Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 55
-------------------------------------------------
Trying to find an order 55 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^63 - 203652374172493620481907533971596847159924749536990451071935693490079261/118177038338135243199369522458882662745162641370259576393835461404150*t^61 + 163820008783103278697399496810637811956703308699100144176399035537002485023/118177038338135243199369522458882662745162641370259576393835461404150*t^59 - 8182172408895330629348826678004997583840411523558547808572273281992246302523/11817703833813524319936952245888266274516264137025957639383546140415*t^57 + 133825015127435553273415732079249539492776168007423759989886174041542560362026424/555432080189235643037036755556748514902264414440220009051026668599505*t^55 - 69031747221043374851778952429975185792314229589083989558818730351019204498980183697/1110864160378471286074073511113497029804528828880440018102053337199010*t^53 + 2741099217542940782857788544811146938886463325079763980938369602530527906214625913699/222172832075694257214814702222699405960905765776088003620410667439802*t^51 - 214766389030923717333815058741479691817587162196193641225939550396283568105017049350672/111086416037847128607407351111349702980452882888044001810205333719901*t^49 + 27023150558818869523499420972841968977168477147280160698075743098541363303087572779813415/111086416037847128607407351111349702980452882888044001810205333719901*t^47 - 117590028668036023119516451658977992880152340922018069244836273880554471689037758200373845/4727081533525409727974780898355306509806505654810383055753418456166*t^45 + 9855031080040201247962050454807049083013530745051005961879040785907406855978124206138512255/4727081533525409727974780898355306509806505654810383055753418456166*t^43 - 340382270181901252245639471682766087019366852051623443704824275074553426329519992324134066845/2363540766762704863987390449177653254903252827405191527876709228083*t^41 + 19448473978698975177293506341519792398510077428888796526958695794343623698334050090466769403810/2363540766762704863987390449177653254903252827405191527876709228083*t^39 - 1841455342953920351243674904475507789993336159449423087643376345489352655625178252366126748182475/4727081533525409727974780898355306509806505654810383055753418456166*t^37 + 72243323561204440308305510709084897684747111021760085044222118147127537963705818643686298456433725/4727081533525409727974780898355306509806505654810383055753418456166*t^35 - 1172815365503883020794515742979528327018171807945192381516581855685322236026008300030117463906332450/2363540766762704863987390449177653254903252827405191527876709228083*t^33 + 31429876043726289206216508399499801400761451286022227246049298336425344958821441916865849423301617925/2363540766762704863987390449177653254903252827405191527876709228083*t^31 - 1384661998333861451322603844730564900905629738992953743350726448387454455969181807919020639736464637175/4727081533525409727974780898355306509806505654810383055753418456166*t^29 + 24929899079386707381392754213704672773026038817908628069686133675761194729928977073371620775742184610125/4727081533525409727974780898355306509806505654810383055753418456166*t^27 - 182089361392188714133695666033341623619767289310675222870005663119241470050289210001427302292557162405625/2363540766762704863987390449177653254903252827405191527876709228083*t^25 + 