Starting with polynomial:
P : 2*t
Extension levels are: 1 22 38
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : 2*t^23 - 253*t^21 + 26565/2*t^19 - 1514205/4*t^17 + 25741485/4*t^15 - 540571185/8*t^13 + 7027425405/16*t^11 - 55215485325/32*t^9 + 496939367925/128*t^7 - 1159525191825/256*t^5 + 1159525191825/512*t^3 - 316234143225/1024*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^61 - 1022611450644699413430127163258571869/758974758347076231570764048418186*t^59 + 1233382930727918279473768309058053682909/2919133685950293198349092493916100*t^57 - 4151430932986201264461425778730492898771831/50598317223138415438050936561212400*t^55 + 1120457175045612193644679441528579759193248751/101196634446276830876101873122424800*t^53 - 44715754519396708454966686215256727529659387581/40478653778510732350440749248969920*t^51 + 2284070534334229849305757791927896249353170966439/26985769185673821566960499499313280*t^49 - 45936993287754455949735495549778823086842474250149/8995256395224607188986833166437760*t^47 + 4441226376706374487914927836501716004450663580634543/17990512790449214377973666332875520*t^45 - 87050623140429364635688055447523904758243967018096857/8995256395224607188986833166437760*t^43 + 558142187396865377268856159712541060115146738286169163/1799051279044921437797366633287552*t^41 - 470903675704104170376244474997665089701215022885952058365/57569640929437486009515732265201664*t^39 + 1576300078011349090057482777016815288129740066363823756609/8856867835298074770694728040800256*t^37 - 56695780476539678755951014460127410777582332648109386223659/17713735670596149541389456081600512*t^35 + 1685325356303511942911460881306156389191454244620397709996819/35427471341192299082778912163201024*t^33 - 10333903177844793205695472444858950344261030964177031958885655/17713735670596149541389456081600512*t^31 + 52116617017034031840783298757588539940025227149840474941488235/8856867835298074770694728040800256*t^29 - 6885054089803541704612066312149739886618282020534528304157207495/141709885364769196331115648652804096*t^27 + 92472772443061835348903865915413747402818752566491546134906432075/283419770729538392662231297305608192*t^25 - 2003426696365094459762825984658432488140574710519060526990812738725/1133679082918153570648925189222432768*t^23 + 17318033050371925841347938629126000887188647203876970460792366880125/2267358165836307141297850378444865536*t^21 - 117866348616128760547425755555351705736139355979782517365474788804875/4534716331672614282595700756889731072*t^19 + 621008289315102283717436307302900297326848383383837702910255036857875/9069432663345228565191401513779462144*t^17 - 1239493550570826701724094778006617872017147591014944615204082919860125/9069432663345228565191401513779462144*t^15 + 3645938568684221069169668353839830098247861383048528246388561634133875/18138865326690457130382803027558924288*t^13 - 