Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^52 - 8049204161305181715573889735897/6273462048095725401053992272*t^50 + 4765126058686701823976988752962225/6273462048095725401053992272*t^48 - 144136923148651368544502394670876175/522788504007977116754499356*t^46 + 35957598208624648183886552927537181375/522788504007977116754499356*t^44 - 13100120041879529600004569290939981694175/1045577008015954233508998712*t^42 + 1807222486251823148956998007913334782693175/1045577008015954233508998712*t^40 - 7433904627831144858485744239614780824023875/40214500308305932058038412*t^38 + 625895841286842455102028693203507898268641375/40214500308305932058038412*t^36 - 167590447752846455614094331178242740855331725625/160858001233223728232153648*t^34 + 527769197819744178538748073256360791644964758625/9462235366660219307773744*t^32 - 2832215901765081210923732811338206671361341727875/1182779420832527413471718*t^30 + 97502809959797929495076420218049903744419248451875/1182779420832527413471718*t^28 - 5369797836257109139322357667305223125608025662063125/2365558841665054826943436*t^26 + 117683248951924290935899152973375132205406634614328125/2365558841665054826943436*t^24 - 1018536385686210072750983741478486922181768024791584375/1182779420832527413471718*t^22 + 13778960594649971907123850541502757942815415473208865625/1182779420832527413471718*t^20 - 1149191719050119679478598084671940508169409631441390140625/9462235366660219307773744*t^18 + 9064249171918055901722041027880892602340247974864894515625/9462235366660219307773744*t^16 - 13200582208279096622962102635868880345116601182859957109375/2365558841665054826943436*t^14 + 55005823781296903975004681338736187971116657681443604359375/2365558841665054826943436*t^12 - 313965133522378915126199858586833528052274617022639110046875/4731117683330109653886872*t^10 + 577185084624226277006471700383165392793000172175352614921875/4731117683330109653886872*t^8 - 311754897251827411277629755980878970924021931493586109609375/2365558841665054826943436*t^6 + 170112339370785136975009917656416227266386044517663707421875/2365558841665054826943436*t^4 - 139562753240811016225441188311791773797048046577762652484375/9462235366660219307773744*t^2 + 4454525410987242344418186756670152669937134246868005609375/9462235366660219307773744
-------------------------------------------------
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:   52 out of 52
Indefinite weights: 0 out of 52
Negative weights:   0 out of 52
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.4046941039461923576 + 7.4413829924859465148e-846j)  +/-  (1.22e-242, 1.22e-242j)
| (9.5224280074221559268 + 2.864609188736118531e-844j)  +/-  (7.5e-243, 7.5e-243j)
| (13.143101163008269317 + 4.65535433978971489e-850j)  +/-  (4.02e-246, 4.02e-246j)
| (5.8865768457685079284 - 3.4849856426295993647e-845j)  +/-  (1.64e-243, 1.64e-243j)
| (-11.444656977841240831 + 1.3782616208636296401e-847j)  +/-  (4.41e-244, 4.41e-244j)
