Starting with polynomial:
P : t
Extension levels are: 1 4 50
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 620793988223763291565050635316437364491185/45435517045280299736853824827158148620189*t^53 + 71506447770245694231388329591863850269584148365/810321871928817792463510899909424980724714503*t^51 - 1396361921851014934269617342530468770118104235025/3897262336419552239943552423373901097771245943*t^49 + 255232828322859108610692032668102628857517675050/248761425728907589783631005747270282836462507*t^47 - 6935827260847820745754692599352690653343408899770/3147372821178787331610287942280680535017851719*t^45 + 24489570191855025423949449972831349609490358103450/6644453733599662144510607878148103351704353629*t^43 - 337774820552458411884122787550113109673039624187050/68659355247196508826609614740863734634278320833*t^41 + 3292505884259053881218097710942497747103298921452275/617934197224768579439486532667773611708504887497*t^39 - 4569454482311049656371467663621053557945233422883775/964844623736919360879198270305821955123805876969*t^37 + 97387545908640511775776089900248509553672570411440885/27980494088370661465496749838868836698590370432101*t^35 - 178340892340378643280456907993084416239866360398317275/83941482265111984396490249516606510095771111296303*t^33 + 2506818312855405781575416699781686403664381038629480300/2322381009334764901636230236626113445983000745864383*t^31 - 31834309828003864325038152053797124190210281563432700/69748929090143106055815591088882161336530611944759*t^29 + 2649383498677473308127786014372025060404379838002333700/16530496194363916135228295088065072236757755030907883*t^27 - 28497331510680029511480913540000546349223414646585340/612240599791256153156603521780187860620657593737329*t^25 + 251899163472480469712328529969836966517685958927125/22675577770046524190985315621488439282246577545827*t^23 - 3966743670532792211666461441746730245166706866273625/1836721799373768459469810565340563581861972781211987*t^21 + 1072657734605995406691322064861373024701302047847022675/3173243028718080641810676053386713681596868308340576207*t^19 - 7005846488618045579648888112714943561766623781678725/167012790985162139042667160704563877978782542544240853*t^17 + 1860299215961017943554374258551554513578840856921510/459857136822158766405152045227634787311442343169759061*t^15 - 62782283604022030034706206013357763803170790180009550/212607282924111403001315295576909816666990176658818605869*t^13 + 10044537848680243799146250416528797222987744689131550/637821848772334209003945886730729450000970529976455817607*t^11 - 1117794807047532494887304007587111404588828473198850/1913465546317002627011837660192188350002911589929367452821*t^9 + 176014154314711689060696304769907084773553644284675/12543829692522572777077602439037679183352420422870297746271*t^7 - 21740628859178521466491228044814071358332128754323333/111460289371191407506185882739142471330208490404151175674115349*t^5 + 1288430991392827642416727154461172420435803094302955/1003142604340722667555672944652282241971876413637360581067038141*t^3 - 44852659221102563790034861733046863309847317262785/17722186010019433793483555355523652941503149974260036932184340491*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (-0.98799865358390581301 - 1.4892188951639476307e-902j)  +/-  (6.12e-236, 6.12e-236j)
