Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^42 - 657685695148890279283238/400553925549962741119*t^40 + 121995418447645220080113810/400553925549962741119*t^38 - 713743112437750486816643295/21081785555261196901*t^36 + 212682060501231966688864199925/84327142221044787604*t^34 - 22500031553589037869420502487985/168654284442089575208*t^32 + 218417071162378440455621231358645/42163571110522393802*t^30 - 12697887153983788281906473228361225/84327142221044787604*t^28 + 2234492843403737187409375518013257525/674617137768358300832*t^26 - 74716958864330552955554329850725460625/1349234275536716601664*t^24 + 948665797692660896514294037403416046625/1349234275536716601664*t^22 - 18190988824208763407080704780203235469125/2698468551073433203328*t^20 + 521233203400935519599772434539599908705625/10793874204293732813312*t^18 - 5489386106722677714632642331464068939693125/21587748408587465626624*t^16 + 10380553624359310892585195296731924131878125/10793874204293732813312*t^14 - 54588697921498161873142685957981116584110625/21587748408587465626624*t^12 + 1524667227222144642931861174821022483349300625/345403974537399450025984*t^10 - 3303284355092249851897095122722945022001928125/690807949074798900051968*t^8 + 1999421568215554916522695223133587143669471875/690807949074798900051968*t^6 - 1128648924757389432818320013802101178248859375/1381615898149597800103936*t^4 + 407284282659393937871233647709769609002565625/5526463592598391200415744*t^2 - 6541867164969248383403585101822786240753125/11052927185196782400831488
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (-5.5366038115799852017 + 7.0638391977654994215e-601j)  +/-  (3e-245, 3e-245j)
| (2.8077175958967351407 - 3.7124134609067473688e-614j)  +/-  (3.08e-247, 3.08e-247j)
| (-8.2144585194216251251 - 4.6503118487641329708e-612j)  +/-  (8.15e-248, 8.15e-248j)
| (5.5366038115799852017 + 2.2469783796538465863e-614j)  +/-  (3.42e-245, 3.42e-245j)
| (-6.4528400830585381144 + 3.8703663169488349614e-621j)  +/-  (1.44e-245, 1.44e-245j)
| (-7.5305354519785872956 + 2.0600548803368268669e-633j)  +/-  (8.93e-247, 8.93e-247j)
| (5.9813667150408023441 - 1.6020936033441039038e-636j)  +/-  (2.61e-245, 2.61e-245j)
| (6.4528400830585381144 + 2.4385841380775889155e-643j)  +/-  (1.19e-245, 1.19e-245j)
| (3.9203434660603967723 - 7.6768770966681918966e-659j)  +/-  (7.66e-246, 7.66e-246j)
| (-4.3064787028366917605 + 3.3083361352996863709e-692j)  +/-  (1.54e-245, 1.54e-245j)
| (-6.9620781909209865699 - 2.286737292800229479e-719j)  +/-  (4.68e-246, 4.68e-246j)
| (5.1119117008159839945 - 2.160669801636626552e-726j)  +/-  (3.23e-245, 3.23e-245j)
| (7.5305354519785872956 + 1.9792854360960241767e-730j)  +/-  (9.34e-247, 9.34e-247j)
| (-5.1119117008159839945 - 2.5796168731580053629e-732j)  +/-  (3.45e-245, 3.45e-245j)
| (-2.4482472857274080988 - 1.0398613144157954995e-741j)  +/-  (6.51e-248, 6.51e-248j)
| (0.7071067811865475244 - 1.5255895590838100761e-747j)  +/-  (1.98e-252, 1.98e-252j)
