Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 49
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^57 - 13132182387145631454933944915593662658569883654269636011056671751573241678023284947465/608444024428199361707909123418736293986760220169627125259202959755744586471367388948*t^55 + 49452673547579459819297590363175654147937172438518179381878077769396165104155396425799655/336137666950015229190814885728696405323412896179165821836379671494150895635136329330636*t^53 - 224124535048422779337832954206651046978242352359697809701979494314668031180477962064616343725/354676952119489146062339060580040660909327284376124429086893842606559064263628079186794924*t^51 + 2268593793476045716699463467463393567023192866531438621745848572570241818626939722644073328430075/1182138281414257323825776088913275522810787838825622722146617177407661361190672387929587481692*t^49 - 2888387458306503400975897100159166491064586561706576130365091505659933959297698121318604253053995/659008122397603220753449888647055894900266783713134506024263598899673287560317365684884975426*t^47 + 8515897277914194605957710726096410179293684093305153593923988743553259092159690806605738213062241575/1089340426323238123905452665933583394270140993477811338458107728981159944337204605477114864379178*t^45 - 368469434296541884669742280760797101405989253136635012641128986015980717695626483626405595536982825/33010315949189034057740989876775254371822454347812464801760840272156361949612260772033783769066*t^43 + 2007261182809180389847751021463654576624341967050682448318375256715519754591465609234460073557274150/154687875901432334014763010701632878044702896536842131571042077089290858903415594082902498359693*t^41 - 684227846512296155697315489639187927887391421495613754064842440541793892566649434122609114093914697075/55068883820909910909255631809781304583914231167115798839290979443787545769615951493513289416050708*t^39 + 5805007540793804225900381033012039972816384469877660951909642889303037673946085917473504218092084315/587779768423403539333240089246837627137840524050923138144806184714699605196489728859729625714196*t^37 - 42341637762098489335076138076163146451530165000909491617170351820500247638423787282617149315510637075/6465577452657438932665640981715213898516245764560154519592868031861695657161387017457025882856156*t^35 + 1948909719204523582266666341828735027938960407031392585586574514297012414182433452296268494039615297375/536642928570567431411248201482362753576848398458492825126208046644520739544395122448933148277060948*t^33 - 554896932399456332092656953550431769995421089131371700409277902076323706736245974355657519516824070925/329303615259211832911447760000540780603975153599529688145627664986410453811333370593663522806378309*t^31 + 26128371510154994875054120456166200900553873451762428358726223841403761297777191868771731233459324848225/40001537006272215875275541341140959123474272152837493408399523993026654803297129974157170076813502761*t^29 - 9595566367863240642334810534954421318189482314827557383281338267950163493183034510949828436786725783555/45518990386447693927037684974401781071539689001504733878523596267926883052027768591282296983960192797*t^27 + 