Starting with polynomial:
P : t
Extension levels are: 1 26 28
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^27 - 351/53*t^25 + 17550/901*t^23 - 1480050/44149*t^21 + 11100375/296429*t^19 - 8436285/296429*t^17 + 11248380/749791*t^15 - 168725700/30741431*t^13 + 42181425/30741431*t^11 - 257775375/1137432947*t^9 + 185598270/7962030629*t^7 - 1533870/1137432947*t^5 + 1278225/35260421357*t^3 - 294975/1022552219353*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 41525/3021*t^53 + 291057745/3258747*t^51 - 11916339513485/32658970743*t^49 + 110757963998332970/105349174992027*t^47 - 3774047112413002942/1660930609980681*t^45 + 3754235236038789696314773070/981638198083131772905423*t^43 - 484921069825271794949203004750/94390044338401459616170647*t^41 + 40019176945287119888457437782524085/7146129822891968593173533674383*t^39 - 336234049416972410716431975586979417419885/67111999257721707330652281158325995391*t^37 + 10286469913896338359073480601968698941692838007/2775471144437614494529933724287294506418095*t^35 - 10293692852443821345625603719464181711197844605/4520053006655543605377320636696451053309469*t^33 + 177215686449236857041892148366113068871041452818064071252/152147148717288841890511376063358516647216173792110561*t^31 - 309425953379633262744157299353972866912865919011089012844/624067585185306341550906463108515205999623660740344311*t^29 + 314829558822811220056591948634941160155713979071727866416812748/1796014239123159405842004416281517432403628168511678572012089*t^27 - 1311356395003162736854218258824955517257528213008575109437604/25584248420557826294045646955577171401761085021533882792195*t^25 + 3340332995931200054995087473555473200236031329627593280222565/271193033257912958716883857729118016858667501228259157597267*t^23 - 10149500086891938194370787442009252320042438395711165619769735/4209387516220648967909892922143266609501925997325587794009753*t^21 + 76172276704357785644326113348915380710957857298992520131625/200447024581935665138566329625869838547710761777408942571893*t^19 - 7848496509763958033318120695039575642197197915175394980375/165280879918438180026537148989752323013024663219968777208403*t^17 + 403503639215875330444619693547511334667563320803563656346/87501642309761389425813784759280641595130704057630529110331*t^15 - 228911163080355424600989033758247984596107104887821681870/675333188083030210696665364424191618464983126188379211851529*t^13 + 19656218961274431250384093992390272843443707122716036845070/1079857767744765306903967917714282397925508018775218359750594871*t^11 - 28633610536502160986135317323386243263008649742059116561970/42114452942045846969254748790857013519094812732233516030273199969*t^9 + 19929203437017424820021017203779551504276998810941899659935/1211960367998874929448553326314662944605061833072053405760084310219*t^7 - 12653356707447003997609017084837807832499674166224373/54981643514897016261332546673078208256819027948648251406799633*t^5 + 60956414601791477856808387025401411407065251103083565/39954737406556316355446812955428448723243796694683079310772010227*t^3 - 228771838098514615817226507879624246478211242796915/75595113496911715921338336249003121293273474497452023296906667237*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:
| (-0.99936554652297716812 + 9.1538184259266320319e-815j)  +/-  (3.11e-236, 3.11e-236j)
| (0.97992347596150122286 - 2.0596686364545128618e-813j)  +/-  (8.51e-236, 8.51e-236j)
| (-0.88427665971018918738 + 4.9891202156388608353e-830j)  +/-  (4.21e-237, 4.21e-237j)
| (0.99617926288898856694 + 2.3969036111835389358e-826j)  +/-  (7.36e-236, 7.36e-236j)
| (0.93172592245498812853 - 3.1749279162843899103e-844j)  +/-  (2.45e-236, 2.45e-236j)
| (0.95090055781470500685 - 1.3583621681668892433e-868j)  +/-  (4.41e-236, 4.41e-236j)
| (-0.99617926288898856694 + 2.8595927393157650164e-884j)  +/-  (7.53e-236, 7.53e-236j)
| (-0.9094823206774911043 + 1.3427769035520098044e-885j)  +/-  (1.24e-236, 1.24e-236j)
| (-0.9669649256262432901 - 1.0305992684082966008e-884j)  +/-  (6.89e-236, 6.89e-236j)
| (0.99936554652297716812 - 1.2652798470088926765e-883j)  +/-  (2.93e-236, 2.93e-236j)
| (0.8562079080182944903 - 1.9229322086636827247e-897j)  +/-  (1.48e-237, 1.48e-237j)
| (-0.5405515645794568949 + 3.1303355065629211389e-904j)  +/-  (1.53e-243, 1.53e-243j)
| (-0.97992347596150122286 - 3.0746527044985308497e-894j)  +/-  (8.54e-236, 8.54e-236j)
| (-0.82534390724636190138 + 8.0367817713364391507e-902j)  +/-  (4.41e-238, 4.41e-238j)
| (0.22645936543953685886 + 9.2904800490599514075e-915j)  +/-  (1.89e-250, 1.89e-250j)
| (0.82534390724636190138 - 1.9299545570948342538e-902j)  +/-  (4.4e-238, 4.4e-238j)
| (0.9094823206774911043 + 1.2484655052183962002e-899j)  +/-  (1.07e-236, 1.07e-236j)
| (0.98970960230169772503 - 8.6899675319333142911e-908j)  +/-  (1.04e-235, 1.04e-235j)
| (-0.75561835042722878432 + 1.7360660030502989929e-917j)  +/-  (2.53e-239, 2.53e-239j)
| (-0.93172592245498812853 + 2.8459972754179870582e-913j)  +/-  (2.36e-236, 2.36e-236j)
| (-0.98970960230169772503 - 5.0463842836492045464e-913j)  +/-  (9.81e-236, 9.81e-236j)
| (0.71701347373942369929 + 3.4342926557867656961e-921j)  +/-  (5.08e-240, 5.08e-240j)
| (-0.95090055781470500685 - 7.6293282113054897081e-918j)  +/-  (4.36e-236, 4.36e-236j)
| (-0.8562079080182944903 + 6.3243841125386032445e-920j)  +/-  (1.57e-237, 1.57e-237j)
| (-0.71701347373942369929 + 3.50880587620449842e-923j)  +/-  (5.02e-240, 5.02e-240j)
| (0.88427665971018918738 - 3.2909400216430724405e-919j)  +/-  (4.36e-237, 4.36e-237j)
| (0.75561835042722878432 - 4.0526302458025574393e-921j)  +/-  (2.43e-239, 2.43e-239j)
| (0.79177163907050822714 + 4.1403507918747498233e-922j)  +/-  (1.18e-238, 1.18e-238j)
| (0.9669649256262432901 - 3.1786938568778886485e-926j)  +/-  (6.86e-236, 6.86e-236j)
| (-0.63290797194649514093 + 8.7644203681766980042e-938j)  +/-  (1.14e-241, 1.14e-241j)
| (-0.79177163907050822714 + 6.9704710974810679282e-939j)  +/-  (1.15e-238, 1.15e-238j)
| (0.67606882688450432389 - 3.0868126775348844371e-940j)  +/-  (8.8e-241, 8.8e-241j)
| (0.63290797194649514093 - 2.7976834289541476465e-943j)  +/-  (1.19e-241, 1.19e-241j)
| (-0.11397258560952996693 - 2.119948626628048931e-955j)  +/-  (4.81e-253, 4.81e-253j)
| (-0.67606882688450432389 - 2.3030725110122315089e-944j)  +/-  (8.93e-241, 8.93e-241j)
| (-0.44114825175002688059 + 3.4585939249912304424e-950j)  +/-  (1.27e-245, 1.27e-245j)
| (0.057082916723187490812 - 7.0304153744929415758e-959j)  +/-  (2.38e-254, 2.38e-254j)
