Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 67
-------------------------------------------------
Trying to find an order 67 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^69 - 2495032925738033801974536347613906346637232782/546783215030858425189388984905997240740705*t^67 + 1340174990871219949778894031766514904354720200886/546783215030858425189388984905997240740705*t^65 - 6939842837550622482753936519410363069897119901448/8412049462013206541375215152399957549857*t^63 + 1643470427319763052592489476242107363407423090328414/8412049462013206541375215152399957549857*t^61 - 291473565111813911659629378542018251154846756602997805/8412049462013206541375215152399957549857*t^59 + 40235881991937853084404964666349291047774761251121482994/8412049462013206541375215152399957549857*t^57 - 466949897900194871176093285306989757420651469479186347501/885478890738232267513180542357890268406*t^55 + 334918889833623112714450293503707606533994309429099312562445/7083831125905858140105444338863122147248*t^53 - 49474407566268045919348613626121332050709717335214000686804195/14167662251811716280210888677726244294496*t^51 + 178758794167538407178234392009197872962054480683563816521427625/833391897165395075306522863395661429088*t^49 - 9193570296127647780858177450656287402869194778156743337708694275/833391897165395075306522863395661429088*t^47 + 1591172635808842679492157666780081839695612496457444977113729830675/3333567588661580301226091453582645716352*t^45 - 116208511771746200689361796864481026152657601259985656096521062336625/6667135177323160602452182907165291432704*t^43 + 14014024276088450910019231599983857419507731573273106409295162740500/26043496786418596103328839481114419659*t^41 - 187367590551276463522153431790401464159939717226844021293732108765298125/13334270354646321204904365814330582865408*t^39 + 66176332390394615378644136649212784609789674072112604491906250701687638625/213348325674341139278469853029289325846528*t^37 - 2465491745453323910639533191892617447904837695245796846878049817675548612375/426696651348682278556939706058578651693056*t^35 + 38649024140815471366245824251640687604237765408932039918848460532710110899375/426696651348682278556939706058578651693056*t^33 - 253919011325155233805806106427407778702090306815621671103704292723156880075625/213348325674341139278469853029289325846528*t^31 + 11128799096590733415202237936876789707988535161219927990439664973265449810171875/853393302697364557113879412117157303386112*t^29 - 202040373886860470196400177214329608989044173739926666641436886474812690805325625/1706786605394729114227758824234314606772224*t^27 + 753548997717174240026256110963789665362486481379432825445058270417490528789911875/853393302697364557113879412117157303386112*t^25 - 18293019475474696009590300393497219866198552096857485361814004478503679425204109375/3413573210789458228455517648468629213544448*t^23 + 713807411609474366113233611124763576817342763984271824190083613561237383189976828125/27308585686315665827644141187749033708355584*t^21 - 5512577016826032024105440267519312813923831282228845331238884321542784785184315171875/54617171372631331655288282375498067416711168*t^19 + 16538237956127961014596381009076818858106137544908789519558891066312904217672174478125/54617171372631331655288282375498067416711168*t^17 - 