Starting with polynomial:
P : 2*t
Extension levels are: 1 2 64
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 64 Kronrod extension for:
P2 : 2*t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^67 - 831261416000492318129199596114803363/387634576082751948649051473144961*t^65 + 418840647826650440453580120255170936600/387634576082751948649051473144961*t^63 - 4256966272996971192539752730571763306620/12504341163959740279001660424031*t^61 + 941559188897478293922494122898693019432525/12504341163959740279001660424031*t^59 - 311175238722208984108130078529986371443193095/25008682327919480558003320848062*t^57 + 39919806759492219172785694871137318887664625955/25008682327919480558003320848062*t^55 - 8157594364551715076699611801030411257782298122625/50017364655838961116006641696124*t^53 + 5406229451055712457131597134273161730410095810799025/400138917246711688928053133568992*t^51 - 735515821199166540409097912831819098096159997140501875/800277834493423377856106267137984*t^49 + 20731384622863950192101855210263244360896158779883571125/400138917246711688928053133568992*t^47 - 41480717668805935837459393728657560588054537618930627625/17027187967945178252257580151872*t^45 + 6536309135817896010086459882916175689548822635187275078125/68108751871780713009030320607488*t^43 - 432627290017183060316452629226560004269845218970434609854375/136217503743561426018060641214976*t^41 + 12043237254007207599775137280786120439422469395601363125678125/136217503743561426018060641214976*t^39 - 563983759838195989168538452459186818951979614497758777674819375/272435007487122852036121282429952*t^37 + 177499522576369162328425646041430582969430917203985802241399411875/4358960119793965632577940518879232*t^35 - 5851735859431667109230479559488318432974841797307627603097939015625/8717920239587931265155881037758464*t^33 + 20133624238531516302208892194264077027405205472411091135071961590625/2179480059896982816288970259439616*t^31 - 460371626394911459990331689038842563540249253943832089070259908296875/4358960119793965632577940518879232*t^29 + 17376771221201731800193792321769199833132298677415534604135443350053125/17435840479175862530311762075516928*t^27 - 268472452294299546285610544860240402232009412061606272552306446788659375/34871680958351725060623524151033856*t^25 + 1680713083674926325366110967269190828673687815199548961410821477030859375/34871680958351725060623524151033856*t^23 - 16840253918775913186633650415404168063420426029769606709615088985529453125/69743361916703450121247048302067712*t^21 + 531743237099467287798402806679653295400060013232046119529889960330180859375/557946895333627600969976386416541696*t^19 - 3242690695365758880202054485929899246689970989487547068887042354181123078125/1115893790667255201939952772833083392*t^17 + 3724644617885365053974736473915883784487695023381098274094141188843442640625/557946895333627600969976386416541696*t^15 - 12478851611393638165784510872950121300027946431894948063571609240254398046875/1115893790667255201939952772833083392*t^13 + 58349427425155725296908116601838155345935153782143720579186777204560130546875/4463575162669020807759811091332333568*t^11 - 