Starting with polynomial:
P : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Extension levels are: 10 20
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Trying to find an order 20 Kronrod extension for:
P1 : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Solvable: 1
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Ending with final polynomial:
P : t^30 - 30861963315/90446489*t^28 + 58594047285555/1175804357*t^26 - 4824067950762525/1175804357*t^24 + 30017137132193625/142130197*t^22 - 13174180849381278015/1847692561*t^20 + 297852724847499221475/1847692561*t^18 - 4527397508382980403525/1847692561*t^16 + 45825643716885858121875/1847692561*t^14 - 23217541605513135001125/142130197*t^12 + 8693651240836419512475/12920927*t^10 - 20999445685393754305125/12920927*t^8 + 26771564505690036293625/12920927*t^6 - 15034567253335707616875/12920927*t^4 + 2726884722974218419375/12920927*t^2 - 99673906355990591625/12920927
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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:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.8594628283323121502 + 4.4257006105679141553e-483j)  +/-  (6.17e-121, 6.17e-121j)
| (7.9522712487074597097 - 2.4035047108466009628e-493j)  +/-  (1.56e-121, 1.56e-121j)
| (-7.0730135565740607188 + 9.2641527960124515844e-495j)  +/-  (4.48e-121, 4.48e-121j)
| (9.0061781569647007902 + 6.0801757510300379659e-496j)  +/-  (2.7e-122, 2.7e-122j)
| (-4.8594628283323121502 + 2.2740380116572207255e-495j)  +/-  (5.95e-121, 5.95e-121j)
| (-4.2033175416572783657 + 2.4144499245549891282e-496j)  +/-  (3.4e-121, 3.4e-121j)
| (-3.5818234835519269228 + 2.1798082601704980624e-497j)  +/-  (1.45e-121, 1.45e-121j)
| (-3.00462466933114858 + 7.438091991611513685e-498j)  +/-  (5.77e-122, 5.77e-122j)
| (-9.0061781569647007902 + 2.1718565656789023093e-499j)  +/-  (2.81e-122, 2.81e-122j)
| (5.5503107444784739861 + 1.1081743578888426847e-496j)  +/-  (8.11e-121, 8.11e-121j)
| (4.2033175416572783657 - 1.6759624615106848256e-503j)  +/-  (3.58e-121, 3.58e-121j)
| (3.5818234835519269228 + 1.938889350359439175e-508j)  +/-  (1.51e-121, 1.51e-121j)
| (0.92532561906056765815 + 2.9505713674915351106e-512j)  +/-  (3.24e-125, 3.24e-125j)
| (-1.9894750321307408488 - 1.3767352247914692776e-513j)  +/-  (3.25e-123, 3.25e-123j)
| (-0.21998379531614182706 + 4.074952841653164516e-518j)  +/-  (1.08e-126, 1.08e-126j)
| (7.0730135565740607188 + 4.7620956956043092451e-526j)  +/-  (4.73e-121, 4.73e-121j)
| (2.4843258416389545809 + 3.5855303740838951276e-533j)  +/-  (1.56e-122, 1.56e-122j)
| (-6.2830178250811602513 - 6.7519921399151477414e-534j)  +/-  (7.26e-121, 7.26e-121j)
| (-0.92532561906056765815 - 3.3320399245383800904e-539j)  +/-  (3.6e-125, 3.6e-125j)
| (-1.4659890943911581833 - 1.20779995925763431e-539j)  +/-  (4.01e-124, 4.01e-124j)
| (0.21998379531614182706 + 7.6788338839042791328e-538j)  +/-  (1.08e-126, 1.08e-126j)
| (1.4659890943911581833 - 3.881912675730216935e-539j)  +/-  (3.68e-124, 3.68e-124j)
| (6.2830178250811602513 - 9.0903736816603078423e-541j)  +/-  (7.78e-121, 7.78e-121j)
| (-5.5503107444784739861 + 4.5275967156866520178e-546j)  +/-  (7.35e-121, 7.35e-121j)
