Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 61
-------------------------------------------------
Trying to find an order 61 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^63 - 33713875610763036320603276766368371322854/8912577376109714820850333034596236377*t^61 + 14921464975626998397066557360068758335894295/8912577376109714820850333034596236377*t^59 - 139382041306855774215418784128731872318634555/302121266986769993927129933376143606*t^57 + 53674778551877575006418477996942833208726079075/604242533973539987854259866752287212*t^55 - 15365628418828949741962803754576929860608140299385/1208485067947079975708519733504574424*t^53 + 3396735000579976312712103721952868853305591197732685/2416970135894159951417039467009148848*t^51 - 594604872819336055603658068792260869928096981578704875/4833940271788319902834078934018297696*t^49 + 83866252968355934574608895069636632211603308264846592375/9667880543576639805668157868036595392*t^47 - 9647995821387032884721548711442511198202471712985675238125/19335761087153279611336315736073190784*t^45 + 913049558587912093148192273592568023615914460593872867217625/38671522174306559222672631472146381568*t^43 - 71496874578657514675471177813759243369512286555159453539306375/77343044348613118445345262944292763136*t^41 + 4649446524598304365552951491332301754692133545179829080220639375/154686088697226236890690525888585526272*t^39 - 251556577320335678012076232427290147110652868018154443609554558125/309372177394452473781381051777171052544*t^37 + 11326505144563306627640314077085259767126203325576074810327911390625/618744354788904947562762103554342105088*t^35 - 423882146731882234717343732858467433927543501878777833194784852474375/1237488709577809895125524207108684210176*t^33 + 13149826450070859115763515241754245604049670970820255064136564252980625/2474977419155619790251048414217368420352*t^31 - 336756885703833299171907623183427390479296409796058315251354776120746875/4949954838311239580502096828434736840704*t^29 + 7078550048192278984653656169716495655515262281841938007095945634805809375/9899909676622479161004193656869473681408*t^27 - 121212519458617453562256525178830805249848655026191936796651477530827640625/19799819353244958322008387313738947362816*t^25 + 1674872109877873667172879979914537335059256707949031598249009917122061515625/39599638706489916644016774627477894725632*t^23 - 18451608392988135205748274132528237410324202304657694693843174325441534796875/79199277412979833288033549254955789451264*t^21 + 159647685775636200384858581203549102483465704402053719447460823925755862734375/158398554825959666576067098509911578902528*t^19 - 1064410929612021415923429725052202453914730939052953297760448318558856910390625/316797109651919333152134197019823157805056*t^17 + 5337297455171395836715045643943551855679489733951294440795680724070345086328125/633594219303838666304268394039646315610112*t^15 - 19500318498673615329428755952883417184537117415730584815985048100490104257859375/1267188438607677332608536788079292631220224*t^13 + 49751963056882104433962960603611749725661133846597198941884711479654277459421875/2534376877215354665217073576158585262440448*t^11 - 83524569776884628088154849413760319791633346278894273665547604673374196962578125/5068753754430709330434147152317170524880896*t^9 + 84474704753488293947257096911638620658897063690354516006471977189581970271953125/10137507508861418660868294304634341049761792*t^7 - 44578421230021496117400590900596325286192287084991182182828886751080670118359375/20275015017722837321736588609268682099523584*t^5 + 9328501511701064389848680886093975089222003602667169315726021960706407944296875/40550030035445674643473177218537364199047168*t^3 - 367502833554351297473919174708629846746443049387478506823459516553476695078125/81100060070891349286946354437074728398094336*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
-------------------------------------------------
The nodes are:
| (8.7159681676454598594 - 4.991764630804659828e-853j)  +/-  (1.03e-241, 1.03e-241j)
| (10.344420960809908946 - 9.61907397211141087e-856j)  +/-  (1.03e-244, 1.03e-244j)
| (-7.8769811230833855433 + 2.9397828883622410861e-850j)  +/-  (8.32e-241, 8.32e-241j)
| (7.8769811230833855433 + 3.1493756265587093418e-854j)  +/-  (8.03e-241, 8.03e-241j)
| (9.1847580606061243172 + 4.6384325563765016878e-857j)  +/-  (1.87e-242, 1.87e-242j)
| (9.7099921720038861144 + 8.3922152559225281547e-858j)  +/-  (2.16e-243, 2.16e-243j)
| (8.2834968221141102015 - 4.8968955464536262619e-855j)  +/-  (3.4e-241, 3.4e-241j)
| (1.2694898582563043322 - 7.3976352640383280403e-864j)  +/-  (1.4e-249, 1.4e-249j)
| (-3.8729575363390108686 - 6.8124473309108880732e-856j)  +/-  (2.32e-242, 2.32e-242j)
| (3.2798884027082471062 + 1.5583394222128986857e-858j)  +/-  (1.49e-243, 1.49e-243j)
| (-3.2798884027082471062 - 2.4072313613192303004e-857j)  +/-  (1.45e-243, 1.45e-243j)
| (-2.4083502007797054381 + 1.1238697707756815112e-859j)  +/-  (8.85e-246, 8.85e-246j)
| (-1.5523194675689887371 - 1.4744102548220818786e-862j)  +/-  (1.52e-248, 1.52e-248j)
| (-2.987255853242285465 + 2.3772969414443920679e-858j)  +/-  (3.23e-244, 3.23e-244j)
| (-4.1740683915477780822 - 3.6178374072914364908e-855j)  +/-  (7.46e-242, 7.46e-242j)
| (7.1190789630504598609 + 5.0035578175878709277e-853j)  +/-  (2.92e-240, 2.92e-240j)
| (6.4129996732151568851 - 3.4072884442620356783e-854j)  +/-  (3.79e-240, 3.79e-240j)
| (-4.7874506793185122238 + 3.8712573357141729324e-854j)  +/-  (4.63e-241, 4.63e-241j)
| (-2.1215775613588133494 + 3.6738764308026578139e-861j)  +/-  (1.22e-246, 1.22e-246j)
| (4.7874506793185122238 - 1.1739999811120735814e-854j)  +/-  (4.61e-241, 4.61e-241j)
| (-8.7159681676454598594 + 3.0968994602953146399e-855j)  +/-  (9.19e-242, 9.19e-242j)
| (7.490206905498943713 + 1.1470631377089103936e-855j)  +/-  (1.56e-240, 1.56e-240j)
| (-10.344420960809908946 - 2.7053819811819563963e-859j)  +/-  (1.05e-244, 1.05e-244j)
| (-7.490206905498943713 + 3.9491057981038024669e-854j)  +/-  (1.83e-240, 1.83e-240j)