| (12.214575638843434256 - 1.0183757859846705241e-846j)  +/-  (6.68e-245, 6.68e-245j)
| (8.9523856801823102257 - 9.1449197470968490041e-845j)  +/-  (1.15e-242, 1.15e-242j)
| (10.756495784028109178 + 1.8448304906484315261e-846j)  +/-  (1.62e-243, 1.62e-243j)
| (-6.3680781654945357903 - 1.6257929087854337282e-844j)  +/-  (3.36e-243, 3.36e-243j)
| (-12.214575638843434256 - 1.0082333957753597647e-850j)  +/-  (6.66e-245, 6.66e-245j)
| (6.3680781654945357903 + 1.6171163235527520243e-847j)  +/-  (3.42e-243, 3.42e-243j)
| (4.487329569846450516 - 2.2707637366941151667e-850j)  +/-  (5.61e-245, 5.61e-245j)
| (-13.143101163008269317 + 1.9577019096823356474e-852j)  +/-  (3.91e-246, 3.91e-246j)
| (7.8751627994850059135 - 2.286187798673504881e-848j)  +/-  (1.23e-242, 1.23e-242j)
| (-5.4132484115748101637 - 6.1273027156244549869e-849j)  +/-  (6.11e-244, 6.11e-244j)
| (-9.5224280074221559268 - 2.5655832279754844095e-850j)  +/-  (7.95e-243, 7.95e-243j)
| (-5.8865768457685079284 - 9.1409853912249862328e-857j)  +/-  (1.46e-243, 1.46e-243j)
| (11.444656977841240831 - 6.7868558856079692821e-862j)  +/-  (4.43e-244, 4.43e-244j)
| (-10.120782381952224287 - 1.9012572863682179016e-865j)  +/-  (3.9e-243, 3.9e-243j)
| (-8.4046941039461923576 - 1.1647040942751289755e-881j)  +/-  (1.34e-242, 1.34e-242j)
| (10.120782381952224287 - 1.749462983385446133e-893j)  +/-  (4.02e-243, 4.02e-243j)
| (-3.1404750754219926319 + 3.6163172836867484017e-902j)  +/-  (4.36e-247, 4.36e-247j)
| (3.1404750754219926319 + 2.0298735964689268372e-902j)  +/-  (3.98e-247, 3.98e-247j)
| (-10.756495784028109178 - 1.8414573387004804872e-896j)  +/-  (1.64e-243, 1.64e-243j)
| (-1.837798991471934587 - 1.6453201607467677058e-908j)  +/-  (9.48e-250, 9.48e-250j)
| (-4.0332748147484011393 + 1.3686933121598691767e-904j)  +/-  (1.2e-245, 1.2e-245j)
| (5.4132484115748101637 - 4.4416653743430463023e-901j)  +/-  (5.9e-244, 5.9e-244j)
| (6.858959322337464273 + 7.6822889505635827253e-906j)  +/-  (5.94e-243, 5.94e-243j)
| (-2.266861140298062893 + 1.0991927235756555946e-924j)  +/-  (8.14e-249, 8.14e-249j)
| (-7.3607038932966957716 - 1.5725511074129457453e-920j)  +/-  (9.79e-243, 9.79e-243j)
| (-7.8751627994850059135 - 2.0168475680342737641e-942j)  +/-  (1.23e-242, 1.23e-242j)
| (4.947102965163371988 - 1.4763863284150541152e-955j)  +/-  (1.77e-244, 1.77e-244j)
| (1.837798991471934587 + 1.1425169020305969889e-960j)  +/-  (9.76e-250, 9.76e-250j)
| (3.58443663262965583 + 4.6672147974463578997e-957j)  +/-  (2.41e-246, 2.41e-246j)
| (-3.58443663262965583 - 5.1756825149062821364e-957j)  +/-  (2.56e-246, 2.56e-246j)
| (-8.9523856801823102257 - 3.5099669426806506034e-954j)  +/-  (1.13e-242, 1.13e-242j)
| (7.3607038932966957716 + 7.7629637632905085772e-962j)  +/-  (8.94e-243, 8.94e-243j)
| (0.19680049128200309877 + 6.4884376244433758608e-974j)  +/-  (2.87e-254, 2.87e-254j)
