Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 60
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^65 - 10714818941859305330295862788640721989628517157161110123743892577083435658098/2727947585273246397408571533222204062597038579454282342044916363740573897*t^63 + 4931223025131748852943846278624313671446288510974284960607364288110649763166817/2727947585273246397408571533222204062597038579454282342044916363740573897*t^61 - 2830355427121285432380954693549533223348081136148103474971923009429542231415387755/5455895170546492794817143066444408125194077158908564684089832727481147794*t^59 + 39207704503642494902854277185268166378285168851180440349530117688402514679797570915/376268632451482261711527108030648836220281183373004460971712601895251572*t^57 - 11730141957395177869917655568004645270364654372348055691555888409608098196638992781565/752537264902964523423054216061297672440562366746008921943425203790503144*t^55 + 2715324346713804349470141135493835372330341455015653848763057029743038773456956383484045/1505074529805929046846108432122595344881124733492017843886850407581006288*t^53 - 498802476797967333466534283460661182642914084221967651394264024734325184072786189575322935/3010149059611858093692216864245190689762249466984035687773700815162012576*t^51 + 74002929091435187382202476978882981539089665589275207107682890303616884746482304785109341375/6020298119223716187384433728490381379524498933968071375547401630324025152*t^49 - 8978071391460160916371958708531074178343942811137875901051638500023927549399211823956578134625/12040596238447432374768867456980762759048997867936142751094803260648050304*t^47 + 898595038139385929492646121277745129516740191777378090866430125225413493454962428992802349545625/24081192476894864749537734913961525518097995735872285502189606521296100608*t^45 - 74654358220148014867615285993361586505652164869570543296826481306478056283799169174134949241035875/48162384953789729499075469827923051036195991471744571004379213042592201216*t^43 + 5168927837507012626939867911157027740948000898488090484840071255916725085186359410604037591821051375/96324769907579458998150939655846102072391982943489142008758426085184402432*t^41 - 7291226215571714972222151964343436859761768346109252962545436362925949129100228986315233687072385625/4698769263784363853568338519797370832799608924072641073597972004155336704*t^39 + 352491913775524046752419490679924925971115637421979209593122931316100370068440827136865895926870005625/9397538527568727707136677039594741665599217848145282147195944008310673408*t^37 - 14236042520247517120914796781999549136003014589955815680223647533094159773876692939133167591255183916875/18795077055137455414273354079189483331198435696290564294391888016621346816*t^35 + 479376423190328152411300606390564347027443178427421095267835357182889661116579841653473581032749456033125/37590154110274910828546708158378966662396871392581128588783776033242693632*t^33 - 13415206185665824013323109031575585573369129777549684429923780036739655750111892591318810721568131730399375/75180308220549821657093416316757933324793742785162257177567552066485387264*t^31 + 310559148854737947441340856959319836319069572573197122009541164591088258010808847253879663875012186233034375/150360616441099643314186832633515866649587485570324514355135104132970774528*t^29 - 5911104652764560995118275844454058183412062344467230020307149064682791307356181408612123861182668955078678125/300721232882199286628373665267031733299174971140649028710270208265941549056*t^27 + 