Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^44 - 7255566411573886299156499/4008520581018195115460*t^42 + 2982078616002310072860882879/8017041162036390230920*t^40 - 73856533187373614442307216401/1603408232407278046184*t^38 + 12333963179539269598533182249361/3206816464814556092368*t^36 - 2945285444152201867625379546494055/12827265859258224369472*t^34 + 260155537620157478965307135034944403/25654531718516448738944*t^32 - 2169352420735601880724822787615295591/6413632929629112184736*t^30 + 110624310583288718677139952583655350005/12827265859258224369472*t^28 - 17352733992565286295097767903242472377895/102618126874065794955776*t^26 + 523918973731987205204170772604002493535875/205236253748131589911552*t^24 - 6070420435761196327530694926605654509185675/205236253748131589911552*t^22 + 107184754620531148553124513090451096414734675/410472507496263179823104*t^20 - 2850406771077732443422122812355574656961933875/1641890029985052719292416*t^18 + 28061519240162300456343655804789281537592851375/3283780059970105438584832*t^16 - 49944328964235906990576796034813851505346279375/1641890029985052719292416*t^14 + 62229240152834318581725492529132370845798810875/820945014992526359646208*t^12 - 6639617089763043117441550702971125787182311774875/52540480959521687017357312*t^10 + 13870415566052556639471835835219221990863457614375/105080961919043374034714624*t^8 - 8209738826724477726039848883270990168041889530625/105080961919043374034714624*t^6 + 4649378585162935288299021942285336257111976140625/210161923838086748069429248*t^4 - 1795116028732864161181804126924245650395734361875/840647695352346992277716992*t^2 + 42429286114339981190579026024662948552547899375/1681295390704693984555433984
-------------------------------------------------
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
Positive weights:   44 out of 44
Indefinite weights: 0 out of 44
Negative weights:   0 out of 44
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-8.4400854874537817379 + 1.2674252061750337547e-684j)  +/-  (1.52e-247, 1.52e-247j)
| (-5.3688567412067536876 - 4.4709484447670974901e-692j)  +/-  (1.16e-244, 1.16e-244j)
| (-7.7622484097552800317 + 1.6467172314058654671e-699j)  +/-  (1.73e-246, 1.73e-246j)
| (5.7886300619294639987 + 3.1468347298795246822e-700j)  +/-  (9.61e-245, 9.61e-245j)
| (-7.1991648878449859352 + 4.4999975077653140161e-699j)  +/-  (8.76e-246, 8.76e-246j)
| (0.7071067811865475244 + 1.2680314048330156856e-715j)  +/-  (2.33e-252, 2.33e-252j)
| (6.6950082751373147271 + 6.1479652187998504723e-709j)  +/-  (2.7e-245, 2.7e-245j)
| (-6.6950082751373147271 - 7.2302597551437782975e-707j)  +/-  (2.91e-245, 2.91e-245j)
| (-3.4551884758271485571 + 5.6033065132915570309e-728j)  +/-  (6.92e-246, 6.92e-246j)
| (3.8201940526237533662 + 4.3831920718868772852e-742j)  +/-  (1.69e-245, 1.69e-245j)
| (-6.2284859218732503041 + 1.2343039463521778936e-746j)  +/-  (5.79e-245, 5.79e-245j)
| (3.0963673107026499297 - 4.002116474986155689e-766j)  +/-  (1.62e-246, 1.62e-246j)
| (8.4400854874537817379 + 1.0510606254057326384e-763j)  +/-  (1.51e-247, 1.51e-247j)
| (-1.7073568077989923453 + 4.7373903129369924353e-765j)  +/-  (2.2e-249, 2.2e-249j)
| (-4.9648191214095832096 + 2.3280431242909414309e-784j)  +/-  (9.39e-245, 9.39e-245j)
