Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 6 43
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Trying to find an order 43 Kronrod extension for:
P3 : 3/2*t^12 - 1595/364*t^10 + 318813/66248*t^8 - 10310751/4183088*t^6 + 2471775/4183088*t^4 - 33827/597584*t^2 + 31245/29281616
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^55 - 12570048650381360999448162656652087235212168781778537035860398348922554307908087647936547578529534897426150509231473666310690818031641923186576522204956561221359316610065922437973/613815375793854320822644774708872798962912778384608320043697373615868175526615513419074958836832952144840550587839908614523326559203523690434144110760111603115725744434777620402*t^53 + 70087186848275207631441644524575791165443043881448795218275038758083771565646710447435213338072078623098432426289973096122279478390324461402193441015066314724568389563504433593450505/530643392373787060351176407735820534703438096913493892677776379490918037742759111350790301914442087129214655983187600997255415810431446230380317583752116480893544906063865252837529*t^51 - 9289003232080348445202290020949546700141008900658083464844431120141786931021964391024312697649937374177512531468864431052791483560362542340618131205245661342172139239140739555075046845135/17356284077761827169966277944223218049080053273846558241704709820388947178490165014061649195017571785822352967898100053418230140327591743303279427529364225857066066787536904689809898532*t^49 + 56305351109505414952015780166979421496883493668126742548750967803156841270811499938000298839173723184777085012999327848879369520911481494768629301576361841538963612992648200003141459650565/36837827430351633177071283799983973002129092662858001166067139210621438909448513499232888087384233994398463442069436848071345603960602883745735927817426112023160631549057920157963866272*t^47 - 75082763082918110541772933123604028736800680683936975911565392750186364472550212018547233476975004119287390141310253990301792771683567643118139927154862493194609857603195297833150205002655395/22949966489109067469315409807390015180326424728960534726459827728217156440586423910022089278440377778510242724409259156348448311267455596573593483030256467790429073455063084258411488687456*t^45 + 112416027201489964979257177659944725201748783441017655704959407911789660265340102012347021596015018546485889623311183346605931541477239605283625024359891258939989119185655856772297138041122188705/20632019873709051654914553416843623647113455831335520719087385127667223640087195095109858261317899622880708209243923981557255031829442581319660541244200564543595737036101712748311928330022944*t^43 - 362544551464572059867244329032144499658534698501508401274470304248381362139937083613111566325802939241710386284429390214927517724546498395186528469707666093164540463635344075253836774644960150695/50106333979007696876221058298048800285846964161814836032069363881477543125926045230981084348914899084138862793878101098067619363014360554633461314450201371034446789944818445245900397372912864*t^41 + 32393554089185093258397999021319987919102698976945765078112490649787685980252057702929094696496099851150978468125527546778383578343310658117810594080525994879060006153241844435888180845207904569755/4158825720257638840726347838738050423725298025430631390661757202162636079451861754171430000959936623983525611891882391139612407130191926034577289099366713795859083565419930955409732981951767712*t^39 - 