43834453867675574052424013496459126459351858755397060479662068712720439786311272835206989805492668495/778102399768336648325430512382936428573328017119739040658523013126955265846628522927902512546328082*t^25 - 468459282243947815785969134898854149918452815795368979373534860809529800224698039011009242718091031425/37867650122059050218504284935969572857235296833160633312048119972178489604535921449157922277254633324*t^23 + 1620102757379008368059975013794750764067769611316131633746308121959684121118635296175762852901956287575/733255406908961608776492062851047183508283475042110445042386323097638025978741024424603404095930627092*t^21 - 232190656737518722498907614228979907842760050741353958413503048912312986718777966434937122281136522725/733255406908961608776492062851047183508283475042110445042386323097638025978741024424603404095930627092*t^19 + 586041653817152211906998686193181142064340912700086172090443733417769219418598133482363725954102648495/16376037420966809262674989403673387098351664275940466605946627882513915913525216212149476024809117338388*t^17 - 90493193015112155149825968535043636878705536773676256701379912622568458010379973357893552034043975275/29030248155350252783832935761057368037987041216439918074178113064456487301249246921537707498525253463506*t^15 + 194513608165052204836668555742845272079743114681991767462898210493325157404567508202460345399193154475/957998189126558341866486880114893145253572360142517296447877731127064080941225148410744347451333364295698*t^13 - 14221280702984951018276046989350296424568811674699916963847435340700589202855664955252949476335877175/1498407424018463047534761530436114919499177281248552694444116451250023306087557283411677056270034236462502*t^11 + 3621129329621774336021940541806866822737813181729801269075465996653772683510667081795817776495517525/12055368820512179973347854131236015488697926308226992132573118721420642053522619961993947225445275447902857*t^9 - 19815940265782561796993058492428154387150857072181995994585603516843025628449221201094577519217870067/3359429444649394152572935351237769649517155464559255140943709083702552252248303429408979960157416758148929484*t^7 + 766943175588032147423320949306973592381133056335014292341135074017825588604998345103503430564183555/12317907963714445226100762954538488714896236703383935516793599973576024924910445907832926520577194779879408108*t^5 - 128574963749289472302380748803749646392238764862410274205593508498351450335254827666067687777675495/480398410584863363817929755227001059880953231431973485154950398969464972071507390405484134302510596415296916212*t^3 + 103511243633863497639395030224929194485576025871718073837327354067377615530712219148227383016425/480398410584863363817929755227001059880953231431973485154950398969464972071507390405484134302510596415296916212*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:
| (0.99999064494509293267 - 5.3754927560578175988e-875j)  +/-  (2.83e-235, 2.83e-235j)
| (-0.9537622596594961383 - 5.6045551262464018549e-888j)  +/-  (3.71e-235, 3.71e-235j)
| (-0.91381608741873176892 - 6.9907057444092107568e-888j)  +/-  (1.69e-235, 1.69e-235j)
| (-0.99745542923352692085 - 2.2423154065568829375e-886j)  +/-  (6.86e-235, 6.86e-235j)
| (0.93497146497751102942 + 2.6250596377391340237e-888j)  +/-  (2.47e-235, 2.47e-235j)
