184018112350227937218851397206946395/1416363933164732987249883361731639145045909394732420857241609895971285266059463823110130779609", "1", "0", "0", "0", "0" ], [ "-1381861/4140987", "-591138465110/1816199713907", "2503888278132613880/26786295311952885193", "2670217237298206015701659/2543037069033000835109838", "-272095692073121986644734755534/1423024250324717754634624019289", "18885521834557057306612598611877378159/18211811164814109945759973502762004109", "-306761790948743256948666597499038364319701/579906229315828439647651333277395539612342", "268280498355258151988414125456438415572101912944/585919671689705953549737557907804094662087418491", "-5567548248599958160538764065834131186776139669160218/5103215492599909841832923320179861341607448134228925", "65435885382811318742047616886240500914322963867334020015723/926447788313449370722641888802352821928202480260357980235341", "-41675533068966123061462030429337334682054656826866667774082010079/363554624784580111036241972813782906378874495126638905517637669981", "-25015748799518630565122787465118321659548340320303177043686051836190543/43926132862658525357569052154322133359990480412915830422637313245758036", "-5744289021745961622217188084218146185529750270092378397620299521776315508/29447327601641883984318877818209351389665000599573369468403546237998798503", "-559498996337205513885641869298611551525291094149218012712781500153021949643042654/766121029669250088010029471653321763415361542732229443714088634013066133788949007", "-26323758041841151452893439183905137403470179592996008320849198839692388475062166954465/4022100614257735642241745143657789950917449845939967491960242443967305620709516997888244", "-183163427537153364419588356950039666923951334610611673694885405520416860656978617829859635863/4249091799494198961749650085194917435137728184197262571724829687913855798178391469330392338827", "213536545369231805562320471211621423501281889906050925680231527436713514463815271515349818682399353/2251121843876590431716568599201863116963596328362311450689434693648127188930965543450253007344649617", "1", "0", "0", "0" ], [ "1156651/4140987", "-4467435807320/1816199713907", "-6294737794740100403/26786295311952885193", "412115354362085102721889/1695358046022000556739892", "-356365251906142692008622275659/158113805591635306070513779921", "1913100021507577895030466768808901367/18211811164814109945759973502762004109", "8925010917788547686036906309463590375019719/4639249834526627517181210666219164316898736", "126494455516583829610724209407679525803261628574/585919671689705953549737557907804094662087418491", "-19616508122971829624632762641616847709969010311453291/5103215492599909841832923320179861341607448134228925", "289140918151805909473426238563467748817805983965570923243026/926447788313449370722641888802352821928202480260357980235341", "-831503413656513131729653021720810251445741451770507902847019267541/363554624784580111036241972813782906378874495126638905517637669981", "-125924947519081636675040432494901445422996537377836610626120956042281219/58568177150211367143425402872429511146653973883887773896849750994344048", "-753634896887729889852097779435151883330660202888570681087241040396648469399/647841207236121447655015312000605730572630013190614128304878017235973567066", "-14004890030588265567353295974533966858261666090127009149201505722402151453965490323/7661210296692500880100294716533217634153615427322294437140886340130661337889490070", "-265120014136569061802570905987023599826621251698302256172541328854315560225537226814993/1005525153564433910560436285914447487729362461484991872990060610991826405177379249472061", "1026147063199241768673385760271644977728437761806549962075526654210159159231131488914159603814/4249091799494198961749650085194917435137728184197262571724829687913855798178391469330392338827", "1361965163461730856773376349717684691797477278864829617159103762211100214489667288296528636393991191/2251121843876590431716568599201863116963596328362311450689434693648127188930965543450253007344649617", "-488871345382108618387284193742043286729205369903014818603350267154234005751282222096812551478256710083678/2264690816657077565531488026706208492504408047662740420903972582190479732250153682491150417074888787480701", "1", "0", "0" ], [ "550561/4140987", "-813842515112/1816199713907", "-1104888551621500748/26786295311952885193", "386497113187336135598999/1271518534516500417554919", "-324556181516681610996619517780/1423024250324717754634624019289", "-7373838928714689963900130272414585422/18211811164814109945759973502762004109", "1128824531356935659178300902152503732599671/4639249834526627517181210666219164316898736", "-223275081834361363095468847906653267727768718434/585919671689705953549737557907804094662087418491", "2189031389738332054213522345123447753986718363838/1020643098519981968366584664035972268321489626845785", "83754749297422888000075864844849178609130425114737502711410/926447788313449370722641888802352821928202480260357980235341", "-38729483692391138849095931999404288309435530941790004682731414941/363554624784580111036241972813782906378874495126638905517637669981", "-6938006795093193029170882128931003824829595755290471737553679243278521/43926132862658525357569052154322133359990480412915830422637313245758036", "-102476311643428176187563203112879031599255038142052880148806969791995355301/1295682414472242895310030624001211461145260026381228256609756034471947134132", "-26451105773062837567510450109891064919590750079426060433048850879203151467807756/1276868382782083480016715786088869605692269237887049072856814390021776889648248345", "204788984981542069802671943830808279533637649687371470138106026911913254151191245919381/4022100614257735642241745143657789950917449845939967491960242443967305620709516997888244", "111105228357322855008291422260725383701948610181297860221657915204032698067173563372645970543/1416363933164732987249883361731639145045909394732420857241609895971285266059463823110130779609", "-417541386100215993027213975435278774447218886637237028993997830875795943490293209113600577371497784/2251121843876590431716568599201863116963596328362311450689434693648127188930965543450253007344649617", "-21069935923202964292135311966242512504053491652538937745194289324507983038036777294109275927219330477446/119194253508267240291130948774010973289705686719091601100209083273183143802639667499534232477625725656879", "-55330559410627534882970289979520733222644278910179469103465412742827937509966993847987534661421334074522244665/1456215882540270438248690245776315230675353760385019056776761329543467901923175679970024322620742758596664175276", "1", "0" ], [ "-8259767/8281974", "-4106134295325/1816199713907", "-14417511824628167551/26786295311952885193", "-2213231093381967481601459/5086074138066001670219676", "-767451778119013544093820548437/1423024250324717754634624019289", "9116558116967014605336298679364475259/18211811164814109945759973502762004109", "696635251470961341492136841085095235614293/1159812458631656879295302666554791079224684", "32702878127636653186824643059453972084682882744/195306557229901984516579185969268031554029139497", "-6199497284494548427175871620517718985822498240999884/5103215492599909841832923320179861341607448134228925", "387902950718569612153879921883656623017026821030829575152199/926447788313449370722641888802352821928202480260357980235341", "-70886049978336430746138421686011995830539304069846349224561213540/363554624784580111036241972813782906378874495126638905517637669981", "-1020182785965297563606055246344327013614815670538592428349767691477449/4505244396170105164878877144033039318973382606452905684373057768795696", "-98248927562275076168926517022255992641874246182558963913535670175240475015/647841207236121447655015312000605730572630013190614128304878017235973567066", "-193771309336930168729520540276481804601270739856500733394121212675971614316574235/510747353112833392006686314435547842276907695154819629142725756008710755859299338", "43285573634740101130228353129114055077417035269274467653017467999239233477370046105635/2011050307128867821120872571828894975458724922969983745980121221983652810354758498944122", "-1198287960033695700235361747188512661870928493177174112325619572834089446281125425138630526144/4249091799494198961749650085194917435137728184197262571724829687913855798178391469330392338827", "94165359491359404329259860545185934520539317510555587867901326336423133813055563487601192640326047/2251121843876590431716568599201863116963596328362311450689434693648127188930965543450253007344649617", "448164954467624671964164622495642259026200394513222783533306703410342154680837581653401058409592387416295/2264690816657077565531488026706208492504408047662740420903972582190479732250153682491150417074888787480701", "-19017206672446846148603620851441490371432144413979496181772544210107294544800536351792625100415760981392853101/242702647090045073041448374296052538445892293397503176129460221590577983653862613328337387103457126432777362546", "-30392672506660591285246186444490117804593368880895590735792965438115798983313039652867225722040142315497457454027422/68683188369797551980584618507334108167350032435880324519725747523043596982694758978060516355262093124023656781081747", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "15446253", "6348980285549/5148751", "300660470993474738902/19046940856647", "246250676023066963197233087/150330235496737369451", "708676201887685590802476775269669/492501352046133926394466174", "352350426833979009721084999699067408390/236225400629228530267492258423223", "519475562008723717758247955240282825438961217/528525640250968514581627499548601112585", "170173405510616022519433571105966097343494500530421/1038951124017447435516495910480565650877922434", "495280339844214943426099438623407143348133760331072579556/170173405510616022519433571105966097343494500530421", "76343796628289863663885610736240608959954280674659776181276184/123820084961053735856524859655851785837033440082768144889", "16937925268881711750357100981152574584053560923254929737336700682057/76343796628289863663885610736240608959954280674659776181276184", "47183833987311072553525762650412596840928708954370141841787729154507213117/67751701075526847001428403924610298336214243693019718949346802728228", "4244692605376647162130298823317217187278873105856797795183239758402563366020417/47183833987311072553525762650412596840928708954370141841787729154507213117", "1186125211529247547201432909264050918833925204120462838858926684897853732357162380071/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "307285580937099902673140141034430424246111419297757825300541951451587348594692995550114110/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "1017822719868897060740498276664813752997665830751412576001943802934840762154518047721328165343/4389794013387141466759144871920434632087305989967968932864885020736962122781328507858773", "1820988069863750958997115813279373630798139864971050769144736473152934834816775792406424298571834131/5089113599344485303702491383324068764988329153757062880009719014674203810772590238606640826715", "1457100541808693579706706937703300365542596691556066726458670109059805192627619894105572128802526253660971/25493832978092513425959621385911230831173958109594710768026310624141087687434861093689940180005677834", "1034697822615491720391771367176420634198221255748586505307834639490442711673302625967659797503463475310342493794/1457100541808693579706706937703300365542596691556066726458670109059805192627619894105572128802526253660971", "21382635319649418476782483793524736028643088123814558960635838949965674596189964146649888317276782583403426089371020/517348911307745860195885683588210317099110627874293252653917319745221355836651312983829898751731737655171246897", "5560751706652352768357597341549993262439216053766671451568471920826360244408618922373174197970350025602245343143739404907/21382635319649418476782483793524736028643088123814558960635838949965674596189964146649888317276782583403426089371020" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-321272/5148751", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "5457071/15446253", "12688538536943/6348980285549", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "5534083/15446253", "-821619914962/577180025959", "33746045016438726499/150330235496737369451", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "3635251/5148751", "7839584418687/6348980285549", "70666862745155469963/300660470993474738902", "-112159859200181183273601773/246250676023066963197233087", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1351879/15446253", "16369050215994/6348980285549", "61894150654806250493/150330235496737369451", "-1745770209615789716011900/246250676023066963197233087", "-85818642378379767900370211636932/236225400629228530267492258423223", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4379858/15446253", "-407327249809/577180025959", "-10800417777691507229/42951495856210676986", "95104980290941126150193241/246250676023066963197233087", "109671212286891229715485799778745/708676201887685590802476775269669", "-32912786919560339194716688855177183808/176175213416989504860542499849533704195", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1728565/15446253", "4064166201279/6348980285549", "-32897333576144986901/300660470993474738902", "-56542363633286442734704337/246250676023066963197233087", "-13669371771971090332585926413163/236225400629228530267492258423223", "62897409397172007746726879876487847393/352350426833979009721084999699067408390", "18769026735055734450452382661319682078118809/519475562008723717758247955240282825438961217", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-9593464/15446253", "-23032610162281/6348980285549", "-101911667069761426915/150330235496737369451", "-138214786202724789749179657/246250676023066963197233087", "305509536277199287653707546052038/708676201887685590802476775269669", "-233446499455359185285736328747331046639/352350426833979009721084999699067408390", "52644847652615940265561981338337929023083988/519475562008723717758247955240282825438961217", "148071646976362749053127394984541807849506127208075/170173405510616022519433571105966097343494500530421", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "301826/5148751", "-4027960288302/6348980285549", "-11187727206712709910/150330235496737369451", "1750398425216179871461922/12960561895950892799854373", "-26524042929623181312041269625222/708676201887685590802476775269669", "-83145642541597101904742467034721778309/176175213416989504860542499849533704195", "245735329511569271749233791126674259801910571/519475562008723717758247955240282825438961217", "24152817264498389100954835107601950985652396186032/170173405510616022519433571105966097343494500530421", "1082545835112494009005626992088614799719058034549514265/123820084961053735856524859655851785837033440082768144889", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1464376/15446253", "-2097239712432/6348980285549", "-32081207778786893857/300660470993474738902", "55941859161601816514926881/246250676023066963197233087", "34233969999180173929278621260387/236225400629228530267492258423223", "-91095953507094616737641915758429310967/352350426833979009721084999699067408390", "207818449129355402536495077629558006494213509/519475562008723717758247955240282825438961217", "50576788343572096744645219681970025042785384502931/170173405510616022519433571105966097343494500530421", "-2803771830987438778215091653749619757344088048941670503/495280339844214943426099438623407143348133760331072579556", "13579351169291147278414063649314386035692669897945948547984209/76343796628289863663885610736240608959954280674659776181276184", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "10741408/15446253", "11519650041851/6348980285549", "-36820319052382566287/150330235496737369451", "-246801465684681197761124267/246250676023066963197233087", "191669949800620704767339204798826/236225400629228530267492258423223", "-36876894533089879197862105464451487743/352350426833979009721084999699067408390", "35105210428638932419002304922032901312368611/519475562008723717758247955240282825438961217", "315767072311892966172955786546179245748300176457281/170173405510616022519433571105966097343494500530421", "29898584769817111666468537812858287689865833980778071713/123820084961053735856524859655851785837033440082768144889", "15392333614217373453571546179120077399196753781228777602368657/76343796628289863663885610736240608959954280674659776181276184", "1374564324764891005546078991650654680933561805608886193923462198983/16937925268881711750357100981152574584053560923254929737336700682057", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "660976/15446253", "2411925252427/6348980285549", "2612764221485822975/300660470993474738902", "27879725093796019165333399/246250676023066963197233087", "-148370328731597950407354969208691/708676201887685590802476775269669", "2804431021445854012962272509901756409/16015928492453591350958409077230336745", "-8894503504744979651712676143214904436896381/519475562008723717758247955240282825438961217", "-58762726967315819556090993047508992976943481107978/170173405510616022519433571105966097343494500530421", "-83551675971166226344476642403814290459297278590850856689/495280339844214943426099438623407143348133760331072579556", "24563082093809779475422691472020196155134559783396659236653/9542974578536232957985701342030076119994285084332472022659523", "910401962487716312363737914099086555977021613562799183830046297566/16937925268881711750357100981152574584053560923254929737336700682057", "-11873478382288411049360019207196704924799022874926164856091230499188416747/47183833987311072553525762650412596840928708954370141841787729154507213117", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1677944/15446253", "-1538511537495/6348980285549", "1963728976322544602/150330235496737369451", "-39740545289760465124598394/246250676023066963197233087", "-2414016228442569083244809464138/708676201887685590802476775269669", "53980882414400514745173003808521201627/176175213416989504860542499849533704195", "-56362950532508770066281031964260570474197358/519475562008723717758247955240282825438961217", "134885943684789132087761231433609053900605434104482/170173405510616022519433571105966097343494500530421", "107804439451073541921520360540878119741200880327221744537/247640169922107471713049719311703571674066880165536289778", "-2765373722002761294741541617314899079678276022761478591333782/9542974578536232957985701342030076119994285084332472022659523", "-7585547312904570422278801479897491860189930262389555641489380061628/16937925268881711750357100981152574584053560923254929737336700682057", "-15512728235800302898684309112809143338845949407411734157601838064826593134/47183833987311072553525762650412596840928708954370141841787729154507213117", "-263873006275144790314567279569435942499631892882826565302878239360901009057719/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "-299969/15446253", "8722558386011/6348980285549", "17293082884477839661/150330235496737369451", "-46106665746803351521413054/246250676023066963197233087", "-363487222949892852566835999948170/708676201887685590802476775269669", "95808956602562514077846102773133049471/176175213416989504860542499849533704195", "-20933914307973216587988467976304576039521929/519475562008723717758247955240282825438961217", "37400747954359685058518766112871507272424390998494/170173405510616022519433571105966097343494500530421", "-36798348973403588492232412743827821225246642739747440121/247640169922107471713049719311703571674066880165536289778", "8086627699685944977981782678792024277343768971722918644217889/76343796628289863663885610736240608959954280674659776181276184", "-801997998403638548150542910906050466284209219458743898672573354037/16937925268881711750357100981152574584053560923254929737336700682057", "-15114229258457805286493085737642024349324013953489144699544259344421461937/47183833987311072553525762650412596840928708954370141841787729154507213117", "4125979376089908165978795161486047084674784483494108135317878597128914696724782/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "373315194492319722255371151680919028065837262246654927860793271957936886010780750591/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "1", "0", "0", "0", "0", "0", "0" ], [ "3409136/15446253", "-8626884581011/6348980285549", "45607952898135458851/300660470993474738902", "164120759426969932880505694/246250676023066963197233087", "-266724170180229749048431943148905/708676201887685590802476775269669", "-64059113186027341148721042110418471547/352350426833979009721084999699067408390", "109816173759153616231835957218887286219593499/519475562008723717758247955240282825438961217", "-79912649357345535375238003832117046047901028087397/170173405510616022519433571105966097343494500530421", "-70264592617565244825977667047080686769646472311582758879/495280339844214943426099438623407143348133760331072579556", "14337562789921228062536815470696327228191307561874503104777113/38171898314144931831942805368120304479977140337329888090638092", "2055870814122100175527093802503419427392921893228862619485879717384/16937925268881711750357100981152574584053560923254929737336700682057", "-5224449400150910096016899000823252432871108448827047719038475520637470155/47183833987311072553525762650412596840928708954370141841787729154507213117", "1901655797342032674695038922281368884592545654285374566349822288273767018967963/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "-241675612193935446369090011076495679176696962557334805541599349548204616017470958800/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "-1475384312760302536349387917496426651584958107187744988977247596309054406212922756535/4389794013387141466759144871920434632087305989967968932864885020736962122781328507858773", "1", "0", "0", "0", "0", "0" ], [ "1327786/15446253", "-4315460397216/6348980285549", "-59098741205114599885/300660470993474738902", "7962425238664974386368905/246250676023066963197233087", "263378622903558192884505352563073/708676201887685590802476775269669", "-30324157883637972946045533462042007936/176175213416989504860542499849533704195", "1765442434568833464537105654612500958571744/519475562008723717758247955240282825438961217", "-248122234115803131628930762852118893942925493050070/170173405510616022519433571105966097343494500530421", "-117105529816950949248906603608219791787425614099686535383/495280339844214943426099438623407143348133760331072579556", "-4231112817497634932877097827577513780735513276886542821030034/9542974578536232957985701342030076119994285084332472022659523", "4577073741039010418524129059956597472066360058969699703974220053178/16937925268881711750357100981152574584053560923254929737336700682057", "23854913562199292724433774451555839140335238328488629844778079762006340883/47183833987311072553525762650412596840928708954370141841787729154507213117", "-1863072873344641246050437807562620519734416772910383950541847889675223936564020/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "-698354053725476456115813779524351869808277202612976281929307011053809664638904688038/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "-17791643457094613456933234762060939102198789417258152063703461911186283741357212725714419/21948970066935707333795724359602173160436529949839844664324425103684810613906642539293865", "-621902720486357813431967632127911356783680664568481957810599948378568480880349283612362761083/1017822719868897060740498276664813752997665830751412576001943802934840762154518047721328165343", "1", "0", "0", "0", "0" ], [ "-720802/15446253", "557740325658/6348980285549", "3228867581325688871/150330235496737369451", "60216975806386578970666474/246250676023066963197233087", "-49490493380369431590149252509654/708676201887685590802476775269669", "22426077231914920545154465393706251687/352350426833979009721084999699067408390", "40810846534062924131616500154956643548819366/519475562008723717758247955240282825438961217", "-21001835139319344294405190733537929316079671889937/170173405510616022519433571105966097343494500530421", "-17774605172577681195332923261693788136877797508451501805/247640169922107471713049719311703571674066880165536289778", "556868162222778248200508526365769609765199486294842066902828/9542974578536232957985701342030076119994285084332472022659523", "-1047447613337858902553096829164075049733672171957953314172928237548/16937925268881711750357100981152574584053560923254929737336700682057", "-6768951963418935595546685749019664218418102134983328312813489119188692610/47183833987311072553525762650412596840928708954370141841787729154507213117", "593515795094187953644622667045887290802252855513548572880961369086779066356087/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "115815757454211897656334091725203961859429652265102418055922342476889762410024634341/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "-12371721486776048378365091560178835105324371527021535900460828813070256764572414124932791/307285580937099902673140141034430424246111419297757825300541951451587348594692995550114110", "-23649758452449571497248660571381762677082587933891891794448052719480650079910673476054992464/339274239956299020246832758888271250999221943583804192000647934311613587384839349240442721781", "282473051609634573048996520545755442106313270274308790921875945445377061147911235619341753097958046/1820988069863750958997115813279373630798139864971050769144736473152934834816775792406424298571834131", "1", "0", "0", "0" ], [ "2527166/15446253", "-243599008793/577180025959", "-29951043437137062647/300660470993474738902", "116355166965587825849331841/246250676023066963197233087", "256398658160961808845947480313185/708676201887685590802476775269669", "-17950239783926407808044161343376721859/176175213416989504860542499849533704195", "-173128186481598196793378224387960417027382779/519475562008723717758247955240282825438961217", "-431422284477221856999271569740073806972867766022798/170173405510616022519433571105966097343494500530421", "-274336363638291056577740874268281018034558070658649468539/247640169922107471713049719311703571674066880165536289778", "-43544392889551945176814263095348466361083443138670152148090969/76343796628289863663885610736240608959954280674659776181276184", "819201467454414316253293324089778372155981558507273667557421080357/16937925268881711750357100981152574584053560923254929737336700682057", "3439402720963535569975389207873865581050977402189898114435644915729481475/6740547712473010364789394664344656691561244136338591691683961307786744731", "-308275363629241355581215821556660203950829559262347477346913812219222505185628/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "-846223107870322697510019758284089953115369242145402402823775663448894468906570140814/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "-127412952097595284845028544284106470706435892646140685859010475835522890459270687788967473/153642790468549951336570070517215212123055709648878912650270975725793674297346497775057055", "-733273502819662382403322763040782809159438196747525860691423563795552856337154025140998285/6401400753892434344279863375250400962249470633656682867936753477577614856317723570574390977", "345562730896505139514269973712974602390675388213643225262456561914117877571185760516167200604203766/1820988069863750958997115813279373630798139864971050769144736473152934834816775792406424298571834131", "-461008157896238928672597051205801502764362770222865796258647351730282466506176423489794770700811418274180/1457100541808693579706706937703300365542596691556066726458670109059805192627619894105572128802526253660971", "1", "0", "0" ], [ "-601327/5148751", "-1880107045175/6348980285549", "-3094540684089000639/300660470993474738902", "-23612316181265617641492212/246250676023066963197233087", "190589781674281112102216844073583/708676201887685590802476775269669", "-43548695519008773284300224689677606596/176175213416989504860542499849533704195", "38071356944344238403241013775584389808832269/519475562008723717758247955240282825438961217", "11406343252304737308622467834974507408019601792108/170173405510616022519433571105966097343494500530421", "13371374588495183500685725375807293746013576763391527760/123820084961053735856524859655851785837033440082768144889", "13029342511663159291039601241604444275874135600974209977007645/76343796628289863663885610736240608959954280674659776181276184", "1779391653391128228675270268851826868442413696339627339312837747547/16937925268881711750357100981152574584053560923254929737336700682057", "4575884847508225451330405181888524860888496691350105679672886255057538901/47183833987311072553525762650412596840928708954370141841787729154507213117", "-1485639956263106539436803988414600290498786356921678674029988184621753375182810/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "-169766780820926999279911989356767901214837685718586321062856448816316143194367091598/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "-29676501180237353235681986249203092389630643999082231526725173486557802567551277895808299/307285580937099902673140141034430424246111419297757825300541951451587348594692995550114110", "48229196581324957023003291842659099320282405791449694152742665129702884700128793790959682665/1017822719868897060740498276664813752997665830751412576001943802934840762154518047721328165343", "109312638100828391480927903029032831379168203260666243861949858265415984868461944705114280740201759/1820988069863750958997115813279373630798139864971050769144736473152934834816775792406424298571834131", "405176010258025078639061720534934445564612218827437580349379459841965073682624948623822421760813556554575/1457100541808693579706706937703300365542596691556066726458670109059805192627619894105572128802526253660971", "-46149117760782678522089604803950767165719380628300161662041314960617064712756843798879031563116056529805537707/517348911307745860195885683588210317099110627874293252653917319745221355836651312983829898751731737655171246897", "1", "0" ], [ "-8259767/15446253", "3015771134998/6348980285549", "77346604587705260195/300660470993474738902", "17709006437486600077555514/246250676023066963197233087", "-547226431705663476104987172586969/708676201887685590802476775269669", "156108053164750597316966643821023353241/352350426833979009721084999699067408390", "24504208413378184737276616067494784849965973/519475562008723717758247955240282825438961217", "263042164685208819977230364967974870227189397552185/170173405510616022519433571105966097343494500530421", "121542279251838030136331726169886415960848227566541067721/495280339844214943426099438623407143348133760331072579556", "4485656113319704668807235195082969229408558667091233457903293/19085949157072465915971402684060152239988570168664944045319046", "-2497387787379266238719578978822728180506490965483511155319833394666/16937925268881711750357100981152574584053560923254929737336700682057", "-10931664129692524211773676271881010273146603590938218192838685920872192373/47183833987311072553525762650412596840928708954370141841787729154507213117", "2275451935208445324310156641379822349339603598988560456067281852562721841798968/4244692605376647162130298823317217187278873105856797795183239758402563366020417", "448072374131710162876420846015295722068236566754450916527600764563654973142729042117/1186125211529247547201432909264050918833925204120462838858926684897853732357162380071", "152473336103864538967217934685520052278357302133384785360929363937448769217855007910309653/153642790468549951336570070517215212123055709648878912650270975725793674297346497775057055", "573461683530272058986663108248052548468602334971944288240250245583328382214510409028967288323/1017822719868897060740498276664813752997665830751412576001943802934840762154518047721328165343", "-364360165690699232311861731846438918325783040649929491456915061947099266880060009708183848829338436/1820988069863750958997115813279373630798139864971050769144736473152934834816775792406424298571834131", "-567187384006743284913779031230980738530880259138774997677263866125686568940531407216936322999546860419712/1457100541808693579706706937703300365542596691556066726458670109059805192627619894105572128802526253660971", "-141003724600356129531687875172758610418527887995710123912844943589935709257205095312073748827144356408192500478/517348911307745860195885683588210317099110627874293252653917319745221355836651312983829898751731737655171246897", "-9203208993782996869087665786488300222716345548164113562824081952810745206437146077643843264222965069155279994802431/21382635319649418476782483793524736028643088123814558960635838949965674596189964146649888317276782583403426089371020", "1" ] ], "reconstruction_exact": true } }, { "shape": [ 1, 2, 2 ], "dimension": 11, "decimal_scale_exponent": 13, "forward": { "positive_definite": true, "pivots": [ "4921588", "1163701517996/1230397", "410382924910201340/290925379499", "48295945311830411182985/82076584982040268", "11189999230784106417194573689/48295945311830411182985", "36653035270648782823029188306807353/111899992307841064171945736890", "3467868566062862632187930528885590010823/36653035270648782823029188306807353", "395689645922930852181536744363128716889379493/1155956188687620877395976842961863336941", "63779079071187971724127593822088947572157736150587/81167106855985815832110101407821275259359896", "6128669831956416859185871044100759384780138571255336500/276376009308481210804552906562385439479350189985877", "3213472828238838540323513005837750309890513122790494441732261/165474085462823255198018518190720503389063741423894085500" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "310820/1230397", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1044161/703084", "-1263074506141/1163701517996", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-312345/2460794", "-32540481447/581850758998", "9633646179345067/82076584982040268", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "801999/2460794", "521776789207/581850758998", "-85079745776268293/205191462455100670", "5386081027196870131306/9659189062366082236597", "1", "0", "0", "0", "0", "0", "0" ], [ "-2795071/4921588", "-408646750804/290925379499", "1021532921046516577/1641531699640805360", "8256136512237569219063/193183781247321644731940", "-1580558269186538354223404017/11189999230784106417194573689", "1", "0", "0", "0", "0", "0" ], [ "3367935/4921588", "255895559991/290925379499", "-462755091400254761/1641531699640805360", "-56697486423404342793839/193183781247321644731940", "1119956621117741943137206536/11189999230784106417194573689", "-2715718628975185457321522216184949/36653035270648782823029188306807353", "1", "0", "0", "0", "0" ], [ "-395830/1230397", "-298717888093/581850758998", "-322286413904200853/820765849820402680", "-56535795651144738842931/96591890623660822365970", "1647270928465849158090670476/11189999230784106417194573689", "2961045691041963442161220071781468/36653035270648782823029188306807353", "1650181113568183151135489771382115692239/1155956188687620877395976842961863336941", "1", "0", "0", "0" ], [ "83606/175771", "2624310270239/1163701517996", "-61417240898743521/328306339928161072", "689693211995715540428237/193183781247321644731940", "914104226335535377424442430/11189999230784106417194573689", "-5550381584562289439718350765165001/73306070541297565646058376613614706", "-5891381476857376333242576494018931197990/3467868566062862632187930528885590010823", "-72607733870224535140445068143823598831571461/60875330141989361874082576055865956444519922", "1", "0", "0" ], [ "-124111/2460794", "-106723018245/290925379499", "-11614853483696887/820765849820402680", "-94370866049518559741057/96591890623660822365970", "-241444570068251534953280526/11189999230784106417194573689", "-6086217076049414837766699533512939/36653035270648782823029188306807353", "759703737241492713159754700148782172123/1155956188687620877395976842961863336941", "52418331485294802755709608143247438308513100/131896548640976950727178914787709572296459831", "-5134588871359712537106494764324526828185119016566/21259693023729323908042531274029649190719245383529", "1", "0" ], [ "702355/4921588", "-108664522941/581850758998", "16770894006583649/1641531699640805360", "-167871245053470541715753/193183781247321644731940", "-616102647497379378562796204/11189999230784106417194573689", "-5526162794641776329556061682110923/36653035270648782823029188306807353", "428378417030039402979397838692912887842/1155956188687620877395976842961863336941", "92791975886542472448561409696081033709823964/395689645922930852181536744363128716889379493", "-43385435290055671107689673327790326763487937103520/191337237213563915172382781466266842716473208451761", "2157643347852908562165647596132814076668727726288707117/6128669831956416859185871044100759384780138571255336500", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "680229", "20107041330/75581", "83672876208463663/60321123990", "111830209413948198594007/251018628625390989", "34425022755281971937245195013/111830209413948198594007", "15307474526958327064965444037487104/34425022755281971937245195013", "3520003250857510716841109304189444968363/15307474526958327064965444037487104", "379831851772104911236368442037335684741346952/3520003250857510716841109304189444968363", "17479418652284552137434755866464075063379980195961/18087231036766900535065163906539794511492712", "27507193756326595116897163357783180615127072140170648614/367067791697975594886129873195745576330979584115181", "3213472828238838540323513005837750309890513122790494441732261/27507193756326595116897163357783180615127072140170648614" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "71444/75581", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-2223239/680229", "-98378887207/20107041330", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "282809/680229", "20960607673/10053520665", "1632534949772216/83672876208463663", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "508720/680229", "-27052431949/10053520665", "56646018017229742/83672876208463663", "36600909915959275872914/111830209413948198594007", "1", "0", "0", "0", "0", "0", "0" ], [ "-70414/226743", "55727569031/20107041330", "-91099031377911129/83672876208463663", "-44299552785540597149338/111830209413948198594007", "-15820869753746313878842815228/34425022755281971937245195013", "1", "0", "0", "0", "0", "0" ], [ "-233345/680229", "-6156694317/3351173555", "4504310994446048/7606625109860333", "55289105352156247953139/111830209413948198594007", "18635080458244273734881588183/34425022755281971937245195013", "-4981736393472402681607486085932019/15307474526958327064965444037487104", "1", "0", "0", "0", "0" ], [ "-588904/680229", "1146630404/10053520665", "-7415417341907512/83672876208463663", "672989850357148607094/111830209413948198594007", "-9949645983959050352458621412/34425022755281971937245195013", "2007139815275909459453615706409973/7653737263479163532482722018743552", "302228261280040133466533430515126081286/3520003250857510716841109304189444968363", "1", "0", "0", "0" ], [ "-836950/680229", "2438528857/427809390", "-82737834488103571/83672876208463663", "-116038567147699746951479/111830209413948198594007", "-57726063333875233258409906259/34425022755281971937245195013", "406219908150596939503835320206381/1913434315869790883120680504685888", "-579960192052915214128865646888981082024/3520003250857510716841109304189444968363", "-6082608645798733789422806265046988388465867/18087231036766900535065163906539794511492712", "1", "0", "0" ], [ "794/680229", "-5169873166/3351173555", "43360189344211154/83672876208463663", "-11101839075590262135160/111830209413948198594007", "11809836990062242357994329922/34425022755281971937245195013", "-2865428485893563144517681673963401/15307474526958327064965444037487104", "177157843568628361209030820238058237489/3520003250857510716841109304189444968363", "-21066435804720785928533956539802970850506971/47478981471513113904546055254666960592668369", "5658031728703927773343020507526599668741930181320/17479418652284552137434755866464075063379980195961", "1", "0" ], [ "702355/680229", "-11489986267/3351173555", "952401039090908/7606625109860333", "5771252348976692509063/111830209413948198594007", "29429149021131038751634709825/34425022755281971937245195013", "4650820566461172754344495271033409/7653737263479163532482722018743552", "6957201992055347941835705121579867822/3520003250857510716841109304189444968363", "189756908932443978670324120470906799618796531/189915925886052455618184221018667842370673476", "-11393478122050259797789923181655993722042228591674/17479418652284552137434755866464075063379980195961", "-14827153955215089202732638206951917239133001841574472989/27507193756326595116897163357783180615127072140170648614", "1" ] ], "reconstruction_exact": true } }, { "shape": [ 1, 4 ], "dimension": 27, "decimal_scale_exponent": 14, "forward": { "positive_definite": true, "pivots": [ "21638825", "19220853765539/21638825", "82217075521642728908/19220853765539", "961692631845074659434120589/82217075521642728908", "5138035778632122279527446470336466/961692631845074659434120589", "20935763851964712354501486843001933954485/5138035778632122279527446470336466", "4811632066337866661462626095790335628839699236/2326195983551634706055720760333548217165", "2081338214618748873771841651477919570543738446031711/1202908016584466665365656523947583907209924809", "66187924821975342552054961766815477752001029681944714384413/8325352858474995495087366605911678282174953784126844", "947838752964334280723672671527611011648108260829016536222004441185/198563774465926027656164885300446433256003089045834143153239", "167717069693312955709367794377612424786739526508093569986560244560362069/49886250156017593722298561659347947981479382148895607169579181115", "12837255361837217856373609093077801885208094677614094537325478464508363061030829/3186624324172946158477988093174636070948051003653777829744644646646879311", "11590085353842380391155616714048164010402473044218049864119444736909502920448688675821/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951/34770256061527141173466850142144492031207419132654149592358334210728508761346066027463", "19468479225470548738274706614709761656583360935160228181874738758135087274425036450452725413966336/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969/19468479225470548738274706614709761656583360935160228181874738758135087274425036450452725413966336", "152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "250088593659486969242663756791032449804069165126168808258680182557970867529028541217314423186195525435426300156401800009730/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "20089450839616137472967658732139784988012978943523672368817691721103889413712670743982500143860842312609422556468407528642100794/13893810758860387180147986488390691655781620284787156014371121253220603751612696734295245732566418079745905564244544444985", "2168532434099463599821326079814113026206000967877436667252963058029191571186165035178338616750199767785277409265933871318890513686306/10044725419808068736483829366069892494006489471761836184408845860551944706856335371991250071930421156304711278234203764321050397", "4286399897294495474149536345608811127278607910019748119110989457411895048572087814960910918474502047642533988026909337848498867142343217090/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "4133541930288818292563390105947869434877619433730840422527355322350963686098695284797467265534714539034732114630884603318972706815658449302793774/2143199948647247737074768172804405563639303955009874059555494728705947524286043907480455459237251023821266994013454668924249433571171608545", "21390239552248789780598379066958932156813243411937203406190048490192147014116327502733588829056593342958594533552772715158628699212047102050724912434119/16534167721155273170253560423791477739510477734923361690109421289403854744394781139189869062138858156138928458523538413275890827262633797211175096", "1934104812660456084454261536888668894676458836471125740892608445037711038086174654987172585177882407966168894426509906307271206553179613929698539413257362353/14260159701499193187065586044639288104542162274624802270793365660128098009410885001822392552704395561972396355701848476772419132808031401367149941622746", "3267494014457727344756960291808649798488829913696624009275607322128735752780730287037349394082882061922313646985260305681534155400893738360669608690379051483672078/5802314437981368253362784610666006684029376509413377222677825335113133114258523964961517755533647223898506683279529718921813619659538841789095618239772087059", "2137998361822955235749056046940505192201752247591199045818894810471818269946213652704795721324188319685836968139774298919540548394517987752689826583316134784994295114159/3267494014457727344756960291808649798488829913696624009275607322128735752780730287037349394082882061922313646985260305681534155400893738360669608690379051483672078" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1103969/21638825", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-366698/21638825", "6079215581762/19220853765539", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4472903/21638825", "-32681494922182/19220853765539", "82358567664527332713/82217075521642728908", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4675758/21638825", "-3095881788977/19220853765539", "-1360925242777208206/20554268880410682227", "-88005287273744214835258292/961692631845074659434120589", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-348911/21638825", "26677700909909/19220853765539", "16305171395508083145/41108537760821364454", "3420093212905374662514342/961692631845074659434120589", "-1059551737586934001955493506808153/5138035778632122279527446470336466", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1653142/21638825", "-10399425525477/19220853765539", "-4243187046912003652/20554268880410682227", "-227483014154556583055547580/961692631845074659434120589", "755129834729342260113852828646105/5138035778632122279527446470336466", "937982268236200622410481134507699100783/6978587950654904118167162281000644651495", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-6679308/21638825", "6608686676752/19220853765539", "3190215169611406419/20554268880410682227", "-53316294621370850727437920/961692631845074659434120589", "-3029251657880025045076974636712837/5138035778632122279527446470336466", "574116504311205722913991005966381152273/2326195983551634706055720760333548217165", "-932147402784509599840293369413823812952825018/1202908016584466665365656523947583907209924809", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "8323724/21638825", "-27172533192131/19220853765539", "-36875772274977623535/82217075521642728908", "-164600159247371360638813679/961692631845074659434120589", "2358448347619473266836547221629719/2569017889316061139763723235168233", "225676515585343928106416811005192933684/775398661183878235351906920111182739055", "2818166064366321440676942363526395927468157557/4811632066337866661462626095790335628839699236", "-1138129893930869374982876397412386560047391622830018/2081338214618748873771841651477919570543738446031711", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1488314/4327765", "-911488350255/19220853765539", "-1476415805322872239/82217075521642728908", "-415992868128504037951128091/961692631845074659434120589", "1789890121615898307600676015738723/2569017889316061139763723235168233", "-15068751176067134307553256177298577692506/20935763851964712354501486843001933954485", "7118391783793471222734441346416385996997634973/14434896199013599984387878287371006886519097708", "-3551663291635872633101440921792839460650835522454240/6244014643856246621315524954433758711631215338095133", "78921933254314257475643725041738713179779683374599996202301/198563774465926027656164885300446433256003089045834143153239", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "359737/1664525", "-8272515990739/19220853765539", "-26198747174949724909/82217075521642728908", "287153930515470525990178919/961692631845074659434120589", "-1033036738277835642513684748122566/2569017889316061139763723235168233", "5964913980909931590669982456844314834486/20935763851964712354501486843001933954485", "-3836506116683005493833045595739146052139096579/7217448099506799992193939143685503443259548854", "-1105688381776089135048977703796583276436460534613777/6244014643856246621315524954433758711631215338095133", "725076888571316425488087276799406181085583806487953170070/8633207585475044680702821100019410141565351697644962745793", "-6583361038263656154779247194776575663459733526349342932465000414/49886250156017593722298561659347947981479382148895607169579181115", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "5623964/21638825", "336456762284/19220853765539", "23967147227073026841/82217075521642728908", "353555037768713908020435893/961692631845074659434120589", "2130941128110945348469899230617407/5138035778632122279527446470336466", "-1614785410398819088387308744073844687783/6978587950654904118167162281000644651495", "-1825409538880434086226102538830233947919299843/2405816033168933330731313047895167814419849618", "-1447008645171536109543121503896709465975504248039526/2081338214618748873771841651477919570543738446031711", "1230471450147438379119050308588176934046936287861535988770/66187924821975342552054961766815477752001029681944714384413", "338338671016702035683895216207872764843603422772985278718227639846/947838752964334280723672671527611011648108260829016536222004441185", "8778002852200610755282162069774817859098207466499561047923178338252817/55905689897770985236455931459204141595579842169364523328853414853454023", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "128179/332905", "-4774652902240/19220853765539", "2438306956023623501/41108537760821364454", "-82130099572359317849951534/961692631845074659434120589", "975490619304363080428652049119183/2569017889316061139763723235168233", "-301056256996113780537859862367095104748/2326195983551634706055720760333548217165", "-320760615419973560092463852324340080139499659/2405816033168933330731313047895167814419849618", "149825104868569286304352666477212197603254086777557/2081338214618748873771841651477919570543738446031711", "-6122202786807079194899854548019432980452562099759383258706/66187924821975342552054961766815477752001029681944714384413", "16470931356007987306082884405978682425589857546400005705572324746/189567750592866856144734534305522202329621652165803307244400888237", "1854209078157027784427575192418574656073856322564871440939344594301140/55905689897770985236455931459204141595579842169364523328853414853454023", "2387590305371753239013570701357532748917258985426801007596446863757217227208449/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-2350116/21638825", "1176289897554/19220853765539", "6534966085122229511