37648271562737777720033865431251206242322147128089705107318184280673331300038747215625/54617171372631331655288282375498067416711168*t^15 + 252335134269760735524798562408428181870605164406401774573660377401967334277884579203125/218468685490525326621153129501992269666844672*t^13 - 597932485582106026746509119256304852415722399222972391231375209328034666787149214984375/436937370981050653242306259003984539333689344*t^11 + 118518233188167337632180784151645916520295732502560102745270675100860736063057636640625/109234342745262663310576564750996134833422336*t^9 - 464563843031699817917202093555353671875042960850942602580728145845895096199505653484375/873874741962101306484612518007969078667378688*t^7 + 3975209459133147321427136040878923051998897418390088997716282651392783054791452703796875/27963991742787241807507600576255010517356118016*t^5 - 931060171646498955976863666492918954336316287225842626768157506485959878632756377578125/55927983485574483615015201152510021034712236032*t^3 + 29007856600718526577809681256341471211507888733963533943229370206076900323325392890625/55927983485574483615015201152510021034712236032*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
Positive weights:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (9.7440548123793702764 + 8.1398079448221890935e-711j)  +/-  (2.17e-241, 2.17e-241j)
| (10.884014402261901739 - 2.0509845523439377442e-713j)  +/-  (7.65e-244, 7.65e-244j)
| (-10.884014402261901739 - 1.1028020293583350465e-714j)  +/-  (8.23e-244, 8.23e-244j)
| (-8.4607144938188752312 - 1.3236075397167819152e-709j)  +/-  (1.52e-239, 1.52e-239j)
| (4.8441072827519156295 - 4.9201239924448315738e-709j)  +/-  (7.33e-240, 7.33e-240j)
| (8.4607144938188752312 + 8.7670340107177595017e-708j)  +/-  (1.35e-239, 1.35e-239j)
| (-9.2837354351271840417 - 1.2513136434906697856e-712j)  +/-  (1.24e-240, 1.24e-240j)
| (-8.8593597330318222526 + 1.8776611508008495366e-712j)  +/-  (5.49e-240, 5.49e-240j)
| (-2.8558835645514514685 + 1.4972105695802978821e-715j)  +/-  (7.03e-244, 7.03e-244j)
| (10.260153229371454691 - 3.5461974026876472229e-714j)  +/-  (2e-242, 2e-242j)
| (5.1404711574223136224 - 3.6202984513383158804e-709j)  +/-  (1.45e-239, 1.45e-239j)
| (6.3731534280089561845 + 2.473448500230307887e-711j)  +/-  (1.01e-238, 1.01e-238j)
| (9.2837354351271840417 - 4.2046791018899484421e-717j)  +/-  (1.25e-240, 1.25e-240j)
| (-2.3077853825924725692 + 2.0139051472829197738e-730j)  +/-  (1.65e-245, 1.65e-245j)
| (-7.3674841478527869004 + 1.1768604084418950282e-723j)  +/-  (9.12e-239, 9.12e-239j)
| (6.0567128864925689899 - 8.6155882301060757396e-723j)  +/-  (7.92e-239, 7.92e-239j)
| (3.1326492483430817483 + 7.8890417291529491021e-742j)  +/-  (3.71e-243, 3.71e-243j)
| (-5.441011147900954062 - 4.0709189087386396948e-737j)  +/-  (2.98e-239, 2.98e-239j)
| (8.081676331611467994 - 5.3000213453259532156e-742j)  +/-  (3.23e-239, 3.23e-239j)
| (3.6924834926140339839 - 4.646660598847294736e-759j)  +/-  (8.17e-242, 8.17e-242j)
| (-10.260153229371454691 + 2.19372271250169225e-766j)  +/-  (2.01e-242, 2.01e-242j)
| (7.3674841478527869004 - 4.1750638243703172608e-760j)  +/-  (8.84e-239, 8.84e-239j)
| (-8.081676331611467994 - 1.7484675032450315142e-775j)  +/-  (3.12e-239, 3.12e-239j)
| (8.8593597330318222526 + 1.2362318840965785548e-775j)  +/-  (5.07e-240, 5.07e-240j)
| (-3.1326492483430817483 - 1.5629522455157630229e-785j)  +/-  (3.89e-243, 3.89e-243j)
