Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 29
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 3818583499171213/8675427718359*t^29 + 731427901189014673/8675427718359*t^27 - 2979961192200516797/321312137717*t^25 + 209280110943647750825/321312137717*t^23 - 9870194503096191138875/321312137717*t^21 + 320278538735533213010175/321312137717*t^19 - 379414632680613946491075/16911165143*t^17 + 5899723735921362524902725/16911165143*t^15 - 62409651689843359527000375/16911165143*t^13 + 436715706392712418855057875/16911165143*t^11 - 1933180648023233166997564125/16911165143*t^9 + 5048348292248712719159516625/16911165143*t^7 - 6941557496075557283373319875/16911165143*t^5 + 4091493448392391333261344375/16911165143*t^3 - 644946308489019778536920625/16911165143*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:
| (2.0857745086766090621 - 3.3920073517182368221e-519j)  +/-  (7.07e-251, 7.07e-251j)
| (-9.725572211045843647 + 9.7102600470484766997e-520j)  +/-  (2.15e-249, 2.15e-249j)
| (-8.7024268764774537693 - 4.6468925680408549265e-536j)  +/-  (1.8e-248, 1.8e-248j)
| (3.8201328449633061619 - 1.9530553530012042486e-543j)  +/-  (9.5e-249, 9.5e-249j)
| (5.695164627605721852 + 1.1441216920634814138e-541j)  +/-  (8.35e-248, 8.35e-248j)
| (9.725572211045843647 + 1.9997591117244990161e-544j)  +/-  (2.14e-249, 2.14e-249j)
| (8.7024268764774537693 + 6.5706942860006616649e-544j)  +/-  (1.73e-248, 1.73e-248j)
| (4.4259073167903750584 + 8.5626227303360965292e-550j)  +/-  (2.58e-248, 2.58e-248j)
| (-6.3693745544479986365 + 2.1606294907227392644e-561j)  +/-  (1.19e-247, 1.19e-247j)
| (3.2291766639290440127 - 8.2540695493115709311e-576j)  +/-  (2.23e-249, 2.23e-249j)
| (-7.8489624660612763905 - 2.3258293514765152915e-592j)  +/-  (5.49e-248, 5.49e-248j)
| (-7.0818625133391223803 + 6.6868858958031245236e-621j)  +/-  (1.02e-247, 1.02e-247j)
| (0.48930618181385580703 - 8.9470225824722015107e-638j)  +/-  (8.1e-254, 8.1e-254j)
| (-4.4259073167903750584 - 7.3273797165665496808e-653j)  +/-  (2.51e-248, 2.51e-248j)
| (-3.2291766639290440127 + 3.2627899535884943819e-682j)  +/-  (2.45e-249, 2.45e-249j)
| (1 + 1.508014120205026352e-697j)  +/-  (1.05e-252, 1.05e-252j)
| (-5.0494665526261427375 + 3.6996275139511045928e-708j)  +/-  (5.88e-248, 5.88e-248j)
| (-5.695164627605721852 + 1.1494768901386414795e-726j)  +/-  (8.63e-248, 8.63e-248j)
| (-2.6512342966716127918 - 1.1351388371198968195e-732j)  +/-  (4.44e-250, 4.44e-250j)
| (-1.5340601980703799201 - 4.4830282277805152541e-736j)  +/-  (1.17e-251, 1.17e-251j)
| (2.6512342966716127918 - 8.124402544557812134e-738j)  +/-  (5.08e-250, 5.08e-250j)
| (5.0494665526261427375 + 2.1336354661068475508e-747j)  +/-  (5.24e-248, 5.24e-248j)
| (7.0818625133391223803 + 8.530476923902103471e-756j)  +/-  (1e-247, 1e-247j)
| (6.3693745544479986365 - 1.3842571029269306215e-758j)  +/-  (1.28e-247, 1.28e-247j)
| (7.8961997221952032787e-767 + 3.6344778115865319355e-766j)  +/-  (1.15e-764, 1.15e-764j)
| (7.8489624660612763905 + 4.9397319338339010009e-759j)  +/-  (5.21e-248, 5.21e-248j)
| (1.5340601980703799201 - 2.1122985179704218734e-762j)  +/-  (1.07e-251, 1.07e-251j)