89467598083401746862125487492302312452266617319389168717304022793919294140625/8927150325338041615519622182664667136*t^9 + 40963493388697995034620659202464184376655800272551734215483322257858866484375/8927150325338041615519622182664667136*t^7 - 19134676983046896161009243358080213126483362362028042297169962826667396328125/17854300650676083231039244365329334272*t^5 + 52599453513911236492828910475681506763257525922927774822481923844893931640625/571337620821634663393255819690538696704*t^3 - 865956555689817470964691287360177081281658185065030741737639414222807421875/1142675241643269326786511639381077393408*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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:
| (-7.8851296899544663201 - 1.3841516793631103138e-703j)  +/-  (1.25e-239, 1.25e-239j)
| (9.5582931943250963541 - 1.9878572280010134722e-703j)  +/-  (9.55e-242, 9.55e-242j)
| (-8.6680544479995440603 + 2.7353492596773859887e-704j)  +/-  (2.02e-240, 2.02e-240j)
| (8.2667685431231062544 + 4.1030171585127416069e-702j)  +/-  (5.49e-240, 5.49e-240j)
| (-9.5582931943250963541 - 4.7351362897880656768e-717j)  +/-  (8.94e-242, 8.94e-242j)
| (10.077441685925807321 - 3.6005267759976587623e-713j)  +/-  (9.09e-243, 9.09e-243j)
| (8.6680544479995440603 + 4.0782342076135163777e-716j)  +/-  (2.17e-240, 2.17e-240j)
| (-0.095778532829960624447 - 6.0721747459874971632e-742j)  +/-  (1.79e-254, 1.79e-254j)
| (-3.4563891215492226716 - 4.7590448640597948271e-731j)  +/-  (1.28e-242, 1.28e-242j)
| (3.4563891215492226716 + 3.8881165873775736933e-730j)  +/-  (1.16e-242, 1.16e-242j)
| (1.7753549944724574567 + 3.0007241569808942573e-735j)  +/-  (1.7e-247, 1.7e-247j)
| (7.5190828591790241612 - 6.4282686282371223548e-726j)  +/-  (2.18e-239, 2.18e-239j)
| (9.0951415229411678365 + 1.482802715284144429e-742j)  +/-  (5.32e-241, 5.32e-241j)
| (-1.2247448713915890491 - 1.2731006246539479743e-761j)  +/-  (1.61e-249, 1.61e-249j)
| (-6.1636163344952278775 + 8.5804464320007571254e-751j)  +/-  (2.96e-239, 2.96e-239j)
| (-10.077441685925807321 + 3.6464839481902026134e-757j)  +/-  (9.22e-243, 9.22e-243j)
| (10.704825833259055319 - 1.1467033152562498586e-752j)  +/-  (4.15e-244, 4.15e-244j)
| (7.1657774156333352239 + 6.8783766673751359749e-765j)  +/-  (2.99e-239, 2.99e-239j)
| (-1.7753549944724574567 - 1.7256774158757891378e-795j)  +/-  (1.89e-247, 1.89e-247j)
| (-7.1657774156333352239 - 2.9864726272152025266e-786j)  +/-  (3.12e-239, 3.12e-239j)
| (6.8231119494539656486 + 9.0223418383357054493e-786j)  +/-  (3.6e-239, 3.6e-239j)
| (2.6087224766912118803 + 5.9817718576370670856e-797j)  +/-  (7.68e-245, 7.68e-245j)
| (-3.7432319608303964145 + 1.0235525039245307817e-794j)  +/-  (5.26e-242, 5.26e-242j)
| (7.8851296899544663201 + 6.8500427134685150775e-792j)  +/-  (1.23e-239, 1.23e-239j)
| (-2.0519238027877268842 - 9.7781861285188028206e-801j)  +/-  (1.58e-246, 1.58e-246j)
| (-5.5312992101187668436 - 5.9914060909357862727e-794j)  +/-  (1.35e-239, 1.35e-239j)
| (1.4997122458542083735 + 5.0448596967943796944e-801j)  +/-  (1.99e-248, 1.99e-248j)
| (4.9199276034927876113 - 4.3197931873479923435e-791j)  +/-  (3.62e-240, 3.62e-240j)
