Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 14 33
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 33 Kronrod extension for:
P2 : 3/2*t^16 - 10827/1972*t^14 + 47593/5916*t^12 - 889889/147900*t^10 + 549549/226780*t^8 - 1001/1972*t^6 + 11011/226780*t^4 - 3861/2525860*t^2 + 1859/366249700
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^49 - 7402723132004854043673542309659150924044539381365980929962270725246091583706812731273268545833746315402607660543/411802559556801402078946987415517437006147513404653665366980852485474256239983776643206148714375261070778051300*t^47 + 108382286898365647572828278828131382877516001143003771113806546067598892039055650408444457872306218892366011653828729/1073569272764581255219814796192253958275026567445932105611719082429631386017637705708838429698376305611518379739100*t^45 - 1389709379645007837046783560692906168811121235490600017809427523025076901683154704426051772369077917416960041051167193/3936420666803464602472654252704931180341764080635084387242969968908648415398004920932407575560713120575567392376700*t^43 + 103359146048396901677677364205007242181680183215648504024945099330267190853405899573671355093723951136765751894009983126983/119962419820835583760354138351182777720915260357354196701229509802491060459254199965415120865212732349540416282679932500*t^41 - 2730190161603671523853007222276292569973495974797588054755977061557645269749163016834629809996962011243991073643696893918257/1751451329384199522901170419927268554725362801217371271837950843116369482705111319495060764632105892303290077727127014500*t^39 + 1347865041072643808634691746161686657021703081373162001696484632516697607164187011445236288160399959354457335953520046473819979/621765221931390830629915499074180336927503794432166801502472549306311166360314518420746571444397591767667977593130090147500*t^37 - 476218206612471675451236025934803083055824081640572345083614147093451151654857628147285519823388542103117885347766328649185317233/200830166683839238293462706200960248827583725601589876885298633425938506734381589449901142576540422140956756762581019117642500*t^35 + 62307321903574054595824515743096190750911234601487350415999361479636224578005379957498067413360915825800152343644504485238129131/30090353608147425008286439499823018322149394375503159968910568216759478743576278983208328703009119155976116885866538693270500*t^33 - 3616704600448074928260125473001976108338945634958118514740441510420467981682238876188416005454963667567297709900857566447454223383/2482454172672162563183631258735399011577325035979010697435121877882656996345043016114687117998252330368029643083989442194816250*t^31 + 412121799231044125854927439689469151964738355764975465192877600119658073383612562866888036854495244536694896293916272614545097763/496490834534432512636726251747079802315465007195802139487024375576531399269008603222937423599650466073605928616797888438963250*t^29 - 32833992275142401516786825323143917307901183717445905755728006409923716386519592701561415338115105342446342913667159849113072867/85601868023178019420125215818462034881976725378586575773624892340781275736035966072920245448215597598897573899447911799821250*t^27 + 372331985860239474074241020143591904596845605198999944128769301646870051081533817022336024204271077412539186322344192001027631/2593996000702364224852279267226122269150809859957168962837117949720644719273817153724855922673199927239320421195391266661250*t^25 - 49427290723613484259870595143174232223727859702127844265450083161074632360379036159619297515549580860407079303442985862239083/1141358240309040258935002877579493798426356338381154343648331897877083676480479547638936605976207967985300985325972157330950*t^23 + 