3808154861741871138372420610015821121944977257649138276945048744450625/18138865326690457130382803027558924288*t^11 + 5369368540347360468150581007274043847621474673565124986216377516704375/36277730653380914260765606055117848576*t^9 - 18964341089642951574292569777307359762874747521995057012225263510764375/290221845227047314086124848440942788608*t^7 + 9271636300008381574681591985582291537096006606691456689128388425284375/580443690454094628172249696881885577216*t^5 - 1966286603320798098596118003397128383007297431202945638774951620303125/1160887380908189256344499393763771154432*t^3 + 91112778854295652373889111602546018731285016284285541680280964478125/2321774761816378512688998787527542308864*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:
| (8.5502786564901319363 - 1.3330424786666469344e-753j)  +/-  (1.75e-244, 1.75e-244j)
| (7.5194030797995587141 + 2.1251737050587709484e-751j)  +/-  (7.98e-243, 7.98e-243j)
| (8.0057447266066034218 + 6.9028200890269589688e-753j)  +/-  (1.5e-243, 1.5e-243j)
| (5.8643094989845725654 + 8.5855333487409161689e-749j)  +/-  (3.38e-241, 3.38e-241j)
| (9.2073591457134859345 + 1.0597948482033600114e-758j)  +/-  (9.46e-246, 9.46e-246j)
| (6.6488214578688237587 - 1.1698154205273349959e-752j)  +/-  (6.75e-242, 6.75e-242j)
| (-8.5502786564901319363 - 9.5073302538799953814e-761j)  +/-  (1.93e-244, 1.93e-244j)
| (-2.8318037871261569014 - 4.1163989995343913651e-760j)  +/-  (1.06e-243, 1.06e-243j)
| (6.2479387024943782257 - 2.4937324073836968157e-755j)  +/-  (1.61e-241, 1.61e-241j)
| (-6.2479387024943782257 + 3.2401137113688156827e-761j)  +/-  (1.56e-241, 1.56e-241j)
| (7.0706019794139448729 + 3.406633266202260294e-760j)  +/-  (2.58e-242, 2.58e-242j)
| (-4.7868816279468649446 + 3.6812737974896281648e-770j)  +/-  (6.41e-241, 6.41e-241j)
| (-7.0706019794139448729 + 7.6140473835235943738e-772j)  +/-  (2.71e-242, 2.71e-242j)
| (-2.5993899426873438391 - 2.4366329867046850386e-773j)  +/-  (2.66e-244, 2.66e-244j)
| (5.4968124368786264091 + 4.7026078027325418905e-768j)  +/-  (7.99e-241, 7.99e-241j)
| (2.3370162114744557864 + 6.5644800352452395608e-783j)  +/-  (4.58e-245, 4.58e-245j)
| (4.1591654421872680309 - 1.5109032416776777368e-798j)  +/-  (1.41e-241, 1.41e-241j)
| (-7.5194030797995587141 - 1.6764302404157292495e-820j)  +/-  (7.24e-243, 7.24e-243j)
| (-2.0705033988590298093 + 2.8755967206691297768e-824j)  +/-  (8.45e-246, 8.45e-246j)
| (-8.0057447266066034218 - 2.3632753711129401224e-821j)  +/-  (1.56e-243, 1.56e-243j)
| (-3.3451271599412245725 + 3.8947093948479896443e-820j)  +/-  (9.12e-243, 9.12e-243j)
| (3.3451271599412245725 + 3.4442174139465023415e-818j)  +/-  (8.84e-243, 8.84e-243j)
| (3.8844727081061018661 - 3.1610444437437318468e-826j)  +/-  (6.88e-242, 6.88e-242j)
| (-1.6504717041475701556 + 1.5061113394737688327e-834j)  +/-  (2.87e-247, 2.87e-247j)
| (-1.1094885691760201544 - 1.1954159227410776944e-836j)  +/-  (2.27e-249, 2.27e-249j)
