Starting with polynomial:
P : 65536*t^16 - 3932160*t^14 + 89456640*t^12 - 984023040*t^10 + 5535129600*t^8 - 15498362880*t^6 + 19372953600*t^4 - 8302694400*t^2 + 518918400
Extension levels are: 16 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 65536*t^16 - 3932160*t^14 + 89456640*t^12 - 984023040*t^10 + 5535129600*t^8 - 15498362880*t^6 + 19372953600*t^4 - 8302694400*t^2 + 518918400
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 65536*t^43 - 465616115826688/13835649*t^41 + 1618623396203167744/235206033*t^39 - 554795812051242631168/705618099*t^37 + 13536290773850294128640/235206033*t^35 - 681744432346301058775040/235206033*t^33 + 24631785131895477853757440/235206033*t^31 - 218309697540049642449162240/78402011*t^29 + 4337844132599596986460853760/78402011*t^27 - 64952331525293709427881350400/78402011*t^25 + 43234758445313884892867424000/4611883*t^23 - 6273922392870285163861875024000/78402011*t^21 + 40143144980085269844762019980000/78402011*t^19 - 190399314755512917048294149850000/78402011*t^17 + 38725704021190181844567979260000/4611883*t^15 - 95323364301430537463510889570000/4611883*t^13 + 161560763746224820795764841269375/4611883*t^11 - 359617302987958212288824978870625/9223766*t^9 + 245067583492026240582823058998125/9223766*t^7 - 183149589532955666652388203721875/18447532*t^5 + 123119907398763238284686924934375/73790128*t^3 - 11692695166596478222344146615625/147580256*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:
| (-7.4131046696027449289 - 6.5239838683107568961e-929j)  +/-  (2.9e-248, 2.9e-248j)
| (-2.234605090330803872 + 2.069609447519190802e-930j)  +/-  (1.25e-247, 1.25e-247j)
| (-5.1372505614844799991 + 5.0896435963809401257e-936j)  +/-  (4.78e-246, 4.78e-246j)
| (7.4131046696027449289 + 2.6683043897431248048e-950j)  +/-  (2.78e-248, 2.78e-248j)
| (-6.1347249689125836803 - 1.1596398895696728851e-945j)  +/-  (1.19e-246, 1.19e-246j)
| (-6.7148379358922658078 - 3.3600820646825278639e-951j)  +/-  (2.55e-247, 2.55e-247j)
| (14.488428857702195957 - 1.4878504334922802603e-963j)  +/-  (1.88e-251, 1.88e-251j)
| (6.7148379358922658078 - 2.8719830378228407407e-958j)  +/-  (2.67e-247, 2.67e-247j)
| (-5.6159099449837373488 - 4.3741496585364105639e-955j)  +/-  (2.83e-246, 2.83e-246j)
| (-1.3802585391988807964 + 5.5733424307126440686e-963j)  +/-  (1.07e-249, 1.07e-249j)
| (-2.8649948160240847139 - 3.1279536694029616866e-961j)  +/-  (1.24e-246, 1.24e-246j)
| (3.1769991619799560268 + 2.008941149237749215e-965j)  +/-  (2.54e-246, 2.54e-246j)
| (4.6887389393058183647 - 2.2609936397833971331e-967j)  +/-  (5.79e-246, 5.79e-246j)
| (2.234605090330803872 - 4.5138289423835025647e-969j)  +/-  (1.14e-247, 1.14e-247j)
| (-3.5049798363493875022 + 3.660153608527459684e-965j)  +/-  (4.15e-246, 4.15e-246j)
| (-14.488428857702195957 - 1.4287185452779864845e-982j)  +/-  (1.97e-251, 1.97e-251j)
| (-3.1769991619799560268 + 1.6233558286819638184e-975j)  +/-  (2.62e-246, 2.62e-246j)
| (-4.6887389393058183647 + 2.5708286642624269371e-989j)  +/-  (5.89e-246, 5.89e-246j)
| (-1.9517879909162539774 - 5.1339299061141589131e-1002j)  +/-  (3.78e-248, 3.78e-248j)
| (3.5049798363493875022 + 4.3088208211487918172e-999j)  +/-  (4.11e-246, 4.11e-246j)
| (5.6159099449837373488 - 1.2124798056309677858e-999j)  +/-  (2.92e-246, 2.92e-246j)
| (0.27348104613815245216 - 6.4806514532166652722e-1011j)  +/-  (7.61e-254, 7.61e-254j)
| (2.5462021578474813622 - 1.157564412973228583e-1003j)  +/-  (3.91e-247, 3.91e-247j)
| (-3.8694479048601226987 - 1.1565978617876670136e-1005j)  +/-  (5.56e-246, 5.56e-246j)
| (-1.0901108418201012506 - 1.2034145022713532783e-1020j)  +/-  (1.25e-250, 1.25e-250j)
| (2.8649948160240847139 + 1.5082068152250799406e-1015j)  +/-  (1.12e-246, 1.12e-246j)
| (0.82295144914465589258 - 9.8233665572682296671e-1023j)  +/-  (1.25e-251, 1.25e-251j)
| (1.3802585391988807964 + 6.386088210365892408e-1023j)  +/-  (9.79e-250, 9.79e-250j)