| (0.58768341187210822029 - 8.04633570937004277e-947j)  +/-  (1.55e-242, 1.55e-242j)
| (0.28168978132000734802 - 2.6050946824516911189e-956j)  +/-  (3.57e-249, 3.57e-249j)
| (-0.33599390363850889973 + 9.9163396615115174557e-954j)  +/-  (6.74e-248, 6.74e-248j)
| (-0.58768341187210822029 - 1.6383636130312993261e-949j)  +/-  (1.46e-242, 1.46e-242j)
| (-0.17049043085087520581 + 2.2900221843088807697e-959j)  +/-  (9.72e-252, 9.72e-252j)
| (0.5405515645794568949 + 9.4908960129419381101e-950j)  +/-  (1.56e-243, 1.56e-243j)
| (0.49165606141217095241 - 1.006866474075313959e-953j)  +/-  (1.49e-244, 1.49e-244j)
| (-6.0370963324774477166e-980 - 1.1962694732246315964e-979j)  +/-  (7.37e-978, 7.37e-978j)
| (-0.49165606141217095241 + 9.9896544198926331312e-955j)  +/-  (1.42e-244, 1.42e-244j)
| (-0.28168978132000734802 - 4.6270069580989070661e-962j)  +/-  (3.47e-249, 3.47e-249j)
| (0.11397258560952996693 - 3.1479032716221232543e-964j)  +/-  (4.75e-253, 4.75e-253j)
| (0.44114825175002688059 - 1.0400832560682323866e-955j)  +/-  (1.18e-245, 1.18e-245j)
| (0.17049043085087520581 + 9.700545029474466393e-964j)  +/-  (9.48e-252, 9.48e-252j)
| (-0.22645936543953685886 - 1.2287221867468860616e-961j)  +/-  (1.95e-250, 1.95e-250j)
| (-0.38920185274720471495 + 6.6921645681313871448e-957j)  +/-  (8.84e-247, 8.84e-247j)
| (-0.057082916723187490812 - 2.2889062582195740092e-965j)  +/-  (1.96e-254, 1.96e-254j)
| (0.33599390363850889973 + 3.0009160505497671261e-958j)  +/-  (5.95e-248, 5.95e-248j)
| (0.38920185274720471495 - 1.5749573299590267109e-956j)  +/-  (8.66e-247, 8.66e-247j)
-------------------------------------------------
The weights are:
| (0.0017088604963509650263 + 9.5436345862269529733e-815j)  +/-  (1.41e-51, 3.34e-164j)
| (0.011393506344486885997 + 2.9652603031339066389e-814j)  +/-  (5.82e-52, 1.38e-164j)
| (0.026650092713661029661 - 8.5105620468194758795e-816j)  +/-  (2.38e-52, 5.64e-165j)
| (0.004783536555319381045 - 6.4137870001977551129e-814j)  +/-  (2.4e-52, 5.69e-165j)
| (0.020723383186119052609 - 8.9251169497501613273e-814j)  +/-  (1.28e-52, 3.02e-165j)
| (0.017619253477651071545 + 1.2649062874215763126e-813j)  +/-  (1.97e-52, 4.66e-165j)
| (0.004783536555319381045 - 1.3881404976163985139e-814j)  +/-  (1.32e-53, 3.12e-166j)
| (0.023744293821437958856 + 1.930327246367719642e-816j)  +/-  (3.7e-54, 8.76e-167j)
| (0.014512882774771543816 + 2.551116043546936525e-815j)  +/-  (1.76e-54, 4.16e-167j)
| (0.0017088604963509650263 + 1.8272843554569467601e-814j)  +/-  (5.93e-54, 1.4e-166j)
| (0.029477308245351115913 + 4.9416044129033048066e-814j)  +/-  (9.9e-56, 2.34e-168j)
| (0.048037222658882904512 + 5.6085743775148544543e-815j)  +/-  (4.64e-57, 1.1e-169j)
| (0.011393506344486885997 - 4.1195189472744411506e-815j)  +/-  (9.26e-55, 2.19e-167j)
| (0.032236632791665027205 - 2.0150719963678927367e-815j)  +/-  (3.48e-56, 8.23e-169j)
| (0.055631999803508207492 + 1.492475639215562605e-814j)  +/-  (4.48e-58, 1.06e-170j)
| (0.032236632791665027205 - 4.3174756092453808e-814j)  +/-  (1.89e-56, 4.48e-169j)
| (0.023744293821437958856 + 6.9817631697202005845e-814j)  +/-  (1.31e-55, 3.11e-168j)
| (0.0081507848991812207039 + 1.7311660153179807261e-813j)  +/-  (1.46e-54, 3.45e-167j)
