Starting with polynomial:
P : t
Extension levels are: 1 2 6 10 24
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P3 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P4 : t^19 - 23713751/205892*t^17 + 2134183615/411784*t^15 - 48885080515/411784*t^13 + 623352876985/411784*t^11 - 4536269518165/411784*t^9 + 18427952550645/411784*t^7 - 38805894891225/411784*t^5 + 36681698574675/411784*t^3 - 11110847880825/411784*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 11040571749013358933481209419687213617101082066309828785108969884646983688213880601188159564236139968639738873667311223600513742139/14272722420317887776996448819841877739536282655840445999859089841783705318879730606022119080762864244048989320317034504928404660*t^41 + 126582162591073893031000226462506283844266822260677093756162051850545559025046491543766532022748563359762524699603097498882664358242723/485272562290808184417879259874623843144233610298575163995209054620645980841910840604752048745937384297665636890779173167565758440*t^39 - 4978781160390977656493454055336177312733375155436120261285715069064692250521021845760836984362893503809221451238453636055989958591425867/97054512458161636883575851974924768628846722059715032799041810924129196168382168120950409749187476859533127378155834633513151688*t^37 + 642380288955154461151290824552281453107764246521603004575545460377229135821875201738700014677029973314445614874476285909949333040114428181/97054512458161636883575851974924768628846722059715032799041810924129196168382168120950409749187476859533127378155834633513151688*t^35 - 405115338395634043928519770088954127376584127402867361751214347403898192247983207449535838172592574363102607812555514478264780767010833747289/679381587207131458185030963824473380401927054418005229593292676468904373178675176846652868244312338016731891647090842434592061816*t^33 + 13223773385479088729892408498883435939076652915373994157716344194471472115550297548992805312290848502582117717473640988186749143744713972658887/339690793603565729092515481912236690200963527209002614796646338234452186589337588423326434122156169008365945823545421217296030908*t^31 - 640232370510325952682382867460818834244036020805123559960256849842069426975220815789210356669544344446576043649956687997074409266533904788975571/339690793603565729092515481912236690200963527209002614796646338234452186589337588423326434122156169008365945823545421217296030908*t^29 + 23322123594675087273312075384075327241560535765945356810095930242992605829639417868077253219631859260550175962488848976580922583380790906546588285/339690793603565729092515481912236690200963527209002614796646338234452186589337588423326434122156169008365945823545421217296030908*t^27 - 644586596140084854910350452547702118825157271253293730552852397706558051074696161040732844481682832948453696924613038008495781665975396044907434455/339690793603565729092515481912236690200963527209002614796646338234452186589337588423326434122156169008365945823545421217296030908*t^25 + 484518450872153369165940486753746513135103245069300100235541563139987960353284084011183709500760618410146324613706477465399669457187030858692590600/12131814057270204610446981496865596078605840257464379099880226365516149521047771015118801218648434607441640922269479329189143961*t^23 - 3196218704026966959112120352417293698685733366708491743075892807675770542833899683459884804857131690962752271136381135211606093604951121664201325500/4995452847111260721948757086944657208837698929544156099950681444624296861607905712107741678267002485417146262110962076724941631*t^21 + 94237292448441820991672460209336567025620015706304061340723199590198264175555656501714510040579773474401190513545718438891691094827867862328783213000/12131814057270204610446981496865596078605840257464379099880226365516149521047771015118801218648434607441640922269479329189143961*t^19 - 101092092758431402286813985118844318673248925147373258664591348904295034551060784236819938291790024808196956451400848253969057656034629920777524720125/1427272242031788777699644881984187773953628265584044599985908984178370531887973060602211908076286424404898932031703450492840466*t^17 + 1364684073514899136796322751274205922428211803291346161827898690647769355782972207424726096149678057824272324980988591296406476610193549495482260639375/2854544484063577555399289763968375547907256531168089199971817968356741063775946121204423816152572848809797864063406900985680932*t^15 - 6669320421351857835388247936499287489584373958762419632071753373371596459948481562096321842857742325317761048367286084374661729647979433924206636816875/2854544484063577555399289763968375547907256531168089199971817968356741063775946121204423816152572848809797864063406900985680932*t^13 + 22827102510010013950340749934489305864313881636040152809739452423107993264934132181168621728116708822347443358527476658237764327486165106963255914504625/2854544484063577555399289763968375547907256531168089199971817968356741063775946121204423816152572848809797864063406900985680932*t^11 - 1857452556528524581771677624224041379723467392915649601990956125240579492150269347426571176190471759076084104711469577991415219722869920270497825334000/101948017287984912692831777284584840996687733256003185713279213155597895134855218614443707719734744600349923716550246463774319*t^9 + 145502211303882904596465117148662980597379857953510142655337591483238373626208183936625403395934917603774019833973180215332699218185980905759019545555625/5709088968127155110798579527936751095814513062336178399943635936713482127551892242408847632305145697619595728126813801971361864*t^7 - 15541150120211047601919893434593695339058146717793834915703051027759252698128943260464488011964843708891002363653827550112760250480839626887589635261875/815584138303879301542654218276678727973501866048025485706233705244783161078841748915549661757877956802799389732401971710194552*t^5 + 4730305143459895636839760561484209717858315145637335423756212768642595522020857806450802774288055934893676796880748146847274915456107729812907197798125/815584138303879301542654218276678727973501866048025485706233705244783161078841748915549661757877956802799389732401971710194552*t^3 - 280685744877167688804622666167778670943586644131086346581972590372160671266507084554536803896127456675829429020029427431409249382403825917944649346875/815584138303879301542654218276678727973501866048025485706233705244783161078841748915549661757877956802799389732401971710194552*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:
| (7.6849114517704882935 + 1.5737504363040156605e-880j)  +/-  (3.96e-246, 3.96e-246j)
| (-14.379122454207497029 - 2.2490716611451679785e-887j)  +/-  (2.67e-250, 2.67e-250j)
| (-7.0036519161906818426 + 7.8785329886773789185e-882j)  +/-  (5.77e-246, 5.77e-246j)
| (-7.6849114517704882935 + 1.4313422311262267673e-890j)  +/-  (3.9e-246, 3.9e-246j)
| (-9.2424490901026157398 - 3.951217381004451366e-905j)  +/-  (4.16e-247, 4.16e-247j)
| (5.7577384103455382459 + 1.1073199258481448991e-916j)  +/-  (6.49e-246, 6.49e-246j)
