Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 11 16
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : t^19 - 150851/1347*t^17 + 6541430/1347*t^15 - 47540390/449*t^13 + 566981260/449*t^11 - 3753992440/449*t^9 + 13180991670/449*t^7 - 21510616050/449*t^5 + 12604959675/449*t^3 - 2144332575/449*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 9101116950133461321155189909073470255447675914700819/23954255306085836476638257585668576661430390905643*t^33 + 68272973868204218922109772864199329026599629226674362306/1077941488773862641448721591355085949764367590753935*t^31 - 3966781890657800747958972701665317778331027855639708855090/646764893264317584869232954813051569858620554452361*t^29 + 2739423957958235295500247810357674830763446358144195962287190/7114413825907493433561562502943567268444826098975971*t^27 - 982158040136997899952486851975725571842880822817727181557486094/59286781882562445279679687524529727237040217491466425*t^25 + 89548535061793731535453708166703062958197067086266689336967327978/177860345647687335839039062573589181711120652474399275*t^23 - 1953347487749901945473678619207643446282862780539700912352735812294/177860345647687335839039062573589181711120652474399275*t^21 + 564080657307073046463132556499773449326672708193270973935979958812196/3260773003540934490382382813849134998037211962030653375*t^19 - 19211251351722405721370634341676371544604805509211255041800524575192744/9782319010622803471147148441547404994111635886091960125*t^17 + 31137792484650029534354255486964203164384549059071956374788888412149114/1956463802124560694229429688309480998822327177218392025*t^15 - 58954018159267327795650682074706093747066360957763773342185825554947682/652154600708186898076476562769826999607442392406130675*t^13 + 227838594947030039203857253396312066258497560794998817911982431204859018/652154600708186898076476562769826999607442392406130675*t^11 - 52045368198128017751204007606714994720330327146811463361203170120982882/59286781882562445279679687524529727237040217491466425*t^9 + 8826021995393154993579646335443311487585380725245659282336103802712954/6587420209173605031075520836058858581893357499051825*t^7 - 1481479977215656284550835788706685244813978247026455613226419544315422/1317484041834721006215104167211771716378671499810365*t^5 + 591903346062803194698060510766556000505421165134737268073165954940887/1317484041834721006215104167211771716378671499810365*t^3 - 27618701003619992880560587497276815829811804402514926763499279692081/439161347278240335405034722403923905459557166603455*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:
| (4.1445471861258943321 - 4.0346180265596746829e-595j)  +/-  (2.05e-247, 2.05e-247j)
| (1.6365190424351079992 - 7.3848393342310134894e-606j)  +/-  (9.28e-251, 9.28e-251j)
| (-7.1030660791312936195 - 7.4853113797196898015e-625j)  +/-  (6.83e-248, 6.83e-248j)
| (7.1030660791312936195 + 5.4830175839055051237e-679j)  +/-  (7.07e-248, 7.07e-248j)
| (5.1580652270647994111 + 5.5944137957578062722e-721j)  +/-  (4.33e-247, 4.33e-247j)
| (5.6717717998812343708 + 4.8646102317632908687e-740j)  +/-  (3.62e-247, 3.62e-247j)
| (2.6377551349274913907 - 4.1551662788001451794e-750j)  +/-  (3.9e-248, 3.9e-248j)
| (9.0027825181482443432 - 2.9935774936572980152e-750j)  +/-  (2.04e-249, 2.04e-249j)
| (-5.1580652270647994111 - 9.8784377914982529174e-749j)  +/-  (4.55e-247, 4.55e-247j)
| (-7.9643403554778095104 + 5.0621314418617533241e-756j)  +/-  (1.62e-248, 1.62e-248j)
| (-9.0027825181482443432 + 9.7908579076798300394e-758j)  +/-  (2.19e-249, 2.19e-249j)
| (-3.0950955154405111371 - 1.7540729117047689031e-754j)  +/-  (1e-247, 1e-247j)
| (6.3410934275277093073 + 7.9445219469553632758e-755j)  +/-  (1.74e-247, 1.74e-247j)
| (3.0950955154405111371 + 8.4840473944554704333e-763j)  +/-  (9.46e-248, 9.46e-248j)
| (-6.3410934275277093073 - 2.2730817065956856271e-760j)  +/-  (1.68e-247, 1.68e-247j)
| (-2.6377551349274913907 - 3.1223559830298275779e-762j)  +/-  (3.84e-248, 3.84e-248j)
| (-3.5734098382559950693 + 7.4859378506692051145e-760j)  +/-  (1.1e-247, 1.1e-247j)
| (7.9643403554778095104 + 1.546364502280908167e-762j)  +/-  (1.59e-248, 1.59e-248j)
| (-2.8024858612875416991 - 1.1622046960939132848e-761j)  +/-  (8.84e-248, 8.84e-248j)
| (-1.6365190424351079992 + 1.3801885755387683752e-764j)  +/-  (7.97e-251, 7.97e-251j)
| (3.5734098382559950693 - 2.5405170075997513164e-761j)  +/-  (1.21e-247, 1.21e-247j)
