Starting with polynomial:
P : t
Extension levels are: 1 2 42
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 1364494424873097033/124522573335021140*t^43 + 592371541037941974099/10584418733476796900*t^41 - 15543751879381937433159/87850675487857414270*t^39 + 34067737941548007816483/87850675487857414270*t^37 - 8681000880212010151179469/13880406727081471454660*t^35 + 20715890931989077550119667/26944318940805209294340*t^33 - 3757958031132977089960126/5103090708485835093625*t^31 + 41501622874437331337736524/74505124343893192366925*t^29 - 1100875541834706512131224331/3283363755568810339480350*t^27 + 1351617336140718070847573787/8390818486453626423116450*t^25 - 3469354003353593661612425301/56218483859239297034880215*t^23 + 229341461471522554038757327/12221409534617238485843525*t^21 - 21953742236834652585375153/4888563813846895394337410*t^19 + 248991674557471005899677251/298202392644660619054582010*t^17 - 1041914445845292642715443842/8796970583017488262110169295*t^15 + 109958329537450938774119337/8796970583017488262110169295*t^13 - 1834549057915189168584112809/1935333528263847417664237244900*t^11 + 275173226994428812101319631/5594873290799122534702067671620*t^9 - 25746134491543097835644259/15852140990597513848322525069590*t^7 + 482714274462158000246439/15852140990597513848322525069590*t^5 - 2758171113084521264860483/10430708771813164112196221495790220*t^3 + 34821925198302866587041/52153543859065820560981107478951100*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:
| (0.5114047255945475266 + 7.5681334506126764519e-927j)  +/-  (2.91e-246, 2.91e-246j)
| (0.98132380834652692847 + 7.6502756899354044469e-919j)  +/-  (4.44e-240, 4.44e-240j)
| (-0.94475755206460393205 + 2.7084459961230496137e-934j)  +/-  (3.1e-240, 3.1e-240j)
| (0.99238613019668857555 - 1.5620476689405904508e-938j)  +/-  (3.56e-240, 3.56e-240j)
| (0.88960044761246962429 + 1.5777317672843673639e-945j)  +/-  (8.78e-241, 8.78e-241j)
| (0.91944075690578682193 - 3.815425701450329349e-951j)  +/-  (1.95e-240, 1.95e-240j)
| (-0.99238613019668857555 - 1.2317662067678871871e-957j)  +/-  (3.32e-240, 3.32e-240j)
| (-0.85539075792856720776 - 2.4258378743481289315e-962j)  +/-  (3.37e-241, 3.37e-241j)
| (-0.99855341163032368546 + 6.9320168686608428231e-960j)  +/-  (1.16e-240, 1.16e-240j)
| (-0.98132380834652692847 + 2.8395589086526470476e-961j)  +/-  (4.99e-240, 4.99e-240j)
| (0.85539075792856720776 - 2.0737329591420001001e-962j)  +/-  (3.38e-241, 3.38e-241j)
| (-0.19322693907740572908 + 1.6362021045284873251e-981j)  +/-  (5.37e-252, 5.37e-252j)
| (-0.56993154558925436082 + 6.1182182745150416385e-975j)  +/-  (2.44e-245, 2.44e-245j)
| (-0.88960044761246962429 - 3.5266731847164371436e-969j)  +/-  (8.49e-241, 8.49e-241j)
| (0.99855341163032368546 + 2.6252874717751886179e-969j)  +/-  (1.16e-240, 1.16e-240j)
| (0.81698927374426241067 + 3.4654070102070311569e-983j)  +/-  (1.08e-241, 1.08e-241j)
| (0.67875502647205929737 - 2.3879656084386383443e-991j)  +/-  (1.23e-243, 1.23e-243j)
| (-0.9654205626957687594 - 8.1794140622693932451e-989j)  +/-  (4.43e-240, 4.43e-240j)
| (-0.81698927374426241067 - 3.4478303364997702854e-992j)  +/-  (1.12e-241, 1.12e-241j)
