Starting with polynomial:
P : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Extension levels are: 16 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 14209476191/13835649*t^41 + 98792931897166/235206033*t^39 - 67724098150786454/705618099*t^37 + 3304758489709544465/235206033*t^35 - 332883023606592313855/235206033*t^33 + 24054477667866677591560/235206033*t^31 - 426386128007909457908520/78402011*t^29 + 16944703642967175728362710/78402011*t^27 - 507440090041357104905323050/78402011*t^25 + 675543100708029451451053500/4611883*t^23 - 196060074777196411370683594500/78402011*t^21 + 2508946561255329365297626248750/78402011*t^19 - 23799914344439114631036768731250/78402011*t^17 + 9681426005297545461141994815000/4611883*t^15 - 47661682150715268731755444785000/4611883*t^13 + 161560763746224820795764841269375/4611883*t^11 - 359617302987958212288824978870625/4611883*t^9 + 490135166984052481165646117996250/4611883*t^7 - 366299179065911333304776407443750/4611883*t^5 + 123119907398763238284686924934375/4611883*t^3 - 11692695166596478222344146615625/4611883*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
Positive weights:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (7.2651694173601492161 - 2.0946821169376692764e-870j)  +/-  (6.36e-246, 6.36e-246j)
| (-10.483713163043523679 - 3.8003946636193809422e-872j)  +/-  (4.09e-248, 4.09e-248j)
| (9.4962148780762016637 - 1.4158470077018813878e-881j)  +/-  (3.82e-247, 3.82e-247j)
| (-7.9420960092619434231 - 3.630121468563893341e-879j)  +/-  (3.93e-246, 3.93e-246j)
| (4.0517145249498709017 - 2.6246499082129359803e-890j)  +/-  (1.87e-246, 1.87e-246j)
| (5.4722257059493430884 - 7.4847052636909916062e-889j)  +/-  (7.8e-246, 7.8e-246j)
| (-9.4962148780762016637 - 1.1975117116666757194e-888j)  +/-  (3.62e-247, 3.62e-247j)
| (8.6758112524650397447 + 5.7978477608272199723e-893j)  +/-  (1.51e-246, 1.51e-246j)
| (0.38676060450055734772 - 1.5888988702994540728e-900j)  +/-  (1.03e-253, 1.03e-253j)
| (6.6308781983931284802 - 1.0366816602446874058e-891j)  +/-  (8.95e-246, 8.95e-246j)
| (7.9420960092619434231 - 4.1883112890035957862e-892j)  +/-  (3.88e-246, 3.88e-246j)
| (10.483713163043523679 - 2.1967050987042043898e-894j)  +/-  (4.23e-248, 4.23e-248j)
| (-20.489732588040174751 - 2.4563673792430148162e-898j)  +/-  (2.29e-251, 2.29e-251j)
| (-4.4929553025200112427 - 4.0363792822258354348e-891j)  +/-  (3.9e-246, 3.9e-246j)
| (-4.0517145249498709017 + 2.8098166138281122244e-898j)  +/-  (1.83e-246, 1.83e-246j)
| (4.4929553025200112427 + 1.0736821643794347238e-907j)  +/-  (3.54e-246, 3.54e-246j)
| (-7.2651694173601492161 + 9.5945519624305555238e-909j)  +/-  (6.5e-246, 6.5e-246j)
| (-6.033043418536264161 + 3.8345021882773102667e-926j)  +/-  (8.95e-246, 8.95e-246j)
| (-5.4722257059493430884 - 3.8822506743232191852e-950j)  +/-  (7.65e-246, 7.65e-246j)
| (20.489732588040174751 - 8.3951148808718241382e-971j)  +/-  (2.86e-251, 2.86e-251j)
