Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 29
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Trying to find an order 29 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 3103716825172866549/6594497324768119*t^31 + 15967748612655295901346/164862433119202975*t^29 - 1897467523807772697847101/164862433119202975*t^27 + 11143965705436400220238176/12681725624554075*t^25 - 23027323480469799204456729/507269024982163*t^23 + 825808497622028022398820678/507269024982163*t^21 - 20767152059304545103623676801/507269024982163*t^19 + 365688963337255623544144162266/507269024982163*t^17 - 4456613667780268932301098239043/507269024982163*t^15 + 36747180195676159279411673161830/507269024982163*t^13 - 197700635846725100154623754431235/507269024982163*t^11 + 656353087944061370531188264224480/507269024982163*t^9 - 1232193814059293061364710130163355/507269024982163*t^7 + 1129618865199628027080955617840090/507269024982163*t^5 - 380249454835700665384917576888675/507269024982163*t^3 + 21319584031338563129540929715475/507269024982163*t
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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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-7.2872274272498552123 - 4.0627409450134451248e-276j)  +/-  (7.02e-120, 7.02e-120j)
| (8.8966544510669965058 - 3.1974534309311608876e-290j)  +/-  (1.05e-120, 1.05e-120j)
| (6.5801194523415497235 - 3.2665063276128743383e-288j)  +/-  (8.69e-120, 8.69e-120j)
| (-2.8949367845600435064 - 3.0436052278231263971e-288j)  +/-  (6.69e-122, 6.69e-122j)
| (-9.9134644884401455429 - 3.7865473073653900919e-290j)  +/-  (1.35e-121, 1.35e-121j)
| (-6.5801194523415497235 - 4.0931903322663393246e-300j)  +/-  (7.87e-120, 7.87e-120j)
| (9.9134644884401455429 - 1.9981512724858200906e-315j)  +/-  (1.35e-121, 1.35e-121j)
| (-5.9112991119305615564 + 2.6293423969345596273e-312j)  +/-  (7.72e-120, 7.72e-120j)
| (-8.8966544510669965058 + 1.980503642868887437e-317j)  +/-  (9.81e-121, 9.81e-121j)
| (5.271045799504011214 + 2.9188309235486561113e-327j)  +/-  (5.18e-120, 5.18e-120j)
| (-8.0488748827561512465 - 1.3627297022072387419e-327j)  +/-  (3.39e-120, 3.39e-120j)
| (4.65300577946354309 - 1.2994854016188141411e-336j)  +/-  (2.72e-120, 2.72e-120j)
| (8.0488748827561512465 - 5.0112723540860086287e-337j)  +/-  (3.57e-120, 3.57e-120j)
| (-1.2536712620079170423 - 2.0976805241717272088e-341j)  +/-  (1.66e-124, 1.66e-124j)
| (-1.7864181525800165828 - 1.3583552100370256543e-337j)  +/-  (1.38e-123, 1.38e-123j)
| (-4.65300577946354309 + 9.797885948839916178e-339j)  +/-  (2.54e-120, 2.54e-120j)
| (-3.4674439819342478733 - 1.9828187860091103289e-346j)  +/-  (2.79e-121, 2.79e-121j)
| (5.9112991119305615564 + 6.8625334391055984244e-352j)  +/-  (7.79e-120, 7.79e-120j)
| (-4.0528140145152205709 - 4.4367216160697745118e-355j)  +/-  (9.34e-121, 9.34e-121j)
| (7.2872274272498552123 + 1.471308280758472679e-359j)  +/-  (6.68e-120, 6.68e-120j)
| (4.0528140145152205709 + 1.1218725995258070743e-361j)  +/-  (8.92e-121, 8.92e-121j)
| (2.8949367845600435064 - 2.1376054300770043415e-364j)  +/-  (5.99e-122, 5.99e-122j)
| (-5.271045799504011214 - 4.6675389070486250026e-365j)  +/-  (5.02e-120, 5.02e-120j)
| (-2.3344142183389772393 - 4.1778086900192451179e-374j)  +/-  (1.15e-122, 1.15e-122j)
| (3.4674439819342478733 - 1.0142908076795360912e-374j)  +/-  (2.72e-121, 2.72e-121j)
| (1.7864181525800165828 + 1.7133733143593956376e-376j)  +/-  (1.41e-123, 1.41e-123j)
| (2.3344142183389772393 + 2.2428862490060365621e-378j)  +/-  (1.07e-122, 1.07e-122j)