| (-7.9522712487074597097 - 1.3053237276498475207e-548j)  +/-  (1.47e-121, 1.47e-121j)
| (3.00462466933114858 - 4.0176027229865645487e-549j)  +/-  (5.82e-122, 5.82e-122j)
| (0.48493570751549765305 - 3.5708208256888001689e-553j)  +/-  (6.5e-126, 6.5e-126j)
| (1.9894750321307408488 - 1.7810421397786140292e-551j)  +/-  (2.99e-123, 2.99e-123j)
| (-2.4843258416389545809 + 3.1029825096599028795e-550j)  +/-  (1.6e-122, 1.6e-122j)
| (-0.48493570751549765305 - 4.2391454719589276505e-554j)  +/-  (7.43e-126, 7.43e-126j)
-------------------------------------------------
The weights are:
| (2.0000325540515823195e-06 - 2.9368555219774433849e-488j)  +/-  (4.34e-35, 2.59e-95j)
| (6.974298225641972083e-15 + 2.2486502294153158382e-494j)  +/-  (1.62e-41, 9.71e-102j)
| (4.5196377496069524745e-12 - 2.3500698448486630536e-493j)  +/-  (1.91e-41, 1.14e-101j)
| (1.1791837741920045428e-18 - 1.3600032699471402068e-496j)  +/-  (2.7e-43, 1.61e-103j)
| (2.0000325540515823195e-06 + 9.1075347301512408111e-490j)  +/-  (3.38e-37, 2.03e-97j)
| (3.7171933357337079546e-05 - 7.950058071095949462e-489j)  +/-  (8.39e-36, 5.02e-96j)
| (0.00039315679527151421361 + 5.6990434136370131906e-488j)  +/-  (1.39e-34, 8.32e-95j)
| (0.0024012020479516419842 - 3.2981131194887244322e-487j)  +/-  (2.28e-33, 1.37e-93j)
| (1.1791837741920045428e-18 - 4.0672814278502890238e-497j)  +/-  (3.19e-46, 1.91e-106j)
| (5.7909447094024686602e-08 - 1.2382695232330086232e-489j)  +/-  (4.07e-41, 2.43e-101j)
| (3.7171933357337079546e-05 + 1.0980743394786676043e-487j)  +/-  (6.29e-39, 3.77e-99j)
| (0.00039315679527151421361 - 3.7653237085097437443e-487j)  +/-  (4.01e-38, 2.4e-98j)
| (0.13773993386820801325 + 6.1418092283115432083e-485j)  +/-  (2.18e-33, 1.3e-93j)
| (0.027841467652058763559 - 4.2485311274504853038e-486j)  +/-  (3.17e-34, 1.89e-94j)
| (0.14878987130898397813 - 2.0318805915374461848e-484j)  +/-  (1.38e-33, 8.27e-94j)
| (4.5196377496069524745e-12 - 1.2668403108564135906e-492j)  +/-  (2.44e-44, 1.46e-104j)
| (0.0090471320491955487848 - 4.2786068112554479169e-486j)  +/-  (6.62e-37, 3.96e-97j)
| (8.0970685739737782045e-10 + 5.432231195101493529e-492j)  +/-  (5.35e-44, 3.2e-104j)
| (0.13773993386820801325 - 4.17694103027149766e-485j)  +/-  (1.98e-34, 1.19e-94j)
| (0.073429898321528304895 + 1.201884063237822766e-485j)  +/-  (6.46e-35, 3.87e-95j)
| (0.14878987130898397813 + 2.2245663655109479757e-484j)  +/-  (2.08e-34, 1.25e-94j)
| (0.073429898321528304895 - 2.2403178732918486219e-485j)  +/-  (6.27e-36, 3.75e-96j)
| (8.0970685739737782045e-10 + 4.2519278239858645112e-491j)  +/-  (2.29e-43, 1.37e-103j)
| (5.7909447094024686602e-08 - 8.217814861806592306e-491j)  +/-  (7.28e-43, 4.36e-103j)
| (6.974298225641972083e-15 + 5.4283396159973606639e-495j)  +/-  (3.99e-47, 2.39e-107j)
| (0.0024012020479516419842 + 1.3983241622969355295e-486j)  +/-  (1.25e-39, 7.5e-100j)
| (0.10031810726721028187 - 1.7825857879052504258e-484j)  +/-  (1.06e-36, 6.48e-97j)
| (0.027841467652058763559 + 1.0138693177944004278e-485j)  +/-  (1.81e-38, 1.08e-98j)
| (0.0090471320491955487848 + 1.3837921739896826096e-486j)  +/-  (2.61e-39, 1.53e-99j)
| (0.10031810726721028187 + 1.4590921358259498525e-484j)  +/-  (5.02e-37, 3.08e-97j)