| (-2.8077175958967351407 + 1.1962749728982628376e-740j)  +/-  (3.41e-247, 3.41e-247j)
| (-3.5427288331335487277 + 3.1572541650202518438e-739j)  +/-  (3.15e-246, 3.15e-246j)
| (-1.741512437396966871 - 1.6643682599667592621e-751j)  +/-  (1.72e-249, 1.72e-249j)
| (8.2144585194216251251 - 7.351588988698163675e-751j)  +/-  (9.35e-248, 9.35e-248j)
| (4.3064787028366917605 - 2.4652872415764068639e-747j)  +/-  (1.67e-245, 1.67e-245j)
| (1.0480911169474805714 + 7.463628083610470369e-755j)  +/-  (2.43e-251, 2.43e-251j)
| (2.093050486708880205 + 5.3806766550399007634e-752j)  +/-  (1.05e-248, 1.05e-248j)
| (-4.7029025895085225057 - 9.9237135697480523518e-747j)  +/-  (2.37e-245, 2.37e-245j)
| (-3.9203434660603967723 + 3.2617123812893083066e-754j)  +/-  (7.72e-246, 7.72e-246j)
| (3.1722326881477394919 - 9.1433339427328056154e-763j)  +/-  (1.22e-246, 1.22e-246j)
| (-0.37590715245871052817 - 1.1305543821730607362e-770j)  +/-  (1.18e-253, 1.18e-253j)
| (1.3932130198433400165 + 2.1932109980240289152e-768j)  +/-  (2.22e-250, 2.22e-250j)
| (3.5427288331335487277 + 3.2755661463894955162e-764j)  +/-  (3.14e-246, 3.14e-246j)
| (-1.0480911169474805714 - 3.5441174201433532846e-770j)  +/-  (2.11e-251, 2.11e-251j)
| (6.9620781909209865699 - 6.3519299431073074218e-763j)  +/-  (4.58e-246, 4.58e-246j)
| (-5.9813667150408023441 - 4.1030611471073568452e-765j)  +/-  (2.54e-245, 2.54e-245j)
| (0.37590715245871052817 + 2.1198887159246809009e-779j)  +/-  (1.18e-253, 1.18e-253j)
| (-2.093050486708880205 - 8.3825634356293100609e-776j)  +/-  (1.08e-248, 1.08e-248j)
| (-1.3932130198433400165 + 9.4493960116573868874e-778j)  +/-  (2.49e-250, 2.49e-250j)
| (4.7029025895085225057 + 2.7441717566176090733e-775j)  +/-  (2.68e-245, 2.68e-245j)
| (-3.1722326881477394919 + 1.2693944917650132642e-779j)  +/-  (1.04e-246, 1.04e-246j)
| (0.094221040100328095463 + 2.8243183859738559809e-794j)  +/-  (1.2e-254, 1.2e-254j)
| (2.4482472857274080988 + 4.6882274112106360322e-790j)  +/-  (6.17e-248, 6.17e-248j)
| (-0.094221040100328095463 + 5.4570081514911798469e-797j)  +/-  (1.2e-254, 1.2e-254j)
| (-0.7071067811865475244 + 2.5798137137358053499e-795j)  +/-  (1.98e-252, 1.98e-252j)
| (1.741512437396966871 + 1.4566813393627192685e-794j)  +/-  (1.7e-249, 1.7e-249j)
-------------------------------------------------
The weights are:
| (1.1910009577721277004e-14 + 4.8098013177701337657e-614j)  +/-  (9.34e-90, 4.34e-211j)
| (7.6964578869079245434e-05 + 1.5964440590361396819e-610j)  +/-  (1.05e-78, 4.9e-200j)
| (2.2040503782369787517e-30 + 2.8812262585214874952e-623j)  +/-  (3.43e-97, 1.59e-218j)
| (1.1910009577721277004e-14 - 7.5976532394150103346e-616j)  +/-  (1.26e-91, 5.85e-213j)
| (2.2706925640925133557e-19 - 3.4403742222713975189e-617j)  +/-  (3.29e-93, 1.53e-214j)
| (8.1102663402320304283e-26 - 8.0965389121113846028e-621j)  +/-  (9.52e-96, 4.42e-217j)
| (7.4723600535895823277e-17 + 5.3557094376414315835e-617j)  +/-  (1.27e-93, 5.9e-215j)
| (2.2706925640925133557e-19 - 2.6291424823663101209e-618j)  +/-  (2.68e-95, 1.24e-216j)
