Starting with polynomial:
P : -t+1
Extension levels are: 1 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 116255489609211944856574390901/165360645067102361392409425*t^26 - 37843517310003118671231821110226/165360645067102361392409425*t^25 + 303272326100771666507845817465950/6614425802684094455696377*t^24 - 41930209145018497548781410097922400/6614425802684094455696377*t^23 + 4252017712475437587741813778463138400/6614425802684094455696377*t^22 - 328137423324238729542352719064331008320/6614425802684094455696377*t^21 + 2819508760579129443061792139993719671360/944917971812013493670911*t^20 - 134289035562005516012120490420423013392000/944917971812013493670911*t^19 + 5118283394146077345942849550739863955664000/944917971812013493670911*t^18 - 157142733324283443407744861537561436122784000/944917971812013493670911*t^17 + 3900267406546329132109642174127519994883065600/944917971812013493670911*t^16 - 78335288268220752992143249156751873644495257600/944917971812013493670911*t^15 + 1271507397636689154795244591132788243429550080000/944917971812013493670911*t^14 - 16620964207296883109247522794505116817553551360000/944917971812013493670911*t^13 + 173966626617195996712007600128170166691918991360000/944917971812013493670911*t^12 - 1446033508489623993538437990944244155154611736576000/944917971812013493670911*t^11 + 9440614862844856824525042192289986707053897568256000/944917971812013493670911*t^10 - 47715964316823734907091646285492158583700816076800000/944917971812013493670911*t^9 + 183247870055013657048030405879959772230804120985600000/944917971812013493670911*t^8 - 521840160408892032059070665147554778861606820249600000/944917971812013493670911*t^7 + 1067003318830727510317036073451556002030827724472320000/944917971812013493670911*t^6 - 1499530249157520456812030064368974123720210148229120000/944917971812013493670911*t^5 + 1362016377718612140727076293872472597360644685824000000/944917971812013493670911*t^4 - 729405714380236146467963997359692359002446430208000000/944917971812013493670911*t^3 + 198288183701303111682435767569585075115206705152000000/944917971812013493670911*t^2 - 20613893880880186251754537859950907844543491604480000/944917971812013493670911*t + 397107901710195496241442875269383059053325844480000/944917971812013493670911
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (90.94488164263597951 + 7.3049992532181740051e-256j)  +/-  (1.69e-117, 1.69e-117j)
| (38.619380562062279505 - 7.4544256672557683413e-263j)  +/-  (7.29e-114, 7.29e-114j)
| (55.010312628175850601 + 4.3845491176100579306e-275j)  +/-  (2.12e-114, 2.12e-114j)
| (78.944145580865444072 + 1.9023316133936579632e-285j)  +/-  (2.72e-116, 2.72e-116j)
| (69.639877155011308926 - 7.6358412880913259295e-300j)  +/-  (1.96e-115, 1.96e-115j)
| (12.04670021508462752 + 1.9688686530724821367e-312j)  +/-  (2.75e-116, 2.75e-116j)
| (61.819343008890834088 - 7.6640845406966168538e-310j)  +/-  (7.55e-115, 7.55e-115j)
| (22.926840051174164958 - 9.5363911271746848878e-313j)  +/-  (1.94e-114, 1.94e-114j)
| (9.9378079192895613953 - 1.699355886555133563e-320j)  +/-  (6.43e-117, 6.43e-117j)
| (14.387109351734218368 - 5.8835013680400137489e-318j)  +/-  (1.04e-115, 1.04e-115j)
| (4.9091542108808992858 - 2.5931469927909699665e-322j)  +/-  (3.33e-119, 3.33e-119j)
| (8.0505677888085656799 + 7.7464149137820101892e-321j)  +/-  (1.38e-117, 1.38e-117j)
| (16.9707748872557747 - 8.9845160302798590791e-317j)  +/-  (3.28e-115, 3.28e-115j)
| (2.5708250348476547815 + 1.1660764203997275012e-325j)  +/-  (3.78e-121, 3.78e-121j)