| (-5.7462326696036321516e-380 + 1.3220157224942095897e-380j)  +/-  (1.95e-378, 1.95e-378j)
| (-0.2632332738020418941 - 4.5709728032614284983e-381j)  +/-  (1.97e-126, 1.97e-126j)
| (-0.74196378430272585765 - 1.8613507599455177873e-381j)  +/-  (1.42e-125, 1.42e-125j)
| (1.2536712620079170423 + 1.2627753288724983435e-379j)  +/-  (1.76e-124, 1.76e-124j)
| (0.74196378430272585765 - 4.7514691511299375264e-382j)  +/-  (1.42e-125, 1.42e-125j)
| (0.2632332738020418941 - 9.8434784577264178081e-385j)  +/-  (1.03e-126, 1.03e-126j)
-------------------------------------------------
The weights are:
| (8.5786962369386693607e-13 - 1.3643537908158253303e-287j)  +/-  (1.33e-32, 1.6e-91j)
| (2.3580864473794436155e-18 - 2.4055510322087173403e-292j)  +/-  (8.16e-36, 9.82e-95j)
| (1.084350002143718703e-10 + 3.4557063888986798296e-288j)  +/-  (9.39e-32, 1.13e-90j)
| (0.003421757906150340472 + 2.9804066201744041017e-283j)  +/-  (1.02e-21, 1.23e-80j)
| (2.131764001173272836e-22 - 1.1370524628346976538e-293j)  +/-  (8.81e-38, 1.06e-96j)
| (1.084350002143718703e-10 + 6.7771092284181936298e-287j)  +/-  (3.55e-32, 4.27e-91j)
| (2.131764001173272836e-22 + 1.7360751008893755757e-294j)  +/-  (5.97e-39, 7.19e-98j)
| (6.7316513204837171923e-09 - 3.3877797989573919742e-286j)  +/-  (2.08e-31, 2.5e-90j)
| (2.3580864473794436155e-18 + 2.4189449739204705195e-291j)  +/-  (1.14e-36, 1.38e-95j)
| (2.3220055816809653738e-07 + 2.7284083439340074024e-286j)  +/-  (5.25e-33, 6.32e-92j)
| (2.7213569846252943046e-15 - 2.1174647571995250019e-289j)  +/-  (2.61e-35, 3.14e-94j)
| (4.8288351570019947361e-06 - 1.6682130795769575179e-285j)  +/-  (3.83e-32, 4.61e-91j)
| (2.7213569846252943046e-15 + 1.0516111562357989373e-290j)  +/-  (2.02e-37, 2.43e-96j)
| (0.095172622783036758401 - 4.8006191027925382357e-282j)  +/-  (5.87e-22, 7.06e-81j)
| (0.04376978387650936692 + 2.0150436551060878536e-282j)  +/-  (1.5e-24, 1.8e-83j)
| (4.8288351570019947361e-06 - 7.5615708771577431552e-285j)  +/-  (4.32e-32, 5.2e-91j)
| (0.00056567059620787937814 - 9.9278837926885341092e-284j)  +/-  (5.27e-30, 6.34e-89j)
| (6.7316513204837171923e-09 - 3.5317139877661398542e-287j)  +/-  (2.16e-35, 2.6e-94j)
| (6.4090544817749074077e-05 + 2.9295325786980392584e-284j)  +/-  (1.3e-31, 1.56e-90j)
| (8.5786962369386693607e-13 - 2.3913772695031030231e-289j)  +/-  (2.01e-37, 2.42e-96j)
| (6.4090544817749074077e-05 + 8.3556300750119810712e-285j)  +/-  (5.85e-34, 7.04e-93j)
| (0.003421757906150340472 + 1.2856611433231371455e-283j)  +/-  (2.24e-33, 2.7e-92j)
| (2.3220055816809653738e-07 + 1.6994549317319797061e-285j)  +/-  (5.48e-35, 6.59e-94j)
| (0.01450336795712543389 - 8.0669622985382305759e-283j)  +/-  (1.47e-31, 1.76e-90j)
| (0.00056567059620787937814 - 3.526129455143379055e-284j)  +/-  (6.45e-34, 7.76e-93j)
| (0.04376978387650936692 + 1.2216006230485460002e-282j)  +/-  (6.13e-33, 7.38e-92j)
| (0.01450336795712543389 - 4.1525304229746571639e-283j)  +/-  (2.18e-33, 2.63e-92j)
| (0.038635891910920737163 + 5.4230108171481117553e-281j)  +/-  (4.04e-31, 4.96e-90j)
| (0.17217844693323715608 - 3.5974052603079390403e-281j)  +/-  (2.95e-31, 3.6e-90j)
| (0.15100124557079286308 + 1.1604746083169200297e-281j)  +/-  (8.79e-32, 1.08e-90j)
| (0.095172622783036758401 - 3.3913065136746805341e-282j)  +/-  (9.69e-33, 1.17e-91j)
| (0.15100124557079286308 + 9.4599967949178783238e-282j)  +/-  (1.1e-32, 1.27e-91j)
| (0.17217844693323715608 - 3.3465710997509405962e-281j)  +/-  (3.21e-32, 4.17e-91j)
