Starting with polynomial:
P : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Extension levels are: 9 22
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Trying to find an order 22 Kronrod extension for:
P1 : 512*t^9 - 9216*t^7 + 48384*t^5 - 80640*t^3 + 30240*t
Solvable: 1
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Ending with final polynomial:
P : 512*t^31 - 6606242868992/67229543*t^29 + 551608721062144/67229543*t^27 - 26476866606751488/67229543*t^25 + 5693787236934396000/470606801*t^23 - 117976989669986502000/470606801*t^21 + 12727192787802028800/3538397*t^19 - 7515886426041133800/208141*t^17 + 52702659478282339350/208141*t^15 - 254758197265525366875/208141*t^13 + 827120294353773795375/208141*t^11 - 1728121173748337511000/208141*t^9 + 17371983578865435716625/1665128*t^7 - 23515937379179817697125/3330256*t^5 + 3513690925793482809375/1665128*t^3 - 1174073053720687745625/6660512*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: 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
Positive weights:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-3.1909932017815276072 - 3.3042955835674843989e-473j)  +/-  (4.57e-120, 4.57e-120j)
| (-6.501936116173976778 + 1.4632268138983540877e-476j)  +/-  (4.21e-122, 4.21e-122j)
| (5.1579651128448970595 + 2.832935723700287394e-474j)  +/-  (1e-120, 1e-120j)
| (4.1020208266616855763 - 8.8574640607509192973e-474j)  +/-  (2.73e-120, 2.73e-120j)
| (5.7689949840258941231 + 2.6682760272626975104e-476j)  +/-  (3.08e-121, 3.08e-121j)
| (1.861258134558091364 + 4.4096388710903059266e-476j)  +/-  (2.73e-122, 2.73e-122j)
| (-4.1020208266616855763 + 3.7625233456707012736e-475j)  +/-  (2.89e-120, 2.89e-120j)
| (-2.2665805845318431118 + 8.9811807733329682172e-479j)  +/-  (1.99e-121, 1.99e-121j)
| (-4.6095982573464320758 - 1.4896176422197186526e-475j)  +/-  (2.01e-120, 2.01e-120j)
| (-2.9359792245332846647 - 1.6872002455972435403e-477j)  +/-  (3.54e-120, 3.54e-120j)
| (4.6095982573464320758 - 1.5055800562366363868e-475j)  +/-  (2.01e-120, 2.01e-120j)
| (2.2665805845318431118 + 6.1052911989128509869e-475j)  +/-  (2.17e-121, 2.17e-121j)
| (6.501936116173976778 - 1.2398612340582119756e-478j)  +/-  (4.52e-122, 4.52e-122j)
| (-5.7689949840258941231 - 1.4770339806841779384e-478j)  +/-  (2.79e-121, 2.79e-121j)
| (-5.1579651128448970595 + 2.3214606442539009083e-477j)  +/-  (9.95e-121, 9.95e-121j)
| (3.6261274119887884119 + 4.047607266076379619e-476j)  +/-  (3.06e-120, 3.06e-120j)
| (0.36168375132121171891 - 1.1655561881387279083e-487j)  +/-  (2.82e-126, 2.82e-126j)
| (-4.4404821126648297155e-487 - 4.2867101768903048479e-487j)  +/-  (1.91e-485, 1.91e-485j)
| (-1.4685532892166679317 + 1.1679478287412145856e-488j)  +/-  (3.49e-123, 3.49e-123j)
| (3.1909932017815276072 - 2.3392159713944684927e-487j)  +/-  (4.31e-120, 4.31e-120j)
| (1.4685532892166679317 + 1.4452347617509030453e-497j)  +/-  (3.66e-123, 3.66e-123j)
| (2.6707976262991183364 - 7.8572095388716657267e-504j)  +/-  (1.34e-120, 1.34e-120j)
| (2.9359792245332846647 + 3.3430558679394441824e-518j)  +/-  (3.65e-120, 3.65e-120j)
| (-3.6261274119887884119 - 1.1601885510138257533e-526j)  +/-  (3.48e-120, 3.48e-120j)
| (-0.72355101875283757332 - 2.5263005177251428687e-540j)  +/-  (3.59e-125, 3.59e-125j)