| (-1.8556770376713710625 + 4.2829709484461115175e-834j)  +/-  (1.97e-246, 1.97e-246j)
| (-2.3370162114744557864 + 2.1710099504279149021e-832j)  +/-  (4.93e-245, 4.93e-245j)
| (5.1842692080763973963 - 2.3958619224173667906e-826j)  +/-  (3.12e-240, 3.12e-240j)
| (-6.6488214578688237587 - 7.3463782350757666792e-830j)  +/-  (7.14e-242, 7.14e-242j)
| (-5.1842692080763973963 - 3.3661467371610092757e-827j)  +/-  (2.9e-240, 2.9e-240j)
| (-3.8844727081061018661 - 3.2503249309745166662e-830j)  +/-  (7.06e-242, 7.06e-242j)
| (2.5993899426873438391 - 1.3648691901130445633e-832j)  +/-  (2.59e-244, 2.59e-244j)
| (4.7868816279468649446 + 2.8938372744949632432e-827j)  +/-  (6.25e-241, 6.25e-241j)
| (1.6504717041475701556 - 2.2276439569863180849e-840j)  +/-  (3.23e-247, 3.23e-247j)
| (-5.4968124368786264091 + 3.8803212188399300247e-834j)  +/-  (7.37e-241, 7.37e-241j)
| (-1.3840395856824952373 + 4.6553064626149050815e-842j)  +/-  (2.25e-248, 2.25e-248j)
| (-9.2073591457134859345 + 7.3834680215857406684e-840j)  +/-  (9.7e-246, 9.7e-246j)
| (0.91915146544256376543 - 1.4999774879727279606e-843j)  +/-  (4.43e-250, 4.43e-250j)
| (-4.1591654421872680309 - 7.7264629359986723752e-835j)  +/-  (1.31e-241, 1.31e-241j)
| (-5.1015346104766771297 + 1.3223891421019872969e-836j)  +/-  (3.08e-240, 3.08e-240j)
| (-0.91915146544256376543 - 2.520790965880355734e-845j)  +/-  (4.56e-250, 4.56e-250j)
| (5.1015346104766771297 - 8.4167467266519275567e-834j)  +/-  (2.99e-240, 2.99e-240j)
| (1.3840395856824952373 + 2.4214936104918272311e-854j)  +/-  (2.17e-248, 2.17e-248j)
| (4.4620911737400066767 - 5.0889755932837767489e-847j)  +/-  (2.66e-241, 2.66e-241j)
| (0.73564975254040643478 - 1.8887917005249571501e-865j)  +/-  (4e-251, 4e-251j)
| (3.2483686509984108735e-906 - 4.0962669570367110618e-906j)  +/-  (3.19e-904, 3.19e-904j)
| (-0.17694599873958756052 - 4.0325680481957997676e-868j)  +/-  (3.59e-254, 3.59e-254j)
| (3.0735260090004970156 + 7.6009189158612551648e-855j)  +/-  (3.28e-243, 3.28e-243j)
| (1.1094885691760201544 + 3.5849123779463369274e-868j)  +/-  (2.15e-249, 2.15e-249j)
| (-3.61994979431864936 + 2.6243788908025814395e-861j)  +/-  (2.99e-242, 2.99e-242j)
| (-0.73564975254040643478 - 5.4391159791254970458e-871j)  +/-  (3.93e-251, 3.93e-251j)
| (-0.45853835006810479776 - 9.722168357694492301e-873j)  +/-  (1.07e-252, 1.07e-252j)
| (-4.4620911737400066767 + 8.2720171799399015052e-861j)  +/-  (2.61e-241, 2.61e-241j)
| (1.8556770376713710625 + 5.1352371957723022205e-867j)  +/-  (1.93e-246, 1.93e-246j)
| (0.45853835006810479776 + 9.8993614633939556264e-873j)  +/-  (1.14e-252, 1.14e-252j)
| (2.8318037871261569014 - 2.8816126101829761445e-861j)  +/-  (1.04e-243, 1.04e-243j)
| (2.0705033988590298093 - 4.0461746548331242939e-869j)  +/-  (9.15e-246, 9.15e-246j)
| (-3.0735260090004970156 + 7.5054494755716040486e-867j)  +/-  (3.03e-243, 3.03e-243j)
