Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 8 24
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P4 : t^17 - 1529814253969/16753860777*t^15 + 159113012962007/50261582331*t^13 - 8081473967104151/150784746993*t^11 + 71537082906692561/150784746993*t^9 - 36627085158415339/16753860777*t^7 + 83781328830792607/16753860777*t^5 - 88756606077394045/16753860777*t^3 + 11500071526304270/5584620259*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 17269618763954452630428658234986370353332354033021419506068405393218059756574545731018816270009777481714990065056280791426914330961280102726040770922888744226337387636625440452581293583963151710047910127/29608085965386344001760983259998076955241787125225105880009980353549861538895780581813907218145201888145245294686407194901458402548258529479395531949748039368587482465275150240064487256826251441343719*t^39 + 229767368157832384706340281745950422999771601149948508546384500415028381000369168747389155248615658478634729677607262246774431483040299395655638910850054517172905701019645905910025706365364121390151900869113/1510012384234703544089810146259901924717331143386480399880508998031042938483684809672509268125405296295407510029006766939974378529961185003449172129437150007797961605729032662243288850098138823508529669*t^37 - 106660736974093957418392994882216086451629318132755378045245078307945811128511657286797223872617848446387293440438152167550125946557434435896063076540257277356805603341398113572009120589128931115490671732963685/4530037152704110632269430438779705774151993430159441199641526994093128815451054429017527804376215888886222530087020300819923135589883555010347516388311450023393884817187097986729866550294416470525589007*t^35 + 10948887524801397977114828475908208410799959337797434032068165012723971646435018815167577806085575578030744085423219941490404906937934978398957925846652378287653151272928229927373441802931579219771305110344297380/4530037152704110632269430438779705774151993430159441199641526994093128815451054429017527804376215888886222530087020300819923135589883555010347516388311450023393884817187097986729866550294416470525589007*t^33 - 614634279832336453685958301614265576689266637995642083710671159980386982165330173109021579943153642286615396192965493389893598392207386494018150830089476049439282082102473164642384615175654942175792978476402751030/3523362229880974936209557007939771157673772667901787599721187662072433523128597889235854958959279024689284190067682456193273549903242765008048068302020016684861910413367742878567673983562323921519902561*t^31 + 290372317782439480367788917161757686269148892913249010920626077342452096395484593334618022516654071807503493209638169376665968703301849828608403584615741433539529938057569483069158446808912500302825156352742659936646/31710260068928774425886013071457940419063954011116088397490688958651901708157381003122694630633511222203557710609142105739461949129184885072432614718180150163757193720309685907109065852060915293679123049*t^29 - 11313573877043548776217802886763741932831148955609075548625062358465976107457322213403335044047445304354114003390856064024534053361774360761462233909286669785470799294966487716593730116074413742602468382628136916726338/31710260068928774425886013071457940419063954011116088397490688958651901708157381003122694630633511222203557710609142105739461949129184885072432614718180150163757193720309685907109065852060915293679123049*t^27 + 12262016157233844638298018414471560655027664446741873482430715302376865035137435167896726554911359658059583288408230277875521281933671917168249078042807871329946880520880783531026859736459109525572109198776984259798596/1174454076626991645403185669313257052557924222633929199907062554024144507709532629745284986319759674896428063355894152064424516634414255002682689434006672228287303471122580959522557994520774640506634187*t^25 - 271034520576682023118474345084952350188216679982153902843846989094624566612231483905193391944932749994636238991619026389163304704831921288434571197380085981928147100398100883308176458668665432797268831478296136846906600/1174454076626991645403185669313257052557924222633929199907062554024144507709532629745284986319759674896428063355894152064424516634414255002682689434006672228287303471122580959522557994520774640506634187*t^23 + 646837301488285966204423415406353218029446419879353715205346791502845103347412485962080201484640114969503200882440073736594467740737448241995367718351057032776595329034235043838613425746149806727424577481877937347667200/167779153803855949343312238473322436079703460376275599986723222003449215387076089963612140902822810699489723336556307437774930947773465000383241347715238889755329067303225851360365427788682091500947741*t^21 - 428118218435215066710712092078110302805799577590839308458532632107942591927835382358590926185888627603941325802986548880458954297184230957733640841048625053312098040161866856307088499487366208044667466684077413232860200/8830481779150313123332223077543286109458076861909242104564380105444695546688215261242744258043305826288932807187174075672364786724919210546486386721854678408175214068590834282124496199404320605313039*t^19 + 236292856683716233264587355082088650020376120554921764570602969106021712688066033753447614710005474421773643254678522741484484442242751515079949886187069763087517328761655174226107845876595079121287358419540293529818550/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^17 - 1630779143442611196024915044068568396767935758468312633082866992993408789626626937676952550853346249158143346029809841408141441003160947310007781293345378603641156402463979016405158650093939208033124870693788384609436950/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^15 + 8107108132199007287608193843717617386037271800771241915367693225585601403442734523332123062921733119180433907079356104865193960490421322111027887312634078766903603433961148256251935162611168759111659226280315935956445750/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^13 - 28187885454904033728517707622122902302262692564396104375923518318462091498003977298202768141029390116579893098732363267082635616247423888115298519738594780405636265024463462617316199615606720783435977631032304390853319250/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^11 + 65780395591159009861455405891270254873047371833500210526337104919503430853030892751780013471023016326354619872961022888976739328777558945385149154815109436698643351644076089335960359415314092132346066023604164546716446125/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^9 - 97175262821511308207923024578473451059701010794046423754803940377676858818432053879687894215501245197544836649788347287071585235377329827993948214673111204885133053527504072324837748752769046347666121163761245169414864625/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^7 + 83176064662009030819824040149620817593149792864056983239965806362817887495221383817311871231771087858909683163134962875049144432138762284355381663421451193223720251449551775114910984204543367786594372579322058591219729125/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^5 - 35188495094096836950914934201933419313990150127375989656972802118290941885820435797451577462948521348673287981575211428169315756628439446505346663308525335868926014979468309016839582978643761061532739056243922359669091875/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*t^3 + 4905856735378009266868915557746370812448535131321274800507806699132627299271874895013786542452111135521964914620764237058646184107069609417552200083429021508611102091975287482435046937486809879540879821790909831770523750/519440104655900771960719004561369771144592756582896594386140006202629149805189133014279074002547401546407812187480827980727340395583482973322728630697334024010306709917107898948499776435548270900767*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:
| (7.1125118206199100796 + 1.0704734752247261139e-533j)  +/-  (3.53e-246, 3.53e-246j)
| (-8.5392476972337027471 + 5.3205219176470792406e-546j)  +/-  (7.67e-247, 7.67e-247j)
| (7.7981087129581153304 - 3.4943434776709182497e-550j)  +/-  (2.07e-246, 2.07e-246j)
| (-10.362399231023928151 + 8.1808538534931807757e-558j)  +/-  (1.94e-248, 1.94e-248j)
| (9.3668475112715471878 + 7.291232292924232062e-553j)  +/-  (1.94e-247, 1.94e-247j)
| (4.6841166119510901872 + 5.1624401125443104783e-554j)  +/-  (3.92e-246, 3.92e-246j)
| (-2.7875367754936262063 + 7.2736124808504503623e-563j)  +/-  (1.1e-247, 1.1e-247j)
| (-7.1125118206199100796 + 1.837870619865050908e-559j)  +/-  (3.67e-246, 3.67e-246j)
| (-1.5093152835436173382 - 3.6632161494082326121e-574j)  +/-  (2.08e-250, 2.08e-250j)
| (8.5392476972337027471 - 1.2719886796988523063e-567j)  +/-  (8.13e-247, 8.13e-247j)
| (2.7875367754936262063 - 1.9708527971601274561e-576j)  +/-  (1.1e-247, 1.1e-247j)
| (5.8511016297812679182 - 1.5690274660113386471e-590j)  +/-  (4.73e-246, 4.73e-246j)
| (1 - 3.2462206859402875754e-606j)  +/-  (1.61e-251, 1.61e-251j)
| (-3.1758615746076673391 + 3.9599370148831269401e-602j)  +/-  (3.69e-247, 3.69e-247j)
| (10.362399231023928151 + 3.5909674516770672951e-603j)  +/-  (1.87e-248, 1.87e-248j)
| (-5.8511016297812679182 + 1.8373463046222680584e-598j)  +/-  (5.15e-246, 5.15e-246j)
| (-7.7981087129581153304 + 4.5099262858826590836e-599j)  +/-  (2.1e-246, 2.1e-246j)
| (-5.2592524580675125269 + 1.0551413233592208816e-600j)  +/-  (4.46e-246, 4.46e-246j)
| (-9.3668475112715471878 + 3.3152946894124225555e-602j)  +/-  (1.82e-247, 1.82e-247j)
| (4.0810766339156860865 + 2.0708077391429334201e-605j)  +/-  (7.67e-246, 7.67e-246j)
| (6.4666598036497565427 - 8.1613997740660740356e-622j)  +/-  (4.62e-246, 4.62e-246j)
| (1.5093152835436173382 - 1.0121872431522134563e-637j)  +/-  (2e-250, 2e-250j)
| (-4.0810766339156860865 + 1.0366986178285216101e-629j)  +/-  (8.45e-246, 8.45e-246j)
| (-2.4494897427831780982 + 6.5344538252910594559e-639j)  +/-  (2e-248, 2e-248j)
| (-3.7932353000477464006 - 5.8847541963018327864e-635j)  +/-  (1.1e-243, 1.1e-243j)
| (5.2592524580675125269 - 1.8928425352535072714e-659j)  +/-  (4.54e-246, 4.54e-246j)
| (1.9983129651543939317 + 1.9488905398941379671e-685j)  +/-  (1.87e-249, 1.87e-249j)
| (3.7932353000477464006 - 1.4263230635186382979e-711j)  +/-  (1.11e-243, 1.11e-243j)
| (-3.7920509035000931049 + 4.0221071899348488189e-731j)  +/-  (1.09e-243, 1.09e-243j)
| (-0.50247391784770602722 + 1.844230193038336639e-745j)  +/-  (1.44e-253, 1.44e-253j)
| (-9.6346537623152346763e-755 + 1.187691297978698364e-754j)  +/-  (6.27e-753, 6.27e-753j)
| (3.1758615746076673391 + 2.8520406797754310564e-735j)  +/-  (3.61e-247, 3.61e-247j)
| (1.175604294567460207 + 7.4722813188190532081e-747j)  +/-  (5.96e-251, 5.96e-251j)
| (-6.4666598036497565427 - 1.202822120516955309e-740j)  +/-  (4.68e-246, 4.68e-246j)
| (-1 - 1.3232836188910788309e-751j)  +/-  (1.96e-251, 1.96e-251j)
| (-4.6841166119510901872 + 1.568764419375199315e-744j)  +/-  (3.81e-246, 3.81e-246j)
| (3.7920509035000931049 - 1.9133935651879145051e-747j)  +/-  (1.05e-243, 1.05e-243j)
| (2.4494897427831780982 + 6.4068671083103229064e-766j)  +/-  (2.2e-248, 2.2e-248j)
| (0.50247391784770602722 + 1.0270354949617193311e-779j)  +/-  (1.44e-253, 1.44e-253j)
| (-1.175604294567460207 - 3.9694044875384844471e-776j)  +/-  (6.29e-251, 6.29e-251j)