/41108537760821364454", "179013883773868360375065518/961692631845074659434120589", "-287738665068414759519596120710845/2569017889316061139763723235168233", "-479514487515133734848594135404347085408/20935763851964712354501486843001933954485", "-1201471009114820667047038169784577563761455141/14434896199013599984387878287371006886519097708", "1350823775145328690211148513895457540306167873125323/6244014643856246621315524954433758711631215338095133", "-25952978358680082006019272979395680066477835795986747878049/198563774465926027656164885300446433256003089045834143153239", "5734142940433790098214915963479384450233392163645638743994204564/49886250156017593722298561659347947981479382148895607169579181115", "53833352520369425265746963312151475360849872583546722337633227334469146/167717069693312955709367794377612424786739526508093569986560244560362069", "-544988660687743598077060887441262279762282096859524291101723744730752687637635/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-264646657430520128229671934369902506447942701526789495174921587800668604205820572028/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "356354/4327765", "-738842415780/19220853765539", "11323205056174458959/20554268880410682227", "-6585906367119003019817988/961692631845074659434120589", "1241679766846311528961999342714067/5138035778632122279527446470336466", "2072717689426941400009982080712230906607/20935763851964712354501486843001933954485", "3103191061265406357719632479051383335505132947/7217448099506799992193939143685503443259548854", "40059532158573239456543073081962965620277280999480/6244014643856246621315524954433758711631215338095133", "2810297605461742134745283983474488107702103955036246552150/28366253495132289665166412185778061893714727006547734736177", "-114503253999473219678578285288308571616217459250790226904634816014/947838752964334280723672671527611011648108260829016536222004441185", "-7061939140816541993373862966568951562997468666633091448943103241397928/55905689897770985236455931459204141595579842169364523328853414853454023", "949196521261730839934009345313390900702217144722442229726584490988409194921117/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-1504214860512535486017816384118004260574463321407769006286321380670081277748985559873/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "-3846154461194776004990160197681483340979299069116230763579485168512518545702967277057204489/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "39398/4327765", "-18575633595060/19220853765539", "-22385936115613091777/41108537760821364454", "-858020785100897924191533430/961692631845074659434120589", "4427948046518661017237313342268247/5138035778632122279527446470336466", "-969786601873428029502445310942314655689/6978587950654904118167162281000644651495", "2302018392519080131891498951002195229270965023/1202908016584466665365656523947583907209924809", "-1120525218026164710659543451759574399214595779476159/2081338214618748873771841651477919570543738446031711", "23505127124076862920108107512939342912714590527433503218888/66187924821975342552054961766815477752001029681944714384413", "150625234611924539523316027837591262972122306501111075290344613451/947838752964334280723672671527611011648108260829016536222004441185", "-12295264855507692741407592549278872978035361901723827197416760050532848/55905689897770985236455931459204141595579842169364523328853414853454023", "9903091026224958423829872628314803238290273425073783247522990616654692443002760/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "137869027907550959821329024370925324570169935732716824209318037772714350546610830875/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "-1533715164848207368159048071805915676458259113679476819916151954447848527412760107509811052/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "16579787575823632993257051378669284923406695575673307541844611995112708886548095570957216130062483/19468479225470548738274706614709761656583360935160228181874738758135087274425036450452725413966336", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-196597/21638825", "-40783061758782/19220853765539", "27359963064618896417/82217075521642728908", "16280113915548503009864669/961692631845074659434120589", "-85749424381753446843093847550061/2569017889316061139763723235168233", "-3356083439902557306093206407273391644918/6978587950654904118167162281000644651495", "2178509884354034709750256395808401227324528699/4811632066337866661462626095790335628839699236", "1662071441547294908795363951434668687844163647724127/2081338214618748873771841651477919570543738446031711", "-2042138038854937798994015201402783924981166491523126870541/66187924821975342552054961766815477752001029681944714384413", "-58671403201398413340922936605731859663792260221809309164764560371/947838752964334280723672671527611011648108260829016536222004441185", "-43996676322869502888659749729460001281407363967285117730442854597375492/55905689897770985236455931459204141595579842169364523328853414853454023", "-1668955999823522617857954724393502359733229078196297712819374615398535393125055/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-3131571238653436977364426680508349425304453628195270718366201222397936533049881804828/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "11961674556393979062009818517071290430814873362634742000616377718413216305335333777166709644/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "2028392573150951894865051853052535590569365471972399617708519288019265251938081947781799421155023/2433559903183818592284338326838720207072920116895028522734342344766885909303129556306590676745792", "41341598849781470580469088209906251048977860092105064673183871346668423260987057463285482664396498276712/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "6566227/21638825", "29474966378462/19220853765539", "39194003642787175013/82217075521642728908", "-354305837827333490803441011/961692631845074659434120589", "2280847132915639422878763996727325/2569017889316061139763723235168233", "-4479514157328016114218816906273360114356/20935763851964712354501486843001933954485", "5930799838890308629551191912589400467025697489/7217448099506799992193939143685503443259548854", "-605397466846981550875229110173537634651198716145157/6244014643856246621315524954433758711631215338095133", "13245946938431505381191770811031503625814311353642585697134/198563774465926027656164885300446433256003089045834143153239", "588065570018278359792158231005729367829571696824191698904838984409/947838752964334280723672671527611011648108260829016536222004441185", "-116002521061849195951982708750578109719974801990350236473828527470389731/167717069693312955709367794377612424786739526508093569986560244560362069", "1920832129456948178632013111541258683427311872365632594804908148327531715987000/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "313505392257610532869226116753874612205226426459230793845064248166611432445590070248/1655726479120340055879373816292594858628924720602578552017063533844214702921241239403", "8269010425301589649472639835337246523408090070116400454343363099430764877268157756927900116/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "121893835416236203286931096229528916240934707624586858581607249107495965336533133388884496165455/202796658598651549357028193903226683922743343074585710227861862063907159108594129692215889728816", "-4919017246708134716594092705690193602060460186819606429384548447653421936233374147450039312804114977056/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "31824825906735840318024965348798490011375848890406627869456577380117904746019836392124174902675706655777583481/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-2449/6227", "10214347334800/19220853765539", "84170196059699764515/82217075521642728908", "146900667624110784658527535/961692631845074659434120589", "37112961122937606070622724893172/2569017889316061139763723235168233", "-51718963255210273458860942109657642304/225115740343706584457005234870988537145", "-59190976270357138184112371902033310053676812/1202908016584466665365656523947583907209924809", "1185190837070078890114336520618522111348067494907757/2081338214618748873771841651477919570543738446031711", "-19439658680930635254849753648098717461564506253597900423660/66187924821975342552054961766815477752001029681944714384413", "-56841819347703753703100459958287334639341307874039416511975077384/947838752964334280723672671527611011648108260829016536222004441185", "-170043447697288021687924587047906018079226013401306404603928010729154949/167717069693312955709367794377612424786739526508093569986560244560362069", "-2066216267849927496844984411915111197147990202009492452260100069247792471569069/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-1157147298219629814218409645901655800938116127007288521892887088259400503895890862950/1655726479120340055879373816292594858628924720602578552017063533844214702921241239403", "-11081293232218361432169825049649583988558516055251469875637762879972421113737076924378363965/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "3584069731647879838530715644637117700365752350109881941125468141696298911932539546364850885856493/4867119806367637184568676653677440414145840233790057045468684689533771818606259112613181353491584", "-22276403175514970633542086597442553270513551920977892723556819402043959623162331584068185589358327409636/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "-4555333851420081616397083768115816356397295273283781772118685764260846583100481794080542950878910751909187809/76413957861030048163661510024317638136027689410881292332594462116679119040574430526060855325892498035941067603", "49428543525861272119868697596483381479413172877644981003190315085639724554974099490395252443479387759345108357892810/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "34181/155675", "-56267187884621/19220853765539", "14659567479687406049/82217075521642728908", "1295490710230442260635939413/961692631845074659434120589", "-208770154182831255023015256912527/2569017889316061139763723235168233", "2499861056938191885224228720174224240358/20935763851964712354501486843001933954485", "-21028340503461896331571347195944511993227281009/14434896199013599984387878287371006886519097708", "2832401106165371863629293006761726375900765131395183/6244014643856246621315524954433758711631215338095133", "-26761622309520283031700711214711189400431483651921895921777/198563774465926027656164885300446433256003089045834143153239", "-332359444577246297120260111191264579850547511810888850491325754992/947838752964334280723672671527611011648108260829016536222004441185", "16091271662390059348544540593260487445893973759760993859947799006838841/55905689897770985236455931459204141595579842169364523328853414853454023", "-7050222463107279322447020764534974641866656186614068253231968952113802604805865/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-6839240109784165889298650996897527642492735227702183025795193957823347843608914518575/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "13581693351016509064089233184810919927357578977639348977636246279927092074846944776221201184/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "-2332573326346913710811092166863164608745198346635558457378346998829270018912099505886472864920207/6489493075156849579424902204903253885527786978386742727291579586045029091475012150150908471322112", "-71019094639264915632663148607234192365644941893679668867501989367441815050149929718151436167149568378439/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "-8714791483284803277317299675152774834088377892685546730044485379363985101217666132355152063321261118474275175/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "-70428482296086575533185200130253448368639386347369113840708285202828854393156450049942940287891484641096150871762921/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "-861962487654567330508260358907355318954422931424506326412478011692408964106886684474171962184546014601353026202286386403/41681432276581161540443959465172074967344860854361468043113363759661811254838090202885737197699254239237716692733633334955", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "14193/4327765", "-5630238129160/19220853765539", "2594347008132002814/20554268880410682227", "105131465204598299660864796/961692631845074659434120589", "750177080737347837831147071569821/5138035778632122279527446470336466", "-190834861289952179112182617708459245007/20935763851964712354501486843001933954485", "-368686836302141036708989591327295834466531691/3608724049753399996096969571842751721629774427", "526921361061124822731157518581132191920768887395346/6244014643856246621315524954433758711631215338095133", "-12981514045297161701226214469555980184287354247389894223096/198563774465926027656164885300446433256003089045834143153239", "9007464855317729481783396311386585030589573063194623441963468522/947838752964334280723672671527611011648108260829016536222004441185", "-4074071427160584545063587743100467449311964207794356286364730392399083/167717069693312955709367794377612424786739526508093569986560244560362069", "1755032252820270762663695990073189119455855846870848642919658069569245141455294/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-401119131080532490699797993393308725787180093219520803781508077436370721679625768918/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "10651397098028157937454455058764890701925169265664614211068587272452594261683695696801680324/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "353575076824977379827153359389372074775460447755161799570318566108651056067131351824373820503195/6489493075156849579424902204903253885527786978386742727291579586045029091475012150150908471322112", "1787233736419393073428759913708697558186863061558661381976317915474949867788876226624467416066239561139/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "14208143473718510386341588683906438301674433877158110558726595286682730178940273953720093301158161160142844857/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "-354900558356398199138553389198349991380953598786985907481338909304991490926571187525650339563732850877218609704171/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "138078892057408360323964238146587365173210300823339810105933994878064844431536011390731554616283904472550781461035601904/2778762151772077436029597297678138331156324056957431202874224250644120750322539346859049146513283615949181112848908888997", "1324614604693827502376263056566045340895096920457171730459194518293468741732685645894522224049922814524506613352037180617959575/10044725419808068736483829366069892494006489471761836184408845860551944706856335371991250071930421156304711278234203764321050397", "1", "0", "0", "0", "0", "0", "0" ], [ "14265487/21638825", "-41677766973003/19220853765539", "-14210972627295006589/82217075521642728908", "-217542835384815842278060261/961692631845074659434120589", "2716017654937431074157527716544599/5138035778632122279527446470336466", "7177311078144486420463873372346560793341/20935763851964712354501486843001933954485", "3875559162961405225262370541477218263430643468/3608724049753399996096969571842751721629774427", "-2679186898340994085909497525909197363157282929480360/6244014643856246621315524954433758711631215338095133", "-9599254854381454431124125538411356071999907555041188032448/28366253495132289665166412185778061893714727006547734736177", "-111603878788223764778893791665505399219035988521985883066973897911/189567750592866856144734534305522202329621652165803307244400888237", "2857968969368793743193859127262787906524013794331089977898012039831860/167717069693312955709367794377612424786739526508093569986560244560362069", "11411346982168573826951594205938075736398500433370301163329421563786672902560301/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "1125854123092096305185508480910369550968404735730524643802140653207820685762914886262/1655726479120340055879373816292594858628924720602578552017063533844214702921241239403", "-31213835925080491683161245439241106324695677858300568014275712428249358346896811247681013962/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "7301708876500263275383502530709328023581488560494983158585894301205045605840887797981289771770081/9734239612735274369137353307354880828291680467580114090937369379067543637212518225226362706983168", "48371539631155076023003888150252320592158818979905221456632731638713338863463251606181055194266498904006/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "-23238219663059357930894492708922748864401006593748327222790313504260501203838509504208998198772572282413770681/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "-3388369279817494055503603261368057771653733959184094004062165058731303611058542587905911934402968095585398449367047/18643709622258811194474732192564012861553939265724170815552994292138276826462458260869037551554300914793123396919063", "-569167753898221778057227949052265106450886387417321154547606473169921586285962670746043488554644176696459200249000148837/13893810758860387180147986488390691655781620284787156014371121253220603751612696734295245732566418079745905564244544444985", "1598815952037009873055858125990502531645620022150979556656115911531396355953888930877755904313508194221228416194034301215502459/10044725419808068736483829366069892494006489471761836184408845860551944706856335371991250071930421156304711278234203764321050397", "1478495506655658921005854822790412856224064723748303111148711311954735419014242919244109528107518350336080692894118906687306563381831/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "1", "0", "0", "0", "0", "0" ], [ "26849611/21638825", "-5141725457534/19220853765539", "5685339952313354079/82217075521642728908", "962179430966149219045347071/961692631845074659434120589", "-2574907867006433023810368579691561/5138035778632122279527446470336466", "2324973082537437744021414038563082585/5002572007637924099044560774910856381", "-12848886825846304264610779180839724751683522095/4811632066337866661462626095790335628839699236", "-2707124453048911713964592999598931529421080961028566/2081338214618748873771841651477919570543738446031711", "24968024845413020136061261516245200351886354167545870739145/66187924821975342552054961766815477752001029681944714384413", "-77180453964749800734819245317960503284397719884720635613732357396/189567750592866856144734534305522202329621652165803307244400888237", "210291331221643045659411437022995029890657751134465503176358645261670040/167717069693312955709367794377612424786739526508093569986560244560362069", "4301960607461294253339120350428561232576898241010182124427642441506829888190754/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "4513170757523387193912445229216167779758840730110530058375025377028630934834102443698/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "-11967541204998786523269991957245721058504745339239493347368762664400443433372971045326237979/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "-612886440902488088164557434667623371687116817625017109880921125945966978902279326435590517328331/1216779951591909296142169163419360103536460058447514261367171172383442954651564778153295338372896", "-26559189926435386438569794204066755291380559587673643999614305500800364113395980806156449891707019492368/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "-5649249560574566306510579563419653580264906850237364554833404734923461990980370890272130056173600851153294699/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "-98472891883438443199008852675562118525005403693834458282328031804872629844826480631050704448571101931170698094446673/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "-25413801704192405671187601663032763796903338691065239593034081009154380649739516812495278474776080520571868709742377504097/41681432276581161540443959465172074967344860854361468043113363759661811254838090202885737197699254239237716692733633334955", "8191824249784805630360729315601346430469378496399630909478562204337158954903715637225226522308903991380153923706316015032895521/20089450839616137472967658732139784988012978943523672368817691721103889413712670743982500143860842312609422556468407528642100794", "600640796535260791839546087399936310758863721175109229029191934732354035600798178840825025566622486633598948790022092764691901167844/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "11981777339518160649486605782800052440533679489140085117043476578639974756182366791120439439810453499487637517793837513929572504351668971/4286399897294495474149536345608811127278607910019748119110989457411895048572087814960910918474502047642533988026909337848498867142343217090", "1", "0", "0", "0", "0" ], [ "-9014352/21638825", "-19512378288712/19220853765539", "-6756431278480596431/82217075521642728908", "-249498979285477792262279/961692631845074659434120589", "2493477833881458095591918130886695/2569017889316061139763723235168233", "-623160800532665322767597491864952256652/2326195983551634706055720760333548217165", "2485793155898377003536364936187298183490393653/4811632066337866661462626095790335628839699236", "367718845377302524473237478953440897856689764635716/2081338214618748873771841651477919570543738446031711", "20116451270160021188142334500925006488391574756013820148953/66187924821975342552054961766815477752001029681944714384413", "80407455008730285912655426978657481671378772196300381358420235062/189567750592866856144734534305522202329621652165803307244400888237", "-17508261753460656126008051117506730194119508449754302943928725299485035/55905689897770985236455931459204141595579842169364523328853414853454023", "-819095017901343043757657008465507928814270122397929465106327738196154331421532/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-1416153034222709714228220196402584404892602002340512887763063360757339651740069590220/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "8156582524691030395204700297572893025324411226995363160531530319010584360402277148000939362/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "251573027531530957742255746258283573694417592394731226459318524663674851602534666346882603905915/19468479225470548738274706614709761656583360935160228181874738758135087274425036450452725413966336", "-1328376202770265160040624017753249584326278385993451993838940420808156652803787226365967619288955715791/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "287526439907847672006506832716742711946112979444906761694287901935034406809410905137517232925712530272899878/2065242104352163463882743514170746976649397011104899792772823300450787001096606230434077170970067514484893719", "47886304897677007796689795569689305548024341396262072379665502380328774862960735791365014887393582065534423409005994/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "-4807987630911142967407112556083060619037072242681311507261743346358957963407805489452452655737115644551364653520593491269/27787621517720774360295972976781383311563240569574312028742242506441207503225393468590491465132836159491811128489088889970", "3104583362372444987324683678529497515948499745242536809627608357503249341906655666892221144623475603962395735484795758614224883/20089450839616137472967658732139784988012978943523672368817691721103889413712670743982500143860842312609422556468407528642100794", "266059770527949558890029653132018783466121235606895061107190002084591294650244655741848846303484414299674607483921974167818149005263/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "-56536148597901636131499286450718402583853289623715991760966359207341914654143062256697342519708490369233334758187649437347795146128647397/428639989729449547414953634560881112727860791001974811911098945741189504857208781496091091847450204764253398802690933784849886714234321709", "-714219748863922274155494525306137952655178178267164880153736486210183579038924154379107130520727586377316011243026092593897521445067140306734565/8267083860577636585126780211895738869755238867461680845054710644701927372197390569594934531069429078069464229261769206637945413631316898605587548", "1", "0", "0", "0" ], [ "2605212/21638825", "6850059219272/19220853765539", "-867334696421679443/20554268880410682227", "115740696627324171647173624/961692631845074659434120589", "523384038448289167530181553765463/2569017889316061139763723235168233", "97589262745212477073605946283836947064/775398661183878235351906920111182739055", "-35281233754676880701424268815480457629908109/2405816033168933330731313047895167814419849618", "-518276008965576554147848144463036693477365657230088/2081338214618748873771841651477919570543738446031711", "1374197729801169216372606806285802291715560420594428798222/9455417831710763221722137395259353964571575668849244912059", "17266397429007326268754943025549179987580211372049886023430758032/86167159360394025520333879229782819240737114620819685111091312835", "75476185550999958842388751492492941375036885426140504343752201835502367/167717069693312955709367794377612424786739526508093569986560244560362069", "288611140382059891000606435415600183801377777061936072180089363195328797559230/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "37305076764223880022613308088329889584043198346972521915870859075821143518275135498/1655726479120340055879373816292594858628924720602578552017063533844214702921241239403", "11063281055319365350119775217500311161169998495951336903615399606676762663810400161853629161/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "-3300545983276374593235687200855902231645311556017161901686922487927739141329406601685582743158981/9734239612735274369137353307354880828291680467580114090937369379067543637212518225226362706983168", "-5812530582996209727467102831910620803515213902127202890503882446814050965089568985717735001790679047454/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "-6936347260352328894657537364783542510698234993715387325349291869099154868559574092046072942424752031747327795/76413957861030048163661510024317638136027689410881292332594462116679119040574430526060855325892498035941067603", "363619995425796604602810656506942222204914152718840678032921816726935425549674103219443550833703854772059421547968/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "-489357362430406389735072117912097498891755919890350491445764374665281672834899924061288339542995053957990215762320882801/9262540505906924786765324325593794437187746856524770676247414168813735834408464489530163821710945386497270376163029629990", "549705975147613297983697796202254045179096780064447720328096408158735447723908738947447769747272426191485242393204323851450008/10044725419808068736483829366069892494006489471761836184408845860551944706856335371991250071930421156304711278234203764321050397", "245364688598060716329826690762453564634228306223701041660381094144458390527644579230364297876032882974092242257385498063400970418571/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "-259972424224764206535258826261366389421787193317798943556130885300851678323312234125907004092901831925631514843455400945437758748870964724/2143199948647247737074768172804405563639303955009874059555494728705947524286043907480455459237251023821266994013454668924249433571171608545", "15023345780295871970146516977045509135233061043269216368087384946715975181654358639765563601545457267493402134274470436068429193170773982139829/2066770965144409146281695052973934717438809716865420211263677661175481843049347642398733632767357269517366057315442301659486353407829224651396887", "601348320071260159283068253770494238496044758391192826443551983489438445624057107733233100879653565167580345308926321306988208846385996213752758233264/7130079850749596593532793022319644052271081137312401135396682830064049004705442500911196276352197780986198177850924238386209566404015700683574970811373", "1", "0", "0" ], [ "-9952367/21638825", "17756291714073/19220853765539", "26178950283947701088/20554268880410682227", "81246903551015324607548088/961692631845074659434120589", "1558880356919774072947070603449321/5138035778632122279527446470336466", "-1290155747772893026111754416726625616973/2326195983551634706055720760333548217165", "-503412818758916169494348750003733839745190482/1202908016584466665365656523947583907209924809", "1181442533738319269098239857604313781924569346804401/2081338214618748873771841651477919570543738446031711", "-21927838460257115703102566866378009719238152386496261324508/66187924821975342552054961766815477752001029681944714384413", "367219070486505782943579813381339515968370949858277051921814354024/947838752964334280723672671527611011648108260829016536222004441185", "-69560817043813419376386754784529501325771401203833100167832515671240867/55905689897770985236455931459204141595579842169364523328853414853454023", "-142502308482227499842755585387642358090416077752326078029590618444169311937527/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-9747711954283654423302909318884241918441407464973033837683481145204371948725318054989/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "13474244750213957374506438984602905760214969257802300224689603645359027342684834618061973883/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "2453374393287697867049278552251275999261971844883271910344605943488106726442051657403982639281585/3244746537578424789712451102451626942763893489193371363645789793022514545737506075075454235661056", "-8152816400282197586505941905001273198163770171316150784055680872632663227696842229071127536555149309454/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "78570105226613402139663524692037809621096578668793983275060452839096683836148839798653732276779447258531857663/152827915722060096327323020048635276272055378821762584665188924233358238081148861052121710651784996071882135206", "107343901199184104304965164679933856041371387115334118413835940277719034519252505199973642260038638016079888945035255/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "18524845539695057314496857681489681527257246475144941222300847775850802306479191658584243285887317098740850614618224141074/41681432276581161540443959465172074967344860854361468043113363759661811254838090202885737197699254239237716692733633334955", "962684001198868706167954005766372206986252830572045134340389494138683089078972938335477256274426408280327399640435583971107623/20089450839616137472967658732139784988012978943523672368817691721103889413712670743982500143860842312609422556468407528642100794", "435111928727494354317142378331615776301311712004085762177599425838929383429461259662298646392202544301406349515177161006385574799631/1084266217049731799910663039907056513103000483938718333626481529014595785593082517589169308375099883892638704632966935659445256843153", "-58807983111860588083096976806548676468461559454124042683712508190042586783967242054891691939577045452957924210591265599161903988290301297/4286399897294495474149536345608811127278607910019748119110989457411895048572087814960910918474502047642533988026909337848498867142343217090", "-272947937138516192462611195680032526928334820496967057528450860808800853645948567866921304552366064275736823602914234521620381859167267480215774/2066770965144409146281695052973934717438809716865420211263677661175481843049347642398733632767357269517366057315442301659486353407829224651396887", "-4574973480300221631414020729330945904266481424832199775143372383417287617682414381002865184023715983101317577832384694849167047192188064463095045252556/21390239552248789780598379066958932156813243411937203406190048490192147014116327502733588829056593342958594533552772715158628699212047102050724912434119", "-1496706650566062712232968109456398057835287000168982704933085895084432930466837575685149321814199372320978368348847054085281090348230591300330476848368108810/1934104812660456084454261536888668894676458836471125740892608445037711038086174654987172585177882407966168894426509906307271206553179613929698539413257362353", "1", "0" ], [ "-769776/4327765", "8711554167995/19220853765539", "-29091474486893179973/82217075521642728908", "32348912844698626144109927/961692631845074659434120589", "-626707075273934463574444889437041/5138035778632122279527446470336466", "-2823682276715568513052446128133616930349/20935763851964712354501486843001933954485", "-8085789793033858870936910584478912191798627763/14434896199013599984387878287371006886519097708", "2305104741423680841274695402578105562396118343058394/6244014643856246621315524954433758711631215338095133", "454099364210441190278958464720551603552876301729182474523/28366253495132289665166412185778061893714727006547734736177", "74141033074933694063843572595114669185596843456989185135861834473/947838752964334280723672671527611011648108260829016536222004441185", "-95279040393822302092231543880552836146526850628282859290085389407880037/167717069693312955709367794377612424786739526508093569986560244560362069", "-1836560564185695491136845002052105656828924061867289711293533627498619668402961/12837255361837217856373609093077801885208094677614094537325478464508363061030829", "-1614957684286246317968380250479311769210860775221093450074472071059099912011308649233/11590085353842380391155616714048164010402473044218049864119444736909502920448688675821", "7184884272729893139811793545146423929361051763889230519121350030422667466015477763420539072/25304737507864499730796915985562376931826608491234674868761977942901178132237886936692087951", "-500661642261541198812773209075300007053959335343676026488060703516883666066675703073461454463145/9734239612735274369137353307354880828291680467580114090937369379067543637212518225226362706983168", "-24265229635954487145576628835142846606678928035148435744480362605616569195345092430480304509642219584630/97797483509125537120276284379768777354914528903905839988687813740270196606326897061367938002965646094969", "13034231993055148409407735951032718061479258238874057385988619875039506908799762851268536964062169381400211683/76413957861030048163661510024317638136027689410881292332594462116679119040574430526060855325892498035941067603", "41616754442777512704438127495279012239720386773429891152923698200426702824914463621702667650266471434913081344534118/205080805844846923139222054118204141477093331922965878971082937213521045091087040869559413067097310062724357366109693", "4320297497662849058299944862354936447122418851888269045072320246387183570089585393022995837442720937979292768106112007477/50017718731897393848532751358206489960813833025233761651736036511594173505805708243462884637239105087085260031280360001946", "-8129744536744738706175393155107026749430672895146785972581131582559969864197842490823647088524125815777830940351845980771420065/60268352518848412418902976196419354964038936830571017106453075163311668241138012231947500431582526937828267669405222585926302382", "-7981152416395475382683821383463788727105837962965693287142768719219503544140230364131724400080615313006508617627882643658446602882265/6505597302298390799463978239442339078618002903632310001758889174087574713558495105535015850250599303355832227797801613956671541058918", "-2499898087356623526073450018219089474769630572419692199006530634807388500005559227526166571547524898653740075402300381564697500465257213737/12859199691883486422448609036826433381835823730059244357332968372235685145716263444882732755423506142927601964080728013545496601427029651270", "-374904886303584296782210386165728955040754759364065259845000025079567610961138181317292043673092805733328747918167261735182627744560905138237634/6200312895433227438845085158921804152316429150596260633791032983526445529148042927196200898302071808552098171946326904978459060223487673954190661", "-8725467338260100326562171626007550007342143185390776861741559584664091248382769161492357376358137625202003198785946802149263695448572735252835928720400/64170718656746369341795137200876796470439730235811610218570145470576441042348982508200766487169780028875783600658318145475886097636141306152174737302357", "-4629504978469384308453174624332281492207684912718375720173210161980005327563754375564318128440404420848010015506905299083976873726270096180548020992472085449/5802314437981368253362784610666006684029376509413377222677825335113133114258523964961517755533647223898506683279529718921813619659538841789095618239772087059", "1788340203541859990935974311255128919370215215935809303930493978287058985612246564294776744942914762681284134261430281626609417893663440664881533893279079529886163/4901241021686591017135440437712974697733244870544936013913410983193103629171095430556024091124323092883470470477890458522301233101340607541004413035568577225508117", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "5497571", "116459807114612/5497571", "230463790325663091369/116459807114612", "2832677216948119172647607770/230463790325663091369", "88775005697376683078106916798058681/2832677216948119172647607770", "1188953655075915851853003755487819451123245/88775005697376683078106916798058681", "525480683981912276687499434611558048779917623804/1188953655075915851853003755487819451123245", "7602779807890812582079933600291583262810748160100125755/525480683981912276687499434611558048779917623804", "14457133534575895981631322572858826899406824367863187516660681/7602779807890812582079933600291583262810748160100125755", "57463238026057940772797443749133883867188141099220866275435033332408/14457133534575895981631322572858826899406824367863187516660681", "59597467165445891976298201257606235271411725679732828066049546727576220269/14365809506514485193199360937283470966797035274805216568858758333102", "634252444252815461264752322323262987935956599676365462708504854344170683178509611/238389868661783567905192805030424941085646902718931312264198186910304881076", "26784327725709865474303511468155266163410724721866675022586161564412692703671828451832/30202497345372164822131062967774427996950314270303117271833564492579556341833791", "89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335/187490294079969058320124580277086863143875073053066725158103130950888848925702799162824", "65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661/53758423342623327120955381707961471287432905005984778254935004229901863528848544139427766001", "636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477/327658826417831101328126222577485582324612989891469188675299449738710653238591597755714006501683305", "432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "974812255967131760961650683024788860223872969529459363467801782814183855400246091120012795839484480018306248688671936536577544098034278/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597/162468709327855293493608447170798143370645494921576560577966963802363975900041015186668799306580746669717708114778656089429590683005713", "280070256488662344563643167884306726719429041722243580851231973223636144890503132822491336810949975404681836605020868849081036017534656603067797823/342316739834473647632905382743043026551034856859059048502435074156983186504304312567832930160916010250866212203433421537582017268836042811194", "330084211868767720878081295179951138219239079243577623389488432133070250587068306553070903610669259556876897160510627745473771182881500876745943686735178/280070256488662344563643167884306726719429041722243580851231973223636144890503132822491336810949975404681836605020868849081036017534656603067797823", "387370202298328952841734074741226159998708757595685237855957437098716608003406950622039400549558673764862670663466066327834240530485731994767105499801050305573/990252635606303162634243885539853414657717237730732870168465296399210751761204919659212710832007778670630691481531883236421313548644502630237831060205534", "39713318709565601214293303782402980200126561149942272814608100410059761792750766553295853046023272832061727203318593175410101730260594302568162511015542919560421025/387370202298328952841734074741226159998708757595685237855957437098716608003406950622039400549558673764862670663466066327834240530485731994767105499801050305573", "4275996723645910471498112093881010384403504495182398091637789620943636539892427305409591442648376639371673936279548597839081096789035975505379653166632269569988590228318/4412590967729511246032589309155886688902951238882474757178677823339973532527862950366205894002585870229080800368732575045566858917843811396462501223949213284491225" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4540900/5497571", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1287392/5497571", "-12400723226327/116459807114612", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1201176/5497571", "28983821501915/116459807114612", "98191395878236040143/230463790325663091369", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-5290054/5497571", "-22269117374953/29114951778653", "474356783144755819996/230463790325663091369", "-3552029890821940337873350919/2832677216948119172647607770", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-8338454/5497571", "-28355965627259/116459807114612", "-326198868359342031487/230463790325663091369", "14162240424424729556931287/283267721694811917264760777", "16643704284639824589793734702706930/88775005697376683078106916798058681", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-428236/5497571", "10994397856479/116459807114612", "13439965544547935345/76821263441887697123", "84607021421404939643598237/2832677216948119172647607770", "6023836906925185846319089955982837/88775005697376683078106916798058681", "76744115500604883336401098692308542300031/1188953655075915851853003755487819451123245", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "618762/5497571", "-13423396416539/116459807114612", "64736547350901872339/76821263441887697123", "-568515494845160677628700201/2832677216948119172647607770", "69107694084044836578642660966865699/88775005697376683078106916798058681", "-305112106413021247163753813047067354655592/1188953655075915851853003755487819451123245", "1831709879527314923288714443047198246314014059547/525480683981912276687499434611558048779917623804", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "3152538/5497571", "82894103493547/116459807114612", "-42956422397857037683/76821263441887697123", "-159137202755155749897888159/2832677216948119172647607770", "-909640955689009473469575053374449/88775005697376683078106916798058681", "-139649646018095113112455334826829999501564/1188953655075915851853003755487819451123245", "-1189560553539811110492082800536746260292227323/10105397768882928397836527588683808630383031227", "1632571271589160695763109276584469296029316371437439436/7602779807890812582079933600291583262810748160100125755", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1006711/5497571", "41235351180133/116459807114612", "196146175209413274589/230463790325663091369", "180679087484089996806322316/1416338608474059586323803885", "-13621307365401214276463213878263638/88775005697376683078106916798058681", "704378476449456120131814605228524178189962/1188953655075915851853003755487819451123245", "-1328412101248162696765503006368429869387629166297/525480683981912276687499434611558048779917623804", "-423268160739794020473255110688267549223888578586677369/1520555961578162516415986720058316652562149632020025151", "-376970241864434703094160085637680770414408964003104862478705/14457133534575895981631322572858826899406824367863187516660681", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "344604/5497571", "33445726437815/116459807114612", "-265730391941743542533/230463790325663091369", "769883810991093594531512857/2832677216948119172647607770", "13107667703055066417148902002236317/88775005697376683078106916798058681", "133410000993925616563665557190753511201172/1188953655075915851853003755487819451123245", "144042097356093577567947854357256211524675699577/131370170995478069171874858652889512194979405951", "159466859199676594630047097750930519384523166636298180/1520555961578162516415986720058316652562149632020025151", "-8648928698603990837564103789963918251754960228174787420147025/14457133534575895981631322572858826899406824367863187516660681", "11832076709424496004061290459973778844461908046802895116059434362999/28731619013028970386398721874566941933594070549610433137717516666204", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-135856/177341", "-1978579931015/29114951778653", "-207190277421973608436/230463790325663091369", "2456483409438397969047476117/2832677216948119172647607770", "-4444348131223926371558494912568179/12682143671053811868300988114008383", "245627772142542308060375980118652638168896/396317885025305283951001251829273150374415", "-718329918186469928028496695992411675307662005593/525480683981912276687499434611558048779917623804", "-4359153144938513393789344791899699228642979104226032149/7602779807890812582079933600291583262810748160100125755", "-1773709978490061398910338698160853017145564831546655199774723/4819044511525298660543774190952942299802274789287729172220227", "3317893712521795823807929202304385575948346839190777259188508668527/57463238026057940772797443749133883867188141099220866275435033332408", "62149167968450059177746353352804916195647971926099213508482347867297881539/119194934330891783952596402515212470542823451359465656132099093455152440538", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1763362/5497571", "22343304885497/116459807114612", "-3348621446030698977/76821263441887697123", "24573028205790066606540417/1416338608474059586323803885", "2914857951123296020436502382784294/88775005697376683078106916798058681", "140648389113660570855284361498012266864032/1188953655075915851853003755487819451123245", "-346580524159015970864077711397949780235459578577/525480683981912276687499434611558048779917623804", "42420685532187747296730764685720214694394683225304487/1520555961578162516415986720058316652562149632020025151", "4640105007292288379580622664562957715634945268676211089774105/14457133534575895981631322572858826899406824367863187516660681", "5515270908425103536128096796483901679807269025853682235550234998835/28731619013028970386398721874566941933594070549610433137717516666204", "10421567012583592504826460714776635504757752701294378900074290686085304123/59597467165445891976298201257606235271411725679732828066049546727576220269", "4979855051456233706911354921671017679569102757964273723860320671606433426598254/30202497345372164822131062967774427996950314270303117271833564492579556341833791", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "242711/5497571", "742709937049/8958446701124", "87078377994133855225/230463790325663091369", "-159698266950556853302437227/2832677216948119172647607770", "-396019490551377862376667386749521/12682143671053811868300988114008383", "-11337499871669833918837685270423952949173/79263577005061056790200250365854630074883", "626018627579270741118930393511395956399833028955/525480683981912276687499434611558048779917623804", "150606020488835045023049238758848098531381042742071547/1520555961578162516415986720058316652562149632020025151", "-945586209143179646838274648535939380125903922328505712413775/4819044511525298660543774190952942299802274789287729172220227", "-7000313431198878243630519630678457723835628926061318019891443832659/57463238026057940772797443749133883867188141099220866275435033332408", "3291188386622884859640902552478305463167603647280025565630505296929621277/119194934330891783952596402515212470542823451359465656132099093455152440538", "-2318631035869750399063088135256980605624987779297102188358464895996599862664333/19219771037964104886810676434038272361695654535647438263894086495277899490257867", "3311271717374271534652892786291996707714867617379028892068125878354216436373265003713/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-52888/148583", "-8734097025579/116459807114612", "64014914849676037889/230463790325663091369", "-107099800028261214509562272/1416338608474059586323803885", "10279713044632122352521592094611766/88775005697376683078106916798058681", "423541934103812791169876064443545791436252/1188953655075915851853003755487819451123245", "-89222175588479112477075417795725487703508295581/262740341990956138343749717305779024389958811902", "-653345441761751095342951159050181624041868259108755086/7602779807890812582079933600291583262810748160100125755", "-2816089400142654435411588610439562106827784519983684421795171/14457133534575895981631322572858826899406824367863187516660681", "11698570154584079700078426629341557723275988577049400733799390546947/28731619013028970386398721874566941933594070549610433137717516666204", "-151509020786892283351091490822840712078007644530276171896182704229557903/59597467165445891976298201257606235271411725679732828066049546727576220269", "-118347944452066065973471629618890756108534253421314956774315124203894657589561812/634252444252815461264752322323262987935956599676365462708504854344170683178509611", "-664866408952808836994303535435106400148822970629878671372634069940513022680951738083/3348040965713733184287938933519408270426340590233334377823270195551586587958978556479", "1510333732655729091068302097027989491916357990602212344628981222129602306851586111845873672/17919474447541109040318460569320490429144301668661592751645001409967287842949514713142588667", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1738479/5497571", "200235284043/2239611675281", "266517627287618894408/230463790325663091369", "-207826585221097848656505596/1416338608474059586323803885", "3944504500479597971751644164561194/12682143671053811868300988114008383", "357527692090321821612880340468378839569799/1188953655075915851853003755487819451123245", "-243291805896117137436372153572813476247834489/20210795537765856795673055177367617260766062454", "-256211131545182266312935578005147515855306965217627754/1520555961578162516415986720058316652562149632020025151", "-90051570411450108815511798715436883719663330316863473685220/4819044511525298660543774190952942299802274789287729172220227", "-18052528939858059320551570042975473708282232801695090797582966852211/57463238026057940772797443749133883867188141099220866275435033332408", "-10917751019727653130347006838182056657366276672402060044819788284031945175/119194934330891783952596402515212470542823451359465656132099093455152440538", "24193656684275427733088326107044459495442851876727506890634817296047738961218939/90607492036116494466393188903323283990850942810909351815500693477738669025501373", "-6069329363397014372973228033548668378415632059084783079158131091335337288018795506553/13392163862854932737151755734077633081705362360933337511293080782206346351835914225916", "51747145770938798756001916195203363812358994195504387703455064017899222138451736237643763642/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "19459268382325907870276669468636082950651889522711494164762198552999986621351618011486329785735401/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1745575/5497571", "-