Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 21
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Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
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Trying to find an order 21 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^35 - 116820468175793942682357308626008/34192744932325195010790009931*t^33 + 141722944911994376696193675558778296/444505684120227535140270129103*t^31 - 53479779632140244311013931167634513420/3111539788841592745981890903721*t^29 + 1855295758756521871633264433905809458370/3111539788841592745981890903721*t^27 - 480624090698277014569852300194427931771145/34226937677257520205800799940931*t^25 + 15805908728028188132314610572410440858792895/68453875354515040411601599881862*t^23 - 52549419573237496242827846913817338160055955/19558250101290011546171885680532*t^21 + 434194796800440830637313968957225751810119825/19558250101290011546171885680532*t^19 - 2535229806824603357909859868550942437411280325/19558250101290011546171885680532*t^17 + 82642650028528546492484680280861643087664453575/156466000810320092369375085444256*t^15 - 460221022314894088938736092940530016683281804325/312932001620640184738750170888512*t^13 + 130544127632101591038815150298375795089326975575/48143384864713874575192333982848*t^11 - 27675574331726927458049125721964067037628417375/8753342702675249922762242542336*t^9 + 5437644698085811796633181654396790136260294875/2500955057907214263646355012096*t^7 - 3916001089920969060598481660191370453394047625/5001910115814428527292710024192*t^5 + 2299898045864887188776939493575407290648603375/20007640463257714109170840096768*t^3 - 128915419102045609903091065023757731672658875/40015280926515428218341680193536*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:
| (6.7395556960986322304 + 9.5475237568507585089e-466j)  +/-  (9.05e-122, 9.05e-122j)
| (4.8785157643168707814 + 2.3628471989026723752e-464j)  +/-  (3.9e-120, 3.9e-120j)
| (1.9929716657853901033 + 3.6530723084670198098e-473j)  +/-  (1.75e-121, 1.75e-121j)
| (-5.4171421172911667907 - 1.1452930370132723489e-474j)  +/-  (1.92e-120, 1.92e-120j)
| (-4.8785157643168707814 - 5.8020288693238482527e-473j)  +/-  (4.15e-120, 4.15e-120j)
| (-1.9929716657853901033 - 3.0796346858597299744e-476j)  +/-  (1.56e-121, 1.56e-121j)
| (-6.7395556960986322304 + 5.2200491648844640114e-476j)  +/-  (9.19e-122, 9.19e-122j)
| (5.4171421172911667907 - 8.4900324793294198291e-475j)  +/-  (1.87e-120, 1.87e-120j)
| (-6.0179513133694986358 - 2.1133016926420810771e-479j)  +/-  (6.59e-121, 6.59e-121j)
| (3.4676872293869892387 - 5.28235459539175921e-478j)  +/-  (3.37e-120, 3.37e-120j)
| (0.84870956007549195307 - 5.0013451530574905683e-487j)  +/-  (5.21e-124, 5.21e-124j)
| (3.0486879132310133212 + 4.9474804646746979097e-488j)  +/-  (2.36e-120, 2.36e-120j)
| (-2.6615039514854707102 - 1.2925929278349936154e-493j)  +/-  (1.33e-120, 1.33e-120j)
| (-2.3166778458612639611 - 5.704003891936536849e-494j)  +/-  (5.1e-121, 5.1e-121j)
| (4.3801549167430512513 - 6.4002801496251290324e-492j)  +/-  (5.24e-120, 5.24e-120j)
| (6.0179513133694986358 - 2.52814924950513511e-499j)  +/-  (6.65e-121, 6.65e-121j)
| (3.911506869286660161 - 9.120444987665229425e-499j)  +/-  (4.97e-120, 4.97e-120j)
| (-4.3801549167430512513 - 1.0075596090913923642e-497j)  +/-  (5.33e-120, 5.33e-120j)
| (-0.84870956007549195307 - 1.0336419632209628105e-502j)  +/-  (5.51e-124, 5.51e-124j)
| (-3.4676872293869892387 - 1.8704103802745769667e-498j)  +/-  (3.68e-120, 3.68e-120j)
| (1.6506801238857845559 + 6.7196307236961071036e-501j)  +/-  (3.69e-122, 3.69e-122j)
| (2.6615039514854707102 + 4.0296643175252568545e-504j)  +/-  (1.16e-120, 1.16e-120j)
| (-0.52464762327529031788 - 1.6044753795441087079e-512j)  +/-  (2.02e-125, 2.02e-125j)
| (-1.6506801238857845559 - 3.049277492990435329e-512j)  +/-  (3.3e-122, 3.3e-122j)
| (-1.0363502036603261655 + 1.1458411304829818288e-512j)  +/-  (2.51e-123, 2.51e-123j)
