Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^28 - 582460197494267451069250148465566204469251543/1577781662339581922781949847515904637793237*t^27 + 4790248151984585283105014228234211455252042762437/37866759896149966146766796340381711307037688*t^26 - 253230341003917351285412471039156397152038994348953/9466689974037491536691699085095427826759422*t^25 + 74118062653850661865068987096972607295558372997368125/18933379948074983073383398170190855653518844*t^24 - 39122298416531636058236587859528544216548554119734000/92810686019975407222467638089170861046661*t^23 + 54692255334813040343069243863594121671543066889764856500/1577781662339581922781949847515904637793237*t^22 - 3519155661698046961833655942899471755397364177691911634000/1577781662339581922781949847515904637793237*t^21 + 180099767468826590711726750991558368163647186292800919159000/1577781662339581922781949847515904637793237*t^20 - 7412376269413562626202125529056175897475060330797405402400000/1577781662339581922781949847515904637793237*t^19 + 247131858393087272664623133227160017008313785165305038663730000/1577781662339581922781949847515904637793237*t^18 - 6703716007851751112933281510735751939689951413064528159169640000/1577781662339581922781949847515904637793237*t^17 + 8720044355122180130031950543364089887602649869401961907132020000/92810686019975407222467638089170861046661*t^16 - 157173730200865365776980991025024914648970283896611919200363520000/92810686019975407222467638089170861046661*t^15 + 2304390352682328291422213811139100284316903181682286105599008000000/92810686019975407222467638089170861046661*t^14 - 27373389070245811952754115605598840482334284096237757945361126400000/92810686019975407222467638089170861046661*t^13 + 261892420937090626653594370467652173868301075892155706146667763200000/92810686019975407222467638089170861046661*t^12 - 2001831008390657421704552041281244981226034532253223678105563443200000/92810686019975407222467638089170861046661*t^11 + 12096354324942010426467078117096289372259180519135860967036018803200000/92810686019975407222467638089170861046661*t^10 - 57006667697383654987447804880911632990528836676590954146012596480000000/92810686019975407222467638089170861046661*t^9 + 205942297551580995593972040888139386839818770005281692278981132928000000/92810686019975407222467638089170861046661*t^8 - 557833820407116064998215091535156574599868640202114628482326503424000000/92810686019975407222467638089170861046661*t^7 + 1100775223641609548411208024079860308846078253152130059701221218304000000/92810686019975407222467638089170861046661*t^6 - 1522788824931433801121876862893946333372811844047954121765676539904000000/92810686019975407222467638089170861046661*t^5 + 1400218964244904812530529961559779804503900549843263215647684710400000000/92810686019975407222467638089170861046661*t^4 - 791477777461203079635254782055434445393425283935814584113475878912000000/92810686019975407222467638089170861046661*t^3 + 242724970726505030629060867581054346308921239587043466740996775936000000/92810686019975407222467638089170861046661*t^2 - 32067857317752484097383026406893678976728439821194260722875006976000000/92810686019975407222467638089170861046661*t + 1032657541367545422247193481971142242102664719880284721574526976000000/92810686019975407222467638089170861046661
-------------------------------------------------
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:
| (93.121547750245850413 - 1.0293691885045029616e-508j)  +/-  (6.31e-245, 6.31e-245j)
| (71.652137254689509886 + 1.2250585714035036404e-509j)  +/-  (7.8e-243, 7.8e-243j)
| (81.032372530547808732 - 5.4952721078032273077e-516j)  +/-  (1.04e-243, 1.04e-243j)
| (63.76156378323055888 - 1.1739152582316545045e-520j)  +/-  (3.35e-242, 3.35e-242j)
| (56.885947351878742673 + 5.6320768610091746061e-529j)  +/-  (8.42e-242, 8.42e-242j)
| (9.1254764719441408497 - 2.515912885365740915e-540j)  +/-  (2e-244, 2e-244j)
| (24.368420857650516578 - 6.9903432438115145709e-544j)  +/-  (1.31e-241, 1.31e-241j)
| (31.629816838444178365 - 5.9654593760192736575e-562j)  +/-  (3.33e-241, 3.33e-241j)
| (1.0726127478327770112 + 3.2270924449193483347e-581j)  +/-  (1.38e-250, 1.38e-250j)