| (-5.2233061277404900827 + 8.7998778973061930122e-803j)  +/-  (7.95e-240, 7.95e-240j)
| (-0.67523444293216001872 - 1.0369370140072848352e-813j)  +/-  (6.63e-252, 6.63e-252j)
| (5.2233061277404900827 + 3.3329330825458808065e-800j)  +/-  (7.57e-240, 7.57e-240j)
| (-8.2667685431231062544 - 1.5450559420849087439e-819j)  +/-  (5.47e-240, 5.47e-240j)
| (2.329641158564861594 - 1.9296695674066075083e-824j)  +/-  (1.18e-245, 1.18e-245j)
| (2.0519238027877268842 - 1.0065075967081012221e-825j)  +/-  (1.49e-246, 1.49e-246j)
| (-7.5190828591790241612 - 8.8862461482277384671e-819j)  +/-  (2.12e-239, 2.12e-239j)
| (-4.0326746734008845904 - 1.3451721092573293803e-820j)  +/-  (1.99e-241, 1.99e-241j)
| (4.6206513658992052262 - 1.1068439139571150001e-817j)  +/-  (1.43e-240, 1.43e-240j)
| (0.67523444293216001872 - 6.0704882934679944667e-861j)  +/-  (7.35e-252, 7.35e-252j)
| (5.5312992101187668436 - 2.4476515763596232706e-847j)  +/-  (1.42e-239, 1.42e-239j)
| (-2.329641158564861594 - 6.1055053579567715991e-880j)  +/-  (1.11e-245, 1.11e-245j)
| (-2.6087224766912118803 + 8.8903026638582570006e-879j)  +/-  (8e-245, 8e-245j)
| (-1.4997122458542083735 - 3.6610302282132434543e-883j)  +/-  (1.73e-248, 1.73e-248j)
| (1.2247448713915890491 - 3.2577925600092085522e-884j)  +/-  (1.59e-249, 1.59e-249j)
| (-4.9199276034927876113 - 1.4324167365122139881e-873j)  +/-  (3.81e-240, 3.81e-240j)
| (6.1636163344952278775 - 2.8249666181729749492e-897j)  +/-  (3.1e-239, 3.1e-239j)
| (-5.844502217574297745 + 1.5978214555034492805e-917j)  +/-  (2.31e-239, 2.31e-239j)
| (-9.0951415229411678365 - 2.8797447006067203497e-921j)  +/-  (5.12e-241, 5.12e-241j)
| (-6.4894797935290761552 - 6.3030327524837278519e-919j)  +/-  (3.75e-239, 3.75e-239j)
| (3.171861085112017458 - 1.7895099182056795621e-926j)  +/-  (2.46e-243, 2.46e-243j)
| (6.4894797935290761552 + 3.9214169955802413157e-926j)  +/-  (3.64e-239, 3.64e-239j)
| (-4.325031318918013446 + 4.9620737096857673908e-939j)  +/-  (5.39e-241, 5.39e-241j)
| (-0.39825201749804784171 - 9.8773012066858591161e-952j)  +/-  (3.9e-253, 3.9e-253j)
| (4.0326746734008845904 - 1.0633702395674739364e-938j)  +/-  (1.72e-241, 1.72e-241j)
| (-10.704825833259055319 - 2.3740870792445745223e-943j)  +/-  (3.84e-244, 3.84e-244j)
| (3.7432319608303964145 + 1.0814619372559404194e-939j)  +/-  (5.26e-242, 5.26e-242j)
| (-0.95011940669304165509 + 4.9414280778072551258e-949j)  +/-  (1.1e-250, 1.1e-250j)
| (5.844502217574297745 + 1.8438844459249763824e-936j)  +/-  (2.27e-239, 2.27e-239j)
| (-4.6206513658992052262 + 6.6383350092190863073e-947j)  +/-  (1.49e-240, 1.49e-240j)
| (-2.8893863936117909243 + 1.1970274915273123443e-949j)  +/-  (4.74e-244, 4.74e-244j)
| (0.39825201749804784171 + 7.6965497312861407323e-959j)  +/-  (4.17e-253, 4.17e-253j)
| (2.4088316682887755738e-991 - 1.3325716431014658754e-990j)  +/-  (9.07e-989, 9.07e-989j)
| (-3.171861085112017458 - 6.3809836224109915879e-949j)  +/-  (2.57e-243, 2.57e-243j)
| (2.8893863936117909243 + 2.5898872608068589828e-949j)  +/-  (5.29e-244, 5.29e-244j)
| (4.325031318918013446 + 3.4642699559605518764e-946j)  +/-  (5.31e-241, 5.31e-241j)