| (-2.6707976262991183364 + 6.5394373600983598494e-536j)  +/-  (1.18e-120, 1.18e-120j)
| (0.72355101875283757332 - 5.3266684621877035972e-542j)  +/-  (3.94e-125, 3.94e-125j)
| (1.090305078202927857 + 1.193176469148161219e-540j)  +/-  (4.58e-124, 4.58e-124j)
| (-1.090305078202927857 + 2.4061306653627843155e-540j)  +/-  (4.27e-124, 4.27e-124j)
| (-1.861258134558091364 - 1.716274797706624068e-540j)  +/-  (2.76e-122, 2.76e-122j)
| (-0.36168375132121171891 + 4.2457841132588832734e-544j)  +/-  (2.82e-126, 2.82e-126j)
-------------------------------------------------
The weights are:
| (8.3540868693055182745e-06 - 1.9474735901603172566e-477j)  +/-  (1.52e-28, 2.75e-88j)
| (2.0781204866698417041e-19 + 1.910950220553033291e-487j)  +/-  (6.13e-38, 1.11e-97j)
| (9.0459028226405565845e-13 - 9.8879006777546112349e-484j)  +/-  (1e-35, 1.81e-95j)
| (1.3640745300632248226e-08 + 2.8152891836954241608e-481j)  +/-  (2.51e-33, 4.54e-93j)
| (1.3012149103756771845e-15 + 1.7593707689492138781e-485j)  +/-  (2.52e-37, 4.56e-97j)
| (0.0070575310814980235958 + 2.6687984913510924984e-477j)  +/-  (2.86e-25, 5.16e-85j)
| (1.3640745300632248226e-08 + 1.6996675678995241728e-480j)  +/-  (2.85e-34, 5.15e-94j)
| (0.0013569572461515987509 + 3.1009127354744512688e-477j)  +/-  (1.36e-28, 2.45e-88j)
| (1.7541108666284513755e-10 - 6.4080452544281729813e-482j)  +/-  (6.01e-36, 1.08e-95j)
| (1.5507151141137350742e-05 + 3.9243407216533296911e-477j)  +/-  (8.45e-31, 1.52e-90j)
| (1.7541108666284513755e-10 + 3.3978646358744206255e-482j)  +/-  (2.05e-36, 3.7e-96j)
| (0.0013569572461515987509 - 1.3794632107325728603e-477j)  +/-  (7.05e-31, 1.27e-90j)
| (2.0781204866698417041e-19 - 1.0925846148899631673e-487j)  +/-  (3.16e-41, 5.71e-101j)
| (1.3012149103756771845e-15 - 3.2947530742747035402e-485j)  +/-  (5.13e-40, 9.27e-100j)
| (9.0459028226405565845e-13 + 1.9079456940808244317e-483j)  +/-  (1.91e-38, 3.44e-98j)
| (5.0586617173629963637e-07 + 2.8254493136060071708e-480j)  +/-  (6.17e-36, 1.11e-95j)
| (0.17890819165943878406 - 6.7124358464954614937e-477j)  +/-  (9.55e-31, 1.72e-90j)
| (0.20416627267670208287 + 9.7341006560836425495e-477j)  +/-  (7.85e-31, 1.42e-90j)
| (0.025160767666253339894 + 6.5449488253543284851e-477j)  +/-  (1.37e-31, 2.48e-91j)
| (8.3540868693055182745e-06 - 8.8722484995263410041e-479j)  +/-  (1.77e-35, 3.2e-95j)
| (0.025160767666253339894 - 4.4438631694852407974e-478j)  +/-  (1.44e-32, 2.61e-92j)
| (0.00017260031568678736197 - 1.2817151399949481498e-477j)  +/-  (4.88e-35, 8.8e-95j)
| (1.5507151141137350742e-05 + 4.590150630715392122e-478j)  +/-  (2.27e-35, 4.09e-95j)
| (5.0586617173629963637e-07 - 4.7477362208812085669e-479j)  +/-  (1.23e-38, 2.22e-98j)
| (0.12138005551520200793 + 1.115591166839841558e-476j)  +/-  (8.97e-35, 1.58e-94j)
| (0.00017260031568678736197 - 3.2952004167020026356e-477j)  +/-  (6.97e-37, 1.26e-96j)
| (0.12138005551520200793 + 3.4241767975529751949e-477j)  +/-  (1.43e-34, 2.55e-94j)
| (0.063856379256173958798 - 8.6502530377316240493e-478j)  +/-  (6.85e-35, 1.23e-94j)
| (0.063856379256173958798 - 9.1628410399734597456e-477j)  +/-  (6.68e-36, 1.16e-95j)
| (0.0070575310814980235958 - 4.3610725063090876179e-477j)  +/-  (1.06e-36, 1.97e-96j)
| (0.17890819165943878406 - 1.1431169188523492089e-476j)  +/-  (1.66e-35, 2.49e-95j)