| (15.645110200183711202 - 2.3879393900576879213e-571j)  +/-  (9.42e-243, 9.42e-243j)
| (0.24093050813739411447 + 1.9772253975469843657e-583j)  +/-  (3.56e-253, 3.56e-253j)
| (18.290072590496002073 + 2.0144457486278427438e-579j)  +/-  (2.85e-242, 2.85e-242j)
| (40.305592012403100799 + 5.1665877472584973817e-601j)  +/-  (4.19e-241, 4.19e-241j)
| (11.073373270112372156 + 6.4151839017454507361e-618j)  +/-  (8.02e-244, 8.02e-244j)
| (5.8659669061640038235 + 2.710592217417013446e-625j)  +/-  (7.09e-246, 7.09e-246j)
| (1.6979829502946955816 - 5.2710912768201696309e-631j)  +/-  (1.97e-249, 1.97e-249j)
| (0.046004830920198220646 + 1.7813772049143575109e-629j)  +/-  (9.31e-255, 9.31e-255j)
| (3.4142135623730950488 + 2.911836885395276443e-630j)  +/-  (1.51e-247, 1.51e-247j)
| (27.839194289031923686 + 1.0039405686694459257e-655j)  +/-  (2.3e-241, 2.3e-241j)
| (35.771868939845068345 + 7.3152386661378431464e-697j)  +/-  (4.02e-241, 4.02e-241j)
| (7.3918360494882523468 + 2.0336934262956932923e-717j)  +/-  (3.72e-245, 3.72e-245j)
| (2.471877304683657441 - 1.8056844246936239244e-726j)  +/-  (1.81e-248, 1.81e-248j)
| (13.243396428176311981 - 2.3992297926068000311e-720j)  +/-  (3.25e-243, 3.25e-243j)
| (50.776904951797646682 + 6.9657650649865579613e-730j)  +/-  (1.76e-241, 1.76e-241j)
| (21.192223421839184255 - 1.9292280491159243894e-740j)  +/-  (6.26e-242, 6.26e-242j)
| (45.283582149802121088 + 3.4120316050566402788e-744j)  +/-  (3.28e-241, 3.28e-241j)
| (0.5857864376269049512 + 2.6083052042439353043e-764j)  +/-  (7.74e-252, 7.74e-252j)
| (4.542197622113407594 - 2.9061938723754818366e-759j)  +/-  (1.16e-246, 1.16e-246j)
-------------------------------------------------
The weights are:
| (5.2188691740678325877e-40 + 9.2173506564586540388e-546j)  +/-  (2.86e-100, 1.3e-220j)
| (6.4947480623704741597e-31 - 4.0349311637090198234e-540j)  +/-  (1.4e-97, 6.37e-218j)
| (6.6895206179352350776e-35 - 8.0856222612097334859e-543j)  +/-  (5.82e-99, 2.64e-219j)
| (1.4920466174297188323e-27 + 5.1303158489332676949e-539j)  +/-  (7.13e-97, 3.23e-217j)
| (1.2737045598071956003e-24 - 8.4930143690295126686e-538j)  +/-  (3.14e-96, 1.43e-216j)
| (0.00020025142833874021097 + 6.617880103045506284e-528j)  +/-  (4.51e-81, 2.05e-201j)
| (8.6702088349323248451e-11 + 3.4031565845086894892e-531j)  +/-  (3.93e-90, 1.78e-210j)
| (7.2625539837097374227e-14 + 1.0144423327267273502e-532j)  +/-  (1.58e-92, 7.15e-213j)
| (0.19012658365960539242 - 2.3719265171588448179e-526j)  +/-  (1.07e-66, 4.84e-187j)
| (4.0460117362147437043e-07 - 2.4855872580219572039e-529j)  +/-  (3.21e-87, 1.46e-207j)
| (0.21307185240724888162 - 1.1325901965764874451e-526j)  +/-  (3.39e-68, 1.54e-188j)
| (3.1576257508436024975e-08 + 6.7029701511037760047e-530j)  +/-  (2.01e-88, 9.12e-209j)
| (1.4853001988417155138e-17 + 1.6323602186066030103e-534j)  +/-  (1.97e-95, 8.92e-216j)
| (3.1932900997888122158e-05 - 2.4589310583958407828e-528j)  +/-  (7.32e-86, 3.32e-206j)
| (0.0040357125585465961051 + 3.5441841530944787683e-527j)  +/-  (5.91e-83, 2.68e-203j)
| (0.12753751174599269302 + 2.3253383263074326543e-526j)  +/-  (9.01e-77, 4.09e-197j)
| (0.1125951650162228202 + 3.4940104626129664859e-527j)  +/-  (1.36e-74, 6.18e-195j)
| (0.033985960908985936569 + 1.2262809701438794762e-526j)  +/-  (2.02e-80, 9.15e-201j)
| (2.9445712042578706448e-12 - 6.3094179220621919593e-532j)  +/-  (2.79e-92, 1.27e-212j)
| (1.2618075159195741251e-15 - 1.3986313579973425447e-533j)  +/-  (1.5e-94, 6.79e-215j)
| (0.0010037509140088674429 - 1.6108887837752110991e-527j)  +/-  (9.14e-86, 4.15e-206j)
| (0.072155712313291567263 - 1.8493992391027974173e-526j)  +/-  (2.05e-82, 9.3e-203j)
| (4.0474807158467720889e-06 + 8.2452117978987684141e-529j)  +/-  (2.18e-88, 9.9e-209j)
| (5.1273046640322767565e-22 + 1.2779443769773101355e-536j)  +/-  (1.05e-98, 4.76e-219j)
| (1.8995409718745908655e-09 - 1.6073447393672363107e-530j)  +/-  (5.89e-92, 2.67e-212j)
| (1.125677638850524453e-19 - 1.5903923055731787974e-535j)  +/-  (1.51e-97, 6.85e-218j)
| (0.23220864634701021688 + 1.9123743127327136456e-526j)  +/-  (1.01e-86, 4.93e-207j)
| (0.013042434152341889739 - 7.0069552864677048856e-527j)  +/-  (1.02e-87, 4.59e-208j)
