Starting with polynomial:
P : t
Extension levels are: 1 2 10 28
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P3 : t^13 - 124943/42780*t^11 + 576433/179676*t^9 - 310453/189658*t^7 + 10439/27094*t^5 - 97669/2763588*t^3 + 3421/4605980*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 3456646554674717718481692338548395717412232611661359053764791118911771492181232687616018083462907/354061146769560851912972996661228874481944839595474445190507162376531917503490972230972649042220*t^39 + 501454589137974068758840198003462860691411299459604496571000886958587847584884967939419066963849207/11400768925979859431597730492491569758318623834974277135134330628524327743612409305837319299159484*t^37 - 4168954584765809634200978775452733472837192058289966520349919446764307128144800458781526572832399971047/34373318311829276186267157434862082821330650862447445562430006845000848146991414057099517686965844260*t^35 + 38442989873646214590258593927541266188224858042873131312645807715538940123907097887938950440018257352067/167938212323508749367190969181754747498501179927957519747872319157004143803872337250400500699175981956*t^33 - 772811599226830611123593701442558983598795698947402929184799088351654749877905551346424493529177435785385/2466578664597357919312388836226490759455094240503146825783061457025682403280128916446840819063556064361*t^31 + 520619819193051449257774556234933934567384811056181443326357513553756546862024823516666914835145311575598621/1619587377996103885406570153593232884151885266627146891574652127669605332863452390137917576517376893228005*t^29 - 202318779576283135710778756140993316682685640079491083141525540949367371348319421283754262227602018441813253/802752004745894969288473902215776299101369219110846720171784098062326121506232923807489581404265068817359*t^27 + 521646679859420079801992028648847428429512011591640144886104271350368050026451417385242166620545363946062827/3419128909102885980302759213141269422098424451768421215546487825080277924933955045846714883758906774592455*t^25 - 29788362357014150204855959856253938104501390358462859107292563112693261963305687632819270877838795682434805/416241780238612206297727208556328451385895150650068669718702865661946877818046701233513116283692998646038*t^23 + 551078655869834906818009425843816394231915525037905280073902807090882629623021737015258261095055288176713415/21228330792169222521184087636372751020680652683153502155653846148759290768720381762909168930468342930947938*t^21 - 384585060349139063631085584742040707304260227575651666792686326579200697893699371259413807003574706843047/53203836571852688023017763499681080252332462865046371317428185836489450548171382864434007344532187796862*t^19 + 16127621345662525498212626755387536630706072195999932391945350783197131528036794785338316470282094927735/10575310844924198272933557758298776812939593733652046893929401029398326002846830042642207534457186117254*t^17 - 193348719226231579145408843571869870823010087779315566643676733580110913759484999074428413548754914575167/809011279636701167879417168509856426189878920624381587385599178748971939217782498262128876385974737969931*t^15 + 349013139762376423279730374023831514882725617129305034330978937597958529064870275869439771445659298183231415/12906156944044293731180342089237739567007138420720759463562463698582349346341284194775741964985454994834309243*t^13 - 11736993611451575797873488071986059456963312617890944478498547127710077196725459748210945265714850955021585/5531210118876125884791575181101888385860202180308896912955341585106721148431978940618175127850909283500418247*t^11 + 8052638350065734836657056264992746481687588617025371117289961886465132236249485938011475900919205407507116/73917080679526409551305595601997962974677247318673440564039564819153455347227354933715613072189424061323771119*t^9 - 110164715182833300805590006485901326425824453279432683098093331176988924706993524767763180957426252426495/32852035857567293133913598045332427988745443252743751361795362141845980154323268859429161365417521805032787164*t^7 + 13278316249412271840519747362387134513887980900249856538229953309774983860235435530866955684754279979/247007788402761602510628556731822766832672505659727453848085429637939700408445630522023769664793397030321708*t^5 - 79998937645499374403802166187038193420996766538238181048783349472561138074499799302709919164564665/230810556376351005624685700552686847696103816764007620808866712940369883988219687536973030670380715257841596*t^3 + 69893760127070073653352038263537062339823635227276724806877683480098653045378433476558518473965205/145487587369226583878760219915043609664444105833579470316522318056746483540574476377472000332563310850859486012*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:
| (-0.99392811680537305572 - 3.420794284930833783e-888j)  +/-  (1.12e-241, 1.12e-241j)
| (0.99392811680537305572 - 1.1963988077866693978e-897j)  +/-  (9.7e-242, 9.7e-242j)
| (-0.90591989788431806766 + 5.238528214764410069e-913j)  +/-  (2.03e-242, 2.03e-242j)
| (0.45966053063221982553 - 1.6287991104173607917e-918j)  +/-  (2.57e-248, 2.57e-248j)
| (0.93773027621034202472 - 2.0962038277492676149e-911j)  +/-  (4.27e-242, 4.27e-242j)
| (0.96311804562766043718 - 2.0973196751093885603e-923j)  +/-  (7.71e-242, 7.71e-242j)
| (-0.99928883759866534555 - 1.6450362319261482708e-930j)  +/-  (5.25e-242, 5.25e-242j)
| (-0.93773027621034202472 + 7.3261415455652840529e-934j)  +/-  (4.13e-242, 4.13e-242j)
| (-0.98189373966174310941 + 2.2039155606394337688e-934j)  +/-  (1.11e-241, 1.11e-241j)
| (0.98189373966174310941 - 3.7558886796454677821e-942j)  +/-  (9.9e-242, 9.9e-242j)
| (0.90591989788431806766 - 4.516839463645947492e-959j)  +/-  (2.13e-242, 2.13e-242j)
| (-0.86792697834945936646 + 5.9719647007506150526e-964j)  +/-  (7.29e-243, 7.29e-243j)
| (-0.96311804562766043718 + 1.7235435964430527008e-966j)  +/-  (7.69e-242, 7.69e-242j)
| (-0.82404021821838639472 - 6.1896110956916990141e-979j)  +/-  (2.1e-243, 2.1e-243j)
| (0.99928883759866534555 - 4.039748344535084177e-991j)  +/-  (4.32e-242, 4.32e-242j)
| (0.77459666924148337704 - 8.0331787139689031927e-1010j)  +/-  (5.64e-244, 5.64e-244j)
| (0.82404021821838639472 - 9.1599595649669386886e-1011j)  +/-  (2.17e-243, 2.17e-243j)
| (-0.24133725075708084523 - 2.1718321731701695891e-1015j)  +/-  (1.71e-251, 1.71e-251j)
| (-0.77459666924148337704 + 9.2172403454168850351e-1014j)  +/-  (5.16e-244, 5.16e-244j)
| (-0.31407812055899103745 - 8.7038886737469647191e-1018j)  +/-  (2.21e-250, 2.21e-250j)
| (0.24133725075708084523 + 2.5181072289998186525e-1015j)  +/-  (1.62e-251, 1.62e-251j)
| (0.71998303173381570985 + 7.4700762482251446539e-1014j)  +/-  (1.11e-244, 1.11e-244j)
| (0.86792697834945936646 + 7.3143923073759110115e-1018j)  +/-  (8.04e-243, 8.04e-243j)
| (-0.66063942041264467191 + 1.8465044487378513475e-1018j)  +/-  (1.79e-245, 1.79e-245j)
| (-0.71998303173381570985 + 2.8232540514776598085e-1020j)  +/-  (1.22e-244, 1.22e-244j)
| (-7.2347780433095886638e-1021 - 3.4212836439458055654e-1021j)  +/-  (3.28e-1019, 3.28e-1019j)
| (0.66063942041264467191 + 3.2026467967284518424e-1021j)  +/-  (1.86e-245, 1.86e-245j)
| (0.38736385932378655649 + 1.1963593599653206965e-1026j)  +/-  (2.63e-249, 2.63e-249j)
| (-0.043217951307532783201 + 2.8216274271805957321e-1025j)  +/-  (8.72e-255, 8.72e-255j)
| (-0.59706738604131558719 + 1.9158240627108384457e-1025j)  +/-  (2.55e-246, 2.55e-246j)
| (-0.1044614586151915911 - 1.6072845775464465621e-1026j)  +/-  (9.91e-254, 9.91e-254j)
| (0.31407812055899103745 - 4.6268785101660452368e-1027j)  +/-  (1.94e-250, 1.94e-250j)
| (0.52984566457483662948 - 7.2073631317652772879e-1024j)  +/-  (2.69e-247, 2.69e-247j)
| (0.043217951307532783201 - 4.0969777952903528992e-1026j)  +/-  (8.72e-255, 8.72e-255j)
| (-0.45966053063221982553 + 2.0234093462177951173e-1025j)  +/-  (2.66e-248, 2.66e-248j)
| (-0.38736385932378655649 - 5.7855749817466417346e-1027j)  +/-  (2.56e-249, 2.56e-249j)
| (0.1044614586151915911 + 1.8590491997060486961e-1026j)  +/-  (8.35e-254, 8.35e-254j)
