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 35
-------------------------------------------------
Trying to find an order 35 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^55 - 1617450184723481142500351533465/1439353401094042506073400538*t^53 + 9663934114002430438277674755070690/16552564112581488819844106187*t^51 - 22633109901028635914954758723878486925/121385470158930918012190112038*t^49 + 2491591485032028572290906354458582832750/60692735079465459006095056019*t^47 - 402049150562645566158491411333387844418405/60692735079465459006095056019*t^45 + 49345758110173372634578063992419258637220800/60692735079465459006095056019*t^43 - 4719177675869805105024352751949539179055427075/60692735079465459006095056019*t^41 + 15538859908128931782190513483695390027430543875/2638814568672411261134567653*t^39 - 3939363320495794918677510590355611204578777401375/11035042741720992546562737458*t^37 + 1058782433245751897171728823700620246636962463263050/60692735079465459006095056019*t^35 - 7612864963204456785755498292498142457542189610722125/11035042741720992546562737458*t^33 + 121993305180820915336004122616873131343236643583595500/5517521370860496273281368729*t^31 - 137660862402977457190806975134696428701031553336733750/239892233515673751012233423*t^29 + 66358062640606501239826195052424863437618936737973890000/5517521370860496273281368729*t^27 - 1117547717070481876104509564317006400082140250823212783750/5517521370860496273281368729*t^25 + 15016105071263584677822643565149572674790319435072049634375/5517521370860496273281368729*t^23 - 13864072992769955596811346351531959554334642607145639603125/479784467031347502024466846*t^21 + 57435153276329142662409125233846891688805161142571409718750/239892233515673751012233423*t^19 - 730764101697366605018505203633836194519293057643132147984375/479784467031347502024466846*t^17 + 1747806276517156098042662907120883510998470372377928440443750/239892233515673751012233423*t^15 - 6117473506340718840308388013001127194412665668651164946640625/239892233515673751012233423*t^13 + 15107528218921386227929387554977402651608523905650771251250000/239892233515673751012233423*t^11 - 25037541456114778088123192160974200278311805698116148137734375/239892233515673751012233423*t^9 + 25895722170111905470748617607703816783467729776453937816484375/239892233515673751012233423*t^7 - 29840586116328757156238987596946094053035661541468939677109375/479784467031347502024466846*t^5 + 3915027382764580455728528471514214492642607868506061808593750/239892233515673751012233423*t^3 - 590723060430682154443963092740687252745393152679878698828125/479784467031347502024466846*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:
| (-7.3140272709262398342 - 4.103622823892303134e-845j)  +/-  (1.22e-241, 1.22e-241j)
| (11.406884301310775369 + 4.3221265494710959678e-847j)  +/-  (4.93e-245, 4.93e-245j)
| (-9.2931561110346752698 - 1.850572998435250965e-848j)  +/-  (5.44e-243, 5.44e-243j)
| (-7.6190485416797582914 - 7.6904077968232601577e-847j)  +/-  (8.35e-242, 8.35e-242j)
| (12.347305685041164935 + 1.1367391108733658995e-850j)  +/-  (2.79e-246, 2.79e-246j)
