Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 11 28
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^15 - 641/6*t^13 + 29116/7*t^11 - 1045605/14*t^9 + 4515555/7*t^7 - 5082165/2*t^5 + 3863970*t^3 - 2916045/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 21689700740120204064175909610475898581468381110060875112070969083653/31036720677502311127603149011835624176656796705630125785511426728*t^41 + 31990365628308358527850625433428761581283013388075388558475729530731831/144838029828344118595481362055232912824398384626273920332386658064*t^39 - 379183361362781464997768308706121740890658232367292489992064741347709529/9052376864271507412217585128452057051524899039142120020774166129*t^37 + 14676554509044845804596983829975200280562082902230908813695062350451613102073/2751922566738538253314145879049425343663569307899204486315346503216*t^35 - 11873551593737651731357006245967751767126969210192042749198003978109348037445/24570737203022662976019159634369869139853297391957182913529879493*t^33 + 6335308036349144922858234857959136768997246168404240287549894141524401266197465/196565897624181303808153277074958953118826379135657463308239035944*t^31 - 79330580697103707718690203420408912735719696200064976233861321845413284304446205/49141474406045325952038319268739738279706594783914365827059758986*t^29 + 12072006704789286902575708876040078623164625704072721784508531532595027049938931405/196565897624181303808153277074958953118826379135657463308239035944*t^27 - 43821370660092640523506245672315740658421592775431514364982173577986974126553729530/24570737203022662976019159634369869139853297391957182913529879493*t^25 + 971355843046508637194993840207901148969849733293482066032621367546103858858012672125/24570737203022662976019159634369869139853297391957182913529879493*t^23 - 16360620845475494050401781288833812026588471087581647023668756814323392087727431083875/24570737203022662976019159634369869139853297391957182913529879493*t^21 + 10922596230310398671947922155746522398574929821521085409879554336833212858835371211000/1293196694895929630316797875493151007360699862734588574396309447*t^19 - 411723671840606523477413623750747216412481437793141194372288780758017069675219574050375/5172786779583718521267191501972604029442799450938354297585237788*t^17 + 5655548944046286494952532265566443606471830969345793758114349249131268288707329807219125/10345573559167437042534383003945208058885598901876708595170475576*t^15 - 6894339260222245258734201550013621543310460880974331707960147882717761607634144638734375/2586393389791859260633595750986302014721399725469177148792618894*t^13 + 92105253599976559057282763803302338662449801889340034846303367635234888097542251591600625/10345573559167437042534383003945208058885598901876708595170475576*t^11 - 200358846604990143497892619380591232239656237640034645430305291261545320999829746724350625/10345573559167437042534383003945208058885598901876708595170475576*t^9 + 527121529945982154111338651304890275751722155494685909974547290759073631637303028845439375/20691147118334874085068766007890416117771197803753417190340951152*t^7 - 23245829889147206192147203432818313240232752547443430725193749867983176285564775464668125/1293196694895929630316797875493151007360699862734588574396309447*t^5 + 112191711225739870573554388775019421953290737099974799427061635688580606464122896226596875/20691147118334874085068766007890416117771197803753417190340951152*t^3 - 2030705825440907966568944460560334442951858787285077552838731387587942504018136378415625/5172786779583718521267191501972604029442799450938354297585237788*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
  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:
| (6.8879161384499516802 - 3.7816115525813890244e-537j)  +/-  (2.51e-244, 2.51e-244j)