| (-0.99511127934965603153 - 1.4111028231393088633e-920j)  +/-  (4.2e-236, 4.2e-236j)
| (-0.94799262726727329297 - 4.8036876304475329559e-933j)  +/-  (3.41e-236, 3.41e-236j)
| (0.99907159067406508559 - 9.2748161692486995113e-938j)  +/-  (1.44e-236, 1.44e-236j)
| (0.94799262726727329297 - 1.1727221649982480441e-937j)  +/-  (3.46e-236, 3.46e-236j)
| (0.92856526725213677257 + 1.1797551043238221567e-938j)  +/-  (2.07e-236, 2.07e-236j)
| (-0.9061798459386639928 - 3.2697807892486391677e-938j)  +/-  (9.87e-237, 9.87e-237j)
| (-0.880902444380467752 - 5.4671725530086837473e-939j)  +/-  (4.06e-237, 4.06e-237j)
| (-0.99907159067406508559 + 5.534297438661659634e-937j)  +/-  (1.37e-236, 1.37e-236j)
| (0.98799865358390581301 - 8.902461191673496613e-950j)  +/-  (6.13e-236, 6.13e-236j)
| (0.82197986387505180043 + 1.2545526884815080848e-954j)  +/-  (4.33e-238, 4.33e-238j)
| (0.16993268994865492387 - 9.2837644554517966779e-969j)  +/-  (1.02e-251, 1.02e-251j)
| (-0.82197986387505180043 - 5.9880428279147438839e-953j)  +/-  (4.67e-238, 4.67e-238j)
| (-0.85280792059736613269 + 1.8907049891332431694e-952j)  +/-  (1.37e-237, 1.37e-237j)
| (0.9061798459386639928 - 3.7967559757913938248e-956j)  +/-  (9.21e-237, 9.21e-237j)
| (0.85280792059736613269 - 1.0354108000418955172e-957j)  +/-  (1.38e-237, 1.38e-237j)
| (0.880902444380467752 + 1.3194763970924222855e-958j)  +/-  (3.99e-237, 3.99e-237j)
| (-0.96440468360130414291 + 3.5584060869665794407e-958j)  +/-  (5.38e-236, 5.38e-236j)
| (-0.78851055306538478071 + 1.2750125611974306466e-980j)  +/-  (1.14e-238, 1.14e-238j)
| (-0.97775311775270566594 - 1.4780647044909878297e-988j)  +/-  (6.18e-236, 6.18e-236j)
| (0.99511127934965603153 - 8.6518412830791388485e-999j)  +/-  (4.26e-236, 4.26e-236j)
| (0.78851055306538478071 + 4.8514889018080334627e-1006j)  +/-  (1.11e-238, 1.11e-238j)
| (-0.92856526725213677257 + 3.1005010961583320694e-1003j)  +/-  (1.94e-236, 1.94e-236j)
| (-0.71406038101611328798 + 1.4409889948132658492e-1013j)  +/-  (4.69e-240, 4.69e-240j)
| (-0.75250090293653425753 + 7.0741607146648895659e-1012j)  +/-  (2.53e-239, 2.53e-239j)
| (0.97775311775270566594 + 4.3613464834098801631e-1010j)  +/-  (6.17e-236, 6.17e-236j)
| (0.75250090293653425753 - 1.9249497906864907966e-1017j)  +/-  (2.68e-239, 2.68e-239j)
| (0.71406038101611328798 - 2.3843250352278546167e-1019j)  +/-  (4.73e-240, 4.73e-240j)
| (-0.11360181322891631485 - 5.6985715902504939058e-1034j)  +/-  (4.15e-253, 4.15e-253j)
| (-0.63036652119345057503 - 1.5540152854364160403e-1023j)  +/-  (1.19e-241, 1.19e-241j)
| (-0.28072484956518661193 + 3.5596488130064487204e-1033j)  +/-  (3.65e-249, 3.65e-249j)
| (0.67330687839901936595 - 4.2925571055572611922e-1021j)  +/-  (7.63e-241, 7.63e-241j)
| (0.63036652119345057503 + 1.4022172893348791504e-1023j)  +/-  (1.23e-241, 1.23e-241j)
| (0.96440468360130414291 - 5.8867371656070976383e-1029j)  +/-  (5.46e-236, 5.46e-236j)
| (-0.58537341379863254076 - 8.7146341607304076062e-1034j)  +/-  (1.58e-242, 1.58e-242j)
| (-0.67330687839901936595 - 1.4452584001783440647e-1036j)  +/-  (8.36e-241, 8.36e-241j)
| (0.22570163819050957393 + 1.1520571571262718027e-1047j)  +/-  (2.08e-250, 2.08e-250j)