91791188725583702281241959312750954999468755281915999520404382051603389933554780597270164038417699850620090625/601442465764398573256747330534063466598349942281298057420540416531883098112*t^25 - 1151692722781884763509782291668743579637390158073097650604042759508905343385926843065661665161165663788443109375/1202884931528797146513494661068126933196699884562596114841080833063766196224*t^23 + 11536437300426021400186038005672115574425209388464679165761463477332768673950495831298488004599951358020731359375/2405769863057594293026989322136253866393399769125192229682161666127532392448*t^21 - 90901640597664178225725166814056240212898359857359016489451451254693130628930970709267362527423250706616676328125/4811539726115188586053978644272507732786799538250384459364323332255064784896*t^19 + 553146471558995280445845313345969673558178926025970870132706034640688721335940011303388527678976365279331853828125/9623079452230377172107957288545015465573599076500768918728646664510129569792*t^17 - 2540002649344135975786885071057711196582851585849577403938956782140227219995989269894960246694804083703984599421875/19246158904460754344215914577090030931147198153001537837457293329020259139584*t^15 + 8545405299395468936304790474360441566644484109692035557312916989624518632734349278461623411241405098072332054546875/38492317808921508688431829154180061862294396306003075674914586658040518279168*t^13 - 20266449262660205427730189177794810312344812617710716916604202867033586297959062017732186153133067903382345149265625/76984635617843017376863658308360123724588792612006151349829173316081036558336*t^11 + 32160332224627891204766036029274925211084038948424172968382153924267868704427328275298918364442347417392813866328125/153969271235686034753727316616720247449177585224012302699658346632162073116672*t^9 - 31711643275388183593791343287891534906645807805753059063532701499333471590581145556619740513256246804283840267421875/307938542471372069507454633233440494898355170448024605399316693264324146233344*t^7 + 17348524061756964636352580921388042769580847429178424411426162984583450605539976436665075292605200925635007892421875/615877084942744139014909266466880989796710340896049210798633386528648292466688*t^5 - 4321722913930349286550454303291361072949074665944947559823859146172436865040654706665763025398155784957271677265625/1231754169885488278029818532933761979593420681792098421597266773057296584933376*t^3 + 156420381155036536867672720130588771738950366478526417589056837023993061617917762373440352081652501807403595390625/1231754169885488278029818532933761979593420681792098421597266773057296584933376*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: 0
  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
Positive weights:   65 out of 65
Indefinite weights: 0 out of 65
Negative weights:   0 out of 65
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.811554099611697315 + 1.9820333219867973384e-506j)  +/-  (3.64e-243, 3.64e-243j)
| (-8.8215166020547751612 - 1.7578377675997051861e-508j)  +/-  (1.73e-241, 1.73e-241j)
| (7.6013617805047464746 + 7.0249482093739445425e-523j)  +/-  (3.42e-240, 3.42e-240j)
| (8.3909261376106581962 - 1.3736518233211069969e-542j)  +/-  (6.77e-241, 6.77e-241j)
| (7.2321176775998855974 + 3.5154025749800609285e-553j)  +/-  (5.52e-240, 5.52e-240j)
| (9.811554099611697315 + 2.0745342499982778139e-558j)  +/-  (3.54e-243, 3.54e-243j)
| (-7.9862717934606838966 - 8.4062229413350989079e-564j)  +/-  (1.69e-240, 1.69e-240j)
| (9.2883718444481108383 + 2.660749727049298409e-564j)  +/-  (3.22e-242, 3.22e-242j)
| (-7.6013617805047464746 - 3.6241797823417884529e-574j)  +/-  (3.27e-240, 3.27e-240j)