| (-7.0274061185925714624 - 2.0541551282239063235e-780j)  +/-  (1.09e-238, 1.09e-238j)
| (-6.0567128864925689899 - 7.78685424704925412e-781j)  +/-  (7.53e-239, 7.53e-239j)
| (4.5514844977194933587 + 1.6745054261256005581e-780j)  +/-  (2.67e-240, 2.67e-240j)
| (7.0274061185925714624 - 9.1309502832556970182e-787j)  +/-  (1.2e-238, 1.2e-238j)
| (-3.6924834926140339839 + 3.4922840062399180544e-801j)  +/-  (7.89e-242, 7.89e-242j)
| (-4.2622227576849005743 + 1.6870774671752633927e-799j)  +/-  (9.94e-241, 9.94e-241j)
| (4.2622227576849005743 + 4.1502438424910250889e-799j)  +/-  (9.84e-241, 9.84e-241j)
| (0.7071067811865475244 - 2.8070289799885061874e-810j)  +/-  (1.41e-251, 1.41e-251j)
| (-3.9759876696604420744 + 9.7627249494393092378e-801j)  +/-  (2.82e-241, 2.82e-241j)
| (-7.7182112242670869195 + 4.0831992417224577462e-798j)  +/-  (5.89e-239, 5.89e-239j)
| (5.441011147900954062 - 3.5794569618194182302e-797j)  +/-  (2.94e-239, 2.94e-239j)
| (-0.45438310628283692287 + 6.728269470460940301e-821j)  +/-  (1.13e-252, 1.13e-252j)
| (1.4978310093662407468 + 7.5212172468963121031e-817j)  +/-  (2.52e-248, 2.52e-248j)
| (7.7182112242670869195 + 3.7441013954990570211e-806j)  +/-  (5.77e-239, 5.77e-239j)
| (-2.5809763449842185747 - 8.164059939466382815e-820j)  +/-  (1.1e-244, 1.1e-244j)
| (5.7462296362524111783 - 2.0051093610418471361e-812j)  +/-  (4.98e-239, 4.98e-239j)
| (2.8558835645514514685 - 8.408009625339221522e-824j)  +/-  (7.13e-244, 7.13e-244j)
| (2.3077853825924725692 - 5.4567277897359760512e-826j)  +/-  (1.69e-245, 1.69e-245j)
| (2.03620948304886627 - 1.3431829634639506335e-826j)  +/-  (2.32e-246, 2.32e-246j)
| (-5.1404711574223136224 - 6.8599428304105842424e-820j)  +/-  (1.49e-239, 1.49e-239j)
| (-4.5514844977194933587 - 1.8458003136958648508e-821j)  +/-  (2.72e-240, 2.72e-240j)
| (-6.3731534280089561845 - 3.0260118167134965817e-819j)  +/-  (1e-238, 1e-238j)
| (3.9759876696604420744 - 2.9892558033278678004e-821j)  +/-  (2.8e-241, 2.8e-241j)
| (0.45438310628283692287 + 9.1392282451844832821e-834j)  +/-  (1.05e-252, 1.05e-252j)
| (-1.4978310093662407468 - 8.3284327564112162513e-831j)  +/-  (2.58e-248, 2.58e-248j)
| (1.7662065275741419007 + 9.6200649655969868533e-829j)  +/-  (2.51e-247, 2.51e-247j)
| (-4.8441072827519156295 - 9.6130723992258614566e-822j)  +/-  (7.51e-240, 7.51e-240j)
| (6.6963809663244959596 - 1.4460454514179678881e-820j)  +/-  (1.21e-238, 1.21e-238j)
| (-1.2313153615510946483 + 6.5677210253335094102e-836j)  +/-  (2.23e-249, 2.23e-249j)
| (2.5809763449842185747 + 1.0332860147171299621e-831j)  +/-  (1.14e-244, 1.14e-244j)
| (-3.411448034808001036 - 1.4313670395610866394e-828j)  +/-  (1.79e-242, 1.79e-242j)
| (-0.21681328952388768085 + 8.2796040466307876594e-840j)  +/-  (8.46e-254, 8.46e-254j)
| (-5.7462296362524111783 - 1.357746521197791566e-824j)  +/-  (5.01e-239, 5.01e-239j)
| (-0.96725920039475192259 - 9.1998316453727764214e-838j)  +/-  (1.92e-250, 1.92e-250j)
| (1.2313153615510946483 - 1.1513288477486808149e-836j)  +/-  (2.41e-249, 2.41e-249j)
| (3.411448034808001036 - 1.3747557801960841143e-829j)  +/-  (1.78e-242, 1.78e-242j)
| (-0.7071067811865475244 + 2.4978525243677218922e-838j)  +/-  (1.3e-251, 1.3e-251j)
| (-2.03620948304886627 + 1.9914055359157341743e-834j)  +/-  (2.19e-246, 2.19e-246j)
