Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^44 - 7255566411573886299156499/8017041162036390230920*t^42 + 2982078616002310072860882879/8017041162036390230920*t^40 - 73856533187373614442307216401/801704116203639023092*t^38 + 12333963179539269598533182249361/801704116203639023092*t^36 - 2945285444152201867625379546494055/1603408232407278046184*t^34 + 260155537620157478965307135034944403/1603408232407278046184*t^32 - 2169352420735601880724822787615295591/200426029050909755773*t^30 + 110624310583288718677139952583655350005/200426029050909755773*t^28 - 17352733992565286295097767903242472377895/801704116203639023092*t^26 + 523918973731987205204170772604002493535875/801704116203639023092*t^24 - 6070420435761196327530694926605654509185675/400852058101819511546*t^22 + 107184754620531148553124513090451096414734675/400852058101819511546*t^20 - 2850406771077732443422122812355574656961933875/801704116203639023092*t^18 + 28061519240162300456343655804789281537592851375/801704116203639023092*t^16 - 49944328964235906990576796034813851505346279375/200426029050909755773*t^14 + 248916960611337274326901970116529483383195243500/200426029050909755773*t^12 - 6639617089763043117441550702971125787182311774875/1603408232407278046184*t^10 + 13870415566052556639471835835219221990863457614375/1603408232407278046184*t^8 - 8209738826724477726039848883270990168041889530625/801704116203639023092*t^6 + 4649378585162935288299021942285336257111976140625/801704116203639023092*t^4 - 1795116028732864161181804126924245650395734361875/1603408232407278046184*t^2 + 42429286114339981190579026024662948552547899375/1603408232407278046184
-------------------------------------------------
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:
| (-10.181156622150560838 - 7.4705300262341222672e-518j)  +/-  (1.43e-245, 1.43e-245j)
| (-10.977476975584906571 + 2.6198010747420911343e-522j)  +/-  (2.8e-246, 2.8e-246j)
| (-11.936083363945473089 + 1.1852474060688608747e-524j)  +/-  (2.14e-247, 2.14e-247j)
| (8.1863591411412570898 - 4.1595991463698043462e-525j)  +/-  (1.33e-244, 1.33e-244j)
| (9.4681715028992923385 + 7.4831581751489776426e-526j)  +/-  (4.66e-245, 4.66e-245j)
| (10.977476975584906571 + 1.2456192324269521325e-529j)  +/-  (2.69e-246, 2.69e-246j)
| (-2.8974543278066626361 - 1.3067531105106027966e-528j)  +/-  (2.09e-248, 2.09e-248j)
| (10.181156622150560838 - 9.4661764068545028991e-529j)  +/-  (1.41e-245, 1.41e-245j)
| (-6.4678390375658200514 + 8.4210573370194906033e-533j)  +/-  (8.42e-245, 8.42e-245j)
| (7.0213145362267065641 - 1.7896220239437295038e-542j)  +/-  (1.34e-244, 1.34e-244j)
| (-9.4681715028992923385 - 9.9232593952092317606e-556j)  +/-  (4.01e-245, 4.01e-245j)
| (3.8789438718725340472 - 1.2087954660200056613e-576j)  +/-  (5.67e-247, 5.67e-247j)
| (-8.8084092637630402841 - 1.8991264065980756108e-579j)  +/-  (9.15e-245, 9.15e-245j)
| (8.8084092637630402841 - 1.1561526949010973814e-591j)  +/-  (9.03e-245, 9.03e-245j)
| (-4.3789246448843945927 - 1.5524498841511876124e-604j)  +/-  (2.36e-246, 2.36e-246j)
| (6.4678390375658200514 - 1.4895183883546468202e-618j)  +/-  (9.04e-245, 9.04e-245j)