| (34.147128225993258685 - 5.8884921192717803611e-317j)  +/-  (7.24e-114, 7.24e-114j)
| (6.3766768714988752034 + 2.0703307866454637072e-335j)  +/-  (2.49e-118, 2.49e-118j)
| (0.49465235039543040483 + 6.1384591995846875348e-343j)  +/-  (1.34e-124, 1.34e-124j)
| (26.33660975320435468 + 3.0849141101504960117e-331j)  +/-  (3.56e-114, 3.56e-114j)
| (48.965671030869153062 + 2.4551540819807303428e-344j)  +/-  (4.03e-114, 4.03e-114j)
| (43.535322798411574491 + 5.2482893826638492307e-356j)  +/-  (5.98e-114, 5.98e-114j)
| (3.6421550981017772859 + 2.8129241593194237686e-370j)  +/-  (3.84e-120, 3.84e-120j)
| (1 + 7.6868701707543859231e-374j)  +/-  (2.02e-123, 2.02e-123j)
| (0.17243083044195381296 - 4.1975204817721904584e-376j)  +/-  (4.75e-126, 4.75e-126j)
| (30.066223176256791055 + 6.7750459008517375455e-364j)  +/-  (5.25e-114, 5.25e-114j)
| (0.024569368064367755785 - 6.5709900609659848526e-384j)  +/-  (1.79e-127, 1.79e-127j)
| (19.811726012882552547 - 1.7565454647303226662e-368j)  +/-  (8.33e-115, 8.33e-115j)
| (1.6911808471587203235 - 5.3262124749382849906e-382j)  +/-  (2.7e-122, 2.7e-122j)
-------------------------------------------------
The weights are:
| (4.5694994260048621478e-39 + 8.5535209030558484483e-292j)  +/-  (2.33e-39, 3.62e-94j)
| (7.9148438271216632555e-17 + 2.9499564875656433166e-279j)  +/-  (2.5e-30, 3.88e-85j)
| (8.2268313704138490915e-24 + 1.1606553730346192258e-283j)  +/-  (3.14e-34, 4.87e-89j)
| (5.3571170782206103386e-34 - 3.8066285491780521952e-289j)  +/-  (2.33e-38, 3.62e-93j)
| (4.816932237076093534e-30 + 4.6927725130932221432e-287j)  +/-  (3.55e-37, 5.51e-92j)
| (1.3034582427833481023e-05 + 8.9999849651320809967e-275j)  +/-  (2.27e-23, 3.52e-78j)
| (1.0309270696329870669e-26 - 2.9028493553414083228e-285j)  +/-  (4.64e-36, 7.2e-91j)
| (3.5978353182285703014e-10 + 8.0132637960160138033e-277j)  +/-  (3.98e-29, 6.18e-84j)
| (9.6460055222831380902e-05 - 2.2674646763256694377e-274j)  +/-  (7.85e-23, 1.22e-77j)
| (1.3889169367740166262e-06 - 3.2225096197570058004e-275j)  +/-  (1.34e-25, 2.08e-80j)
| (0.010082097213447835374 + 1.9681324396805276596e-273j)  +/-  (8.96e-20, 1.39e-74j)
| (0.00056745539436410432135 + 5.1575592600574382031e-274j)  +/-  (2.62e-22, 4.07e-77j)
| (1.1550905457137508003e-07 + 1.0404552046243072552e-275j)  +/-  (2.34e-27, 3.63e-82j)
| (0.074552241821659917557 + 4.9856419828679314178e-273j)  +/-  (1.85e-18, 2.87e-73j)
| (6.3156777691717153381e-15 - 1.1783948078297714206e-278j)  +/-  (1.41e-33, 2.19e-88j)
| (0.0026695952855903251364 - 1.0598737422425291601e-273j)  +/-  (5.03e-23, 7.81e-78j)
| (0.25198679832601398899 - 8.3895227778704414127e-273j)  +/-  (1e-20, 1.56e-75j)
| (1.3008266663223535459e-11 - 1.9469075219860897677e-277j)  +/-  (1.02e-31, 1.58e-86j)
| (3.1023781137711194636e-21 - 3.5705880371928484946e-282j)  +/-  (4.35e-37, 6.75e-92j)
| (6.3892344929849167088e-19 + 1.078390832692542282e-280j)  +/-  (4.35e-36, 6.75e-91j)
| (0.030608037855898248709 - 3.3001668147625586528e-273j)  +/-  (4.09e-26, 6.35e-81j)
| (0.21994061986475136515 + 8.1044951810411666768e-273j)  +/-  (2.73e-25, 4.23e-80j)
| (0.19538255799305637301 + 6.8438111535556560494e-273j)  +/-  (2.36e-25, 3.67e-80j)
| (3.4150928223468116464e-13 + 4.5305180658775485075e-278j)  +/-  (1.84e-33, 2.86e-88j)
| (0.069435110553585823689 - 2.7558114999842242978e-273j)  +/-  (3.14e-26, 4.86e-81j)
| (7.4021202205094115209e-09 - 3.0322457650361596964e-276j)  +/-  (3.49e-31, 5.42e-86j)