2138206326831501360735744287820378073734484729676288427750468515129717426646531122090660108253134714482500/2363540766762704863987390449177653254903252827405191527876709228083*t^23 - 39895748112248222480819537868978507833880568508273716765453289678386544671308432591250348425256898661170625/4727081533525409727974780898355306509806505654810383055753418456166*t^21 + 291372791863457340286504500604287553308148083357328280665976875361709065843410916578092963208182054061299375/4727081533525409727974780898355306509806505654810383055753418456166*t^19 - 817492427122830078583102024509746756261719171347620683010401190372090535309807539321034739271728882782187500/2363540766762704863987390449177653254903252827405191527876709228083*t^17 + 3440472874580129688789692855014381375905600464573021640553311796943611182240778315224562055098097950389009375/2363540766762704863987390449177653254903252827405191527876709228083*t^15 - 21042953272370771358371803243839017818956591269010561976478481002249895464521054793161992154801184449130559375/4727081533525409727974780898355306509806505654810383055753418456166*t^13 + 44815021655985573888175974825297652559553840458832364084454724121141423665414082273681045998673862029190488125/4727081533525409727974780898355306509806505654810383055753418456166*t^11 - 31339232059946579295499564543190353005348649016691024435227733427385860588312281147697561278687146774972236875/2363540766762704863987390449177653254903252827405191527876709228083*t^9 + 26483622537802195392397224769808426038610231625937535418574371639092867398117756128386788138266659605443431250/2363540766762704863987390449177653254903252827405191527876709228083*t^7 - 23955044338674042390903969763221746184153961095035305259995985646779372146541060630059213740363791842046090625/4727081533525409727974780898355306509806505654810383055753418456166*t^5 + 4844846093644958118700695677551590455457804346061496377184576013904719717065855779336311731939027785915034375/4727081533525409727974780898355306509806505654810383055753418456166*t^3 - 159566292152745665819956607591852041305405698887364127703677763164702672074335856724522036396833853909281250/2363540766762704863987390449177653254903252827405191527876709228083*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: 0
  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
Positive weights:   63 out of 63
Indefinite weights: 0 out of 63
Negative weights:   0 out of 63
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.163962645244009178 + 5.725400239442965201e-869j)  +/-  (7.45e-241, 7.45e-241j)
| (11.91480712601450272 - 2.4705064009504061404e-872j)  +/-  (5.11e-242, 5.11e-242j)
| (13.333533921703012622 - 7.7767669548142596e-879j)  +/-  (1.21e-243, 1.21e-243j)
| (8.6239709680878967552 + 8.4957964093906803808e-881j)  +/-  (1.35e-240, 1.35e-240j)
| (12.584008299902727963 + 6.866439841108370978e-902j)  +/-  (1e-242, 1e-242j)
| (-12.584008299902727963 + 5.0892887033529675036e-912j)  +/-  (9.9e-243, 9.9e-243j)
| (10.716591833815187334 - 1.5320150674651966892e-922j)  +/-  (3.84e-241, 3.84e-241j)
| (-3.3407726797505548607 + 3.9075629517975232546e-941j)  +/-  (3.9e-245, 3.9e-245j)
| (-10.716591833815187334 - 1.3213075076697015704e-935j)  +/-  (3.97e-241, 3.97e-241j)
| (-8.1395029755996606793 - 4.1775495453134239503e-934j)  +/-  (1.09e-240, 1.09e-240j)
| (14.238549238741685919 - 1.0388478044858642316e-938j)  +/-  (5.7e-245, 5.7e-245j)
