Starting with polynomial:
P : t
Extension levels are: 1 4 16 22
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^21 - 35335620166/7135347843*t^19 + 180709480704313/17231865040845*t^17 - 96664607452792/7789747210245*t^15 + 1734603690026/192752697357*t^13 - 41778582658804/10122121377423*t^11 + 37797535859134/31699057228983*t^9 - 534118021610248/2553535165668075*t^7 + 1205860438533401/58731308810365725*t^5 - 234576601175962/246671497003536045*t^3 + 1112587844447/82223832334512015*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 43521574156667978828272854728636198154609645150098160468121802863752506920190945426587911983014861581522066881056140446722459450636058830813333925340663596759776019154418448336533/4183141568875748506053399092197492005004678598388979470206292088931319011889614085415962550011603686628924867344099439475362709942996805857813472713063091298913761548487615666375*t^41 + 81236734646408144300363269813425992318963149858775047826034030219408252168667648867102999304797547251695100906451037009340727900371918419644622674775082000950158512688480578745462276242/1614345444835822236210609617463579522095390550654479790203601624084107839111404199001472019412828059932774798030832823384013550933071498326229801949007169004802902115507695175120440875*t^39 - 3078430010757752716975815506506994178219761234555913773568533196681543699896033922993293825586985018226054471494194430490332072086099967585846445764007978726941939975832209319621949630502/20489769107531589921134660529345432395826110835229935798738020613375214881029360987326375631008971529915987821160570450643248915688984401832916717045090991214806065312213054145759441875*t^37 + 15968954043636125798324787085012970214221822791541247848969744068988156501492991759526204282271254504139214418866138273414301237816204205996008604202965934120741438511585097260003878971567/51501311540552374666635768357543924670589954261523892683314484244429594160425150589766295504968496007626672091025217619184382409704744577580033910410634113053431461460427406366368326875*t^35 - 60092033138017225239200247103165589574500388900523164913980227373832037084655238186773864118383754816699945772410148294420983832361262370224803185903654643696578050648665148827051378660473/128017545829373045599923195631609184181180743450073676098524575121867848341628231465990505969493118647529156340548398081972607704123222235698941434449290509589958204201633838682115555375*t^33 + 59059031019637400919511539310550199621749402939307251056501539362548907308762309339779591104291757992611946306295850208172194352551610749920618399352451359494363752134579465145635523081464/109396811890555148058116185357920575573008998948244777756921000558687070401027761434573705101203210480615824509195903815503864765341662637779095407620302799104146101772305280328353292775*t^31 - 326417960700214890298626058869929254576468145620592862085349637931871777791938248241594060987935156927351710000441014901677912795670022629653585300623056451359918000791231099323897523015448/677189386174571077801353249740631816533698641987744369540895848842150775063091760159513536026914200583567367512430706043691888119161682513059695153956601865422216970370276846526458369625*t^29 + 960451553352944669131590678215539231060545222996511967386003289401392629410378651483358723447441138275239018011873300876127149605403838114108374854873871178241010618906589580232489355541163414/2836939821367042408074954864092004002835816096612943376683824395328010211246452266668247777712751276016159007471718636390180659870630905670782222912825335671929501808015481217769770241321875*t^27 - 970026397750364258533876205469520311670926009336510092317175607982104569150517708877181997642134165337425236703882832556825856725279843662727371476331873923636308017102005682599441769905602822/5148520416555002888728621790389192449590925508667934276203977606336018531521339298768301522515733797214510791337563451226624160505959791772901071212164498071279466244176243691508101549065625*t^25 + 