Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 62
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 62 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^67 - 116419263608413987561981260807926297785033128055858737087924284335311663725943/27750703105967347575413821218925198136229958356922454770752195399473137990*t^65 + 114703131551046500143849264457044803945282742308655604023310137235342590773194791/55501406211934695150827642437850396272459916713844909541504390798946275980*t^63 - 70635743147353192500916278329279495746289853980391380339771999124038448523494811863/111002812423869390301655284875700792544919833427689819083008781597892551960*t^61 + 6104194825702032750760913810337499129429174363664713633361659448835166725849442359969/44401124969547756120662113950280317017967933371075927633203512639157020784*t^59 - 1969544784906764537119458486437976778111101312470613481791021627367722524068282091380653/88802249939095512241324227900560634035935866742151855266407025278314041568*t^57 + 493101461023105610337788881134624065657083664802226499054719084634996468930602152122273643/177604499878191024482648455801121268071871733484303710532814050556628083136*t^55 - 98273735907126275982264662563960426555020330653390870959982096086795944499439341728902775699/355208999756382048965296911602242536143743466968607421065628101113256166272*t^53 + 15870901672748608642535824942325701539904539418403036388133607954408111489580118771080255560097/710417999512764097930593823204485072287486933937214842131256202226512332544*t^51 - 2103533513289417005945552411434492126283385902359617425596900037516949138996210943039989998747025/1420835999025528195861187646408970144574973867874429684262512404453024665088*t^49 + 230913623711172527035815528326509035866893183791765250602464829083499263979522471895223660546087175/2841671998051056391722375292817940289149947735748859368525024808906049330176*t^47 - 21130942776686939180677931211228710493093653900347646583276936509117164749054072779786881154196438375/5683343996102112783444750585635880578299895471497718737050049617812098660352*t^45 + 1619108924492711987371904169320514864036053899078390579078550546193322448231773044279609746416774193925/11366687992204225566889501171271761156599790942995437474100099235624197320704*t^43 - 104161094489174165337710879459070654637120147428865536719391260714942248836356026795468314558622122101025/22733375984408451133779002342543522313199581885990874948200198471248394641408*t^41 + 5633305466314737139088394886762929295545458127593992400162166148258540670689821302666039602708439140218375/45466751968816902267558004685087044626399163771981749896400396942496789282816*t^39 - 256119559491495336908881814877777394709146165243613091619305157109610499144654741305333633859870022609157375/90933503937633804535116009370174089252798327543963499792800793884993578565632*t^37 + 9777108737404030264490876167023869031171007332735331422636523832662094330342191850160299989330894664239042125/181867007875267609070232018740348178505596655087926999585601587769987157131264*t^35 - 