| (4.5534248915447849225e-08 - 2.4556489705768103265e-612j)  +/-  (3.09e-88, 1.43e-209j)
| (1.9463588811859637189e-09 - 3.5536108437956679066e-612j)  +/-  (2.61e-90, 1.21e-211j)
| (2.681239498553677426e-22 + 7.0432309712699329964e-619j)  +/-  (5.76e-96, 2.67e-217j)
| (1.0518406281641839212e-12 + 8.0410657955008660027e-615j)  +/-  (3.68e-92, 1.71e-213j)
| (8.1102663402320304283e-26 - 1.2354613125206951764e-621j)  +/-  (2.18e-99, 1.01e-220j)
| (1.0518406281641839212e-12 - 2.0161762497559231903e-613j)  +/-  (1.56e-92, 7.23e-214j)
| (0.00050261337156403002477 + 1.2635149852980794596e-609j)  +/-  (9.22e-86, 4.28e-207j)
| (0.11563274738876090267 + 3.2128646805507492208e-608j)  +/-  (8.33e-82, 3.87e-203j)
| (7.6964578869079245434e-05 - 4.8815672566014370597e-610j)  +/-  (2.64e-87, 1.23e-208j)
| (7.4699839203471185156e-07 - 5.2194010797946451177e-611j)  +/-  (7.04e-90, 3.27e-211j)
| (0.0095098661690295144599 + 6.2754507369446766325e-609j)  +/-  (1.03e-83, 4.8e-205j)
| (2.2040503782369787517e-30 + 5.6108430584847600221e-624j)  +/-  (2.69e-103, 1.25e-224j)
| (1.9463588811859637189e-09 + 4.441074080254370104e-613j)  +/-  (2.75e-93, 1.28e-214j)
| (0.064583383957883002795 - 1.555484692482365732e-608j)  +/-  (8.23e-82, 3.82e-203j)
| (0.0024943599295396770693 + 1.3317542449209285419e-609j)  +/-  (9e-88, 4.18e-209j)
| (5.6303291380446736148e-11 + 8.1670564014217309723e-613j)  +/-  (1.89e-93, 8.76e-215j)
| (4.5534248915447849225e-08 + 1.4368318412838519307e-611j)  +/-  (9.7e-92, 4.5e-213j)
| (8.833954863972067764e-06 - 4.5882508434639772181e-611j)  +/-  (8.34e-92, 3.87e-213j)
| (0.15677650127915996156 + 8.0604409505103583264e-608j)  +/-  (9.09e-86, 4.22e-207j)
| (0.028083702783525630047 + 7.3661820187274460002e-609j)  +/-  (3.12e-87, 1.45e-208j)
| (7.4699839203471185156e-07 + 1.1462112183766317973e-611j)  +/-  (1.14e-92, 5.29e-214j)
| (0.064583383957883002795 + 2.2819122516024583664e-608j)  +/-  (5.05e-88, 2.36e-209j)
| (2.681239498553677426e-22 + 8.0328031657007450922e-620j)  +/-  (4.65e-101, 2.17e-222j)
| (7.4723600535895823277e-17 + 1.3869615349086321004e-615j)  +/-  (3.44e-98, 1.61e-219j)
| (0.15677650127915996156 - 7.0355033605258843189e-608j)  +/-  (5.75e-88, 2.68e-209j)
| (0.0024943599295396770693 - 2.9506801036841379347e-609j)  +/-  (1.05e-90, 4.92e-212j)
| (0.028083702783525630047 - 1.2319931735645515491e-608j)  +/-  (8.41e-90, 3.91e-211j)
| (5.6303291380446736148e-11 - 6.6496221159101147892e-614j)  +/-  (7.46e-96, 3.41e-217j)
| (8.833954863972067764e-06 + 1.690019307924312279e-610j)  +/-  (1.17e-92, 5.51e-214j)
| (0.12233023205043728175 + 1.4654433402099891211e-607j)  +/-  (1.58e-89, 7.75e-211j)
| (0.00050261337156403002477 - 4.8869852221426020916e-610j)  +/-  (1.63e-92, 7.21e-214j)
| (0.12233023205043728175 - 1.5161842012457592694e-607j)  +/-  (8.68e-90, 4.47e-211j)
| (0.11563274738876090267 - 4.1536824733643829326e-608j)  +/-  (1.59e-90, 8.3e-212j)
| (0.0095098661690295144599 - 3.2722628290418594051e-609j)  +/-  (1.14e-91, 4.79e-213j)
