Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^42 - 328842847574445139641619/400553925549962741119*t^40 + 121995418447645220080113810/400553925549962741119*t^38 - 1427486224875500973633286590/21081785555261196901*t^36 + 212682060501231966688864199925/21081785555261196901*t^34 - 22500031553589037869420502487985/21081785555261196901*t^32 + 1747336569299027523644969850869160/21081785555261196901*t^30 - 101583097231870306255251785826889800/21081785555261196901*t^28 + 4468985686807474374818751036026515050/21081785555261196901*t^26 - 149433917728661105911108659701450921250/21081785555261196901*t^24 + 3794663190770643586057176149613664186500/21081785555261196901*t^22 - 72763955296835053628322819120812941876500/21081785555261196901*t^20 + 1042466406801871039199544869079199817411250/21081785555261196901*t^18 - 10978772213445355429265284662928137879386250/21081785555261196901*t^16 + 83044428994874487140681562373855393055025000/21081785555261196901*t^14 - 436709583371985294985141487663848932672885000/21081785555261196901*t^12 + 1524667227222144642931861174821022483349300625/21081785555261196901*t^10 - 3303284355092249851897095122722945022001928125/21081785555261196901*t^8 + 3998843136431109833045390446267174287338943750/21081785555261196901*t^6 - 2257297849514778865636640027604202356497718750/21081785555261196901*t^4 + 407284282659393937871233647709769609002565625/21081785555261196901*t^2 - 6541867164969248383403585101822786240753125/21081785555261196901
-------------------------------------------------
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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   42 out of 42
Indefinite weights: 0 out of 42
Negative weights:   0 out of 42
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-1.9703007479372274463 - 4.8010925435494157294e-697j)  +/-  (3.18e-250, 3.18e-250j)
| (2.4628705080082161944 + 4.6450473159507004968e-699j)  +/-  (2.39e-249, 2.39e-249j)
| (2.9600203850353059052 + 2.7716623049192902194e-704j)  +/-  (1.45e-248, 1.45e-248j)
| (1 + 2.4229300231058078079e-711j)  +/-  (2.67e-252, 2.67e-252j)
| (-0.53161299320015917137 - 7.2106556148410287072e-709j)  +/-  (1.53e-253, 1.53e-253j)
| (0.13324867277078323681 + 5.8995307919543327161e-712j)  +/-  (1.11e-254, 1.11e-254j)
| (-1.4822246721898926723 - 8.6430068108460112711e-710j)  +/-  (2.88e-251, 2.88e-251j)
| (0.53161299320015917137 + 1.1496876235622852784e-720j)  +/-  (1.53e-253, 1.53e-253j)
| (1.9703007479372274463 - 1.7842953623605720485e-707j)  +/-  (3.18e-250, 3.18e-250j)
| (-0.13324867277078323681 + 1.2997145225345733902e-714j)  +/-  (1.94e-254, 1.94e-254j)
| (1.4822246721898926723 - 1.9464371640048220592e-711j)  +/-  (2.92e-251, 2.92e-251j)
| (-1 - 1.6906563598136179987e-717j)  +/-  (2.78e-252, 2.78e-252j)
| (10.649785368119523379 - 2.5892310255422279103e-732j)  +/-  (1.33e-246, 1.33e-246j)
| (9.8458653999024013799 - 9.9965519742067056963e-757j)  +/-  (6.13e-246, 6.13e-246j)
| (-10.649785368119523379 + 1.2250356390623602449e-763j)  +/-  (1.31e-246, 1.31e-246j)