312620749646028134767925037239565907824214603365485116110730437015190091978618446019094055833024871435789837875/363734015750535218140464037480696357011193310175853999171203175539974314262528*t^33 + 8342400432515115867746569041450100235419543883023674906374790941816682237611292720869985789168578536695596408625/727468031501070436280928074961392714022386620351707998342406351079948628525056*t^31 - 184884170477884179424785030058791997669707423565801198121495808362398789000423627567306769795229391170818712350625/1454936063002140872561856149922785428044773240703415996684812702159897257050112*t^29 + 3381441664356236715989360120634812649271186121666238593702139722963470408144126594594366424589866312312568681691875/2909872126004281745123712299845570856089546481406831993369625404319794514100224*t^27 - 50636183764326623825642972377783049896380347612498605221681115815214852178718417943389872828759789924048265534474375/5819744252008563490247424599691141712179092962813663986739250808639589028200448*t^25 + 614790054864628690087098589253107171938551440653419588813409903508182752433904870020146149312133454064506803871590625/11639488504017126980494849199382283424358185925627327973478501617279178056400896*t^23 - 5979546432221759532136811606370301648416657749544543698153532147210333873171204312586684547437377629890659374919365625/23278977008034253960989698398764566848716371851254655946957003234558356112801792*t^21 + 45902456694338347227097988266225975362679743678273785160114573733752987890022005537782476844099852198816817487709171875/46557954016068507921979396797529133697432743702509311893914006469116712225603584*t^19 - 273037882082534259223727551533952460114722782301634036777392765959607979640223090488120431748190873156221258409881796875/93115908032137015843958793595058267394865487405018623787828012938233424451207168*t^17 + 1229602618590857664517489806259313733081596473824124506485838291026698112416659394133976919892954449065931368462526978125/186231816064274031687917587190116534789730974810037247575656025876466848902414336*t^15 - 4069849310476059174259251608334090415054654738663397710607881085695329822878576405627069316344190620124404001288106378125/372463632128548063375835174380233069579461949620074495151312051752933697804828672*t^13 + 9522373641833514167883221467431174883353448770924086966675994685987734188699314303427368141514818161916097178959397384375/744927264257096126751670348760466139158923899240148990302624103505867395609657344*t^11 - 14936300434648722396474593491008007101294123160965308415917571467561392413991980254781494654346695425658347045235195296875/1489854528514192253503340697520932278317847798480297980605248207011734791219314688*t^9 + 14558298288880413043985934922635554509720225902425890187645199758644115628831612707812917533950740752490232907773147078125/2979709057028384507006681395041864556635695596960595961210496414023469582438629376*t^7 - 7841686060558293977772579852979768307796993439524520286521718474238267086737028399490081978284589850947726530106365203125/5959418114056769014013362790083729113271391193921191922420992828046939164877258752*t^5 + 1900189338564547606379997804178228805094335299186240694616885426331921807285785715532837546684545498566978222279340921875/11918836228113538028026725580167458226542782387842383844841985656093878329754517504*t^3 - 65040234416869822969914797274408488120912087203532138018701649424371113905411498650140257572314626116976284234638921875/11918836228113538028026725580167458226542782387842383844841985656093878329754517504*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:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.8064091946225295551 + 8.3171270079006854696e-688j)  +/-  (9.39e-240, 9.39e-240j)
| (-8.1884224612071060853 - 8.3995219460528126202e-686j)  +/-  (4.47e-240, 4.47e-240j)
| (-9.0177337922871699545 + 1.9611985145944306337e-693j)  +/-  (4.44e-241, 4.44e-241j)
| (-7.8064091946225295551 - 4.1392472358594124743e-708j)  +/-  (1e-239, 1e-239j)
| (5.1443063116504938742 + 3.966979725711203236e-726j)  +/-  (5.34e-240, 5.34e-240j)
| (9.4814637789265459499 - 3.4603004867338192642e-727j)  +/-  (7.23e-242, 7.23e-242j)
| (-7.4400496278773484756 + 2.7785093797269660976e-723j)  +/-  (1.75e-239, 1.75e-239j)
| (10.629526535832380482 + 8.8857843456386821478e-741j)  +/-  (3.28e-244, 3.28e-244j)
| (-3.9568055445173965862 + 9.4217207990473611911e-739j)  +/-  (1.4e-241, 1.4e-241j)
| (2.8222430007858291458 + 2.9037694343522033043e-744j)  +/-  (3.82e-244, 3.82e-244j)
| (2.5454463942161793377 - 2.2737797359355103104e-745j)  +/-  (6.97e-245, 6.97e-245j)
| (7.4400496278773484756 + 1.0417489003680264315e-738j)  +/-  (1.7e-239, 1.7e-239j)
| (-9.4814637789265459499 - 3.7102711565423534477e-738j)  +/-  (7.26e-242, 7.26e-242j)
| (-2.0001016616222078699 - 3.0180090131330116485e-760j)  +/-  (1.46e-246, 1.46e-246j)
| (-5.4519809965344199416 - 2.4862898409846335316e-752j)  +/-  (9.84e-240, 9.84e-240j)
| (10.001291481639130687 - 6.9057791155613381491e-773j)  +/-  (8.3e-243, 8.3e-243j)
| (8.5901446377943339008 - 1.1199021837970879546e-767j)  +/-  (1.73e-240, 1.73e-240j)
| (7.0864956147215070819 - 4.2229728682983805796e-767j)  +/-  (2.37e-239, 2.37e-239j)
| (-0.7071067811865475244 + 8.0394092013910884944e-779j)  +/-  (1.85e-251, 1.85e-251j)
| (6.0840318749393237269 + 4.0743081136405825216e-767j)  +/-  (2.18e-239, 2.18e-239j)
| (-0.95419186335895105029 + 3.8167494285318189231e-778j)  +/-  (2.2e-250, 2.2e-250j)
| (9.0177337922871699545 - 2.6424391274355392682e-769j)  +/-  (4.53e-241, 4.53e-241j)
| (-2.8222430007858291458 + 8.3225383333871003032e-773j)  +/-  (4.11e-244, 4.11e-244j)
| (3.9568055445173965862 + 1.0509678202773185322e-769j)  +/-  (1.33e-241, 1.33e-241j)
| (8.1884224612071060853 + 4.6410368355448661798e-768j)  +/-  (4.74e-240, 4.74e-240j)
| (-10.001291481639130687 - 4.2071265484495694849e-767j)  +/-  (8.04e-243, 8.04e-243j)
| (4.2480262308250602582 - 2.9014737948705552318e-771j)  +/-  (3.98e-241, 3.98e-241j)
| (-10.629526535832380482 - 5.0293183472672799648e-769j)  +/-  (3.38e-244, 3.38e-244j)
| (-6.7436504690647189816 - 6.7094623796569188389e-774j)  +/-  (2.75e-239, 2.75e-239j)