| (0.95011940669304165509 - 9.7192550296780903656e-956j)  +/-  (1.27e-250, 1.27e-250j)
| (-6.8231119494539656486 + 8.8370158169600215063e-945j)  +/-  (3.54e-239, 3.54e-239j)
| (0.095778532829960624447 - 2.5753044515753673606e-959j)  +/-  (1.79e-254, 1.79e-254j)
-------------------------------------------------
The weights are:
| (2.0945541006895244756e-28 - 2.2965085827785672003e-730j)  +/-  (4.03e-62, 6.72e-179j)
| (5.7666695760752750078e-41 - 1.4886773925638871915e-737j)  +/-  (3.59e-68, 5.98e-185j)
| (5.451267299338619871e-34 + 5.8137312266248893282e-734j)  +/-  (2.96e-65, 4.93e-182j)
| (4.610674065130485141e-31 - 1.5787351076269279557e-731j)  +/-  (1.38e-64, 2.29e-181j)
| (5.7666695760752750078e-41 + 8.5219130678574085672e-738j)  +/-  (8.76e-69, 1.46e-185j)
| (2.4786682123243914031e-45 + 6.7183340648552269016e-740j)  +/-  (2.74e-70, 4.56e-187j)
| (5.451267299338619871e-34 - 1.5716387322329130412e-733j)  +/-  (4.47e-66, 7.46e-183j)
| (0.23928443498361862096 + 4.1568073915255454623e-717j)  +/-  (9.04e-24, 1.51e-140j)
| (1.0444569249825067748e-06 - 4.7340010599742285069e-721j)  +/-  (2.08e-45, 3.47e-162j)
| (1.0444569249825067748e-06 + 1.0040758820717272343e-720j)  +/-  (1.9e-45, 3.17e-162j)
| (0.0066618321792893248316 + 8.7993072055400738994e-719j)  +/-  (3.13e-29, 5.22e-146j)
| (5.6664981537576829792e-26 - 9.4275297070178974449e-730j)  +/-  (1.02e-63, 1.69e-180j)
| (2.9661340877963275079e-37 + 1.7205522987726899192e-735j)  +/-  (1.57e-67, 2.62e-184j)
| (0.034584984313738162516 + 8.4617358055167570691e-720j)  +/-  (9.04e-24, 1.51e-140j)
| (5.7651937798019884231e-18 + 2.9517853573927849508e-726j)  +/-  (2.36e-62, 3.94e-179j)
| (2.4786682123243914031e-45 - 4.1778551903447867493e-740j)  +/-  (2.21e-74, 3.69e-191j)
| (6.991078929377198477e-51 - 8.0419431910671378135e-743j)  +/-  (5.74e-74, 9.57e-191j)
| (9.8241788492863328706e-24 + 8.6911705708427182722e-729j)  +/-  (9.32e-64, 1.55e-180j)
| (0.0066618321792893248316 - 1.338312939721829012e-719j)  +/-  (9.11e-37, 1.52e-153j)
| (9.8241788492863328706e-24 - 8.9502817837207349469e-729j)  +/-  (4.96e-67, 8.26e-184j)
| (1.1526918323900694185e-21 - 7.40422001641197261e-728j)  +/-  (1.9e-63, 3.16e-180j)
| (0.0001748904041694437834 - 1.3008771008009836833e-719j)  +/-  (5.11e-46, 8.52e-163j)
| (1.3357239204764073974e-07 + 1.8501245919032213497e-721j)  +/-  (5.18e-54, 8.64e-171j)
| (2.0945541006895244756e-28 + 1.089281945612118187e-730j)  +/-  (1.92e-65, 3.2e-182j)
| (0.0023201866108183870627 + 1.1153631615940271222e-719j)  +/-  (2.12e-42, 3.53e-159j)
| (9.038920306494231361e-15 + 8.6624507099483405937e-725j)  +/-  (1.2e-62, 2e-179j)
| (0.016382461408902248736 - 1.4693090577537496618e-718j)  +/-  (4.06e-38, 6.77e-155j)
| (5.2233926704025249807e-12 - 2.623945012167476859e-723j)  +/-  (6.23e-60, 1.04e-176j)
| (2.4419990414027584415e-13 - 3.9975031288246520977e-724j)  +/-  (6.46e-62, 1.08e-178j)
| (0.098484621188864707533 + 1.7953410995286764578e-718j)  +/-  (9.53e-37, 1.59e-153j)
| (2.4419990414027584415e-13 + 6.0199450914529144571e-724j)  +/-  (4.57e-61, 7.62e-178j)
| (4.610674065130485141e-31 - 3.5151826414118105715e-732j)  +/-  (1.01e-71, 1.68e-188j)