| (0.91381608741873176892 - 3.3528157815442226699e-892j)  +/-  (1.59e-235, 1.59e-235j)
| (0.99150493563761208412 + 3.2520129395514167876e-898j)  +/-  (7.51e-235, 7.51e-235j)
| (-0.892622162247715022 + 1.1578907308475954154e-909j)  +/-  (1.17e-235, 1.17e-235j)
| (-0.99999064494509293267 - 6.0740984187315522964e-908j)  +/-  (2.74e-235, 2.74e-235j)
| (0.9537622596594961383 + 2.5235693962833801485e-908j)  +/-  (3.61e-235, 3.61e-235j)
| (0.892622162247715022 - 2.2673284692670597097e-916j)  +/-  (1.09e-235, 1.09e-235j)
| (0.98219129046748981137 + 7.5475946769210553135e-921j)  +/-  (6.37e-235, 6.37e-235j)
| (-0.85110112875893547946 - 4.7751307807268733631e-948j)  +/-  (1.55e-236, 1.55e-236j)
| (-0.87433478634630166799 - 1.0146808182723422835e-947j)  +/-  (5.5e-236, 5.5e-236j)
| (0.99745542923352692085 + 3.3390162258728306032e-944j)  +/-  (6.78e-235, 6.78e-235j)
| (0.87433478634630166799 - 1.4593125201385364294e-963j)  +/-  (5.74e-236, 5.74e-236j)
| (0.85110112875893547946 - 2.7819262421910751312e-965j)  +/-  (1.48e-236, 1.48e-236j)
| (-0.93497146497751102942 - 1.0155045150433527519e-964j)  +/-  (2.38e-235, 2.38e-235j)
| (-0.75050583958771164539 - 7.2064581590857702719e-969j)  +/-  (6.22e-239, 6.22e-239j)
| (-0.98219129046748981137 - 2.5240369959264107758e-963j)  +/-  (6.37e-235, 6.37e-235j)
| (0.96957500034783005714 + 1.0331645543869147277e-973j)  +/-  (5.31e-235, 5.31e-235j)
| (0.75050583958771164539 - 8.9519991364727334055e-991j)  +/-  (6.33e-239, 6.33e-239j)
| (-0.99150493563761208412 + 8.3602999024474856302e-987j)  +/-  (7.56e-235, 7.56e-235j)
| (-0.78742472530355947775 + 1.813753654514894021e-993j)  +/-  (4.14e-238, 4.14e-238j)
| (-0.82124972033285703141 - 3.0021601238806415577e-993j)  +/-  (2.6e-237, 2.6e-237j)
| (0.66863578150396761745 + 9.0829283619341733098e-999j)  +/-  (1.21e-240, 1.21e-240j)
| (0.71083728686842194405 - 2.527151442578359062e-997j)  +/-  (8.74e-240, 8.74e-240j)
| (0.78742472530355947775 - 3.0514457175716273511e-995j)  +/-  (4.43e-238, 4.43e-238j)
| (-0.96957500034783005714 - 1.6801998290834721224e-997j)  +/-  (5.39e-235, 5.39e-235j)
| (-0.62408270459895336102 - 4.163863170266636995e-1007j)  +/-  (1.36e-241, 1.36e-241j)
| (-0.37212260253630192749 + 5.4181256677170705769e-1009j)  +/-  (4.08e-247, 4.08e-247j)
| (0.82124972033285703141 + 1.7983301069697915294e-1002j)  +/-  (2.72e-237, 2.72e-237j)
| (0.62408270459895336102 - 1.5575600329786751701e-1006j)  +/-  (1.25e-241, 1.25e-241j)
| (0.032067195370717029462 - 6.3353126791844852954e-1020j)  +/-  (4.63e-255, 4.63e-255j)
| (-0.66863578150396761745 + 5.8172348610403485255e-1006j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.71083728686842194405 - 2.1064496883514967037e-1012j)  +/-  (9.46e-240, 9.46e-240j)
| (0.0888329854471765768 - 1.9935766547619223204e-1023j)  +/-  (1.32e-253, 1.32e-253j)
| (0.57735026918962576451 - 5.852460105440353579e-1012j)  +/-  (1.27e-242, 1.27e-242j)
| (0.26110947339685811112 - 8.8637312270400983806e-1022j)  +/-  (9.85e-250, 9.85e-250j)
| (-0.31715486448988654502 - 3.3590086386611065045e-1020j)  +/-  (2.08e-248, 2.08e-248j)
| (-0.57735026918962576451 + 5.1666305305287703178e-1016j)  +/-  (1.22e-242, 1.22e-242j)