| (5.7649952557569136658 + 1.6521868408309352429e-789j)  +/-  (1.47e-239, 1.47e-239j)
| (-5.7649952557569136658 - 1.9794638633460149133e-788j)  +/-  (1.55e-239, 1.55e-239j)
| (3.1016933667508591039 + 2.5350285811339605055e-801j)  +/-  (1.97e-243, 1.97e-243j)
| (1.2080969948929758032 - 4.1779576697121873336e-807j)  +/-  (2.55e-249, 2.55e-249j)
| (5.4519809965344199416 + 1.6916005042145951135e-797j)  +/-  (9.67e-240, 9.67e-240j)
| (-2.2713447746179773982 - 1.6395640052576453634e-804j)  +/-  (1.1e-245, 1.1e-245j)
| (-3.3838469154807670819 + 8.6042021581710308244e-800j)  +/-  (9.31e-243, 9.31e-243j)
| (4.5427753282745036864 + 8.3397007404946838313e-799j)  +/-  (1.12e-240, 1.12e-240j)
| (2.2713447746179773982 - 2.700281546708750348e-803j)  +/-  (1.12e-245, 1.12e-245j)
| (-2.5454463942161793377 + 5.6001652483879953415e-802j)  +/-  (6.9e-245, 6.9e-245j)
| (4.8413988646632637769 + 2.2644509452189079884e-799j)  +/-  (2.59e-240, 2.59e-240j)
| (-3.668824159152592534 + 4.2514304557979078824e-799j)  +/-  (3.57e-242, 3.57e-242j)
| (-4.8413988646632637769 + 2.419907020117277415e-796j)  +/-  (2.44e-240, 2.44e-240j)
| (1.7320508075688772935 - 3.8885906302460966574e-812j)  +/-  (1.96e-247, 1.96e-247j)
| (2.0001016616222078699 - 2.2324344812876958304e-808j)  +/-  (1.71e-246, 1.71e-246j)
| (3.3838469154807670819 - 5.5895953540705654511e-805j)  +/-  (9.68e-243, 9.68e-243j)
| (-4.2480262308250602582 + 1.6551059812293861212e-800j)  +/-  (4e-241, 4e-241j)
| (-0.46697376400676651853 + 6.8507980148253227096e-817j)  +/-  (1.23e-252, 1.23e-252j)
| (0.95419186335895105029 - 1.5751516031269777455e-815j)  +/-  (2.25e-250, 2.25e-250j)
| (2.5161300712550809413e-848 + 3.733225690728097214e-848j)  +/-  (3.02e-846, 3.02e-846j)
| (-8.5901446377943339008 - 5.0718697034143606683e-803j)  +/-  (1.7e-240, 1.7e-240j)
| (-4.5427753282745036864 + 3.3996114235556222943e-822j)  +/-  (1.15e-240, 1.15e-240j)
| (-0.23218713495468214557 - 3.0645100289535960978e-869j)  +/-  (9.94e-254, 9.94e-254j)
| (0.23218713495468214557 + 9.6411623758484635875e-870j)  +/-  (1.09e-253, 1.09e-253j)
| (-7.0864956147215070819 - 3.5421926682445738598e-854j)  +/-  (2.33e-239, 2.33e-239j)
| (0.7071067811865475244 + 1.5738763801344617367e-890j)  +/-  (2.15e-251, 2.15e-251j)
| (-1.4677608908069340465 + 7.2994231009579164186e-889j)  +/-  (2.4e-248, 2.4e-248j)
| (6.7436504690647189816 + 5.610560264675086396e-878j)  +/-  (2.92e-239, 2.92e-239j)
| (-3.1016933667508591039 - 1.6965191339377033049e-880j)  +/-  (1.95e-243, 1.95e-243j)
| (-6.4099143863898509348 + 2.7142284019049395392e-899j)  +/-  (2.64e-239, 2.64e-239j)
| (3.668824159152592534 + 1.9753778429369895426e-924j)  +/-  (3.74e-242, 3.74e-242j)
| (6.4099143863898509348 - 4.8185195228331651345e-922j)  +/-  (2.61e-239, 2.61e-239j)
| (-1.7320508075688772935 - 4.5582609563909208775e-930j)  +/-  (1.96e-247, 1.96e-247j)
| (-1.2080969948929758032 + 6.0653530997771916493e-932j)  +/-  (2.57e-249, 2.57e-249j)
| (-6.0840318749393237269 + 4.5183362822433689178e-920j)  +/-  (2.23e-239, 2.23e-239j)
| (0.46697376400676651853 - 5.8375533648778977326e-938j)  +/-  (1.32e-252, 1.32e-252j)