| (-7.8299401998229871892 - 2.3150158970925496098e-765j)  +/-  (4.39e-245, 4.39e-245j)
| (-11.61699864571727645 - 1.3978700678782709508e-773j)  +/-  (1.33e-247, 1.33e-247j)
| (5.0101751636276741548 + 1.1122672966463279729e-775j)  +/-  (4.92e-246, 4.92e-246j)
| (-2.4628705080082161944 + 4.990693027138333422e-783j)  +/-  (2.66e-249, 2.66e-249j)
| (-5.5442028988633605633 + 3.299148448323903662e-784j)  +/-  (1.1e-245, 1.1e-245j)
| (9.1256939612861137269 - 1.0223974773598169392e-798j)  +/-  (1.83e-245, 1.83e-245j)
| (4.4862144905817941586 - 3.155530752413252218e-809j)  +/-  (1.47e-246, 1.47e-246j)
| (3.9707123034307439209 + 4.0021976618269684359e-814j)  +/-  (4.61e-247, 4.61e-247j)
| (7.8299401998229871892 + 1.85241277956689547e-819j)  +/-  (4.65e-245, 4.65e-245j)
| (-8.4589299299377103649 + 2.2593421401457937136e-823j)  +/-  (3.34e-245, 3.34e-245j)
| (11.61699864571727645 - 1.6944760032787508338e-830j)  +/-  (1.18e-247, 1.18e-247j)
| (3.462344515518818509 + 6.4532937035061074865e-834j)  +/-  (8.87e-248, 8.87e-248j)
| (-6.6509086246025011133 + 1.0078914610999693841e-829j)  +/-  (4.07e-245, 4.07e-245j)
| (-3.9707123034307439209 + 1.5572709156371729921e-837j)  +/-  (4.07e-247, 4.07e-247j)
| (-9.8458653999024013799 - 2.2593497534910743297e-836j)  +/-  (6.11e-246, 6.11e-246j)
| (-6.0902805876225432407 - 9.305400033993565508e-841j)  +/-  (2.62e-245, 2.62e-245j)
| (6.6509086246025011133 + 4.7927528072426638206e-851j)  +/-  (4.03e-245, 4.03e-245j)
| (7.2293348569476799769 - 5.4762435307870022491e-866j)  +/-  (4.8e-245, 4.8e-245j)
| (6.0902805876225432407 + 3.457989227793126023e-875j)  +/-  (2.4e-245, 2.4e-245j)
| (-4.4862144905817941586 - 2.999306836348724015e-882j)  +/-  (1.51e-246, 1.51e-246j)
| (-3.462344515518818509 - 2.1717311890541353265e-883j)  +/-  (9.04e-248, 9.04e-248j)
| (-2.9600203850353059052 + 3.6078399971340366868e-886j)  +/-  (1.53e-248, 1.53e-248j)
| (-7.2293348569476799769 - 3.0835995347354784759e-883j)  +/-  (5.07e-245, 5.07e-245j)
| (-5.0101751636276741548 - 4.3851880149777733427e-891j)  +/-  (4.48e-246, 4.48e-246j)
| (8.4589299299377103649 - 1.5904713897870614186e-896j)  +/-  (3.53e-245, 3.53e-245j)
| (5.5442028988633605633 + 4.0888491256293013547e-911j)  +/-  (1.13e-245, 1.13e-245j)
| (-9.1256939612861137269 + 3.4208409703689866975e-932j)  +/-  (1.99e-245, 1.99e-245j)
-------------------------------------------------
The weights are:
| (0.028083702783525630047 - 2.0064467960159847409e-698j)  +/-  (1.2e-55, 3.94e-179j)
| (0.0095098661690295144599 - 1.4911942620715819283e-699j)  +/-  (6.15e-60, 2.01e-183j)
| (0.0024943599295396770693 + 5.0644837750214012388e-700j)  +/-  (2.5e-63, 8.18e-187j)
| (0.11563274738876090267 + 1.8093121027603027063e-698j)  +/-  (5.75e-48, 1.88e-171j)
| (0.15677650127915996156 + 7.6629070812056941311e-698j)  +/-  (1.1e-46, 3.59e-170j)
| (0.12233023205043728175 + 1.0427101202297035495e-697j)  +/-  (5.88e-47, 1.93e-170j)
| (0.064583383957883002795 + 5.5478058659344516012e-698j)  +/-  (2.88e-52, 9.42e-176j)
| (0.15677650127915996156 - 4.4315735452247743326e-698j)  +/-  (1.8e-47, 5.88e-171j)
