Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 50
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Trying to find an order 50 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
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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
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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:   56 out of 58
Indefinite weights: 0 out of 58
Negative weights:   2 out of 58
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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