| (1.4677608908069340465 - 6.6121901805567531902e-934j)  +/-  (2.35e-248, 2.35e-248j)
| (-5.1443063116504938742 + 4.0665957151607877307e-924j)  +/-  (4.99e-240, 4.99e-240j)
-------------------------------------------------
The weights are:
| (7.210274031920010942e-28 - 4.6328036214852927987e-714j)  +/-  (1.51e-57, 2.64e-175j)
| (1.6753549190552292864e-30 - 1.1846872133918445493e-714j)  +/-  (3.21e-59, 5.62e-177j)
| (1.2067903284534416129e-36 + 1.200395046112217617e-718j)  +/-  (2.15e-62, 3.76e-180j)
| (7.210274031920010942e-28 + 8.3617266045090438791e-714j)  +/-  (4.34e-58, 7.6e-176j)
| (5.5321578548839181028e-13 + 9.6986217871766470994e-709j)  +/-  (5.62e-49, 9.83e-167j)
| (2.4932877601966864629e-40 + 2.1583514743573669739e-721j)  +/-  (7.06e-66, 1.23e-183j)
| (1.8497256962373839251e-25 - 7.4836217076731553445e-713j)  +/-  (5.92e-58, 1.03e-175j)
| (3.4899458149604065336e-50 + 1.443961775030935278e-726j)  +/-  (1.63e-69, 2.85e-187j)
| (2.5924513843256531386e-08 + 1.6016074528629817248e-704j)  +/-  (5.11e-44, 8.93e-162j)
| (5.4510567197080331773e-05 + 3.3589733237817367735e-703j)  +/-  (5.65e-36, 9.88e-154j)
| (0.00023854384375573326527 - 9.1706537042844724999e-703j)  +/-  (1.59e-33, 2.78e-151j)
| (1.8497256962373839251e-25 + 2.5215938715556590924e-713j)  +/-  (8.15e-60, 1.43e-177j)
| (2.4932877601966864629e-40 - 1.0065077970599816087e-720j)  +/-  (2.3e-66, 4.02e-184j)
| (0.0027860144823034306626 - 1.1838138703779379519e-701j)  +/-  (7e-31, 1.22e-148j)
| (2.1583041526183646259e-14 - 1.2507595739200256461e-707j)  +/-  (2.03e-53, 3.56e-171j)
| (1.1450730835173346491e-44 - 1.0961803520928994524e-723j)  +/-  (3.4e-68, 5.95e-186j)
| (2.0937967951207365624e-33 + 1.3484610327594030997e-717j)  +/-  (2.23e-64, 3.9e-182j)
| (3.0429450153144242335e-23 - 1.5494083868482989382e-712j)  +/-  (2.75e-60, 4.8e-178j)
| (0.083324708143269586789 + 1.8651562046249327826e-700j)  +/-  (6.92e-36, 1.21e-153j)
| (1.527896931197984518e-17 + 2.9358551187234816007e-710j)  +/-  (4.28e-58, 7.49e-176j)
| (0.056890944898988254587 - 1.2427735307560793955e-700j)  +/-  (6.21e-36, 1.09e-153j)
| (1.2067903284534416129e-36 - 2.0950974762209711972e-719j)  +/-  (4.86e-66, 8.5e-184j)
| (5.4510567197080331773e-05 + 1.0630605748173845794e-702j)  +/-  (3.85e-46, 6.73e-164j)
| (2.5924513843256531386e-08 + 2.4552668540146541958e-705j)  +/-  (2.07e-51, 3.62e-169j)
| (1.6753549190552292864e-30 - 7.7433110222760755726e-716j)  +/-  (2.15e-63, 3.76e-181j)
| (1.1450730835173346491e-44 + 4.3974693288067125107e-723j)  +/-  (2.62e-74, 4.59e-192j)
| (2.4045425357769059365e-09 - 5.3834654264728230207e-706j)  +/-  (1.76e-53, 3.08e-171j)
| (3.4899458149604065336e-50 - 5.0793839739911287635e-726j)  +/-  (8.66e-77, 1.51e-194j)
| (3.3890797741122446223e-21 - 6.3103528742919091271e-711j)  +/-  (1.61e-65, 2.81e-183j)
| (6.5633435863921800795e-16 - 1.1061009384642210259e-709j)  +/-  (3.21e-59, 5.62e-177j)
| (6.5633435863921800795e-16 + 2.2196143531907058101e-708j)  +/-  (3.79e-63, 6.64e-181j)
| (1.0511669901310393391e-05 - 1.1340200504827118652e-703j)  +/-  (1.36e-50, 2.37e-168j)