450537263933620234403715043931965023937219332489577715622163736461106098482619131854878657403522121903712806614449066630351653/43092738705605558582141826342414997025093080246717741002840112163877277448502122786086121519573240824331740508434055946258250*t^21 - 3952331005530319404617308231365956626331480020646473030672115969903417631282388090466072950974174248765911294489580567949191899911/1978327304140163346724116248823393132426188183814466084602985573286576379472304554137313318393480083707916142305495700814391495950*t^19 + 77482689475964630197808309597898502899913113154906483599715450051134747395794156934780478953731186254999061140909748014381172323/260306224228968861411067927476762254266603708396640274289866522800865313088461125544383331367563168908936334513881013265051512625*t^17 - 35290531393017960740289863388466304692259197142677280917341147190626733173767267626228838259460391387965873544213130253337052963/1041224896915875445644271709907049017066414833586561097159466091203461252353844502177533325470252675635745338055524053060206050500*t^15 + 119603948361578398715875002249253106486921122052800486609824830627975726630304473402164456419900774038440894651334982678531539/41648995876635017825770868396281960682656593343462443886378643648138450094153780087101333018810107025429813522220962122408242020*t^13 - 88415286387359304896683052257114757428716327908161635945281388269379801952419080216605564480444244199483533302965384730619/506186143371840274985061599371438510970546832079028243636104079340525645286263734651207255940813162681451306784406442907246500*t^11 + 137434719970708062414855654568181179623254698169951236376270448833727943501805902041137453194067134204666362148681510988001/18931361762106826284441303816491800310298451519755656311990292567335659133706263675955151372186412284286278873736800964731019100*t^9 - 18186203979079510266076844976581148649526232570486918605900345659582017669588845326056589729424121773781366813469504549023/94656808810534131422206519082459001551492257598778281559951462836678295668531318379775756860932061421431394368684004823655095500*t^7 + 275112403577442994401119946187528132886230392171531275152499664618175011949777037210844327248240986054558314868727627607/94656808810534131422206519082459001551492257598778281559951462836678295668531318379775756860932061421431394368684004823655095500*t^5 - 35858792102480349473656722118001950878768095426910922799998236808791253578834144210014983043392575373782004544233617/1721032887464256934949209437862890937299859229068696028362753869757787193973296697814104670198764753116934443066981905884638100*t^3 + 14830184190372603934283316036819945447848059238714739587458590797485875082416973774275424822324240741707821671356861/321833149955816046835502164880360605275073675835846157303834973644706205273006482491237573327169008832866740853525616400427324700*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.99952050523022899281 + 2.1582172046950888717e-842j)  +/-  (1.16e-238, 1.16e-238j)
| (-0.98812513120329170302 - 1.4439230018294334662e-842j)  +/-  (2.68e-238, 2.68e-238j)
| (-0.93798437900993878791 - 4.2538844099020257539e-843j)  +/-  (7.71e-239, 7.71e-239j)
| (0.99952050523022899281 - 2.8373265198942842089e-839j)  +/-  (1.07e-238, 1.07e-238j)
| (0.93798437900993878791 + 8.2396564218463415416e-853j)  +/-  (8.21e-239, 8.21e-239j)
| (0.959052303746616228 + 2.2485213798983246857e-867j)  +/-  (1.37e-238, 1.37e-238j)
| (-0.85001680456214491633 + 2.6980229920059858862e-890j)  +/-  (4.51e-240, 4.51e-240j)
| (-0.91269995295408258327 + 8.9113064904782323275e-889j)  +/-  (3.6e-239, 3.6e-239j)
| (0.97579292499445023313 - 1.1591056555129940701e-889j)  +/-  (2.11e-238, 2.11e-238j)
| (-0.99600593660669224382 + 1.0034779236368226916e-905j)  +/-  (2.41e-238, 2.41e-238j)
| (0.85001680456214491633 + 2.5478125208065768693e-910j)  +/-  (4.17e-240, 4.17e-240j)
