Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^58 - 17392010149223995452877145897730707518500457601339737431671/11998724209199654391509790114482532688358698626274742307*t^56 + 128655825981263233338502526515785021565985161817053035849549970/131985966301196198306607691259307859571945684889022165377*t^54 - 254994760223921940386133350379054273681263861958395337695551592030/630599616772381836353792302683359773510407161136439234579*t^52 + 219561547228761046016463213664041560208481380172376753919266398649735/1891798850317145509061376908050079320531221483409317703737*t^50 - 46355559924206138373946286878836901135740395642657047032740031067790075/1891798850317145509061376908050079320531221483409317703737*t^48 + 2490971936506414958503498543655968112160709885622155997769991604653134700/630599616772381836353792302683359773510407161136439234579*t^46 - 314181154966361411181754390496538644685873726739416562963938834170148253500/630599616772381836353792302683359773510407161136439234579*t^44 + 66636522948988214590611002978426139819228939897579989538855223480685620875/1333191578799961599056643346053614743150966514030526923*t^42 - 5377390885873434245767995059054142182597521202866440505208295005055634545375/1333191578799961599056643346053614743150966514030526923*t^40 + 351686400697283749820587081237755407374591645760581955159473088237393881214250/1333191578799961599056643346053614743150966514030526923*t^38 - 18727810960010844244076698600733312527892288408540608837980327534442394329265250/1333191578799961599056643346053614743150966514030526923*t^36 + 813939975701605990445592001924320648114817392855071683149695266666669265228038125/1333191578799961599056643346053614743150966514030526923*t^34 - 28883406325853818945081525578502062224197983488492915396048542728371261264711735625/1333191578799961599056643346053614743150966514030526923*t^32 + 835729602776548259235279911420593401161953458972660560679162025691199179091703905000/1333191578799961599056643346053614743150966514030526923*t^30 - 19657361569620523733105034663237770750537910355628519589255079841446804069060609245000/1333191578799961599056643346053614743150966514030526923*t^28 + 374086928643544282641895543344996431144184946216076574138335687366870284114445550725625/1333191578799961599056643346053614743150966514030526923*t^26 - 5722317121751329112713433691832682566977476670677909304354242336946411964747346024203125/1333191578799961599056643346053614743150966514030526923*t^24 + 69760540708199265454330820035097844988563932702122677970253082181453712429707818369656250/1333191578799961599056643346053614743150966514030526923*t^22 - 670397587024113811311841716249996896290882335423591189665394903463226896643260416017531250/1333191578799961599056643346053614743150966514030526923*t^20 + 5008260872676358522594146072793203305685298871235664655208135424330093515730241728502484375/1333191578799961599056643346053614743150966514030526923*t^18 - 28570441701518965220123992454394398768480593178541301439016301573606454134906394077749796875/1333191578799961599056643346053614743150966514030526923*t^16 + 121598807661440480246423315381926500882807813903184802725683440348013448572368373903634687500/1333191578799961599056643346053614743150966514030526923*t^14 - 374361315273915153367799765686256171464797844540835499828656102144470928602542610505745937500/1333191578799961599056643346053614743150966514030526923*t^12 + 799086745330153294035019062385132015234617843617258012336957057788978005113125654103971640625/1333191578799961599056643346053614743150966514030526923*t^10 - 1113366501459433878685099928897545333556077967023342638749207092071416909409460631496502078125/1333191578799961599056643346053614743150966514030526923*t^8 + 924854667020710851963642771555528461387271603697402409379816941693363187900865405076299593750/1333191578799961599056643346053614743150966514030526923*t^6 - 394816847101503924860523558465382330085078985632750929579868584416291676854273839241731718750/1333191578799961599056643346053614743150966514030526923*t^4 + 64945822705011873162067838694306759161249913484825142399511844723149137271651972818880234375/1333191578799961599056643346053614743150966514030526923*t^2 - 1738573502600879937515969716334431816807563020346735078396880856652599805394380357183046875/1333191578799961599056643346053614743150966514030526923
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-10.580383940668159888 + 3.9004019652337248969e-639j)  +/-  (1.97e-242, 1.97e-242j)
| (-12.650208177521978347 - 3.8793050615523650469e-651j)  +/-  (2.26e-244, 2.26e-244j)
| (-8.3643157837852441374 + 1.1413201134256149164e-658j)  +/-  (9.52e-242, 9.52e-242j)
| (8.8864716031762250591 + 1.5018174678876962726e-673j)  +/-  (8.85e-242, 8.85e-242j)
| (-11.888747536880214755 + 2.8996614510526747678e-676j)  +/-  (1.49e-243, 1.49e-243j)
| (-11.208489022865682041 + 1.8700875570734395404e-699j)  +/-  (6.62e-243, 6.62e-243j)
| (-13.569032572023935204 - 1.847419043964205723e-714j)  +/-  (1.09e-245, 1.09e-245j)
| (10.580383940668159888 + 3.8056634129828764985e-725j)  +/-  (1.9e-242, 1.9e-242j)
| (-6.4060213608191052741 - 3.0540214162387230604e-738j)  +/-  (2.11e-242, 2.11e-242j)
| (-9.4268096947274750161 + 8.0504731876347181477e-771j)  +/-  (6.74e-242, 6.74e-242j)
| (13.569032572023935204 + 5.6007947071419637269e-797j)  +/-  (1.13e-245, 1.13e-245j)
| (-2.7898705330466143396 + 2.269785268173263145e-793j)  +/-  (5.42e-245, 5.42e-245j)
| (11.888747536880214755 + 1.2651745770883333424e-793j)  +/-  (1.53e-243, 1.53e-243j)
| (5.9405650179840528715 + 3.0973971768893166068e-791j)  +/-  (9.97e-243, 9.97e-243j)
| (-9.9894788760309057583 - 3.4625289723317163143e-794j)  +/-  (4.41e-242, 4.41e-242j)
| (4.1445471861258943321 + 1.1874928946229803491e-811j)  +/-  (1.13e-244, 1.13e-244j)
| (1.6365190424351079992 + 2.6592771467062401873e-817j)  +/-  (1.48e-249, 1.48e-249j)
| (11.208489022865682041 + 3.7072051960630927313e-809j)  +/-  (7.12e-243, 7.12e-243j)
| (-1.6365190424351079992 - 5.9531846410712515728e-816j)  +/-  (1.45e-249, 1.45e-249j)
| (-3.2761508419413487925 - 5.9627186612900279625e-813j)  +/-  (1.12e-245, 1.12e-245j)
| (-2.0364186191285602081 - 2.1222331116261549075e-814j)  +/-  (2.18e-248, 2.18e-248j)
| (-7.8572869225475821394 - 1.2743041286445014041e-806j)  +/-  (8.47e-242, 8.47e-242j)
| (7.3630534860018272953 + 3.49011174983821676e-819j)  +/-  (6.06e-242, 6.06e-242j)
| (5.0308248440701244156 + 3.3729390729727079643e-822j)  +/-  (1.31e-243, 1.31e-243j)
| (6.879786686854225328 + 9.2672404796025992201e-820j)  +/-  (3.81e-242, 3.81e-242j)
| (7.8572869225475821394 - 8.0579004108165092529e-820j)  +/-  (7.91e-242, 7.91e-242j)
| (2.7898705330466143396 - 1.1483264499145992109e-822j)  +/-  (5.94e-245, 5.94e-245j)
| (3.7087038851490785734 + 7.3632756696849047232e-823j)  +/-  (3.32e-245, 3.32e-245j)
| (-6.879786686854225328 - 4.5010534167640528035e-818j)  +/-  (4.17e-242, 4.17e-242j)
| (9.4268096947274750161 + 1.0032308194434870013e-826j)  +/-  (6.62e-242, 6.62e-242j)
| (2.0364186191285602081 - 3.4106810466126718583e-833j)  +/-  (2.05e-248, 2.05e-248j)
| (8.3643157837852441374 - 7.9133573300428262017e-825j)  +/-  (1.04e-241, 1.04e-241j)
| (12.650208177521978347 - 7.8226516011963835031e-828j)  +/-  (2.22e-244, 2.22e-244j)
| (9.9894788760309057583 - 2.63943025676146309e-826j)  +/-  (4.03e-242, 4.03e-242j)