| (0.00069027489932066374605 + 2.6319343058927112759e-719j)  +/-  (2.68e-48, 4.47e-165j)
| (0.0023201866108183870627 - 4.9702111821883428182e-719j)  +/-  (1.8e-46, 3e-163j)
| (5.6664981537576829792e-26 + 1.3197963059472304771e-729j)  +/-  (1.74e-69, 2.91e-186j)
| (1.4203235167447204253e-08 - 6.5799431573338626106e-722j)  +/-  (1.05e-58, 1.75e-175j)
| (8.9611884850271102454e-11 + 1.0354586658508565676e-722j)  +/-  (3.16e-60, 5.27e-177j)
| (0.098484621188864707533 + 5.5382364212657160119e-718j)  +/-  (1.51e-43, 2.51e-160j)
| (9.038920306494231361e-15 - 1.2448985981830584527e-724j)  +/-  (4.68e-63, 7.8e-180j)
| (0.00069027489932066374605 - 7.5444554742691436878e-720j)  +/-  (1.6e-51, 2.66e-168j)
| (0.0001748904041694437834 + 4.4361795939024395186e-720j)  +/-  (2.08e-53, 3.47e-170j)
| (0.016382461408902248736 + 9.7948026050456792488e-720j)  +/-  (1e-46, 1.67e-163j)
| (0.034584984313738162516 + 2.335606952032194845e-718j)  +/-  (1.48e-45, 2.47e-162j)
| (5.2233926704025249807e-12 + 1.6625919930886047129e-723j)  +/-  (3.43e-63, 5.71e-180j)
| (5.7651937798019884231e-18 - 3.8282022413087748332e-726j)  +/-  (1.42e-66, 2.36e-183j)
| (2.6087651000451208041e-16 - 1.6875937780908458779e-725j)  +/-  (4.25e-66, 7.09e-183j)
| (2.9661340877963275079e-37 - 8.6034553337528973313e-736j)  +/-  (3.67e-77, 6.12e-194j)
| (9.5447590006175433949e-20 - 4.6438568641013011949e-727j)  +/-  (1.39e-68, 2.31e-185j)
| (6.8329526812277292295e-06 - 2.5486962433898629854e-720j)  +/-  (3.35e-60, 5.58e-177j)
| (9.5447590006175433949e-20 + 5.6463888398156854842e-727j)  +/-  (1.11e-68, 1.86e-185j)
| (1.2468001771060783606e-09 + 2.1280543431915900375e-722j)  +/-  (1.03e-63, 1.72e-180j)
| (0.13472953211233735204 - 5.0885596492469387558e-718j)  +/-  (1.76e-53, 2.94e-170j)
| (1.4203235167447204253e-08 + 1.216031134029314113e-721j)  +/-  (9.4e-64, 1.57e-180j)
| (6.991078929377198477e-51 + 5.3215726908804884329e-743j)  +/-  (3.91e-85, 6.52e-202j)
| (1.3357239204764073974e-07 - 3.6454899926411155854e-721j)  +/-  (5.98e-63, 9.96e-180j)
| (0.062819767088282610268 - 5.859112223958569476e-719j)  +/-  (9.69e-56, 1.62e-172j)
| (2.6087651000451208041e-16 + 2.3098565657489965697e-725j)  +/-  (1.39e-67, 2.31e-184j)
| (8.9611884850271102454e-11 - 6.249050083292256777e-723j)  +/-  (2.11e-65, 3.52e-182j)
| (3.7602721219311726615e-05 - 2.3271080621755689053e-720j)  +/-  (2.49e-62, 4.13e-179j)
| (0.13472953211233735204 - 9.4632365584099792901e-718j)  +/-  (9.4e-59, 1.52e-175j)
| (-0.19235722887536643744 - 7.9751350131448514345e-717j)  +/-  (5.5e-58, 8.97e-175j)
| (6.8329526812277292295e-06 + 1.1017930665810130662e-720j)  +/-  (6.08e-63, 1.01e-179j)
| (3.7602721219311726615e-05 + 5.9800921258392152064e-720j)  +/-  (3.82e-63, 6.2e-180j)
| (1.2468001771060783606e-09 - 3.7146026853025454208e-722j)  +/-  (7.77e-66, 1.25e-182j)
| (0.062819767088282610268 - 3.5928475633044586899e-718j)  +/-  (7.82e-61, 1.19e-177j)
| (1.1526918323900694185e-21 + 6.6399043420908564919e-728j)  +/-  (1.2e-72, 2.41e-189j)
| (0.23928443498361862096 + 4.8042748100919309571e-717j)  +/-  (1.55e-59, 2.14e-176j)