| (4.3072720169635712203 - 1.3563145007055316916e-572j)  +/-  (2.17e-241, 2.17e-241j)
| (-8.3909261376106581962 - 5.2974739284716501514e-576j)  +/-  (6.69e-241, 6.69e-241j)
| (-4.0091030343276776813 - 1.0297019554862251282e-580j)  +/-  (7.14e-242, 7.14e-242j)
| (-10.443650067604447959 + 1.3339978891698485267e-583j)  +/-  (1.47e-244, 1.47e-244j)
| (-2.5647663057374773499 - 1.473157811920218228e-584j)  +/-  (4.25e-245, 4.25e-245j)
| (8.8215166020547751612 - 3.8133713523217057868e-578j)  +/-  (1.79e-241, 1.79e-241j)
| (1.1991279902467483489 + 4.9661162428956499878e-597j)  +/-  (1.77e-249, 1.77e-249j)
| (5.2262049270886516407 + 7.0465313308750496409e-586j)  +/-  (2.51e-240, 2.51e-240j)
| (-9.2883718444481108383 + 1.0178913220045545948e-595j)  +/-  (3.56e-242, 3.56e-242j)
| (-1.1991279902467483489 - 2.706288398909622245e-605j)  +/-  (1.73e-249, 1.73e-249j)
| (-4.3072720169635712203 + 8.6957788799556102693e-598j)  +/-  (2.16e-241, 2.16e-241j)
| (2.8480848755144490657 + 4.4378467988333024578e-600j)  +/-  (2.3e-244, 2.3e-244j)
| (2.0063804733856228519 + 1.1744705264497980979e-602j)  +/-  (9.39e-247, 9.39e-247j)
| (7.9862717934606838966 + 1.1780727970846847779e-594j)  +/-  (1.65e-240, 1.65e-240j)
| (-3.4227565066839605049 + 1.2298818616248553339e-611j)  +/-  (5.27e-243, 5.27e-243j)
| (-2.8480848755144490657 - 1.467447192082494026e-612j)  +/-  (2.34e-244, 2.34e-244j)
| (-6.1932441951422636307 + 1.1868920444423208043e-608j)  +/-  (7.99e-240, 7.99e-240j)
| (1.4622437734705034859 - 3.7090732230112869768e-617j)  +/-  (1.66e-248, 1.66e-248j)
| (5.8643805528081001531 + 1.7367538796476875684e-606j)  +/-  (6.22e-240, 6.22e-240j)
| (4.0091030343276776813 + 9.7814927812381583186e-618j)  +/-  (7.15e-242, 7.15e-242j)
| (-1.4622437734705034859 + 4.0127905929685513234e-634j)  +/-  (1.57e-248, 1.57e-248j)
| (3.1340531862156999385 + 4.859638987759493023e-623j)  +/-  (1.27e-243, 1.27e-243j)
| (5.5423117086010188505 - 3.6208646791314744897e-624j)  +/-  (3.99e-240, 3.99e-240j)
| (3.4227565066839605049 + 3.5868516557670770786e-636j)  +/-  (5.47e-243, 5.47e-243j)
| (-5.2262049270886516407 - 1.5171977737877979761e-635j)  +/-  (2.45e-240, 2.45e-240j)
| (-6.5299200009273540328 - 1.2773663750758108391e-638j)  +/-  (8.54e-240, 8.54e-240j)
| (6.8756739565612896995 - 5.4152577959541944057e-656j)  +/-  (7.68e-240, 7.68e-240j)
| (-3.1340531862156999385 - 5.1007321330982637894e-675j)  +/-  (1.22e-243, 1.22e-243j)
| (4.6092214408786243039 - 6.7775251680314570593e-670j)  +/-  (5.24e-241, 5.24e-241j)
| (-4.9153685116295717144 + 1.4019275715724983917e-672j)  +/-  (1.15e-240, 1.15e-240j)
| (-5.5423117086010188505 - 4.4878891996253384144e-672j)  +/-  (3.96e-240, 3.96e-240j)
| (-2.2841275850653160384 - 4.8996619998505566773e-678j)  +/-  (6.54e-246, 6.54e-246j)
| (-6.8756739565612896995 + 1.3395307020788843519e-671j)  +/-  (7.36e-240, 7.36e-240j)
| (10.443650067604447959 + 3.4986781536356289734e-676j)  +/-  (1.58e-244, 1.58e-244j)
| (-7.2321176775998855974 + 7.1531657091209686058e-674j)  +/-  (5.48e-240, 5.48e-240j)
| (-5.8643805528081001531 - 2.7971446235714888177e-678j)  +/-  (6.03e-240, 6.03e-240j)
| (-0.94637194250166867417 - 5.5290295282315741341e-704j)  +/-  (1.88e-250, 1.88e-250j)
| (-1.7320508075688772935 - 2.3641675138737859447e-701j)  +/-  (1.31e-247, 1.31e-247j)
| (6.5299200009273540328 + 2.3153170797149738818e-691j)  +/-  (7.72e-240, 7.72e-240j)
| (0.47621524187135925688 + 2.2211805916946845032e-729j)  +/-  (1.87e-252, 1.87e-252j)
| (4.9153685116295717144 + 4.7246111551104182238e-716j)  +/-  (1.14e-240, 1.14e-240j)