| (0.99600593660669224382 - 6.1161922731201302388e-914j)  +/-  (2.71e-238, 2.71e-238j)
| (-0.34482357270979449848 - 2.0926269344920281667e-948j)  +/-  (1.19e-248, 1.19e-248j)
| (-0.88333016636517017316 - 3.0084010241961572761e-938j)  +/-  (1.26e-239, 1.26e-239j)
| (0.98812513120329170302 + 7.0535390504051508696e-936j)  +/-  (2.65e-238, 2.65e-238j)
| (0.81290899580354554239 + 6.7682705922515022521e-952j)  +/-  (1.1e-240, 1.1e-240j)
| (0.91269995295408258327 - 4.447114237319702915e-949j)  +/-  (3.52e-239, 3.52e-239j)
| (-0.959052303746616228 - 4.6220520225532392819e-954j)  +/-  (1.41e-238, 1.41e-238j)
| (-0.81290899580354554239 - 4.1165363988596366521e-959j)  +/-  (1.13e-240, 1.13e-240j)
| (-0.97579292499445023313 + 3.1096704568850338e-960j)  +/-  (2.1e-238, 2.1e-238j)
| (0.88333016636517017316 - 8.1907100021541650058e-964j)  +/-  (1.33e-239, 1.33e-239j)
| (0.77217041820495993065 - 3.8091159694682858517e-966j)  +/-  (2.74e-241, 2.74e-241j)
| (0.28360660057996518919 + 1.2682193730525269378e-975j)  +/-  (8.22e-250, 8.22e-250j)
| (-0.72799373091578229991 + 4.2946217907020285857e-968j)  +/-  (5.16e-242, 5.16e-242j)
| (-0.77217041820495993065 + 2.3239733195538513664e-969j)  +/-  (2.55e-241, 2.55e-241j)
| (-0.061237645707923134607 - 1.6905680717278929046e-981j)  +/-  (2.02e-254, 2.02e-254j)
| (0.68061242889025150426 - 1.444617881309531099e-966j)  +/-  (9.3e-243, 9.3e-243j)
| (0.72799373091578229991 + 2.1783839779028261401e-971j)  +/-  (5.34e-242, 5.34e-242j)
| (-0.11761869816309705582 - 5.1734263382691735749e-983j)  +/-  (4.02e-253, 4.02e-253j)
| (-0.63029977975560870417 + 2.0711930069319068353e-974j)  +/-  (1.37e-243, 1.37e-243j)
| (-0.68061242889025150426 - 1.0407275707849756816e-975j)  +/-  (9e-243, 9e-243j)
| (0.52205018440139691806 + 6.6550311338352502373e-977j)  +/-  (1.85e-245, 1.85e-245j)
| (0.63029977975560870417 - 2.3766134830853167471e-976j)  +/-  (1.31e-243, 1.31e-243j)
| (0.11761869816309705582 + 1.5546873553691944784e-985j)  +/-  (3.75e-253, 3.75e-253j)
| (-0.57735026918962576451 + 9.4232028759466895077e-978j)  +/-  (1.6e-244, 1.6e-244j)
| (-0.40545074306610185911 - 7.7395798650232692219e-981j)  +/-  (1.49e-247, 1.49e-247j)
| (0.061237645707923134607 - 1.1312153509889434718e-987j)  +/-  (2.02e-254, 2.02e-254j)
| (0.57735026918962576451 - 1.66088993671511095e-978j)  +/-  (1.62e-244, 1.62e-244j)
| (0.22374161346734564129 - 2.1607428383580456185e-986j)  +/-  (6.55e-251, 6.55e-251j)
| (-0.22374161346734564129 + 1.2615729860427708724e-985j)  +/-  (6.32e-251, 6.32e-251j)
| (-0.52205018440139691806 - 3.9234685672085984905e-980j)  +/-  (1.83e-245, 1.83e-245j)
| (-0.16883492201661298743 - 2.2284144975780428131e-987j)  +/-  (5.74e-252, 5.74e-252j)
| (0.34482357270979449848 - 1.081717184769569889e-982j)  +/-  (1.06e-248, 1.06e-248j)
| (0.46466059051237979643 - 1.508154336698174511e-980j)  +/-  (1.83e-246, 1.83e-246j)
| (9.3977222910985310251e-998 - 4.8325514842910388515e-998j)  +/-  (5.18e-996, 5.18e-996j)
| (-0.46466059051237979643 + 3.5749865461190975236e-982j)  +/-  (1.91e-246, 1.91e-246j)
| (-0.28360660057996518919 - 1.5800486735678479534e-985j)  +/-  (8.02e-250, 8.02e-250j)
| (0.16883492201661298743 + 2.0560313658231506626e-987j)  +/-  (5.49e-252, 5.49e-252j)
| (0.40545074306610185911 + 1.4781616257078771498e-981j)  +/-  (1.58e-247, 1.58e-247j)
-------------------------------------------------
The weights are:
| (0.0015353289422453768665 + 4.2710766103624895136e-842j)  +/-  (7.87e-61, 2.31e-175j)
| (0.010109725154868406156 + 8.9119389737829293275e-842j)  +/-  (5.27e-61, 1.55e-175j)
| (0.02319669885743242378 - 1.3829696622450501299e-841j)  +/-  (2.05e-61, 6.03e-176j)
| (0.0015353289422453768665 + 2.3235204832587593783e-839j)  +/-  (1.18e-62, 3.47e-177j)
| (0.02319669885743242378 - 4.3979472214630693034e-840j)  +/-  (8.73e-63, 2.56e-177j)