| (0.59706738604131558719 - 4.0069115972155998376e-1026j)  +/-  (2.55e-246, 2.55e-246j)
| (0.17101852249474448773 - 2.9021870186464072089e-1030j)  +/-  (1.08e-252, 1.08e-252j)
| (-0.17101852249474448773 - 7.4086959620640919401e-1031j)  +/-  (1.11e-252, 1.11e-252j)
| (-0.52984566457483662948 - 6.7728272626012653517e-1027j)  +/-  (2.73e-247, 2.73e-247j)
-------------------------------------------------
The weights are:
| (0.0086450299740093325715 - 3.4014334944289799819e-889j)  +/-  (8.82e-73, 1.77e-190j)
| (0.0086450299740093325715 - 1.4876764421715656228e-890j)  +/-  (2.6e-73, 5.21e-191j)
| (0.03494574438815696282 - 9.3709113915996609803e-889j)  +/-  (2.8e-73, 5.62e-191j)
| (0.071400969113803506758 - 5.7395132021982296345e-889j)  +/-  (1.39e-73, 2.78e-191j)
| (0.028634973724565617665 + 3.4815997227074066944e-890j)  +/-  (6.74e-74, 1.35e-191j)
| (0.02210889478180052703 - 2.7777231913286058369e-890j)  +/-  (8.06e-74, 1.62e-191j)
| (0.0023136972970964333139 - 2.106968101982824851e-888j)  +/-  (2.89e-74, 5.79e-192j)
| (0.028634973724565617665 + 1.1967117125961395269e-888j)  +/-  (8.41e-75, 1.69e-192j)
| (0.015420249650812713588 + 3.5269493787376685942e-888j)  +/-  (1.46e-74, 2.92e-192j)
| (0.015420249650812713588 + 2.1482015908548086704e-890j)  +/-  (5.42e-76, 1.09e-193j)
| (0.03494574438815696282 - 4.3409641647739631983e-890j)  +/-  (1.03e-76, 2.06e-194j)
| (0.04099197279577266811 + 8.0553306550993685089e-889j)  +/-  (2.81e-76, 5.65e-194j)
| (0.02210889478180052703 - 1.7644011924776423743e-888j)  +/-  (3.45e-75, 6.92e-193j)
| (0.046725391723247251976 - 7.4362077633115560698e-889j)  +/-  (3.95e-77, 7.93e-195j)
| (0.0023136972970964333139 + 5.6666531753767995037e-891j)  +/-  (5.98e-77, 1.2e-194j)
| (0.052097314980089667343 + 9.0457213876388567067e-890j)  +/-  (1.66e-79, 3.34e-197j)
| (0.046725391723247251976 - 6.9490853132043869323e-890j)  +/-  (4.11e-79, 8.25e-197j)
| (0.071844850804607082637 + 5.8535289798509616964e-888j)  +/-  (6.07e-82, 1.22e-199j)
| (0.052097314980089667343 + 7.2937933451033484076e-889j)  +/-  (6.34e-80, 1.27e-197j)
| (0.073308748356427402678 - 3.4557236158276960156e-888j)  +/-  (5.2e-82, 1.04e-199j)
| (0.071844850804607082637 + 3.5662883121928897205e-888j)  +/-  (4.47e-83, 8.96e-201j)
| (0.057056733654232555576 - 1.2091203870463511041e-889j)  +/-  (3.73e-81, 7.49e-199j)
| (0.04099197279577266811 + 5.4514490982745518674e-890j)  +/-  (1e-79, 2.01e-197j)
| (0.061547144511369711832 + 8.2871568605366838872e-889j)  +/-  (1.46e-82, 2.93e-200j)
| (0.057056733654232555576 - 7.5647457415128442085e-889j)  +/-  (7.54e-82, 1.51e-199j)
| (0.033676973080435780197 + 5.4915989014523685417e-887j)  +/-  (1.58e-84, 3.17e-202j)
| (0.061547144511369711832 + 1.6693278697425649816e-889j)  +/-  (1.68e-83, 3.36e-201j)
| (0.07300800351806800837 + 9.7715675750233710787e-889j)  +/-  (1.74e-84, 3.49e-202j)
| (0.055715017738594397071 - 4.1440614517276599893e-887j)  +/-  (6.85e-85, 1.37e-202j)
| (0.065500944190221094482 - 9.606937670610428115e-889j)  +/-  (1.93e-85, 3.88e-203j)
| (0.064518613390558087033 + 2.0169330550793260514e-887j)  +/-  (2.57e-85, 5.15e-203j)
| (0.073308748356427402678 - 1.7961486872028882416e-888j)  +/-  (1.15e-85, 2.31e-203j)
| (0.068829035459880847247 + 3.6054247771522389728e-889j)  +/-  (6.26e-86, 1.26e-203j)
| (0.055715017738594397071 - 3.7986947735660862763e-887j)  +/-  (7.26e-86, 1.46e-203j)
| (0.071400969113803506758 - 1.5615566909379866039e-888j)  +/-  (1.8e-87, 3.61e-205j)
| (0.07300800351806800837 + 2.2252197896230988119e-888j)  +/-  (2.99e-87, 6.01e-205j)
| (0.064518613390558087033 + 1.6332954574346677405e-887j)  +/-  (9.14e-87, 1.83e-204j)
| (0.065500944190221094482 - 2.3963715123822900662e-889j)  +/-  (6.8e-88, 1.36e-205j)
| (0.0685481834064682418 - 7.4951203941308468321e-888j)  +/-  (3.75e-87, 7.52e-205j)
| (0.0685481834064682418 - 1.061041866181290318e-887j)  +/-  (1.25e-87, 2.55e-205j)
| (0.068829035459880847247 + 1.1838094126337976789e-888j)  +/-  (6.69e-89, 1.28e-206j)