| (3.61994979431864936 + 6.4564873504423056366e-872j)  +/-  (2.69e-242, 2.69e-242j)
| (-5.8643094989845725654 + 1.1734154500275008902e-879j)  +/-  (3.24e-241, 3.24e-241j)
| (0.17694599873958756052 + 6.2705122135578211522e-892j)  +/-  (3.59e-254, 3.59e-254j)
-------------------------------------------------
The weights are:
| (5.8787939669516670225e-33 + 1.2939519318967276015e-775j)  +/-  (4.79e-71, 2.03e-191j)
| (7.3031065323987572509e-26 + 4.1406663444269458907e-771j)  +/-  (3.99e-68, 1.69e-188j)
| (4.214204443054835599e-29 - 3.2704142687183881527e-773j)  +/-  (1.37e-69, 5.81e-190j)
| (2.4593553336710859233e-16 - 1.955082816122339363e-763j)  +/-  (1.9e-63, 8.09e-184j)
| (6.515977929573047914e-38 - 1.3425296967917805521e-778j)  +/-  (2.13e-74, 9.03e-195j)
| (1.4655851326253270906e-20 + 2.3695514592102177115e-767j)  +/-  (2.69e-66, 1.14e-186j)
| (5.8787939669516670225e-33 - 2.4111104564183051013e-776j)  +/-  (2.37e-78, 1.01e-198j)
| (4.2096915809985413635e-05 + 1.0923824658472063066e-756j)  +/-  (5.64e-52, 2.4e-172j)
| (2.4607534351717041772e-18 - 1.7245993458586821879e-765j)  +/-  (2.47e-65, 1.05e-185j)
| (2.4607534351717041772e-18 + 5.4622158842186112976e-767j)  +/-  (3.93e-71, 1.67e-191j)
| (4.7539432943136583707e-23 - 3.4797427775745221818e-769j)  +/-  (5.37e-68, 2.28e-188j)
| (2.0921649003567026152e-11 - 1.4179387068568200265e-761j)  +/-  (1.83e-65, 7.77e-186j)
| (4.7539432943136583707e-23 + 3.2452448952451116207e-770j)  +/-  (3.14e-74, 1.33e-194j)
| (0.00016220046105253788898 - 2.8658123173901743294e-756j)  +/-  (1.74e-52, 7.41e-173j)
| (1.5253234280458803336e-14 + 2.0077974565071382031e-762j)  +/-  (4.3e-65, 1.83e-185j)
| (0.00065141062464957725861 + 1.7720575332759589044e-755j)  +/-  (8.83e-52, 3.75e-172j)
| (4.9993255728990104885e-09 - 3.655151043789469096e-759j)  +/-  (1.02e-61, 4.34e-182j)
| (7.3031065323987572509e-26 - 5.1207801211939989405e-772j)  +/-  (2.44e-76, 1.04e-196j)
| (0.0019455490800001687205 - 2.4674533789676986109e-755j)  +/-  (1.1e-51, 4.68e-172j)
| (4.214204443054835599e-29 + 5.0492698830166958842e-774j)  +/-  (4.56e-78, 1.94e-198j)
| (2.1641277638916446988e-06 + 6.8846813099339163417e-758j)  +/-  (1.26e-60, 5.35e-181j)
| (2.1641277638916446988e-06 + 2.5168520266371167505e-757j)  +/-  (1.29e-60, 5.48e-181j)
| (4.1715382922816290156e-08 + 1.7154398131843819099e-758j)  +/-  (1.68e-62, 7.14e-183j)
| (0.008963335109137715628 - 9.4663265890820084375e-755j)  +/-  (3.22e-50, 1.37e-170j)
| (0.042180575635307481373 - 3.8589424082611346208e-754j)  +/-  (1.62e-45, 6.88e-166j)
| (0.0033239030209415386227 + 6.020079327359192772e-755j)  +/-  (8.98e-52, 3.82e-172j)
| (0.00065141062464957725861 + 7.6214058504354870218e-756j)  +/-  (2.46e-55, 1.05e-175j)
| (1.8116008164145129061e-13 - 4.8791678744353566285e-761j)  +/-  (2.5e-68, 1.06e-188j)
