Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 31
-------------------------------------------------
Trying to find an order 31 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^35 - 6246253458237767058744/1443135744069879083*t^33 + 745885939502428711685656/1443135744069879083*t^31 - 51994168731331552404930060/1443135744069879083*t^29 + 336858186496529456001490530/206162249152839869*t^27 - 10487741419621003668704288325/206162249152839869*t^25 + 461163665434202804370024459225/412324498305679738*t^23 - 14511931838171337956574662899425/824648996611359476*t^21 + 163869891553582246838116131838875/824648996611359476*t^19 - 2640370574138905012147776537235875/1649297993222718952*t^17 + 59824792643376918852889253082255375/6597191972890875808*t^15 - 464940945336834394272863557088925375/13194383945781751616*t^13 + 2386764470522851715068164631536672375/26388767891563503232*t^11 - 7639929127541490824160428874528841875/52777535783127006464*t^9 + 13916865421140508702791748396951261875/105555071566254012928*t^7 - 12291859050074700234138603502611586875/211110143132508025856*t^5 + 7410609050729163897085013986179114375/844440572530032103424*t^3 - 86800623777045184080147973836811875/1688881145060064206848*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: 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:
| (-4.9689870855001087553 - 2.4265467930234435782e-270j)  +/-  (2.15e-119, 2.15e-119j)
| (-5.989479816603888414 + 1.1420730891758339183e-270j)  +/-  (6.98e-120, 6.98e-120j)
| (-7.2883749009185892552 - 4.6200475073122837361e-272j)  +/-  (2.35e-121, 2.35e-121j)
| (-4.061851599884095305 - 2.361888160349279526e-269j)  +/-  (1.87e-119, 1.87e-119j)
| (-5.4599565260376033606 - 1.852741573870787121e-271j)  +/-  (1.47e-119, 1.47e-119j)
| (-4.5052176407165413698 + 9.1949290469332166045e-271j)  +/-  (2.23e-119, 2.23e-119j)
| (-3.219806864796497174 - 7.7559781472762682304e-272j)  +/-  (4.01e-120, 4.01e-120j)
| (-6.579635419786359558 - 6.3488716426448438616e-272j)  +/-  (1.91e-120, 1.91e-120j)
| (-3.6344230677350736813 - 4.8161006402994771364e-272j)  +/-  (9.66e-120, 9.66e-120j)
| (3.6344230677350736813 - 1.8740813153255818186e-269j)  +/-  (9.47e-120, 9.47e-120j)
| (4.9689870855001087553 - 6.048231643315152783e-276j)  +/-  (2.09e-119, 2.09e-119j)
| (3.219806864796497174 + 4.6821949940887467939e-280j)  +/-  (3.78e-120, 3.78e-120j)
| (7.2883749009185892552 + 2.2663846823368869085e-281j)  +/-  (2.51e-121, 2.51e-121j)
| (-1.6506801238857845559 - 8.910719971939734557e-289j)  +/-  (1.1e-122, 1.1e-122j)
| (-2.4203950482980058524 + 3.3577618284185734962e-288j)  +/-  (3.48e-121, 3.48e-121j)
| (2.4203950482980058524 - 5.4262265113408375308e-285j)  +/-  (3.59e-121, 3.59e-121j)
| (-2.0324570074917621841 - 4.311900015560802617e-293j)  +/-  (6.93e-122, 6.93e-122j)
| (1.6506801238857845559 + 2.2926062483536936966e-292j)  +/-  (1.25e-122, 1.25e-122j)
| (2.0324570074917621841 + 1.1373949022400531204e-289j)  +/-  (6.66e-122, 6.66e-122j)
| (0.52464762327529031788 - 4.8075487260944137623e-296j)  +/-  (7.67e-126, 7.67e-126j)
| (-1.2737941219387040103 - 2.3348798243532235601e-294j)  +/-  (1.49e-123, 1.49e-123j)
| (6.579635419786359558 - 2.8568891529098607709e-289j)  +/-  (2.26e-120, 2.26e-120j)
| (2.8157128225700179109 + 4.1388937818188084883e-305j)  +/-  (1.32e-120, 1.32e-120j)
| (4.061851599884095305 - 1.1847112375522111232e-336j)  +/-  (1.64e-119, 1.64e-119j)
| (5.989479816603888414 - 9.6033226787913654169e-361j)  +/-  (6.91e-120, 6.91e-120j)
| (4.63453610167906696e-383 + 6.7730229928513703902e-384j)  +/-  (1.64e-381, 1.64e-381j)
| (-0.89996830964085704897 - 3.6807743635800339931e-380j)  +/-  (1.32e-124, 1.32e-124j)
| (-2.8157128225700179109 + 1.1083552261719903558e-374j)  +/-  (1.35e-120, 1.35e-120j)