2430594009523538460747728612014389094049833961691688002261073518163809756148970331622589868131636773976476032158347805146011288711703297370674011134718970648259148654771001341252906995532584488985/353584372977370103867422285884611574486766228882766231594724296540143148455421444686639797652464247383214728136556802485554091294469758893628028627881380525154011153335297773536859889153794016*t^37 + 11347754978410410250057638935638410815280506496687089272543661891916365852046684994574495104531507225699928107547922862452599838676939707441231088691869078168728849788571206603763797758442350828865/2264851253936127422069704912287917382523340439059880996971612385946322329295537361911719784963081800805997042388215194299359990183495482642968723913726680661121639009201772225087453884579707616*t^35 - 19218754986381029036040524570055062633265508668641627096946097039163348275780039212144127113846851442923571164174584248155755173214333493130028922120987786776163764785633229931525726445751751845/6344121159484950762100013759910132724155015235461851532133368027860846860771813338688290714182301963042008522095840880390364118161051772109156089394192382804262294143422331162709954858766688*t^33 + 11267499808621796924466692214512467421307168195316714701056364891220141338423076706555746875063398869021457784576956386004042301388376112604381130427957554675105749876904446206594181732156959611/7401474686065775889116682719895154844847517774705493454155596032504321337567115561803005833212685623549009942445147693788758137854560400794015437626557779938306009833992719689828280668561136*t^31 - 33237131724883346479137791163012446487252584238377893578628761904297623940389187939122780367141845029243020966283396620681777324756506961503188315477494317080648149472645107109456311629017459167/52287837298335642571501726311517384226503432021306550530970178423175689449264461549511557337857359727652683141789914352894775231940281541093205833555359800209323101730464697163625595690802864*t^29 + 12071458377073528952493022433952518055549533392605598259025391891766220687902022795570663031741362126293155916096199192780703355585575812174428265448986925749884560733817314117877128705260685833/54863592830273358954334323666764546011060251332700961887175605931706511589622316798255969029377426709310450784242619493431463667011231370703708583976806095786137047628517145299764787596753744*t^27 - 29473389208211480514695852118018080009863339715025569234350616244230254535138609312294745338423013021266331062092750450680001295915762440306831539690119043020543451890483190755230001208852645/468919596839943238925934390314226888983420951561546682796372700270995825552327494002187769481858347942824365677287346097704817666762661288065885333135094835778949125030061070938160577750032*t^25 + 42080812553019586587485927722381987629831859577566239922212588612392922245023141031886578431011134388214568408181163260081239660697513856047328583529287211594066608537135321895795834595432344295/2859002781933133927731421977745841342131917541670750125009484353552261548392540730931338830530890347407400157534420949157706273314251945873337702876124673213744252815308282349509965042541945104*t^23 - 104040597206587256502598520355142853290623304077467357644697459988159077964167475813977234366857641898925120988945149821897968006829031682854666402473486888864802963073877015264516731396895541555/37167036165130741060508485710695937447714928041719751625123296596179400129103029502107404796901574516296202047947472339050181553085275296353390137389620751778675286599007670543629545553045286352*t^21 + 2267414404396570404728337400571315563010411722875430686102976272423847840383458212823961503900568157144030880935175024194984466295721286186157963165688449821694255798145684092714733960741469245/5309576595018677294358355101527991063959275434531393089303328085168485732729004214586772113843082073756600292563924619864311650440753613764770019627088678825525040942715381506232792221863612336*t^19 - 5732676635257125485060707593969030210658148426199387422095533176244664552810649830712968566237133501414915024220486406918435430383688334840293232095878180274039757063292430564975863970842513805/111501108495392223181525457132087812343144784125159254875369889788538200387309088506322214390704723548888606143842417017150544659255825889060170412168862255336025859797023011630888636659135859056*t^17 + 20971603695074694248210624669111032261281399690334979084656642922334135006480862615102546035452985443638682946297276374872846304536178263661959789882926719380348320215790072301211404609510379115/4385710267485427445140001313862120618830361508922930691764548998349169215234157481248673766034385792922951841657801736007921423264062484969700036211975248709883683818682905124148286375259343789536*t^15 - 242513930800558138149371709644318412387565429454286421972454790039158998362618442066849848992612411444204636244950772372580148548986148321472683931500307680653512104768363707368102436188894705955/726148314287944344131037360395171113889198426977382381679301755583812445779484074395316127833407590571100169211627458861882989937578345725697477424239901893536455649407641005555409129846511350296032*t^13 + 12898331379773140922040064587301208911121842664057123131906694850702420130945090477166092537007429657858583219524214889017981241848471405867551674717063254987908811674139145687941463657277215/765172090925125757777700063640854703782084749185861308408115653934470438123797760163662937653748778262487006545445162130540558416837034484401978318482509898352429556804679668656911622599063593568*t^11 - 683504344422819930369445321683722368291858523580307499148508616424053447162453024806464167014094141185587171257253151419206701059967777457909402285418851434794755282699207326670648624761360835/1173008815388217786673214197561430260897935920501925385789641297481543181643781966330895283423196877076392581034167433546118676053011173864588232762233687674174274510581573932051045517444364488939744*t^9 + 84715963185669245367544441869365277330535259734477082034781019192582145799291585510413762595147856831015319494824117155291494192957278970469651861483378851779746462414706439278636625115448935/6647049953866567457814880452848104811754970216177577186141300685728744695981431142541739939398115636766224625860282123428005830967063318565999985652657563486987555559962252281622591265518065437325216*t^7 - 1033869056572907449420053142677715924906910454030597801984411192993718474633099406571155233928537854649926545317504496792067119881275981376719805399482753075571479698585647206583343750789583/6647049953866567457814880452848104811754970216177577186141300685728744695981431142541739939398115636766224625860282123428005830967063318565999985652657563486987555559962252281622591265518065437325216*t^5 + 