| (0.21681328952388768085 + 4.8371248805123190203e-841j)  +/-  (8.46e-254, 8.46e-254j)
| (0.96725920039475192259 - 3.3568491008052160952e-838j)  +/-  (2.04e-250, 2.04e-250j)
| (1.6588791077660026689e-871 + 2.665168123442171236e-872j)  +/-  (1.16e-869, 1.16e-869j)
| (-9.7440548123793702764 + 4.9190792313368950625e-828j)  +/-  (2.07e-241, 2.07e-241j)
| (-6.6963809663244959596 - 1.1071347922321212191e-837j)  +/-  (1.14e-238, 1.14e-238j)
| (-1.7662065275741419007 - 2.2894786610959802762e-847j)  +/-  (2.59e-247, 2.59e-247j)
-------------------------------------------------
The weights are:
| (1.5888764575771456929e-42 - 1.6700817543706405717e-736j)  +/-  (5.84e-63, 5.34e-182j)
| (1.4524489695793890827e-52 - 1.1631791750299219259e-741j)  +/-  (2.94e-66, 2.69e-185j)
| (1.4524489695793890827e-52 + 4.5389214361147276298e-742j)  +/-  (8.39e-68, 7.67e-187j)
| (1.7860582411955588615e-32 - 7.6584316799841025825e-732j)  +/-  (8.25e-61, 7.53e-180j)
| (1.0703303365667930088e-11 + 2.3410857769132750037e-719j)  +/-  (7.6e-46, 6.94e-165j)
| (1.7860582411955588615e-32 + 2.7470131415171054188e-731j)  +/-  (1.1e-60, 1e-179j)
| (9.2076238048023848462e-39 - 4.7184212122745932988e-735j)  +/-  (7.78e-64, 7.11e-183j)
| (1.8943194594124117875e-35 + 2.3123808533343790926e-733j)  +/-  (2.49e-62, 2.28e-181j)
| (4.4657896315501466955e-05 - 1.9300749168528095849e-717j)  +/-  (8.25e-35, 7.54e-154j)
| (5.9966892135166722834e-47 + 8.8287410818995882372e-739j)  +/-  (1.16e-66, 1.06e-185j)
| (5.62595641334486742e-13 + 4.9266295256008937096e-720j)  +/-  (1.15e-49, 1.05e-168j)
| (4.1339772130998057579e-19 + 4.0073565482872665343e-724j)  +/-  (1.11e-55, 1.01e-174j)
| (9.2076238048023848462e-39 + 1.4703049156648743595e-734j)  +/-  (1.58e-64, 1.45e-183j)
| (0.00074746003210129521153 - 1.0539174429112974865e-716j)  +/-  (5.15e-34, 4.71e-153j)
| (5.1992988433253456852e-25 + 5.171438840041011826e-728j)  +/-  (6.15e-62, 5.62e-181j)
| (2.0695522108523155255e-17 - 3.6896248829162946609e-723j)  +/-  (9.53e-55, 8.7e-174j)
| (8.5730437476160722587e-06 + 3.594975092229075931e-717j)  +/-  (4.17e-42, 3.81e-161j)
| (2.3738318537715975619e-14 + 1.7774617970972196296e-722j)  +/-  (3.03e-56, 2.77e-175j)
| (9.0189773605033750143e-30 - 7.1999016702695413772e-730j)  +/-  (6.63e-62, 6.06e-181j)
| (1.9083879485645910694e-07 + 6.8565433012004742853e-718j)  +/-  (3.91e-46, 3.58e-165j)
| (5.9966892135166722834e-47 - 3.2220185877768528949e-739j)  +/-  (1.05e-71, 9.58e-191j)
| (5.1992988433253456852e-25 - 2.4149420139768847528e-727j)  +/-  (2.4e-60, 2.19e-179j)
| (9.0189773605033750143e-30 + 1.8546842863672406889e-730j)  +/-  (5.7e-65, 5.21e-184j)
| (1.8943194594124117875e-35 - 7.7124680244475219364e-733j)  +/-  (3.13e-64, 2.86e-183j)
| (8.5730437476160722587e-06 + 7.6287028714389193651e-718j)  +/-  (3.44e-47, 3.14e-166j)
| (6.7529481009259704281e-23 - 6.3564631630151558124e-727j)  +/-  (7.74e-63, 7.07e-182j)
| (2.0695522108523155255e-17 + 4.4476234976847825506e-724j)  +/-  (1.46e-60, 1.33e-179j)
| (1.6530807690447715075e-10 - 6.8554129692814683699e-719j)  +/-  (3.09e-53, 2.82e-172j)
| (6.7529481009259704281e-23 + 3.3164649025553484995e-726j)  +/-  (1.13e-60, 1.03e-179j)
| (1.9083879485645910694e-07 + 8.9607100143231310435e-719j)  +/-  (1.4e-52, 1.28e-171j)
| (2.0928096675813587308e-09 + 7.6134916126714609018e-720j)  +/-  (1.03e-55, 9.46e-175j)
