Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 48
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : t^11 - 41*t^9 + 528*t^7 - 2520*t^5 + 4095*t^3 - 1575*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 1497869309712682652522026677854718342261654301183236773893806290150571223783180882415962511/1026756831816408822689166684730024563406024079681980894780703722893334797076566661632991*t^57 + 305300772720022783006644855555437707662408956232700885931804644420402789581810177112573841153628/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^55 - 127595513655017866158927591394278988571381548483585515428706041431909918226362813368210259926408660/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^53 + 36917076290505607373739684042107947946250667378371545923329032754173494617088342295870028730502719995/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^51 - 7862240547358036562946625709622152084563458139733807445833126944148582239498028696241928474319566031355/309053806376739055629439172103737393585213247984276249328991820590893773920046565151530291*t^49 + 182779905473445215745169029681452490021715779724016315187555757364202515537535345413185306369418859716640/44150543768105579375634167443391056226459035426325178475570260084413396274292366450218613*t^47 - 23290997791632493859940224782063531538356074765647244743486502502075465204066428269494582878165084812167920/44150543768105579375634167443391056226459035426325178475570260084413396274292366450218613*t^45 + 4995385613469543289141693100190256344826058712514202574253776038075473989264862986836857741196038484598825/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^43 - 408064177782434781861260066299583789875741837944199297132153943727579952212391941428033052511237229059388025/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^41 + 27047295083372033501779781535314566749453136398803998791599562685871297174409986596590110654468624880475700100/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^39 - 1461667251053898574142249698803158885132039063428787007895320900008671815216435066253536282295330831849829111100/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^37 + 64567400375521718627836888891693012391408794387813782627586615468734597184165114596669974894305485592681214887425/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^35 - 2332905590501484340392328042539287589625838969966275000475634714924632938085150590022601350582193045076650889802625/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^33 + 68871085208166826151787546631737376357480465973551962650317066226888909247617091643278020341496609473745610312204000/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^31 - 1656809216447328567194416147848433233255970705373946695458838598239872547682356919157341771907350794791333875296616000/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^29 + 32341192664547681489123434342432178404273553748722705819444919515256157222390424652475857079670966168167410371116670375/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^27 - 509245707617924748025707804465523869580529227821405682108184286779623346720150013997790276798406455913859579003120812375/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^25 + 6418789871368827989178126648118182998995102826376579952714193040706610785818005597443563288150029058059473365366883987500/93341530165128074789924244066365869400547643607452808616427611172121345188778787421181*t^23 - 5830793431851204322623977626539891492631367441120457789378740951434323811576194372209344396696946382630549280952139787500/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^21 + 45632449135299488126631753144844228681440302433143050180210705429175745939162856083494468730873614043713289929619799978125/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^19 - 275499921040293716568548589494727335983667404604069670797282219229477411875556451862384549219935046394096653734205101978125/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^17 + 1258808286520968111578823519526575151682028361212748444304301654224853171243005990571371704296656246195702346496720135200000/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^15 - 4246834568968210415774837879878005621976900965126346078302017987369656371137841855221900725214294789408607557908774665750000/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^13 + 10236811672963344259755070240769652204010474716062017936378738558220867203869944652108487900110904383321842357656244648765625/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^11 - 16842638187470089935037296409458826610923299239828367753395670569450733895414770503786124237694022305616001953619455906015625/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^9 + 17681117469820850445455164779008263442838007417891124530320684532000284048673391842499120986348130650314397852168628736562500/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^7 - 10628242790818035286953621730016186832978257576874035719104328816362487409120811749013242393950391121901604055117624360937500/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^5 + 3002728248808490344476916285769778450674123805531008141384226117492127954607162677958744328112190808400942538628698544140625/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*t^3 - 251527118863511410654670827811834054237585294396890096243967481690228028147935284668283297961721439489772513621675744140625/8485593651375279526356749460578715400049785782495709874220691924738304108070798856471*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: 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
Positive weights:   59 out of 59
Indefinite weights: 0 out of 59
Negative weights:   0 out of 59
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.9059445883004563462 + 2.3059464130507383785e-706j)  +/-  (9.68e-242, 9.68e-242j)
| (-11.902826177606434357 + 1.5098319503816429635e-723j)  +/-  (1.67e-243, 1.67e-243j)
| (-3.7810916210592795496 + 1.7228504940144261545e-723j)  +/-  (6.68e-245, 6.68e-245j)
| (10.596377524000490107 - 1.7774560319567143968e-719j)  +/-  (2.09e-242, 2.09e-242j)
| (-13.581250399032524401 + 1.4328354580398277076e-734j)  +/-  (1.33e-245, 1.33e-245j)
| (12.663375751719868695 - 5.0750870597964099658e-730j)  +/-  (2.2e-244, 2.2e-244j)
| (13.581250399032524401 - 1.6804382919872606166e-732j)  +/-  (1.39e-245, 1.39e-245j)
| (-12.663375751719868695 + 7.5712286864478592647e-736j)  +/-  (2.21e-244, 2.21e-244j)