| (-5.0308248440701244156 - 7.0019396730878280969e-826j)  +/-  (1.32e-243, 1.32e-243j)
| (-2.4534538311091646702 + 2.1583195318125814301e-839j)  +/-  (4.39e-247, 4.39e-247j)
| (3.2761508419413487925 - 1.7257794101892233085e-838j)  +/-  (1.06e-245, 1.06e-245j)
| (-5.9405650179840528715 + 2.3415626017380501743e-834j)  +/-  (9e-243, 9e-243j)
| (4.5850543553956884017 + 2.1671330598586948571e-846j)  +/-  (4.36e-244, 4.36e-244j)
| (-8.8864716031762250591 + 1.4238861129738000874e-847j)  +/-  (9.01e-242, 9.01e-242j)
| (-4.5850543553956884017 - 6.7985866827771117121e-858j)  +/-  (4.13e-244, 4.13e-244j)
| (2.8024858612875416991 + 6.7975236649032444503e-860j)  +/-  (5.92e-245, 5.92e-245j)
| (1.2544846768418446757 + 5.9286046140730938978e-866j)  +/-  (9.95e-251, 9.95e-251j)
| (2.4534538311091646702 + 2.3195766620855480238e-862j)  +/-  (4.58e-247, 4.58e-247j)
| (6.4060213608191052741 + 7.9794381505308665354e-858j)  +/-  (2.3e-242, 2.3e-242j)
| (-1.2544846768418446757 - 2.5524021223134846019e-865j)  +/-  (1.12e-250, 1.12e-250j)
| (-3.7087038851490785734 - 1.5277508525366208102e-859j)  +/-  (3.33e-245, 3.33e-245j)
| (-5.4824367335049145238 - 1.0773428081258554527e-856j)  +/-  (3.86e-243, 3.86e-243j)
| (0.53907981135137510807 - 5.2340099930679794352e-875j)  +/-  (5.87e-253, 5.87e-253j)
| (5.4824367335049145238 - 1.61516232492045344e-865j)  +/-  (3.93e-243, 3.93e-243j)
| (-2.8024858612875416991 + 3.3286230751640756402e-866j)  +/-  (5.76e-245, 5.76e-245j)
| (-0.53907981135137510807 + 1.1794636440205082529e-874j)  +/-  (5.87e-253, 5.87e-253j)
| (-4.1445471861258943321 + 8.6769546934371897698e-864j)  +/-  (1.18e-244, 1.18e-244j)
| (-0.89204520231373744045 + 8.7816469730432443227e-876j)  +/-  (7.88e-252, 7.88e-252j)
| (0.89204520231373744045 - 1.7460293039838775756e-875j)  +/-  (8.34e-252, 8.34e-252j)
| (0.18122196088264159576 - 1.1140532298407264453e-886j)  +/-  (2.86e-254, 2.86e-254j)
| (-0.18122196088264159576 - 3.2439471736523694853e-878j)  +/-  (3.94e-254, 3.94e-254j)
| (-7.3630534860018272953 - 1.0051000520924796725e-864j)  +/-  (6.4e-242, 6.4e-242j)
-------------------------------------------------
The weights are:
| (1.1915754694447739407e-25 + 2.6406316160370561077e-663j)  +/-  (2.52e-58, 8.21e-179j)
| (5.8192885613576560983e-36 + 7.5181727261793944656e-670j)  +/-  (3.7e-63, 1.21e-183j)
| (1.318241409625811616e-16 + 1.8654975727423557535e-659j)  +/-  (6.23e-54, 2.03e-174j)
| (1.5057258260359772167e-18 + 1.7575884142666314218e-661j)  +/-  (6.41e-58, 2.09e-178j)
| (5.7882271486948986452e-32 - 1.5303982892078503327e-667j)  +/-  (9.86e-62, 3.21e-182j)
| (1.3620514989991616151e-28 + 1.9710758188152077975e-665j)  +/-  (2.24e-60, 7.29e-181j)
| (4.4234721322582721269e-41 - 1.0775965129487714263e-672j)  +/-  (5.13e-66, 1.67e-186j)
| (1.1915754694447739407e-25 - 2.1963396266190673482e-665j)  +/-  (9.08e-65, 2.96e-185j)
| (2.2981958577452108152e-10 + 4.1480168566318726511e-656j)  +/-  (1.62e-51, 5.28e-172j)
| (1.1093991506920737571e-20 + 1.9874905646578042209e-661j)  +/-  (7.57e-58, 2.47e-178j)
| (4.4234721322582721269e-41 - 1.333596338398275209e-673j)  +/-  (1.18e-71, 3.84e-192j)
| (-0.016808756205717618075 - 2.399411665126717886e-649j)  +/-  (7.93e-38, 2.58e-158j)
| (5.7882271486948986452e-32 - 8.9114143611003275243e-669j)  +/-  (2.38e-68, 7.76e-189j)
| (3.9996622848979714424e-09 + 6.1332861298501766408e-656j)  +/-  (1.79e-55, 5.82e-176j)
| (4.9201821779961246988e-23 - 2.0288624098239953556e-662j)  +/-  (2.13e-60, 6.93e-181j)
| (3.2542181809428117844e-05 + 3.650735427619978443e-653j)  +/-  (4.18e-49, 1.36e-169j)
| (0.040955047756978039924 - 1.7581034977044653043e-650j)  +/-  (1.31e-32, 4.25e-153j)