| (3.3853927918559316282 - 8.5105967567419649835e-628j)  +/-  (1.18e-247, 1.18e-247j)
| (-7.5927100178528091789 - 2.594410295928473877e-638j)  +/-  (1.5e-244, 1.5e-244j)
| (-1.936561649878146128 - 2.9289685518894647879e-660j)  +/-  (4.06e-250, 4.06e-250j)
| (-4.8863744030699763703 + 7.732506643455138012e-657j)  +/-  (7.65e-246, 7.65e-246j)
| (1.936561649878146128 - 3.285347166745136906e-673j)  +/-  (3.6e-250, 3.6e-250j)
| (4.8863744030699763703 + 2.1088335405418119648e-667j)  +/-  (7.92e-246, 7.92e-246j)
| (-7.0213145362267065641 - 6.68341080576669599e-679j)  +/-  (1.35e-244, 1.35e-244j)
| (-0.16528753520190883315 - 2.4407089428074759777e-712j)  +/-  (1.91e-254, 1.91e-254j)
| (-5.4025702401175491804 - 7.9992960410227662423e-709j)  +/-  (2.18e-245, 2.18e-245j)
| (11.936083363945473089 - 1.1151819886074036131e-724j)  +/-  (2.48e-247, 2.48e-247j)
| (1.4640807559782978698 - 4.5567058119568344585e-734j)  +/-  (3.55e-251, 3.55e-251j)
| (0.16528753520190883315 - 1.3322707665855655786e-736j)  +/-  (1.91e-254, 1.91e-254j)
| (-5.9290776947324464337 + 5.9419892394999300373e-733j)  +/-  (5.1e-245, 5.1e-245j)
| (-1.4640807559782978698 - 1.6420111699685878491e-746j)  +/-  (3.6e-251, 3.6e-251j)
| (-3.3853927918559316282 + 1.144326202909991801e-740j)  +/-  (1.39e-247, 1.39e-247j)
| (0.55509048742819193237 - 6.0864085116420544988e-752j)  +/-  (2.47e-253, 2.47e-253j)
| (4.3789246448843945927 - 5.8802524015769152206e-746j)  +/-  (2.12e-246, 2.12e-246j)
| (5.4025702401175491804 + 1.4922603212089860838e-744j)  +/-  (2.41e-245, 2.41e-245j)
| (-3.8789438718725340472 - 5.6504601771809972511e-744j)  +/-  (5.53e-247, 5.53e-247j)
| (2.8974543278066626361 + 4.09560712507426688e-748j)  +/-  (1.9e-248, 1.9e-248j)
| (5.9290776947324464337 + 1.3415509960252777431e-743j)  +/-  (5.38e-245, 5.38e-245j)
| (-1 + 1.5001375931686070565e-756j)  +/-  (3.44e-252, 3.44e-252j)
| (7.5927100178528091789 - 4.365943785548592557e-748j)  +/-  (1.56e-244, 1.56e-244j)
| (-8.1863591411412570898 - 1.4951900162783955825e-758j)  +/-  (1.37e-244, 1.37e-244j)
| (-0.55509048742819193237 + 8.3035018741010484343e-774j)  +/-  (2.47e-253, 2.47e-253j)
| (-2.4145671533993687162 - 7.5284140342012035603e-771j)  +/-  (3.18e-249, 3.18e-249j)
| (1 - 3.870306285419398701e-773j)  +/-  (3.27e-252, 3.27e-252j)
| (2.4145671533993687162 + 2.9119424664184926228e-770j)  +/-  (2.84e-249, 2.84e-249j)
-------------------------------------------------
The weights are:
| (9.2464254363390811904e-24 - 3.5925316858712558428e-540j)  +/-  (6.37e-85, 2.76e-207j)
| (2.3231984097520045371e-27 - 1.2641830797880926139e-542j)  +/-  (1.69e-86, 7.32e-209j)
| (5.0992831647380575271e-32 + 2.4507333537168730567e-545j)  +/-  (2.2e-88, 9.52e-211j)
| (6.782444179176424201e-16 - 3.2945317102448061074e-538j)  +/-  (2.58e-84, 1.12e-206j)
| (9.3088834261376281707e-21 - 1.0366997363203796802e-540j)  +/-  (3.83e-87, 1.66e-209j)
| (2.3231984097520045371e-27 - 4.162147940568204242e-544j)  +/-  (1.61e-90, 6.96e-213j)
| (0.0029104278596619334467 - 9.3635933392226002129e-532j)  +/-  (3.6e-70, 1.56e-192j)
| (9.2464254363390811904e-24 + 2.9353509680918509334e-542j)  +/-  (8.11e-89, 3.51e-211j)