15854577585743651672316515070329604949469271328360454335027946166489338922429028506464623112795233228800999854293773238438424776883410032506994407594267638843372800662425975803214763180002531804/190357961534760306805926242996656408836208485807149089972181732031597058505448985006460001625815064262344512325054179336685717294440353367816728939617762042022106131934676316754026207940786375*t^23 - 1560893117448335882842408753749175104075568096541535148039290329993367287713216942498423979202401323601873076619546194844293884778994625718651443241762849330391940339943375809491297607627079692/53456020911807370044221742918242643708991538981138030892443872575624954025315341569589023474461621626612346427854089235724019843809592838328073753376036501826156658021553605062895339212016225*t^21 + 1746776717851064339065476121041918872185696976970664585045372989071088588701006343689827874630226607338887581942568352830107054996389679919290853450412481692550807253327154920782073209926962098/216369608452553640655183245145267843584013372066511077421796627091815290102466858734050809301392278012478545065123694525549604129705494821804108049379195364534443615801526496683147801572446625*t^19 - 1885498205666635731235413618497223102159991447486017937104566150664971632534775975229554422088776698764417335323825281038471838142425362184123209860322838915636386903538741324800113629540059822/1081848042262768203275916225726339217920066860332555387108983135459076450512334293670254046506961390062392725325618472627748020648527474109020540246895976822672218079007632483415739007862233125*t^17 + 55305080377925972278658005097248725454458374151361643175721978491389216324017496444783975645372611536340831779830405374828508347775146210119403235729795127230246017099870586366729337534750193912/191105274759711347908092730932717451259644751857568460440486844457859210640502346111280758921200297315139138479578369017713370941619294397022863668319330494028510052427054138099850837682958004375*t^15 - 1023840821833270060529884155492773522181631579094031261795038320128519164255294261136963023136344738619914578531154573134345046648750724942170821933949812523682417158443226958406322988723416/28306792234069216247720855279371267225552376223423339283404444624355134384990039056495878941069320845734094452428590058469523908965006876398030207681559792145779026560984019334632322481512625*t^13 + 71786247633096098174041387474067008085954924228733623298745549865336824451028216381612322030565739081170271886611795346350563876909886088983080875825652641263488097410948407483696156751077931/21756600511105599607998249367724755989559556365323178573224656138279356288303344018822732554105880002031224996136614318939676076430504285199526017624046856243245759814772317260598403059290603575*t^11 - 6234780459781008792507677079482684118039791830841383459861527724183756005320447026129995190594194135610725738371583521728992955554732373858591555418899445044108598468266395464255163739672141/29668091606053090374543067319624667258490304134531607145306349279471849484050014571121908028326200002769852267459019525826831013314324025272080933123700258513516945201962250809906913262669004875*t^9 + 262758584355164772180813433029386207636053457485155224624058390220055924504867978670622271580669906779432449520628012589320511021684167026198473854704695734455802508462508811928319980841174/30055909796981888941530558395698192320692791770277118349820157766785206993645439598195397022160529414570765368994431545772279784730197541942304213295251895879706709191530384807422036311854220625*t^7 - 150549841822670387399309846503407123625522917001437999028883681999562660547172552343879507615556944923631389224068052653758371199575820908314444969985276529969092838084351224294003967594578/705598263329146249913074537575200419719121254416505683164825608525005097517485796281444320567863857208732729853059750098368282565332732770359808435931389746128352744353546652859955423892577655625*t^5 + 3192228455454423142775069692302428156204993993130404806943859407349534152308103018984991028662733162839540279165058730792873605587918308496833402496262940912605580954730034475375197894189/1270076873992463249843534167635360755494418257949710229696686095345009175531474433306599777022154942975718913735507550177062908617598918986647655184676501543031034939836383975147919763006639780125*t^3 - 26867104412586988624291065890246729639845946578043443756767628523165422183395921830025301635323714151791974489123256188931729085326562891382124266342193382857409158733267974523018936923/2963512705982414249634913057815841762820309268549323869292267555805021409573440344382066146385028200276677465382850950413146786774397477635511195430911836933739081526284895942011812780348826153625*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (-0.99261540453781165524 + 1.0407852013107538896e-852j)  +/-  (4.36e-241, 4.36e-241j)
| (0.99876345470551067944 + 6.3088794473184339634e-852j)  +/-  (1.63e-241, 1.63e-241j)
| (-0.9061798459386639928 + 2.9590876971647229874e-870j)  +/-  (1.59e-241, 1.59e-241j)
| (0.99261540453781165524 - 3.7637433429219884286e-868j)  +/-  (3.98e-241, 3.98e-241j)
| (0.9061798459386639928 + 3.9322330278126663385e-893j)  +/-  (1.45e-241, 1.45e-241j)
| (0.93656357559295783003 + 9.1430544872301160621e-920j)  +/-  (2.47e-241, 2.47e-241j)
| (-0.98016719931028024351 + 2.7459711530775711331e-928j)  +/-  (5.09e-241, 5.09e-241j)
| (-0.93656357559295783003 - 7.2785748359216564332e-930j)  +/-  (2.8e-241, 2.8e-241j)
| (-0.96134856368178933391 + 4.0262185584649830787e-933j)  +/-  (4.55e-241, 4.55e-241j)
| (0.96134856368178933391 + 2.7108216141603186841e-937j)  +/-  (4.43e-241, 4.43e-241j)
| (0.87032808764810700892 - 3.5419422828816402135e-948j)  +/-  (6.68e-242, 6.68e-242j)
| (-0.99876345470551067944 + 6.0423838401590645214e-950j)  +/-  (1.53e-241, 1.53e-241j)
| (-0.87032808764810700892 - 8.0014208815139215421e-953j)  +/-  (6.59e-242, 6.59e-242j)
| (-0.73415620079730241944 - 2.1757388396887456891e-953j)  +/-  (3.12e-243, 3.12e-243j)
| (0.98016719931028024351 + 7.3849965432834037703e-950j)  +/-  (5.16e-241, 5.16e-241j)
| (0.82914919218009739841 + 1.6418346357724844549e-959j)  +/-  (2.96e-242, 2.96e-242j)
| (0.78329303812765274646 - 3.8915352830260484856e-960j)  +/-  (9.83e-243, 9.83e-243j)
| (-0.37240752327919283826 - 3.6020844861517276376e-959j)  +/-  (1.07e-248, 1.07e-248j)
| (-0.78329303812765274646 + 3.2361492181024636422e-961j)  +/-  (1e-242, 1e-242j)
| (-0.82914919218009739841 - 6.7573482175054699386e-965j)  +/-  (2.85e-242, 2.85e-242j)
| (0.73415620079730241944 - 3.1139815908990535914e-965j)  +/-  (3.06e-243, 3.06e-243j)
| (0.68327726203571528858 - 1.5873670362013186621e-969j)  +/-  (8.75e-244, 8.75e-244j)
| (0.15500602137286204479 - 2.5093901431956452362e-970j)  +/-  (5.63e-253, 5.63e-253j)
| (-0.68327726203571528858 - 2.7438685852880835623e-974j)  +/-  (9.06e-244, 9.06e-244j)
| (-0.57841876335392393691 + 1.1307179574761775577e-975j)  +/-  (7.35e-245, 7.35e-245j)
| (0.23092952235512749606 - 9.9405546384193040435e-978j)  +/-  (1.74e-251, 1.74e-251j)
| (0.63087264370021210705 + 4.9256449168741526064e-979j)  +/-  (2.41e-244, 2.41e-244j)
| (0.49591603458375549133 - 9.7699943517262882776e-980j)  +/-  (3.05e-246, 3.05e-246j)
| (-0.15500602137286204479 - 2.7959048838195171522e-979j)  +/-  (6.02e-253, 6.02e-253j)
| (-0.63087264370021210705 + 5.8889006118257730567e-981j)  +/-  (2.56e-244, 2.56e-244j)
| (-0.30384202795433928862 + 7.8161349700799727923e-982j)  +/-  (4.52e-250, 4.52e-250j)
| (0.43678909447140196308 - 1.6830915161034968095e-985j)  +/-  (1.79e-247, 1.79e-247j)
| (0.57841876335392393691 + 3.8018063394750946771e-982j)  +/-  (6.91e-245, 6.91e-245j)
| (-1.8055758455820745279e-983 + 2.4477307691417607013e-985j)  +/-  (7.76e-982, 7.76e-982j)
| (-0.53846931010568309104 - 7.2455834097850186828e-984j)  +/-  (2.21e-245, 2.21e-245j)
| (-0.43678909447140196308 + 3.6189269230020887933e-986j)  +/-  (2.01e-247, 2.01e-247j)
| (0.07769373577500865365 + 3.9807813965767822154e-986j)  +/-  (2.66e-254, 2.66e-254j)
| (0.53846931010568309104 - 2.3220523389713381019e-987j)  +/-  (2.06e-245, 2.06e-245j)
| (0.37240752327919283826 + 2.0405788040336683119e-991j)  +/-  (9.98e-249, 9.98e-249j)
| (-0.23092952235512749606 + 5.9649413605069174514e-989j)  +/-  (1.53e-251, 1.53e-251j)