| (2.701245236017604357 - 2.9838620667609550896e-968j)  +/-  (6.14e-248, 6.14e-248j)
| (-1.415023264676833242 + 2.2201884125532663875e-972j)  +/-  (8.06e-251, 8.06e-251j)
| (-0.59412192214635693336 + 3.2899532320341038274e-974j)  +/-  (4.61e-253, 4.61e-253j)
| (-2.701245236017604357 + 3.8127996798945739333e-968j)  +/-  (5.9e-248, 5.9e-248j)
| (4.0332748147484011393 + 6.6859985539317060452e-966j)  +/-  (1.31e-245, 1.31e-245j)
| (2.266861140298062893 - 9.6814280512720113708e-971j)  +/-  (8.46e-249, 8.46e-249j)
| (-0.19680049128200309877 + 4.7605449597440778693e-974j)  +/-  (3.33e-254, 3.33e-254j)
| (-6.858959322337464273 + 1.5661631138715135733e-964j)  +/-  (6.02e-243, 6.02e-243j)
| (-4.487329569846450516 - 3.2094510259113629446e-969j)  +/-  (5.13e-245, 5.13e-245j)
| (1.415023264676833242 + 5.0604078205254889902e-977j)  +/-  (7.98e-251, 7.98e-251j)
| (0.59412192214635693336 + 1.0638379659073407817e-979j)  +/-  (4.61e-253, 4.61e-253j)
| (-4.947102965163371988 - 2.43777565282604228e-976j)  +/-  (1.87e-244, 1.87e-244j)
| (-1 - 3.2797144894960641759e-983j)  +/-  (6.79e-252, 6.79e-252j)
| (1 + 9.535440877029954366e-984j)  +/-  (6.18e-252, 6.18e-252j)
-------------------------------------------------
The weights are:
| (9.832650185311170121e-17 + 8.795713639628473757e-858j)  +/-  (7.7e-64, 7.03e-185j)
| (4.7468260301534046879e-21 + 3.9598045440607715791e-860j)  +/-  (8.87e-67, 8.09e-188j)
| (1.3206966388825494374e-38 - 2.7238621008233521161e-869j)  +/-  (8.56e-75, 7.81e-196j)
| (5.6898517501397425297e-09 + 5.9745007694566224757e-853j)  +/-  (2.29e-58, 2.09e-179j)
| (1.0412787821401903482e-29 - 1.2722893545064084807e-864j)  +/-  (4.88e-75, 4.45e-196j)
| (1.3233546445215437649e-33 + 1.0360773669243401223e-866j)  +/-  (3.42e-73, 3.12e-194j)
| (8.795739386516851203e-19 - 6.6088586952081925719e-859j)  +/-  (2.81e-66, 2.57e-187j)
| (1.9731549049855903664e-26 + 5.6188763733363930788e-863j)  +/-  (1.57e-70, 1.43e-191j)
| (3.0316077853383064311e-10 - 1.6086739863962939157e-853j)  +/-  (1.54e-65, 1.41e-186j)
| (1.3233546445215437649e-33 + 1.1920096587783939763e-866j)  +/-  (4.51e-78, 4.12e-199j)
| (3.0316077853383064311e-10 + 9.1873791904975098772e-854j)  +/-  (2.31e-62, 2.11e-183j)
| (7.7294513862677136431e-06 - 5.7318739802394594457e-852j)  +/-  (8.83e-58, 8.06e-179j)
| (1.3206966388825494374e-38 - 3.0896641460245571531e-869j)  +/-  (3.4e-80, 3.1e-201j)
| (7.0978663130471015862e-15 - 9.7859551893595119237e-857j)  +/-  (1.04e-65, 9.47e-187j)
| (8.1190497935201022392e-08 - 9.1575678151646095223e-853j)  +/-  (8.19e-65, 7.47e-186j)
| (4.7468260301534046879e-21 + 4.9212843219147605555e-860j)  +/-  (9.93e-75, 9.06e-196j)
| (5.6898517501397425297e-09 + 4.6098372558359129168e-853j)  +/-  (1.93e-66, 1.76e-187j)
| (1.0412787821401903482e-29 - 1.0894602193757059799e-864j)  +/-  (3.46e-75, 3.16e-196j)
| (1.404296801423295829e-23 - 2.165344574073870776e-861j)  +/-  (7.31e-76, 6.67e-197j)
