Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 56
-------------------------------------------------
Trying to find an order 56 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^58 - 741005200594733567886876265044318998/229056310072211802412061184914799*t^56 + 279028842434932943044799127312720313270/229056310072211802412061184914799*t^54 - 2409474363327892251669499551153170675405/8483567039711548237483747589437*t^52 + 1560830590052600344771890315722157800921275/33934268158846192949934990357748*t^50 - 373424020918607991038291095112292043792013575/67868536317692385899869980715496*t^48 + 17128893721893458187551045955014805038840794425/33934268158846192949934990357748*t^46 - 2470228358104824674881856400734742851448277729125/67868536317692385899869980715496*t^44 + 1138902374478371010580157254736884897357255715362125/542948290541539087198959845723968*t^42 - 106131331036498968544374458654276618085369876870470625/1085896581083078174397919691447936*t^40 + 4028999061668117305986641057610258658618929321880620375/1085896581083078174397919691447936*t^38 - 250451816152516428330554799461429239633784428400587192875/2171793162166156348795839382895872*t^36 + 25558466325025533682016152462581845515280523791885311141875/8687172648664625395183357531583488*t^34 - 1071056537401128352339291738518564715962821226119902346529375/17374345297329250790366715063166976*t^32 + 4602025069085608744192595975485739403404289219647954343234375/4343586324332312697591678765791744*t^30 - 129363192989306108769881527588431502590223591556468179117606875/8687172648664625395183357531583488*t^28 + 23675587546299487588095598886789770309045608395454533951187789375/138994762378634006322933720505335808*t^26 - 437823398572149364768950967311408567898538902687611127410180046875/277989524757268012645867441010671616*t^24 + 3243193740682983010358922642328783667383166649915475693130040609375/277989524757268012645867441010671616*t^22 - 38051066806540085567368952507757551609616347136904761241192099921875/555979049514536025291734882021343232*t^20 + 696762784550754176167109064916837933999909695071906042052260416265625/2223916198058144101166939528085372928*t^18 - 4885474326948511864894944234500057394038935503096243235230773947828125/4447832396116288202333879056170745856*t^16 + 6401637382829357751429868241345857574522669336626012431538744293515625/2223916198058144101166939528085372928*t^14 - 24298045787113262935893270114947938819491055534383023208895492635703125/4447832396116288202333879056170745856*t^12 + 255946615133353214625247676894628417850664438888485708683949401558984375/35582659168930305618671032449365966848*t^10 - 440306507895228966520204888544693115636469080417764691726087091425421875/71165318337860611237342064898731933696*t^8 + 226104904604073463615749823904106581076322707373368134980573601562515625/71165318337860611237342064898731933696*t^6 - 119512049762363559331968427422817064039705420033470883222748034215703125/142330636675721222474684129797463867392*t^4 + 48604398700103654756984884480484487968242096368363582052695076574765625/569322546702884889898736519189855469568*t^2 - 1585839569036258564541296061371091819883118665303830044677275711328125/1138645093405769779797473038379710939136
-------------------------------------------------
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:   58 out of 58
Indefinite weights: 0 out of 58
Negative weights:   0 out of 58