39286810482240883623890582686299577585883771468529963942094826250253238748639553426429775665813797123289104826862897010545586639745220117081663677573630987355504696811666370477752383422121/46529349677065972204704163169936733682284791513243040302989104800101212871870017997792179575786809457363572381021974863996040816769443229961999899568602944408912888919735765971358138858626458061276512*t^3 - 712268531711816821464187282990684199055008761822092018798042417125706974426567370335550469289124435891702926971408547031936736173401113898644121665647680096045939766985068860199305535/588979109836278129173470419872616882054237867256241016493532972153179909770506556934078222478314043764095852924328795746785326794549914303316454424919024612771049226832098303434913150109195671661728*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:
| (-0.99105250481616767714 + 7.4102357957018828927e-913j)  +/-  (2.14e-235, 2.14e-235j)
| (0.82194301646462735183 - 1.550482745888272249e-934j)  +/-  (1.39e-238, 1.39e-238j)
| (-0.91248695683407599658 + 3.416473166748992191e-932j)  +/-  (4.57e-237, 4.57e-237j)
| (0.99895894904090277886 - 4.4566805100355959916e-932j)  +/-  (3.55e-236, 3.55e-236j)
| (0.93595032870630800986 - 1.439854887665166339e-932j)  +/-  (1.21e-236, 1.21e-236j)
| (0.91248695683407599658 + 7.5274933646405051663e-934j)  +/-  (4.69e-237, 4.69e-237j)
| (-0.9949918486233806301 + 1.1315206239027500653e-930j)  +/-  (1.6e-235, 1.6e-235j)
| (-0.88555936249019063371 - 3.7620049125597875701e-951j)  +/-  (1.55e-237, 1.55e-237j)
| (0.98409724641985428154 + 7.0957255955015975448e-948j)  +/-  (1.4e-235, 1.4e-235j)
| (0.9949918486233806301 + 6.944032927402927369e-949j)  +/-  (1.53e-235, 1.53e-235j)
| (0.85531787164873259005 - 1.3129058916139783478e-953j)  +/-  (5.56e-238, 5.56e-238j)
| (-0.099658788148001079785 + 8.9766461627511912983e-969j)  +/-  (2.23e-253, 2.23e-253j)
| (-0.97195391649070983393 + 6.2211014688473708843e-949j)  +/-  (5.91e-236, 5.91e-236j)
| (-0.85531787164873259005 + 1.9480799691656123996e-970j)  +/-  (5.07e-238, 5.07e-238j)
| (0.99105250481616767714 + 1.0155563915573110895e-969j)  +/-  (2.19e-235, 2.19e-235j)
| (0.88555936249019063371 + 2.5333593891695771862e-980j)  +/-  (1.81e-237, 1.81e-237j)
| (0.78566084262796249692 - 2.4200392236433250568e-982j)  +/-  (3.7e-239, 3.7e-239j)
| (-0.99895894904090277886 + 2.1614220800775685298e-976j)  +/-  (3.41e-236, 3.41e-236j)
| (-0.74677180221832073614 + 1.778836696992759234e-1004j)  +/-  (7.62e-240, 7.62e-240j)
| (-0.98409724641985428154 - 1.009218559702098344e-999j)  +/-  (1.35e-235, 1.35e-235j)
| (-0.27187747586123949878 + 4.054009007375715558e-1029j)  +/-  (1.7e-249, 1.7e-249j)
| (0.70570962211433256244 + 5.1384297951910555291e-1019j)  +/-  (1.93e-240, 1.93e-240j)
| (-0.93595032870630800986 - 2.4476049979342117364e-1014j)  +/-  (1.22e-236, 1.22e-236j)
| (-0.82194301646462735183 - 2.1698347793140161489e-1017j)  +/-  (1.56e-238, 1.56e-238j)
| (-0.78566084262796249692 + 1.3336665670277071884e-1019j)  +/-  (3.63e-239, 3.63e-239j)
| (0.97195391649070983393 - 6.9914979001459976172e-1014j)  +/-  (6.16e-236, 6.16e-236j)
| (0.74677180221832073614 - 9.030686263802475471e-1022j)  +/-  (8.09e-240, 8.09e-240j)
| (0.95581778635647441925 + 1.1697499104426549099e-1023j)  +/-  (2.95e-236, 2.95e-236j)
| (-0.21433703252169090976 + 2.0342291288639755778e-1037j)  +/-  (8.29e-251, 8.29e-251j)
| (-0.62009884404198510773 - 7.8234083137144114167e-1028j)  +/-  (5.93e-242, 5.93e-242j)
| (-0.95581778635647441925 - 6.9474694548975090006e-1031j)  +/-  (3.01e-236, 3.01e-236j)
| (0.6631504971886688873 - 1.1268352765028609136e-1048j)  +/-  (3.3e-241, 3.3e-241j)