| (-9.1847580606061243172 + 1.1630201566695892547e-864j)  +/-  (1.99e-242, 1.99e-242j)
| (2.987255853242285465 + 6.4114363497350515208e-868j)  +/-  (3.1e-244, 3.1e-244j)
| (0.98772148258735349938 + 1.2857717313340300147e-875j)  +/-  (1.2e-250, 1.2e-250j)
| (6.0743005398859686141 - 2.5766980441975184041e-862j)  +/-  (3.28e-240, 3.28e-240j)
| (-3.575016019620898647 + 2.3972562324757546594e-867j)  +/-  (6.06e-243, 6.06e-243j)
| (-8.2834968221141102015 + 1.33409913420200851e-863j)  +/-  (3.12e-241, 3.12e-241j)
| (-7.1190789630504598609 - 1.0822782391977604417e-874j)  +/-  (2.78e-240, 2.78e-240j)
| (5.1006962905543418113 + 4.1827159591127213491e-884j)  +/-  (9.77e-241, 9.77e-241j)
| (2.6968303175141864986 - 7.0093497377579793971e-898j)  +/-  (5.75e-245, 5.75e-245j)
| (2.4083502007797054381 + 6.2660644126344151284e-898j)  +/-  (8.47e-246, 8.47e-246j)
| (-5.1006962905543418113 + 4.169299654645324843e-891j)  +/-  (9.4e-241, 9.4e-241j)
| (-6.7607177148067763691 + 1.6789405119900077528e-908j)  +/-  (3.23e-240, 3.23e-240j)
| (-9.7099921720038861144 - 2.2984110074357481267e-923j)  +/-  (2.25e-243, 2.25e-243j)
| (0.7071067811865475244 + 1.0229385497909553435e-935j)  +/-  (6.92e-252, 6.92e-252j)
| (5.4190894047672313762 + 2.8715820323960527132e-924j)  +/-  (1.82e-240, 1.82e-240j)
| (4.4787482190339010518 + 3.1020891055774658051e-934j)  +/-  (1.95e-241, 1.95e-241j)
| (-1.2694898582563043322 + 2.0523648113947155957e-943j)  +/-  (1.46e-249, 1.46e-249j)
| (-2.6968303175141864986 - 6.3901560254942556946e-937j)  +/-  (6.02e-245, 6.02e-245j)
| (2.1215775613588133494 - 1.693693240254201557e-940j)  +/-  (1.3e-246, 1.3e-246j)
| (1.8362972565081318386 - 8.1018918575974851325e-941j)  +/-  (1.59e-247, 1.59e-247j)
| (-6.0743005398859686141 + 2.1648730202693046027e-931j)  +/-  (3.43e-240, 3.43e-240j)
| (-1.8362972565081318386 + 1.8355502066924050306e-951j)  +/-  (1.52e-247, 1.52e-247j)
| (5.7433410759447649792 + 2.1761324220456836041e-943j)  +/-  (2.7e-240, 2.7e-240j)
| (-6.4129996732151568851 + 2.6123953537934682392e-945j)  +/-  (3.98e-240, 3.98e-240j)
| (1.5523194675689887371 - 9.7456001732896171039e-963j)  +/-  (1.53e-248, 1.53e-248j)
| (6.7607177148067763691 - 3.297517576774725318e-954j)  +/-  (3.51e-240, 3.51e-240j)
| (-0.42846071956108795241 + 1.3974112034103720106e-966j)  +/-  (4.8e-253, 4.8e-253j)
| (-4.4787482190339010518 - 1.7349745138944182835e-953j)  +/-  (1.93e-241, 1.93e-241j)
| (-5.4190894047672313762 - 3.4988613391524305873e-961j)  +/-  (1.86e-240, 1.86e-240j)
| (0.15882935212400742547 + 5.6289248988393456076e-981j)  +/-  (4.07e-254, 4.07e-254j)
| (4.1740683915477780822 + 2.2576000877836424979e-969j)  +/-  (8.03e-242, 8.03e-242j)
| (-9.2876410728025942845e-1009 - 3.1442493505714588031e-1008j)  +/-  (2.07e-1006, 2.07e-1006j)
| (-0.7071067811865475244 - 3.6092477328333564355e-979j)  +/-  (7.39e-252, 7.39e-252j)
| (-0.98772148258735349938 + 1.8400189753966535024e-978j)  +/-  (1.13e-250, 1.13e-250j)
| (3.8729575363390108686 - 3.2474900227906042893e-970j)  +/-  (2.35e-242, 2.35e-242j)