| (-5.5787388058932011527 - 6.4058014791616055855e-848j)  +/-  (7.03e-243, 7.03e-243j)
| (5.5787388058932011527 + 1.9421532058593033405e-846j)  +/-  (6.86e-243, 6.86e-243j)
| (-2.0982869532692753804 - 4.1747103138144197469e-859j)  +/-  (2.96e-248, 2.96e-248j)
| (9.2931561110346752698 + 9.6132909029042252569e-853j)  +/-  (5.45e-243, 5.45e-243j)
| (-8.1305093064777550817 + 4.5885394865310458825e-859j)  +/-  (3.33e-242, 3.33e-242j)
| (-12.347305685041164935 + 5.5528980720623815446e-863j)  +/-  (2.72e-246, 2.72e-246j)
| (6.9860602978313131489 - 1.4750089737110635266e-857j)  +/-  (7.51e-242, 7.51e-242j)
| (-4.7345813340460553439 - 3.407259828372609839e-869j)  +/-  (1.14e-243, 1.14e-243j)
| (-9.9331317886931566762 + 1.1428550636238018353e-870j)  +/-  (1.58e-243, 1.58e-243j)
| (-2.8234372923909522152 - 1.324020894082313156e-872j)  +/-  (1.27e-246, 1.27e-246j)
| (3.5606526039428800276 - 2.7567844118324051966e-869j)  +/-  (2.98e-245, 2.98e-245j)
| (3.9439673506573162603 - 9.0065062182428149899e-869j)  +/-  (1.19e-244, 1.19e-244j)
| (-5.1457642070264283228 - 8.1952898259880328789e-875j)  +/-  (3.11e-243, 3.11e-243j)
| (-10.628008963883542656 - 1.8074594032561642139e-875j)  +/-  (3.56e-244, 3.56e-244j)
| (7.6190485416797582914 - 4.849037116008025209e-872j)  +/-  (8.63e-242, 8.63e-242j)
| (1.7452473208141267149 - 5.0350877254914954809e-896j)  +/-  (3.49e-249, 3.49e-249j)
| (10.628008963883542656 - 1.5948345002626169602e-888j)  +/-  (3.67e-244, 3.67e-244j)
| (5.1457642070264283228 + 2.0038329776839479049e-899j)  +/-  (2.82e-243, 2.82e-243j)
| (6.0352749160261158348 - 2.001309421926050502e-909j)  +/-  (1.36e-242, 1.36e-242j)
| (9.9331317886931566762 - 9.3205102753340991971e-919j)  +/-  (1.58e-243, 1.58e-243j)
| (-11.406884301310775369 - 1.0185107605329895878e-919j)  +/-  (4.88e-245, 4.88e-245j)
| (1.0429453488027510315 - 1.8726894062872167179e-926j)  +/-  (2.97e-251, 2.97e-251j)
| (-6.9860602978313131489 + 9.4364292502587203273e-916j)  +/-  (7.45e-242, 7.45e-242j)
| (3.1890148165533894149 + 1.0853105768290325515e-918j)  +/-  (6.68e-246, 6.68e-246j)
| (-0.69360444664914155551 - 3.3816383708642216778e-932j)  +/-  (1.88e-252, 1.88e-252j)
| (-3.9439673506573162603 + 1.3871254938449832858e-923j)  +/-  (1.2e-244, 1.2e-244j)
| (2.8234372923909522152 - 1.1506670048130475081e-922j)  +/-  (1.26e-246, 1.26e-246j)
| (-8.6940719115821442661 - 3.7804821796662751378e-920j)  +/-  (1.42e-242, 1.42e-242j)
| (4.3361579251525951707 - 2.9028868001718812145e-921j)  +/-  (4.25e-244, 4.25e-244j)
| (-2.4586636111723677513 + 2.7935433957137730963e-930j)  +/-  (1.99e-247, 1.99e-247j)
| (-4.3361579251525951707 - 1.112129427131588397e-926j)  +/-  (4.06e-244, 4.06e-244j)
| (2.4586636111723677513 - 3.5735018826030512991e-930j)  +/-  (2e-247, 2e-247j)
| (-6.5105901570136544864 - 6.4450011686592601798e-924j)  +/-  (3.1e-242, 3.1e-242j)
| (-6.0352749160261158348 + 4.0503838469989316499e-926j)  +/-  (1.42e-242, 1.42e-242j)
| (-1.0429453488027510315 + 1.4705648230586843822e-934j)  +/-  (3.03e-251, 3.03e-251j)