| (-0.62582200827490670876 - 1.5770948879809820633e-997j)  +/-  (1.9e-244, 1.9e-244j)
| (0.9654205626957687594 - 3.7048004076661483367e-992j)  +/-  (4.22e-240, 4.22e-240j)
| (0.77459666924148337704 + 1.5078103304114737738e-1008j)  +/-  (2.91e-242, 2.91e-242j)
| (0.1280820709211599132 + 6.8218770522648382669e-1021j)  +/-  (3.59e-253, 3.59e-253j)
| (-0.67875502647205929737 + 3.2009015243905792406e-1015j)  +/-  (1.17e-243, 1.17e-243j)
| (-0.77459666924148337704 + 4.3148622711631248179e-1013j)  +/-  (2.95e-242, 2.95e-242j)
| (-7.069540403872062904e-1023 + 3.6980517607844372685e-1022j)  +/-  (1.69e-1020, 1.69e-1020j)
| (0.72843646453669396918 - 9.7469659724017381405e-1012j)  +/-  (6.83e-243, 6.83e-243j)
| (0.94475755206460393205 - 2.7666720054518784988e-1021j)  +/-  (3.22e-240, 3.22e-240j)
| (-0.91944075690578682193 + 1.8991747352493102201e-1042j)  +/-  (1.93e-240, 1.93e-240j)
| (-0.72843646453669396918 - 1.4706567072210420361e-1049j)  +/-  (6.7e-243, 6.7e-243j)
| (-0.25865636042642628176 + 1.6654172776859445259e-1057j)  +/-  (8.12e-251, 8.12e-251j)
| (0.45059415417275136725 + 1.8279628876172359417e-1052j)  +/-  (2.72e-247, 2.72e-247j)
| (0.62582200827490670876 + 7.1697645286768404873e-1051j)  +/-  (1.83e-244, 1.83e-244j)
| (0.063692883543839287524 + 7.8831317654063312117e-1063j)  +/-  (1.88e-254, 1.88e-254j)
| (-0.45059415417275136725 + 1.8893460348398367616e-1056j)  +/-  (2.52e-247, 2.52e-247j)
| (-0.38789183847016823359 + 4.1826927066163688698e-1058j)  +/-  (2.07e-248, 2.07e-248j)
| (0.19322693907740572908 + 1.3017369869334299041e-1059j)  +/-  (5.69e-252, 5.69e-252j)
| (0.56993154558925436082 - 3.5854168653098124704e-1056j)  +/-  (2.37e-245, 2.37e-245j)
| (0.25865636042642628176 + 2.4884515201603238059e-1062j)  +/-  (8.49e-251, 8.49e-251j)
| (-0.32374172538777687861 - 3.922579465859017226e-1059j)  +/-  (1.53e-249, 1.53e-249j)
| (-0.5114047255945475266 - 3.621448994092567815e-1057j)  +/-  (2.82e-246, 2.82e-246j)
| (-0.1280820709211599132 - 4.1666340942686007085e-1064j)  +/-  (3.41e-253, 3.41e-253j)
| (0.32374172538777687861 - 2.3358817003277254161e-1060j)  +/-  (1.6e-249, 1.6e-249j)
| (0.38789183847016823359 + 2.0482846599313811011e-1059j)  +/-  (2.17e-248, 2.17e-248j)
| (-0.063692883543839287524 + 1.4331304236179773822e-1065j)  +/-  (1.88e-254, 1.88e-254j)
-------------------------------------------------
The weights are:
| (0.059730414952167081968 - 3.7334024477419372995e-919j)  +/-  (9.02e-71, 6.65e-187j)
| (0.013494202323903793858 - 2.837992605090110943e-919j)  +/-  (4.14e-71, 3.06e-187j)
| (0.023009604962715428563 - 1.2364172890307105338e-920j)  +/-  (1.93e-72, 1.43e-188j)
| (0.0086212293470859027068 - 4.725142533099746221e-919j)  +/-  (2.43e-71, 1.79e-187j)
| (0.032052656100992419502 - 4.5202472015519800081e-919j)  +/-  (1.05e-71, 7.78e-188j)
| (0.027602266586682742118 + 5.1885483369194154701e-919j)  +/-  (1.17e-71, 8.65e-188j)
| (0.0086212293470859027068 + 2.6483652254035545076e-921j)  +/-  (1.34e-73, 9.9e-190j)
| (0.036337119381402432028 + 2.8282597304837618942e-920j)  +/-  (3.93e-74, 2.9e-190j)
| (0.0037114863705129180685 - 7.5177134098430166939e-922j)  +/-  (6.34e-74, 4.68e-190j)