| (0.58537341379863254076 - 5.1865107777130325762e-1039j)  +/-  (1.46e-242, 1.46e-242j)
| (0.28072484956518661193 + 1.4107526362406779836e-1048j)  +/-  (3.81e-249, 3.81e-249j)
| (-0.33482149350481248504 - 1.2188460529888617435e-1043j)  +/-  (6.63e-248, 6.63e-248j)
| (-0.53846931010568309104 + 1.3029632495810264577e-1040j)  +/-  (1.6e-243, 1.6e-243j)
| (-0.22570163819050957393 - 3.9812744371476226617e-1048j)  +/-  (2.09e-250, 2.09e-250j)
| (0.43953090769863682076 + 1.0964998367074705122e-1042j)  +/-  (1.25e-245, 1.25e-245j)
| (0.53846931010568309104 - 2.0091928557807452616e-1041j)  +/-  (1.64e-243, 1.64e-243j)
| (-0.056895063383692666753 + 1.2928205957578176525e-1053j)  +/-  (2.16e-254, 2.16e-254j)
| (-0.43953090769863682076 + 2.6392907197293464142e-1044j)  +/-  (1.34e-245, 1.34e-245j)
| (-0.38781443131383101158 - 7.7341543740434149541e-1046j)  +/-  (9.66e-247, 9.66e-247j)
| (0.11360181322891631485 - 3.6646341652774373219e-1053j)  +/-  (4.64e-253, 4.64e-253j)
| (0.48980321319898298544 + 3.3507785594794345185e-1044j)  +/-  (1.61e-244, 1.61e-244j)
| (0.056895063383692666753 - 7.445063391334123519e-1055j)  +/-  (2.4e-254, 2.4e-254j)
| (-0.16993268994865492387 + 2.1043396452716431605e-1051j)  +/-  (9.85e-252, 9.85e-252j)
| (-0.48980321319898298544 + 8.1239723862319941478e-1045j)  +/-  (1.44e-244, 1.44e-244j)
| (-4.9280736723751655645e-1064 + 6.0718053872290424666e-1064j)  +/-  (4.3e-1062, 4.3e-1062j)
| (0.33482149350481248504 - 1.0675033292727562803e-1047j)  +/-  (6.49e-248, 6.49e-248j)
| (0.38781443131383101158 + 1.8543449982270622504e-1046j)  +/-  (9.47e-247, 9.47e-247j)
-------------------------------------------------
The weights are:
| (0.0086832901040679676493 - 5.2822350181134804841e-903j)  +/-  (2.47e-49, 5.44e-163j)
| (0.0055386045925843639122 - 9.3210826960621004054e-903j)  +/-  (1.62e-49, 3.57e-163j)
| (0.017928508200199279507 + 9.3591210386707182018e-903j)  +/-  (4.75e-50, 1.05e-163j)
| (0.0023822542657800298772 - 9.5663832984038903513e-906j)  +/-  (4.7e-52, 1.03e-165j)
| (0.017928508200199279507 + 1.9340027317116405918e-904j)  +/-  (7.62e-52, 1.68e-165j)
| (0.020916670025492017541 - 2.4344004868950239133e-904j)  +/-  (3.38e-52, 7.44e-166j)
| (0.02384315808055977396 + 6.8523467769515784344e-903j)  +/-  (1.29e-50, 2.83e-164j)
| (0.02669916796655465979 - 6.1161291584720362016e-903j)  +/-  (5.05e-51, 1.11e-164j)
| (0.0023822542657800298772 + 1.7167148555660552446e-903j)  +/-  (1.71e-50, 3.77e-164j)
| (0.0086832901040679676493 - 6.5441990473673990328e-905j)  +/-  (4.34e-53, 9.54e-167j)
| (0.032164785388688595222 - 4.6350673913625503074e-904j)  +/-  (1.12e-53, 2.48e-167j)
| (0.056080759051811964927 - 1.3525529599457752583e-903j)  +/-  (2.98e-54, 6.57e-168j)
| (0.032164785388688595222 - 5.0532668139872182212e-903j)  +/-  (1.53e-52, 3.36e-166j)
| (0.029475947396032494925 + 5.5343833959538969041e-903j)  +/-  (6.69e-52, 1.47e-165j)
| (0.02384315808055977396 + 2.9598627743014015693e-904j)  +/-  (1.74e-53, 3.84e-167j)
| (0.029475947396032494925 + 4.0645082347139849756e-904j)  +/-  (2.35e-54, 5.18e-168j)
| (0.02669916796655465979 - 3.5048095834735025322e-904j)  +/-  (4.93e-54, 1.08e-167j)
| (0.014887549484819604577 - 1.2124277724570725748e-902j)  +/-  (2.4e-53, 5.28e-167j)