| (-0.0888329854471765768 + 3.1237445194891028325e-1026j)  +/-  (1.22e-253, 1.22e-253j)
| (0.42581416983117062617 + 4.5371453507051596002e-1016j)  +/-  (6.01e-246, 6.01e-246j)
| (0.52861046641473066866 + 1.8998702244346086881e-1015j)  +/-  (1.09e-243, 1.09e-243j)
| (-0.14665566170969021896 + 5.7902573245614494278e-1026j)  +/-  (2.39e-252, 2.39e-252j)
| (-0.52861046641473066866 - 3.1041749240957446973e-1017j)  +/-  (1e-243, 1e-243j)
| (-0.2041968861768067152 - 6.2385262885819952263e-1026j)  +/-  (5.32e-251, 5.32e-251j)
| (0.2041968861768067152 + 2.3247615214436825421e-1025j)  +/-  (5.11e-251, 5.11e-251j)
| (0.47803849513752428319 + 4.6810152473865298747e-1018j)  +/-  (7.98e-245, 7.98e-245j)
| (0.14665566170969021896 + 1.6747145782494526752e-1026j)  +/-  (2.34e-252, 2.34e-252j)
| (-0.26110947339685811112 + 4.9467943489225741921e-1024j)  +/-  (1.01e-249, 1.01e-249j)
| (-0.47803849513752428319 - 1.9458581617913061992e-1020j)  +/-  (8.18e-245, 8.18e-245j)
| (-3.5890492602374061796e-1038 - 1.198065475157973308e-1037j)  +/-  (7.13e-1036, 7.13e-1036j)
| (0.31715486448988654502 - 7.6160272543462030019e-1022j)  +/-  (2.18e-248, 2.18e-248j)
| (0.37212260253630192749 + 2.0855334496181574234e-1020j)  +/-  (3.74e-247, 3.74e-247j)
| (-0.032067195370717029462 - 5.2746114838374286898e-1029j)  +/-  (4.63e-255, 4.63e-255j)
| (-0.42581416983117062617 + 1.4134568830119404673e-1020j)  +/-  (5.72e-246, 5.72e-246j)
-------------------------------------------------
The weights are:
| (0.00070054082962571889602 + 2.7610355797418166746e-875j)  +/-  (5.68e-45, 3.5e-157j)
| (0.017354431970611652758 - 1.6654930709886435075e-877j)  +/-  (2.64e-45, 1.62e-157j)
| (0.021844692508855522894 - 4.0352156871103804866e-877j)  +/-  (2.08e-45, 1.28e-157j)
| (0.0042551134595010416122 - 4.7961157502437365803e-878j)  +/-  (5.46e-46, 3.36e-158j)
| (0.020141407501948257847 + 7.3067253368651461327e-876j)  +/-  (1.69e-46, 1.04e-158j)
| (0.021844692508855522894 - 8.9616044088523191085e-876j)  +/-  (1.16e-46, 7.13e-159j)
| (0.0076397173354794861632 + 1.6067717416035535871e-875j)  +/-  (4.08e-47, 2.51e-159j)
| (0.019562940374346604608 + 6.7280830817559377105e-877j)  +/-  (1.56e-47, 9.59e-160j)
| (0.00070054082962571889602 + 1.882893677234752602e-878j)  +/-  (1.47e-47, 9.06e-160j)
| (0.017354431970611652758 - 7.0388829363104989583e-876j)  +/-  (2.3e-47, 1.42e-159j)
| (0.019562940374346604608 + 1.1859771029504072291e-875j)  +/-  (4.72e-48, 2.9e-160j)
| (0.010977803542471558489 - 1.0147436994154978724e-875j)  +/-  (1.05e-47, 6.47e-160j)
| (0.027179267901939610393 + 5.4188686390871399683e-877j)  +/-  (7.25e-50, 4.46e-162j)
| (0.019134060431873539659 - 7.4994740780981852104e-877j)  +/-  (2.96e-49, 1.82e-161j)
| (0.0042551134595010416122 - 3.7787642807712254714e-875j)  +/-  (1.94e-47, 1.19e-159j)
| (0.019134060431873539659 - 1.1186470046269009558e-875j)  +/-  (1.69e-49, 1.04e-161j)
| (0.027179267901939610393 + 6.737091647666313754e-876j)  +/-  (1.73e-50, 1.06e-162j)
| (0.020141407501948257847 + 2.455227869153072409e-877j)  +/-  (1.17e-50, 7.22e-163j)
| (0.03833532099338785369 - 2.232685899405562809e-877j)  +/-  (1.14e-53, 7.04e-166j)
| (0.010977803542471558489 - 9.1120711525034275572e-878j)  +/-  (7.84e-52, 4.83e-164j)
