Starting with polynomial:
P : t^20 - 190*t^18 + 14535*t^16 - 581400*t^14 + 13226850*t^12 - 174594420*t^10 + 1309458150*t^8 - 5237832600*t^6 + 9820936125*t^4 - 6547290750*t^2 + 654729075
Extension levels are: 20 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : t^20 - 190*t^18 + 14535*t^16 - 581400*t^14 + 13226850*t^12 - 174594420*t^10 + 1309458150*t^8 - 5237832600*t^6 + 9820936125*t^4 - 6547290750*t^2 + 654729075
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 2921481652577027702412362575475/3006477738722676008953699127*t^49 + 1296237457590554807728338943619850/3006477738722676008953699127*t^47 - 348982152231431208016511446901179050/3006477738722676008953699127*t^45 + 63906409661983980958014834996268803000/3006477738722676008953699127*t^43 - 8457172401138633610855157923897707838440/3006477738722676008953699127*t^41 + 838878260714907891676070631182327788015950/3006477738722676008953699127*t^39 - 63846492566583416813947000675429759043675550/3006477738722676008953699127*t^37 + 3786283755056071567706189334248027915447421375/3006477738722676008953699127*t^35 - 176697093670665806239965166155744478415432578875/3006477738722676008953699127*t^33 + 6527390470355261070658765052022779825491825920900/3006477738722676008953699127*t^31 - 191382831422355964938697178794203112844203280746500/3006477738722676008953699127*t^29 + 4453247608618458117778437042152248273887956171841000/3006477738722676008953699127*t^27 - 82016307348427145199403208350870038722460097696545000/3006477738722676008953699127*t^25 + 1189302096115214890062915200682883415255193114039037500/3006477738722676008953699127*t^23 - 13470095718973311469074812965010589824142364829935897500/3006477738722676008953699127*t^21 + 117837217036864492695642637386468035173913933058524353125/3006477738722676008953699127*t^19 - 784365401785990149265692068706823603494793005064567865625/3006477738722676008953699127*t^17 + 3894598450602186289033861515399221995097005749078466031250/3006477738722676008953699127*t^15 - 14050214825901065410889427170456311793287835123686295531250/3006477738722676008953699127*t^13 + 35546357840873536391205342822398160918061147103365452900000/3006477738722676008953699127*t^11 - 60059715910581619221265671743585592451762290722509161750000/3006477738722676008953699127*t^9 + 63186980494550523898737740383000209652674758696058640593750/3006477738722676008953699127*t^7 - 37155285495985677207054228019298015131319138413574829843750/3006477738722676008953699127*t^5 + 10048369615026694281722716635370944013410801035429741953125/3006477738722676008953699127*t^3 - 769679417750370574915694903165493979565123437643879765625/3006477738722676008953699127*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:
| (10.30144790297705002 + 1.5599807254412511496e-860j)  +/-  (2.24e-245, 2.24e-245j)
| (-6.0155522378512863164 - 1.1063404442204523289e-861j)  +/-  (9.53e-244, 9.53e-244j)
