Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^33 - 108486669455500322/107745194932861*t^31 + 11996350518445808505/107745194932861*t^29 - 53111919992551954695/7430703098818*t^27 + 4408636421389309466175/14861406197636*t^25 - 249402111805931094471825/29722812395272*t^23 + 9879061282851902684367825/59445624790544*t^21 - 277250005536611326555210875/118891249581088*t^19 + 5517489689061351613884397125/237782499162176*t^17 - 77199047703306501408950889375/475564998324352*t^15 + 745738304438368740184977666375/951129996648704*t^13 - 4828105038488863528629612505125/1902259993297408*t^11 + 20021134625234264956426340473125/3804519986594816*t^9 - 49606489358938814972216188516875/7609039973189632*t^7 + 65654755018151036636108382046875/15218079946379264*t^5 - 37933183998595900542594987545625/30436159892758528*t^3 + 3009049811102291561979786286875/30436159892758528*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: 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:
| (7.1441996160033135299 + 1.0892458926713300012e-449j)  +/-  (1.47e-121, 1.47e-121j)
| (5.3001866502117438451 + 1.0140304952591423383e-453j)  +/-  (7.85e-120, 7.85e-120j)
| (-6.4298913738319696109 + 2.8223961214864438467e-462j)  +/-  (1.14e-120, 1.14e-120j)
| (-3.4543174185826907615 - 1.342741192013956619e-460j)  +/-  (3.93e-120, 3.93e-120j)
| (-7.1441996160033135299 - 1.5319737637114215495e-462j)  +/-  (1.21e-121, 1.21e-121j)
| (4.335472524247692012 + 5.5952938296997984444e-460j)  +/-  (9.96e-120, 9.96e-120j)
| (6.4298913738319696109 - 2.8703910811878488437e-467j)  +/-  (1.17e-120, 1.17e-120j)
| (5.834656399121053786 - 5.0328330536304973294e-466j)  +/-  (3.79e-120, 3.79e-120j)
| (-5.834656399121053786 + 3.9268212329430954781e-466j)  +/-  (3.8e-120, 3.8e-120j)
| (-5.3001866502117438451 + 1.475209207056219184e-466j)  +/-  (7.47e-120, 7.47e-120j)
| (1.4490537123043727789 - 1.4398189481478234225e-469j)  +/-  (3.32e-123, 3.32e-123j)
| (-2.6251182723726196433 + 1.1559462221689649411e-469j)  +/-  (4.63e-121, 4.63e-121j)
| (3.0344180708957271791 + 2.6631503694378375393e-468j)  +/-  (1.48e-120, 1.48e-120j)
| (-1.8330080056269856077 - 3.0813979728380792005e-476j)  +/-  (2.25e-122, 2.25e-122j)
| (3.4543174185826907615 + 8.2484497843012788725e-473j)  +/-  (3.93e-120, 3.93e-120j)
| (0.7071067811865475244 + 1.3467290103812854278e-484j)  +/-  (3.56e-125, 3.56e-125j)
| (2.224940995194667116 + 6.4562515854910092604e-482j)  +/-  (1.21e-121, 1.21e-121j)
| (-4.8042662549817291715 - 2.6195322870075522123e-486j)  +/-  (1.01e-119, 1.01e-119j)
| (-1.0734675492625714095 - 6.2061240322957279515e-493j)  +/-  (3.56e-124, 3.56e-124j)
| (-4.335472524247692012 - 1.8503885241057854267e-487j)  +/-  (1.01e-119, 1.01e-119j)
| (3.8869772719765532402 - 2.0444572235397791069e-492j)  +/-  (7.07e-120, 7.07e-120j)
| (0.35020536149120907853 + 6.268217334745982725e-504j)  +/-  (3.42e-126, 3.42e-126j)
| (4.8042662549817291715 + 2.8843704938144932483e-502j)  +/-  (1.08e-119, 1.08e-119j)
| (-1.4490537123043727789 - 2.1371809142909215317e-510j)  +/-  (3.38e-123, 3.38e-123j)
| (-3.8869772719765532402 + 6.4804826095097496227e-509j)  +/-  (6.93e-120, 6.93e-120j)
| (-2.224940995194667116 - 6.4403608165071774597e-511j)  +/-  (1.1e-121, 1.1e-121j)
| (4.8285049087315801696e-520 - 8.312759206462698271e-521j)  +/-  (1.62e-518, 1.62e-518j)
| (2.6251182723726196433 - 6.8668979776935111137e-512j)  +/-  (4.52e-121, 4.52e-121j)
