Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^30 - 5551889582589847/14034565486637*t^28 + 10446823022283250821/154380220353007*t^26 - 1018951218627262616475/154380220353007*t^24 + 2736181514635588869525/6712183493609*t^22 - 10219444445714530223925/610198499419*t^20 + 285672334235558196305925/610198499419*t^18 - 5466076290997159029376275/610198499419*t^16 + 71094019363512913815854625/610198499419*t^14 - 616457662947059781468859875/610198499419*t^12 + 3444381417064654515554980875/610198499419*t^10 - 11747550342411579500016337125/610198499419*t^8 + 22435126401148897969032625125/610198499419*t^6 - 20712361223497629609450174375/610198499419*t^4 + 6902164669750959186681114375/610198499419*t^2 - 344707237908050990670140625/610198499419
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (5.3520529302413262773 + 2.8390091173101611657e-301j)  +/-  (1.63e-120, 1.63e-120j)
| (9.4015298956619226129 + 5.2621782123304564188e-310j)  +/-  (6.16e-122, 6.16e-122j)
| (-9.4015298956619226129 + 2.4062852036322095987e-311j)  +/-  (5.79e-122, 5.79e-122j)
| (1.7854537750287638429 - 5.9041099547918783245e-312j)  +/-  (1.18e-123, 1.18e-123j)
| (-8.3720225445947767034 - 6.2482895501025587631e-310j)  +/-  (3.71e-121, 3.71e-121j)
| (8.3720225445947767034 + 3.3407683174977583998e-308j)  +/-  (3.8e-121, 3.8e-121j)
| (-2.3344142183389772393 - 6.3862004494458507384e-313j)  +/-  (7.34e-123, 7.34e-123j)
| (7.5136973643312424082 + 2.2027377308115009267e-310j)  +/-  (1.08e-120, 1.08e-120j)
| (-2.9005274489009084396 - 5.2108068105282589762e-316j)  +/-  (3.43e-122, 3.43e-122j)
| (4.706453851925551501 + 3.0776732463259602727e-318j)  +/-  (1.05e-120, 1.05e-120j)
| (2.3344142183389772393 - 1.0196246505951877319e-327j)  +/-  (7.37e-123, 7.37e-123j)
| (-6.027686670010465457 - 1.4454884239432267887e-324j)  +/-  (2.17e-120, 2.17e-120j)
| (-0.24514455497773425829 + 5.6289523738519758836e-333j)  +/-  (1.13e-126, 1.13e-126j)
| (-4.084932475683047787 - 1.8408370446737697227e-327j)  +/-  (5.28e-121, 5.28e-121j)
| (-5.3520529302413262773 + 7.8411334270190901211e-327j)  +/-  (1.79e-120, 1.79e-120j)
| (-6.7428406424772848546 + 1.4465450399737281499e-326j)  +/-  (2.07e-120, 2.07e-120j)
| (0.24514455497773425829 + 1.5908704479544183731e-334j)  +/-  (1.13e-126, 1.13e-126j)
| (-7.5136973643312424082 + 7.7141547133480182971e-328j)  +/-  (1.18e-120, 1.18e-120j)
| (-1.7854537750287638429 - 1.8699150968446537003e-335j)  +/-  (1.19e-123, 1.19e-123j)
| (4.084932475683047787 - 4.2736001732727394612e-333j)  +/-  (5.16e-121, 5.16e-121j)
| (2.9005274489009084396 + 3.8271410185619399671e-350j)  +/-  (3.71e-122, 3.71e-122j)
| (0.74196378430272585765 - 4.7372001121881538416e-362j)  +/-  (1.4e-125, 1.4e-125j)
| (6.7428406424772848546 + 1.5463682576819856656e-363j)  +/-  (1.94e-120, 1.94e-120j)
| (-1.2544826586349862084 - 1.8492818400437917806e-380j)  +/-  (1.41e-124, 1.41e-124j)
| (-4.706453851925551501 + 7.0082670251631074205e-377j)  +/-  (1.04e-120, 1.04e-120j)
| (6.027686670010465457 + 1.1796411882323702953e-390j)  +/-  (2.16e-120, 2.16e-120j)