| (0.033688664472856753846 + 4.848685971576037644e-701j)  +/-  (2.78e-39, 4.87e-157j)
| (2.1583041526183646259e-14 + 2.1579507984468940004e-709j)  +/-  (1.92e-58, 3.35e-176j)
| (0.00088430248463970288805 + 5.6488855470685407325e-702j)  +/-  (2.18e-49, 3.81e-167j)
| (1.7028848719287999613e-06 + 1.5186260339901959645e-703j)  +/-  (8.93e-56, 1.56e-173j)
| (1.8246480955303450803e-10 + 9.940990592361628736e-707j)  +/-  (1.62e-56, 2.83e-174j)
| (0.00088430248463970288805 + 2.3218115806455709e-702j)  +/-  (4.63e-49, 8.1e-167j)
| (0.00023854384375573326527 - 2.5321969919988888572e-702j)  +/-  (4.37e-52, 7.65e-170j)
| (1.1221625687978865689e-11 - 1.4040968291094044282e-707j)  +/-  (1.94e-57, 3.4e-175j)
| (2.3053899254981749508e-07 - 5.1317023929462605769e-704j)  +/-  (6.93e-58, 1.21e-175j)
| (1.1221625687978865689e-11 - 2.9066366832048604665e-706j)  +/-  (3.51e-63, 6.13e-181j)
| (0.0074798644510721697944 + 1.2094029249987334154e-701j)  +/-  (2.08e-49, 3.64e-167j)
| (0.0027860144823034306626 - 5.4784833342094668817e-702j)  +/-  (2.49e-50, 4.36e-168j)
| (1.7028848719287999613e-06 + 3.5029678515644871537e-704j)  +/-  (3.65e-55, 6.39e-173j)
| (2.4045425357769059365e-09 - 4.5992283501350257467e-705j)  +/-  (1.89e-61, 3.31e-179j)
| (0.10753613067466443469 - 2.5137630726700739677e-700j)  +/-  (4.43e-49, 7.75e-167j)
| (0.056890944898988254587 - 8.7286683632542842692e-701j)  +/-  (4.45e-50, 7.78e-168j)
| (0.13076983156503088785 - 3.0678116012039499601e-700j)  +/-  (3.9e-50, 6.82e-168j)
| (2.0937967951207365624e-33 - 1.1313912644831134138e-716j)  +/-  (8.62e-75, 1.51e-192j)
| (1.8246480955303450803e-10 + 1.2103492733672972862e-705j)  +/-  (6.56e-63, 1.15e-180j)
| (0.12456512329788795715 + 2.9789998853927216297e-700j)  +/-  (4.65e-50, 8.13e-168j)
| (0.12456512329788795715 + 2.7359845841622547564e-700j)  +/-  (1.13e-50, 1.98e-168j)
| (3.0429450153144242335e-23 + 7.1433090098759972921e-712j)  +/-  (9.32e-71, 1.63e-188j)
| (0.083324708143269586789 + 1.4373647143889024234e-700j)  +/-  (5.25e-53, 9.18e-171j)
| (0.017153803283765378083 - 4.3463982170011074569e-701j)  +/-  (3.77e-55, 6.58e-173j)
| (3.3890797741122446223e-21 + 1.0113674139800776426e-711j)  +/-  (9.16e-69, 1.6e-186j)
| (1.0511669901310393391e-05 - 4.1658719531584881003e-703j)  +/-  (9.2e-60, 1.61e-177j)
| (2.6643082296909900013e-19 + 4.998510587673049595e-710j)  +/-  (1.55e-69, 2.71e-187j)
| (2.3053899254981749508e-07 - 9.8066965703762601276e-705j)  +/-  (4.68e-61, 8.18e-179j)
| (2.6643082296909900013e-19 - 5.9457990009836593008e-711j)  +/-  (6.11e-68, 1.07e-185j)
| (0.0074798644510721697944 + 2.3362767275562111383e-701j)  +/-  (8.54e-59, 1.49e-176j)
| (0.033688664472856753846 + 7.6069516168256347274e-701j)  +/-  (6.17e-58, 1.07e-175j)
| (1.527896931197984518e-17 - 3.5269733732482556237e-709j)  +/-  (3.71e-69, 6.45e-187j)
| (0.10753613067466443469 - 2.117640246018828412e-700j)  +/-  (2.41e-58, 3.31e-176j)
| (0.017153803283765378083 - 2.5028143129951142982e-701j)  +/-  (1.1e-59, 1.36e-177j)
| (5.5321578548839181028e-13 + 6.3411394630124169045e-707j)  +/-  (9.82e-67, 1.8e-184j)
