Starting with polynomial:
P : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Extension levels are: 10 19
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Trying to find an order 19 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^29 - 36319341/100451*t^27 + 5560099308/100451*t^25 - 5231312668350/1104961*t^23 + 25243883322525/100451*t^21 - 9606769654189365/1104961*t^19 + 221412760668214290/1104961*t^17 - 3415957438459667220/1104961*t^15 + 34969152127489840575/1104961*t^13 - 17866654016364182925/84997*t^11 + 6730776353380060800/7727*t^9 - 16325461315901956050/7727*t^7 + 20835501697003733775/7727*t^5 - 11506310395149016125/7727*t^3 + 1746473811066069750/7727*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:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.5666882721987670436 - 1.0861113770317466961e-375j)  +/-  (6.11e-121, 6.11e-121j)
| (8.1596333947924732936 + 2.3808917599120686297e-379j)  +/-  (9.44e-122, 9.44e-122j)
| (-9.7951976958888146605 + 2.2407524918307750941e-379j)  +/-  (9.16e-123, 9.16e-123j)
| (-8.1596333947924732936 - 2.3631338534921700545e-385j)  +/-  (9.49e-122, 9.49e-122j)
| (7.1727138520827974824 - 2.4077959368540345205e-387j)  +/-  (3.32e-121, 3.32e-121j)
| (9.7951976958888146605 - 2.5811706088914337101e-389j)  +/-  (9.45e-123, 9.45e-123j)
| (-1.4659890943911581833 - 1.3283826404920424126e-390j)  +/-  (3.8e-124, 3.8e-124j)
| (6.3297219741386415162 + 4.0381150009383427388e-388j)  +/-  (5.05e-121, 5.05e-121j)
| (-4.1982775787633784091 - 3.150004589431766992e-386j)  +/-  (2.87e-121, 2.87e-121j)
| (1.9729727941714332334 - 4.508179990692024021e-394j)  +/-  (2.8e-123, 2.8e-123j)
| (3.0127393892824778406 + 4.2778337519739744897e-393j)  +/-  (4.73e-122, 4.73e-122j)
| (4.8594628283323121502 - 5.1370007546582927718e-393j)  +/-  (4.35e-121, 4.35e-121j)
| (-5.5666882721987670436 - 3.2087685454198705573e-393j)  +/-  (5.74e-121, 5.74e-121j)
| (-4.8594628283323121502 + 6.4294516573896612771e-402j)  +/-  (4.42e-121, 4.42e-121j)
| (-3.5818234835519269228 + 3.0446130366236366953e-407j)  +/-  (1.44e-121, 1.44e-121j)
| (3.5818234835519269228 - 3.6575249656084653632e-410j)  +/-  (1.36e-121, 1.36e-121j)
| (2.4843258416389545809 + 1.0425113382680213204e-411j)  +/-  (1.39e-122, 1.39e-122j)
| (1.3600025878843503306e-414 - 1.1904278666019378669e-414j)  +/-  (5.24e-413, 5.24e-413j)
| (-2.4843258416389545809 + 1.9716484671149113928e-414j)  +/-  (1.33e-122, 1.33e-122j)
| (-6.3297219741386415162 - 5.1244117167529823717e-419j)  +/-  (5.47e-121, 5.47e-121j)
| (0.97019039804809437832 + 1.4961151040219989299e-434j)  +/-  (4.63e-125, 4.63e-125j)
| (0.48493570751549765305 + 3.8387196850824260988e-435j)  +/-  (3.33e-126, 3.33e-126j)
| (-7.1727138520827974824 - 5.6517028296411302632e-433j)  +/-  (3.27e-121, 3.27e-121j)
| (-0.48493570751549765305 + 3.7375405387298758096e-442j)  +/-  (3.13e-126, 3.13e-126j)
| (-3.0127393892824778406 - 9.4943263671896023997e-438j)  +/-  (4.5e-122, 4.5e-122j)