| (-1.7452473208141267149 - 2.8629319228837443267e-932j)  +/-  (3.35e-249, 3.35e-249j)
| (2.0982869532692753804 - 1.2030371189291380911e-931j)  +/-  (3.01e-248, 3.01e-248j)
| (8.6940719115821442661 + 2.8838525476928466852e-924j)  +/-  (1.47e-242, 1.47e-242j)
| (-3.1890148165533894149 - 2.1290700244629058429e-934j)  +/-  (7.2e-246, 7.2e-246j)
| (4.7345813340460553439 - 8.5698741962438155322e-930j)  +/-  (1.14e-243, 1.14e-243j)
| (0.69360444664914155551 - 7.540734196272255876e-951j)  +/-  (1.67e-252, 1.67e-252j)
| (1.9958875488723162185e-964 - 5.5434902014549567846e-964j)  +/-  (3.24e-962, 3.24e-962j)
| (1.3945402824482059962 - 6.3765421144378724193e-948j)  +/-  (3.5e-250, 3.5e-250j)
| (8.1305093064777550817 + 6.5593400782899390676e-939j)  +/-  (3.69e-242, 3.69e-242j)
| (-3.5606526039428800276 + 7.2687300255305287119e-950j)  +/-  (2.85e-245, 2.85e-245j)
| (-0.34696415708135592797 + 2.6070691374075572793e-958j)  +/-  (9.95e-254, 9.95e-254j)
| (6.5105901570136544864 + 9.2610491873381511197e-957j)  +/-  (3e-242, 3e-242j)
| (7.3140272709262398342 + 2.125348872698026575e-976j)  +/-  (1.15e-241, 1.15e-241j)
| (-1.3945402824482059962 + 2.5363981319221019389e-986j)  +/-  (3.64e-250, 3.64e-250j)
| (0.34696415708135592797 + 3.9809816023541490332e-988j)  +/-  (9.95e-254, 9.95e-254j)
-------------------------------------------------
The weights are:
| (1.97330709582227766e-13 - 4.2612210694573595884e-857j)  +/-  (2.8e-63, 8.16e-183j)
| (1.861673664813588246e-29 - 1.0324395512101166766e-868j)  +/-  (7.1e-75, 2.07e-194j)
| (4.3493993153775138142e-20 - 8.1274334067344850843e-864j)  +/-  (1.44e-69, 4.2e-189j)
| (4.4921869099452936958e-14 - 3.5360544312685066887e-858j)  +/-  (1.73e-64, 5.06e-184j)
| (3.3991258405713110724e-34 + 1.4963969869758445375e-871j)  +/-  (2.01e-77, 5.85e-197j)
| (3.0992918503522336964e-08 - 1.6053069229902450833e-854j)  +/-  (2.72e-59, 7.93e-179j)
| (3.0992918503522336964e-08 - 2.422766577899172414e-853j)  +/-  (3.49e-61, 1.02e-180j)
| (0.015735024071325612539 + 3.0000289480299796311e-850j)  +/-  (1.09e-40, 3.19e-160j)
| (4.3493993153775138142e-20 + 1.0869355790653213895e-862j)  +/-  (1.04e-71, 3.03e-191j)
| (9.6042195657692018625e-16 + 1.7252911455571762301e-860j)  +/-  (1.14e-66, 3.33e-186j)
| (3.3991258405713110724e-34 - 3.7544734318083458318e-872j)  +/-  (2.05e-78, 5.98e-198j)
| (4.5468149975508194277e-12 - 2.430766799627662121e-856j)  +/-  (2.21e-67, 6.45e-187j)
| (2.1808243347899378731e-06 - 2.5279893647677469195e-853j)  +/-  (1.88e-58, 5.47e-178j)
| (9.9528830968128129488e-23 + 2.2187153145569749441e-865j)  +/-  (1.97e-72, 5.75e-192j)
| (0.0027056014553009849006 + 6.6945035236511168251e-851j)  +/-  (1.5e-50, 4.38e-170j)
| (0.00026578092261612675746 + 3.4322472648499564815e-851j)  +/-  (1.08e-56, 3.14e-176j)
| (6.498331618765030841e-05 - 1.3334503818451462657e-851j)  +/-  (2e-58, 5.84e-178j)
| (2.9883453174911193781e-07 + 6.7243552425502526216e-854j)  +/-  (2.1e-60, 6.11e-180j)
| (8.6387586395733569428e-26 - 3.2083658867091838198e-867j)  +/-  (8.77e-75, 2.56e-194j)
| (4.4921869099452936958e-14 - 7.8909589198235024222e-858j)  +/-  (8.53e-71, 2.49e-190j)