| (-9.4450107581779399518 + 4.8935469114036251272e-733j)  +/-  (8.43e-242, 8.43e-242j)
| (10.00652845105889844 - 1.4536325273712110884e-731j)  +/-  (5.07e-242, 5.07e-242j)
| (-8.3852112792694871896 - 9.3579323770117085999e-741j)  +/-  (1.11e-241, 1.11e-241j)
| (-11.223499855719980333 + 1.2590741122738363584e-742j)  +/-  (7.07e-243, 7.07e-243j)
| (-10.596377524000490107 + 6.6901207969058896089e-743j)  +/-  (2.03e-242, 2.03e-242j)
| (-2.0251480575947975726 + 2.1975708383078262546e-747j)  +/-  (6.3e-248, 6.3e-248j)
| (-3.3747086797406716539 - 2.0543028059109619839e-744j)  +/-  (1.87e-245, 1.87e-245j)
| (-5.5185151787545581891 - 4.898894722589583969e-741j)  +/-  (6.04e-243, 6.04e-243j)
| (5.0719089991387711035 + 5.3571946201668454041e-742j)  +/-  (2.19e-243, 2.19e-243j)
| (-2.6509189197059792975 + 4.5861460530759568204e-755j)  +/-  (1.36e-246, 1.36e-246j)
| (-4.6328811754148542753 + 1.5148796752748089732e-749j)  +/-  (7.43e-244, 7.43e-244j)
| (-8.9059445883004563462 + 6.8525461101838781331e-749j)  +/-  (1.11e-241, 1.11e-241j)
| (3.3747086797406716539 + 3.7019165627200955803e-752j)  +/-  (1.64e-245, 1.64e-245j)
| (1.1133333106091358352 - 3.9306883677008799664e-762j)  +/-  (5.84e-251, 5.84e-251j)
| (6.9063037047830335885 - 2.0642181526085640797e-753j)  +/-  (5.1e-242, 5.1e-242j)
| (11.223499855719980333 + 8.2624575217513260943e-762j)  +/-  (6.73e-243, 6.73e-243j)
| (-2.3344142183389772393 - 9.2479269236053994497e-776j)  +/-  (3.12e-247, 3.12e-247j)
| (5.5185151787545581891 + 2.8354706619780120249e-769j)  +/-  (5.92e-243, 5.92e-243j)
| (1.7570365249604729082 - 2.738714118326952011e-792j)  +/-  (1.32e-248, 1.32e-248j)
| (5.9727611532980052905 - 1.9818930860205910489e-786j)  +/-  (1.47e-242, 1.47e-242j)
| (-10.00652845105889844 - 1.5370524277692230845e-795j)  +/-  (4.87e-242, 4.87e-242j)
| (-7.87979382774092033 - 1.9265438184626258765e-793j)  +/-  (1.07e-241, 1.07e-241j)
| (-7.387411240610474185 + 8.2719457376974734231e-800j)  +/-  (7.59e-242, 7.59e-242j)
| (7.387411240610474185 - 1.3091413647655051427e-814j)  +/-  (8.73e-242, 8.73e-242j)
| (2.9933301069662518637 - 1.268679635584557448e-840j)  +/-  (4.69e-246, 4.69e-246j)
| (9.4450107581779399518 + 1.0893068300839862944e-834j)  +/-  (8.24e-242, 8.24e-242j)
| (-2.9933301069662518637 + 4.213134078822912565e-851j)  +/-  (4.97e-246, 4.97e-246j)
| (-5.0719089991387711035 + 2.6090838935599276168e-847j)  +/-  (2.15e-243, 2.15e-243j)
| (-1.1133333106091358352 - 2.8654975833537843789e-862j)  +/-  (5.7e-251, 5.7e-251j)
| (1.4655215253859805014 - 9.3140317949979045034e-861j)  +/-  (1.21e-249, 1.21e-249j)
| (11.902826177606434357 + 6.2446924808639322e-853j)  +/-  (1.68e-243, 1.68e-243j)
| (-6.4351034987706258171 - 2.0377434881928669765e-857j)  +/-  (2.98e-242, 2.98e-242j)
| (-6.6334748040550627708e-893 - 9.8453737558061358569e-893j)  +/-  (7e-891, 7e-891j)
| (4.6328811754148542753 + 4.9831171165747140558e-869j)  +/-  (7.13e-244, 7.13e-244j)
| (8.3852112792694871896 + 6.3648534451380056787e-896j)  +/-  (1.12e-241, 1.12e-241j)
| (2.3344142183389772393 - 4.7875189624530758316e-926j)  +/-  (3.47e-247, 3.47e-247j)
| (7.87979382774092033 + 1.9599744096194775644e-925j)  +/-  (1.01e-241, 1.01e-241j)