| (0.42846071956108795241 - 6.4865153966592540515e-980j)  +/-  (5.22e-253, 5.22e-253j)
| (3.575016019620898647 - 4.7518672330329368638e-972j)  +/-  (6.46e-243, 6.46e-243j)
| (-5.7433410759447649792 + 2.3502245869949302018e-977j)  +/-  (2.67e-240, 2.67e-240j)
| (-0.15882935212400742547 + 1.1466084031001086178e-992j)  +/-  (3.26e-254, 3.26e-254j)
-------------------------------------------------
The weights are:
| (2.5736400655309369267e-34 + 3.8072468370488887498e-878j)  +/-  (1.52e-59, 2.1e-178j)
| (1.3929953877996334341e-47 - 2.4180744158754151146e-885j)  +/-  (1.23e-64, 1.7e-183j)
| (2.5254227063724265978e-28 + 3.1690786852493318652e-874j)  +/-  (1.4e-59, 1.94e-178j)
| (2.5254227063724265978e-28 + 7.0798200589976539633e-875j)  +/-  (9.93e-58, 1.37e-176j)
| (6.4071400202740982952e-38 - 4.2317547600611071737e-880j)  +/-  (1.66e-61, 2.29e-180j)
| (3.6048374925351136361e-42 + 2.1131459460437950895e-882j)  +/-  (2.66e-63, 3.68e-182j)
| (3.7422323525469325213e-31 - 2.0029778693369993039e-876j)  +/-  (4.4e-59, 6.09e-178j)
| (0.031784440298759398894 + 2.527821911698047556e-860j)  +/-  (5.55e-19, 7.67e-138j)
| (5.1693820162312443751e-08 + 1.7749135380206217813e-863j)  +/-  (3e-46, 4.15e-165j)
| (3.5279701349582889218e-06 - 1.5767162584234728262e-862j)  +/-  (1.44e-41, 1.99e-160j)
| (3.5279701349582889218e-06 - 4.8582357634139067329e-862j)  +/-  (1.77e-42, 2.45e-161j)
| (0.00049116035540357845383 + 4.1697844855119475991e-861j)  +/-  (4.04e-36, 5.59e-155j)
| (0.014364139968373510799 - 2.1295406690396276406e-860j)  +/-  (4.6e-27, 6.36e-146j)
| (2.1904141272918115855e-05 + 1.4199997110661142234e-861j)  +/-  (1.16e-40, 1.6e-159j)
| (4.6341484157727748058e-09 - 8.7468313424773824645e-863j)  +/-  (5.8e-49, 8.02e-168j)
| (2.0059852113815812472e-23 + 3.6646939491525685183e-872j)  +/-  (3.46e-60, 4.78e-179j)
| (2.6646599993534535004e-19 + 8.2672779232090473345e-870j)  +/-  (9.19e-59, 1.27e-177j)
| (1.9504143184166445271e-11 + 4.6283984484512767356e-864j)  +/-  (4.35e-54, 6.01e-173j)
| (0.0017905261375143425353 - 7.4336557104869724345e-861j)  +/-  (1.64e-36, 2.26e-155j)
| (1.9504143184166445271e-11 + 1.1966761412548099832e-864j)  +/-  (1.34e-54, 1.86e-173j)
| (2.5736400655309369267e-34 + 2.2207685156902402303e-877j)  +/-  (2.01e-70, 2.77e-189j)
| (9.2056572072086761391e-26 - 1.8317157027770835385e-873j)  +/-  (1.7e-61, 2.34e-180j)
| (1.3929953877996334341e-47 - 2.9768000589227666761e-884j)  +/-  (6.36e-76, 8.79e-195j)
| (9.2056572072086761391e-26 - 7.3485524332120574014e-873j)  +/-  (4.41e-67, 6.1e-186j)
| (6.4071400202740982952e-38 - 2.9400378389789712969e-879j)  +/-  (1.97e-72, 2.73e-191j)
| (2.1904141272918115855e-05 + 3.9180701090305265351e-862j)  +/-  (7.03e-51, 9.72e-170j)
| (0.059813296116338843111 - 4.4548624742163453208e-860j)  +/-  (7.28e-38, 1.01e-156j)
| (1.7855964963781132675e-17 - 9.8158826067931456202e-869j)  +/-  (1.21e-61, 1.67e-180j)
| (4.7077539415219887975e-07 + 8.4353537359323635168e-863j)  +/-  (9.86e-52, 1.36e-170j)