| (1.7944067675317741853e-10 - 1.4077886493727376753e-534j)  +/-  (3.34e-83, 1.45e-205j)
| (4.4197633088729234646e-12 - 3.3784993153179948784e-536j)  +/-  (3.14e-84, 1.36e-206j)
| (9.3088834261376281707e-21 + 3.337014786781680994e-539j)  +/-  (1.94e-88, 8.41e-211j)
| (0.000107074110091719438 - 3.5570205723791113294e-532j)  +/-  (9.34e-78, 4.05e-200j)
| (3.6171310387913252154e-18 - 3.7119347828101024781e-538j)  +/-  (8.46e-88, 3.66e-210j)
| (3.6171310387913252154e-18 + 2.2801504568815689007e-539j)  +/-  (1.96e-87, 8.49e-210j)
| (1.3776391091834916645e-05 - 4.5418674051251293385e-532j)  +/-  (3.62e-80, 1.57e-202j)
| (1.7944067675317741853e-10 + 2.4084532240757348595e-535j)  +/-  (2.89e-84, 1.25e-206j)
| (0.00063527636866258757735 + 1.0179973382101667232e-531j)  +/-  (2.18e-77, 9.43e-200j)
| (7.0342677010402402653e-14 - 3.2722389121874836747e-536j)  +/-  (7.78e-87, 3.37e-209j)
| (0.029084512707419004674 + 5.7164688807330019362e-531j)  +/-  (6.02e-73, 2.61e-195j)
| (1.3337696788359581729e-06 + 1.2738749899629662128e-532j)  +/-  (3.04e-82, 1.32e-204j)
| (0.029084512707419004674 - 1.2802328010495796845e-530j)  +/-  (1.34e-74, 5.82e-197j)
| (1.3337696788359581729e-06 - 2.9891001962483172436e-533j)  +/-  (2.66e-83, 1.15e-205j)
| (4.4197633088729234646e-12 + 2.3390382262712178872e-535j)  +/-  (3.07e-86, 1.33e-208j)
| (0.1362197701602995029 + 1.3687534390220519536e-529j)  +/-  (6.56e-75, 2.84e-197j)
| (9.5445974206876181582e-08 - 3.231446572676322473e-533j)  +/-  (5.33e-84, 2.31e-206j)
| (5.0992831647380575271e-32 + 1.7205060736648927215e-546j)  +/-  (1.91e-97, 8.28e-220j)
| (0.064077754813243482576 + 2.5308654503035444499e-530j)  +/-  (7.87e-76, 3.41e-198j)
| (0.1362197701602995029 - 1.3753798497983344618e-529j)  +/-  (4.83e-75, 2.09e-197j)
| (4.9369514854027127103e-09 + 7.2398853275751008629e-534j)  +/-  (6.68e-85, 2.89e-207j)
| (0.064077754813243482576 - 2.0340506281886930756e-530j)  +/-  (9.83e-77, 4.26e-199j)
| (0.00063527636866258757735 - 5.6427338059006418581e-531j)  +/-  (1.39e-81, 6.01e-204j)
| (0.14584123327150032133 + 8.8023742791878709264e-530j)  +/-  (2.66e-76, 1.15e-198j)
| (1.3776391091834916645e-05 + 1.1010849642195791248e-532j)  +/-  (1.09e-84, 4.72e-207j)
| (9.5445974206876181582e-08 + 7.0370351194783684424e-534j)  +/-  (7.55e-87, 3.27e-209j)
| (0.000107074110091719438 + 1.5320021987666064379e-531j)  +/-  (7.93e-84, 3.43e-206j)
| (0.0029104278596619334467 - 2.6067569198363951192e-531j)  +/-  (1.12e-83, 4.85e-206j)
| (4.9369514854027127103e-09 - 1.4181845149071906352e-534j)  +/-  (7.03e-88, 3.04e-210j)
| (0.1107197573718226937 + 4.45191521442024423e-530j)  +/-  (4.41e-82, 1.92e-204j)
| (7.0342677010402402653e-14 + 3.8053036008000323214e-537j)  +/-  (1.39e-90, 6.03e-213j)
| (6.782444179176424201e-16 + 3.8106046106907721132e-537j)  +/-  (8.72e-92, 3.79e-214j)
| (0.14584123327150032133 - 8.6096354372138192561e-530j)  +/-  (2.48e-82, 1.08e-204j)
| (0.010388982609670926594 + 5.3696115117723357929e-531j)  +/-  (2.91e-84, 1.27e-206j)
| (0.1107197573718226937 - 4.7813356214875516988e-530j)  +/-  (1e-83, 4.73e-206j)
| (0.010388982609670926594 + 6.0361387622408558772e-531j)  +/-  (9.27e-85, 3.78e-207j)