| (-0.74196378430272585765 - 8.0796922759181657605e-951j)  +/-  (2.85e-252, 2.85e-252j)
| (-4.2020053625706506189 - 1.1041494374945482447e-943j)  +/-  (2.21e-244, 2.21e-244j)
| (6.4351034987706258171 - 1.7790050564798661692e-939j)  +/-  (2.81e-242, 2.81e-242j)
| (0.36960789397760717348 + 9.1881842716033666003e-965j)  +/-  (1.52e-253, 1.52e-253j)
| (4.2020053625706506189 - 1.3560128688938569911e-953j)  +/-  (2.26e-244, 2.26e-244j)
| (-6.9063037047830335885 - 2.7174139385110391186e-952j)  +/-  (5.21e-242, 5.21e-242j)
| (-1.4655215253859805014 - 1.9063538301557977731e-959j)  +/-  (1.24e-249, 1.24e-249j)
| (2.6509189197059792975 - 2.3722796570407544438e-956j)  +/-  (1.28e-246, 1.28e-246j)
| (-5.9727611532980052905 + 6.4748956199677143762e-953j)  +/-  (1.34e-242, 1.34e-242j)
| (-0.36960789397760717348 + 6.9270678409867632886e-963j)  +/-  (1.52e-253, 1.52e-253j)
| (-1.7570365249604729082 - 5.9663972253694913745e-958j)  +/-  (1.2e-248, 1.2e-248j)
| (0.74196378430272585765 + 7.624722999171813358e-962j)  +/-  (2.85e-252, 2.85e-252j)
| (2.0251480575947975726 - 4.750334545508446715e-958j)  +/-  (6.77e-248, 6.77e-248j)
| (3.7810916210592795496 - 4.5865715286853341788e-954j)  +/-  (6.89e-245, 6.89e-245j)
-------------------------------------------------
The weights are:
| (1.2630228397720145419e-18 - 1.4678348901582449542e-723j)  +/-  (3.55e-58, 1.39e-177j)
| (4.8893847691292298196e-32 + 6.147606887263142271e-733j)  +/-  (5.08e-66, 1.99e-185j)
| (0.00013008841316599682381 + 3.0334445626815707623e-716j)  +/-  (4.59e-38, 1.8e-157j)
| (1.0042662832898501041e-25 - 1.9713847739434670928e-728j)  +/-  (4.97e-63, 1.94e-182j)
| (3.7438284093590303193e-41 + 8.0241766202079551983e-738j)  +/-  (1.01e-69, 3.94e-189j)
| (4.9204576700641238245e-36 + 2.4878226620437444626e-734j)  +/-  (4.86e-68, 1.9e-187j)
| (3.7438284093590303193e-41 - 3.8594528695305566517e-737j)  +/-  (5.65e-70, 2.21e-189j)
| (4.9204576700641238245e-36 - 4.333851160839786428e-735j)  +/-  (2.22e-68, 8.68e-188j)
| (9.3228232772914782066e-21 + 1.0037340307484942655e-726j)  +/-  (5.76e-63, 2.25e-182j)
| (4.1411402780472249638e-23 + 8.2662404233611069826e-727j)  +/-  (6.73e-64, 2.63e-183j)
| (1.103363350898604166e-16 + 2.1589653667616661413e-724j)  +/-  (6.09e-61, 2.38e-180j)
| (1.1493135033550243098e-28 - 4.1655827866085788844e-731j)  +/-  (1.43e-66, 5.59e-186j)
| (1.0042662832898501041e-25 + 1.708767669622446239e-729j)  +/-  (1.45e-65, 5.68e-185j)
| (0.015032652171882715454 - 1.2191387632430830449e-713j)  +/-  (4.96e-36, 1.94e-155j)
| (0.0005320137947750061283 - 1.3703590010921431793e-715j)  +/-  (2.51e-45, 9.83e-165j)
| (4.3800922288562050687e-08 + 4.980737068648772488e-719j)  +/-  (2.87e-55, 1.12e-174j)
| (4.5836602718914876338e-07 - 9.8195461096266245071e-718j)  +/-  (4.13e-57, 1.61e-176j)
| (0.0038429057479634831271 - 2.0176713288634236628e-714j)  +/-  (2.83e-42, 1.11e-161j)
| (3.7910641328888510729e-06 + 1.3617198370297622094e-717j)  +/-  (5.53e-52, 2.16e-171j)
| (1.2630228397720145419e-18 - 1.6351230114285565061e-725j)  +/-  (2.96e-63, 1.16e-182j)
| (0.0005320137947750061283 - 3.0425214225305211128e-715j)  +/-  (4.94e-51, 1.93e-170j)
| (0.078734121052183804206 + 2.2496470316402408214e-713j)  +/-  (6.19e-33, 2.42e-152j)