| (1.2544826586349862084 - 2.2511412426815376032e-404j)  +/-  (1.43e-124, 1.43e-124j)
| (3.4837038756214692458 - 3.7504715034931141437e-406j)  +/-  (1.4e-121, 1.4e-121j)
| (-3.4837038756214692458 - 5.4231342989610634605e-414j)  +/-  (1.56e-121, 1.56e-121j)
| (-0.74196378430272585765 + 2.7588935283412744747e-423j)  +/-  (1.4e-125, 1.4e-125j)
-------------------------------------------------
The weights are:
| (1.5848443824820115628e-07 - 1.3482120857283362515e-307j)  +/-  (4.42e-32, 1.16e-91j)
| (3.028691333127769107e-20 - 1.7440579082642602753e-315j)  +/-  (2.22e-39, 5.82e-99j)
| (3.028691333127769107e-20 - 4.7869879421695005812e-316j)  +/-  (2.23e-40, 5.84e-100j)
| (0.043770329845233304175 - 2.8720843690305913652e-305j)  +/-  (2.97e-21, 7.76e-81j)
| (2.2143567116954878825e-16 + 5.4741694190460042463e-314j)  +/-  (5.1e-39, 1.33e-98j)
| (2.2143567116954878825e-16 + 2.4877043166904154038e-313j)  +/-  (1.8e-38, 4.71e-98j)
| (0.014585317840073117674 - 5.8976343012541684806e-306j)  +/-  (1e-26, 2.63e-86j)
| (1.7728179975787436202e-13 - 1.2020673626243952086e-311j)  +/-  (1.92e-37, 5.03e-97j)
| (0.0034149519107210465573 + 2.0431451894727967989e-306j)  +/-  (2.77e-29, 7.25e-89j)
| (3.9101729410229565783e-06 + 4.2977152362823564929e-307j)  +/-  (3.8e-33, 9.94e-93j)
| (0.014585317840073117674 + 1.5022332813538621768e-305j)  +/-  (2.4e-27, 6.29e-87j)
| (3.5668721245466323631e-09 - 4.8223654831300546106e-310j)  +/-  (1.85e-37, 4.83e-97j)
| (0.19026190192168223102 - 6.8345682560936597211e-305j)  +/-  (6.74e-27, 1.77e-86j)
| (5.799699361112612378e-05 + 1.4218101419429569309e-307j)  +/-  (3.26e-34, 8.54e-94j)
| (1.5848443824820115628e-07 + 4.2034222099022446893e-309j)  +/-  (1.25e-36, 3.28e-96j)
| (3.9540244420170023822e-11 + 3.9093967729366780946e-311j)  +/-  (4.2e-39, 1.1e-98j)
| (0.19026190192168223102 + 7.4907214669059806524e-305j)  +/-  (1.69e-30, 4.42e-90j)
| (1.7728179975787436202e-13 - 2.0196585170403257911e-312j)  +/-  (2.33e-40, 6.09e-100j)
| (0.043770329845233304175 + 1.4351753642094486751e-305j)  +/-  (2.93e-31, 7.67e-91j)
| (5.799699361112612378e-05 - 1.0589049841047155682e-306j)  +/-  (3.72e-37, 9.73e-97j)
| (0.0034149519107210465573 - 6.8778482015671351633e-306j)  +/-  (2.32e-35, 6.07e-95j)
| (0.15260698636074683714 - 6.576683727408149133e-305j)  +/-  (2.45e-32, 6.41e-92j)
| (3.9540244420170023822e-11 + 3.3997811201916110716e-310j)  +/-  (1.75e-41, 4.57e-101j)
| (0.094751619820247469906 - 2.935518302033072706e-305j)  +/-  (9.42e-34, 2.46e-93j)
| (3.9101729410229565783e-06 - 2.7584621064018386069e-308j)  +/-  (1.62e-38, 4.21e-98j)
| (3.5668721245466323631e-09 - 8.1223391370288905899e-309j)  +/-  (1.74e-40, 4.55e-100j)
| (0.094751619820247469906 + 4.7329525932688083258e-305j)  +/-  (3.02e-35, 7.87e-95j)
| (0.00054682304371572400951 + 2.8041589042991908644e-306j)  +/-  (2.36e-37, 6.19e-97j)
| (0.00054682304371572400951 - 5.9294836963722083629e-307j)  +/-  (1.51e-37, 3.89e-97j)
| (0.15260698636074683714 + 4.9752240363317769257e-305j)  +/-  (2.93e-35, 6.79e-95j)