| (0.0373987947325034857 - 3.0734472751360904384e-815j)  +/-  (6.74e-58, 1.6e-170j)
| (0.020723383186119052609 + 5.5181464669397162148e-816j)  +/-  (3.43e-56, 8.12e-169j)
| (0.0081507848991812207039 + 6.8669861404834803759e-815j)  +/-  (7.54e-56, 1.79e-168j)
| (0.039793035290743862212 + 3.1255088756747533346e-814j)  +/-  (6.34e-61, 1.5e-173j)
| (0.017619253477651071545 - 1.436318391294981288e-815j)  +/-  (3.09e-56, 7.32e-169j)
| (0.029477308245351115913 + 1.4526867558716976428e-815j)  +/-  (7.67e-58, 1.82e-170j)
| (0.039793035290743862212 + 3.5846178849579433805e-815j)  +/-  (2.9e-60, 6.86e-173j)
| (0.026650092713661029661 - 5.7771241386367161834e-814j)  +/-  (1.14e-59, 2.71e-172j)
| (0.0373987947325034857 - 3.4452630916227602657e-814j)  +/-  (5.37e-62, 1.27e-174j)
| (0.034885782764645987104 + 3.8326444285403215506e-814j)  +/-  (1.9e-61, 4.49e-174j)
| (0.014512882774771543816 - 2.3266291547902157051e-813j)  +/-  (1.14e-59, 2.69e-172j)
| (0.044219641308865595579 + 4.5912261636295404983e-815j)  +/-  (1.82e-64, 4.3e-177j)
| (0.034885782764645987104 + 2.5518628166383966967e-815j)  +/-  (1.01e-61, 2.39e-174j)
| (0.042076049883697133524 - 2.8545760491720518198e-814j)  +/-  (1.25e-64, 2.96e-177j)
| (0.044219641308865595579 + 2.6222715371275343192e-814j)  +/-  (1.17e-65, 2.76e-178j)
| (0.056732581852837114168 + 1.0192829425240161406e-814j)  +/-  (6.66e-70, 1.58e-182j)
| (0.042076049883697133524 - 4.0886437656538039487e-815j)  +/-  (4.13e-65, 9.78e-178j)
| (0.051257312049126774322 + 6.6531982010004072975e-815j)  +/-  (1.03e-68, 2.45e-181j)
| (0.057017310146644013037 - 1.2345104834238544258e-814j)  +/-  (2.58e-70, 6.11e-183j)
| (0.046203032841401990932 - 2.4211429864809366598e-814j)  +/-  (4.65e-68, 1.1e-180j)
| (0.054797154957272254207 - 1.5916914617345084964e-814j)  +/-  (3.29e-70, 7.78e-183j)
| (0.053783094025116511898 + 7.7528296045723076404e-815j)  +/-  (2.44e-70, 5.77e-183j)
| (0.046203032841401990932 - 5.0974314974487025815e-815j)  +/-  (9.29e-68, 2.2e-180j)
| (0.056273933611951210319 - 9.5435707735676261245e-815j)  +/-  (6.06e-71, 1.44e-183j)
| (0.048037222658882904512 + 2.2440767198764218487e-814j)  +/-  (8.22e-70, 1.95e-182j)
| (0.049728898953217361222 - 2.0859154946284557278e-814j)  +/-  (1.34e-70, 3.17e-183j)
| (0.057115970127565464439 + 1.1586746249875303369e-814j)  +/-  (7.76e-72, 1.84e-184j)
| (0.049728898953217361222 - 6.1257336916800968334e-815j)  +/-  (4.37e-70, 1.03e-182j)
| (0.054797154957272254207 - 8.3269153391960561218e-815j)  +/-  (1.14e-71, 2.71e-184j)
| (0.056732581852837114168 + 1.3150437464777657997e-814j)  +/-  (1.44e-72, 3.41e-185j)
| (0.051257312049126774322 + 1.9439244293209872979e-814j)  +/-  (6.16e-73, 1.46e-185j)
| (0.056273933611951210319 - 1.4006826236875489501e-814j)  +/-  (7.84e-73, 1.86e-185j)
| (0.055631999803508207492 + 8.9221509277654424652e-815j)  +/-  (7.82e-73, 1.85e-185j)
| (0.052605634749807609177 - 7.1952488295098064084e-815j)  +/-  (1.22e-72, 2.9e-185j)
| (0.057017310146644013037 - 1.0871764174687170676e-814j)  +/-  (3.01e-73, 7.12e-186j)
| (0.053783094025116511898 + 1.6991690943717900722e-814j)  +/-  (1.52e-74, 3.62e-187j)
| (0.052605634749807609177 - 1.8158903713319359123e-814j)  +/-  (1.43e-74, 3.38e-187j)