| (0.14466447885273008406 - 6.7515056515918383252e-273j)  +/-  (1.34e-26, 2.07e-81j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^27 + 116255489609211944856574390901/165360645067102361392409425*t^26 - 37843517310003118671231821110226/165360645067102361392409425*t^25 + 303272326100771666507845817465950/6614425802684094455696377*t^24 - 41930209145018497548781410097922400/6614425802684094455696377*t^23 + 4252017712475437587741813778463138400/6614425802684094455696377*t^22 - 328137423324238729542352719064331008320/6614425802684094455696377*t^21 + 2819508760579129443061792139993719671360/944917971812013493670911*t^20 - 134289035562005516012120490420423013392000/944917971812013493670911*t^19 + 5118283394146077345942849550739863955664000/944917971812013493670911*t^18 - 157142733324283443407744861537561436122784000/944917971812013493670911*t^17 + 3900267406546329132109642174127519994883065600/944917971812013493670911*t^16 - 78335288268220752992143249156751873644495257600/944917971812013493670911*t^15 + 1271507397636689154795244591132788243429550080000/944917971812013493670911*t^14 - 16620964207296883109247522794505116817553551360000/944917971812013493670911*t^13 + 173966626617195996712007600128170166691918991360000/944917971812013493670911*t^12 - 1446033508489623993538437990944244155154611736576000/944917971812013493670911*t^11 + 9440614862844856824525042192289986707053897568256000/944917971812013493670911*t^10 - 47715964316823734907091646285492158583700816076800000/944917971812013493670911*t^9 + 183247870055013657048030405879959772230804120985600000/944917971812013493670911*t^8 - 521840160408892032059070665147554778861606820249600000/944917971812013493670911*t^7 + 1067003318830727510317036073451556002030827724472320000/944917971812013493670911*t^6 - 1499530249157520456812030064368974123720210148229120000/944917971812013493670911*t^5 + 1362016377718612140727076293872472597360644685824000000/944917971812013493670911*t^4 - 729405714380236146467963997359692359002446430208000000/944917971812013493670911*t^3 + 198288183701303111682435767569585075115206705152000000/944917971812013493670911*t^2 - 20613893880880186251754537859950907844543491604480000/944917971812013493670911*t + 397107901710195496241442875269383059053325844480000/944917971812013493670911
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (90.94488164263597951 + 7.3049992532181740051e-256j)  +/-  (1.69e-117, 1.69e-117j)
| (38.619380562062279505 - 7.4544256672557683413e-263j)  +/-  (7.29e-114, 7.29e-114j)
| (55.010312628175850601 + 4.3845491176100579306e-275j)  +/-  (2.12e-114, 2.12e-114j)
| (78.944145580865444072 + 1.9023316133936579632e-285j)  +/-  (2.72e-116, 2.72e-116j)
| (69.639877155011308926 - 7.6358412880913259295e-300j)  +/-  (1.96e-115, 1.96e-115j)
| (12.04670021508462752 + 1.9688686530724821367e-312j)  +/-  (2.75e-116, 2.75e-116j)
| (61.819343008890834088 - 7.6640845406966168538e-310j)  +/-  (7.55e-115, 7.55e-115j)
| (22.926840051174164958 - 9.5363911271746848878e-313j)  +/-  (1.94e-114, 1.94e-114j)
| (9.9378079192895613953 - 1.699355886555133563e-320j)  +/-  (6.43e-117, 6.43e-117j)
| (14.387109351734218368 - 5.8835013680400137489e-318j)  +/-  (1.04e-115, 1.04e-115j)
| (4.9091542108808992858 - 2.5931469927909699665e-322j)  +/-  (3.33e-119, 3.33e-119j)
| (8.0505677888085656799 + 7.7464149137820101892e-321j)  +/-  (1.38e-117, 1.38e-117j)
| (16.9707748872557747 - 8.9845160302798590791e-317j)  +/-  (3.28e-115, 3.28e-115j)
| (2.5708250348476547815 + 1.1660764203997275012e-325j)  +/-  (3.78e-121, 3.78e-121j)