| (10.163962645244009178 - 1.7363745345939740173e-933j)  +/-  (7.37e-241, 7.37e-241j)
| (-11.91480712601450272 + 3.6907678220503292563e-941j)  +/-  (5.3e-242, 5.3e-242j)
| (-14.238549238741685919 + 2.3037769304482329987e-945j)  +/-  (6.1e-245, 6.1e-245j)
| (8.1395029755996606793 - 6.4211085522705901871e-939j)  +/-  (1.06e-240, 1.06e-240j)
| (-0.53907981135137510807 - 6.1609414177290469518e-958j)  +/-  (1.34e-252, 1.34e-252j)
| (7.6659951151624957021 + 2.4456129605159705701e-945j)  +/-  (7.66e-241, 7.66e-241j)
| (6.7463013622500942389 - 3.892462394538219832e-948j)  +/-  (2.77e-241, 2.77e-241j)
| (-8.6239709680878967552 + 3.5682875563999892604e-950j)  +/-  (1.27e-240, 1.27e-240j)
| (6.2979468560429079911 + 2.4682916219329347184e-950j)  +/-  (1.25e-241, 1.25e-241j)
| (-4.9896440134615966792 + 1.054150674697238765e-956j)  +/-  (6.01e-243, 6.01e-243j)
| (-4.5643136634729453093 + 5.0754866260520938372e-956j)  +/-  (1.65e-243, 1.65e-243j)
| (-4.1445471861258943321 - 9.9494246181073580388e-957j)  +/-  (4.73e-244, 4.73e-244j)
| (-13.333533921703012622 + 1.3579651599125782522e-957j)  +/-  (1.2e-243, 1.2e-243j)
| (11.297256054852087042 - 4.2352082595677734729e-952j)  +/-  (1.74e-241, 1.74e-241j)
| (-2.4359479541443871437 + 1.7694039449906700043e-970j)  +/-  (2.95e-247, 2.95e-247j)
| (-5.4201770623583446494 + 1.0753359964943224248e-964j)  +/-  (1.87e-242, 1.87e-242j)
| (9.6335361351085789665 + 1.5811718328132263513e-961j)  +/-  (1.14e-240, 1.14e-240j)
| (-2.0383346316010786378 + 7.1124035405516167229e-977j)  +/-  (2.08e-248, 2.08e-248j)
| (7.2019908744188589838 + 1.4176706585541676749e-968j)  +/-  (5.79e-241, 5.79e-241j)
| (-9.6335361351085789665 + 4.4305733085441627091e-972j)  +/-  (1.15e-240, 1.15e-240j)
| (-9.1212126488861513624 + 7.8864695023751418112e-973j)  +/-  (1.28e-240, 1.28e-240j)
| (2.8024858612875416991 - 3.3263866571354363175e-980j)  +/-  (4.05e-246, 4.05e-246j)
| (-3.7325698423944996081 - 9.1366807917320315387e-980j)  +/-  (1.36e-244, 1.36e-244j)
| (-0.8458067868614667495 - 1.0380220325356706392e-986j)  +/-  (8.94e-252, 8.94e-252j)
| (2.0383346316010786378 + 2.0671642063209022531e-983j)  +/-  (2.11e-248, 2.11e-248j)
| (4.9896440134615966792 - 4.2020313958245974731e-976j)  +/-  (5.77e-243, 5.77e-243j)
| (9.1212126488861513624 - 4.1048213014701918737e-977j)  +/-  (1.35e-240, 1.35e-240j)
| (3.0453382967480763343 - 1.5972996837496389941e-989j)  +/-  (1.53e-245, 1.53e-245j)
| (-7.2019908744188589838 - 2.2088603657018715413e-983j)  +/-  (5.02e-241, 5.02e-241j)
| (-1.2362616999296802718 - 7.1993458889390147305e-995j)  +/-  (9.47e-251, 9.47e-251j)
| (1.2362616999296802718 + 5.6266191673096466412e-995j)  +/-  (9.71e-251, 9.71e-251j)
| (-11.297256054852087042 + 3.6653001081770569895e-986j)  +/-  (1.62e-241, 1.62e-241j)
| (0.8458067868614667495 + 4.6473262972939217191e-997j)  +/-  (8.66e-252, 8.66e-252j)
| (5.4201770623583446494 - 4.937482351274405953e-986j)  +/-  (1.79e-242, 1.79e-242j)
| (-7.6659951151624957021 + 5.0030176376395198401e-984j)  +/-  (8.02e-241, 8.02e-241j)
| (5.8561210819943774874 + 1.9725569433906951003e-986j)  +/-  (5.33e-242, 5.33e-242j)
| (-6.8687516239970341427e-1024 - 8.1465284486544058217e-1024j)  +/-  (6.71e-1022, 6.71e-1022j)
| (0.53907981135137510807 + 3.5989320210873149799e-1000j)  +/-  (1.26e-252, 1.26e-252j)
| (-2.8024858612875416991 - 6.9440068130532694367e-994j)  +/-  (3.85e-246, 3.85e-246j)