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-7.005782997703156817 + 1.1120911541152329749e-864j)  +/-  (1.99e-241, 1.99e-241j)
| (9.2563666415152082401 - 5.8575005643726498428e-874j)  +/-  (4.57e-244, 4.57e-244j)
| (-9.2563666415152082401 - 1.9978462515886654629e-872j)  +/-  (4.48e-244, 4.48e-244j)
| (7.3981630312974027045 - 1.5033594879487083316e-872j)  +/-  (1.21e-241, 1.21e-241j)
| (-7.8104671572622696993 - 7.0807120986911663459e-870j)  +/-  (5.23e-242, 5.23e-242j)
| (-8.2489733864026794486 + 1.0151021927091672532e-872j)  +/-  (1.8e-242, 1.8e-242j)
| (-7.3981630312974027045 - 9.8713438220101877308e-878j)  +/-  (1.24e-241, 1.24e-241j)
| (9.8989574071003468054 - 1.1710466288512746567e-891j)  +/-  (2.23e-245, 2.23e-245j)
| (-6.2654891533140825057 - 2.8666672864183144929e-894j)  +/-  (3.26e-241, 3.26e-241j)
| (-9.8989574071003468054 - 1.4306845452429182708e-911j)  +/-  (2.26e-245, 2.26e-245j)
| (5.9125339846501468227 + 1.3793337885842610193e-905j)  +/-  (3e-241, 3e-241j)
| (3.3346762801788389056 - 3.0902492574105685752e-913j)  +/-  (5.45e-244, 5.45e-244j)
| (-4.9035039526276052118 - 1.7167685618762630118e-921j)  +/-  (9.55e-242, 9.55e-242j)
| (-2.437888802170997108 - 1.2671807733161261983e-940j)  +/-  (4.71e-246, 4.71e-246j)
| (-5.5686961841015547441 + 4.1586628050835973837e-935j)  +/-  (2.5e-241, 2.5e-241j)
| (-8.7241564797919737861 + 2.1737320099098851967e-944j)  +/-  (3.5e-243, 3.5e-243j)
| (3.9490652337111393997 + 1.1062459419977276688e-942j)  +/-  (6.38e-243, 6.38e-243j)
| (3.0327611055315134691 - 4.1433684333661399661e-946j)  +/-  (1.4e-244, 1.4e-244j)
| (-1.8532338617827793367 + 7.0694220366385184413e-950j)  +/-  (9.04e-248, 9.04e-248j)
| (4.9035039526276052118 + 3.0107864031804151112e-941j)  +/-  (9.02e-242, 9.02e-242j)
| (5.2326954407251194642 - 2.1440184038445374677e-941j)  +/-  (1.74e-241, 1.74e-241j)
| (2.437888802170997108 + 5.971092753888679633e-947j)  +/-  (4.53e-246, 4.53e-246j)
| (6.2654891533140825057 + 6.4499166552160195271e-941j)  +/-  (3.26e-241, 3.26e-241j)
| (7.8104671572622696993 - 1.9272742955828525015e-943j)  +/-  (5.5e-242, 5.5e-242j)
| (-4.2623304189839081247 - 4.0845307341468451786e-944j)  +/-  (1.81e-242, 1.81e-242j)
| (1.2769554215249512225 - 5.5147898144701669068e-956j)  +/-  (1.16e-249, 1.16e-249j)
| (5.5686961841015547441 - 2.8225451291737127413e-946j)  +/-  (2.49e-241, 2.49e-241j)
| (4.5802813974728746293 - 6.4363425485224200682e-949j)  +/-  (4.51e-242, 4.51e-242j)
| (-3.3346762801788389056 - 2.9746281346580308491e-949j)  +/-  (6.15e-244, 6.15e-244j)
| (-5.2326954407251194642 + 2.1414169685692136172e-949j)  +/-  (1.65e-241, 1.65e-241j)
| (-1.5641613832278189567 - 3.2272117556033259742e-968j)  +/-  (1.12e-248, 1.12e-248j)
| (-6.6291929266428762956 - 4.0061691237639546867e-960j)  +/-  (2.8e-241, 2.8e-241j)
| (8.7241564797919737861 + 5.2802018197620383856e-968j)  +/-  (3.62e-243, 3.62e-243j)
| (-3.6399888834598335677 + 1.4760527147857651676e-968j)  +/-  (2.03e-243, 2.03e-243j)
| (8.2489733864026794486 - 1.0810860126880377499e-968j)  +/-  (1.64e-242, 1.64e-242j)
| (4.2623304189839081247 - 2.6708472492894223159e-970j)  +/-  (1.72e-242, 1.72e-242j)
| (-0.99136576457816671933 + 1.1127964978105227309e-979j)  +/-  (9.06e-251, 9.06e-251j)
| (3.6399888834598335677 - 2.1429802503673679435e-971j)  +/-  (2.02e-243, 2.02e-243j)
| (2.7339251336130074138 - 3.6045258177693793797e-974j)  +/-  (2.68e-245, 2.68e-245j)
