Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 59
-------------------------------------------------
Trying to find an order 59 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^61 - 520183474972410893682977930769284382386/146996893367385334241715463617070179*t^59 + 214883771474186898743656349975464314345088/146996893367385334241715463617070179*t^57 - 967208953801650176000621486967047092581301/2578892866094479548100271291527547*t^55 + 691733028237392907214153655481081083277502065/10315571464377918192401085166110188*t^53 - 183360375321157889990906318158644145406369770695/20631142928755836384802170332220376*t^51 + 18708407356384593817569138192087124077780122054325/20631142928755836384802170332220376*t^49 - 1506521086131277593182776326704737847315210301673725/20631142928755836384802170332220376*t^47 + 779150183313337749725307196970682005568369234598833075/165049143430046691078417362657763008*t^45 - 81842829152999195636885616829319852512915403125731956625/330098286860093382156834725315526016*t^43 + 1760379043545067716000016502966345250630477549309245608125/165049143430046691078417362657763008*t^41 - 249452381736030262583239812532518502043845399255486487683875/660196573720186764313669450631052032*t^39 + 29201359063379655294547202558186291180948275176369289233404625/2640786294880747057254677802524208128*t^37 - 1413730955557805824969447383607073887801136507750836473877581375/5281572589761494114509355605048416256*t^35 + 28293393753939011287656953479859756697827496622982368149354211875/5281572589761494114509355605048416256*t^33 - 233596041380016909393475720511008900862951413615083258813526411875/2640786294880747057254677802524208128*t^31 + 50733875621148645773420083217826076697517349240391790114711064025625/42252580718091952916074844840387330048*t^29 - 1126212275194470835636468643249299357730928758529549962202503431756875/84505161436183905832149689680774660096*t^27 + 2536901802656620113520675820873209007068830242418454577956560892381875/21126290359045976458037422420193665024*t^25 - 147073337970108477800681641504815841873801366479229334087022294938296875/169010322872367811664299379361549320192*t^23 + 3388208862937226521636190116895753943308576188068778989710633982156046875/676041291489471246657197517446197280768*t^21 - 30554622752307085549151347037196670872099778042130558270196039023731828125/1352082582978942493314395034892394561536*t^19 + 105814632401508316041178990609761868072737700200250883090951391741578296875/1352082582978942493314395034892394561536*t^17 - 274610283524504913463323336423213566844353931743485328903570737562896078125/1352082582978942493314395034892394561536*t^15 + 4136602855627459097781403782394360795789002252835092995180099459376224765625/10816660663831539946515160279139156492288*t^13 - 10818680338677376495058505433433350616021649384496681331788858355573516671875/21633321327663079893030320558278312984576*t^11 + 4617440261815763781511026044411502453894121593347432581960282229655064078125/10816660663831539946515160279139156492288*t^9 - 9369234764882645110925015856378416064840681417152525738444910107992561828125/43266642655326159786060641116556625969152*t^7 + 9637943247384880206730943391489238378945557878067846887493601405357429171875/173066570621304639144242564466226503876608*t^5 - 1800701499119238878301504482210638848493135734623070747351668154733108828125/346133141242609278288485128932453007753216*t^3 + 13898714612184573920996251816077016246803954874930404261139205036113828125/346133141242609278288485128932453007753216*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:
| (10.158594282248246296 - 7.7554960850491884061e-707j)  +/-  (5.21e-245, 5.21e-245j)
| (-8.0845415826483305848 - 1.132701634914400386e-706j)  +/-  (1.64e-241, 1.64e-241j)
| (9.520354190954800957 - 4.879015603001590198e-707j)  +/-  (1.15e-243, 1.15e-243j)
| (6.9116246559126243163 - 6.6613527153836556353e-710j)  +/-  (1.04e-240, 1.04e-240j)
| (8.0845415826483305848 - 1.6241820667452679954e-717j)  +/-  (1.59e-241, 1.59e-241j)
| (8.9918162174733940259 - 1.5668879080156499353e-728j)  +/-  (1.01e-242, 1.01e-242j)
| (-8.5199552801834052415 + 1.5013907507321300569e-742j)  +/-  (4.92e-242, 4.92e-242j)
| (-5.5245741938999589018 + 1.7415007014417426365e-741j)  +/-  (8.17e-241, 8.17e-241j)
| (-10.158594282248246296 + 6.6725567265078349551e-750j)  +/-  (5.63e-245, 5.63e-245j)
| (8.5199552801834052415 - 6.3520342337858711167e-745j)  +/-  (4.92e-242, 4.92e-242j)
| (-7.6751583531848445391 + 8.907410626288674738e-759j)  +/-  (4.13e-241, 4.13e-241j)
| (-9.520354190954800957 - 4.2246836431498529217e-761j)  +/-  (1.14e-243, 1.14e-243j)
| (-3.9402331491034160301 + 6.9766703949253255106e-760j)  +/-  (1.62e-242, 1.62e-242j)
| (-8.9918162174733940259 + 1.681571761853354263e-760j)  +/-  (1.03e-242, 1.03e-242j)
| (-3.0360804789905082202 + 3.4107696352729774682e-762j)  +/-  (2.25e-244, 2.25e-244j)
| (3.9402331491034160301 + 5.1333739366189045619e-758j)  +/-  (1.56e-242, 1.56e-242j)
| (3.0360804789905082202 + 3.457317787217494438e-761j)  +/-  (2.37e-244, 2.37e-244j)
| (-1.8625336883181901067 + 3.2474916897126169858e-765j)  +/-  (1.43e-247, 1.43e-247j)
| (-0.7071067811865475244 - 9.424575163200547757e-770j)  +/-  (7.68e-252, 7.68e-252j)
| (7.6751583531848445391 - 6.1514940959719118075e-757j)  +/-  (4.13e-241, 4.13e-241j)
| (-7.2855585634061243724 + 4.7486823835672169911e-761j)  +/-  (7e-241, 7e-241j)
| (1.5728544619449814255 - 4.6846468250525892136e-770j)  +/-  (1.29e-248, 1.29e-248j)
| (-4.8760772637170367242 - 1.0148692551431336469e-761j)  +/-  (2.55e-241, 2.55e-241j)
| (-3.334636012653858685 + 7.0756655312506079918e-765j)  +/-  (9.22e-244, 9.22e-244j)
| (5.1974200444681561248 - 5.3312018183361481738e-761j)  +/-  (5.11e-241, 5.11e-241j)
| (-5.1974200444681561248 - 1.281571775417497692e-764j)  +/-  (4.83e-241, 4.83e-241j)
| (3.334636012653858685 + 2.8545683447095162656e-769j)  +/-  (9.61e-244, 9.61e-244j)
| (4.8760772637170367242 - 7.4868113860067920179e-765j)  +/-  (2.47e-241, 2.47e-241j)
| (-4.2480550381478758828 + 8.2838569345800732397e-769j)  +/-  (4.37e-242, 4.37e-242j)
| (-2.1534091079756964651 - 2.449437474713674175e-772j)  +/-  (9.53e-247, 9.53e-247j)
| (2.1534091079756964651 + 8.0919313289107560399e-772j)  +/-  (9.83e-247, 9.83e-247j)
| (5.5245741938999589018 + 1.5428088881675916527e-765j)  +/-  (7.43e-241, 7.43e-241j)
| (1.8625336883181901067 + 3.6626640681559415754e-786j)  +/-  (1.2e-247, 1.2e-247j)
| (6.5504605619892016408 + 5.7326532324350389991e-778j)  +/-  (1.34e-240, 1.34e-240j)
| (-3.6358971861835611142 + 2.2599201884468636168e-790j)  +/-  (4.21e-243, 4.21e-243j)
| (-1.5728544619449814255 - 7.2696835516976276579e-797j)  +/-  (1.33e-248, 1.33e-248j)
| (-5.8583972563729575323 - 2.7957392307659194411e-787j)  +/-  (1.1e-240, 1.1e-240j)
| (0.7071067811865475244 + 1.1819683577285171434e-799j)  +/-  (6.93e-252, 6.93e-252j)
| (4.2480550381478758828 + 3.2943686384318433906e-792j)  +/-  (4.44e-242, 4.44e-242j)
| (-1.284053295841142568 - 3.615985165885260971e-801j)  +/-  (1.24e-249, 1.24e-249j)
| (-0.091977350582929901221 - 1.2997466530576468006e-807j)  +/-  (1.03e-254, 1.03e-254j)
