Starting with polynomial:
P : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Extension levels are: 9 14 26
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 512*t^23 - 847253248/18099*t^21 + 10526171264/6033*t^19 - 69724285120/2011*t^17 + 2436061827136/6033*t^15 - 5743770803680/2011*t^13 + 24755471460720/2011*t^11 - 63531751923640/2011*t^9 + 92322361281150/2011*t^7 - 70208873169435/2011*t^5 + 50216778386775/4022*t^3 - 12961617443775/8044*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 512*t^49 - 2687276332023929663795686490499335529569343342061942969064554193980565218613076062332636457849802207395924631172736/13423746162173595341629052375822682190056805916938167382709861175241526604500687539895039846171182794464646051*t^47 + 73199628484905869711152646609014240183182035985822278685428548559525238594557923398803563577664115980234873942299470912/2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803*t^45 - 2627643089701331501207951926732904619769360832556808695075780134168836492845381375435234298390177595326052752630015416160/684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601*t^43 + 575395585999715717709126750033219544041151085711989694855465128960976413838349940799155170151060109208666439653761826224336/2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803*t^41 - 90703800267463748320914064194411716769648330632431882721421424216178182023770045013128744148303794980640283492210819846516248/6161499488437680261807735040502611125236073915874618828663826279435860711465815580811823289392572902659272537409*t^39 + 1185743924332657425782833112910294296124129229309118184143785754814608013901366812353660979198201629514492009053343015153971956/2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803*t^37 - 11838645150566807932214424948385453377495773894659766823018340252632750469993716406896780575305567091343400023272861141745412222/684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601*t^35 + 824671142364804732598950646306120857270160786728859611354282631577448061078058194711786768386473550609942041117205795233928394535/2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803*t^33 - 4994827992012840526803887097043961922506022656350249844866186654191719881384747425303408765145170302661677093350315583602652141375/684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601*t^31 + 47597132478042263984967309152762330603466478553737523490598308355477380256667320158842038797565219861112045196871910999128930224865/456407369513902241615387780777971194461931401175897691012135279958211904553023376356431354769820215011797965734*t^29 - 3217411420615447543809440231647493970980685197566784460084475598206476776224100936710738474379451699233984575251204295465629276415715/2738444217083413449692326684667827166771588407055386146072811679749271427318140258138588128618921290070787794404*t^27 + 2114066654187450609791323855241157728710091928507330429117110526085094910332663705538455659359978803148939656106786620493587507564765/202847719783956551829061235901320530871969511633732307116504568870316402023565945047302824342142317783021318104*t^25 - 29416036275805506407892898257229914783003941200104355217998430553853388756537854798759870974179417576463648658064123554726760464450125/405695439567913103658122471802641061743939023267464614233009137740632804047131890094605648684284635566042636208*t^23 + 318850757983765116497309075631008207686466428147908841610249739714412332342631767990210282770048588110884923120105289389963826548873625/811390879135826207316244943605282123487878046534929228466018275481265608094263780189211297368569271132085272416*t^21 - 