| (1.4655851326253270906e-20 - 1.4854889470478747594e-768j)  +/-  (1.58e-75, 6.72e-196j)
| (1.8116008164145129061e-13 - 3.003120068619665154e-762j)  +/-  (1.45e-71, 6.17e-192j)
| (4.1715382922816290156e-08 + 3.4838061872257884563e-759j)  +/-  (2.78e-67, 1.18e-187j)
| (0.00016220046105253788898 - 7.4290928239876561425e-756j)  +/-  (2.39e-62, 1.02e-182j)
| (2.0921649003567026152e-11 - 1.4017429061820618345e-760j)  +/-  (2.15e-69, 9.15e-190j)
| (0.008963335109137715628 - 1.6881854900808279193e-754j)  +/-  (3.96e-58, 1.68e-178j)
| (1.5253234280458803336e-14 + 6.4945756854261207422e-764j)  +/-  (2.75e-73, 1.17e-193j)
| (0.023229471677688348681 + 1.5198428043923985729e-754j)  +/-  (5.55e-57, 2.36e-177j)
| (6.515977929573047914e-38 + 2.9778701302186779619e-779j)  +/-  (4.54e-87, 1.93e-207j)
| (0.032247454996140427904 + 9.745932869806932213e-754j)  +/-  (4.73e-57, 2.01e-177j)
| (4.9993255728990104885e-09 - 6.2179536431701677411e-760j)  +/-  (2.13e-69, 9.06e-190j)
| (6.042955872747112024e-13 + 5.581979579868568353e-762j)  +/-  (1.93e-71, 8.18e-192j)
| (0.032247454996140427904 + 7.104805280091519103e-754j)  +/-  (1.33e-58, 5.66e-179j)
| (6.042955872747112024e-13 + 8.0248168308423689091e-761j)  +/-  (7.81e-72, 3.32e-192j)
| (0.023229471677688348681 + 2.4588595314043910835e-754j)  +/-  (5.13e-62, 2.18e-182j)
| (4.0164496453953160611e-10 + 6.6391007475234752889e-760j)  +/-  (4.96e-71, 2.11e-191j)
| (0.082906371113330144321 - 9.3486566874418047984e-754j)  +/-  (2.81e-60, 1.19e-180j)
| (0.058936757551324305501 + 1.824143482485202301e-753j)  +/-  (1.5e-60, 6.37e-181j)
| (0.1433769713274944778 - 1.2776849718603233261e-753j)  +/-  (1.43e-60, 6.08e-181j)
| (1.158441053244908132e-05 - 9.884274105903574007e-757j)  +/-  (1.54e-68, 6.53e-189j)
| (0.042180575635307481373 - 5.6598327484457087831e-754j)  +/-  (7.52e-62, 3.2e-182j)
| (3.0933536550221958549e-07 - 1.5703657360579944862e-758j)  +/-  (1.69e-69, 7.19e-190j)
| (0.082906371113330144321 - 7.2646012416556618325e-754j)  +/-  (3.61e-62, 1.54e-182j)
| (0.13148817625104753412 + 6.8508076639079863769e-754j)  +/-  (3.4e-62, 1.45e-182j)
| (4.0164496453953160611e-10 + 9.0151961301126537831e-761j)  +/-  (6.56e-72, 2.79e-192j)
| (0.0033239030209415386227 + 1.1593716984208624013e-754j)  +/-  (3.29e-66, 1.4e-186j)
| (0.13148817625104753412 + 8.0130322295851749932e-754j)  +/-  (1.92e-63, 8.13e-184j)
| (4.2096915809985413635e-05 + 3.1325543392649803705e-756j)  +/-  (6.95e-69, 2.94e-189j)
| (0.0019455490800001687205 - 5.160725016966670848e-755j)  +/-  (3.75e-67, 1.61e-187j)
| (1.158441053244908132e-05 - 3.0863008407879295867e-757j)  +/-  (1.06e-69, 4.64e-190j)
| (3.0933536550221958549e-07 - 6.6360891755833701361e-758j)  +/-  (3.85e-71, 1.57e-191j)
| (2.4593553336710859233e-16 - 1.8002749147685819543e-765j)  +/-  (2.5e-78, 1.12e-198j)
| (0.1433769713274944778 - 1.3571880239150317046e-753j)  +/-  (7.34e-66, 2.03e-186j)