| (-2.0063804733856228519 + 5.862959865532509672e-744j)  +/-  (1.04e-246, 1.04e-246j)
| (-0.47621524187135925688 - 5.3226825678332899715e-750j)  +/-  (1.7e-252, 1.7e-252j)
| (2.2841275850653160384 - 6.1137593405998266736e-737j)  +/-  (7.37e-246, 7.37e-246j)
| (6.1932441951422636307 - 1.4740292858070269724e-737j)  +/-  (7.93e-240, 7.93e-240j)
| (2.5647663057374773499 - 9.6888651073271151218e-757j)  +/-  (3.84e-245, 3.84e-245j)
| (1.5038715450191675389e-788 - 3.7515662905402844279e-789j)  +/-  (1.01e-786, 1.01e-786j)
| (-0.7071067811865475244 - 2.5774464818554842206e-761j)  +/-  (1.87e-251, 1.87e-251j)
| (0.24149030281760740472 - 4.0365755999108144901e-763j)  +/-  (1.01e-253, 1.01e-253j)
| (3.714362090138800645 + 4.244486049606424811e-751j)  +/-  (2.08e-242, 2.08e-242j)
| (0.7071067811865475244 + 1.6237212566401693075e-762j)  +/-  (1.81e-251, 1.81e-251j)
| (-0.24149030281760740472 + 4.3172331518914421283e-763j)  +/-  (1.01e-253, 1.01e-253j)
| (-4.6092214408786243039 + 2.5444567802063901461e-750j)  +/-  (5.23e-241, 5.23e-241j)
| (-3.714362090138800645 - 1.1291094648780583054e-752j)  +/-  (2.07e-242, 2.07e-242j)
| (1.7320508075688772935 + 8.718649828309590902e-758j)  +/-  (1.21e-247, 1.21e-247j)
| (0.94637194250166867417 - 1.7242564784990947031e-761j)  +/-  (1.92e-250, 1.92e-250j)
-------------------------------------------------
The weights are:
| (4.9451660327423712653e-43 + 7.3842001394866768464e-547j)  +/-  (2.88e-62, 2.79e-182j)
| (4.025320988157954849e-35 - 6.3915022011076572536e-542j)  +/-  (2.48e-59, 2.4e-179j)
| (1.7114800181358123702e-26 + 1.1794418537164140772e-539j)  +/-  (8.22e-57, 7.96e-177j)
| (6.2119324200359664918e-32 + 1.7589828702707661734e-542j)  +/-  (7.87e-60, 7.62e-180j)
| (3.9402934972943115605e-24 - 2.02276766928974247e-538j)  +/-  (7.53e-56, 7.29e-176j)
| (4.9451660327423712653e-43 - 3.3519288665266282024e-548j)  +/-  (5.63e-65, 5.45e-185j)
| (4.4396644955015406768e-29 - 1.078058587815429212e-539j)  +/-  (1.66e-60, 1.61e-180j)
| (9.4111962687315329833e-39 + 5.3093230244930311107e-546j)  +/-  (1.48e-63, 1.44e-183j)
| (1.7114800181358123702e-26 + 1.5972316208092735149e-538j)  +/-  (9.52e-60, 9.22e-180j)
| (1.4833755129899555872e-09 + 1.356174749568129585e-530j)  +/-  (1.31e-47, 1.27e-167j)
| (6.2119324200359664918e-32 + 7.1022595339121607641e-541j)  +/-  (8.57e-62, 8.3e-182j)
| (1.7495658290835093948e-08 - 1.4696351374601999194e-529j)  +/-  (9.55e-48, 9.24e-168j)
| (1.7641915841717933019e-48 - 6.2552753352761621445e-550j)  +/-  (3.65e-69, 3.53e-189j)
| (0.00022124183323595269069 + 3.1143748357366077673e-527j)  +/-  (1.5e-38, 1.45e-158j)
| (4.025320988157954849e-35 - 3.9518499334115579049e-544j)  +/-  (4.47e-64, 4.33e-184j)
| (0.034648124229226526293 - 1.0638166489967955114e-525j)  +/-  (5.8e-24, 5.62e-144j)
| (2.4293921685335091149e-13 - 1.1005555560554585504e-532j)  +/-  (2.8e-54, 2.71e-174j)
| (9.4111962687315329833e-39 - 2.1190373095402302341e-544j)  +/-  (3.49e-65, 3.38e-185j)
| (0.034648124229226526293 - 1.3990778000498180823e-525j)  +/-  (9.48e-26, 9.18e-146j)
| (1.4833755129899555872e-09 + 3.950957118619473757e-530j)  +/-  (1.73e-50, 1.67e-170j)
| (4.8183601470296664372e-05 - 6.3090793338400429644e-528j)  +/-  (1.44e-43, 1.39e-163j)
| (0.0027816975668563345642 + 1.041885651522889264e-526j)  +/-  (5.7e-37, 5.52e-157j)
| (4.4396644955015406768e-29 - 5.3166839004448529654e-541j)  +/-  (5.14e-62, 4.98e-182j)
| (1.3369961907546428561e-06 - 1.572555315032814426e-528j)  +/-  (4.68e-47, 4.53e-167j)
| (4.8183601470296664372e-05 - 1.2337685597878445785e-527j)  +/-  (8.72e-44, 8.45e-164j)