| (0.034757015756913050951 + 4.6427568496716088575e-903j)  +/-  (1.01e-55, 2.22e-169j)
| (0.011802769823112807399 + 1.986813075877218299e-902j)  +/-  (2.79e-53, 6.13e-167j)
| (0.0055386045925843639122 + 3.3431012495927477604e-905j)  +/-  (2.2e-56, 4.83e-170j)
| (0.034757015756913050951 + 5.2134531115502552746e-904j)  +/-  (5.54e-58, 1.22e-171j)
| (0.020916670025492017541 - 7.8502747866391405095e-903j)  +/-  (3.6e-54, 7.93e-168j)
| (0.039617354411656544213 + 3.9677632430665140119e-903j)  +/-  (1.67e-58, 3.68e-172j)
| (0.037244037791907952095 - 4.2847760961839214908e-903j)  +/-  (1.52e-57, 3.34e-171j)
| (0.011802769823112807399 + 1.0355307753306000295e-904j)  +/-  (6.87e-57, 1.51e-170j)
| (0.037244037791907952095 - 5.7975029576923027879e-904j)  +/-  (3e-59, 6.6e-173j)
| (0.039617354411656544213 + 6.3859254389437083173e-904j)  +/-  (2.62e-60, 5.77e-174j)
| (0.056549972773260101211 + 1.8044558469486275912e-903j)  +/-  (4.66e-64, 1.03e-177j)
| (0.04398973266126951393 + 3.4278278767928324443e-903j)  +/-  (1.34e-61, 2.95e-175j)
| (0.054589781899275142581 - 2.1608747102388749224e-903j)  +/-  (4.52e-64, 9.94e-178j)
| (0.041868625534914669326 - 6.9782798190930824477e-904j)  +/-  (6.4e-62, 1.41e-175j)
| (0.04398973266126951393 + 7.5749368075318258616e-904j)  +/-  (6.47e-63, 1.42e-176j)
| (0.014887549484819604577 - 1.4651677716688486515e-904j)  +/-  (2.36e-59, 5.2e-173j)
| (0.045972849797876521831 - 3.195403620551980291e-903j)  +/-  (1.31e-63, 2.88e-177j)
| (0.041868625534914669326 - 3.6839395819522258596e-903j)  +/-  (4.76e-62, 1.05e-175j)
| (0.055426490507684771551 + 1.2768515745546464998e-903j)  +/-  (7.48e-67, 1.65e-180j)
| (0.045972849797876521831 - 8.1770242119257662896e-904j)  +/-  (2.98e-65, 6.55e-179j)
| (0.054589781899275142581 - 1.2046202915962666634e-903j)  +/-  (3.67e-67, 8.09e-181j)
| (0.053573971322891375315 + 2.2992916811355186712e-903j)  +/-  (1.62e-67, 3.56e-181j)
| (0.047810515930242750192 + 2.983587736588829703e-903j)  +/-  (2.78e-66, 6.11e-180j)
| (0.055426490507684771551 + 2.0329544748248023951e-903j)  +/-  (6.31e-68, 1.39e-181j)
| (0.051021890053618319237 + 1.0037157209496487184e-903j)  +/-  (1.15e-68, 2.53e-182j)
| (0.047810515930242750192 + 8.7863634766146431736e-904j)  +/-  (1.39e-67, 3.06e-181j)
| (0.056832254472129647893 - 1.7020202516605656086e-903j)  +/-  (1.55e-69, 3.41e-183j)
| (0.051021890053618319237 + 2.6124304911803688898e-903j)  +/-  (9.05e-69, 1.99e-182j)
| (0.052383100687961543204 - 2.4493753047682616164e-903j)  +/-  (9.25e-69, 2.04e-182j)
| (0.056549972773260101211 + 1.4322892361301616398e-903j)  +/-  (9.43e-71, 2.07e-184j)
| (0.049495704953191398595 - 9.4054034594726711952e-904j)  +/-  (2.43e-70, 5.34e-184j)
| (0.056832254472129647893 - 1.5166682899709361421e-903j)  +/-  (3.83e-71, 8.43e-185j)
| (0.056080759051811964927 - 1.9144708809902949399e-903j)  +/-  (6.53e-71, 1.44e-184j)
| (0.049495704953191398595 - 2.7899337616409861076e-903j)  +/-  (1.44e-70, 3.17e-184j)
| (0.056926474131006277182 + 1.6063440122701486231e-903j)  +/-  (2.19e-71, 4.81e-185j)
| (0.053573971322891375315 + 1.1353356038482359532e-903j)  +/-  (1.39e-72, 3.06e-186j)
| (0.052383100687961543204 - 1.0685146321668660659e-903j)  +/-  (1.28e-72, 2.8e-186j)