| (9.545864341097949768 - 5.4485060184453545809e-861j)  +/-  (8.62e-245, 8.62e-245j)
| (-2.7601313651193058853 + 4.5855031008569682809e-872j)  +/-  (5.64e-247, 5.64e-247j)
| (3.1890148165533894149 + 1.3525539672245636061e-868j)  +/-  (2.5e-246, 2.5e-246j)
| (12.438616210018673755 - 8.1183215307469618439e-876j)  +/-  (1.55e-247, 1.55e-247j)
| (-10.30144790297705002 - 6.2074491712105056787e-876j)  +/-  (2.34e-245, 2.34e-245j)
| (-8.2210759902289213071 + 9.440912748272749913e-876j)  +/-  (4.79e-244, 4.79e-244j)
| (5.5787388058932011527 + 3.297704360426663271e-881j)  +/-  (7.71e-244, 7.71e-244j)
| (-9.545864341097949768 - 1.3469986920255170174e-897j)  +/-  (8.9e-245, 8.9e-245j)
| (-11.177966896412757097 + 6.1541713461098524774e-901j)  +/-  (3.1e-246, 3.1e-246j)
| (6.0155522378512863164 + 5.1458713940125768645e-895j)  +/-  (8.71e-244, 8.71e-244j)
| (8.2210759902289213071 - 8.7179890484922481592e-903j)  +/-  (4.4e-244, 4.4e-244j)
| (-12.438616210018673755 - 4.2997039303590289453e-908j)  +/-  (1.67e-247, 1.67e-247j)
| (-7.0485775481045367357 - 1.0635672119582214205e-904j)  +/-  (8.54e-244, 8.54e-244j)
| (-3.60784610779171663 - 4.0925449112069707957e-906j)  +/-  (1.56e-245, 1.56e-245j)
| (-2.4586636111723677513 - 4.5400446343454911492e-908j)  +/-  (1.65e-247, 1.65e-247j)
| (-8.859668773914408446 + 9.7192701033415427926e-906j)  +/-  (2.48e-244, 2.48e-244j)
| (-3.1890148165533894149 - 1.6957603803304513381e-907j)  +/-  (2.44e-246, 2.44e-246j)
| (11.177966896412757097 + 1.0161777646048308491e-906j)  +/-  (3.45e-246, 3.45e-246j)
| (-7.6190485416797582914 - 4.0001342857817335859e-905j)  +/-  (7.16e-244, 7.16e-244j)
| (3.60784610779171663 + 4.0589711788867715043e-905j)  +/-  (1.42e-245, 1.42e-245j)
| (-4.7345813340460553439 - 2.6816096488299932161e-905j)  +/-  (2.11e-244, 2.11e-244j)
| (6.5105901570136544864 + 2.540327693467882481e-903j)  +/-  (1.03e-243, 1.03e-243j)
| (-1.7452473208141267149 - 1.8205561550222599169e-918j)  +/-  (2.07e-249, 2.07e-249j)
| (-4.3018703451864706957 - 4.5561130338751017568e-912j)  +/-  (1.08e-244, 1.08e-244j)
| (8.859668773914408446 + 7.5735699257915160461e-912j)  +/-  (2.43e-244, 2.43e-244j)
| (3.9439673506573162603 - 3.6569711757588948212e-912j)  +/-  (5.19e-245, 5.19e-245j)
| (-3.9439673506573162603 - 2.3509597875916529127e-923j)  +/-  (4.73e-245, 4.73e-245j)
| (-1.335241343258781775 + 1.9004577910083500737e-930j)  +/-  (1.96e-250, 1.96e-250j)
| (1.335241343258781775 + 5.5865312624074604823e-928j)  +/-  (1.87e-250, 1.87e-250j)
| (7.0485775481045367357 - 1.1349889115139325943e-920j)  +/-  (8.77e-244, 8.77e-244j)
| (0.73093962946990448834 - 1.8787573402210543626e-942j)  +/-  (2.59e-252, 2.59e-252j)
| (-2.166995564843874653 - 3.6845335324819266058e-942j)  +/-  (3.15e-248, 3.15e-248j)
| (4.7345813340460553439 + 2.2705903683185708798e-939j)  +/-  (2.31e-244, 2.31e-244j)
| (2.166995564843874653 + 3.1287568168542347236e-952j)  +/-  (3.08e-248, 3.08e-248j)