| (-0.49591603458375549133 - 1.2430684514473997126e-989j)  +/-  (3.27e-246, 3.27e-246j)
| (-0.07769373577500865365 - 4.9818537883177088273e-994j)  +/-  (2.66e-254, 2.66e-254j)
| (0.30384202795433928862 + 1.0603117690545410642e-993j)  +/-  (4.15e-250, 4.15e-250j)
-------------------------------------------------
The weights are:
| (0.0092069385163639277069 + 3.9032417398523727976e-853j)  +/-  (1.7e-68, 1.51e-185j)
| (0.0033180012871896956121 - 6.8507610612193878915e-852j)  +/-  (7.13e-69, 6.31e-186j)
| (0.03312423268860904194 + 8.4031326442725383219e-853j)  +/-  (2.65e-69, 2.34e-186j)
| (0.0092069385163639277069 + 1.0322749795902314198e-851j)  +/-  (5.82e-69, 5.15e-186j)
| (0.03312423268860904194 + 4.0231976338960168049e-852j)  +/-  (5.29e-70, 4.68e-187j)
| (0.027626120871246940052 - 4.0606422604051108326e-852j)  +/-  (7.18e-70, 6.36e-187j)
| (0.015684009122904221949 - 1.3893709782594155519e-852j)  +/-  (7.66e-71, 6.78e-188j)
| (0.027626120871246940052 - 8.0725131933168275446e-853j)  +/-  (2.95e-71, 2.61e-188j)
| (0.021878340273426172634 + 9.018102328327751855e-853j)  +/-  (3.65e-71, 3.23e-188j)
| (0.021878340273426172634 + 4.5254844745171021288e-852j)  +/-  (6.53e-72, 5.78e-189j)
| (0.038565622308459787393 - 4.2997236094987245946e-852j)  +/-  (7.97e-73, 7.05e-190j)
| (0.0033180012871896956121 + 5.0384609319048218025e-853j)  +/-  (5.72e-72, 5.06e-189j)
| (0.038565622308459787393 - 9.6754740560993379119e-853j)  +/-  (2.9e-73, 2.57e-190j)
| (0.050197833411276594877 + 2.7454922835143982463e-852j)  +/-  (2.02e-75, 1.79e-192j)
| (0.015684009122904221949 - 5.9190548324835965196e-852j)  +/-  (2.41e-72, 2.14e-189j)
| (0.043688736113275159076 + 4.9988136545491393522e-852j)  +/-  (2.09e-74, 1.85e-191j)
| (0.047783430836423922058 - 6.4376514826727420691e-852j)  +/-  (2.94e-75, 2.6e-192j)
| (0.066328498601209558656 - 6.6649425558076880884e-852j)  +/-  (2.09e-78, 1.85e-195j)
| (0.047783430836423922058 - 1.7473853789801935395e-852j)  +/-  (5.06e-76, 4.48e-193j)
| (0.043688736113275159076 + 1.2300623629565088285e-852j)  +/-  (1.31e-75, 1.16e-192j)
| (0.050197833411276594877 + 9.1396594772167201694e-852j)  +/-  (2.38e-77, 2.11e-194j)
| (0.051543129650973458817 - 1.3755136821092988787e-851j)  +/-  (3.24e-78, 2.87e-195j)
| (0.076850653257180465613 + 4.0733410944556741497e-852j)  +/-  (3.19e-81, 2.82e-198j)
| (0.051543129650973458817 - 4.5691375695805132802e-852j)  +/-  (1.17e-78, 1.03e-195j)
| (0.049172800036725795113 - 1.579901560808480146e-851j)  +/-  (6.31e-80, 5.59e-197j)
| (0.074711712427948147829 - 5.316659578117836671e-852j)  +/-  (1.29e-81, 1.14e-198j)
| (0.053256078454124073171 + 2.1832312512106142187e-851j)  +/-  (2.65e-80, 2.35e-197j)
| (0.053672305859871319236 - 3.5989627929258946385e-851j)  +/-  (9.34e-82, 8.27e-199j)
| (0.076850653257180465613 + 3.2389606407342689915e-852j)  +/-  (2.16e-83, 1.91e-200j)
| (0.053256078454124073171 + 8.0085314921186758425e-852j)  +/-  (4.74e-81, 4.19e-198j)
| (0.070859292590305783585 + 4.8391454794185697409e-852j)  +/-  (4.59e-83, 4.06e-200j)
| (0.062456602250420896683 + 1.9178871568354066498e-851j)  +/-  (5.32e-83, 4.71e-200j)
| (0.049172800036725795113 - 3.9154081402780235703e-851j)  +/-  (4.49e-82, 3.97e-199j)
| (0.077730151344443631157 + 3.1316492140165047078e-852j)  +/-  (1.47e-84, 1.3e-201j)
| (0.03360459021489123773 + 2.1462707212590655055e-851j)  +/-  (3.51e-83, 3.1e-200j)
| (0.062456602250420896683 + 9.8520171958206778842e-852j)  +/-  (7.87e-84, 6.96e-201j)
| (0.077605995554951984692 - 3.4334095853967408917e-852j)  +/-  (5.53e-85, 4.9e-202j)
| (0.03360459021489123773 + 4.9581648862780682927e-851j)  +/-  (1.02e-83, 9.04e-201j)
| (0.066328498601209558656 - 1.1695750251175497106e-851j)  +/-  (4.28e-85, 3.8e-202j)
| (0.074711712427948147829 - 3.7718349755253603567e-852j)  +/-  (8.49e-86, 7.56e-203j)
| (0.053672305859871319236 - 1.6756571694917051517e-851j)  +/-  (6.17e-85, 5.48e-202j)
| (0.077605995554951984692 - 3.0618929997136270084e-852j)  +/-  (3.75e-86, 3.35e-203j)
| (0.070859292590305783585 + 7.626510580528208611e-852j)  +/-  (5.53e-86, 4.82e-203j)