| (0.62009884404198510773 + 1.4519700884730775845e-1049j)  +/-  (5.82e-242, 5.82e-242j)
| (-0.32853789905884356941 - 4.1460697816037772539e-1053j)  +/-  (3.3e-248, 3.3e-248j)
| (-0.70570962211433256244 - 3.1061563573348977894e-1048j)  +/-  (1.83e-240, 1.83e-240j)
| (-0.6631504971886688873 + 1.2080478294024184213e-1048j)  +/-  (3.67e-241, 3.67e-241j)
| (0.21433703252169090976 + 2.2775240894607136228e-1059j)  +/-  (8.24e-251, 8.24e-251j)
| (0.57735026918962576451 - 1.1298188059455468054e-1053j)  +/-  (9.25e-243, 9.25e-243j)
| (0.27187747586123949878 - 1.1821570177181139502e-1058j)  +/-  (1.67e-249, 1.67e-249j)
| (-0.57735026918962576451 - 3.317468182667360454e-1050j)  +/-  (1e-242, 1e-242j)
| (-0.53382975036548165594 - 1.9461255009742195782e-1053j)  +/-  (1.19e-243, 1.19e-243j)
| (-0.15655801081562154215 + 2.95424080723358783e-1063j)  +/-  (4.29e-252, 4.29e-252j)
| (0.43693939954921891801 - 1.9628445109998609439e-1057j)  +/-  (8.39e-246, 8.39e-246j)
| (0.53382975036548165594 - 1.0523958751240501365e-1057j)  +/-  (1.28e-243, 1.28e-243j)
| (0.046303137710923745752 - 1.9889953738296084821e-1066j)  +/-  (1.44e-254, 1.44e-254j)
| (-0.43693939954921891801 + 2.358031198831804568e-1056j)  +/-  (8.9e-246, 8.9e-246j)
| (-0.38376952576068355376 + 4.1585726222629848591e-1058j)  +/-  (5.38e-247, 5.38e-247j)
| (0.099658788148001079785 + 8.4151299703742599627e-1066j)  +/-  (2.13e-253, 2.13e-253j)
| (0.48721889185250859528 + 3.8672321403723848046e-1058j)  +/-  (1.21e-244, 1.21e-244j)
| (0.15655801081562154215 - 2.3525694449328090503e-1064j)  +/-  (4.4e-252, 4.4e-252j)
| (-0.046303137710923745752 - 4.0903991910840644133e-1068j)  +/-  (1.44e-254, 1.44e-254j)
| (-0.48721889185250859528 + 1.6563021765479589326e-1056j)  +/-  (1.12e-244, 1.12e-244j)
| (-3.2264226439125488324e-1085 + 5.875946095646656226e-1085j)  +/-  (3.69e-1083, 3.69e-1083j)
| (0.32853789905884356941 + 1.4432493018594963739e-1061j)  +/-  (3.24e-248, 3.24e-248j)
| (0.38376952576068355376 - 9.8777900082163803923e-1060j)  +/-  (5.3e-247, 5.3e-247j)
-------------------------------------------------
The weights are:
| (0.0040557089519072391182 - 1.4472466804334398488e-913j)  +/-  (3.09e-48, 8.52e-161j)
| (0.034871079864173666468 + 1.0558963243559345387e-915j)  +/-  (1.25e-48, 3.45e-161j)
| (0.025218576744825641863 - 1.8269036388853852181e-914j)  +/-  (6.89e-49, 1.9e-161j)
| (0.0026394379099979131241 + 1.7708717523887839707e-916j)  +/-  (2.03e-49, 5.61e-162j)
| (0.021686493421571689258 + 7.3880918921094303558e-916j)  +/-  (3.92e-49, 1.08e-161j)
| (0.025218576744825641863 - 7.5402526919549692622e-916j)  +/-  (3.94e-49, 1.09e-161j)
| (0.0046628028741130778064 + 4.7641589426130965218e-913j)  +/-  (2.23e-51, 6.15e-164j)
| (0.028611727153132134622 + 1.4379077558669841161e-914j)  +/-  (2.81e-51, 7.76e-164j)
| (0.0099102235246194229796 - 1.2374181445249168863e-915j)  +/-  (5.93e-50, 1.64e-162j)
| (0.0046628028741130778064 - 9.449768830518904778e-916j)  +/-  (4.97e-50, 1.37e-162j)
| (0.031841400765896156737 - 9.0483807121586147799e-916j)  +/-  (1.78e-51, 4.92e-164j)
| (0.055786488461245309901 - 1.8888097861390556391e-914j)  +/-  (2.25e-55, 6.22e-168j)
| (0.014210958640211987938 + 9.1469567437547414702e-914j)  +/-  (1.21e-53, 3.33e-166j)
| (0.031841400765896156737 - 1.2308326704870956732e-914j)  +/-  (1.95e-54, 5.39e-167j)
| (0.0040557089519072391182 + 1.516254663921480329e-915j)  +/-  (4e-50, 1.1e-162j)