| (-2.0857745086766090621 + 6.5777162263355691952e-762j)  +/-  (7.85e-251, 7.85e-251j)
| (-0.48930618181385580703 - 4.0112200704846373948e-768j)  +/-  (9.46e-254, 9.46e-254j)
| (-1 + 3.8105164983704646061e-764j)  +/-  (1.04e-252, 1.04e-252j)
| (-3.8201328449633061619 + 6.4132842058415259677e-759j)  +/-  (9.78e-249, 9.78e-249j)
-------------------------------------------------
The weights are:
| (0.025329350915519978804 + 1.214295550917727414e-520j)  +/-  (4.83e-72, 2.8e-197j)
| (1.3570975721916379206e-21 - 4.0805057887971310836e-532j)  +/-  (2.08e-92, 1.21e-217j)
| (1.3110639267256284644e-17 + 4.8991970563792072573e-530j)  +/-  (5.5e-91, 3.19e-216j)
| (0.0001616849214915868168 + 2.3572314451033560021e-522j)  +/-  (1.1e-81, 6.37e-207j)
| (2.3791996191013260547e-08 - 9.427844793549326506e-525j)  +/-  (5.12e-87, 2.97e-212j)
| (1.3570975721916379206e-21 + 6.3085792737962315371e-532j)  +/-  (1.96e-94, 1.14e-219j)
| (1.3110639267256284644e-17 - 7.9879554931043681664e-530j)  +/-  (6.13e-93, 3.56e-218j)
| (1.3661720230160406263e-05 - 4.4290089213764905508e-523j)  +/-  (7.59e-85, 4.4e-210j)
| (4.2772298987880134624e-10 - 4.8435036413695078221e-526j)  +/-  (4.47e-91, 2.59e-216j)
| (0.0012681901806394284325 - 1.1660062774172651292e-521j)  +/-  (7.96e-83, 4.62e-208j)
| (1.3425175702065564868e-14 - 1.8839429816375800295e-528j)  +/-  (3.93e-93, 2.28e-218j)
| (3.7791892832680971485e-12 + 3.7875969230066181265e-527j)  +/-  (3.08e-92, 1.78e-217j)
| (0.17630427992593597244 - 2.7331840781577193633e-520j)  +/-  (2.08e-82, 1.21e-207j)
| (1.3661720230160406263e-05 + 1.5916731434659520257e-523j)  +/-  (9.61e-90, 5.57e-215j)
| (0.0012681901806394284325 + 2.5084220851887065687e-522j)  +/-  (4.59e-88, 2.66e-213j)
| (0.12660716005726576324 + 2.7801009718350361831e-520j)  +/-  (1.59e-82, 9.22e-208j)
| (7.3486956512254267941e-07 - 2.9741049876183426021e-524j)  +/-  (8.52e-91, 4.94e-216j)
| (2.3791996191013260547e-08 + 4.3733499548684340731e-525j)  +/-  (1.38e-91, 8e-217j)
| (0.0067884215696268717132 - 7.7293990000559459343e-522j)  +/-  (5.5e-88, 3.19e-213j)
| (0.066883993225240786238 - 4.8013027732887802155e-521j)  +/-  (6.47e-86, 3.75e-211j)
| (0.0067884215696268717132 + 6.4751255363889946335e-521j)  +/-  (1.95e-88, 1.13e-213j)
| (7.3486956512254267941e-07 + 7.1603107622535677961e-524j)  +/-  (3.43e-93, 1.99e-218j)
| (3.7791892832680971485e-12 - 6.9501005144761424522e-527j)  +/-  (1.29e-97, 7.5e-223j)
| (4.2772298987880134624e-10 + 9.5603102225152038382e-526j)  +/-  (1.79e-96, 1.04e-221j)
| (0.19328499678194504183 + 2.3865058998713299776e-520j)  +/-  (2.75e-90, 1.58e-215j)
| (1.3425175702065564868e-14 + 3.2475911188633369133e-528j)  +/-  (5.95e-99, 3.45e-224j)
| (0.066883993225240786238 - 3.150167049160122902e-520j)  +/-  (6.61e-91, 3.81e-216j)
| (0.025329350915519978804 + 2.0596028992937741895e-521j)  +/-  (1.14e-92, 6.64e-218j)
| (0.17630427992593597244 - 1.6944874109118192575e-520j)  +/-  (2.59e-91, 1.49e-216j)
| (0.12660716005726576324 + 9.7821884200209742484e-521j)  +/-  (7.47e-92, 4.13e-217j)
| (0.0001616849214915868168 - 6.9223639337847667426e-523j)  +/-  (2.88e-94, 1.7e-219j)