| (-3.0344180708957271791 - 1.0392248814313094826e-514j)  +/-  (1.42e-120, 1.42e-120j)
| (-0.7071067811865475244 + 2.7823890415656105239e-519j)  +/-  (3.04e-125, 3.04e-125j)
| (-0.35020536149120907853 - 4.8295336063485692356e-520j)  +/-  (3.42e-126, 3.42e-126j)
| (1.8330080056269856077 + 4.9272766618530664894e-517j)  +/-  (2.26e-122, 2.26e-122j)
| (1.0734675492625714095 + 1.3662169358206503545e-518j)  +/-  (3.92e-124, 3.92e-124j)
-------------------------------------------------
The weights are:
| (3.1647497330877845593e-23 - 3.4998150800490512568e-471j)  +/-  (2.37e-39, 1.1e-98j)
| (1.8243626802259243966e-13 - 9.9495062301564460828e-466j)  +/-  (2.62e-35, 1.22e-94j)
| (3.9961683471027803655e-19 - 1.6195438171281826983e-470j)  +/-  (4.17e-39, 1.94e-98j)
| (1.5796100667128964611e-06 - 7.9044932477206709146e-464j)  +/-  (1.16e-31, 5.39e-91j)
| (3.1647497330877845593e-23 + 1.2245304810331430558e-472j)  +/-  (1.34e-40, 6.22e-100j)
| (1.7738350010639430359e-09 - 2.1393357680025356874e-464j)  +/-  (1.45e-34, 6.76e-94j)
| (3.9961683471027803655e-19 + 2.6126859592946625812e-469j)  +/-  (2.93e-39, 1.36e-98j)
| (5.1827068095070961593e-16 - 1.8119212981155102978e-467j)  +/-  (6.57e-38, 3.06e-97j)
| (5.1827068095070961593e-16 + 6.757296029352133099e-469j)  +/-  (9.3e-40, 4.32e-99j)
| (1.8243626802259243966e-13 - 1.461947337391485574e-467j)  +/-  (5.12e-39, 2.38e-98j)
| (0.026252392571733857364 + 4.6881928743916071016e-461j)  +/-  (1.1e-27, 5.12e-87j)
| (0.0002320384041750508841 - 1.3406419308048664257e-462j)  +/-  (2.94e-33, 1.37e-92j)
| (2.343640692864656392e-05 + 1.3877834084179232701e-462j)  +/-  (1.41e-34, 6.58e-94j)
| (0.0076034478471017272155 - 1.1339753441511879022e-461j)  +/-  (3.49e-31, 1.62e-90j)
| (1.5796100667128964611e-06 - 3.9825021828983022495e-463j)  +/-  (1.2e-35, 5.57e-95j)
| (0.1237088619135879007 + 1.1666282092289321172e-460j)  +/-  (1.24e-29, 5.76e-89j)
| (0.0015818277363499173543 + 1.0730046676422207011e-461j)  +/-  (8.33e-33, 3.88e-92j)
| (2.5679114882924647723e-11 + 1.9996858242238120093e-466j)  +/-  (2.97e-39, 1.38e-98j)
| (0.066144446749521115681 - 5.1896332450796531739e-461j)  +/-  (5.23e-30, 2.43e-89j)
| (1.7738350010639430359e-09 - 1.9205117671770791112e-465j)  +/-  (1.03e-38, 4.78e-98j)
| (6.8119377809733200858e-08 + 9.8334904682532380409e-464j)  +/-  (1.13e-37, 5.28e-97j)
| (0.17603179101979988716 - 1.4501220000948128811e-460j)  +/-  (3.89e-32, 1.81e-91j)
| (2.5679114882924647723e-11 + 4.6650261375761512025e-465j)  +/-  (1.85e-39, 8.59e-99j)
| (0.026252392571733857364 + 2.6139250026987842449e-461j)  +/-  (6.73e-34, 3.13e-93j)
| (6.8119377809733200858e-08 + 1.3791596072171175887e-464j)  +/-  (1.68e-38, 7.79e-98j)
| (0.0015818277363499173543 + 4.225052457116737323e-462j)  +/-  (5.16e-36, 2.4e-95j)
| (0.19684021564332060711 + 1.4949624779881047967e-460j)  +/-  (3.22e-34, 1.5e-93j)
| (0.0002320384041750508841 - 4.1544433232072578091e-462j)  +/-  (2.86e-37, 1.34e-96j)
| (2.343640692864656392e-05 + 3.5813558567519658872e-463j)  +/-  (2.17e-37, 1.01e-96j)
| (0.1237088619135879007 + 8.8223316856521424446e-461j)  +/-  (4.05e-35, 1.88e-94j)
| (0.17603179101979988716 - 1.2635131425458784145e-460j)  +/-  (4.98e-35, 2.32e-94j)
| (0.0076034478471017272155 - 2.4037098541853140878e-461j)  +/-  (5.71e-37, 2.85e-96j)
| (0.066144446749521115681 - 7.9588154227894778713e-461j)  +/-  (3.99e-36, 1.66e-95j)