| (7.1991648878449859352 + 3.5031491595781477513e-803j)  +/-  (9.9e-246, 9.9e-246j)
| (7.7622484097552800317 + 3.4078030000400005817e-809j)  +/-  (1.92e-246, 1.92e-246j)
| (-3.8201940526237533662 - 1.0746915828796801254e-831j)  +/-  (1.57e-245, 1.57e-245j)
| (-1.0352614307569813532 + 2.7828047287844751168e-857j)  +/-  (2.51e-251, 2.51e-251j)
| (2.0488096033704009389 + 1.7093538939764259678e-858j)  +/-  (1.37e-248, 1.37e-248j)
| (1.7073568077989923453 + 5.4910751333992217568e-860j)  +/-  (2.21e-249, 2.21e-249j)
| (-0.11687593698687992057 + 1.6866992331126977959e-860j)  +/-  (1.74e-254, 1.74e-254j)
| (-4.5734528430858644528 + 2.3134892638179179313e-857j)  +/-  (6.08e-245, 6.08e-245j)
| (-2.3938342001013874738 - 8.1224517937603013339e-869j)  +/-  (8.52e-248, 8.52e-248j)
| (-1.3693558748146457325 - 8.132378293110461905e-878j)  +/-  (2.63e-250, 2.63e-250j)
| (1.3693558748146457325 - 1.3634453849647954711e-878j)  +/-  (2.94e-250, 2.94e-250j)
| (-2.742827515643071369 - 1.6788626702681801232e-872j)  +/-  (4.05e-247, 4.05e-247j)
| (5.3688567412067536876 - 2.8819520658225222474e-880j)  +/-  (1.04e-244, 1.04e-244j)
| (3.4551884758271485571 + 4.5370491544828755818e-884j)  +/-  (6.26e-246, 6.26e-246j)
| (-0.7071067811865475244 - 1.3372120118539341362e-892j)  +/-  (2.44e-252, 2.44e-252j)
| (-5.7886300619294639987 - 4.8250245918987840577e-884j)  +/-  (9.13e-245, 9.13e-245j)
| (6.2284859218732503041 - 1.3178799743827220401e-896j)  +/-  (7e-245, 7e-245j)
| (-2.0488096033704009389 - 8.4014850464127579737e-899j)  +/-  (1.4e-248, 1.4e-248j)
| (2.742827515643071369 - 2.3209261792857735287e-906j)  +/-  (4.03e-247, 4.03e-247j)
| (0.11687593698687992057 + 1.7603609404958864644e-913j)  +/-  (1.27e-254, 1.27e-254j)
| (2.3938342001013874738 - 9.9135076438302044123e-908j)  +/-  (9.58e-248, 9.58e-248j)
| (4.9648191214095832096 - 6.9192179585006911926e-904j)  +/-  (1.05e-244, 1.05e-244j)
| (1.0352614307569813532 - 8.924618654504515219e-913j)  +/-  (2.47e-251, 2.47e-251j)
| (4.5734528430858644528 - 4.5875183695974776573e-905j)  +/-  (5.91e-245, 5.91e-245j)
| (4.1924910441272156199 - 2.2186489724156959123e-907j)  +/-  (3.71e-245, 3.71e-245j)
| (-0.3925082478326205222 - 9.9282316993283415656e-913j)  +/-  (1.86e-253, 1.86e-253j)
| (-4.1924910441272156199 - 4.1631468994564424395e-912j)  +/-  (3.48e-245, 3.48e-245j)
| (0.3925082478326205222 + 1.7850013349679367568e-934j)  +/-  (1.86e-253, 1.86e-253j)
| (-3.0963673107026499297 - 2.4643845235311024498e-925j)  +/-  (1.59e-246, 1.59e-246j)
-------------------------------------------------
The weights are:
| (5.0992831647380575271e-32 + 1.1081622496321352753e-714j)  +/-  (5.64e-89, 2.36e-210j)
| (7.0342677010402402653e-14 - 1.7430425235861491906e-704j)  +/-  (2.88e-81, 1.21e-202j)
| (2.3231984097520045371e-27 - 1.8740797895314287687e-712j)  +/-  (1.09e-87, 4.58e-209j)
| (6.782444179176424201e-16 - 2.4912215784085755339e-707j)  +/-  (1.1e-85, 4.62e-207j)
| (9.2464254363390811904e-24 + 1.5522125447955671932e-710j)  +/-  (1.13e-86, 4.73e-208j)
| (0.1107197573718226937 - 4.4905458410716757482e-699j)  +/-  (4.86e-70, 2.04e-191j)
| (9.3088834261376281707e-21 - 7.3786090639759538775e-710j)  +/-  (7.27e-89, 3.05e-210j)