| (7.2855585634061243724 - 4.9822348957465588532e-791j)  +/-  (6.92e-241, 6.92e-241j)
| (2.4457683512040692508 - 5.4700751684848168554e-808j)  +/-  (7.01e-246, 7.01e-246j)
| (1.284053295841142568 + 2.9712111029370892049e-812j)  +/-  (1.25e-249, 1.25e-249j)
| (-6.9116246559126243163 - 4.8244593086956197791e-803j)  +/-  (1.14e-240, 1.14e-240j)
| (5.8583972563729575323 + 9.1414789928160491852e-802j)  +/-  (1.13e-240, 1.13e-240j)
| (-4.5598265458956792925 + 9.4257880557938233522e-813j)  +/-  (1.04e-241, 1.04e-241j)
| (3.6358971861835611142 + 8.659141474031633172e-814j)  +/-  (4.04e-243, 4.04e-243j)
| (0.99571546102465784412 - 2.2522566805759706262e-822j)  +/-  (1e-250, 1e-250j)
| (-6.5504605619892016408 - 1.6975433380304719206e-811j)  +/-  (1.34e-240, 1.34e-240j)
| (-6.1999298040220602723 - 2.8405156407822199446e-812j)  +/-  (1.31e-240, 1.31e-240j)
| (-0.41600408776805729877 + 9.6364127093033485565e-825j)  +/-  (3.86e-253, 3.86e-253j)
| (2.7398946978339437346 + 1.2616884864472585442e-816j)  +/-  (4.23e-245, 4.23e-245j)
| (-1.0726963600369481766e-845 - 1.2695077615355048743e-845j)  +/-  (1.01e-843, 1.01e-843j)
| (4.5598265458956792925 - 3.9950825596075550428e-817j)  +/-  (1.12e-241, 1.12e-241j)
| (-0.99571546102465784412 + 2.6443047995466390252e-833j)  +/-  (9.94e-251, 9.94e-251j)
| (-2.4457683512040692508 + 4.8334969943232234661e-827j)  +/-  (6.82e-246, 6.82e-246j)
| (-2.7398946978339437346 + 1.7828848730223158818e-828j)  +/-  (4.03e-245, 4.03e-245j)
| (0.091977350582929901221 + 1.6379188993832758057e-837j)  +/-  (1.03e-254, 1.03e-254j)
| (0.41600408776805729877 - 8.2349984369903287218e-836j)  +/-  (3.66e-253, 3.66e-253j)
| (6.1999298040220602723 + 2.8146526637359882811e-832j)  +/-  (1.35e-240, 1.35e-240j)
-------------------------------------------------
The weights are:
| (6.3263397141545952718e-46 + 6.3766135533437557407e-744j)  +/-  (1.71e-73, 2.87e-193j)
| (9.7816715405306167021e-30 - 9.3233677772691763612e-735j)  +/-  (6.25e-69, 1.05e-188j)
| (1.391038049347346494e-40 - 4.0115781069252795175e-741j)  +/-  (5.98e-72, 1e-191j)
| (3.7133757276179693567e-22 + 1.750782202679940829e-730j)  +/-  (3.41e-65, 5.72e-185j)
| (9.7816715405306167021e-30 + 2.8577051219319073446e-735j)  +/-  (7.4e-69, 1.24e-188j)
| (2.1504327194466677188e-36 + 6.682074947788419732e-739j)  +/-  (4.64e-71, 7.78e-191j)
| (7.5977851638238022204e-33 - 6.1412777932396603301e-737j)  +/-  (2.37e-73, 3.97e-193j)
| (1.0358784968767196744e-14 + 3.3754494762784381653e-728j)  +/-  (2.53e-64, 4.23e-184j)
| (6.3263397141545952718e-46 + 2.1321465254095120885e-744j)  +/-  (6.08e-79, 1.02e-198j)
| (7.5977851638238022204e-33 - 5.4671126649504334309e-737j)  +/-  (6.04e-72, 1.01e-191j)
| (5.8694086544224041223e-27 + 7.5903776133775452806e-734j)  +/-  (1.1e-71, 1.85e-191j)
| (1.391038049347346494e-40 - 1.8022405359270382584e-741j)  +/-  (2.71e-77, 4.54e-197j)
| (3.1227977579111792547e-08 - 6.7663645200760370391e-725j)  +/-  (1.19e-60, 1.99e-180j)
| (2.1504327194466677188e-36 + 4.2383666779163232782e-739j)  +/-  (1.35e-75, 2.26e-195j)
| (1.6649909024259568345e-05 + 1.961281195314571158e-723j)  +/-  (5.55e-56, 9.3e-176j)
| (3.1227977579111792547e-08 - 1.4459936456611443835e-724j)  +/-  (1.04e-62, 1.75e-182j)
| (1.6649909024259568345e-05 + 3.4231351520261441406e-723j)  +/-  (7.11e-58, 1.19e-177j)
| (0.0051001521082702330633 + 5.6435354830105617111e-722j)  +/-  (1.43e-48, 2.4e-168j)
| (0.098965349218941590441 + 6.92116779723853234e-721j)  +/-  (5.92e-48, 9.92e-168j)
| (5.8694086544224041223e-27 - 1.1417233860550095013e-733j)  +/-  (7.67e-74, 1.29e-193j)