| (-3.911506869286660161 + 6.4486124969932072969e-510j)  +/-  (4.8e-120, 4.8e-120j)
| (1.0363502036603261655 - 3.196240247315937204e-514j)  +/-  (2.11e-123, 2.11e-123j)
| (2.3166778458612639611 + 1.5249058472715346432e-518j)  +/-  (4.79e-121, 4.79e-121j)
| (-8.3756503153268351073e-528 - 1.583614187027891253e-527j)  +/-  (6.27e-526, 6.27e-526j)
| (-1.3009282866163125663 + 1.9853530130273166726e-525j)  +/-  (6.94e-123, 6.94e-123j)
| (-3.0486879132310133212 - 7.6649715890620863391e-527j)  +/-  (2.34e-120, 2.34e-120j)
| (1.3009282866163125663 + 4.5862501587156499458e-533j)  +/-  (8.02e-123, 8.02e-123j)
| (0.52464762327529031788 - 2.4951171517778208836e-537j)  +/-  (1.85e-125, 1.85e-125j)
| (0.18980675578014987883 - 2.4990080744588601618e-539j)  +/-  (1.04e-126, 1.04e-126j)
| (-0.18980675578014987883 - 3.7364054637778622727e-538j)  +/-  (8.93e-127, 8.93e-127j)
-------------------------------------------------
The weights are:
| (8.8046544495310886826e-21 - 5.0491138147600976412e-481j)  +/-  (2.71e-39, 6.18e-99j)
| (1.342736260725539166e-11 - 1.9865641369598233532e-474j)  +/-  (1.37e-34, 3.13e-94j)
| (0.00350804789303054478 + 6.5253015066842715006e-469j)  +/-  (2.06e-22, 4.71e-82j)
| (5.735176371030755269e-14 + 9.9687945276965875277e-478j)  +/-  (1.43e-37, 3.27e-97j)
| (1.342736260725539166e-11 - 3.2516620790523233995e-476j)  +/-  (2.54e-36, 5.79e-96j)
| (0.00350804789303054478 + 2.7401675778284423107e-469j)  +/-  (8.68e-26, 1.98e-85j)
| (8.8046544495310886826e-21 + 8.086816096805061903e-482j)  +/-  (1.44e-41, 3.3e-101j)
| (5.735176371030755269e-14 - 1.9055224939639240701e-476j)  +/-  (8.68e-39, 1.98e-98j)
| (6.8056640408691447333e-17 - 1.6089724025911802988e-479j)  +/-  (1.31e-39, 3e-99j)
| (1.4603646030259957498e-06 + 7.9099476383305887363e-472j)  +/-  (5.11e-34, 1.17e-93j)
| (0.076478665538196355079 + 3.9225974286574015188e-467j)  +/-  (1.96e-28, 4.47e-88j)
| (2.1005343270391736037e-05 - 5.9292506134590153585e-471j)  +/-  (1.05e-32, 2.4e-92j)
| (0.00017362535084538573795 + 1.1316810727591705369e-470j)  +/-  (2.59e-32, 5.9e-92j)
| (0.00085875586622269928947 - 6.5952543083153986293e-470j)  +/-  (1.05e-30, 2.4e-90j)
| (1.2661155888499371608e-09 + 1.2850832338124541567e-473j)  +/-  (2.5e-37, 5.71e-97j)
| (6.8056640408691447333e-17 + 1.538700297043339463e-478j)  +/-  (7.33e-42, 1.67e-101j)
| (5.8283096513337657795e-08 - 9.8212246242243559881e-473j)  +/-  (3.05e-36, 6.96e-96j)
| (1.2661155888499371608e-09 + 6.9171006045691267566e-475j)  +/-  (1.96e-39, 4.47e-99j)
| (0.076478665538196355079 + 2.7600274495494491261e-467j)  +/-  (3.6e-31, 8.22e-91j)
| (1.4603646030259957498e-06 + 1.3370798111697350583e-472j)  +/-  (1.17e-37, 2.66e-97j)
| (0.013013961824612033931 - 2.179627152015483393e-468j)  +/-  (1.56e-32, 3.55e-92j)
| (0.00017362535084538573795 + 3.8488383664298364428e-470j)  +/-  (5.42e-35, 1.24e-94j)
| (0.14602632808656426995 - 3.3435398452299753388e-467j)  +/-  (2.76e-31, 6.29e-91j)
| (0.013013961824612033931 - 1.0775404725076984484e-468j)  +/-  (2.43e-33, 5.55e-93j)
| (0.031495023636390003241 - 1.903400456626928353e-467j)  +/-  (9.97e-32, 2.28e-91j)
| (5.8283096513337657795e-08 - 1.0804488020326692661e-473j)  +/-  (3.98e-39, 9.09e-99j)
| (0.031495023636390003241 - 2.9302135906163150417e-467j)  +/-  (9.4e-33, 2.15e-92j)
| (0.00085875586622269928947 - 1.8523519120430409254e-469j)  +/-  (4.28e-35, 9.76e-95j)
| (0.042132675363925090273 - 1.279704521772644524e-466j)  +/-  (6.62e-33, 1.51e-92j)
| (0.035000623278839521639 + 5.2942486762852930634e-468j)  +/-  (1.89e-33, 4.32e-93j)
| (2.1005343270391736037e-05 - 1.3686383663578288881e-471j)  +/-  (3.95e-37, 9.01e-97j)
| (0.035000623278839521639 + 9.1445810039088108058e-468j)  +/-  (3.48e-34, 7.97e-94j)
| (0.14602632808656426995 - 4.1493443206699867044e-467j)  +/-  (8.5e-34, 1.94e-93j)
| (0.17235610557276633886 + 8.9610291289737229908e-467j)  +/-  (8.99e-34, 2.07e-93j)
| (0.17235610557276633886 + 8.2898538510092622801e-467j)  +/-  (7.88e-34, 1.73e-93j)