| (0.030510172033862897523 - 9.370920249120133186e-850j)  +/-  (1.15e-48, 3.36e-168j)
| (8.6387586395733569428e-26 + 1.9238164847109991869e-866j)  +/-  (1.18e-77, 3.45e-197j)
| (2.9883453174911193781e-07 + 7.6027698231709373003e-853j)  +/-  (1.04e-64, 3.03e-184j)
| (2.2955372049984693974e-09 - 2.1709967753065641512e-854j)  +/-  (3.46e-67, 1.01e-186j)
| (9.9528830968128129488e-23 - 1.7955231439349199453e-864j)  +/-  (2.07e-76, 6.03e-196j)
| (1.861673664813588246e-29 + 2.1469768524238529909e-869j)  +/-  (8.74e-80, 2.55e-199j)
| (0.081304815222204388598 - 1.7808563299312492561e-849j)  +/-  (1.16e-48, 3.38e-168j)
| (4.5468149975508194277e-12 + 1.0182543731485694574e-856j)  +/-  (1.69e-69, 4.94e-189j)
| (0.00090656549651635935687 - 8.0440905504208826186e-851j)  +/-  (5.44e-61, 1.59e-180j)
| (0.10899845651206244812 + 1.7432880459342473261e-849j)  +/-  (4.4e-50, 1.28e-169j)
| (6.498331618765030841e-05 - 3.1751819566758978721e-852j)  +/-  (5.25e-64, 1.53e-183j)
| (0.0027056014553009849006 + 1.6917525842712584833e-850j)  +/-  (2.18e-60, 6.36e-180j)
| (8.9483673696741866396e-18 + 6.4675298821032368697e-863j)  +/-  (1.5e-73, 4.37e-193j)
| (1.3023014861877955531e-05 + 4.939198686803165371e-852j)  +/-  (4.59e-65, 1.34e-184j)
| (0.007061467576438205613 - 1.481450428279799143e-850j)  +/-  (1.92e-60, 5.59e-180j)
| (1.3023014861877955531e-05 + 9.2970286810369832025e-853j)  +/-  (3.81e-65, 1.11e-184j)
| (0.007061467576438205613 - 3.2644989140595479571e-850j)  +/-  (2.2e-61, 6.43e-181j)
| (1.1995779416518863874e-10 - 2.3676183367868184226e-856j)  +/-  (9.66e-70, 2.82e-189j)
| (2.2955372049984693974e-09 + 7.4090165703431329944e-856j)  +/-  (6.07e-69, 1.77e-188j)
| (0.081304815222204388598 - 1.2945646851417398509e-849j)  +/-  (1.54e-59, 4.49e-179j)
| (0.030510172033862897523 - 5.4404141007242268638e-850j)  +/-  (2.66e-61, 7.77e-181j)
| (0.015735024071325612539 + 5.8202369134751299923e-850j)  +/-  (1.36e-62, 3.96e-182j)
| (8.9483673696741866396e-18 - 5.0058911676264501583e-861j)  +/-  (7.34e-79, 2.14e-198j)
| (0.00090656549651635935687 - 2.7448654281280898021e-851j)  +/-  (5.43e-66, 1.58e-185j)
| (2.1808243347899378731e-06 - 1.8185821086891903543e-852j)  +/-  (1.28e-69, 3.72e-189j)
| (0.10899845651206244812 + 2.1526223679400722781e-849j)  +/-  (3.83e-63, 1.12e-182j)
| (0.1385573949408836191 + 2.3485787872664543953e-849j)  +/-  (2.37e-63, 6.9e-183j)
| (0.053009622551052080687 + 1.3524020132956495222e-849j)  +/-  (1.17e-63, 3.4e-183j)
| (9.6042195657692018625e-16 + 2.0192439308039186294e-859j)  +/-  (7.26e-78, 2.12e-197j)
| (0.00026578092261612675746 + 9.922091842463526134e-852j)  +/-  (1.37e-68, 4.01e-188j)
| (0.13014327728505947936 - 2.1260864885092308675e-849j)  +/-  (1.98e-65, 5.78e-185j)
| (1.1995779416518863874e-10 + 1.7508451071054036223e-855j)  +/-  (1.13e-74, 3.29e-194j)
| (1.97330709582227766e-13 + 5.8120161738559060036e-857j)  +/-  (6.02e-76, 1.76e-195j)
| (0.053009622551052080687 + 8.7985196395737303989e-850j)  +/-  (9.26e-68, 2.87e-187j)
| (0.13014327728505947936 - 2.3618466237163710698e-849j)  +/-  (2.82e-67, 7.52e-187j)