| (5.1687937382026490725 - 6.4801866535749962382e-957j)  +/-  (4.98e-244, 4.98e-244j)
| (1.7452473208141267149 - 4.0848236939326972056e-970j)  +/-  (1.9e-249, 1.9e-249j)
| (-6.5105901570136544864 + 2.2601637995337172662e-964j)  +/-  (9.81e-244, 9.81e-244j)
| (-1.0429453488027510315 - 1.4251586829754778629e-972j)  +/-  (3.17e-251, 3.17e-251j)
| (-0.73093962946990448834 + 1.3389551219367607036e-974j)  +/-  (2.89e-252, 2.89e-252j)
| (2.7601313651193058853 - 1.0909585183684191419e-966j)  +/-  (5.53e-247, 5.53e-247j)
| (-5.1687937382026490725 + 3.5954929618579734732e-965j)  +/-  (4.92e-244, 4.92e-244j)
| (2.4586636111723677513 + 3.4278859965461968195e-969j)  +/-  (1.8e-247, 1.8e-247j)
| (-5.5787388058932011527 - 6.4415879497279706104e-968j)  +/-  (7.68e-244, 7.68e-244j)
| (-0.34696415708135592797 + 3.3125014193259752225e-980j)  +/-  (9.19e-254, 9.19e-254j)
| (1.5788892369713419587e-984 - 3.0220513445869978874e-984j)  +/-  (1.74e-982, 1.74e-982j)
| (1.0429453488027510315 + 1.0932227104225356734e-978j)  +/-  (3.18e-251, 3.18e-251j)
| (0.34696415708135592797 + 6.5125991989183735101e-980j)  +/-  (9.19e-254, 9.19e-254j)
| (4.3018703451864706957 - 2.7973356930194698213e-977j)  +/-  (1.11e-244, 1.11e-244j)
| (7.6190485416797582914 - 3.3499368167216655835e-988j)  +/-  (6.5e-244, 6.5e-244j)
-------------------------------------------------
The weights are:
| (2.8966259512290639594e-24 + 1.5244230302819578737e-881j)  +/-  (8.38e-85, 7.61e-205j)
| (2.5851870110382675202e-09 - 1.5059543944626011509e-869j)  +/-  (1.89e-74, 1.72e-194j)
| (4.661468172683653062e-21 - 1.0992960835872021053e-879j)  +/-  (2.6e-83, 2.37e-203j)
| (0.0035169475079444010459 - 1.9417391666944114583e-865j)  +/-  (5.93e-59, 5.38e-179j)
| (0.0010829681979160227955 + 1.6683047079480057854e-866j)  +/-  (2.89e-62, 2.62e-182j)
| (2.1150819532675394949e-34 + 3.8945488738084477661e-887j)  +/-  (1.7e-89, 1.54e-209j)
| (2.8966259512290639594e-24 - 5.7462949191258467752e-881j)  +/-  (3.77e-87, 3.42e-207j)
| (5.2058689038981148646e-16 + 1.2962400665697762009e-875j)  +/-  (8.89e-83, 8.08e-203j)
| (2.86590343476020497e-08 + 2.1183698081826242071e-870j)  +/-  (4.74e-76, 4.3e-196j)
| (4.661468172683653062e-21 + 5.5110885471347187693e-879j)  +/-  (8.5e-86, 7.72e-206j)
| (2.870501947397658287e-28 + 2.503766646206671911e-883j)  +/-  (1.25e-89, 1.14e-209j)
| (2.5851870110382675202e-09 - 2.3654582323450529387e-871j)  +/-  (1.52e-78, 1.38e-198j)
| (5.2058689038981148646e-16 - 1.9770623062844508598e-876j)  +/-  (2.08e-84, 1.89e-204j)
| (2.1150819532675394949e-34 - 1.1084397764058159909e-886j)  +/-  (7.27e-93, 6.6e-213j)
| (3.60410603490021283e-12 + 1.3066193942604234677e-872j)  +/-  (5.48e-82, 4.97e-202j)
| (0.0002278660902011166433 - 2.278872844421681808e-866j)  +/-  (1.22e-72, 1.11e-192j)
| (0.0042858198282112229289 + 4.5216986570267754302e-865j)  +/-  (4.62e-67, 4.19e-187j)
| (2.3752344048898965622e-18 - 3.160029968950359376e-877j)  +/-  (1.17e-85, 1.06e-205j)