| (-9.8358454729573188581 + 1.0925756321091374715e-538j)  +/-  (8.02e-247, 8.02e-247j)
| (-10.823404842764564684 + 1.8095828435885006581e-543j)  +/-  (6.75e-248, 6.75e-248j)
| (-8.2753103443262389744 + 2.8042348808583229024e-554j)  +/-  (1.47e-245, 1.47e-245j)
| (10.823404842764564684 + 1.0455174860846606763e-568j)  +/-  (6.64e-248, 6.64e-248j)
| (-6.8879161384499516802 - 2.3238030852688972398e-579j)  +/-  (2.62e-244, 2.62e-244j)
| (-9.0137366988270846714 + 3.4504240435340933307e-615j)  +/-  (4.17e-246, 4.17e-246j)
| (-7.5863342304621308608 - 1.7028318386862054349e-666j)  +/-  (3.79e-245, 3.79e-245j)
| (-6.4641099819901204704 - 1.0567891275548123963e-707j)  +/-  (4.01e-244, 4.01e-244j)
| (6.612633292961629502 - 7.7716370433537259458e-722j)  +/-  (6.06e-244, 6.06e-244j)
| (8.2753103443262389744 + 2.4698877964221592599e-725j)  +/-  (1.37e-245, 1.37e-245j)
| (5.2223117617903654322 + 1.7574868420587732291e-731j)  +/-  (1.34e-245, 1.34e-245j)
| (9.0137366988270846714 - 2.1839614069415468171e-729j)  +/-  (4.16e-246, 4.16e-246j)
| (-3.2073341618684212087 + 6.4399258901686181294e-731j)  +/-  (1.41e-247, 1.41e-247j)
| (-4.675116635118447815 - 7.5217235044480518893e-732j)  +/-  (4.79e-246, 4.79e-246j)
| (2.7727565284152240061 + 4.2252510112710535005e-739j)  +/-  (3.07e-248, 3.07e-248j)
| (5.7963943386878669963 + 8.3633284674458649461e-735j)  +/-  (3.86e-245, 3.86e-245j)
| (6.4641099819901204704 + 1.464368431107915215e-737j)  +/-  (3.95e-244, 3.95e-244j)
| (-0.74196378430272585765 + 8.6785409975437421609e-753j)  +/-  (9.6e-253, 9.6e-253j)
| (9.8358454729573188581 - 1.5277261351402428947e-746j)  +/-  (8.31e-247, 8.31e-247j)
| (3.2073341618684212087 - 5.8155510557785904638e-747j)  +/-  (1.42e-247, 1.42e-247j)
| (1.5154507704216881063 - 9.8123785813273217336e-751j)  +/-  (1.52e-250, 1.52e-250j)
| (-3.6625195325512155724 + 6.2598248272535657452e-744j)  +/-  (5.09e-247, 5.09e-247j)
| (-6.612633292961629502 + 8.5811122779900629473e-752j)  +/-  (5.95e-244, 5.95e-244j)
| (-1.5154507704216881063 + 8.1395895925880245743e-772j)  +/-  (1.41e-250, 1.41e-250j)
| (0.74196378430272585765 + 6.6295051591704378921e-774j)  +/-  (9.6e-253, 9.6e-253j)
| (1.1540518205301321416 + 3.5151721553297393871e-773j)  +/-  (1.76e-251, 1.76e-251j)
| (4.675116635118447815 + 2.7593624511828484767e-767j)  +/-  (4.56e-246, 4.56e-246j)
| (-2.7727565284152240061 + 2.3271117218023328979e-770j)  +/-  (3.44e-248, 3.44e-248j)
| (-5.2223117617903654322 + 3.9219171581260829461e-766j)  +/-  (1.24e-245, 1.24e-245j)
| (-1.1540518205301321416 + 7.7984544149438816478e-778j)  +/-  (1.75e-251, 1.75e-251j)
| (4.1533469233083435108 + 5.514995141613899551e-774j)  +/-  (1.64e-246, 1.64e-246j)
| (2.3344142183389772393 - 5.3823609662025384683e-776j)  +/-  (5.65e-249, 5.65e-249j)
| (3.6625195325512155724 - 4.4418825657024315715e-774j)  +/-  (4.73e-247, 4.73e-247j)
| (-4.1533469233083435108 + 9.2203691202313915959e-772j)  +/-  (1.62e-246, 1.62e-246j)
| (-1.9016638644450435883 + 5.5471289327710005724e-781j)  +/-  (9.67e-250, 9.67e-250j)
| (-2.3344142183389772393 - 2.0793988659943025374e-780j)  +/-  (5.68e-249, 5.68e-249j)
| (0.3203204479447927311 - 1.7647009785576343135e-784j)  +/-  (7.6e-254, 7.6e-254j)
| (7.5863342304621308608 - 1.0453042102067749696e-773j)  +/-  (3.8e-245, 3.8e-245j)
| (-5.7963943386878669963 - 6.508546778146399388e-779j)  +/-  (3.63e-245, 3.63e-245j)
| (-0.3203204479447927311 - 1.261384683463407781e-793j)  +/-  (7.6e-254, 7.6e-254j)
| (7.9765092697928670941e-801 + 3.1412616660564562217e-801j)  +/-  (3.69e-799, 3.69e-799j)
| (1.9016638644450435883 + 1.1076682143845049604e-789j)  +/-  (9.08e-250, 9.08e-250j)
-------------------------------------------------
The weights are:
| (1.7442503674643719629e-11 + 5.990899305364657744e-547j)  +/-  (3.21e-80, 6.52e-202j)
| (3.4603440140945690796e-22 + 1.5462419672744399487e-556j)  +/-  (5.09e-87, 1.03e-208j)
| (1.6560095162290956784e-26 - 4.4191193703444901024e-559j)  +/-  (6.22e-89, 1.26e-210j)
| (3.8131121253031440713e-16 + 9.5913529709267338079e-553j)  +/-  (1.18e-84, 2.39e-206j)
| (1.6560095162290956784e-26 + 1.9893026382390746277e-558j)  +/-  (8.31e-92, 1.69e-213j)
| (1.7442503674643719629e-11 + 4.7884792052702692625e-549j)  +/-  (1.76e-82, 3.56e-204j)
| (7.0197921828261541914e-19 - 1.6382882862161366694e-554j)  +/-  (2.45e-86, 4.98e-208j)
| (8.5525118139405671918e-14 - 4.3531343425733156974e-551j)  +/-  (6.64e-84, 1.35e-205j)
| (3.9424649836563748439e-10 + 5.2757694764716396872e-548j)  +/-  (3.33e-82, 6.76e-204j)
| (-1.1379849405081710522e-10 - 1.9284886419472361875e-546j)  +/-  (3.73e-86, 7.56e-208j)
| (3.8131121253031440713e-16 - 1.0481160024282815035e-551j)  +/-  (1.61e-90, 3.27e-212j)
| (2.6704160315100282218e-07 + 4.2407975418348810197e-546j)  +/-  (1.39e-84, 2.83e-206j)
| (7.0197921828261541914e-19 + 1.2251303520418395798e-553j)  +/-  (3.28e-92, 6.66e-214j)
| (0.0010247977866262353219 + 3.4476940502122707345e-544j)  +/-  (3.35e-79, 6.8e-201j)
| (3.829176970651634519e-06 - 3.3419147833756503465e-546j)  +/-  (3.22e-83, 6.53e-205j)
| (0.003708481375847686947 - 2.5799848578295195911e-543j)  +/-  (6.48e-79, 1.31e-200j)
| (1.1948663844391848373e-08 - 1.2142003613204457263e-546j)  +/-  (3.41e-86, 6.91e-208j)
| (3.9424649836563748439e-10 + 1.6620370812220035206e-546j)  +/-  (1.1e-86, 2.22e-208j)
| (0.13050892691801458196 + 4.7337657766978981288e-542j)  +/-  (1.16e-75, 2.35e-197j)
| (3.4603440140945690796e-22 - 8.7594069952371514754e-556j)  +/-  (7.61e-95, 1.54e-216j)
| (0.0010247977866262353219 + 9.4563040078553826853e-544j)  +/-  (5.13e-82, 1.04e-203j)
| (0.045235192180923764486 + 3.1198031697354166556e-542j)  +/-  (3.38e-76, 6.86e-198j)
| (0.00023057496470131185634 - 8.7270362142859721769e-545j)  +/-  (4.02e-84, 8.16e-206j)
| (-1.1379849405081710522e-10 - 3.9325234123229202451e-548j)  +/-  (3.53e-88, 7.16e-210j)
| (0.045235192180923764486 + 1.9945774554620195524e-542j)  +/-  (2.26e-78, 4.59e-200j)
| (0.13050892691801458196 + 5.8767015998374822383e-542j)  +/-  (4.58e-76, 9.29e-198j)
| (0.078693125605997543857 - 4.5441225305926602569e-542j)  +/-  (3.57e-76, 7.25e-198j)
| (3.829176970651634519e-06 - 1.7462715783598183144e-545j)  +/-  (3.91e-86, 7.93e-208j)
| (0.003708481375847686947 - 1.0990136740776216951e-543j)  +/-  (5.17e-83, 1.05e-204j)
| (2.6704160315100282218e-07 + 5.8328802984244137937e-547j)  +/-  (1.18e-87, 2.39e-209j)
| (0.078693125605997543857 - 3.2399453094236605669e-542j)  +/-  (1.69e-78, 3.43e-200j)
| (3.6355744517693873016e-05 + 7.306683772540701899e-545j)  +/-  (7.92e-86, 1.61e-207j)
| (0.011527718024069551582 + 6.3742927906690439491e-543j)  +/-  (4.15e-83, 8.41e-205j)
| (0.00023057496470131185634 - 2.8545963080563840424e-544j)  +/-  (3.76e-85, 7.63e-207j)
| (3.6355744517693873016e-05 + 1.8096791668840236193e-545j)  +/-  (4.72e-87, 9.56e-209j)
| (0.027250770790397770257 - 8.7625713870524232268e-543j)  +/-  (6.43e-84, 1.3e-205j)
| (0.011527718024069551582 + 3.1473300992308009522e-543j)  +/-  (1.15e-84, 2.34e-206j)
| (0.14840945847903488294 - 9.0501903710433473448e-542j)  +/-  (1.96e-83, 3.98e-205j)
| (8.5525118139405671918e-14 + 9.020726238312875041e-550j)  +/-  (1.49e-93, 3.03e-215j)
| (1.1948663844391848373e-08 - 1.0449016862581318011e-547j)  +/-  (5.74e-90, 1.17e-211j)
| (0.14840945847903488294 - 8.2458569504172002397e-542j)  +/-  (2.85e-84, 5.81e-206j)
| (0.10674097932930982954 + 1.109269130946782955e-541j)  +/-  (2.4e-84, 4.84e-206j)
| (0.027250770790397770257 - 1.5446180383339653308e-542j)  +/-  (1.67e-85, 3.32e-207j)