| (3.7422323525469325213e-31 - 1.0115188019995369418e-875j)  +/-  (1.48e-69, 2.04e-188j)
| (2.0059852113815812472e-23 + 1.3397972706765979963e-871j)  +/-  (6.88e-67, 9.52e-186j)
| (8.9460258685065668587e-13 + 1.3655652371339399497e-865j)  +/-  (9.09e-61, 1.26e-179j)
| (0.00011333469137823870295 - 8.6039402487159152135e-862j)  +/-  (3.42e-52, 4.72e-171j)
| (0.00049116035540357845383 + 1.8566186690243525822e-861j)  +/-  (3.83e-51, 5.3e-170j)
| (8.9460258685065668587e-13 + 3.8296880917243233485e-865j)  +/-  (6.9e-62, 9.53e-181j)
| (2.8082911787971278439e-21 - 2.0021835724054914764e-870j)  +/-  (4.19e-67, 5.79e-186j)
| (3.6048374925351136361e-42 + 1.8433916385252503596e-881j)  +/-  (6.24e-76, 8.62e-195j)
| (0.095779767519096499659 + 7.9301276396256665618e-860j)  +/-  (1.48e-46, 2.05e-165j)
| (3.194993792582361939e-14 - 1.1157164042759545197e-866j)  +/-  (1.33e-63, 1.84e-182j)
| (3.3606121514942149968e-10 - 3.5272161184443523387e-864j)  +/-  (1.66e-61, 2.29e-180j)
| (0.031784440298759398894 + 3.5114912450684034263e-860j)  +/-  (3.01e-49, 4.16e-168j)
| (0.00011333469137823870295 - 2.3246871225198870914e-861j)  +/-  (2.52e-54, 3.48e-173j)
| (0.0017905261375143425353 - 3.8248781449500375934e-861j)  +/-  (5.92e-54, 8.19e-173j)
| (0.0055109197204371896688 + 7.4975786858725197867e-861j)  +/-  (3.98e-53, 5.5e-172j)
| (1.7855964963781132675e-17 - 2.8461678549598563379e-868j)  +/-  (4.88e-67, 6.75e-186j)
| (0.0055109197204371896688 + 1.2620752245563616578e-860j)  +/-  (1.21e-53, 1.67e-172j)
| (8.7286580316955139717e-16 + 1.0614538602458611307e-867j)  +/-  (2.23e-65, 3.08e-184j)
| (2.6646599993534535004e-19 + 2.5428164042807612036e-869j)  +/-  (1.06e-67, 1.46e-186j)
| (0.014364139968373510799 - 1.403046198263144559e-860j)  +/-  (4.1e-55, 5.65e-174j)
| (2.8082911787971278439e-21 - 5.9655095606761056862e-871j)  +/-  (2.44e-68, 3.36e-187j)
| (0.12995853867349734873 - 1.7104514485661459436e-859j)  +/-  (2.49e-55, 3.43e-174j)
| (3.3606121514942149968e-10 - 2.0115318164792849542e-863j)  +/-  (1.17e-62, 1.61e-181j)
| (3.194993792582361939e-14 - 3.0268168340758345466e-866j)  +/-  (1.15e-65, 1.59e-184j)
| (0.13899651166722258633 + 4.1321031518536293625e-859j)  +/-  (1.68e-56, 2.25e-175j)
| (4.6341484157727748058e-09 + 7.5350236727618733766e-864j)  +/-  (1.02e-63, 1.39e-182j)
| (0.042742810561430109139 - 6.2768299816943619288e-859j)  +/-  (1.07e-56, 1.44e-175j)
| (0.095779767519096499659 + 9.4465294054817257196e-860j)  +/-  (1.64e-57, 2.22e-176j)
| (0.059813296116338843111 - 5.7139017632622894504e-860j)  +/-  (8.34e-58, 1.14e-176j)
| (5.1693820162312443751e-08 - 1.9130454067964052792e-863j)  +/-  (1.27e-63, 1.74e-182j)
| (0.12995853867349734873 - 1.5402274309642494911e-859j)  +/-  (1.06e-58, 1.06e-177j)
| (4.7077539415219887975e-07 + 4.7127143750214716946e-863j)  +/-  (4.41e-63, 6.05e-182j)
| (8.7286580316955139717e-16 + 2.9388257051543873797e-867j)  +/-  (4.63e-68, 7.61e-187j)
| (0.13899651166722258633 + 4.2949211900151983706e-859j)  +/-  (2.54e-58, 2.09e-177j)