| (-2.1444019694284182633 - 7.7350051365905436779e-976j)  +/-  (6.96e-247, 6.96e-247j)
| (2.1444019694284182633 - 2.2403276055647810267e-975j)  +/-  (7.23e-247, 7.23e-247j)
| (-0.7071067811865475244 + 4.089812420968569672e-981j)  +/-  (6.89e-252, 6.89e-252j)
| (1.5641613832278189567 - 4.5370428407420500376e-977j)  +/-  (1.05e-248, 1.05e-248j)
| (0.14121187113537450192 + 3.0589822349745105629e-983j)  +/-  (3.64e-254, 3.64e-254j)
| (7.005782997703156817 - 1.1558287606483589274e-970j)  +/-  (2.03e-241, 2.03e-241j)
| (-1.2769554215249512225 + 3.9730342974308781188e-984j)  +/-  (1.19e-249, 1.19e-249j)
| (-0.42384768543438699844 - 4.8173187134035663508e-988j)  +/-  (4.83e-253, 4.83e-253j)
| (-5.9125339846501468227 - 4.2664148639823266698e-975j)  +/-  (3.01e-241, 3.01e-241j)
| (0.42384768543438699844 - 3.0584118119370120667e-992j)  +/-  (4.34e-253, 4.34e-253j)
| (1.8532338617827793367 - 5.3459155556290468011e-988j)  +/-  (9.63e-248, 9.63e-248j)
| (-4.5802813974728746293 - 3.5494153803974020135e-982j)  +/-  (4.29e-242, 4.29e-242j)
| (-3.0327611055315134691 + 7.4832120708532585408e-988j)  +/-  (1.38e-244, 1.38e-244j)
| (6.6291929266428762956 - 2.1588773652628428126e-986j)  +/-  (2.98e-241, 2.98e-241j)
| (0.99136576457816671933 + 2.4297554725150905287e-996j)  +/-  (9.36e-251, 9.36e-251j)
| (-3.9490652337111393997 - 4.7173558576329118988e-992j)  +/-  (6.14e-243, 6.14e-243j)
| (0.7071067811865475244 - 2.4148826735644382232e-1002j)  +/-  (8.19e-252, 8.19e-252j)
| (-2.7339251336130074138 - 2.6353687494051254781e-998j)  +/-  (2.75e-245, 2.75e-245j)
| (-0.14121187113537450192 + 1.8476087969477555638e-1007j)  +/-  (2.54e-254, 2.54e-254j)
-------------------------------------------------
The weights are:
| (1.047271224309206671e-22 + 8.3053036871193331786e-886j)  +/-  (1.38e-62, 2.66e-182j)
| (1.990864076587820974e-38 + 7.6764899600572523652e-896j)  +/-  (1.75e-70, 3.39e-190j)
| (1.990864076587820974e-38 + 5.5468379622641672563e-895j)  +/-  (5.29e-70, 1.02e-189j)
| (3.8456350067884289795e-25 + 4.6693999938484137017e-889j)  +/-  (1.23e-65, 2.38e-185j)
| (7.6818021871411736165e-28 - 3.5587816564864825785e-889j)  +/-  (7.34e-66, 1.42e-185j)
| (7.1980817059731562387e-31 + 6.7114587532786664916e-891j)  +/-  (2.07e-67, 4e-187j)
| (3.8456350067884289795e-25 + 1.7140979638144786337e-887j)  +/-  (7.73e-65, 1.5e-184j)
| (1.1634180346799444958e-43 - 1.6770766967281703198e-898j)  +/-  (1.17e-75, 2.27e-195j)
| (1.8051634740514481018e-18 + 2.2750371552402856442e-884j)  +/-  (7.88e-63, 1.53e-182j)
| (1.1634180346799444958e-43 - 9.7991140920310807275e-898j)  +/-  (1.95e-73, 3.76e-193j)
| (1.2915449725274514144e-16 + 1.158095629329696681e-884j)  +/-  (1.24e-65, 2.4e-185j)
| (2.536777074807674541e-06 + 3.0939004067125010908e-879j)  +/-  (2.36e-54, 4.56e-174j)
| (6.6438589332556202216e-12 + 1.8777897233510457864e-881j)  +/-  (5.08e-60, 9.83e-180j)
| (0.00043620861318204142803 + 1.088752430303354854e-877j)  +/-  (1.24e-48, 2.41e-168j)
| (6.5301427019803386484e-15 + 7.7789964651673440555e-883j)  +/-  (7.75e-62, 1.5e-181j)
| (2.4826525077998024738e-34 - 8.5678447524928708e-893j)  +/-  (8.88e-70, 1.72e-189j)
| (2.9610406254223470104e-08 + 2.8228043547703278131e-880j)  +/-  (5.89e-60, 1.14e-179j)
| (1.7160653373459270398e-05 - 8.7720854994090157322e-879j)  +/-  (2.96e-55, 5.73e-175j)
| (0.005276836322019410782 + 3.7450340205619875846e-877j)  +/-  (4.77e-47, 9.22e-167j)