| (0.028611727153132134622 + 8.0831529515494958269e-916j)  +/-  (2.22e-51, 6.12e-164j)
| (0.037644108488016324944 - 1.2853577071658135933e-915j)  +/-  (6.14e-53, 1.7e-165j)
| (0.0026394379099979131241 - 4.4571933607533808274e-914j)  +/-  (1.26e-53, 3.47e-166j)
| (0.040063519760623161038 + 1.1632115660892018768e-914j)  +/-  (9.95e-57, 2.74e-169j)
| (0.0099102235246194229796 - 3.5140119907389876135e-913j)  +/-  (1.76e-53, 4.87e-166j)
| (0.057192362236337755558 + 1.1850316179101620681e-914j)  +/-  (1.32e-58, 3.66e-171j)
| (0.04195066373001111925 - 2.174206293359003349e-915j)  +/-  (9.62e-57, 2.65e-169j)
| (0.021686493421571689258 + 2.5837226431919149557e-914j)  +/-  (5.97e-55, 1.65e-167j)
| (0.034871079864173666468 + 1.1320094015154805627e-914j)  +/-  (1.88e-56, 5.19e-169j)
| (0.037644108488016324944 - 1.1118816461347227552e-914j)  +/-  (4.68e-57, 1.29e-169j)
| (0.014210958640211987938 + 8.8993066646944108575e-916j)  +/-  (1.11e-55, 3.05e-168j)
| (0.040063519760623161038 + 1.6350912890561435594e-915j)  +/-  (1.7e-58, 4.7e-171j)
| (0.018026976948292515992 - 7.7144330822494647104e-916j)  +/-  (4.02e-56, 1.11e-168j)
| (0.057786835391035569686 - 1.2688975736856299726e-914j)  +/-  (5.63e-62, 1.55e-174j)
| (0.042937902740971200748 - 1.7902656817867109264e-914j)  +/-  (1.76e-61, 4.85e-174j)
| (0.018026976948292515992 - 4.2625572837347510069e-914j)  +/-  (7.64e-57, 2.11e-169j)
| (0.042995156240946927332 + 2.995417598437338058e-915j)  +/-  (1.04e-60, 2.88e-173j)
| (0.042937902740971200748 - 4.1219318649848127974e-915j)  +/-  (1.1e-61, 3.04e-174j)
| (0.056039654564842837089 - 1.1895924230038939483e-914j)  +/-  (2.25e-63, 6.2e-176j)
| (0.04195066373001111925 - 1.2928694277475230784e-914j)  +/-  (1.31e-61, 3.6e-174j)
| (0.042995156240946927332 + 1.5111309685002428482e-914j)  +/-  (3.4e-62, 9.39e-175j)
| (0.057786835391035569686 - 8.1763807276377883154e-915j)  +/-  (6.48e-67, 1.79e-179j)
| (0.042740445432844649822 + 5.2485734454015648588e-915j)  +/-  (9.72e-65, 2.68e-177j)
| (0.057192362236337755558 + 6.7481583394347888019e-915j)  +/-  (6.05e-67, 1.67e-179j)
| (0.042740445432844649822 + 1.9898072677499512762e-914j)  +/-  (9.44e-65, 2.61e-177j)
| (0.044767633710891573148 - 1.9447265305072759176e-914j)  +/-  (1.91e-65, 5.28e-178j)
| (0.057601179679621968628 + 1.4764726465124078857e-914j)  +/-  (8.19e-67, 2.26e-179j)
| (0.05187989377215504281 - 5.6225957412221165419e-915j)  +/-  (1.96e-68, 5.41e-181j)
| (0.044767633710891573148 - 5.8310942888239022577e-915j)  +/-  (2.69e-67, 7.43e-180j)
| (0.050055520232899511353 + 2.3138322785261665679e-914j)  +/-  (2.23e-69, 6.15e-182j)
| (0.05187989377215504281 - 1.4489859784342101963e-914j)  +/-  (4.61e-68, 1.27e-180j)
| (0.054320387963230236059 + 1.2753870743783755197e-914j)  +/-  (4.61e-68, 1.27e-180j)
| (0.055786488461245309901 - 1.5436469634141841573e-914j)  +/-  (3.19e-70, 8.79e-183j)
| (0.048525520944606829941 + 5.8042240365023917089e-915j)  +/-  (6.32e-70, 1.74e-182j)
| (0.057601179679621968628 + 1.0736293169801704101e-914j)  +/-  (1.94e-70, 5.34e-183j)
| (0.050055520232899511353 + 2.5406388758374777065e-914j)  +/-  (1.6e-70, 4.41e-183j)
| (0.048525520944606829941 + 1.7029864924151405029e-914j)  +/-  (2.88e-70, 7.96e-183j)
| (0.043954679701957073572 - 2.8500264717302955796e-914j)  +/-  (1.29e-70, 3.56e-183j)
| (0.056039654564842837089 - 5.9724771627922051879e-915j)  +/-  (2.33e-72, 6.44e-185j)
| (0.054320387963230236059 + 5.6336081671049656723e-915j)  +/-  (2.21e-72, 6.07e-185j)