| (0.89996830964085704897 - 1.7360496938347531069e-381j)  +/-  (1.5e-124, 1.5e-124j)
| (-0.078102510527405942264 + 1.0908252139749198225e-383j)  +/-  (2.69e-127, 2.69e-127j)
| (0.078102510527405942264 - 1.0610205349740299173e-383j)  +/-  (2.69e-127, 2.69e-127j)
| (5.4599565260376033606 - 3.2749638105323072641e-376j)  +/-  (1.48e-119, 1.48e-119j)
| (1.2737941219387040103 - 2.0623956905024161755e-387j)  +/-  (1.37e-123, 1.37e-123j)
| (4.5052176407165413698 - 5.2106976560077133474e-382j)  +/-  (2.11e-119, 2.11e-119j)
| (-0.52464762327529031788 - 1.6155217633329679423e-398j)  +/-  (8.19e-126, 8.19e-126j)
-------------------------------------------------
The weights are:
| (5.0805104561088472811e-12 + 3.5391993748924346286e-279j)  +/-  (3.12e-25, 6.42e-84j)
| (8.2343920064479520882e-17 + 2.6396899218700380154e-282j)  +/-  (2.73e-28, 5.6e-87j)
| (3.9211359044055294333e-24 + 3.5763548773746749015e-287j)  +/-  (9.61e-32, 1.97e-90j)
| (1.6766168145029544925e-08 - 1.9449664801153779352e-276j)  +/-  (8.14e-24, 1.67e-82j)
| (3.2381446574259100802e-14 - 1.217747523503093477e-280j)  +/-  (3.14e-27, 6.45e-86j)
| (3.911488674060320661e-10 - 9.2171636636583258837e-278j)  +/-  (5.31e-25, 1.09e-83j)
| (7.2573410899853835002e-06 - 2.2448853483666839154e-275j)  +/-  (6.82e-23, 1.4e-81j)
| (5.6497244547842025448e-20 - 2.6035898610515206499e-284j)  +/-  (5.28e-31, 1.09e-89j)
| (4.3517878194968955723e-07 + 6.5133662031921532615e-276j)  +/-  (1.16e-23, 2.38e-82j)
| (4.3517878194968955723e-07 + 3.3816623333014670622e-275j)  +/-  (3.98e-30, 8.17e-89j)
| (5.0805104561088472811e-12 + 1.1444422138247838464e-278j)  +/-  (1.88e-34, 3.86e-93j)
| (7.2573410899853835002e-06 - 1.003005553331653611e-274j)  +/-  (5.24e-29, 1.08e-87j)
| (3.9211359044055294333e-24 + 1.6913122743241266103e-285j)  +/-  (4.53e-40, 9.31e-99j)
| (0.014022834890966238204 - 1.5744162494794095783e-273j)  +/-  (8.69e-22, 1.79e-80j)
| (0.00063071172040376944317 - 2.1860356600214693414e-274j)  +/-  (1.78e-24, 3.65e-83j)
| (0.00063071172040376944317 - 5.2342726537859017042e-274j)  +/-  (1.9e-27, 3.9e-86j)
| (0.0034872478239210125755 + 6.1273230474479166087e-274j)  +/-  (1.74e-23, 3.57e-82j)
| (0.014022834890966238204 - 2.7345128925419216814e-273j)  +/-  (6.08e-25, 1.25e-83j)
| (0.0034872478239210125755 + 1.2350569039743752218e-273j)  +/-  (2.03e-26, 4.17e-85j)
| (0.16289227472785392845 + 2.4601438213231065146e-272j)  +/-  (1.67e-24, 3.42e-83j)
| (0.041758049185687454669 + 3.7438638050934813568e-273j)  +/-  (1.37e-24, 2.82e-83j)
| (5.6497244547842025448e-20 - 3.1073103555322022246e-283j)  +/-  (1.25e-39, 2.58e-98j)
| (8.1226329136812468616e-05 + 2.1549387701958400868e-274j)  +/-  (1.3e-29, 2.68e-88j)
| (1.6766168145029544925e-08 + 3.037242858547578373e-276j)  +/-  (1.32e-33, 2.72e-92j)
| (8.2343920064479520882e-17 + 1.7962139723344784267e-281j)  +/-  (8.02e-39, 1.64e-97j)
| (-1.1029555928072224516 + 7.3804532206570839546e-271j)  +/-  (4.98e-26, 1.01e-84j)
| (0.093699670708658459048 - 8.529214668100849575e-273j)  +/-  (2.44e-27, 4.94e-86j)
| (8.1226329136812468616e-05 + 7.2834201004512104711e-275j)  +/-  (4.29e-30, 8.72e-89j)
| (0.093699670708658459048 - 1.1404430997256374715e-272j)  +/-  (9.51e-28, 1.92e-86j)
| (0.73489807133468162911 - 3.801820232076201696e-271j)  +/-  (2.14e-26, 4.33e-85j)
| (0.73489807133468162911 - 3.89759869041722642e-271j)  +/-  (2.08e-26, 4.22e-85j)
| (3.2381446574259100802e-14 - 5.537173470144320923e-280j)  +/-  (8.84e-38, 1.81e-96j)
| (0.041758049185687454669 + 5.6814666643002036981e-273j)  +/-  (6.35e-30, 1.17e-88j)
| (3.911488674060320661e-10 - 1.8650894104012027433e-277j)  +/-  (1.34e-35, 2.8e-94j)
| (0.16289227472785392845 + 2.0799881348109361924e-272j)  +/-  (4.58e-29, 6.96e-88j)