| (-1.9983129651543939317 + 4.6902283170091937751e-774j)  +/-  (1.79e-249, 1.79e-249j)
-------------------------------------------------
The weights are:
| (2.7411054315676529835e-12 - 1.41540609574973985e-544j)  +/-  (5.88e-86, 2.28e-207j)
| (4.5423914948513287371e-17 - 1.5227024709488426622e-549j)  +/-  (3.57e-90, 1.39e-211j)
| (1.7672343021965541717e-14 - 1.514245015431778428e-546j)  +/-  (9.19e-88, 3.57e-209j)
| (2.2058300074305174674e-24 - 5.7678305271135619348e-554j)  +/-  (5.64e-94, 2.19e-215j)
| (3.1478049967536503238e-20 - 1.2573690776823179744e-550j)  +/-  (1.08e-91, 4.18e-213j)
| (3.9193547925002855935e-06 - 1.0116742425826231826e-540j)  +/-  (1.59e-81, 6.19e-203j)
| (0.0025783750724716461324 + 2.5874443163369556584e-538j)  +/-  (4.61e-75, 1.79e-196j)
| (2.7411054315676529835e-12 - 2.0627597755131438159e-546j)  +/-  (9.3e-89, 3.61e-210j)
| (0.062865385851119754654 - 2.1533405468482274122e-537j)  +/-  (9.63e-67, 3.74e-188j)
| (4.5423914948513287371e-17 + 1.6704544466294502531e-548j)  +/-  (5.06e-90, 1.96e-211j)
| (0.0025783750724716461324 + 5.9227681557006589279e-538j)  +/-  (1.83e-76, 7.09e-198j)
| (8.8492481523497740569e-09 - 8.2007829919828529824e-543j)  +/-  (2.8e-85, 1.09e-206j)
| (0.11694104276064291717 - 7.4569306814761995336e-537j)  +/-  (2.78e-65, 1.08e-186j)
| (0.0012035222795035881094 - 9.328466071770148552e-539j)  +/-  (7.27e-79, 2.82e-200j)
| (2.2058300074305174674e-24 + 3.1014097626762279647e-553j)  +/-  (1.87e-94, 7.26e-216j)
| (8.8492481523497740569e-09 - 7.9796819602197853914e-544j)  +/-  (7.11e-88, 2.76e-209j)
| (1.7672343021965541717e-14 + 6.9625652029742210804e-548j)  +/-  (1.8e-91, 6.98e-213j)
| (2.2887361125862154989e-07 + 1.2595445343644438347e-542j)  +/-  (4.86e-87, 1.89e-208j)
| (3.1478049967536503238e-20 + 1.7200498702980881492e-551j)  +/-  (9.7e-95, 3.76e-216j)
| (7.6388400545988245403e-05 + 3.9587142986463909598e-539j)  +/-  (4.92e-85, 1.91e-206j)
| (2.0858209325143881287e-10 + 9.4746235124977951143e-544j)  +/-  (4.31e-89, 1.67e-210j)
| (0.062865385851119754654 - 3.3134175766388426616e-537j)  +/-  (8.09e-78, 3.14e-199j)
| (7.6388400545988245403e-05 + 1.0720946073520273848e-539j)  +/-  (1.83e-85, 7.09e-207j)
| (0.0079871053792400478543 - 4.3912760507122906214e-538j)  +/-  (1.42e-81, 5.52e-203j)
| (-0.029421730657189159034 - 7.394912066549643222e-537j)  +/-  (8.25e-85, 3.2e-206j)
| (2.2887361125862154989e-07 + 8.4083147737104761094e-542j)  +/-  (1.41e-88, 5.47e-210j)
| (0.026021299450872424593 + 1.289952603831038862e-537j)  +/-  (7.26e-83, 2.82e-204j)
| (-0.029421730657189159034 - 2.4296572002221834747e-536j)  +/-  (1.42e-86, 5.53e-208j)
| (0.029610257326886374604 + 7.4055850718741386759e-537j)  +/-  (1.45e-85, 5.61e-207j)
| (0.17641970626659349236 + 2.1455604498096867476e-537j)  +/-  (4.48e-84, 1.74e-205j)
| (0.20059066405726452837 - 1.9062995036205467141e-537j)  +/-  (5.3e-84, 2.05e-205j)
| (0.0012035222795035881094 - 2.4379799106691117876e-538j)  +/-  (6.87e-88, 2.66e-209j)
| (0.0054191585516878333917 + 8.4828493317735701335e-537j)  +/-  (3.86e-84, 1.49e-205j)
| (2.0858209325143881287e-10 + 4.5063166405839201276e-545j)  +/-  (1.84e-94, 7.12e-216j)
| (0.11694104276064291717 - 5.6185529147966594183e-537j)  +/-  (1.35e-85, 5.22e-207j)
| (3.9193547925002855935e-06 - 2.0825822373433829794e-541j)  +/-  (8.84e-91, 3.42e-212j)
| (0.029610257326886374604 + 2.4320318456001257834e-536j)  +/-  (1.4e-86, 5.45e-208j)
| (0.0079871053792400478543 - 9.0047586653772945375e-538j)  +/-  (9.83e-88, 3.83e-209j)
| (0.17641970626659349236 + 2.4717577216113612769e-537j)  +/-  (7.2e-87, 2.85e-208j)
| (0.0054191585516878333917 + 6.0763979823944231359e-537j)  +/-  (2.92e-87, 1.24e-208j)
| (0.026021299450872424593 + 7.2409186711812429823e-538j)  +/-  (3.46e-88, 1.22e-209j)