| (3.7325698423944996081 + 4.7760707487717457849e-992j)  +/-  (1.24e-244, 1.24e-244j)
| (-1.6365190424351079992 + 1.5383221850608969858e-997j)  +/-  (1.34e-249, 1.34e-249j)
| (4.1445471861258943321 - 8.0437157345179463843e-991j)  +/-  (4.85e-244, 4.85e-244j)
| (-5.8561210819943774874 - 3.1399542578050920136e-988j)  +/-  (5.52e-242, 5.52e-242j)
| (4.5643136634729453093 + 1.8385829326840552955e-990j)  +/-  (1.64e-243, 1.64e-243j)
| (-6.7463013622500942389 - 5.5872536893454275706e-988j)  +/-  (2.73e-241, 2.73e-241j)
| (-3.0453382967480763343 - 1.2078809533404044376e-994j)  +/-  (1.47e-245, 1.47e-245j)
| (-6.2979468560429079911 + 1.6212863006831926761e-999j)  +/-  (1.21e-241, 1.21e-241j)
| (3.3407726797505548607 - 7.0984217164350023819e-1006j)  +/-  (4.06e-245, 4.06e-245j)
| (0.35105185132299784618 + 2.4646800069982099025e-1014j)  +/-  (2.22e-253, 2.22e-253j)
| (2.4359479541443871437 - 1.0211075809875759666e-1007j)  +/-  (2.88e-247, 2.88e-247j)
| (1.6365190424351079992 + 5.0570526295662660529e-1010j)  +/-  (1.39e-249, 1.39e-249j)
| (-0.35105185132299784618 - 1.372001883748682231e-1014j)  +/-  (2.22e-253, 2.22e-253j)
-------------------------------------------------
The weights are:
| (7.9661251376296169152e-24 + 2.5060915373960181524e-891j)  +/-  (8.59e-57, 1.75e-176j)
| (3.8055341417398212039e-32 - 7.365169346035712118e-898j)  +/-  (2.22e-61, 4.54e-181j)
| (7.9912167276528438479e-40 - 6.3065512358640547529e-902j)  +/-  (8.44e-65, 1.72e-184j)
| (1.3857964728522390096e-17 - 6.4207224872072745884e-890j)  +/-  (1.48e-54, 3.01e-174j)
| (1.1502766192041515303e-35 + 9.9171055617033252236e-900j)  +/-  (4.23e-63, 8.64e-183j)
| (1.1502766192041515303e-35 - 9.3218732429565990889e-899j)  +/-  (1.72e-66, 3.52e-186j)
| (2.6000394954764021843e-26 - 9.9993208788590410519e-895j)  +/-  (6.12e-60, 1.25e-179j)
| (0.00055233813321993023713 - 2.0369226713605575358e-880j)  +/-  (7.07e-35, 1.45e-154j)
| (2.6000394954764021843e-26 + 3.7781496410907899704e-893j)  +/-  (3.95e-62, 8.06e-182j)
| (7.8461832362254722924e-16 + 5.7491360345876119972e-888j)  +/-  (2.18e-56, 4.45e-176j)
| (3.9497315249919409162e-45 + 1.0312620050371314982e-904j)  +/-  (2.01e-68, 4.11e-188j)
| (7.9661251376296169152e-24 + 2.2436733171607186177e-893j)  +/-  (1.08e-59, 2.2e-179j)
| (3.8055341417398212039e-32 + 9.2878145691676343118e-897j)  +/-  (1.85e-65, 3.77e-185j)
| (3.9497315249919409162e-45 - 6.1761770933485170417e-904j)  +/-  (3.48e-71, 7.11e-191j)
| (7.8461832362254722924e-16 + 6.3588456480136519477e-889j)  +/-  (1.11e-56, 2.27e-176j)
| (0.065202474282060509926 - 3.3939775699252255823e-878j)  +/-  (1.16e-41, 2.36e-161j)
| (3.2393545713458047725e-14 - 5.4415190590709704092e-888j)  +/-  (4.46e-56, 9.12e-176j)
| (2.3604555082117042561e-11 - 2.728242167135526336e-886j)  +/-  (8.98e-55, 1.83e-174j)
| (1.3857964728522390096e-17 - 7.8332979520592666301e-889j)  +/-  (1.03e-61, 2.11e-181j)
| (4.3279530185487242869e-10 + 1.6404799039592216887e-885j)  +/-  (5.1e-54, 1.04e-173j)
| (6.6998303502844731132e-07 - 6.3205139889983136587e-883j)  +/-  (1.49e-52, 3.04e-172j)
| (5.0478946000385195063e-06 + 2.5732509043437664775e-882j)  +/-  (4.99e-51, 1.02e-170j)
| (3.094428160007289163e-05 - 1.0376320634755922357e-881j)  +/-  (1.54e-49, 3.14e-169j)
| (7.9912167276528438479e-40 + 4.6753334431317576998e-901j)  +/-  (4.49e-73, 9.18e-193j)