| (1.907683359479909468e-24 - 7.980377256511020687e-733j)  +/-  (2.97e-72, 4.97e-192j)
| (0.013747016779266244112 - 1.4604117135827091885e-721j)  +/-  (4.49e-48, 7.52e-168j)
| (8.4907698656548293094e-12 + 9.8324085872041657178e-727j)  +/-  (5.92e-66, 9.92e-186j)
| (2.5064687997418454464e-06 - 6.9741455795506785042e-724j)  +/-  (1.58e-59, 2.65e-179j)
| (3.3919990388300880606e-13 - 6.0414134892868793809e-727j)  +/-  (1.29e-69, 2.16e-189j)
| (3.3919990388300880606e-13 - 1.932672778916959631e-727j)  +/-  (3.45e-67, 5.79e-187j)
| (2.5064687997418454464e-06 - 1.2967480270369446974e-723j)  +/-  (1.94e-62, 3.25e-182j)
| (8.4907698656548293094e-12 + 2.7367581969694736406e-726j)  +/-  (9.69e-69, 1.62e-188j)
| (2.5416784618597787217e-09 + 1.8295332284047544995e-725j)  +/-  (5.68e-65, 9.52e-185j)
| (0.0015932014751987108589 - 2.7096866919199384235e-722j)  +/-  (1.07e-56, 1.8e-176j)
| (0.0015932014751987108589 - 3.9754197026537006422e-722j)  +/-  (3.93e-58, 6.58e-178j)
| (1.0358784968767196744e-14 + 1.2171785006313543936e-727j)  +/-  (3.31e-71, 5.55e-191j)
| (0.0051001521082702330633 + 7.8435614761926407594e-722j)  +/-  (7.78e-57, 1.3e-176j)
| (4.6491508279481578551e-20 - 8.1505052741855608734e-730j)  +/-  (2.25e-74, 3.77e-194j)
| (3.0990051799280638998e-07 + 2.2737179909192689332e-724j)  +/-  (1.51e-64, 2.52e-184j)
| (0.013747016779266244112 - 1.1077808352661800806e-721j)  +/-  (4.62e-57, 7.73e-177j)
| (2.3677680834222043969e-16 - 5.2041137602914473243e-729j)  +/-  (1.48e-72, 2.48e-192j)
| (0.098965349218941590441 + 7.8259468607207543875e-721j)  +/-  (3.97e-57, 6.66e-177j)
| (2.5416784618597787217e-09 + 4.2288090964123833528e-725j)  +/-  (1.96e-68, 3.29e-188j)
| (0.031295970333382649443 + 2.0728286959395576894e-721j)  +/-  (1.41e-57, 2.35e-177j)
| (0.28760154381777067733 + 1.0776859663851715845e-719j)  +/-  (2.39e-57, 4e-177j)
| (1.907683359479909468e-24 + 4.4626958854547418778e-732j)  +/-  (2.53e-76, 4.24e-196j)
| (0.00041756741207800553543 + 1.8873620145455038007e-722j)  +/-  (6.54e-63, 1.1e-182j)
| (0.031295970333382649443 + 2.5946755529916967469e-721j)  +/-  (2.09e-58, 3.5e-178j)
| (3.7133757276179693567e-22 + 8.5974154794234930972e-732j)  +/-  (2.97e-76, 4.98e-196j)
| (2.3677680834222043969e-16 - 2.2665342800880990572e-728j)  +/-  (1.97e-73, 3.31e-193j)
| (1.653410009309195512e-10 - 4.4724757671506635058e-726j)  +/-  (1.59e-69, 2.67e-189j)
| (3.0990051799280638998e-07 + 4.5212347564104863709e-724j)  +/-  (5.71e-68, 9.56e-188j)
| (0.060351643452606899708 - 4.4825652036893793307e-721j)  +/-  (1.53e-61, 2.57e-181j)
| (4.6491508279481578551e-20 - 8.3147184986825515033e-731j)  +/-  (9.28e-76, 1.55e-195j)
| (3.9476454111579254295e-18 + 7.0386401384008399151e-730j)  +/-  (9.23e-75, 1.55e-194j)
| (0.13977271435188680499 - 1.4317024849110424132e-720j)  +/-  (1.5e-63, 2.52e-183j)
| (9.1441767563411977718e-05 - 8.3468356169301738368e-723j)  +/-  (1.76e-67, 2.95e-187j)
| (-0.27791220187828966582 - 1.9705397325628918904e-719j)  +/-  (3.84e-64, 6.3e-184j)
| (1.653410009309195512e-10 - 1.1277257381153218366e-725j)  +/-  (1.65e-71, 2.76e-191j)
| (0.060351643452606899708 - 3.7686457923425397897e-721j)  +/-  (2.59e-65, 4.27e-185j)
| (0.00041756741207800553543 + 1.2167129098324125926e-722j)  +/-  (1.13e-68, 1.86e-188j)
| (9.1441767563411977718e-05 - 5.0790587642841006249e-723j)  +/-  (3.75e-69, 6.2e-189j)
| (0.28760154381777067733 + 1.0949997488000098346e-719j)  +/-  (1.45e-65, 2.16e-185j)
| (0.13977271435188680499 - 1.5388190119846423616e-720j)  +/-  (1.47e-66, 2.02e-186j)
| (3.9476454111579254295e-18 + 4.0592621343902440994e-729j)  +/-  (4.28e-77, 9.53e-197j)