44866390429095/116459807114612", "35384355762490349383/76821263441887697123", "-820533561527860866393645009/2832677216948119172647607770", "13362426363214455020447555336556671/88775005697376683078106916798058681", "-67415622145690608964870972632701717920099/396317885025305283951001251829273150374415", "447430028137976446773924703427470548882196564257/525480683981912276687499434611558048779917623804", "177286644712623042724605435949769420245531507296954133/1520555961578162516415986720058316652562149632020025151", "-2333810620337620504007167417257853653625552460156813875425280/14457133534575895981631322572858826899406824367863187516660681", "-15470603554993473845715442444905262971881884221347321092940354054293/57463238026057940772797443749133883867188141099220866275435033332408", "6210867065359606828827708085649974428559475337344256831075750578516850131/119194934330891783952596402515212470542823451359465656132099093455152440538", "-2562680672631997976962073255875532823544565474766731252010345517715722763734973/57659313113892314660432029302114817085086963606942314791682259485833698470773601", "650570051277793212725862972918042118038436201460594063290375722041951282028353767834/3348040965713733184287938933519408270426340590233334377823270195551586587958978556479", "45618390575207462436164937208042609329459438744569878753248812080901153896613521890373841776/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "-9654421073921894972090780846289496119935391314223781569224078379532439557749071126620414816406294/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "34939263220631867191028021638455640601351201883461604101722599563236581583691637319739071093368746728751/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-2054950/5497571", "779169901763/58229903557306", "72178283219232695130/76821263441887697123", "492433272197630907887483673/1416338608474059586323803885", "-4179212708299017725026432143721864/88775005697376683078106916798058681", "390808362574373162833153163687964854327371/1188953655075915851853003755487819451123245", "-335328324633101496409878897970031285137515639649/131370170995478069171874858652889512194979405951", "-2097529691702123060888504092740495337356578598860922476/7602779807890812582079933600291583262810748160100125755", "-10760239410602027466147369315362295243449740407127715621184986/14457133534575895981631322572858826899406824367863187516660681", "37887575998112951978449442974033395632215350233530896120900116773519/57463238026057940772797443749133883867188141099220866275435033332408", "27666850970431468245320462620707904386938840871469248459235157979987755255/119194934330891783952596402515212470542823451359465656132099093455152440538", "191375737444739743764695075028586277730458463429620794141353988505236073743904837/634252444252815461264752322323262987935956599676365462708504854344170683178509611", "-5864099768217308672257348229587411393178967585410403676414144610322208912545695639183/6696081931427466368575877867038816540852681180466668755646540391103173175917957112958", "-5261680930584408723405124919517398586716581496865898759439651835479596634170495409351282780/17919474447541109040318460569320490429144301668661592751645001409967287842949514713142588667", "35049132268204653723437323022129990427306697278450247970270012496272106478611501249398472065865292/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "132050869053008730742974060984506067332648221101477514175638668054393376521093615627358261087325522803460/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "44011381145348666484161627410139158468242073715312853123125321455750441588818883456775704270386463112838835407/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-3097019/5497571", "-43378749237065/116459807114612", "157332688353992778467/230463790325663091369", "169348360128632555953138409/283267721694811917264760777", "14260375924110239760703921158959840/88775005697376683078106916798058681", "147754119064377760122186196293266130000743/396317885025305283951001251829273150374415", "-208068241043783473166009649741345291503107406331/131370170995478069171874858652889512194979405951", "-777711669515427660829164310009759722944158301110107252/7602779807890812582079933600291583262810748160100125755", "670283455103867706895583594637295804744117049271350484737188/14457133534575895981631322572858826899406824367863187516660681", "3462839385283399419151147825945914623333258280422387448498500889698/7182904753257242596599680468641735483398517637402608284429379166551", "23468611204423949756276409170411309790077109444561005082606257237596140850/59597467165445891976298201257606235271411725679732828066049546727576220269", "405550077056460674901392107786950955051052195999470600995306810415507439069096630/634252444252815461264752322323262987935956599676365462708504854344170683178509611", "18388583398611780574823734781328974891852286654269949539964257487110613840064216595819/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "-130763123087256363424560487185443432977002725151455678716110661843443974263132268358956342419/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "-1413793826302135130331123069036652414713032908265192041335300461236659782066937733428987136936271/9361680754795174323660749216499588066417513996899119676437127135391732949674045650163257328619523", "-182953477459448052110496901205551311671610696399331802802476061807962194790634272136441951450646771651209/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "8904266540531920294702589394842825798004235261135049873302334937695576071172301186811526811777667526623912858/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "284026448321122718641922481395288288751557665714929820645052093038559634324340070604419148466193136195581312085528775/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "2854925/5497571", "2647565021253/29114951778653", "-33005191482122727784/76821263441887697123", "-100112931039179902109920563/566535443389623834529521554", "-4672847693371214765343892044878765/88775005697376683078106916798058681", "-85296181877613466607166906825953060479499/237790731015183170370600751097563890224649", "19133719110128838457080682748060247039192288605/20210795537765856795673055177367617260766062454", "-88886276091663944228666467958653579020366374444995130/1520555961578162516415986720058316652562149632020025151", "1531116040433524835281020911955644304584818323263805137661550/14457133534575895981631322572858826899406824367863187516660681", "-17894222513341603909490705243363932537164169475894460882409503187349/57463238026057940772797443749133883867188141099220866275435033332408", "-5151704957806604009371028749092824909359928115092841591310391924368916289/119194934330891783952596402515212470542823451359465656132099093455152440538", "-65920253919192480532997691539425704975931823729164921780296439036740834186442639/211417481417605153754917440774420995978652199892121820902834951448056894392836537", "8415177758579489549276031252012261352152191529810148341848065660590964442188537713349/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "15989189738729494538687963458050633462985128464166014566733670933431642494493797018860512731/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "5357526150416644502863959215681034309594295656867791963541456626144613174355012534975558184520654/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-71621188774839074247546110727735443780045441786064532955946974609461107159486854041802635167099294202094/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "193508206439603734211007332072378517444805873840331489475476548863360260075662438947145896831299601192350022922/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "-136763739327385650246498785532321369665356748406426366629365986323218408782517761097616376407535064668519474898012157/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "355157737998174538293503545267548671178492789444095381779761164527458385563793734372401234797937448245605269156164743919987/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "-1032694/5497571", "-6158628332443/116459807114612", "-32165823056412449049/76821263441887697123", "174752103052165319288256729/566535443389623834529521554", "-16445120449261533456227677041043285/88775005697376683078106916798058681", "128012016295907040495442048949412126524686/1188953655075915851853003755487819451123245", "-26574035315146370543221669283603114128940831011/525480683981912276687499434611558048779917623804", "294863261006887694385667081289674194582904639872613713/7602779807890812582079933600291583262810748160100125755", "-168557103923147918727688038019599726432619514742523274078582/14457133534575895981631322572858826899406824367863187516660681", "3054868758221058888427450057841924479506797456385924573609198937175/28731619013028970386398721874566941933594070549610433137717516666204", "3093713975828284975804686697616588557617449145600832574259278292570853647/59597467165445891976298201257606235271411725679732828066049546727576220269", "21934796530407963660656864562824318430281639922921325069792264206337599093090194/211417481417605153754917440774420995978652199892121820902834951448056894392836537", "4905379160459532060099078023781750490106337176388533937649978591860259131065647499147/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "-11666546001165572613938216230798553190860341498310336098569194550841610477518655415495644987/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "-10972811139119271778979416799400155103295017597367320083776652952912468861288099188098275189967269/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-26277936354203546721044507139049389199221588946398563260913368174350870396413472694271820033066465600897/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "-48113005300754873692190948443548591086401308271292504703853460292809001645810554989311010849713315776176551206/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "11748805500818391176916847225064010024820119377779044203451497898455025394097465157786159292472956619484275333603660/285032396151687426143202541499727122529598895194525678882431231301811836098393338294403332898400862724818852186776807", "-27210189365809454816951854060143213942080471405176737089472399164391999109879578182144312589829723700298670154298331657288/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "-215805902348575046332042810402250687777639194485499175209771523204787938653712434812882651857604787844406500340095680421119520368/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "1", "0", "0", "0", "0", "0", "0" ], [ "-393268/5497571", "345615410951/6129463532348", "76192871640949346285/230463790325663091369", "-449018969141805039639154868/1416338608474059586323803885", "-10921516390184366852007724509944486/88775005697376683078106916798058681", "-75765906125986297242924560396612084247136/1188953655075915851853003755487819451123245", "-49446783625007545273952451032202874391914177016/131370170995478069171874858652889512194979405951", "-283901788439276520714653772358786392412148586422112656/7602779807890812582079933600291583262810748160100125755", "8078209888438245584811584257505783572533683608690480323161519/14457133534575895981631322572858826899406824367863187516660681", "-6588043162421600515048975145258172797280963318036296920679742589933/57463238026057940772797443749133883867188141099220866275435033332408", "-21484544482281675236567155951833220620987199755587784767715534246330330477/119194934330891783952596402515212470542823451359465656132099093455152440538", "-16219070481600688837039176859675369308103388289319579953050348373375593872313969/90607492036116494466393188903323283990850942810909351815500693477738669025501373", "12456359818070675458437499288837059104255272433659881430297544866934412642669070527173/13392163862854932737151755734077633081705362360933337511293080782206346351835914225916", "-3909606793999714939655461077954282543278597093191905431822484305904082372905151972074545698/17919474447541109040318460569320490429144301668661592751645001409967287842949514713142588667", "-37313406691006768384746074580083224963717247162593963620972717566364861135167422476802766995647934/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-190116634321534763419256826353344171217430393369652028768844676815953493875430099886620963048355546228650/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "-61244009501086035037930916521373135928144089583721191446251731572692976445567797547654485107095037210599477052/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "-528633131637803300738297973477226037077551700471304598269766831012919082855696536810346903628513678486776291827200005/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "388089738385981562759376398805179371473446679796434572419718165201202398935897582989630437050673535200272107357433360617447/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "1890801907468793724109415647107610975112596411894327818616479251078350717972762380139830517981783503221069143471820594902601458977/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "108198459804726138612736162251671031130135847680800525631101130775415198834067012001121491410630941753702326830068213967712803635676868/162468709327855293493608447170798143370645494921576560577966963802363975900041015186668799306580746669717708114778656089429590683005713", "1", "0", "0", "0", "0", "0" ], [ "-1483981/5497571", "155129122247/29114951778653", "44567219137357391372/76821263441887697123", "740610702465925334278125303/2832677216948119172647607770", "6789923718153760504230588208416773/88775005697376683078106916798058681", "3704488751358286464755074866993200246771/9361839803747368912228376027463145284435", "-72309724900325325413108657744760089415849447248/131370170995478069171874858652889512194979405951", "-147963417243250907695984624111633470250207838303272072/7602779807890812582079933600291583262810748160100125755", "-146203058010922533789655172681010934279613512768151285376862/14457133534575895981631322572858826899406824367863187516660681", "15002020732400701483417105832182288466519834488255213547016602042903/57463238026057940772797443749133883867188141099220866275435033332408", "-17521248740450851306396373309996630276473357270357769283931509306181561629/119194934330891783952596402515212470542823451359465656132099093455152440538", "6999980995772763799851704846197932670941005489850563434885403314179557970406001/57659313113892314660432029302114817085086963606942314791682259485833698470773601", "479328790336490173553222917078339870875521000892342428374510597156062012800318253047/13392163862854932737151755734077633081705362360933337511293080782206346351835914225916", "-43233642256449742656237218034184064193562612691235498016372263723012767978130318744678902438/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "39215626707324683353998122954145629833978091741006300246293177512418698617200369501489265745273479/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-215615165711686262101690555334515590663496815040247489173039246485983929101075406346981241586127455420743/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "16936923838182951719509694763316459706579565209431862072914754043128294474488411710162985416488620130202639556/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "-97398144629559954647731655910655887019292012274197596664044302476880156260828021036787341536999179877282830364342411/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "107855476988019737667269322170159369265961789166568202460103259726235577395581029564098427467676241176155344341569890510289/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "-672556926472863628836901919684479828490883762687461948264885928509581333142795758231672103146366681143410823447739017817410066486/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "-180144222575088230024421497234668263653497181517791535085529104962166085152326631215054467256355257153141779646894236322552202651275595/324937418655710586987216894341596286741290989843153121155933927604727951800082030373337598613161493339435416229557312178859181366011426", "-9805107580922187028797147224107132008845874594188620759825344431876746012317669300384364660116610898882697999486855218620147362846954067942/171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597", "1", "0", "0", "0", "0" ], [ "-2602804/5497571", "28274088839253/116459807114612", "135712482318090150205/230463790325663091369", "-436274440729973136722237501/2832677216948119172647607770", "41385774548467287652346900715918209/88775005697376683078106916798058681", "-25258238645407650559099841241076744444026/396317885025305283951001251829273150374415", "150025784046182712393940880883114761462040091722/131370170995478069171874858652889512194979405951", "4254485627113046915010627776199062885628380943528980212/7602779807890812582079933600291583262810748160100125755", "909928558266460223118060063298731472853370868573571935099164/4819044511525298660543774190952942299802274789287729172220227", "188176181379780177484566399922627085824580541025107024973692771219/57463238026057940772797443749133883867188141099220866275435033332408", "59695100587477232447240154463661929101473925025525450439675908764257882359/119194934330891783952596402515212470542823451359465656132099093455152440538", "-6640957635569550564643605425287249150479987154957882584647900990331174388608559/90607492036116494466393188903323283990850942810909351815500693477738669025501373", "3748263208347077256490467297334515296553996782145149012293174600968690297807331524457/13392163862854932737151755734077633081705362360933337511293080782206346351835914225916", "58711887656853690205989501919877001196621234388736856095279379150732144878887651992126515382/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "-6403474962480157944430635925385624904882702499332102394568517976171240923853809003068751442655744/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "353910631307126614408011042822333945048911934079299386840778632540789862752723237558669290593454882271532/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "-155466683680568367394688277982790006834148087892688146517983042373347963402695008052808402046983864966090859142/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "-218583135616703369536586996654139360582590745573847738242800939168927997802584406010965828543827901545338444223012171/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "353543575978071272986961033793134848003964341382672872446933738498474420641663430206129783216835746960217262611472911686189/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "-806222516901310903959297203586439678503362430447222033724707667049872151677880545914287810202235702454997723215677807825701897961/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "171974103989506509973090473482436481406796187472577267581161406362400928580071207241342297638343261976177188802199095834250262386667270/487406127983565880480825341512394430111936484764729681733900891407091927700123045560006397919742240009153124344335968268288772049017139", "64214354589436436972388150513268408379300621927545605998796529657852331345521636824366532757013921725908093277099982894611242122010071379076/171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597", "-184101526565495970176921997884580793601997068848273336005937730777767181006164250357284848809774502780165121734162299432081489706963645493615577336/280070256488662344563643167884306726719429041722243580851231973223636144890503132822491336810949975404681836605020868849081036017534656603067797823", "1", "0", "0", "0" ], [ "-1320981/5497571", "9575844821130/29114951778653", "11957382908173116936/76821263441887697123", "-474883480145514918422197161/2832677216948119172647607770", "1715998847783746429498882651392739/88775005697376683078106916798058681", "-130679951628648589542436402605661109023573/1188953655075915851853003755487819451123245", "-72132811014078286663128469346468300813182122713/131370170995478069171874858652889512194979405951", "70918722566483770547278204583569026932098665429965404/7602779807890812582079933600291583262810748160100125755", "2304723704515610302906948285093941189254171707193624423393689/14457133534575895981631322572858826899406824367863187516660681", "343856114570380425671067198327270526748729583651994177381231361225/28731619013028970386398721874566941933594070549610433137717516666204", "198105701268050197162659074263532523731838534788830149412203654694126865/2591194224584603998969487011200271098757031551292731655045632466416357403", "-63204807298650171727192967149566477693709400862742499778473277491515091649299404/634252444252815461264752322323262987935956599676365462708504854344170683178509611", "14390105272260972630583767351574504141515035431295618788567778492110092468997494199729/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "6538785456279755188998513653753209170682246668120287200659597844633863643120084178207026199/89597372237705545201592302846602452145721508343307963758225007049836439214747573565712943335", "17192245367892896921493417167555367682491224627746955533564574402972403339521675920195144765743493/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-15510517441759338250159873315969717317909591748287120785278133132904274815580203586405569863022895217181/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "-136910401971523724068555019062590137621753311422454840929783397325169339651299386187958812538477080113021602905/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "18473991165157421354834569797599600746686001584481434294534634025802540056305645636440607520681892212840867362304139/1140129584606749704572810165998908490118395580778102715529724925207247344393573353177613331593603450899275408747107228", "292680401408573633126798634516025456631967525943256823276624458811547856324240889984764703646929751579812257645504381447099/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "458501065781127497026215704014188500687606911160468677489661700006380358764012646158299695319462441195207517814612424054249621829/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "353448230798741344229213823777451655210594335702845251869846544358207522917039427427156695760295476676880098033172632574232124127947077/974812255967131760961650683024788860223872969529459363467801782814183855400246091120012795839484480018306248688671936536577544098034278", "12811053842018969630101621625572206533439193776755286191156582381758991862519288156626747243718699065746484692655917336683379406277909703643/171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597", "-2782815401295647748908257481054668167522839327999181729085062809359847117783731794322666139818991827086001905762712563835978518356390091471478399/31118917387629149395960351987145191857714337969138175650136885913737349432278125869165704090105552822742426289446763205453448446392739622563088647", "64794518583328319782695055315635798702711950718322859503256881269718340612069906841579198402462284536860103272942772878216663876198109509742945935632301/330084211868767720878081295179951138219239079243577623389488432133070250587068306553070903610669259556876897160510627745473771182881500876745943686735178", "1", "0", "0" ], [ "206227/5497571", "391663480673/58229903557306", "59737028125471121162/230463790325663091369", "-191364195393013492390697891/1416338608474059586323803885", "-4811486288484456173433098278665692/88775005697376683078106916798058681", "24565451527795220414493323225209269870446/1188953655075915851853003755487819451123245", "-116934271478729342929409400854729225784415218823/262740341990956138343749717305779024389958811902", "-552437662999319551409449461811266587035446601919750578/7602779807890812582079933600291583262810748160100125755", "1744091411271218450926146712880458623600071006278587125707702/14457133534575895981631322572858826899406824367863187516660681", "3632389648288561941138004738235946231622948507855386547593656326543/57463238026057940772797443749133883867188141099220866275435033332408", "-9376992274092657587402777519661957656035780413141672026624400653615616233/119194934330891783952596402515212470542823451359465656132099093455152440538", "-3259695753635063394718796238453619679488227528018716715438201263685230243525399/48788649557908881635750178640250999071996661513566574054500373411090052552193047", "255922577740312460751155365089879236886461491060440110285362622425110673102611695101/6696081931427466368575877867038816540852681180466668755646540391103173175917957112958", "379126568419588149635478383169204937023027887790048289568055359015178947046377967635418036/17919474447541109040318460569320490429144301668661592751645001409967287842949514713142588667", "-6683070260867483243062770472250117575726717814710973859503212252434671799876918481743609226398256/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-22644993046536493751250913232509963157877715847819072233080491901842591062268118665946506057002704233100/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "-38396607772412736134403092592819238349129263384144474813639076370617456818872415646274045999894997199145134775/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "-21695580761268794140158281108733150100332086475090520449980885944468790506044219280227869568259420459071305125806595/285032396151687426143202541499727122529598895194525678882431231301811836098393338294403332898400862724818852186776807", "-9243514897574468890028874369742924183461182171388198037203097710511651546522301888273005614166210925566869249499513176252/109743485487350624374917058244372321642389153431817106677096656194439285425717220517537395702698702997181769193228032306245", "-188430556116206099744589809767118009737237057454744641564512030248263112398884166116021468233189122294244310769701415535131070768/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "-451376377325835139577404067917076474458614555638709211264538965925538211796553714072651866148358778507792569956642624952985482188729187/974812255967131760961650683024788860223872969529459363467801782814183855400246091120012795839484480018306248688671936536577544098034278", "-4626868601953776821096178976311334836352682426027667034421774040099552734893586597325196972288092392641893670129261194793612159026724078607/171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597", "15983969364564907664300983550968116527361252609501220276863021917949136289739312719714402937222270793736286287382550542201423531762623353615763809/280070256488662344563643167884306726719429041722243580851231973223636144890503132822491336810949975404681836605020868849081036017534656603067797823", "-859087479434591210034597085359293050363612933245633663972241167836484657160428017909951056566522413195543727713249597873539219975559624649820677055441/165042105934383860439040647589975569109619539621788811694744216066535125293534153276535451805334629778438448580255313872736885591440750438372971843367589", "-76233176408977812302493405243513375257672536355762688858783649342161703701207867366790014035264328193590608541539488955405999034011969654482406703098826118308/387370202298328952841734074741226159998708757595685237855957437098716608003406950622039400549558673764862670663466066327834240530485731994767105499801050305573", "1", "0" ], [ "-3848880/5497571", "-37236465008557/116459807114612", "114442770449396066615/230463790325663091369", "-1591673936980059314472507643/2832677216948119172647607770", "20628914259350482385225651192708137/88775005697376683078106916798058681", "634684782910775642842165155425608798952782/1188953655075915851853003755487819451123245", "-607177789211137308186317755973460118166954917087/525480683981912276687499434611558048779917623804", "71022987819521185074216981363629043153684167645127029/7602779807890812582079933600291583262810748160100125755", "-3766150041077688012906386275715589452929993301459749394433896/14457133534575895981631322572858826899406824367863187516660681", "7083812953418461815143216235358447491347175136660796307302166164831/7182904753257242596599680468641735483398517637402608284429379166551", "25250011362415979921512817178122576927952836482933696387524464040655200046/59597467165445891976298201257606235271411725679732828066049546727576220269", "-1183390278971122651057312476612786021973715769583872589276479479612192782918050/19219771037964104886810676434038272361695654535647438263894086495277899490257867", "-8755339021432622845264635328530936913904828366959705168996047188553728493882744379305/26784327725709865474303511468155266163410724721866675022586161564412692703671828451832", "-6990006226811787176953591531950415351740322383857322031051527898858368554930370185849630587/17919474447541109040318460569320490429144301668661592751645001409967287842949514713142588667", "18603421133680823295929879366424788087938672172066417677225731557818715314592180296358438612813499/65531765283566220265625244515497116464922597978293837735059889947742130647718319551142801300336661", "-77076919527770469230148574116694803811312247011423397719971325694728968317245462169620676969650110368930/636521120043387572881195077008148831760923511823266255889688775473081875979669926858766620343754923467477", "14380051121713024889160106584493736187565988628344364587039167268514621004772386926761800504340772497314253033/432187524458851371849273623492666225897401859359823958113905324889666259521036464061843608223531467546760364221", "58246143158624419337660083256597173840636851797748895615709183028116820335670271237279452066535298271585498653064447/285032396151687426143202541499727122529598895194525678882431231301811836098393338294403332898400862724818852186776807", "-247319995899377692506353488122832091518701744461518749929969407495338831715624269043965434604070261865331091274336651433904/2085126224259661863123424106643074111205393915204525026864836467694346423088627189833210518351275356946453614671332613818655", "73856294057517524353023922614991198358598791464117757349365817208606669064499210566326597330479386774100955655207932198185991271/3513618207763405232261537218945117549057180867735899799813291897892188499253186575753741183425900513223682878394544946632000497047", "-98876760387344829045431422108769223462254492930615861681287703251913993656299369194605839370580030576541773545992244657215431441294083/324937418655710586987216894341596286741290989843153121155933927604727951800082030373337598613161493339435416229557312178859181366011426", "17505045441419582933481913893810983269594578922569624903956862063086062972823320947467227436929574906857016943000645329442621933610349411591/171158369917236823816452691371521513275517428429529524251217537078491593252152156283916465080458005125433106101716710768791008634418021405597", "51380746858520958282049057906589452775748975233944633199426606793151558953848408632232958799736100406067556291821360103225282945153434048100894289/280070256488662344563643167884306726719429041722243580851231973223636144890503132822491336810949975404681836605020868849081036017534656603067797823", "6070327571533309116779183325537529350654433807055201213690879714724573654145101362547318863125929499896531392310343978757758172521019569869691708328911/330084211868767720878081295179951138219239079243577623389488432133070250587068306553070903610669259556876897160510627745473771182881500876745943686735178", "-1071933408483581197357177447611970781774563026489814263038096121362808653083100244652846810651992495041996938828756412281242820504921596916637469856889521637/387370202298328952841734074741226159998708757595685237855957437098716608003406950622039400549558673764862670663466066327834240530485731994767105499801050305573", "12738296020772436347236218044151925931606567979986843175884737679668961208426686634194913825455149645755661746383368432304521824814966178081139737866832444854413119/13237772903188533738097767927467660066708853716647424271536033470019920597583588851098617682007757610687242401106197725136700576753531434189387503671847639853473675", "1" ] ], "reconstruction_exact": true } }, { "shape": [ 2, 3 ], "dimension": 22, "decimal_scale_exponent": 14, "forward": { "positive_definite": true, "pivots": [ "17001745", "14090048500086/3400349", "188325317085546981523/35225121250215", "1910775174966778739885330921/376650634171093963046", "7356170911665227949952927305815648/1910775174966778739885330921", "217068836648945712813219338149611958435/229880340989538373436028978306739", "213877586739566609420870064795337512834487689487/6946202772766262810023018820787582669920", "621484988473843550074937864561328425291901309120452031/213877586739566609420870064795337512834487689487", "16320686909321065466095090558458537340837591634013432179562/3634415137273938889327122014978528802876615842809661", "168671181906981519211208606117309027738348809181254587593209084154/155046525638550121927903360305356104737957120523127605705839", "11918100241333271758425122031775762238557451636391917111022986928024809285/1518040637162833672900877455055781249645139282631291288338881757386", "9300109886059849372636040438920857065106721889905582467225383358666792124727237/4767240096533308703370048812710304895422980654556766844409194771209923714", "151060493309408237434261968838618958822847318357877851616475428830995984820488126084006/46500549430299246863180202194604285325533609449527912336126916793333960623636185", "403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "285429744550000853290752098319382307454401613287386631507836189312961617336605946575675856917567608/134620474194472596802684088163511792155072630218394639826067506255308707673642088737151145009", "154357477641460864462893937761033047010464353551256636833284868865979540855771077148715268610308476497976/35678718068750106661344012289922788431800201660923328938479523664120202167075743321959482114695951", "2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901/617429910565843457851575751044132188041857414205026547333139475463918163423084308594861074441233905991904", "2575348012185068795177896085444518921955391232760878617499315671799741702363736623298172057066610779865532809334304544/6598242224857915515292116855386808065423369558858678776621826717059351400193978127732285666298891562178824626703", "2071571931043198409386358675884048842599957484125779661091858081068588638289564083796644984381845864962403086000744954159057/2575348012185068795177896085444518921955391232760878617499315671799741702363736623298172057066610779865532809334304544", "614035098361381474667916423006465197242178489254035117063320910587564887679283656781326739486208324458572430796143062799051757807/4143143862086396818772717351768097685199914968251559322183716162137177276579128167593289968763691729924806172001489908318114", "278505598933317712225977073662164280567035054741640014066324034540459865839870719161346972230978120203631299760587998654244283546442128/614035098361381474667916423006465197242178489254035117063320910587564887679283656781326739486208324458572430796143062799051757807", "16051075966563983638023340943659637014598389254633833605578669248797928560151642157820172520648441758130520495164022291803640162753855243004/17406599933332357014123567103885267535439690921352500879145252158778741614991919947584185764436132512726956235036749915890267721652633" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "505410/3400349", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "5536296/17001745", "5472552396668/7045024250043", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-6681691/17001745", "-1667652116573/14090048500086", "-136906455795333928703/188325317085546981523", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1894258/17001745", "5886258208109/7045024250043", "57072943444315515094/188325317085546981523", "-633291399019486050304683184/1910775174966778739885330921", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-1068497/17001745", "-6794275498753/14090048500086", "-15873875814415214581/188325317085546981523", "-179464584919694777017947237/1910775174966778739885330921", "-22809640608529276274305582443016/229880340989538373436028978306739", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "2181374/17001745", "2388997945357/1565560944454", "92755857935884968657/188325317085546981523", "-417726212405704085665815167/1910775174966778739885330921", "-6169106545489021086492090788234051/7356170911665227949952927305815648", "-395085841943998045481200351352258716226/217068836648945712813219338149611958435", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "2283451/17001745", "-2496635365231/14090048500086", "64336828675649344133/188325317085546981523", "-51269113299363442179533105/1910775174966778739885330921", "2412369075298433005511985948378549/3678085455832613974976463652907824", "123054379039324345639953986598766442777/217068836648945712813219338149611958435", "-29779428697470217574758586483485864238551284114/213877586739566609420870064795337512834487689487", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1174152/3400349", "790493696048/782780472227", "150068181976145789895/188325317085546981523", "756934037346288870856709378/1910775174966778739885330921", "-464097371086964668439934049987265/1839042727916306987488231826453912", "-82055279006416678572384872845626142416/217068836648945712813219338149611958435", "-11465001123074030950443300391281346443826958668/213877586739566609420870064795337512834487689487", "-1049438526305282777030383621830150455751381641540775/3634415137273938889327122014978528802876615842809661", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "5122348/17001745", "-1792277847383/7045024250043", "12393839136665114564/188325317085546981523", "-77332382038478614070038268/1910775174966778739885330921", "-1047312376130105359015378926324207/7356170911665227949952927305815648", "-6425467039403129002972576602897671554/43413767329789142562643867629922391687", "-970712624977083929617213975859279481220797845/213877586739566609420870064795337512834487689487", "203760268646556411627914145294072418907461498688859682/621484988473843550074937864561328425291901309120452031", "292411768541473692716324809884069515365474371362226264964/2720114484886844244349181759743089556806265272335572029927", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "11944156/17001745", "22484204002051/14090048500086", "16288201166880001438/188325317085546981523", "848776920559220693474602047/1910775174966778739885330921", "-268576029011198887479317482203399/3678085455832613974976463652907824", "-277561555286135958842494436142585165047/217068836648945712813219338149611958435", "127999183990923802164145889181610664598549000134/213877586739566609420870064795337512834487689487", "586926063907093984494284921403693548142973426602648730/621484988473843550074937864561328425291901309120452031", "9990514509924512749414139887460896692539259732677277771373/16320686909321065466095090558458537340837591634013432179562", "23667838911244436044320431539879918588929230091937739613811247986/84335590953490759605604303058654513869174404590627293796604542077", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4278803/17001745", "4282626020029/7045024250043", "16171698438314886494/188325317085546981523", "913811447465534405751847444/1910775174966778739885330921", "2991072461593780506739344843580863/7356170911665227949952927305815648", "-68925809344810972616301783503399317609/217068836648945712813219338149611958435", "6996638041955897056263191267254352537880487173/213877586739566609420870064795337512834487689487", "157294342778705494550316661602326050500496615719324475/621484988473843550074937864561328425291901309120452031", "428742232476895130677256729501297847257233260920398142931/1813409656591229496232787839828726371204176848223714686618", "15820366363682961486405000300153946337087634841767295770344628647/168671181906981519211208606117309027738348809181254587593209084154", "402059056753785894235397033475704275742526074922593486596747347989266293/2383620048266654351685024406355152447711490327278383422204597385604961857", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-12939117/17001745", "-835767813943/541924942311", "-264945969577910148476/188325317085546981523", "522047487771105126323624624/1910775174966778739885330921", "-2319698293316743426476056967293037/3678085455832613974976463652907824", "83560354288005589468700074122255432047/217068836648945712813219338149611958435", "10986442852347567322406173560271717006638124386/213877586739566609420870064795337512834487689487", "-49740896908939576719965647020984051799138098358723/1760580703891908073866679503006596105642779912522527", "-6017157248172307087695028811018934816025106039020047811433/16320686909321065466095090558458537340837591634013432179562", "268217773340794457949742291884637358692573923508545400164751968185/168671181906981519211208606117309027738348809181254587593209084154", "1572385840041071578833191752022507348811218541804190923081489096945426203/11918100241333271758425122031775762238557451636391917111022986928024809285", "-1876541643761261060481749710078285838735477579128660053050204960443164731807065/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-653324/17001745", "1186143607503/1565560944454", "-59601942278137220922/188325317085546981523", "849855955797499426742569633/1910775174966778739885330921", "1571287903345152806347366423902061/3678085455832613974976463652907824", "-11966115904885716431923995992015610256/217068836648945712813219338149611958435", "-20299778846106585158099235681285861564206147138/213877586739566609420870064795337512834487689487", "282074806854204113137120283672353938712927317802894892/621484988473843550074937864561328425291901309120452031", "86954954207310397888891706918141709420984158089184334380/480020203215325454885149722307604039436399753941571534693", "-12303977993728236944310908044801007078496610572488922447947687458/84335590953490759605604303058654513869174404590627293796604542077", "8812363560229311189814501929832131203444232557567392154676404681751509308/11918100241333271758425122031775762238557451636391917111022986928024809285", "457853897806494814632392242764125624659461777360381762346973204651265625645810/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "8778398795624833377300252386486557631373162928093948358282672838280915960717727106351/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "12048267/17001745", "15344083244167/7045024250043", "178173423544070235836/188325317085546981523", "763417158857653910241231946/1910775174966778739885330921", "-9445896185196598045103093416900113/7356170911665227949952927305815648", "-271376189152766270530469647130827951632/217068836648945712813219338149611958435", "128499812186366002929832534382309550925388841269/213877586739566609420870064795337512834487689487", "49963518648306453012893818528128863163024372199654411/207161662824614516691645954853776141763967103040150677", "2017534826076382126869242999924133612237329806265032016912/2720114484886844244349181759743089556806265272335572029927", "-9882755061110760020150856770901599622668185604958214626371290269/84335590953490759605604303058654513869174404590627293796604542077", "1790719588754775220913581119262817847164752465246309090456187164198554006/11918100241333271758425122031775762238557451636391917111022986928024809285", "-908214094417993536616588941427184272217466962984812297722058243536133637202318/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "-71490458255617547677108158994777041180373843862643386245625175075318205741861304870313/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "-5360161561470854233131523552089655494311821169719616375710383972479622282123248954592432091/134620474194472596802684088163511792155072630218394639826067506255308707673642088737151145009", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "-379243/3400349", "18123430755823/7045024250043", "315019232425155469205/188325317085546981523", "-2822387606276137509755694900/1910775174966778739885330921", "15720376910086653374906952281986201/7356170911665227949952927305815648", "-131657040063582545499725279482012671014/217068836648945712813219338149611958435", "99443183922242378729758020602195084019497162243/213877586739566609420870064795337512834487689487", "-8820493479487578890366076466322839256225125720579043/207161662824614516691645954853776141763967103040150677", "-133975816804752511586964107941293881299502018256727403819/16320686909321065466095090558458537340837591634013432179562", "-1133759793601950948608071829942165488111778997007067631426718704/746332663305227961111542504943845255479419509651568971651367629", "439768889431146741395158649984407796105136028282638923916251520720593083/2383620048266654351685024406355152447711490327278383422204597385604961857", "473506171231957062737097631329424954078110840574166861562837638705972706084/59236368701018148870293251203317560924246636241436831001435562794056000794441", "-73629561903137868893012619653302776656752131956100465951630225868042600970752216075165/75530246654704118717130984419309479411423659178938925808237714415497992410244063042003", "-16398955678071172188107821384424671996502552553845104612477699105626594465647650017084754410/134620474194472596802684088163511792155072630218394639826067506255308707673642088737151145009", "11426577167819296015773232420847798596594599848224174141073568613471963927639807997095801467671765/71357436137500213322688024579845576863600403321846657876959047328240404334151486643918964229391902", "1", "0", "0", "0", "0", "0", "0" ], [ "4000099/17001745", "-13908357617591/4696682833362", "-116201228681943343473/188325317085546981523", "-913525098518039416288678315/1910775174966778739885330921", "1069832593316521168917903877271313/3678085455832613974976463652907824", "164811525946016874301517083205870840291/217068836648945712813219338149611958435", "-35777638408114648436780700397568549299859755082/213877586739566609420870064795337512834487689487", "731431100817606328316151611128777365029847003519919694/621484988473843550074937864561328425291901309120452031", "-4887331608603184786452477372683651781229950209875432106815/16320686909321065466095090558458537340837591634013432179562", "521135966786405611093672734205314136271521541640604954885404772831/168671181906981519211208606117309027738348809181254587593209084154", "15095922088793470393839469807019024001885589239069808034244378993273023/340517149752379193097860629479307492530212903896911917457799626514994551", "-2696974603069406166011517454787834092510147485033286887714695275208152453487477/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "31932277548192274737307449692502100142020146731964796990932435547634305775657574579900/75530246654704118717130984419309479411423659178938925808237714415497992410244063042003", "-201414614529166632569347931419947096827202873382620785925873951393828182991094677783211665464/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "-27138604577964286480242956773087914740749235634330406292946589706827754569871407971335613782016849/285429744550000853290752098319382307454401613287386631507836189312961617336605946575675856917567608", "25423301115456592834489397470939263554498994401408748996053797960508839067107830333845601326574498661147/308714955282921728925787875522066094020928707102513273666569737731959081711542154297430537220616952995952", "1", "0", "0", "0", "0", "0" ], [ "-814376/17001745", "642515426617/1565560944454", "17479946062738088757/188325317085546981523", "162432732297035503047545433/1910775174966778739885330921", "-569409492277723139555984917185137/7356170911665227949952927305815648", "-143280628890369658278415056489120149421/217068836648945712813219338149611958435", "11972798920186823889242404435508782796323587797/213877586739566609420870064795337512834487689487", "8823985439466104822302213931170831524022682792231297/207161662824614516691645954853776141763967103040150677", "-449721207740176693728000646425282502082387311731266986309/16320686909321065466095090558458537340837591634013432179562", "8009889904141140536188729118801619397883235483259353884418026979/168671181906981519211208606117309027738348809181254587593209084154", "1127605199003802066802998146950623411112602892361910168007774672049829781/11918100241333271758425122031775762238557451636391917111022986928024809285", "1329993203840689852816785980789058625497212693951249116938948101242011662104379/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "-2884976198137695294879933735742029988269392225202674961126531556318284453898839913313/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "73449380889023990601191650313788165470586600833689063819816741934305010754569464482013016719/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "37658067704120266359932860808829857376486502651327205781307804833236963268495582245098147009218481/285429744550000853290752098319382307454401613287386631507836189312961617336605946575675856917567608", "107998524749363498376950823720348360608029955744724475946482863475971309232318954789224608442948227527/2781215813359655215547638518216811657846204568491110573572700339927559294698577966643518353338891468432", "-191404322881021424162525196648677854978440755016970978849551058083180180316092190784122335448216741075791161/2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901", "1", "0", "0", "0", "0" ], [ "-2263423/17001745", "1293642710557/4696682833362", "37274043472082745231/188325317085546981523", "-283632433602029025761196477/1910775174966778739885330921", "2078214482005978927063970109069705/3678085455832613974976463652907824", "56428283491894138014771995680407901503/217068836648945712813219338149611958435", "5633341135937159825457901242676426279449664134/213877586739566609420870064795337512834487689487", "-23680812538750278744408532372159113211836078639377002/69053887608204838897215318284592047254655701013383559", "-846375097989058766266075128425092472288142394967003615320/8160343454660532733047545279229268670418795817006716089781", "-45346181609948046285661980283267320203716294386685958151141327486/84335590953490759605604303058654513869174404590627293796604542077", "-1002811531026444736441735811865595145643224212056321740682489807583624228/11918100241333271758425122031775762238557451636391917111022986928024809285", "1649416291861307731006444812830271118525277649151851311944621693922189107778304/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "-16644496960014805187867496474792670510662690880427392656242550312632592259193219067631/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "-53207124731997206157494738802846770368271924705259258389680465444935464979189313509622499369/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "-44279746769515264659882975262893236039275831538301747777053792618571684967266432236564898124322715/285429744550000853290752098319382307454401613287386631507836189312961617336605946575675856917567608", "28994301041746453980638552591753432766080988372296461908377130888791161222795680859231689275435794521883/308714955282921728925787875522066094020928707102513273666569737731959081711542154297430537220616952995952", "-65271423276926819480929468191568096904311228364562161120825163853750770657421343308264871220033318681845020739/2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901", "-235245341706750739813327545754147189334050400671721079931744536455551571465852544454613786155222334845397764326008775/2575348012185068795177896085444518921955391232760878617499315671799741702363736623298172057066610779865532809334304544", "1", "0", "0", "0" ], [ "-227986/17001745", "65305880591/14090048500086", "5535431922917768492/188325317085546981523", "129918294634143149189319841/1910775174966778739885330921", "123860177605283825802884808072673/7356170911665227949952927305815648", "25882732445877330303765375547442631377/217068836648945712813219338149611958435", "-1857010484925355389565823560079780153979139269/213877586739566609420870064795337512834487689487", "-54369115066018048663660358675191275393838177669436342/621484988473843550074937864561328425291901309120452031", "38349074895670153209936908829052313348203894969576881778/2720114484886844244349181759743089556806265272335572029927", "-8717742078593538086393011120417399828022061267645916463646147803/84335590953490759605604303058654513869174404590627293796604542077", "-22858331713002628823754757536932357661951407310030421012249117799896422/2383620048266654351685024406355152447711490327278383422204597385604961857", "1758742347751174929745777176322249891046669494012109409820147226056513393802890/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "158843285118599250388900285050586144647763104940406786647963745941442529171351991755/151060493309408237434261968838618958822847318357877851616475428830995984820488126084006", "-3057984839382875551979645456356709540857937151090786147082789536346178451783312924460104823/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "-3574172178438426480414582923948444992673426757391396414012563579083739736097166390150584811728583/285429744550000853290752098319382307454401613287386631507836189312961617336605946575675856917567608", "-16192518142759640128484561267238509258411861640287448935315261550327544084963331043986801002462959177767/308714955282921728925787875522066094020928707102513273666569737731959081711542154297430537220616952995952", "16210510210217966283285021603338534812014080119476284105548798306644520754307729050842771438222046774445149175/2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901", "-24499238373379746512151963210439103343147972251988185393732555165011061850088122668633437547804168302814424554670161/111971652703698643268604177628022561824147444902646896413013724860858334885379853186877045959417859994153600405839328", "33908468483435852199109775835754484315681298764444012684640415161194919254969650505452077779214301325148350425268769884417/2071571931043198409386358675884048842599957484125779661091858081068588638289564083796644984381845864962403086000744954159057", "1", "0", "0" ], [ "-7748966/17001745", "4719495932531/14090048500086", "-46086752904551404438/188325317085546981523", "280328585468246022435613611/1910775174966778739885330921", "-1754611332686144298812090068674943/1839042727916306987488231826453912", "-68243217075216666490126278205278538074/217068836648945712813219338149611958435", "39165179115899065860015510916414559549235606188/213877586739566609420870064795337512834487689487", "-337014052535461998766208052027422159922321109207018985/621484988473843550074937864561328425291901309120452031", "-5269520423575997248034733133850029390513303143433330438007/16320686909321065466095090558458537340837591634013432179562", "-226002625631623814753790226255682955051574651713874991920396550893/168671181906981519211208606117309027738348809181254587593209084154", "-1361959371219555799843383236534871575401813951705368411857870786230982527/11918100241333271758425122031775762238557451636391917111022986928024809285", "-2593334736924175115765664962271619563782907201097260998382891813045119004062723/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "-4511680018173708834779115896754772439119654172391672307140685464554151745730126329367/75530246654704118717130984419309479411423659178938925808237714415497992410244063042003", "133675928813786024451959426618843568068720445309096711929614575675840858965469756988907547128/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "29044406484276622746161346720427778038618400647477155364048616909834332171362253542093825443763877/142714872275000426645376049159691153727200806643693315753918094656480808668302973287837928458783804", "-3801471823523794874654419545185028259829612149895335389031644241201287981829534711152234738005537905705/77178738820730432231446968880516523505232176775628318416642434432989770427885538574357634305154238248988", "-719172662281806219310357571001326427627171697003415964520170901125777461488401830629320092881819754257451271940/2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901", "709034439766642403700908006609810284789402712819829321708467135000419623009137319736871597107914750970275852277632861/1287674006092534397588948042722259460977695616380439308749657835899870851181868311649086028533305389932766404667152272", "-71797464510525096249398892232615212309902936101264718601786435199192998827626912847586953431605043504178215526787131468902/2071571931043198409386358675884048842599957484125779661091858081068588638289564083796644984381845864962403086000744954159057", "-116979792748080435170046613116189013402656109903126912256179064529800214258619400853225217208082739765726698962582594517212589365/614035098361381474667916423006465197242178489254035117063320910587564887679283656781326739486208324458572430796143062799051757807", "1", "0" ], [ "-15099711/17001745", "28912884179185/14090048500086", "-51698991112323607058/188325317085546981523", "8652090294253078511331281/32386019914691165082802219", "-488533250354524077920059067488251/1839042727916306987488231826453912", "-67207956311927724236124424674907105943/217068836648945712813219338149611958435", "42006459252714416291315272398188414992806063516/213877586739566609420870064795337512834487689487", "-647218578203291526559009496317125417287659918692023261/621484988473843550074937864561328425291901309120452031", "-2116563115580388321354979831104590066183502349311739951412/8160343454660532733047545279229268670418795817006716089781", "-510422061550638777726795748481739432249983572187924384306224151485/168671181906981519211208606117309027738348809181254587593209084154", "-539780277964033067740947887995875045664298160391069087867876165402925414/11918100241333271758425122031775762238557451636391917111022986928024809285", "2056564515192190063775392423349559517973245170027929168992450715754356871663213/9300109886059849372636040438920857065106721889905582467225383358666792124727237", "-17556201285689688532949668308639897064637726786959215675094806530792358339793097828499/75530246654704118717130984419309479411423659178938925808237714415497992410244063042003", "268849995754068818075337918039778154716941401362030115678229267017859097595353874901575143316/403861422583417790408052264490535376465217890655183919478202518765926123020926266211453435027", "11593909504024463242804329741406733515293797592288746901351929899078212908317390028383237755649591/71357436137500213322688024579845576863600403321846657876959047328240404334151486643918964229391902", "-48928203172937871571912436280625158210079024421762702866394289935144989990683358303045737485333408149/38589369410365216115723484440258261752616088387814159208321217216494885213942769287178817152577119124494", "-1385378555069235691100263780665327336824855501338181763225279314916228562075826198076577791939038954077715027208/2199414074952638505097372285128936021807789852952892925540608905686450466731326042577428555432963854059608208901", "568673190120630075081800595654689060922378277232068960902306232758982026192921670435927140759182594853469862445236933/2575348012185068795177896085444518921955391232760878617499315671799741702363736623298172057066610779865532809334304544", "272343647642663508088924090462263829168369968367625612250820196946384002447981944744652637832556842378716315526395018301997/2071571931043198409386358675884048842599957484125779661091858081068588638289564083796644984381845864962403086000744954159057", "163977210337140282832692691976131564057023688366659239247375451002230481864173002581327554406458130086885717913801099575872224771/614035098361381474667916423006465197242178489254035117063320910587564887679283656781326739486208324458572430796143062799051757807", "51168276982788603734620067665316572049213907550721413859843866730726106541607624383807816322368517536117098055635869430938897954583843/69626399733329428056494268415541070141758763685410003516581008635114966459967679790336743057744530050907824940146999663561070886610532", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "50740836", "70645278977141/12685209", "21531523551251069054/70645278977141", "49657420191636417958520905/21531523551251069054", "1247624723114318232538533751006/1013416738604824856296345", "1654953194604372719469627481313208737651/122267222865203186788776307598588", "81209051428341235521112351043879940997685563761/3309906389208745438939254962626417475302", "1006944206317306260051545962073463397083476967395215595/81209051428341235521112351043879940997685563761", "5229692131529864070562520443758176258538202101212861113151961/1006944206317306260051545962073463397083476967395215595", "28664651776673804545476107054207086258006324553007120100874824239442/5229692131529864070562520443758176258538202101212861113151961", "20253855266707999236540880497756407445225741895943392109211695173417466534/14332325888336902272738053527103543129003162276503560050437412119721", "42362174515676335863846963457707519882629626417569701269948911938632923880462856/10126927633353999618270440248878203722612870947971696054605847586708733267", "1703709807161520054137076488401520749502386940805089007230039770578787373089517923426/5295271814459541982980870432213439985328703302196212658743613992329115485057857", "1734635395569002739720343288771910697377216055070230308215314270073298231808216258183266240/851854903580760027068538244200760374751193470402544503615019885289393686544758961713", "56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503/27754166329104043835525492620350571158035456881123684931445028321172771708931460130932259840", "301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695/113135045716461578446803931743698461835969186794665475718844546641431306829644984183175394563711006", "151396915504099357316130439969424068581754492121689135431186398929195763729697913304374092270669610036465347556/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793/75698457752049678658065219984712034290877246060844567715593199464597881864848956652187046135334805018232673778", "94394255895686927308273984903485865285840737843659312531429241516807934615837738165577796172060698353136800706397613505008/53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793", "92942684449542433497009720849893866513592191529601952866778122132969029237003355401896783577609803083603354682804692984511895439/94394255895686927308273984903485865285840737843659312531429241516807934615837738165577796172060698353136800706397613505008", "182703471616822988787622912516117073889048296478542601419727344290040412767850070571752373697364801733285418676306327771289513028266245/371770737798169733988038883399575466054368766118407811467112488531876116948013421607587134310439212334413418731218771938047581756", "256817215465023738208373455098554192233574228074141337689258707980766856962426274525122760330375068130088327922624356668858242604061683888064/182703471616822988787622912516117073889048296478542601419727344290040412767850070571752373697364801733285418676306327771289513028266245" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "10309715/25370418", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "423767/25370418", "-3548475733912/70645278977141", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1590079/12685209", "-28995712833037/70645278977141", "5048976308808307131/21531523551251069054", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1261802/12685209", "-2578213267676/70645278977141", "-14118064390321327371/21531523551251069054", "-1642827918144033767068929/7093917170233773994074415", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-47014529/50740836", "97262690622685/141290557954282", "37692423035846125/43063047102502138108", "41254469251064887400452711/99314840383272835917041810", "-5452273928390833357388495596161/4366686530900113813884868128521", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "4258467/8456806", "-155053976126052/70645278977141", "-93848968107908508447/21531523551251069054", "7620045238267934570878253/3819801553202801381424685", "19002298246557683018454385695959/8733373061800227627769736257042", "-843041700568193894515060667677950717722/1654953194604372719469627481313208737651", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "3870479/16913612", "-13453384319061/141290557954282", "-72669363280120115363/43063047102502138108", "-11193169896048664395354617/7639603106405602762849370", "2565457901012813017786664584937/793943005618202511615430568822", "-2099643196667621179062544284844104972571/1654953194604372719469627481313208737651", "27742858590465903620055613660726087221055660393/81209051428341235521112351043879940997685563761", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "2495001/16913612", "-91761210656073/141290557954282", "-39264416832248778677/43063047102502138108", "-15580719405732450114687461/14187834340467547988148830", "48322107529475602853546169077/113420429374028930230775795546", "289631272289357321464223796425747138565/1654953194604372719469627481313208737651", "-9555790801894123403175725343058541971196444725/81209051428341235521112351043879940997685563761", "-37374709419062777241826543942274266437936060167698067/1006944206317306260051545962073463397083476967395215595", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-3952727/50740836", "18353105795969/12844596177662", "27630980280931339851/43063047102502138108", "-4283004449270156198663955/19862968076654567183408362", "-12386606060324197132774112189435/8733373061800227627769736257042", "1873988160935011429507889933631224506097/1654953194604372719469627481313208737651", "-23109817839826257467628762602194200898982785709/81209051428341235521112351043879940997685563761", "-1527099152731529297658486229931239522443964964106710/201388841263461252010309192414692679416695393479043119", "413272275709146071776249532183731158420030072310897427007040/5229692131529864070562520443758176258538202101212861113151961", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "787079/50740836", "-9159046970459/12844596177662", "28018326654780916487/43063047102502138108", "-7811224605390317726478957/14187834340467547988148830", "1251337687457678730681818481879/1247624723114318232538533751006", "-238282823059233774474363585092454512269/1654953194604372719469627481313208737651", "-7106388288582756255103076939518092616817454085/81209051428341235521112351043879940997685563761", "33141213537123033536130246218248783364033123413523441/201388841263461252010309192414692679416695393479043119", "195783444310184635595276345005746213004389376706702104200855/1743230710509954690187506814586058752846067367070953704383987", "18372060192425745201406764914460450011132003622994163337624243309/14332325888336902272738053527103543129003162276503560050437412119721", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "221093/4228403", "-47562357601416/70645278977141", "-28689671242573973186/10765761775625534527", "-80337086755371039958040944/49657420191636417958520905", "11447671771397498338174068305223/4366686530900113813884868128521", "-965557205472574429695761499232302090672/1654953194604372719469627481313208737651", "6575802984878064184421611983872023061514686684/27069683809447078507037450347959980332561854587", "869301018942623987115640034337478441174223478041641578/1006944206317306260051545962073463397083476967395215595", "1527025979390154687150733450316120832610888805074997326989697/1743230710509954690187506814586058752846067367070953704383987", "5190611402354328939607767169256093823590605889020347639855331479621/14332325888336902272738053527103543129003162276503560050437412119721", "9632181333858419898533386951892516805378916628777563695494541411090096654/10126927633353999618270440248878203722612870947971696054605847586708733267", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-5555945/25370418", "1556674151311/70645278977141", "-7000665006602561941/21531523551251069054", "-15440864148385410455496739/49657420191636417958520905", "2991717591748788348537995148821/8733373061800227627769736257042", "-153095875052266722842047006796380380174/1654953194604372719469627481313208737651", "224967908663878173897975411195916391296849469/81209051428341235521112351043879940997685563761", "97593608356908924696684838573618591442465532869434057/1006944206317306260051545962073463397083476967395215595", "-118024849467063060238755231230264084838164800205700423216856/5229692131529864070562520443758176258538202101212861113151961", "-241162022018448265072354283121238684528294304002075883171727295154/14332325888336902272738053527103543129003162276503560050437412119721", "16347604135296172035656643884415137116280160318513649912896322024175763/10126927633353999618270440248878203722612870947971696054605847586708733267", "-32468379246049308940497217094091497868577294631289665017956329405679718776169/5295271814459541982980870432213439985328703302196212658743613992329115485057857", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "623392/12685209", "-41774374130419/70645278977141", "3093977987783210716/10765761775625534527", "-35140954779602778624706614/49657420191636417958520905", "4868586958960688184000553441028/4366686530900113813884868128521", "-1252083670440445481263394078420853157032/1654953194604372719469627481313208737651", "-4665334066474339665484330467381521591945876954/81209051428341235521112351043879940997685563761", "151426066445801635294385934986953663455541240389557483/1006944206317306260051545962073463397083476967395215595", "-426935983587004407509614033995671850391476326350621685876384/5229692131529864070562520443758176258538202101212861113151961", "192296031007923352014426292356330137503870661329479791726891956832/14332325888336902272738053527103543129003162276503560050437412119721", "-5119828368935778203339716295989013522656780975914841678371256069432204830/10126927633353999618270440248878203722612870947971696054605847586708733267", "-5122336030004779896231159815615333129651249321599595228831018198065216430877359/21181087257838167931923481728853759941314813208784850634974455969316461940231428", "-839684701605361416202084617796898570856627136649106869572418578201293130902387810293/1703709807161520054137076488401520749502386940805089007230039770578787373089517923426", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-4388513/25370418", "-39642347633852/70645278977141", "-7813438595824643351/21531523551251069054", "290479407486984973270823/3819801553202801381424685", "-1352531878533678077547656534671/8733373061800227627769736257042", "77703982298264848350935956904970804352/1654953194604372719469627481313208737651", "5078759810062251235376366237025851844613641655/81209051428341235521112351043879940997685563761", "-114862306160056418442971921443935452840741746874834284/1006944206317306260051545962073463397083476967395215595", "953882107441451517497436260442666084464214199180913050691387/5229692131529864070562520443758176258538202101212861113151961", "-4313377706097043223401209740246198291947012773361609066648820294402/14332325888336902272738053527103543129003162276503560050437412119721", "2105069161376348825502559407395363615452748676852638726160900410010965751/10126927633353999618270440248878203722612870947971696054605847586708733267", "-150481778785386658851139745209316942721740290380598273589726318271660249586147/1033223768675032582045047889212378533722673815062675640730461266795924972694216", "-144084666504156289288139859854027401820262294517741111123107417995020523311304628033/851854903580760027068538244200760374751193470402544503615019885289393686544758961713", "-657399250491610578146482281894521736362954216605340904455407014237129025206450705687194671/6938541582276010958881373155087642789508864220280921232861257080293192927232865032733064960", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "1454656/4228403", "31486931363253/70645278977141", "-48849469276491115269/21531523551251069054", "-7108020224660447748782781/49657420191636417958520905", "12673649310082941320652870196207/4366686530900113813884868128521", "-933693365421239930327355992611059929614/1654953194604372719469627481313208737651", "43568640247391609039304440135010093771234552874/81209051428341235521112351043879940997685563761", "178981888280148445963378980376903709983202784060727276/201388841263461252010309192414692679416695393479043119", "-1017589587977819712275460602316385733505522155257867285317325/5229692131529864070562520443758176258538202101212861113151961", "8751101983766263897038709175480370735086306821836249673778141473444/14332325888336902272738053527103543129003162276503560050437412119721", "12332059414640607204710693843757206740664295301091946570282383872767801297/20253855266707999236540880497756407445225741895943392109211695173417466534", "14790743182821643619380603234935481362875777484781938960915842374321545903119961/21181087257838167931923481728853759941314813208784850634974455969316461940231428", "60419030745402252149401535315755571332142782013815953065758737684051579964922004224/65527300275443079005272172630827721134707190030964961816539991176107206657289150901", "-537426629965903910867878503610775872906619876632064230413166155894764079270474860758009837/3469270791138005479440686577543821394754432110140460616430628540146596463616432516366532480", "-7950105938469215104571066910119633357929760612829223771058732646986697639108816504746225260359398/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "1", "0", "0", "0", "0", "0", "0" ], [ "-1672823/25370418", "16303728550282/70645278977141", "6570917523590431585/10765761775625534527", "2180416580666378037427182/9931484038327283591704181", "-5859374380063884099051073297745/8733373061800227627769736257042", "11153870389801576981239726232279237606/97350187917904277615860440077247572803", "1434799246896789512078860750953027958119523501/81209051428341235521112351043879940997685563761", "1329663987378848182730942428439947236997425219714158/1006944206317306260051545962073463397083476967395215595", "143876757690017848710141346936368299657269436416006183574902/1743230710509954690187506814586058752846067367070953704383987", "150897299019799607682339070101666582676666582765377861688842689436/14332325888336902272738053527103543129003162276503560050437412119721", "-289707443295857408220602125441726545124622118152301789284291575324061826/10126927633353999618270440248878203722612870947971696054605847586708733267", "-4267029263608825792434433453678349730125185881083733136563903352209864033163281/42362174515676335863846963457707519882629626417569701269948911938632923880462856", "-54694832539694592413089255995099551858238688605387955174427265117388486020398317993/851854903580760027068538244200760374751193470402544503615019885289393686544758961713", "178822576246506097862769982397099124515063491519599253527609086432507507779534059393649827/6938541582276010958881373155087642789508864220280921232861257080293192927232865032733064960", "5199697329273322816766547096060965583984301948398004924311611890456265906225140485447054961586429/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "-20814421945483644988507031360249485271232799655817091791679812367324307338499897652773644467139224323748/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "1", "0", "0", "0", "0", "0" ], [ "3505349/50740836", "-138127290820069/141290557954282", "-48498135748827899019/43063047102502138108", "1050037687772382349254693/2837566868093509597629766", "471043091952642889100225587845/1247624723114318232538533751006", "-203082606582985058105404646320887853337/1654953194604372719469627481313208737651", "11073011376025772283031936702122197480772584155/81209051428341235521112351043879940997685563761", "-48798514429659961862017958971635502067233043769578353/1006944206317306260051545962073463397083476967395215595", "-30580138027925696177144710500502888216823681290273059247331/5229692131529864070562520443758176258538202101212861113151961", "-6778613117195369898933452299680812271736829411847463380827752655/28664651776673804545476107054207086258006324553007120100874824239442", "-515704213244288671289576835329589502005854836270718838234882703739081954/10126927633353999618270440248878203722612870947971696054605847586708733267", "1006775565937936576324175513171134194586410048979159485523882842258223159337685/21181087257838167931923481728853759941314813208784850634974455969316461940231428", "500942580467321545548279528450621078988670430036397298174298159104986567737265250353/1703709807161520054137076488401520749502386940805089007230039770578787373089517923426", "-24912597853796557709796600636766808555671326221936786577671256339173387678038870162827387/157694126869909339974576662615628245216110550460930028019574024552118021073474205289387840", "920205131379362979962647152183535968966334772215963555896529964449486338859304917461147973660324/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "28039488341165563450193603145181671799138743149766027687379402513493691463438174949803602665632483728638/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "-22118429972641843831608095003636181373494209021004106318525873639456683856878664845083111404185090068286675243/75698457752049678658065219984712034290877246060844567715593199464597881864848956652187046135334805018232673778", "1", "0", "0", "0", "0" ], [ "3675031/25370418", "20164930835647/70645278977141", "9717058396680180360/10765761775625534527", "-23711096525782492876861334/49657420191636417958520905", "-1980854154325596854165700046907/4366686530900113813884868128521", "651553517563682708640827021892505892206/1654953194604372719469627481313208737651", "-24485769751815041650563249868726144876086358166/81209051428341235521112351043879940997685563761", "77910504105965968090535690827127018065385250778527419/1006944206317306260051545962073463397083476967395215595", "837446017583560136399480831688170612344587668629408422750928/5229692131529864070562520443758176258538202101212861113151961", "8329131959066711226872644250346453317551665866791755002652909524599/28664651776673804545476107054207086258006324553007120100874824239442", "11088147329142544601844953437818758081370810843203759665968730509357398769/20253855266707999236540880497756407445225741895943392109211695173417466534", "-4264545226667519328538831300576654497126876836582073705833293999275393209125317/42362174515676335863846963457707519882629626417569701269948911938632923880462856", "-990975751441663585105874473015033960436693282312358265679295102931058391501526937269/851854903580760027068538244200760374751193470402544503615019885289393686544758961713", "20740853830037078809817599518446726990544647252377123132617432136141175996423726602616641/630776507479637359898306650462512980864442201843720112078296098208472084293896821157551360", "9894570201260579845060696530439203980880795894263096747726047406712596936628866634273826419260117/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "-26931498842119348060141716656272503544335147932215957838577863280865032698896558923263322944356746620487/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "-50867508878630698355326026971189263508165558783488404437188850665292495944400017303004714984234155009687607323/75698457752049678658065219984712034290877246060844567715593199464597881864848956652187046135334805018232673778", "-17169878340744529199381750379921834031327557276113112136387934439330725707747003185224939386745015294714064533907751/53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793", "1", "0", "0", "0" ], [ "110215/25370418", "-36065033590643/70645278977141", "-3437895899701745285/21531523551251069054", "105824503586048133257759/9931484038327283591704181", "4966338981190207284419439492715/4366686530900113813884868128521", "-932742285264119145171361448634220213528/1654953194604372719469627481313208737651", "10132282220163820906661186873081208964226965940/81209051428341235521112351043879940997685563761", "30538941336619662342503913535773058459316310097671919/1006944206317306260051545962073463397083476967395215595", "-251389446980141096954663047664718655771866802732608495125417/5229692131529864070562520443758176258538202101212861113151961", "-2784792008048670242719072874246364148106255107152888520047014897521/14332325888336902272738053527103543129003162276503560050437412119721", "-6360069560045438937264169475724423802054015286578794146252498931676929677/20253855266707999236540880497756407445225741895943392109211695173417466534", "-6994591055311620682255941121264927716139520934052552836449319100385144702588247/42362174515676335863846963457707519882629626417569701269948911938632923880462856", "9438520422969013613521633846130468307591372193762174451187642449771678273618932315/65527300275443079005272172630827721134707190030964961816539991176107206657289150901", "592173662306299253892531306410162730099901489407049029555114080805286883271616849634467969/6938541582276010958881373155087642789508864220280921232861257080293192927232865032733064960", "16384323748322892738289977466294018068053301948245698802853069388120733496202171012399701220680543/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "9432561071031984270225467201750485295157072023202971471987352939538276854634302898339074713311174768495/60325635636799591141689543536767045340602024390801576908064952283763376985339967301392896997519951129339", "1937797327675012568365122398676284243153171458312601269260317920602077486382991791940858260920905170172095865/37849228876024839329032609992356017145438623030422283857796599732298940932424478326093523067667402509116336889", "14038336622009136480651306932023964863694750832042558619039745739190696141884027266073971174341322651194148716507750/53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793", "-26633000943340877034222047525205600167425337784984300431778190266670312395026322703131976913721144272551205729943428261809/94394255895686927308273984903485865285840737843659312531429241516807934615837738165577796172060698353136800706397613505008", "1", "0", "0" ], [ "6258575/50740836", "-58532164603303/141290557954282", "-33217942951229865271/43063047102502138108", "-37525004691181630172226793/99314840383272835917041810", "3666562436590476864009797439951/8733373061800227627769736257042", "-401231763891496834927654766296033494467/1654953194604372719469627481313208737651", "88277777150194873293530495483015570700975809/27069683809447078507037450347959980332561854587", "132340099821272705682484718029027930636376564736799497/1006944206317306260051545962073463397083476967395215595", "-127400709129387856312110098158315939538009917339805317386646/5229692131529864070562520443758176258538202101212861113151961", "-379561463121517769433875062309179341669706247606143229532014652023/28664651776673804545476107054207086258006324553007120100874824239442", "-1088064389731799103903142657561029989474034240361184111285150971227997628/10126927633353999618270440248878203722612870947971696054605847586708733267", "571794431425551495328296754691410770703991331276512685283509256213889750904309/42362174515676335863846963457707519882629626417569701269948911938632923880462856", "735660685004039952814661972922649957785463243893657912212935617228401352513422696795/1703709807161520054137076488401520749502386940805089007230039770578787373089517923426", "-1592113928199811062358906086060150149244809466209112835722336307963999883585436489997609189/6938541582276010958881373155087642789508864220280921232861257080293192927232865032733064960", "-5291275421185112103238409899041942871611352217330434296261023107755730163675321716428074856272763/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "-15027687425686364929568199506344172721497160297584945230884999724464823681604309706223735337328885311166/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "-34973766339336322736243347926296958865215020995461812354212472833634207767665453066407038926117831201563135983/151396915504099357316130439969424068581754492121689135431186398929195763729697913304374092270669610036465347556", "33272046634197295733100334108087939135285528162449032382724074802078976141103139832125623632798247822594201785069026/53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793", "-3240584281968376024905745599153424002847325020463177172553680665891271366957336710877652517980745239366391898201554251283/47197127947843463654136992451742932642920368921829656265714620758403967307918869082788898086030349176568400353198806752504", "19492354523210029739644776159595076304754055814129206838713879174849191153206023038853308576467564257043769361906523355700249866/92942684449542433497009720849893866513592191529601952866778122132969029237003355401896783577609803083603354682804692984511895439", "1", "0" ], [ "-5033237/16913612", "-40920789495423/141290557954282", "-8023806624703668503/43063047102502138108", "-43897847822731967504987249/99314840383272835917041810", "1260676462534596296690153837269/4366686530900113813884868128521", "-979741546445512490112728287561514656029/1654953194604372719469627481313208737651", "-2985618686083771062732391519453968217082453432/81209051428341235521112351043879940997685563761", "223658023913054610874631658097922124726149878145837036/1006944206317306260051545962073463397083476967395215595", "606542399733432170972903587784155904699631214140053924717017/5229692131529864070562520443758176258538202101212861113151961", "-7059431799620206723228151603802700866954369859221516222879898902220/14332325888336902272738053527103543129003162276503560050437412119721", "5245944132208565453680610300775270644438371141087375492985852117426896550/10126927633353999618270440248878203722612870947971696054605847586708733267", "18589306018110761773053552479539939711530261967050763818458314072191259608386251/42362174515676335863846963457707519882629626417569701269948911938632923880462856", "970353734704498607631441847887091882894800475995611562019054389967444606989972605451/851854903580760027068538244200760374751193470402544503615019885289393686544758961713", "-3035014390664034013226878512426642291590336362765752009417829592181740715079889520348377577/6938541582276010958881373155087642789508864220280921232861257080293192927232865032733064960", "-33426596691575013991513174659151874195570677540527824650328294216442824577716187221749451014149879/56567522858230789223401965871849230917984593397332737859422273320715653414822492091587697281855503", "-34293794970085688865914153251155285883901070647175420091510252604415607193229178724250897230004231249074/301628178183997955708447717683835226703010121954007884540324761418816884926699836506964484987599755646695", "16974798919155232363679513906071677991593696846059547416103978570586049246288805055222720151159164610321317843/151396915504099357316130439969424068581754492121689135431186398929195763729697913304374092270669610036465347556", "44015272961890626295588878132508586427078997480846268600670995172192760890501604146880931474332728976555778563155269/53885008986812393707157569303517564474757409360866126879094150489141611493138069977037410988560813834174863534265793", "-2049172040878919700345330756008142892003240285468529872727501069384141173476939748248596841505372575975249163370881815083/11799281986960865913534248112935733160730092230457414066428655189600991826979717270697224521507587294142100088299701688126", "9951488830568497738361739071828637020883145849465304353504262730589128102724313111488274662677882032914220553764487423081466840/92942684449542433497009720849893866513592191529601952866778122132969029237003355401896783577609803083603354682804692984511895439", "-1945379163503408547541836004904897310738537189946045042084115705090752875213872000497755375041273283574225635880170478088295815870891/182703471616822988787622912516117073889048296478542601419727344290040412767850070571752373697364801733285418676306327771289513028266245", "1" ] ], "reconstruction_exact": true } }, { "shape": [ 5 ], "dimension": 12, "decimal_scale_exponent": 15, "forward": { "positive_definite": true, "pivots": [ "3616397", "3054955377847/3616397", "11299504833555481991/3054955377847", "7487399835287655381990093/11299504833555481991", "10109929757988503549979834158815/7487399835287655381990093", "33244468745436553379488089093217600017/10109929757988503549979834158815", "136768843386318899359642969833023863305441038/33244468745436553379488089093217600017", "74459055170634553991603235377485348247057954903677/19538406198045557051377567119003409043634434", "55917830830496385226797819999372035344347696331492771752/74459055170634553991603235377485348247057954903677", "1549142464391061937989814525120591932781456208585877773577762/494223252289740778519677702014651827538426608990466417", "4119667433878142399538699185058665597179554339271396067104163061693/2840094518050280219647993296054418543432669715740775918225897", "4052944202510249835420100958016489958012405758743966567077152858287680622/12359002301634427198616097555175996791538663017814188201312489185079" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-219419/3616397", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "1005407/3616397", "146628381501/3054955377847", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "842091/3616397", "-674629817951/3054955377847", "-3350445696344874306/11299504833555481991", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "186248/3616397", "72083088816/3054955377847", "3592529347284967624/11299504833555481991", "-8171389874182686653352194/7487399835287655381990093", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "5630326/3616397", "-1181705227884/3054955377847", "4477593936708240925/11299504833555481991", "9481777912472078797227776/7487399835287655381990093", "4365476334811226510658614175218/10109929757988503549979834158815", "1", "0", "0", "0", "0", "0", "0" ], [ "3598595/3616397", "-1812516866296/3054955377847", "-5248395138244790871/11299504833555481991", "12349500060333513374068199/7487399835287655381990093", "-6051980268356768110787956249432/10109929757988503549979834158815", "3433368800339822846847580979087904107/33244468745436553379488089093217600017", "1", "0", "0", "0", "0", "0" ], [ "-2799721/3616397", "6519537395981/3054955377847", "-12015543824050721531/11299504833555481991", "6512778916059581887974572/2495799945095885127330031", "-11056695425263845953063299967634/10109929757988503549979834158815", "-4965292498856695568385743827638804672/11081489581812184459829363031072533339", "3580796637410778698964057493602456641053161/19538406198045557051377567119003409043634434", "1", "0", "0", "0", "0" ], [ "-212971/3616397", "1663236424440/3054955377847", "-2471778776338456306/11299504833555481991", "395426240227891241736665/2495799945095885127330031", "-3140169414543990501259272667992/10109929757988503549979834158815", "-23123170681856180154456948147828301/11081489581812184459829363031072533339", "-22724786319861633287942281795050235972231083/136768843386318899359642969833023863305441038", "-1982225571192595731335117813089907420873901984023/74459055170634553991603235377485348247057954903677", "1", "0", "0", "0" ], [ "17130/3616397", "-197309409333/3054955377847", "-11438879222434351396/11299504833555481991", "21179240419838199368779966/7487399835287655381990093", "-11395289028744908153812407864236/10109929757988503549979834158815", "1513375438472333782312920262504583267/11081489581812184459829363031072533339", "39616256759725768735195751610335363507979297/136768843386318899359642969833023863305441038", "3816561368449221015513904902616755569633089994627/10637007881519221998800462196783621178151136414811", "-65612042043487462938208776022372313738399248757320226/211809965267031762222719015149136497516468546710199893", "1", "0", "0" ], [ "919824/3616397", "-1793932451752/3054955377847", "2182248314874811563/11299504833555481991", "-7339443981670198841757982/7487399835287655381990093", "253579345877113023025359497410/2021985951597700709995966831763", "702640716765397193192367307854882420/11081489581812184459829363031072533339", "2059529991754833997598665471949318242893393/68384421693159449679821484916511931652720519", "-23926175017798698238941175881441667622279746622142/74459055170634553991603235377485348247057954903677", "252354126151045427300318058373364936373407087944583631/1553273078624899589633272777760334315120769342541465882", "-88880018285254905849034039266407783759005953339133789170586/258190410731843656331635754186765322130242701430979628929627", "1", "0" ], [ "-418081/3616397", "-2768429236474/3054955377847", "-128713512701395340/230602139460315959", "16267881527862531522016166/7487399835287655381990093", "-10592372206175926913125952270647/10109929757988503549979834158815", "-406853197701089163345105501681420008/33244468745436553379488089093217600017", "36799002826568078068510381551400699860852391/136768843386318899359642969833023863305441038", "34867348162634959521237701299729468267817191230559/74459055170634553991603235377485348247057954903677", "-30556010218181287590172331466393040433893601206865611981/27958915415248192613398909999686017672173848165746385876", "1987123286625502329029940684132062275431428967183791642939081/4647427393173185813969443575361775798344368625757633320733286", "-10920362681285606637966681118178314429569947205455810677975038635977/12359002301634427198616097555175996791538663017814188201312489185079", "1" ] ], "reconstruction_exact": true }, "reverse": { "positive_definite": true, "pivots": [ "10569070", "625223873334/310855", "494535673606187788/104203978889", "7323623296747635808619611/8407106451305192396", "673208220558333996413931095649023/87883479560971629703435332", "3821540804474953610122690404992415618041/673208220558333996413931095649023", "24446585773509876654260006742536871010270209744/3821540804474953610122690404992415618041", "990173937759478857566700889865251524679699764453343/2716287308167764072695556304726319001141134416", "349379465359371639006642318106477150532122357473160614923/990173937759478857566700889865251524679699764453343", "478995735357191027742975870517403818338762162597491826585334002/349379465359371639006642318106477150532122357473160614923", "301810056847236394121671981012874881442122005074593337301781743978656/2155480809107359624843391417328317182524429731688713219634003009", "18238248911296124259390454311074204811055825914347849551847187862294562799/18863128552952274632604498813304680090132625317162083581361358998666" ], "L": [ [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-119507/310855", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "2070859/2113814", "-23427215745/208407957778", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "-325129/10569070", "-65011653501/208407957778", "139432751472697929/494535673606187788", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "819482/1056907", "-794329090465/625223873334", "724532550227200193/989071347212375576", "16654681570337646967878523/14647246593495271617239222", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "156509/310855", "589477590667/625223873334", "422899695849938159/989071347212375576", "-3126155550699434803461339/14647246593495271617239222", "-59994820743749938791278562642311/673208220558333996413931095649023", "1", "0", "0", "0", "0", "0", "0" ], [ "-402/5284535", "424556403917/625223873334", "184200407072220213/989071347212375576", "-11909155694107014855434297/14647246593495271617239222", "-407988702464931557146032404570221/673208220558333996413931095649023", "2868035580068340510730897121269167289915/3821540804474953610122690404992415618041", "1", "0", "0", "0", "0", "0" ], [ "-3681887/10569070", "-85328823259/625223873334", "-123187159486268491/494535673606187788", "-424824783996151542791981/563355638211356600663047", "-52463499548145177681310232782060/673208220558333996413931095649023", "34235715976631395165850965028603113864/3821540804474953610122690404992415618041", "-143021512431600477192683756622905146359608117/8148861924503292218086668914178957003423403248", "1", "0", "0", "0", "0" ], [ "2123549/10569070", "431136063/3110566534", "99158623864243919/494535673606187788", "653499326372212378582465/7323623296747635808619611", "-20430331459781462651255084932038/673208220558333996413931095649023", "543925650112671520180129531897177948436/3821540804474953610122690404992415618041", "939245091506853894916515484801477633295493323/8148861924503292218086668914178957003423403248", "76513347913309985461521495872043763142663901266383/990173937759478857566700889865251524679699764453343", "1", "0", "0", "0" ], [ "-2217477/10569070", "4856827606/104203978889", "-324964627294316905/989071347212375576", "-7492059782719963807100963/14647246593495271617239222", "-99980872472861022611553034139925/673208220558333996413931095649023", "509412198793257852386185192206395025475/3821540804474953610122690404992415618041", "516620017490490207657894348485648592583229135/2037215481125823054521667228544739250855850812", "-875665181236660139839521834514974753462905371754868/990173937759478857566700889865251524679699764453343", "-387069283994005020319227948137243595319885390203365789112/349379465359371639006642318106477150532122357473160614923", "1", "0", "0" ], [ "-148031/2113814", "-260003387305/625223873334", "59968730129378299/494535673606187788", "226110096320200742209041/7323623296747635808619611", "90672337087880422326261812076056/673208220558333996413931095649023", "197474390150077484280366644739903970099/3821540804474953610122690404992415618041", "419123235125777758926279550702916040095508641/12223292886754938327130003371268435505135104872", "-962400671796460546757282745047917382337015835933958/2970521813278436572700102669595754574039099293360029", "-348693052313068535489210812175476395363963376171784539124/1048138396078114917019926954319431451596367072419481844769", "-57603086073094515054582359527188582754702843364010638232418582/718493603035786541614463805776105727508143243896237739878001003", "1", "0" ], [ "-24593/621710", "235968283453/625223873334", "13339287316993735/123633918401546947", "-1121563155940342130796688/7323623296747635808619611", "-152438554035250133801136889400924/673208220558333996413931095649023", "1811877281114823618349420095351540074354/3821540804474953610122690404992415618041", "195314986230313698334220333529271142314421519/679071827041941018173889076181579750285283604", "119941803843766847785804406867237308267447484602212/990173937759478857566700889865251524679699764453343", "78143250083496273767036324975030346167235577000085768052/349379465359371639006642318106477150532122357473160614923", "9024752121723864958855005808155216977010956324479945196573351/478995735357191027742975870517403818338762162597491826585334002", "5596981437199023986587802591479864234103266874844442185081518081781/9431564276476137316302249406652340045066312658581041790680679499333", "1" ] ], "reconstruction_exact": true } } ], "total_pivots_per_order": 98, "checks": [ { "name": "one_literal_data_assignment", "passed": true }, { "name": "verifier_bytes_match_paper_and_wrapper_checksum", "passed": true }, { "name": "six_blocks_with_expected_dimensions", "passed": true }, { "name": "block_0_literal_contract", "passed": true }, { "name": "block_0_positive_and_exact_reconstruction", "passed": true }, { "name": "block_0_paper_order_pivots_above_40000", "passed": true }, { "name": "block_0_negative_diagonal_refused", "passed": true }, { "name": "block_1_literal_contract", "passed": true }, { "name": "block_1_positive_and_exact_reconstruction", "passed": true }, { "name": "block_1_paper_order_pivots_above_40000", "passed": true }, { "name": "block_1_negative_diagonal_refused", "passed": true }, { "name": "block_2_literal_contract", "passed": true }, { "name": "block_2_positive_and_exact_reconstruction", "passed": true }, { "name": "block_2_paper_order_pivots_above_40000", "passed": true }, { "name": "block_2_negative_diagonal_refused", "passed": true }, { "name": "block_3_literal_contract", "passed": true }, { "name": "block_3_positive_and_exact_reconstruction", "passed": true }, { "name": "block_3_paper_order_pivots_above_40000", "passed": true }, { "name": "block_3_negative_diagonal_refused", "passed": true }, { "name": "block_4_literal_contract", "passed": true }, { "name": "block_4_positive_and_exact_reconstruction", "passed": true }, { "name": "block_4_paper_order_pivots_above_40000", "passed": true }, { "name": "block_4_negative_diagonal_refused", "passed": true }, { "name": "block_5_literal_contract", "passed": true }, { "name": "block_5_positive_and_exact_reconstruction", "passed": true }, { "name": "block_5_paper_order_pivots_above_40000", "passed": true }, { "name": "block_5_negative_diagonal_refused", "passed": true }, { "name": "ldl_control_identity", "passed": true }, { "name": "ldl_control_positive_fraction", "passed": true }, { "name": "ldl_control_singular", "passed": true }, { "name": "ldl_control_indefinite", "passed": true }, { "name": "ldl_control_zero", "passed": true }, { "name": "asymmetric_matrix_refused", "passed": true }, { "name": "paper_stage_arithmetic", "passed": true }, { "name": "displayed_negative_bound_arithmetic", "passed": true } ], "passed": 35, "upstream_verifier_execution": "not_run", "moment_identity_expansion": "not_run", "main_binary64_pipeline": "named_artifacts_missing_in_pinned_checkout_not_run", "lean_kernel": "not_run", "interpretation": "Exact checks establish positive definiteness of the six literal integer Gram matrices and arithmetic consistency of stated numbers. They do not establish the expanded moment identities, the seven-basis contradiction, the five-basis theorem, or the stronger exactly-three result." }