2665467255432820263873594786503331672003234676437351683111491457526838762985789059666800220418798244337782669857483833363416068381105625/1622781758271652414632489887210564246975756093069858456932036550962531216188527560378422594737138542264170544832*t^19 + 498495083336450384532419303485513648914925999141413785775007420955116543843842329065891962735468345626534484260329374152748683178894375/95457750486567789096028816894739073351515064298226968054825679468384189187560444728142505572772855427304149696*t^17 - 9467186302601486795926326189148784613386567781173741233608786625706146152423498584751800737223724466832950155722687838937841945820170625/763662003892542312768230535157912586812120514385815744438605435747073513500483557825140044582182843418433197568*t^15 + 32742809911466960393632018258254467244403135803077010097500349930394096699241971232210467935599207032396734837288493503028733585793828125/1527324007785084625536461070315825173624241028771631488877210871494147027000967115650280089164365686836866395136*t^13 - 79779796483547503935763109170043481546749990924885439814441715387405927352293864870681625042366184114855537395102320154534375252003268125/3054648015570169251072922140631650347248482057543262977754421742988294054001934231300560178328731373673732790272*t^11 + 130734733531873512122844046379557769357154540501967210516601076351710357886824124153044123531705985234257369786830959512387992480201445625/6109296031140338502145844281263300694496964115086525955508843485976588108003868462601120356657462747347465580544*t^9 - 134719215476321992952514769168067402388773071924540825301576284455540702294133764869296528325820365745016839768716081357992715882509513125/12218592062280677004291688562526601388993928230173051911017686971953176216007736925202240713314925494694931161088*t^7 + 78674745079800699706859298489814672507510339102104231501021947234636566742817779373846973739139495639187669511233562443941971792509460625/24437184124561354008583377125053202777987856460346103822035373943906352432015473850404481426629850989389862322176*t^5 - 21553872588401710738228946401522692571865352665061919994616822027148734401698840062096271251004928953316099559373326267790535504914340625/48874368249122708017166754250106405555975712920692207644070747887812704864030947700808962853259701978779724644352*t^3 + 1685186845127382673824269330494937470004866243534082482931040765862865430004991700089068725149736818561694734479541907437747976425034375/97748736498245416034333508500212811111951425841384415288141495775625409728061895401617925706519403957559449288704*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:
| (-7.2171094125068892232 - 1.5083080966516202048e-859j)  +/-  (1.54e-246, 1.54e-246j)
| (5.668985002654550257 + 3.177761598859747097e-858j)  +/-  (6.54e-245, 6.54e-245j)
| (-7.9049372795856585164 + 3.2266503300343449218e-860j)  +/-  (1.18e-247, 1.18e-247j)
| (-4.4436725456953199306 + 4.540029906602026301e-856j)  +/-  (2.21e-244, 2.21e-244j)
| (1.4685532892166679317 - 5.1200522647146620143e-871j)  +/-  (5.28e-248, 5.28e-248j)
| (6.1375212115440669092 + 1.2238682582307188428e-868j)  +/-  (2.73e-245, 2.73e-245j)
| (7.2171094125068892232 - 2.9813564419072155019e-869j)  +/-  (1.44e-246, 1.44e-246j)
| (-2.9382321011972359479 + 1.8876980133605849642e-866j)  +/-  (6.85e-245, 6.85e-245j)
| (-5.668985002654550257 + 2.2416101736080852777e-871j)  +/-  (6.38e-245, 6.38e-245j)
| (-6.1375212115440669092 + 1.3809425873074289687e-874j)  +/-  (2.56e-245, 2.56e-245j)
| (5.2317324539479656178 + 3.2941726775052799672e-874j)  +/-  (1.34e-244, 1.34e-244j)
| (-6.6466797522227010501 + 1.0166839043389032279e-877j)  +/-  (8.87e-246, 8.87e-246j)
| (6.6466797522227010501 + 7.8633313910760589229e-878j)  +/-  (9.04e-246, 9.04e-246j)
| (-4.8225787874384532493 - 7.9748220762499574586e-875j)  +/-  (1.95e-244, 1.95e-244j)