| (0.013494202323903793858 - 5.2599543323683270678e-921j)  +/-  (7.28e-74, 5.37e-190j)
| (0.036337119381402432028 + 4.1249741859353042531e-919j)  +/-  (7.69e-75, 5.67e-191j)
| (0.065389063371694258143 + 3.4047932595113478536e-919j)  +/-  (6.98e-77, 5.14e-193j)
| (0.057264585053000769471 + 9.6468403436833350936e-920j)  +/-  (6.52e-77, 4.81e-193j)
| (0.032052656100992419502 - 2.2160825861348346771e-920j)  +/-  (3.44e-75, 2.54e-191j)
| (0.0037114863705129180685 + 8.6387070162722138075e-920j)  +/-  (2.41e-75, 1.77e-191j)
| (0.040432398971571763174 - 3.8752276085669001311e-919j)  +/-  (1.38e-75, 1.02e-191j)
| (0.051354154049167316724 + 3.5829343673927488669e-919j)  +/-  (8.9e-77, 6.56e-193j)
| (0.018298745163832831485 + 8.5000965102811474971e-921j)  +/-  (3.34e-75, 2.46e-191j)
| (0.040432398971571763174 - 3.5412839676118967086e-920j)  +/-  (7.08e-77, 5.22e-193j)
| (0.054462898974526278859 - 7.9367588349947756486e-920j)  +/-  (3.1e-78, 2.28e-194j)
| (0.018298745163832831485 + 1.0405118137767723965e-918j)  +/-  (8.1e-77, 5.97e-193j)
| (0.044315556246633258099 + 3.7168937094994524669e-919j)  +/-  (1.31e-77, 9.65e-194j)
| (0.064814875925765219322 - 5.4340468165409583551e-919j)  +/-  (9.18e-81, 6.77e-197j)
| (0.051354154049167316724 + 6.5303169541533856249e-920j)  +/-  (5.97e-79, 4.4e-195j)
| (0.044315556246633258099 + 4.3759544750924635728e-920j)  +/-  (1.34e-78, 9.91e-195j)
| (0.063545642534164545348 - 5.4706045928753545168e-919j)  +/-  (1.71e-81, 1.26e-197j)
| (0.047963798624399244933 - 3.6238516699397192427e-919j)  +/-  (1.89e-79, 1.4e-195j)
| (0.023009604962715428563 - 6.5126718663712352922e-919j)  +/-  (3.51e-78, 2.58e-194j)
| (0.027602266586682742118 + 1.6892318529634680217e-920j)  +/-  (1.25e-78, 9.24e-195j)
| (0.047963798624399244933 - 5.3599691355221367683e-920j)  +/-  (1.48e-79, 1.09e-195j)
| (0.065362052003807096271 - 2.7339728868728104354e-919j)  +/-  (6.21e-83, 4.58e-199j)
| (0.061825601093552486689 + 3.8802143947129048487e-919j)  +/-  (2.81e-83, 2.07e-199j)
| (0.054462898974526278859 - 3.5880348870411014727e-919j)  +/-  (4.62e-82, 3.41e-198j)
| (0.063969411554186986507 + 5.6229508065447157826e-919j)  +/-  (1.36e-83, 1e-199j)
| (0.061825601093552486689 + 1.4381723390009117724e-919j)  +/-  (7.84e-84, 5.78e-200j)
| (0.063505333544246671757 - 1.7704472154085337697e-919j)  +/-  (4.38e-84, 3.23e-200j)
| (0.065389063371694258143 + 5.074379346080060058e-919j)  +/-  (4.53e-85, 3.34e-201j)
| (0.057264585053000769471 + 3.6375775045095898596e-919j)  +/-  (1.5e-84, 1.1e-200j)
| (0.065362052003807096271 - 4.691054208062409265e-919j)  +/-  (1.28e-85, 9.47e-202j)
| (0.064709724131070827081 + 2.1941999419849529409e-919j)  +/-  (2.45e-85, 1.8e-201j)
| (0.059730414952167081968 - 1.1752954509193586129e-919j)  +/-  (3.72e-85, 2.74e-201j)
| (0.064814875925765219322 - 4.1793140164265331956e-919j)  +/-  (3.73e-86, 2.75e-202j)
| (0.064709724131070827081 + 4.3547030962982750493e-919j)  +/-  (5.66e-87, 4.17e-203j)
| (0.063505333544246671757 - 4.084923247741030704e-919j)  +/-  (4.69e-87, 3.45e-203j)
| (0.063969411554186986507 + 4.9375226115335681777e-919j)  +/-  (9.73e-87, 7.2e-203j)