| (6.6438589332556202216e-12 - 3.3147559568694899936e-882j)  +/-  (1.55e-64, 3e-184j)
| (2.4081297637889024403e-13 + 5.8338250213472786996e-883j)  +/-  (6.91e-66, 1.34e-185j)
| (0.00043620861318204142803 - 5.2662841441001235524e-878j)  +/-  (1.21e-54, 2.35e-174j)
| (1.8051634740514481018e-18 - 1.269053926908116337e-885j)  +/-  (4.16e-70, 8.05e-190j)
| (7.6818021871411736165e-28 - 1.9328066882861887605e-890j)  +/-  (1.53e-75, 2.96e-195j)
| (2.2930947583459401992e-09 + 2.9709514122595433896e-880j)  +/-  (2.92e-65, 5.65e-185j)
| (0.031634467854668653813 - 6.2831223766767896042e-877j)  +/-  (2.79e-49, 5.4e-169j)
| (6.5301427019803386484e-15 - 8.89030319510526079e-884j)  +/-  (1.61e-67, 3.11e-187j)
| (1.4001440644011869398e-10 + 1.6481084447026666635e-881j)  +/-  (8.77e-65, 1.7e-184j)
| (2.536777074807674541e-06 - 8.7146339324652254661e-879j)  +/-  (2.24e-63, 4.33e-183j)
| (2.4081297637889024403e-13 - 4.0267126943495635162e-882j)  +/-  (5.08e-68, 9.83e-188j)
| (0.014074169000263592701 - 6.0919092740384533621e-877j)  +/-  (1.75e-55, 3.38e-175j)
| (1.7128815162265936265e-20 - 4.1503451426609482144e-885j)  +/-  (2.96e-71, 5.73e-191j)
| (2.4826525077998024738e-34 - 9.3597037379233665255e-894j)  +/-  (4.98e-80, 9.63e-200j)
| (3.0517766540485592055e-07 + 3.1170743716769693617e-879j)  +/-  (8.74e-66, 1.69e-185j)
| (7.1980817059731562387e-31 + 5.4695210967601180991e-892j)  +/-  (1.65e-78, 3.2e-198j)
| (2.2930947583459401992e-09 - 7.2333885989086205121e-881j)  +/-  (5.19e-67, 1e-186j)
| (0.060151897783525991139 - 1.2416603158335970545e-876j)  +/-  (2.97e-59, 5.75e-179j)
| (3.0517766540485592055e-07 - 9.8550210255419037998e-880j)  +/-  (9.06e-66, 1.75e-185j)
| (9.5211042217360222738e-05 + 2.2542861158910943396e-878j)  +/-  (3.3e-64, 6.39e-184j)
| (0.0016601732305123466943 - 2.109976261979839974e-877j)  +/-  (3.11e-64, 6.01e-184j)
| (0.0016601732305123466943 + 1.1210045049239637809e-877j)  +/-  (1.35e-63, 2.61e-183j)
| (0.097081625661326527959 + 1.5550587267243615131e-876j)  +/-  (1.24e-60, 2.4e-180j)
| (0.014074169000263592701 + 3.868154062969153451e-877j)  +/-  (1.18e-62, 2.29e-182j)
| (0.15621430025986745115 - 1.7983655690831482946e-876j)  +/-  (1.7e-61, 3.28e-181j)
| (1.047271224309206671e-22 - 8.3121406966497314837e-888j)  +/-  (2.87e-76, 5.54e-196j)
| (0.031634467854668653813 + 9.0841377949024263089e-877j)  +/-  (2.32e-62, 4.5e-182j)
| (0.13335507557389620027 - 1.783552300383007476e-876j)  +/-  (9.67e-62, 1.87e-181j)
| (1.2915449725274514144e-16 - 1.3684573459466168632e-883j)  +/-  (8.93e-74, 1.73e-193j)
| (0.13335507557389620027 + 1.5800551020080321583e-876j)  +/-  (5.21e-63, 1.01e-182j)
| (0.005276836322019410782 - 2.17817305362163237e-877j)  +/-  (2.18e-64, 4.23e-184j)
| (1.4001440644011869398e-10 - 7.8726357349683225415e-881j)  +/-  (2.7e-71, 5.24e-191j)
| (1.7160653373459270398e-05 + 2.2164229034083557284e-878j)  +/-  (4.91e-69, 9.55e-189j)
| (1.7128815162265936265e-20 + 1.1463010907306564383e-886j)  +/-  (2.99e-76, 5.68e-196j)
| (0.060151897783525991139 + 9.3381571643375226793e-877j)  +/-  (3.85e-66, 7.22e-186j)
| (2.9610406254223470104e-08 - 1.0116535344776679701e-879j)  +/-  (1.32e-70, 2.53e-190j)
| (0.097081625661326527959 - 1.2699275754953564951e-876j)  +/-  (1.62e-66, 2.84e-186j)
| (9.5211042217360222738e-05 - 5.1397049046625011392e-878j)  +/-  (9.19e-69, 1.83e-188j)
| (0.15621430025986745115 + 1.8723543332339020572e-876j)  +/-  (1.95e-66, 3.01e-186j)