| (34.147128225993258685 - 5.8884921192717803611e-317j)  +/-  (7.24e-114, 7.24e-114j)
| (6.3766768714988752034 + 2.0703307866454637072e-335j)  +/-  (2.49e-118, 2.49e-118j)
| (0.49465235039543040483 + 6.1384591995846875348e-343j)  +/-  (1.34e-124, 1.34e-124j)
| (26.33660975320435468 + 3.0849141101504960117e-331j)  +/-  (3.56e-114, 3.56e-114j)
| (48.965671030869153062 + 2.4551540819807303428e-344j)  +/-  (4.03e-114, 4.03e-114j)
| (43.535322798411574491 + 5.2482893826638492307e-356j)  +/-  (5.98e-114, 5.98e-114j)
| (3.6421550981017772859 + 2.8129241593194237686e-370j)  +/-  (3.84e-120, 3.84e-120j)
| (1 + 7.6868701707543859231e-374j)  +/-  (2.02e-123, 2.02e-123j)
| (0.17243083044195381296 - 4.1975204817721904584e-376j)  +/-  (4.75e-126, 4.75e-126j)
| (30.066223176256791055 + 6.7750459008517375455e-364j)  +/-  (5.25e-114, 5.25e-114j)
| (0.024569368064367755785 - 6.5709900609659848526e-384j)  +/-  (1.79e-127, 1.79e-127j)
| (19.811726012882552547 - 1.7565454647303226662e-368j)  +/-  (8.33e-115, 8.33e-115j)
| (1.6911808471587203235 - 5.3262124749382849906e-382j)  +/-  (2.7e-122, 2.7e-122j)
-------------------------------------------------
The weights are:
| (4.5694994260048621478e-39 + 8.5535209030558484483e-292j)  +/-  (2.33e-39, 3.62e-94j)
| (7.9148438271216632555e-17 + 2.9499564875656433166e-279j)  +/-  (2.5e-30, 3.88e-85j)
| (8.2268313704138490915e-24 + 1.1606553730346192258e-283j)  +/-  (3.14e-34, 4.87e-89j)
| (5.3571170782206103386e-34 - 3.8066285491780521952e-289j)  +/-  (2.33e-38, 3.62e-93j)
| (4.816932237076093534e-30 + 4.6927725130932221432e-287j)  +/-  (3.55e-37, 5.51e-92j)
| (1.3034582427833481023e-05 + 8.9999849651320809967e-275j)  +/-  (2.27e-23, 3.52e-78j)
| (1.0309270696329870669e-26 - 2.9028493553414083228e-285j)  +/-  (4.64e-36, 7.2e-91j)
| (3.5978353182285703014e-10 + 8.0132637960160138033e-277j)  +/-  (3.98e-29, 6.18e-84j)
| (9.6460055222831380902e-05 - 2.2674646763256694377e-274j)  +/-  (7.85e-23, 1.22e-77j)
| (1.3889169367740166262e-06 - 3.2225096197570058004e-275j)  +/-  (1.34e-25, 2.08e-80j)
| (0.010082097213447835374 + 1.9681324396805276596e-273j)  +/-  (8.96e-20, 1.39e-74j)
| (0.00056745539436410432135 + 5.1575592600574382031e-274j)  +/-  (2.62e-22, 4.07e-77j)
| (1.1550905457137508003e-07 + 1.0404552046243072552e-275j)  +/-  (2.34e-27, 3.63e-82j)
| (0.074552241821659917557 + 4.9856419828679314178e-273j)  +/-  (1.85e-18, 2.87e-73j)
| (6.3156777691717153381e-15 - 1.1783948078297714206e-278j)  +/-  (1.41e-33, 2.19e-88j)
| (0.0026695952855903251364 - 1.0598737422425291601e-273j)  +/-  (5.03e-23, 7.81e-78j)
| (0.25198679832601398899 - 8.3895227778704414127e-273j)  +/-  (1e-20, 1.56e-75j)
| (1.3008266663223535459e-11 - 1.9469075219860897677e-277j)  +/-  (1.02e-31, 1.58e-86j)
| (3.1023781137711194636e-21 - 3.5705880371928484946e-282j)  +/-  (4.35e-37, 6.75e-92j)
| (6.3892344929849167088e-19 + 1.078390832692542282e-280j)  +/-  (4.35e-36, 6.75e-91j)
| (0.030608037855898248709 - 3.3001668147625586528e-273j)  +/-  (4.09e-26, 6.35e-81j)
| (0.21994061986475136515 + 8.1044951810411666768e-273j)  +/-  (2.73e-25, 4.23e-80j)
| (0.19538255799305637301 + 6.8438111535556560494e-273j)  +/-  (2.36e-25, 3.67e-80j)
| (3.4150928223468116464e-13 + 4.5305180658775485075e-278j)  +/-  (1.84e-33, 2.86e-88j)
| (0.069435110553585823689 - 2.7558114999842242978e-273j)  +/-  (3.14e-26, 4.86e-81j)
| (7.4021202205094115209e-09 - 3.0322457650361596964e-276j)  +/-  (3.49e-31, 5.42e-86j)
| (0.14466447885273008406 - 6.7515056515918383252e-273j)  +/-  (1.34e-26, 2.07e-81j)