| (9.2424490901026157398 + 7.7275860706444157156e-926j)  +/-  (4.31e-247, 4.31e-247j)
| (-8.421333430076143364 - 7.9111944531398236629e-928j)  +/-  (1.55e-246, 1.55e-246j)
| (-6.3633944943363699876 - 4.8032361072846526184e-936j)  +/-  (7.55e-246, 7.55e-246j)
| (6.3633944943363699876 + 2.0332881239468346265e-950j)  +/-  (7.31e-246, 7.31e-246j)
| (10.227233313952107471 - 3.845462201397362866e-961j)  +/-  (5.26e-248, 5.26e-248j)
| (5.187016039913656066 + 7.4909271959920083253e-964j)  +/-  (6.8e-246, 6.8e-246j)
| (14.379122454207497029 + 4.2266609411493380068e-975j)  +/-  (2.63e-250, 2.63e-250j)
| (-2.5960831150492021594 - 7.1750807800981240039e-971j)  +/-  (2.95e-247, 2.95e-247j)
| (-4.1849560176727318607 + 3.2740815768279974854e-969j)  +/-  (3.66e-246, 3.66e-246j)
| (2.9547735149543920688 - 9.574678578988543795e-969j)  +/-  (4.63e-246, 4.63e-246j)
| (-10.227233313952107471 - 6.6671288362497952335e-975j)  +/-  (5.9e-248, 5.9e-248j)
| (-5.7577384103455382459 + 6.5722022426817616337e-973j)  +/-  (6.78e-246, 6.78e-246j)
| (-1.2304236340273060078 + 9.9302919227611810558e-980j)  +/-  (1.32e-251, 1.32e-251j)
| (-3.7241288497376452983 + 2.1433316798500833604e-972j)  +/-  (2.47e-246, 2.47e-246j)
| (2.8612795760570581173 - 4.409018757451703932e-973j)  +/-  (3.13e-246, 3.13e-246j)
| (0.74109534999454084186 - 1.933019439584994389e-982j)  +/-  (6.63e-253, 6.63e-253j)
| (-2.8612795760570581173 + 9.5323817529538005905e-974j)  +/-  (3.31e-246, 3.31e-246j)
| (-0.74109534999454084186 - 2.3112799983715246493e-982j)  +/-  (6.37e-253, 6.37e-253j)
| (-2.2396100665822224289 - 2.9099036205189010182e-978j)  +/-  (1.59e-248, 1.59e-248j)
| (1.7320508075688772935 - 5.2834283522093148696e-979j)  +/-  (3.99e-250, 3.99e-250j)
| (0.27722751199340428588 + 7.8313953842542632737e-983j)  +/-  (5.11e-254, 5.11e-254j)
| (4.1849560176727318607 + 2.6349906066518499622e-974j)  +/-  (3.73e-246, 3.73e-246j)
| (1.2304236340273060078 - 2.0969522919013285188e-986j)  +/-  (1.32e-251, 1.32e-251j)
| (7.0036519161906818426 - 4.5115769824389491464e-979j)  +/-  (5.88e-246, 5.88e-246j)
| (-5.187016039913656066 - 1.8741035690626456587e-982j)  +/-  (6.27e-246, 6.27e-246j)
| (2.2396100665822224289 - 1.4279503075047131752e-986j)  +/-  (1.48e-248, 1.48e-248j)
| (2.5960831150492021594 + 1.2058336339659108611e-984j)  +/-  (2.86e-247, 2.86e-247j)
| (-4.660209757859578847 + 3.1143504671040363764e-984j)  +/-  (5.4e-246, 5.4e-246j)
| (-1.7320508075688772935 - 1.5444482452202452132e-989j)  +/-  (4.02e-250, 4.02e-250j)
| (-3.2053337944991945187 + 1.1935391184332611521e-985j)  +/-  (2.87e-246, 2.87e-246j)
| (4.660209757859578847 - 3.2463079701992516914e-985j)  +/-  (5.23e-246, 5.23e-246j)
| (3.7241288497376452983 + 5.878096671645992535e-993j)  +/-  (2.23e-246, 2.23e-246j)
| (2.0817420984352238501e-1017 - 3.9372129047050838268e-1018j)  +/-  (9.11e-1016, 9.11e-1016j)
| (-2.9547735149543920688 - 3.3768985616946123835e-998j)  +/-  (4.91e-246, 4.91e-246j)
| (-0.27722751199340428588 - 3.0998818471940251359e-1006j)  +/-  (5.11e-254, 5.11e-254j)
| (8.421333430076143364 - 6.0888129037336777012e-1003j)  +/-  (1.65e-246, 1.65e-246j)
| (3.2053337944991945187 + 4.3102347082629956397e-1009j)  +/-  (2.81e-246, 2.81e-246j)
-------------------------------------------------
The weights are:
| (4.2192185144819603168e-14 - 3.329509412138683684e-893j)  +/-  (1.24e-90, 1.64e-213j)
| (5.4619194747831809695e-38 - 2.4111748076349984695e-909j)  +/-  (2.63e-102, 3.46e-225j)
| (5.8691588525173485589e-12 + 2.3557028304578095242e-892j)  +/-  (1.09e-89, 1.43e-212j)