| (0.0010829681979160227955 + 5.442732408574061806e-866j)  +/-  (4.13e-71, 3.75e-191j)
| (2.870501947397658287e-28 - 7.6453124565991231514e-884j)  +/-  (1.61e-93, 1.47e-213j)
| (5.7985785742659332883e-14 - 4.3059227597630699089e-874j)  +/-  (2.15e-83, 1.95e-203j)
| (0.0002278660902011166433 - 5.6896756591379418705e-867j)  +/-  (1.16e-76, 1.06e-196j)
| (2.3978640189833300961e-06 + 6.5831250289254397098e-868j)  +/-  (4.27e-78, 3.88e-198j)
| (1.2940397998548653033e-10 + 1.7483030033140874015e-872j)  +/-  (1.45e-84, 1.32e-204j)
| (0.037584558073270017359 + 7.9662718056043201646e-865j)  +/-  (2.41e-68, 2.19e-188j)
| (1.5608484845096455208e-05 - 3.013137475137893413e-867j)  +/-  (4.72e-77, 4.29e-197j)
| (2.3752344048898965622e-18 + 5.858128930511879502e-878j)  +/-  (1.78e-89, 1.62e-209j)
| (5.2497419571368781985e-05 + 2.1265197516352738807e-867j)  +/-  (2.32e-79, 2.1e-199j)
| (5.2497419571368781985e-05 + 1.0247911694251288759e-866j)  +/-  (1.97e-76, 1.79e-196j)
| (0.059928187779396892631 - 1.7101735076686889121e-864j)  +/-  (2.14e-69, 1.94e-189j)
| (0.059928187779396892631 - 1.0881332376448629174e-864j)  +/-  (7.17e-71, 6.51e-191j)
| (3.60410603490021283e-12 - 1.0252779813412041746e-873j)  +/-  (2.42e-86, 2.2e-206j)
| (0.11419952802434886227 - 2.1257614294967041891e-864j)  +/-  (1.29e-70, 1.17e-190j)
| (0.014801226632806757857 - 5.943537419895617094e-865j)  +/-  (5.35e-73, 4.86e-193j)
| (2.3978640189833300961e-06 + 7.8197844491211178703e-869j)  +/-  (4.14e-82, 3.76e-202j)
| (0.014801226632806757857 - 2.792239647957395717e-865j)  +/-  (3.95e-77, 3.59e-197j)
| (2.645215675564187692e-07 - 1.3118983005434450833e-869j)  +/-  (9.2e-83, 8.36e-203j)
| (0.037584558073270017359 + 4.3793686748914779808e-865j)  +/-  (2.71e-76, 2.46e-196j)
| (1.2940397998548653033e-10 - 4.450669938924258241e-871j)  +/-  (1.78e-85, 1.62e-205j)
| (0.058306996660842202848 + 2.6848013702321890543e-864j)  +/-  (2.34e-74, 2.12e-194j)
| (0.11419952802434886227 - 2.7148167082683124349e-864j)  +/-  (1.69e-74, 1.53e-194j)
| (0.0035169475079444010459 - 7.1920353318287145437e-866j)  +/-  (4.55e-79, 4.13e-199j)
| (2.645215675564187692e-07 - 1.7391521682215134597e-868j)  +/-  (4.2e-83, 3.81e-203j)
| (0.0042858198282112229289 + 1.8953666310099824793e-865j)  +/-  (2.66e-79, 2.41e-199j)
| (2.86590343476020497e-08 + 5.6465920630145425143e-869j)  +/-  (5.52e-84, 5.02e-204j)
| (0.14028924750904567754 + 2.6173114411640271551e-864j)  +/-  (4.52e-77, 4.1e-197j)
| (0.13141170805745173536 - 2.6737537869698168466e-864j)  +/-  (2.36e-77, 2.15e-197j)
| (0.058306996660842202848 + 1.8903953745659485258e-864j)  +/-  (3.05e-78, 2.77e-198j)
| (0.14028924750904567754 + 2.331445396627387957e-864j)  +/-  (5.54e-78, 5.04e-198j)
| (1.5608484845096455208e-05 - 4.9912208944458704698e-868j)  +/-  (4.29e-83, 3.78e-203j)
| (5.7985785742659332883e-14 + 5.0117827341321003976e-875j)  +/-  (2.91e-90, 2.72e-210j)