| (9.832650185311170121e-17 + 1.183137353900759252e-857j)  +/-  (1.44e-73, 1.32e-194j)
| (1.404296801423295829e-23 - 1.786737253969662679e-861j)  +/-  (2.28e-73, 2.08e-194j)
| (0.0012714428050223593251 + 4.1398963565239371469e-851j)  +/-  (8.46e-62, 7.72e-183j)
| (0.0012714428050223593251 + 4.0259143001864678741e-851j)  +/-  (2.35e-61, 2.15e-182j)
| (1.9731549049855903664e-26 + 6.6739163845441532282e-863j)  +/-  (4.27e-77, 3.9e-198j)
| (0.031407389126915366477 - 1.5814429730934120393e-850j)  +/-  (1.4e-56, 1.28e-177j)
| (5.2850318571938121258e-05 + 1.078573053600762724e-851j)  +/-  (4.88e-65, 4.45e-186j)
| (8.1190497935201022392e-08 - 1.6347671653661857376e-852j)  +/-  (4.57e-67, 4.17e-188j)
| (1.2041026389943619913e-11 - 8.8103189421393336039e-855j)  +/-  (2.89e-69, 2.64e-190j)
| (0.013194299507443541572 + 1.1174894530428026504e-850j)  +/-  (2.66e-60, 2.43e-181j)
| (3.4796576414310975406e-13 + 1.5576851318970392441e-855j)  +/-  (7.79e-73, 7.11e-194j)
| (7.0978663130471015862e-15 - 1.410697858980335042e-856j)  +/-  (1.28e-73, 1.17e-194j)
| (8.9518905820260330513e-07 + 2.8227412860167101275e-852j)  +/-  (4.31e-68, 3.93e-189j)
| (0.031407389126915366477 - 1.3167722434028383464e-850j)  +/-  (6.63e-63, 6.05e-184j)
| (0.0002888319162188930527 - 2.2450102635726860305e-851j)  +/-  (8.41e-67, 7.68e-188j)
| (0.0002888319162188930527 - 2.2013768499362782122e-851j)  +/-  (1.37e-67, 1.25e-188j)
| (8.795739386516851203e-19 - 8.4922896861074749521e-859j)  +/-  (4.1e-76, 3.74e-197j)
| (3.4796576414310975406e-13 + 9.5553464075484400526e-856j)  +/-  (3.46e-72, 3.16e-193j)
| (0.15427774570617988208 + 4.9243853717311099727e-852j)  +/-  (1.15e-63, 1.05e-184j)
| (0.0045371228635318689104 - 6.6234931043699915189e-851j)  +/-  (1.71e-66, 1.56e-187j)
| (0.06144871206794869826 + 1.9903294364347747819e-850j)  +/-  (3.81e-64, 3.48e-185j)
| (0.13415777878602286334 + 1.894599962817692328e-850j)  +/-  (6.5e-64, 5.94e-185j)
| (0.0045371228635318689104 - 7.1288782005725748631e-851j)  +/-  (8.59e-67, 7.84e-188j)
| (5.2850318571938121258e-05 + 1.1634569433156061338e-851j)  +/-  (3.02e-68, 2.75e-189j)
| (0.013194299507443541572 + 9.8829309953164158184e-851j)  +/-  (1.33e-66, 1.22e-187j)
| (0.15427774570617988208 - 1.119697803045126686e-850j)  +/-  (3.74e-65, 3.4e-186j)
| (1.2041026389943619913e-11 - 1.9252118227501398945e-854j)  +/-  (1.12e-73, 1.03e-194j)
| (7.7294513862677136431e-06 - 4.917247353550059505e-852j)  +/-  (3.64e-71, 3.28e-192j)
| (0.06144871206794869826 + 1.5228351841281476546e-850j)  +/-  (5e-68, 3.93e-189j)
| (0.13415777878602286334 + 9.021197718815141302e-851j)  +/-  (7.39e-68, 5.87e-189j)
| (8.9518905820260330513e-07 + 2.1278274632297103266e-852j)  +/-  (8.29e-72, 7.67e-193j)
| (0.099355115065793465444 - 2.1610541025900371115e-850j)  +/-  (3.83e-68, 3.86e-189j)
| (0.099355115065793465444 - 1.4339978101358524621e-850j)  +/-  (2.74e-68, 1.98e-189j)