| (2.0928096675813587308e-09 + 1.2667036432212295352e-718j)  +/-  (4.92e-54, 4.49e-173j)
| (0.088049108105583653133 - 5.902381846960688571e-715j)  +/-  (2.3e-44, 2.1e-163j)
| (2.1901093807425275453e-08 - 2.7267997542794146444e-719j)  +/-  (2.6e-54, 2.38e-173j)
| (2.7068299089376538212e-27 - 3.4620587688498406914e-729j)  +/-  (6.69e-66, 6.11e-185j)
| (2.3738318537715975619e-14 - 2.3856610199784095926e-721j)  +/-  (5.51e-58, 5.04e-177j)
| (0.11328814625315374952 + 7.1499145972948045237e-715j)  +/-  (9.31e-45, 8.5e-164j)
| (0.016011039640212187199 + 1.6043769837627722936e-715j)  +/-  (1.37e-44, 1.25e-163j)
| (2.7068299089376538212e-27 + 1.466417828126361189e-728j)  +/-  (6.93e-65, 6.33e-184j)
| (0.00019778552176966059596 + 4.6493549789299365237e-717j)  +/-  (2.64e-51, 2.41e-170j)
| (7.9355946954134054937e-16 + 3.1105263333648955221e-722j)  +/-  (4.97e-59, 4.54e-178j)
| (4.4657896315501466955e-05 - 7.7079231500787749675e-717j)  +/-  (7.01e-53, 6.41e-172j)
| (0.00074746003210129521153 - 3.0303960053200730083e-716j)  +/-  (1.71e-51, 1.56e-170j)
| (0.0024177199491981274584 + 5.5503529592436701709e-716j)  +/-  (1.8e-50, 1.64e-169j)
| (5.62595641334486742e-13 - 9.4356512543502216733e-722j)  +/-  (1.41e-63, 1.29e-182j)
| (1.6530807690447715075e-10 - 1.9417065906244044066e-720j)  +/-  (8.14e-62, 7.44e-181j)
| (4.1339772130998057579e-19 - 5.8048422201277870343e-725j)  +/-  (8.47e-68, 7.74e-187j)
| (2.1901093807425275453e-08 - 2.8932367731299756735e-718j)  +/-  (4.58e-59, 4.18e-178j)
| (0.11328814625315374952 + 8.6525925392134546448e-715j)  +/-  (5.37e-52, 4.9e-171j)
| (0.016011039640212187199 + 8.3842258340373197481e-716j)  +/-  (2.93e-54, 2.68e-173j)
| (0.0067102673565284172297 - 9.6621940920438086663e-716j)  +/-  (7.59e-54, 6.94e-173j)
| (1.0703303365667930088e-11 + 4.5014822899738744443e-721j)  +/-  (3.69e-63, 3.37e-182j)
| (6.1868469269885066334e-21 - 3.8965409822575809694e-725j)  +/-  (3.07e-66, 2.8e-185j)
| (0.032879790103666161274 - 1.50783646664782148e-715j)  +/-  (1.66e-54, 1.51e-173j)
| (0.00019778552176966059596 + 1.5695010502947339405e-716j)  +/-  (7.67e-57, 7.01e-176j)
| (1.3934415208288582587e-06 - 2.7141245460571818863e-718j)  +/-  (5.52e-60, 5.04e-179j)
| (0.12201415476231523626 - 1.0780449073281714882e-714j)  +/-  (1.43e-54, 1.31e-173j)
| (7.9355946954134054937e-16 - 2.9882820655166179828e-723j)  +/-  (3.85e-66, 3.52e-185j)
| (0.058098152223119910609 + 2.6081605791436467113e-715j)  +/-  (7.55e-56, 6.89e-175j)
| (0.032879790103666161274 - 2.5549204769094711515e-715j)  +/-  (4.44e-56, 4.05e-175j)
| (1.3934415208288582587e-06 - 1.5995153198719853011e-717j)  +/-  (3.16e-59, 2.88e-178j)
| (0.088049108105583653133 - 4.3806522738335701307e-715j)  +/-  (8.84e-56, 8.08e-175j)
| (0.0024177199491981274584 + 2.2311373250628960905e-716j)  +/-  (7.83e-59, 7.15e-178j)
| (0.12201415476231523626 - 1.1805227623197367691e-714j)  +/-  (9.22e-56, 8.43e-175j)
| (0.058098152223119910609 + 3.9321915306638605153e-715j)  +/-  (2.47e-56, 2.26e-175j)
| (0.11906307332294158948 + 1.304936705301750159e-714j)  +/-  (7.69e-56, 7.02e-175j)
| (1.5888764575771456929e-42 + 5.7184737393740372886e-737j)  +/-  (1.82e-80, 1.66e-199j)
| (6.1868469269885066334e-21 + 6.5686982386783801884e-726j)  +/-  (1.97e-69, 1.81e-188j)
| (0.0067102673565284172297 - 4.444987847456564622e-716j)  +/-  (2.08e-59, 1.87e-178j)