| (1.5416495369919389106 + 6.5468137299918678663e-968j)  +/-  (1.87e-250, 1.87e-250j)
| (3.6008736241715482882 - 1.1890810578747439503e-963j)  +/-  (6.24e-247, 6.24e-247j)
| (-2.3693530231419822035 - 4.334307483462421122e-964j)  +/-  (1.17e-248, 1.17e-248j)
| (-8.6758112524650397447 + 8.5169743038794531911e-970j)  +/-  (1.68e-246, 1.68e-246j)
| (-1.9519803457163334645 + 2.961629951439902726e-981j)  +/-  (1.52e-249, 1.52e-249j)
| (-6.6308781983931284802 - 1.3956155664965033273e-978j)  +/-  (8.6e-246, 8.6e-246j)
| (0.78304851505841161867 + 5.9610532821096020656e-990j)  +/-  (1.7e-252, 1.7e-252j)
| (6.033043418536264161 + 1.0500170521284040289e-983j)  +/-  (9.79e-246, 9.79e-246j)
| (-2.7602450476307016168 - 4.4746913784135865263e-985j)  +/-  (4.34e-248, 4.34e-248j)
| (-1.1638291005549647742 + 2.4889237665093414221e-989j)  +/-  (1.92e-251, 1.92e-251j)
| (4.956790020409534999 + 1.0987601180928944569e-984j)  +/-  (5.84e-246, 5.84e-246j)
| (2.3693530231419822035 - 1.8737681560659926601e-987j)  +/-  (9.58e-249, 9.58e-249j)
| (1.1638291005549647742 - 4.6297637588529585511e-990j)  +/-  (1.92e-251, 1.92e-251j)
| (3.1602088252937779973 - 5.862232070322750183e-988j)  +/-  (1.9e-247, 1.9e-247j)
| (-3.6008736241715482882 - 3.5885558948698685152e-984j)  +/-  (6.41e-247, 6.41e-247j)
| (-3.1602088252937779973 + 6.8397276472764391329e-988j)  +/-  (1.84e-247, 1.84e-247j)
| (1.9519803457163334645 - 1.7510551443045689429e-991j)  +/-  (1.4e-249, 1.4e-249j)
| (2.1229103339688667048e-1008 - 1.5267433075810781342e-1009j)  +/-  (9.15e-1007, 9.15e-1007j)
| (-1.5416495369919389106 - 6.1469346748804574502e-992j)  +/-  (1.74e-250, 1.74e-250j)
| (-4.956790020409534999 + 2.0325700005005604579e-994j)  +/-  (5.87e-246, 5.87e-246j)
| (-0.78304851505841161867 - 3.2318440272411605005e-1005j)  +/-  (1.87e-252, 1.87e-252j)
| (-0.38676060450055734772 + 2.1145874890214914923e-1006j)  +/-  (1.03e-253, 1.03e-253j)
| (2.7602450476307016168 + 1.5527351858641488362e-1002j)  +/-  (4.84e-248, 4.84e-248j)
-------------------------------------------------
The weights are:
| (9.0134181288993150632e-13 + 8.9767071798941768945e-882j)  +/-  (1.66e-83, 1.3e-206j)
| (6.1794876432061847577e-25 + 5.3615398232746107125e-891j)  +/-  (6.27e-91, 4.9e-214j)
| (9.2148214970493218842e-21 + 1.0727062569144165658e-887j)  +/-  (8.26e-89, 6.45e-212j)
| (5.6276416321561927653e-15 - 4.808346460212710127e-885j)  +/-  (2.29e-86, 1.79e-209j)
| (4.8375061978830251988e-05 + 5.20799991618238502e-877j)  +/-  (5.77e-75, 4.51e-198j)
| (6.7746851628926766637e-08 - 3.4309235454584404854e-879j)  +/-  (8.47e-80, 6.62e-203j)
| (9.2148214970493218842e-21 - 1.4278333371487709801e-888j)  +/-  (6.52e-90, 5.1e-213j)
| (1.3891914008439135864e-17 - 1.2992761232419455153e-885j)  +/-  (1.57e-87, 1.23e-210j)
| (0.14583822139078647823 - 2.6940404350664712429e-874j)  +/-  (2.91e-76, 2.27e-199j)
| (6.9588928722441967252e-11 - 5.5940605057187267157e-881j)  +/-  (2.24e-83, 1.75e-206j)