| (0.018920519046133731994 + 5.7681147095197491583e-840j)  +/-  (8.01e-63, 2.35e-177j)
| (0.035236238111610323058 + 2.2145832931475262143e-841j)  +/-  (1.6e-63, 4.69e-178j)
| (0.0273501160524964705 + 1.6605179512290468886e-841j)  +/-  (5.32e-63, 1.56e-177j)
| (0.014547112778835919611 - 8.3160739367496072327e-840j)  +/-  (3.58e-63, 1.05e-177j)
| (0.0056561314853437851546 - 9.3696983523283395623e-842j)  +/-  (1.26e-62, 3.71e-177j)
| (0.035236238111610323058 + 2.7266518700002079327e-840j)  +/-  (4.03e-65, 1.18e-179j)
| (0.0056561314853437851546 - 3.2214976418592526416e-839j)  +/-  (1.48e-63, 4.36e-178j)
| (0.061119497054077865196 + 2.235874896329932139e-840j)  +/-  (1.19e-67, 3.48e-182j)
| (0.031365759100004504165 - 1.9070855690087704689e-841j)  +/-  (7.57e-65, 2.22e-179j)
| (0.010109725154868406156 + 1.3978122050308815271e-839j)  +/-  (1.31e-63, 3.86e-178j)
| (0.038952366477802152826 - 2.507193687841817652e-840j)  +/-  (5.89e-67, 1.73e-181j)
| (0.0273501160524964705 + 3.5817672306455468568e-840j)  +/-  (2.82e-65, 8.28e-180j)
| (0.018920519046133731994 + 1.1217038374278408158e-841j)  +/-  (1.42e-65, 4.18e-180j)
| (0.038952366477802152826 - 2.5896400192800050162e-841j)  +/-  (5.11e-68, 1.5e-182j)
| (0.014547112778835919611 - 8.9652171311551991035e-842j)  +/-  (1.89e-65, 5.54e-180j)
| (0.031365759100004504165 - 3.064641545197682812e-840j)  +/-  (4.61e-67, 1.35e-181j)
| (0.042492903642784351095 + 2.3754400091107331989e-840j)  +/-  (3.76e-69, 1.11e-183j)
| (0.061014055957006694986 - 6.1239411859944083255e-840j)  +/-  (7.8e-73, 2.29e-187j)
| (0.045821550116958780859 - 3.6478276132718520545e-841j)  +/-  (1.46e-70, 4.28e-185j)
| (0.042492903642784351095 + 3.0551958840541791547e-841j)  +/-  (1.1e-69, 3.24e-184j)
| (0.059612044949009236658 - 9.5572580657182325509e-840j)  +/-  (4.4e-74, 1.29e-188j)
| (0.048895187053847483059 + 2.3262190767882866206e-840j)  +/-  (1.64e-72, 4.83e-187j)
| (0.045821550116958780859 - 2.3168473129650000933e-840j)  +/-  (1.24e-71, 3.63e-186j)
| (0.052799754534192450694 + 9.8567588609881545184e-840j)  +/-  (1.01e-74, 2.97e-189j)
| (0.051680484973347295512 - 5.4523045959282996389e-841j)  +/-  (5.19e-74, 1.52e-188j)
| (0.048895187053847483059 + 4.4213386945998083345e-841j)  +/-  (3.54e-73, 1.04e-187j)
| (0.05638667895045968153 - 2.796893357284322184e-840j)  +/-  (4.81e-76, 1.41e-190j)
| (0.051680484973347295512 - 2.4042032074816921294e-840j)  +/-  (8.58e-75, 2.52e-189j)
| (0.052799754534192450694 + 1.248456798150421718e-839j)  +/-  (2.04e-77, 5.99e-192j)
| (0.054170439678719449866 + 6.8503821708537962261e-841j)  +/-  (3.35e-76, 9.85e-191j)
| (0.060007279410726981237 - 1.5667870852393665782e-840j)  +/-  (1.47e-77, 4.32e-192j)
| (0.059612044949009236658 - 1.0804169135125971466e-839j)  +/-  (1.3e-77, 3.81e-192j)
| (0.054170439678719449866 + 2.5565263743832592213e-840j)  +/-  (7.25e-77, 2.13e-191j)
| (0.058036361042488412402 + 8.7572940999204384919e-840j)  +/-  (4.6e-78, 1.35e-192j)
| (0.058036361042488412402 + 5.5549869197230858929e-840j)  +/-  (1.71e-78, 5.02e-193j)
| (0.05638667895045968153 - 8.7828015475791535962e-841j)  +/-  (2.89e-78, 8.5e-193j)
| (0.051729375878639336758 - 8.3853405621550452602e-840j)  +/-  (2.58e-78, 7.58e-193j)
| (0.061119497054077865196 + 4.5894264013021174557e-840j)  +/-  (7.95e-80, 2.33e-194j)
| (0.058349610412823362389 + 3.1562735712387012162e-840j)  +/-  (6.72e-80, 1.98e-194j)
| (0.062029560676291047296 + 9.5284193764438297375e-840j)  +/-  (2.57e-79, 7.61e-194j)
| (0.058349610412823362389 + 1.1536290439301919611e-840j)  +/-  (6.28e-80, 1.85e-194j)
| (0.061014055957006694986 - 3.4178006580010169281e-840j)  +/-  (8.54e-80, 2.52e-194j)
| (0.051729375878639336758 - 1.1792052204969691896e-839j)  +/-  (4.04e-80, 1.22e-194j)
| (0.060007279410726981237 - 3.7037420033519352834e-840j)  +/-  (7.98e-81, 2.26e-195j)