| (8.3405852173163255294e-12 - 1.4409330388838794578e-720j)  +/-  (1.08e-63, 4.21e-183j)
| (1.1493135033550243098e-28 + 3.6180741171058804975e-730j)  +/-  (2.41e-72, 9.43e-192j)
| (0.0082453551821544288896 + 5.4188784294698097943e-714j)  +/-  (9.29e-44, 3.63e-163j)
| (4.3800922288562050687e-08 + 2.1209133171869536377e-718j)  +/-  (6.33e-60, 2.48e-179j)
| (0.022060594753373289886 + 2.7621034799936239706e-713j)  +/-  (3.01e-44, 1.18e-163j)
| (3.2769745922364991482e-09 - 4.3043530273910634773e-719j)  +/-  (2.34e-61, 9.14e-181j)
| (4.1411402780472249638e-23 - 4.8104183924987384642e-728j)  +/-  (4.5e-68, 1.76e-187j)
| (6.5420372332629697543e-15 - 2.3771726645896256095e-723j)  +/-  (6.03e-65, 2.36e-184j)
| (2.7379283324406360137e-13 + 2.2325781245503369902e-722j)  +/-  (1.74e-64, 6.81e-184j)
| (2.7379283324406360137e-13 + 2.3954817886993335976e-721j)  +/-  (1.59e-67, 6.23e-187j)
| (0.0016435084975368638786 + 1.1697208342365184154e-714j)  +/-  (3.7e-56, 1.45e-175j)
| (9.3228232772914782066e-21 - 3.4169234515731156063e-725j)  +/-  (1.3e-71, 5.07e-191j)
| (0.0016435084975368638786 + 5.8122100050632304666e-715j)  +/-  (2.64e-54, 1.03e-173j)
| (4.5836602718914876338e-07 - 2.6934385181504122795e-718j)  +/-  (4.25e-61, 1.66e-180j)
| (0.078734121052183804206 + 1.7496894493279307646e-713j)  +/-  (5.35e-48, 2.09e-167j)
| (0.04488334430313924584 - 2.6637636880101052511e-713j)  +/-  (9.55e-51, 3.73e-170j)
| (4.8893847691292298196e-32 - 4.2685751393257625782e-732j)  +/-  (1.8e-77, 7.02e-197j)
| (1.8953343380872787774e-10 + 1.313568101884803448e-720j)  +/-  (4.29e-65, 1.68e-184j)
| (0.14717120493466586311 - 1.9736011638327175908e-713j)  +/-  (1.79e-50, 6.99e-170j)
| (3.7910641328888510729e-06 + 4.3144895900964318603e-717j)  +/-  (2.9e-63, 1.13e-182j)
| (1.103363350898604166e-16 + 7.1689300496088866527e-723j)  +/-  (1.46e-70, 5.7e-190j)
| (0.0082453551821544288896 + 9.2687904411098372672e-714j)  +/-  (8.04e-59, 3.14e-178j)
| (6.5420372332629697543e-15 - 3.8885707686758208424e-722j)  +/-  (9.69e-70, 3.79e-189j)
| (0.11308855909500270031 - 1.7606296748289028914e-713j)  +/-  (7.46e-56, 2.92e-175j)
| (2.4919646549940185756e-05 - 6.5401093415141984608e-717j)  +/-  (1.02e-62, 3.98e-182j)
| (1.8953343380872787774e-10 + 8.1557294405212856437e-720j)  +/-  (2.77e-67, 1.08e-186j)
| (0.13819203816872816941 + 2.0301686111182104501e-713j)  +/-  (1.16e-56, 4.55e-176j)
| (2.4919646549940185756e-05 - 1.8224603212231429142e-716j)  +/-  (2.81e-64, 1.1e-183j)
| (8.3405852173163255294e-12 - 1.8222257591380892587e-721j)  +/-  (8e-69, 3.15e-188j)
| (0.04488334430313924584 - 1.9109669318887816785e-713j)  +/-  (6.98e-60, 2.75e-179j)
| (0.0038429057479634831271 - 3.7278747341745941558e-714j)  +/-  (3.12e-62, 1.22e-181j)
| (3.2769745922364991482e-09 - 8.4855882074441810402e-720j)  +/-  (2.62e-67, 1.03e-186j)
| (0.13819203816872816941 + 1.8683741851354652462e-713j)  +/-  (8.83e-60, 3.51e-179j)
| (0.022060594753373289886 + 1.8518295803220172381e-713j)  +/-  (1.77e-60, 6.99e-180j)
| (0.11308855909500270031 - 2.0806508722440847318e-713j)  +/-  (1.52e-60, 6.07e-180j)
| (0.015032652171882715454 - 1.9367697779905847777e-713j)  +/-  (1.19e-61, 4.84e-181j)
| (0.00013008841316599682381 + 7.5095658842924909305e-716j)  +/-  (1.92e-64, 7.26e-184j)