| (4.1982775787633784091 + 5.422931559458043132e-441j)  +/-  (2.75e-121, 2.75e-121j)
| (-0.97019039804809437832 - 4.6298675519297955708e-445j)  +/-  (4.38e-125, 4.38e-125j)
| (1.4659890943911581833 - 1.1434898467081392819e-445j)  +/-  (3.76e-124, 3.76e-124j)
| (-1.9729727941714332334 - 3.8934271004531168605e-444j)  +/-  (2.69e-123, 2.69e-123j)
-------------------------------------------------
The weights are:
| (5.4554257583915369995e-08 + 2.0483685138884732181e-382j)  +/-  (5.15e-36, 6.81e-97j)
| (1.543537861163443848e-15 + 1.1075111542739730205e-387j)  +/-  (7.3e-41, 9.65e-102j)
| (2.9131094038728798915e-21 + 2.7476255129978296324e-391j)  +/-  (3.27e-44, 4.33e-105j)
| (1.543537861163443848e-15 - 2.0921264887533590098e-388j)  +/-  (4.28e-42, 5.66e-103j)
| (2.4120638296787852578e-12 - 1.0106491852556713275e-385j)  +/-  (7.22e-40, 9.55e-101j)
| (2.9131094038728798915e-21 - 9.9819379607249524305e-391j)  +/-  (2.85e-44, 3.77e-105j)
| (0.068484813972903174336 - 2.8222154324142358275e-379j)  +/-  (5.43e-27, 7.19e-88j)
| (6.3442343720041970399e-10 + 5.242789371832706074e-384j)  +/-  (1.01e-38, 1.34e-99j)
| (3.794767326192014468e-05 + 4.7712125676306765312e-382j)  +/-  (9.56e-38, 1.26e-98j)
| (0.029020482326216455552 + 2.734653005223963458e-379j)  +/-  (9.1e-31, 1.2e-91j)
| (0.0023284117287841914983 + 4.7500470961248933636e-380j)  +/-  (3.37e-34, 4.46e-95j)
| (2.0313075598872194266e-06 - 8.5988360939463071008e-382j)  +/-  (2.36e-37, 3.12e-98j)
| (5.4554257583915369995e-08 + 5.3220158223505502013e-384j)  +/-  (1.94e-41, 2.57e-102j)
| (2.0313075598872194266e-06 - 5.8327527558073172632e-383j)  +/-  (3.55e-40, 4.69e-101j)
| (0.00038738348673742631258 - 2.9941007088121281018e-381j)  +/-  (2.5e-38, 3.31e-99j)
| (0.00038738348673742631258 - 1.3800216808046733096e-380j)  +/-  (1.41e-37, 1.86e-98j)
| (0.0093973816013661811759 - 1.2814418290127745575e-379j)  +/-  (1.59e-35, 2.1e-96j)
| (0.19378451902025261678 + 8.8030182049341142687e-379j)  +/-  (1.2e-34, 1.59e-95j)
| (0.0093973816013661811759 - 4.9060505904939280672e-380j)  +/-  (2.32e-37, 3.07e-98j)
| (6.3442343720041970399e-10 - 3.3627166024473861785e-385j)  +/-  (1.46e-43, 1.93e-104j)
| (0.12182521895505218798 + 7.1771075534155978365e-379j)  +/-  (2.12e-35, 2.8e-96j)
| (0.1716240142468976389 - 8.75714433491492366e-379j)  +/-  (3.13e-35, 4.14e-96j)
| (2.4120638296787852578e-12 + 1.2741013601342356304e-386j)  +/-  (5.21e-45, 6.89e-106j)
| (0.1716240142468976389 - 7.3536692040289736316e-379j)  +/-  (5.14e-36, 6.77e-97j)
| (0.0023284117287841914983 + 1.414007828494466175e-380j)  +/-  (5.01e-39, 6.6e-100j)
| (3.794767326192014468e-05 + 3.4047326363709362388e-381j)  +/-  (1.83e-40, 2.5e-101j)
| (0.12182521895505218798 + 5.0466838366744864974e-379j)  +/-  (3.16e-37, 4.4e-98j)
| (0.068484813972903174336 - 4.8400844448260181227e-379j)  +/-  (8.59e-38, 1.36e-98j)
| (0.029020482326216455552 + 1.3034491795570668457e-379j)  +/-  (2.54e-38, 3.08e-99j)