| (0.014237933151032528399 + 7.8419035011772187648e-876j)  +/-  (3.43e-50, 2.11e-162j)
| (0.03833532099338785369 - 1.5665518435434484356e-876j)  +/-  (5.11e-55, 3.15e-167j)
| (0.0076397173354794861632 + 6.8464113607995935221e-878j)  +/-  (1.31e-51, 8.07e-164j)
| (0.035449824348087610291 + 2.7017886966064944654e-877j)  +/-  (2.96e-54, 1.82e-166j)
| (0.032077083815410379722 - 3.5968959235253485417e-877j)  +/-  (1.76e-53, 1.08e-165j)
| (0.043406307933526067671 - 9.1880796394785115071e-877j)  +/-  (1.21e-57, 7.47e-170j)
| (0.04096683009629903006 + 1.1656575642073712302e-876j)  +/-  (5.74e-57, 3.54e-169j)
| (0.035449824348087610291 + 2.2718687225072964207e-876j)  +/-  (5.15e-56, 3.17e-168j)
| (0.014237933151032528399 + 1.2110109179912333174e-877j)  +/-  (2.15e-54, 1.32e-166j)
| (0.045671271966488086424 + 1.7562460335616077032e-877j)  +/-  (1.52e-60, 9.35e-173j)
| (0.054362043179226672994 - 2.3125353884399691277e-877j)  +/-  (7.17e-63, 4.41e-175j)
| (0.032077083815410379722 - 3.6649760311574645154e-876j)  +/-  (3.36e-56, 2.07e-168j)
| (0.045671271966488086424 + 7.5876885590642028906e-877j)  +/-  (6.66e-60, 4.1e-172j)
| (0.054028592293562079798 - 2.9660511539651387637e-876j)  +/-  (1.77e-64, 1.09e-176j)
| (0.043406307933526067671 - 1.8245635009278399041e-877j)  +/-  (1.4e-60, 8.61e-173j)
| (0.04096683009629903006 + 1.970120973659054335e-877j)  +/-  (7.5e-60, 4.62e-172j)
| (0.05775284288391166661 + 1.2404964587812928712e-876j)  +/-  (2.73e-65, 1.68e-177j)
| (0.047764984135988392571 - 6.5212461103893683218e-877j)  +/-  (9e-63, 5.54e-175j)
| (0.056515501413778292094 - 5.620240573862877028e-877j)  +/-  (9.69e-66, 5.97e-178j)
| (0.055540407651560268107 + 2.6969269640411689922e-877j)  +/-  (9.34e-66, 5.75e-178j)
| (0.047764984135988392571 - 1.7473343155510191629e-877j)  +/-  (7.77e-64, 4.79e-176j)
| (0.05775284288391166661 + 1.0380816676394868101e-876j)  +/-  (1.31e-66, 8.06e-179j)
| (0.052989267027254851681 + 5.1106390224308635134e-877j)  +/-  (2.22e-66, 1.37e-178j)
| (0.049685442459929733481 + 5.8103922136617829213e-877j)  +/-  (4.06e-65, 2.5e-177j)
| (0.05775921676898749867 - 6.1056782780594962839e-877j)  +/-  (2.52e-67, 1.55e-179j)
| (0.049685442459929733481 + 1.7917713775937446577e-877j)  +/-  (1.67e-66, 1.03e-178j)
| (0.057270756739205712963 + 4.2772400275500681662e-877j)  +/-  (1.38e-67, 8.49e-180j)
| (0.057270756739205712963 + 6.4722788436000566729e-877j)  +/-  (2.19e-68, 1.35e-180j)
| (0.051428540926911118723 - 5.357137889579602512e-877j)  +/-  (1.37e-67, 8.43e-180j)
| (0.05775921676898749867 - 8.2043436454118068172e-877j)  +/-  (2.1e-68, 1.29e-180j)
| (0.056515501413778292094 - 3.2929105938929577488e-877j)  +/-  (9.46e-69, 5.82e-181j)
| (0.051428540926911118723 - 1.8918230788052944564e-877j)  +/-  (5.7e-69, 3.51e-181j)
| (0.011935712717598325463 + 4.3035512801533849453e-876j)  +/-  (7.31e-69, 4.5e-181j)
| (0.055540407651560268107 + 5.2021955228238559117e-877j)  +/-  (5.48e-70, 3.37e-182j)
| (0.054362043179226672994 - 5.0537059180727598104e-877j)  +/-  (5.21e-70, 3.2e-182j)
| (0.054028592293562079798 - 2.7817340776999329614e-876j)  +/-  (1.73e-69, 1.07e-181j)
| (0.052989267027254851681 + 2.0580718125882204223e-877j)  +/-  (1.48e-70, 8.89e-183j)