| (4.2192185144819603168e-14 + 2.0472062256966600503e-894j)  +/-  (1.96e-91, 2.57e-214j)
| (9.9261997156014909724e-20 + 1.1562846488085338969e-898j)  +/-  (3.11e-95, 4.09e-218j)
| (1.486536435717964575e-08 + 3.3626412080935022766e-890j)  +/-  (2.68e-89, 3.52e-212j)
| (9.9261997156014909724e-20 + 1.3279339725883740037e-897j)  +/-  (2.01e-97, 2.65e-220j)
| (1.226196149478643574e-16 - 1.8965711607866800713e-896j)  +/-  (1.02e-93, 1.34e-216j)
| (4.0003057542577694775e-10 - 1.7511989281812355955e-891j)  +/-  (6.33e-90, 8.33e-213j)
| (4.0003057542577694775e-10 - 2.8997898262039725015e-891j)  +/-  (1.48e-91, 1.95e-214j)
| (8.7544909871323872981e-24 - 3.3844212436788430666e-900j)  +/-  (6.25e-100, 8.22e-223j)
| (3.1601836322128924726e-07 - 3.7189677670884075861e-889j)  +/-  (1.92e-89, 2.53e-212j)
| (5.4619194747831809695e-38 + 3.0597321394788100828e-908j)  +/-  (4.49e-107, 5.91e-230j)
| (0.0013996625229156806051 + 1.2628512219288671694e-884j)  +/-  (1.35e-82, 1.78e-205j)
| (2.8680231806477781251e-05 - 1.5776064756776451792e-887j)  +/-  (2.31e-88, 3.04e-211j)
| (-0.003879955862387715701 + 3.4592637811658600219e-884j)  +/-  (2.28e-85, 3e-208j)
| (8.7544909871323872981e-24 - 2.0633081493798461115e-901j)  +/-  (2.14e-100, 2.82e-223j)
| (1.486536435717964575e-08 + 1.7383425139883058444e-890j)  +/-  (9.57e-92, 1.26e-214j)
| (0.092871158444257545599 - 5.4135468431567521602e-885j)  +/-  (7.31e-78, 9.61e-201j)
| (0.00018478946568835742263 + 1.1789177371970297637e-886j)  +/-  (9.94e-88, 1.31e-210j)
| (0.0067354758901013294997 - 4.2957622067445658238e-884j)  +/-  (1.73e-86, 2.27e-209j)
| (0.14586329263214735347 + 1.0109039258556199427e-884j)  +/-  (1.07e-78, 1.4e-201j)
| (0.0067354758901013294997 - 2.8791113337943467632e-884j)  +/-  (2.04e-85, 2.68e-208j)
| (0.14586329263214735347 + 9.1053444713477290166e-885j)  +/-  (1.2e-79, 1.58e-202j)
| (0.016361687349383240209 - 6.3546051181576365521e-885j)  +/-  (7.75e-84, 1.02e-206j)
| (0.045061232904186497563 + 5.5782223683972129938e-885j)  +/-  (7.26e-84, 9.55e-207j)
| (0.1648809136874366887 - 2.3631075954921364097e-884j)  +/-  (1.34e-80, 1.77e-203j)
| (2.8680231806477781251e-05 - 2.7887993025947370978e-887j)  +/-  (2.34e-91, 3.08e-214j)
| (0.092871158444257545599 - 6.4391410019855250328e-885j)  +/-  (5.39e-82, 7.09e-205j)
| (5.8691588525173485589e-12 + 2.7013972855200253519e-892j)  +/-  (1.05e-96, 1.38e-219j)
| (3.1601836322128924726e-07 - 1.9222411549140830897e-889j)  +/-  (3.41e-92, 4.48e-215j)
| (0.016361687349383240209 - 8.7047102673186284321e-885j)  +/-  (1.64e-86, 2.15e-209j)
| (0.0013996625229156806051 + 1.8171822822224225789e-884j)  +/-  (4.04e-87, 5.32e-210j)
| (3.8388076194739857724e-06 + 1.9541864595936867361e-888j)  +/-  (1.54e-91, 2.03e-214j)
| (0.045061232904186497563 + 4.3708830025513400114e-885j)  +/-  (9.67e-87, 1.27e-209j)
| (0.00150909333211638847 - 2.625883267136790405e-885j)  +/-  (7.53e-89, 9.91e-212j)
| (3.8388076194739857724e-06 + 3.6333493818229987525e-888j)  +/-  (1.11e-93, 1.46e-216j)
| (0.00018478946568835742263 + 1.9708090481765308427e-886j)  +/-  (4.82e-92, 6.33e-215j)
| (0.057959598610118109478 + 3.4019841959148794699e-884j)  +/-  (4.63e-88, 6.21e-211j)
| (-0.003879955862387715701 + 2.2892837132427040634e-884j)  +/-  (6.23e-89, 8.3e-212j)
| (0.1648809136874366887 - 2.2724277103418517165e-884j)  +/-  (1.72e-88, 2.31e-211j)
| (1.226196149478643574e-16 - 2.1682156361256094907e-895j)  +/-  (4.37e-102, 5.89e-225j)
| (0.00150909333211638847 - 4.1035449528955662746e-885j)  +/-  (1.03e-90, 1.34e-213j)