| (1.3620514989991616151e-28 + 5.681995306808572391e-667j)  +/-  (6.69e-67, 2.18e-187j)
| (0.040955047756978039924 + 2.4014875124011853215e-650j)  +/-  (6.72e-33, 2.19e-153j)
| (0.0008055232360509586963 - 1.7552722286267104135e-651j)  +/-  (2.02e-44, 6.58e-165j)
| (0.020445948876973041982 - 1.7649384157122686681e-650j)  +/-  (9.9e-37, 3.23e-157j)
| (7.8364968102670899525e-15 - 1.5273460397211437361e-658j)  +/-  (5.57e-58, 1.81e-178j)
| (3.2901433935625336853e-13 - 1.985284419225805052e-658j)  +/-  (1.4e-60, 4.54e-181j)
| (5.7139383476995771554e-07 + 1.6860235938692398976e-654j)  +/-  (9.93e-55, 3.23e-175j)
| (1.0062612432273087793e-11 + 1.5153341693467202265e-657j)  +/-  (1.2e-59, 3.92e-180j)
| (7.8364968102670899525e-15 + 2.2557683545054435946e-659j)  +/-  (4.02e-62, 1.31e-182j)
| (-0.016808756205717618075 + 1.3980772605579055203e-649j)  +/-  (1.42e-48, 4.61e-169j)
| (0.00017842170883243359792 - 1.7004118735525440653e-652j)  +/-  (6.1e-52, 1.99e-172j)
| (1.0062612432273087793e-11 - 7.1496548637494484281e-657j)  +/-  (2.68e-61, 8.72e-182j)
| (1.1093991506920737571e-20 - 1.1459467885506955576e-662j)  +/-  (2.12e-66, 6.91e-187j)
| (0.020445948876973041982 + 1.1951976379934429393e-650j)  +/-  (4.51e-47, 1.47e-167j)
| (1.318241409625811616e-16 - 2.1821775102407797104e-660j)  +/-  (5.2e-64, 1.69e-184j)
| (5.8192885613576560983e-36 + 6.6986222504912293492e-671j)  +/-  (1.04e-74, 3.38e-195j)
| (4.9201821779961246988e-23 + 5.828259935909144039e-664j)  +/-  (7.29e-68, 2.38e-188j)
| (5.7139383476995771554e-07 - 4.7428752233709141295e-654j)  +/-  (2.33e-62, 7.59e-183j)
| (0.008511882563820627109 + 1.9391767694116195808e-650j)  +/-  (1.27e-53, 4.13e-174j)
| (0.0008055232360509586963 + 9.25261453224361892e-652j)  +/-  (1.03e-55, 3.34e-176j)
| (3.9996622848979714424e-09 - 2.1838720171744741625e-655j)  +/-  (5.51e-64, 1.79e-184j)
| (4.8120918874980161354e-06 - 7.9788652161926709073e-654j)  +/-  (2.73e-59, 8.87e-180j)
| (1.5057258260359772167e-18 - 2.0198636617006094718e-660j)  +/-  (7.95e-69, 2.58e-189j)
| (4.8120918874980161354e-06 + 2.0182875084302950404e-653j)  +/-  (5.79e-62, 1.88e-182j)
| (0.019257098841532638309 - 1.335934359331267991e-649j)  +/-  (1.53e-54, 4.99e-175j)
| (0.067531986943573770257 + 2.7404975733406137334e-650j)  +/-  (4.57e-53, 1.49e-173j)
| (0.008511882563820627109 - 1.2091261492615326121e-650j)  +/-  (2.53e-55, 8.23e-176j)
| (2.2981958577452108152e-10 - 1.0193637817761901428e-656j)  +/-  (9.56e-64, 3.11e-184j)
| (0.067531986943573770257 - 3.4777802986673125263e-650j)  +/-  (6.24e-55, 2.03e-175j)
| (0.00017842170883243359792 + 3.5358652330939089187e-652j)  +/-  (2.86e-61, 9.27e-182j)
| (5.393380524844564032e-08 + 1.0552307464770215671e-654j)  +/-  (1.96e-64, 6.44e-185j)
| (0.12210952411154043844 + 5.0054248438858166266e-650j)  +/-  (4.11e-57, 1.31e-177j)
| (5.393380524844564032e-08 - 3.3490448197338532654e-655j)  +/-  (5.57e-63, 1.81e-183j)
| (0.019257098841532638309 + 2.2986461653806094159e-649j)  +/-  (2.48e-58, 7.99e-179j)
| (0.12210952411154043844 - 5.542869670937190443e-650j)  +/-  (4.17e-58, 1.21e-178j)
| (3.2542181809428117844e-05 - 8.3527332628365529412e-653j)  +/-  (2.07e-62, 6.58e-183j)
| (0.095099012638221406326 + 4.7006084151077281919e-650j)  +/-  (2.83e-58, 7.99e-179j)
| (0.095099012638221406326 - 3.9696114950321683817e-650j)  +/-  (1.06e-58, 3.03e-179j)
| (0.14187632568697585161 - 5.5845000007952146899e-650j)  +/-  (8.58e-59, 2.41e-179j)
| (0.14187632568697585161 + 5.7791376153761726037e-650j)  +/-  (6.73e-59, 1.76e-179j)
| (3.2901433935625336853e-13 + 1.1072169070744567981e-657j)  +/-  (3.37e-68, 1.25e-188j)