| (4.1248277917894110246e-18 + 1.7304312212831902642e-534j)  +/-  (3.21e-59, 3.11e-179j)
| (0.017752278645761167097 + 5.1498918365027787598e-526j)  +/-  (4.82e-34, 4.67e-154j)
| (2.1277652282259374797e-16 - 2.473034269397087839e-534j)  +/-  (2.32e-58, 2.25e-178j)
| (1.7495658290835093948e-08 - 5.5036514920464879674e-530j)  +/-  (1.05e-51, 1.01e-171j)
| (0.017752278645761167097 + 7.1998694314889958889e-526j)  +/-  (6.59e-37, 6.38e-157j)
| (8.7905450931160922914e-06 + 2.170566394319209888e-528j)  +/-  (4.64e-48, 4.49e-168j)
| (8.2194967241379022926e-15 + 1.7599119463877864506e-533j)  +/-  (1.53e-57, 1.48e-177j)
| (1.3369961907546428561e-06 - 6.9250226793117133494e-529j)  +/-  (1.14e-49, 1.11e-169j)
| (2.4293921685335091149e-13 - 4.3102524810938579747e-532j)  +/-  (2.85e-59, 2.76e-179j)
| (5.8330930913139211871e-20 - 2.1235757166695012155e-535j)  +/-  (2.82e-63, 2.73e-183j)
| (5.8244323564410924221e-22 + 2.7831067424368064339e-537j)  +/-  (5.23e-63, 5.06e-183j)
| (8.7905450931160922914e-06 + 4.5678678661818715496e-528j)  +/-  (2.14e-51, 2.08e-171j)
| (1.0179054077951622322e-10 - 3.0313547904817460121e-531j)  +/-  (5.8e-56, 5.61e-176j)
| (5.5926904182269026596e-12 + 2.1520302536780405478e-531j)  +/-  (1.18e-58, 1.15e-178j)
| (8.2194967241379022926e-15 + 7.7291526543180367468e-533j)  +/-  (7.99e-61, 7.73e-181j)
| (0.00085427501005117503396 - 7.3874643303402332518e-527j)  +/-  (1.14e-50, 1.11e-170j)
| (5.8244323564410924221e-22 + 2.2549330863354797367e-536j)  +/-  (3.63e-65, 3.52e-185j)
| (1.7641915841717933019e-48 + 5.4039398759400919508e-551j)  +/-  (3.78e-79, 3.66e-199j)
| (3.9402934972943115605e-24 - 2.0535276324904157807e-537j)  +/-  (2.64e-66, 2.56e-186j)
| (2.1277652282259374797e-16 - 1.2317886798864809494e-533j)  +/-  (2.08e-62, 2.01e-182j)
| (0.056714856116816174559 + 2.5288164573092015976e-525j)  +/-  (4.74e-50, 4.59e-170j)
| (0.0076493151727574248733 - 3.5326483869808637863e-526j)  +/-  (2.91e-52, 2.82e-172j)
| (5.8330930913139211871e-20 - 3.1580354595330879769e-536j)  +/-  (1.15e-66, 1.12e-186j)
| (0.10393000346465860939 + 4.7019053287863480062e-525j)  +/-  (1.83e-52, 1.77e-172j)
| (5.5926904182269026596e-12 + 6.1064678359478017749e-532j)  +/-  (1.86e-62, 1.8e-182j)
| (0.0027816975668563345642 + 1.6564675359315874592e-526j)  +/-  (1.33e-54, 1.28e-174j)
| (0.10393000346465860939 + 5.2393297861092021148e-525j)  +/-  (8.2e-54, 7.94e-174j)
| (0.00085427501005117503396 - 4.3452795337770885769e-527j)  +/-  (1.65e-57, 1.59e-177j)
| (4.1248277917894110246e-18 + 3.0190180016679468261e-535j)  +/-  (5.59e-66, 5.41e-186j)
| (0.00022124183323595269069 + 1.7098270021647985663e-527j)  +/-  (3.26e-58, 3.15e-178j)
| (0.13705174047828155815 + 5.814772902222077797e-525j)  +/-  (1.23e-54, 1.2e-174j)
| (0.079786545145283619515 - 3.9984702839979692929e-525j)  +/-  (2.35e-54, 2.27e-174j)
| (0.12707729378980140999 - 5.4897844340709464119e-525j)  +/-  (6.53e-55, 6.32e-175j)
| (1.6855698824882821707e-07 + 2.0380629645492267565e-529j)  +/-  (9.42e-61, 9.12e-181j)
| (0.079786545145283619515 - 3.4042471691217863201e-525j)  +/-  (6.2e-56, 6e-176j)
| (0.12707729378980140999 - 5.7992633432506344357e-525j)  +/-  (3.9e-55, 3.78e-175j)
| (1.0179054077951622322e-10 - 9.6838030881346910738e-531j)  +/-  (1.44e-63, 1.39e-183j)
| (1.6855698824882821707e-07 + 5.0095711261355413533e-529j)  +/-  (1.16e-61, 1.13e-181j)
| (0.0076493151727574248733 - 2.3717244388534206594e-526j)  +/-  (3.95e-59, 3.9e-179j)
| (0.056714856116816174559 + 2.0381744275674680489e-525j)  +/-  (6.1e-58, 5.77e-178j)