| (9.3088834261376281707e-21 - 7.1208360752971479404e-709j)  +/-  (7.14e-86, 2.99e-207j)
| (1.3337696788359581729e-06 + 1.0937978640948029707e-701j)  +/-  (8.76e-78, 3.67e-199j)
| (9.5445974206876181582e-08 + 5.4368837299105916632e-703j)  +/-  (4.69e-81, 1.96e-202j)
| (3.6171310387913252154e-18 + 2.2954950935269428049e-707j)  +/-  (3.6e-85, 1.51e-206j)
| (1.3776391091834916645e-05 + 8.7417174471901901067e-702j)  +/-  (3.08e-78, 1.29e-199j)
| (5.0992831647380575271e-32 + 1.1961552623285373675e-715j)  +/-  (9.12e-95, 3.82e-216j)
| (0.010388982609670926594 - 1.0051692613686383239e-699j)  +/-  (2.64e-71, 1.11e-192j)
| (4.4197633088729234646e-12 + 6.6412843938304919997e-704j)  +/-  (1.13e-83, 4.74e-205j)
| (9.2464254363390811904e-24 + 2.0755762101750642413e-711j)  +/-  (9.13e-92, 3.82e-213j)
| (2.3231984097520045371e-27 - 2.9199987836545915348e-713j)  +/-  (3.14e-93, 1.31e-214j)
| (9.5445974206876181582e-08 - 3.2781492760366459747e-702j)  +/-  (3.08e-82, 1.29e-203j)
| (0.064077754813243482576 - 3.4009848811743378097e-699j)  +/-  (3.51e-70, 1.47e-191j)
| (0.0029104278596619334467 - 2.1829601858433924168e-700j)  +/-  (1.96e-77, 8.2e-199j)
| (0.010388982609670926594 + 5.1702175474607089312e-700j)  +/-  (1.47e-75, 6.16e-197j)
| (0.1362197701602995029 + 1.4742761739536030287e-698j)  +/-  (1.09e-70, 4.57e-192j)
| (1.7944067675317741853e-10 - 2.3249199187462648921e-703j)  +/-  (2.68e-84, 1.12e-205j)
| (0.00063527636866258757735 - 2.1997381633085126437e-700j)  +/-  (3.94e-79, 1.65e-200j)
| (0.029084512707419004674 + 1.9050444376110093476e-699j)  +/-  (1.19e-74, 5e-196j)
| (0.029084512707419004674 - 1.1254360588215367328e-699j)  +/-  (1.43e-75, 5.99e-197j)
| (0.000107074110091719438 + 8.953715198384657727e-701j)  +/-  (2.22e-80, 9.31e-202j)
| (7.0342677010402402653e-14 + 2.84256568506156116e-706j)  +/-  (4.4e-90, 1.84e-211j)
| (1.3337696788359581729e-06 - 2.33945110562117985e-702j)  +/-  (3.77e-85, 1.58e-206j)
| (0.1107197573718226937 + 5.8667996896613740636e-699j)  +/-  (4.64e-76, 1.94e-197j)
| (6.782444179176424201e-16 - 6.8654737889581557553e-706j)  +/-  (1.29e-88, 5.39e-210j)
| (3.6171310387913252154e-18 + 1.626515301133861832e-708j)  +/-  (9.66e-92, 4.04e-213j)
| (0.0029104278596619334467 + 4.9128504985731806571e-700j)  +/-  (1.56e-80, 6.52e-202j)
| (0.000107074110091719438 - 2.8690454259912782961e-701j)  +/-  (4.93e-84, 2.07e-205j)
| (0.1362197701602995029 - 1.4109033371063432575e-698j)  +/-  (7.6e-80, 3.18e-201j)
| (0.00063527636866258757735 + 8.3573024567073020552e-701j)  +/-  (3.06e-83, 1.28e-204j)
| (4.4197633088729234646e-12 - 2.5319498297315593991e-705j)  +/-  (3.81e-90, 1.6e-211j)
| (0.064077754813243482576 + 2.2933208936898231778e-699j)  +/-  (2.59e-82, 1.08e-203j)
| (1.7944067675317741853e-10 + 1.8203010980528662081e-704j)  +/-  (1.04e-89, 4.35e-211j)
| (4.9369514854027127103e-09 - 1.0829966602355867003e-703j)  +/-  (6.66e-89, 2.79e-210j)
| (0.14584123327150032133 - 9.9967774045069223799e-699j)  +/-  (4.28e-84, 1.85e-205j)
| (4.9369514854027127103e-09 + 8.967359255657510749e-703j)  +/-  (4.9e-90, 2.06e-211j)
| (0.14584123327150032133 + 8.6232928587348246796e-699j)  +/-  (9.41e-85, 4.45e-206j)
| (1.3776391091834916645e-05 - 3.2955471642668199321e-701j)  +/-  (4.28e-88, 1.77e-209j)