| (4.6027868752353357586e-29 + 3.2858759498410872133e-896j)  +/-  (6.75e-67, 1.38e-186j)
| (0.0080304706814788901861 + 9.7747098438302605698e-880j)  +/-  (3.22e-43, 6.57e-163j)
| (7.2136433682262656153e-08 + 1.4948265600714710608e-883j)  +/-  (2.83e-55, 5.78e-175j)
| (1.4629347748032114084e-21 - 3.9115899008366746372e-892j)  +/-  (6.51e-64, 1.33e-183j)
| (0.020044059109648994868 - 1.3988440835429489176e-879j)  +/-  (5.54e-42, 1.13e-161j)
| (1.0004949730763497378e-12 + 4.0857172860402065761e-887j)  +/-  (4e-59, 8.18e-179j)
| (1.4629347748032114084e-21 - 1.45995222786968604e-890j)  +/-  (5.16e-66, 1.05e-185j)
| (1.728801685711243279e-19 + 1.0174330527711144232e-889j)  +/-  (5.12e-65, 1.05e-184j)
| (0.0025091122709929487389 - 4.9828001572796510084e-880j)  +/-  (1.41e-51, 2.88e-171j)
| (0.0001527887429543282166 + 4.3565689710762091846e-881j)  +/-  (1.17e-51, 2.4e-171j)
| (0.10504484877319893182 + 1.2826637209126783986e-878j)  +/-  (3.03e-44, 6.18e-164j)
| (0.020044059109648994868 - 9.3150379776529838985e-880j)  +/-  (6.87e-48, 1.4e-167j)
| (6.6998303502844731132e-07 - 2.1581891753273796096e-883j)  +/-  (7.33e-59, 1.5e-178j)
| (1.728801685711243279e-19 + 5.5012611255859821047e-891j)  +/-  (1.43e-64, 2.93e-184j)
| (0.00082993523363951458105 + 3.3126967267329864867e-880j)  +/-  (2.34e-53, 4.78e-173j)
| (1.0004949730763497378e-12 + 2.3954445086214898123e-886j)  +/-  (5.53e-64, 1.13e-183j)
| (0.073908742917535707265 - 4.821006952549474693e-879j)  +/-  (7.35e-46, 1.5e-165j)
| (0.073908742917535707265 - 3.7754088063499167836e-879j)  +/-  (5.69e-47, 1.16e-166j)
| (4.6027868752353357586e-29 - 6.222487858591461175e-895j)  +/-  (3.44e-71, 7.02e-191j)
| (0.10504484877319893182 + 1.0855867928369145577e-878j)  +/-  (1.12e-46, 2.28e-166j)
| (7.2136433682262656153e-08 + 4.5502260486604163122e-884j)  +/-  (3.54e-60, 7.22e-180j)
| (3.2393545713458047725e-14 - 3.8840407204311979085e-887j)  +/-  (6.08e-65, 1.24e-184j)
| (6.2558497550510860988e-09 - 8.9913510229390092623e-885j)  +/-  (1.07e-60, 2.19e-180j)
| (0.14969611330949032463 - 2.6243551693944946182e-878j)  +/-  (1.39e-48, 2.84e-168j)
| (0.065202474282060509926 - 3.0520888126200199693e-878j)  +/-  (6.25e-49, 1.28e-168j)
| (0.0025091122709929487389 - 8.7766662723937026099e-880j)  +/-  (1.02e-54, 2.08e-174j)
| (0.0001527887429543282166 + 2.0162442917812484108e-881j)  +/-  (1.61e-58, 3.29e-178j)
| (0.042004691896700583622 + 2.3903480120295975967e-879j)  +/-  (7.33e-53, 1.5e-172j)
| (3.094428160007289163e-05 - 4.3651910956204752885e-882j)  +/-  (2.09e-59, 4.26e-179j)
| (6.2558497550510860988e-09 - 3.3437212887928908026e-884j)  +/-  (6.17e-63, 1.26e-182j)
| (5.0478946000385195063e-06 + 9.7834262225999419098e-883j)  +/-  (1.66e-60, 3.38e-180j)
| (2.3604555082117042561e-11 - 1.3499085879308510132e-885j)  +/-  (5.39e-65, 1.1e-184j)
| (0.00082993523363951458105 + 6.1470318336279907639e-880j)  +/-  (2.68e-58, 5.47e-178j)
| (4.3279530185487242869e-10 + 6.9853402714709660229e-885j)  +/-  (3.01e-64, 6.15e-184j)
| (0.00055233813321993023713 - 1.0291434165832196879e-880j)  +/-  (1.95e-60, 3.97e-180j)
| (0.10683574029487237694 + 3.5209650096710979043e-878j)  +/-  (3.66e-57, 7.42e-177j)
| (0.0080304706814788901861 + 5.9952090392740902781e-880j)  +/-  (6.33e-60, 1.31e-179j)
| (0.042004691896700583622 + 1.7273495954481786836e-879j)  +/-  (1.81e-59, 3.46e-179j)
| (0.10683574029487237694 + 3.7728864680035213179e-878j)  +/-  (3.22e-58, 1.06e-177j)