| (0.028083702783525630047 + 3.6138387499148524686e-699j)  +/-  (1.19e-56, 3.91e-180j)
| (0.12233023205043728175 - 1.1923464506985402056e-697j)  +/-  (2.75e-47, 9e-171j)
| (0.064583383957883002795 - 8.0297309522868015131e-699j)  +/-  (1.19e-52, 3.88e-176j)
| (0.11563274738876090267 - 5.4715800162554492196e-698j)  +/-  (5.07e-49, 1.66e-172j)
| (8.1102663402320304283e-26 - 3.3423425486040442445e-712j)  +/-  (1.29e-87, 4.21e-211j)
| (2.681239498553677426e-22 + 2.2190983027785942182e-710j)  +/-  (3.29e-86, 1.08e-209j)
| (8.1102663402320304283e-26 - 4.8901554358674633016e-712j)  +/-  (8.68e-90, 2.84e-213j)
| (1.1910009577721277004e-14 - 3.7772231366696632876e-706j)  +/-  (4.14e-85, 1.36e-208j)
| (2.2040503782369787517e-30 + 2.1024295971141781246e-714j)  +/-  (2.03e-91, 6.63e-215j)
| (7.4699839203471185156e-07 + 3.8621158281209453629e-702j)  +/-  (5.75e-78, 1.88e-201j)
| (0.0095098661690295144599 - 1.2762172005798106005e-698j)  +/-  (5.59e-68, 1.83e-191j)
| (4.5534248915447849225e-08 - 1.71096656971130354e-702j)  +/-  (2.3e-80, 7.52e-204j)
| (2.2706925640925133557e-19 - 7.4159788644000214233e-709j)  +/-  (3.12e-87, 1.02e-210j)
| (8.833954863972067764e-06 - 1.5980753025026254307e-701j)  +/-  (1.1e-76, 3.59e-200j)
| (7.6964578869079245434e-05 + 5.7587637296257968526e-701j)  +/-  (3.66e-75, 1.2e-198j)
| (1.1910009577721277004e-14 - 2.2384209392205647155e-706j)  +/-  (8.66e-86, 2.84e-209j)
| (7.4723600535895823277e-17 + 2.5006602083324010295e-707j)  +/-  (1.69e-88, 5.53e-212j)
| (2.2040503782369787517e-30 + 1.4842641141827982141e-714j)  +/-  (1.16e-92, 3.81e-216j)
| (0.00050261337156403002477 - 1.8248441278666774444e-700j)  +/-  (1.3e-74, 4.24e-198j)
| (5.6303291380446736148e-11 - 3.8285553288153493859e-704j)  +/-  (1.08e-85, 3.53e-209j)
| (7.6964578869079245434e-05 + 1.7551180212826495305e-700j)  +/-  (8.67e-81, 2.84e-204j)
| (2.681239498553677426e-22 + 3.3521560191494484926e-710j)  +/-  (1.52e-91, 4.97e-215j)
| (1.9463588811859637189e-09 + 2.7930764740675095374e-703j)  +/-  (9.85e-85, 3.22e-208j)
| (5.6303291380446736148e-11 - 2.0559589415595029712e-704j)  +/-  (4.8e-86, 1.57e-209j)
| (1.0518406281641839212e-12 + 2.4251355031541925595e-705j)  +/-  (4.11e-87, 1.35e-210j)
| (1.9463588811859637189e-09 + 1.4101096624315917852e-703j)  +/-  (3.1e-85, 1.01e-208j)
| (8.833954863972067764e-06 - 4.1844297683765847112e-701j)  +/-  (1.12e-84, 3.67e-208j)
| (0.00050261337156403002477 - 6.895851369806037177e-700j)  +/-  (4.66e-83, 1.53e-206j)
| (0.0024943599295396770693 + 2.7082581557931945559e-699j)  +/-  (3.1e-82, 1.02e-205j)
| (1.0518406281641839212e-12 + 4.2841930734157497338e-705j)  +/-  (1.11e-89, 3.67e-213j)
| (7.4699839203471185156e-07 + 9.016767951795972335e-702j)  +/-  (5.28e-86, 1.71e-209j)
| (7.4723600535895823277e-17 + 1.5432414918294130734e-707j)  +/-  (3.47e-92, 1.1e-215j)
| (4.5534248915447849225e-08 - 8.0231619995426664184e-703j)  +/-  (2.09e-87, 6.52e-211j)
| (2.2706925640925133557e-19 - 1.1585713909094233372e-708j)  +/-  (1.19e-93, 4.14e-217j)