| (4.0997623639174693016 - 9.4258004606431986083e-881j)  +/-  (2.74e-244, 2.74e-244j)
| (2.6602671868269422397 - 8.4556594628940607332e-891j)  +/-  (3.07e-245, 3.07e-245j)
| (-3.7832466850882959409 + 1.1874977934824393731e-902j)  +/-  (2.27e-244, 2.27e-244j)
| (3.7832466850882959409 - 8.4472768853191156567e-918j)  +/-  (2.27e-244, 2.27e-244j)
| (-1.4685532892166679317 - 6.3193649505284679053e-926j)  +/-  (5.38e-248, 5.38e-248j)
| (7.9049372795856585164 - 5.5102242211526840977e-933j)  +/-  (1.09e-247, 1.09e-247j)
| (-3.4755279338209517704 + 3.3639106794352663442e-928j)  +/-  (1.81e-244, 1.81e-244j)
| (-2.4627498551741779549 + 1.6388854037613052273e-943j)  +/-  (1.47e-245, 1.47e-245j)
| (4.8225787874384532493 + 7.2084992735814244044e-948j)  +/-  (1.7e-244, 1.7e-244j)
| (-3.1909932017815276072 - 4.1003344470659167977e-953j)  +/-  (1.27e-244, 1.27e-244j)
| (2.4627498551741779549 - 2.1815164572790782705e-963j)  +/-  (1.4e-245, 1.4e-245j)
| (-1.9366468705568828024 - 7.4614400247661664607e-965j)  +/-  (3.03e-247, 3.03e-247j)
| (0.72355101875283757332 + 6.6543193410981624317e-968j)  +/-  (2.8e-251, 2.8e-251j)
| (-5.2317324539479656178 - 6.2807600804721826121e-962j)  +/-  (1.21e-244, 1.21e-244j)
| (3.1909932017815276072 + 7.3243240433334437697e-962j)  +/-  (1.32e-244, 1.32e-244j)
| (-0.54431479141505793416 - 9.9122447434430845397e-976j)  +/-  (2.81e-252, 2.81e-252j)
| (-4.0997623639174693016 - 1.2067811372857115587e-967j)  +/-  (2.55e-244, 2.55e-244j)
| (-0.72355101875283757332 + 2.1110576860282675497e-982j)  +/-  (2.37e-251, 2.37e-251j)
| (1.2824912083026645136 + 7.1644276032981657198e-980j)  +/-  (5.11e-249, 5.11e-249j)
| (2.9382321011972359479 + 1.6651219233250053846e-974j)  +/-  (6.65e-245, 6.65e-245j)
| (1.5664430647489162541 - 3.0581243939451773874e-979j)  +/-  (8.36e-248, 8.36e-248j)
| (2.2665805845318431118 + 5.1935781303845794094e-976j)  +/-  (3.54e-246, 3.54e-246j)
| (3.4755279338209517704 - 3.0115599784413698521e-975j)  +/-  (1.87e-244, 1.87e-244j)
| (0.93588957168758885766 - 5.3462333420145155022e-982j)  +/-  (1.62e-250, 1.62e-250j)
| (0.24818520446629368019 + 1.9799829388643941411e-985j)  +/-  (6.29e-254, 6.29e-254j)
| (4.4436725456953199306 + 2.2548562221835119247e-977j)  +/-  (2.32e-244, 2.32e-244j)
| (-0.24818520446629368019 + 4.5809545625321900777e-987j)  +/-  (7.1e-254, 7.1e-254j)
| (-1.5664430647489162541 - 2.2388754668071038618e-981j)  +/-  (8.78e-248, 8.78e-248j)
| (-1.7740078453741537124e-1001 - 2.4727700484602848866e-1000j)  +/-  (1.21e-998, 1.21e-998j)
| (1.9366468705568828024 - 2.8798028294469045767e-980j)  +/-  (3.24e-247, 3.24e-247j)
| (-2.2665805845318431118 - 1.0256064008013305663e-980j)  +/-  (3.61e-246, 3.61e-246j)
| (-1.2824912083026645136 + 8.3281424446153898518e-986j)  +/-  (5.14e-249, 5.14e-249j)
| (-0.93588957168758885766 - 2.3208035395476526399e-986j)  +/-  (1.52e-250, 1.52e-250j)
| (-2.6602671868269422397 + 6.5990780250328307645e-987j)  +/-  (3.07e-245, 3.07e-245j)
| (0.54431479141505793416 + 7.3122646731234838816e-994j)  +/-  (2.86e-252, 2.86e-252j)
-------------------------------------------------
The weights are:
| (8.2893852573991399198e-24 - 1.2305510641394576794e-875j)  +/-  (1.97e-89, 5.58e-211j)
| (2.814436316009826028e-15 - 1.5477263689290307493e-870j)  +/-  (2.43e-85, 6.9e-207j)
| (3.2572484000295312589e-28 + 2.002660949983828692e-878j)  +/-  (1.8e-91, 5.12e-213j)
| (5.424475979706164566e-10 + 1.96940479041586419e-864j)  +/-  (1.37e-80, 3.88e-202j)
| (-0.014421413993247601686 - 2.3527597985990734123e-858j)  +/-  (4.66e-60, 1.32e-181j)
| (1.1998475194529683442e-17 + 3.0920296903876274017e-872j)  +/-  (2.46e-87, 6.98e-209j)
| (8.2893852573991399198e-24 + 2.9139379910936672106e-876j)  +/-  (4.12e-91, 1.17e-212j)