| (2.8024858612875416991 + 9.9333438986079830293e-765j)  +/-  (8.46e-248, 8.46e-248j)
| (-2.1820439883586330339 - 1.2938304360486955805e-765j)  +/-  (1.77e-249, 1.77e-249j)
| (-4.7053933880834975273 - 6.3446169071916556602e-763j)  +/-  (3.8e-247, 3.8e-247j)
| (4.7053933880834975273 + 6.7633850674006466008e-769j)  +/-  (3.86e-247, 3.86e-247j)
| (1.0827625511336051722 - 1.1542239876935232935e-781j)  +/-  (9.02e-252, 9.02e-252j)
| (-4.1445471861258943321 + 1.7802030404757852136e-778j)  +/-  (1.87e-247, 1.87e-247j)
| (-1.0827625511336051722 + 3.0995285778791858809e-783j)  +/-  (7.69e-252, 7.69e-252j)
| (0.79867251029900488539 - 3.5845913364995572465e-784j)  +/-  (2.18e-252, 2.18e-252j)
| (-0.53907981135137510807 - 1.7565855740986375117e-785j)  +/-  (3.01e-253, 3.01e-253j)
| (-0.79867251029900488539 - 6.4136094767509853828e-784j)  +/-  (1.91e-252, 1.91e-252j)
| (2.1820439883586330339 - 4.7590672200769186057e-784j)  +/-  (1.86e-249, 1.86e-249j)
| (0.53907981135137510807 + 5.5503811257273025285e-789j)  +/-  (2.93e-253, 2.93e-253j)
| (-5.6717717998812343708 - 3.1294167337616164682e-787j)  +/-  (3.36e-247, 3.36e-247j)
| (-2.7440315296586137888e-839 - 2.1106058426354496388e-838j)  +/-  (7.45e-837, 7.45e-837j)
-------------------------------------------------
The weights are:
| (4.3269700334782130937e-05 + 6.5688798147718103065e-599j)  +/-  (4.23e-86, 5.86e-209j)
| (0.05793489399677642445 + 4.5445902898339053869e-597j)  +/-  (5.02e-73, 6.95e-196j)
| (3.5591212129905138926e-12 - 1.6812731930799035179e-606j)  +/-  (3.85e-95, 5.33e-218j)
| (3.5591212129905138926e-12 + 6.3918167679056135168e-606j)  +/-  (1.24e-94, 1.71e-217j)
| (2.8690865601732511378e-07 - 3.7769102786403039864e-601j)  +/-  (5.19e-90, 7.19e-213j)
| (2.503400069292366569e-08 + 1.9586233577511172834e-602j)  +/-  (1.98e-91, 2.74e-214j)
| (0.0039345339652577013822 + 8.0171563556053600041e-597j)  +/-  (6.92e-83, 9.59e-206j)
| (1.1997833129747585414e-18 + 1.7166134517807992522e-610j)  +/-  (2.84e-99, 3.93e-222j)
| (2.8690865601732511378e-07 + 4.1149373278596666933e-602j)  +/-  (3.65e-94, 5.06e-217j)
| (6.22891555692574154e-15 + 1.8109379595224228108e-608j)  +/-  (7.77e-100, 1.08e-222j)
| (1.1997833129747585414e-18 - 6.3432744980416047988e-611j)  +/-  (5.77e-102, 7.99e-225j)
| (0.0012979820625351371588 + 2.9758397111447797394e-598j)  +/-  (3.31e-90, 4.59e-213j)
| (5.3287945803580580395e-10 - 4.2214147455928046776e-604j)  +/-  (1.42e-95, 1.97e-218j)
| (0.0012979820625351371588 + 2.0528831241872697488e-597j)  +/-  (2.21e-88, 3.07e-211j)
| (5.3287945803580580395e-10 + 8.8430769609355700217e-605j)  +/-  (2.01e-97, 2.78e-220j)
| (0.0039345339652577013822 + 1.7811337359209048954e-597j)  +/-  (1.36e-89, 1.88e-212j)
| (0.00036705516944793029382 - 2.4209337707776661016e-599j)  +/-  (1.31e-92, 1.81e-215j)
| (6.22891555692574154e-15 - 5.7407412192052064612e-608j)  +/-  (8.99e-101, 1.25e-223j)
| (0.0012272737272695666662 - 1.4837623888006109955e-597j)  +/-  (4.3e-90, 5.95e-213j)
| (0.05793489399677642445 + 1.9716017594443534792e-597j)  +/-  (2.8e-88, 3.88e-211j)
| (0.00036705516944793029382 - 3.2714832728374206517e-598j)  +/-  (2.02e-92, 2.79e-215j)
| (0.0012272737272695666662 - 7.6805330409902163832e-597j)  +/-  (2.23e-90, 3.08e-213j)
| (0.019454218867366154876 - 1.200322211071734648e-597j)  +/-  (2.31e-90, 3.2e-213j)
| (3.2008540927802801453e-06 - 2.6529748495432718182e-601j)  +/-  (2.25e-96, 3.11e-219j)
| (3.2008540927802801453e-06 + 4.1862937968217063889e-600j)  +/-  (1.32e-95, 1.83e-218j)
| (0.1225783322098984755 - 1.4025079333946199864e-596j)  +/-  (2.11e-90, 2.92e-213j)
| (4.3269700334782130937e-05 + 2.1061011630938658816e-600j)  +/-  (2.71e-95, 3.75e-218j)
| (0.1225783322098984755 - 8.2148896013044594906e-597j)  +/-  (2.67e-91, 3.7e-214j)
| (-0.0014745277943370985579 + 2.559620337889639731e-596j)  +/-  (1.52e-90, 2.1e-213j)
| (0.18749035811676949962 - 1.4883687319645279289e-596j)  +/-  (4.89e-91, 6.75e-214j)
| (-0.0014745277943370985579 + 1.7325082423180775431e-596j)  +/-  (5.05e-91, 6.99e-214j)
| (0.019454218867366154876 - 3.8695212900779433177e-597j)  +/-  (7.45e-93, 1.05e-215j)
| (0.18749035811676949962 - 1.9334425334974430769e-596j)  +/-  (1.47e-91, 2.04e-214j)
| (2.503400069292366569e-08 - 3.0472296238599264754e-603j)  +/-  (7.41e-99, 1.03e-221j)
| (0.21428619329097425318 + 9.3859475836862528688e-597j)  +/-  (6.68e-92, 8.94e-215j)