| (5.6276416321561927653e-15 + 1.0802043950965007166e-883j)  +/-  (4.08e-86, 3.19e-209j)
| (6.1794876432061847577e-25 - 2.9567351897941186426e-890j)  +/-  (3.36e-92, 2.62e-215j)
| (9.3144047178559449742e-51 - 3.605978046598785438e-905j)  +/-  (9.47e-108, 7.4e-231j)
| (7.3285400216085639096e-06 - 3.0465961948542300902e-878j)  +/-  (1.6e-83, 1.25e-206j)
| (4.8375061978830251988e-05 + 1.4788228415532469243e-877j)  +/-  (2.7e-82, 2.11e-205j)
| (7.3285400216085639096e-06 - 1.2921900051294403168e-877j)  +/-  (9.56e-82, 7.47e-205j)
| (9.0134181288993150632e-13 + 1.2993657656932052012e-883j)  +/-  (3.26e-90, 2.55e-213j)
| (2.8888656258934507779e-09 + 3.9161560010250198836e-881j)  +/-  (2.5e-88, 1.95e-211j)
| (6.7746851628926766637e-08 - 4.8294404440463379044e-880j)  +/-  (2.85e-87, 2.23e-210j)
| (9.3144047178559449742e-51 + 7.5680011589134506553e-905j)  +/-  (6.73e-111, 5.26e-234j)
| (0.047797536036386561922 + 1.2391811304050365457e-874j)  +/-  (2.13e-76, 1.66e-199j)
| (0.00027586372853494393916 - 1.8855207670462402803e-876j)  +/-  (2.27e-83, 1.77e-206j)
| (0.0097716559971146063693 + 1.8019610276691860302e-875j)  +/-  (2.68e-81, 2.09e-204j)
| (1.3891914008439135864e-17 + 1.149746844476780658e-886j)  +/-  (8e-94, 6.25e-217j)
| (0.025036582220223534051 - 3.8752873281405549168e-875j)  +/-  (1.97e-80, 1.54e-203j)
| (6.9588928722441967252e-11 - 2.5534313352999918532e-882j)  +/-  (7.21e-90, 5.64e-213j)
| (0.11528860466903793687 + 2.4002217946435302067e-874j)  +/-  (7.43e-79, 5.81e-202j)
| (2.8888656258934507779e-09 + 4.2266710864869160636e-880j)  +/-  (5.22e-89, 4.08e-212j)
| (0.0033947409163929450149 - 7.7036449681776338115e-876j)  +/-  (9.04e-84, 7.07e-207j)
| (0.075173440492336461678 - 1.3853344123450246066e-874j)  +/-  (1.65e-79, 1.29e-202j)
| (9.0119588811167431076e-07 + 2.4352369674555438828e-878j)  +/-  (3.36e-87, 2.63e-210j)
| (0.0097716559971146063693 + 3.5460965054700739642e-875j)  +/-  (2.42e-84, 1.89e-207j)
| (0.075173440492336461678 - 1.9138389594715175045e-874j)  +/-  (2.58e-81, 2.02e-204j)
| (0.0011427907490117847538 + 6.3933080654156223036e-876j)  +/-  (2.42e-85, 1.89e-208j)
| (0.00027586372853494393916 - 6.358435673687735152e-877j)  +/-  (5.19e-87, 4.07e-210j)
| (0.0011427907490117847538 + 2.5173446749614558803e-876j)  +/-  (2.68e-86, 2.1e-209j)
| (0.025036582220223534051 - 6.7227250797139280595e-875j)  +/-  (1.37e-84, 1.07e-207j)
| (0.15244777659214605955 + 2.7412457928096448546e-874j)  +/-  (1.83e-83, 1.44e-206j)
| (0.047797536036386561922 + 8.0533924709800581932e-875j)  +/-  (6.1e-85, 4.8e-208j)
| (9.0119588811167431076e-07 + 4.5994654268159952331e-879j)  +/-  (1.32e-89, 1.04e-212j)
| (0.11528860466903793687 + 1.9331642136227177947e-874j)  +/-  (6.94e-85, 5.48e-208j)
| (0.14583822139078647823 - 2.4217041774788642935e-874j)  +/-  (7.81e-85, 6.2e-208j)
| (0.0033947409163929450149 - 1.7143961936474632883e-875j)  +/-  (1.08e-86, 7.61e-210j)