| (2.613049504478179365e-05 - 8.236126440683046154e-861j)  +/-  (8.74e-75, 2.48e-196j)
| (2.814436316009826028e-15 + 1.2174079556252942437e-869j)  +/-  (1.94e-86, 5.52e-208j)
| (1.1998475194529683442e-17 - 1.9578822452296372723e-871j)  +/-  (5.43e-88, 1.54e-209j)
| (3.0959786885338353333e-13 + 5.1105100769086539974e-869j)  +/-  (6.22e-87, 1.77e-208j)
| (1.9644453783001010004e-20 + 2.1463816222737278323e-873j)  +/-  (1.18e-89, 3.34e-211j)
| (1.9644453783001010004e-20 - 4.2350690114915068967e-874j)  +/-  (3.55e-91, 1.01e-212j)
| (1.7673794863316482299e-11 + 3.2748712264368530329e-866j)  +/-  (8.68e-85, 2.46e-206j)
| (9.252080099274661958e-09 - 4.1796757634117347749e-865j)  +/-  (1.9e-84, 5.39e-206j)
| (0.0001336193772032507225 + 1.0001447370479827149e-860j)  +/-  (6.53e-79, 1.86e-200j)
| (1.0649863477679264681e-07 + 5.6703689978407298705e-863j)  +/-  (8.44e-83, 2.4e-204j)
| (1.0649863477679264681e-07 + 4.5636715427084660097e-864j)  +/-  (1.22e-83, 3.47e-205j)
| (-0.014421413993247601686 - 4.6726841344098308573e-858j)  +/-  (1.59e-72, 4.53e-194j)
| (3.2572484000295312589e-28 - 5.5956470362970927022e-879j)  +/-  (1.09e-96, 3.08e-218j)
| (9.6800230990062679088e-07 - 3.5209118197472507522e-862j)  +/-  (3.99e-82, 1.13e-203j)
| (0.00015241417269951793021 - 1.0533046343176497984e-859j)  +/-  (2.07e-79, 5.87e-201j)
| (1.7673794863316482299e-11 - 1.347945774409274258e-867j)  +/-  (5.22e-88, 1.48e-209j)
| (5.5875793051289960803e-06 + 2.0080040945631429417e-861j)  +/-  (2.2e-81, 6.24e-203j)
| (0.00015241417269951793021 - 3.0245825548936290947e-860j)  +/-  (2.96e-81, 8.41e-203j)
| (0.0045887593110137392239 - 2.5921417722721409501e-859j)  +/-  (2.45e-78, 6.95e-200j)
| (0.034932128326139349604 + 5.2695923435009925241e-858j)  +/-  (2.81e-76, 7.97e-198j)
| (3.0959786885338353333e-13 - 6.192013772233588664e-868j)  +/-  (1.71e-88, 4.86e-210j)
| (5.5875793051289960803e-06 + 3.3004952538268578427e-862j)  +/-  (1.69e-84, 4.81e-206j)
| (0.11986500954046976368 - 6.8090678451262189106e-858j)  +/-  (2.81e-77, 7.98e-199j)
| (9.252080099274661958e-09 - 1.0349610927359504841e-863j)  +/-  (4.3e-85, 1.22e-206j)
| (0.034932128326139349604 + 7.317398049240834116e-858j)  +/-  (1.96e-77, 5.55e-199j)
| (0.042769095772447628598 + 1.7993904116062465375e-858j)  +/-  (5.47e-78, 1.55e-199j)
| (2.613049504478179365e-05 - 1.6821932187101965243e-861j)  +/-  (9.97e-84, 2.83e-205j)
| (0.023767859477484452363 + 1.3341166310118594492e-858j)  +/-  (8.84e-80, 2.51e-201j)
| (0.00099176649908915380632 + 4.760545948489408364e-860j)  +/-  (2.59e-82, 7.35e-204j)
| (9.6800230990062679088e-07 - 4.3134570468485222328e-863j)  +/-  (7.6e-86, 2.16e-207j)
| (0.074152343992411337489 - 2.6933889433997577177e-858j)  +/-  (4.79e-80, 1.36e-201j)
| (0.14958155115265065143 + 4.5978794352568075704e-858j)  +/-  (2.4e-80, 6.82e-202j)
| (5.424475979706164566e-10 + 2.7831001104399020208e-866j)  +/-  (3.83e-89, 1.09e-210j)
| (0.14958155115265065143 + 5.1413749197682416096e-858j)  +/-  (7.37e-81, 2.09e-202j)
| (0.023767859477484452363 + 2.7849947889794192431e-858j)  +/-  (3.4e-83, 9.66e-205j)
| (0.1269081279676605044 - 5.2607326730240506355e-858j)  +/-  (5.2e-81, 1.48e-202j)
| (0.0045887593110137392239 - 1.0193754114322676297e-859j)  +/-  (3.33e-83, 9.46e-205j)
| (0.00099176649908915380632 + 1.465808124898135673e-859j)  +/-  (4.75e-85, 1.35e-206j)
| (0.042769095772447628598 + 3.2577547889592978867e-858j)  +/-  (2.19e-83, 6.2e-205j)
| (0.074152343992411337489 - 4.1291029717268297816e-858j)  +/-  (3.82e-83, 1.08e-204j)
| (0.0001336193772032507225 + 3.9788125762399509661e-860j)  +/-  (5.77e-86, 1.65e-207j)
| (0.11986500954046976368 - 5.3240898758644342038e-858j)  +/-  (5.73e-83, 1.49e-204j)