| (5.1372505614844799991 + 3.7839586314613745654e-1017j)  +/-  (4.83e-246, 4.83e-246j)
| (-0.82295144914465589258 - 1.3505908841708722714e-1022j)  +/-  (1.35e-251, 1.35e-251j)
| (-2.5462021578474813622 - 2.8502679585255783738e-1017j)  +/-  (3.88e-247, 3.88e-247j)
| (1.9517879909162539774 + 4.6009462975713779289e-1023j)  +/-  (3.63e-248, 3.63e-248j)
| (1.6753855896885424828 + 4.1625288361989898017e-1024j)  +/-  (6.94e-249, 6.94e-249j)
| (4.266005912439862797 + 9.289970770124768868e-1020j)  +/-  (5.95e-246, 5.95e-246j)
| (-0.27348104613815245216 - 9.6911503486513074714e-1036j)  +/-  (7.61e-254, 7.61e-254j)
| (3.8694479048601226987 + 5.337402902952528628e-1034j)  +/-  (5.03e-246, 5.03e-246j)
| (9.0930002278496192945e-1044 - 3.5495546762941907527e-1043j)  +/-  (1.58e-1041, 1.58e-1041j)
| (1.0901108418201012506 + 5.3799703184540100332e-1042j)  +/-  (1.24e-250, 1.24e-250j)
| (6.1347249689125836803 + 8.1430166538348384295e-1039j)  +/-  (1.13e-246, 1.13e-246j)
| (-4.266005912439862797 - 3.3369862672175506368e-1054j)  +/-  (6.16e-246, 6.16e-246j)
| (-0.55369891499585922862 - 3.6440411102959426889e-1064j)  +/-  (1.27e-252, 1.27e-252j)
| (-1.6753855896885424828 - 3.2514704595734700958e-1062j)  +/-  (6.53e-249, 6.53e-249j)
| (0.55369891499585922862 + 1.5883195692295854721e-1065j)  +/-  (1.28e-252, 1.28e-252j)
-------------------------------------------------
The weights are:
| (6.1794876432061847577e-25 - 1.6564448945752689444e-948j)  +/-  (2.01e-92, 2.09e-215j)
| (0.0011427907490117847538 + 1.027272241523723041e-932j)  +/-  (1.58e-71, 1.65e-194j)
| (9.0134181288993150632e-13 - 5.8618740435567237561e-941j)  +/-  (2.94e-86, 3.06e-209j)
| (6.1794876432061847577e-25 + 8.8892831297050478665e-949j)  +/-  (5.57e-95, 5.81e-218j)
| (1.3891914008439135864e-17 - 4.2351323345476239548e-944j)  +/-  (1.45e-89, 1.51e-212j)
| (9.2148214970493218842e-21 + 4.814178911889148084e-946j)  +/-  (3.28e-91, 3.42e-214j)
| (9.3144047178559449742e-51 - 5.3934457858162636736e-963j)  +/-  (2.13e-108, 2.22e-231j)
| (9.2148214970493218842e-21 - 2.4099741697403012051e-946j)  +/-  (2.1e-94, 2.19e-217j)
| (5.6276416321561927653e-15 + 1.9488910666314008341e-942j)  +/-  (1.85e-88, 1.92e-211j)
| (0.025036582220223534051 - 3.7677906936003242739e-932j)  +/-  (1.38e-70, 1.44e-193j)
| (4.8375061978830251988e-05 - 2.3925157858452336611e-934j)  +/-  (3.78e-80, 3.94e-203j)
| (7.3285400216085639096e-06 - 5.9654960292260380744e-936j)  +/-  (1.75e-84, 1.83e-207j)
| (6.9588928722441967252e-11 - 4.6186946181422554624e-940j)  +/-  (3.91e-90, 4.08e-213j)
| (0.0011427907490117847538 + 5.2920433889189039866e-934j)  +/-  (5.71e-80, 5.95e-203j)
| (9.0119588811167431076e-07 - 3.9878397150431859564e-936j)  +/-  (3.62e-84, 3.77e-207j)
| (9.3144047178559449742e-51 + 7.3605079709716910259e-963j)  +/-  (9.35e-110, 9.74e-233j)
| (7.3285400216085639096e-06 + 3.4256384854525985442e-935j)  +/-  (6.29e-83, 6.55e-206j)
| (6.9588928722441967252e-11 + 1.3029863020752846387e-939j)  +/-  (5.41e-88, 5.64e-211j)
| (0.0033947409163929450149 - 2.4610102594442744912e-932j)  +/-  (1.03e-78, 1.07e-201j)
| (9.0119588811167431076e-07 + 8.8264758977606586771e-937j)  +/-  (2.86e-88, 2.98e-211j)
| (5.6276416321561927653e-15 - 8.3939929079225110438e-943j)  +/-  (4.38e-95, 4.56e-218j)
| (0.14583822139078647823 - 6.6583943267813741515e-932j)  +/-  (4.07e-79, 4.24e-202j)
| (0.00027586372853494393916 - 1.3023872116049602756e-934j)  +/-  (2.8e-85, 2.92e-208j)
| (6.7746851628926766637e-08 + 3.3909633026235837392e-937j)  +/-  (1.23e-87, 1.28e-210j)
| (0.047797536036386561922 + 5.58476001534579331e-932j)  +/-  (1.86e-79, 1.93e-202j)
| (4.8375061978830251988e-05 + 2.9575122253725603126e-935j)  +/-  (1.76e-86, 1.83e-209j)
| (0.075173440492336461678 - 3.4417229385672133493e-932j)  +/-  (3.55e-80, 3.69e-203j)
| (0.025036582220223534051 - 8.9048862283674608702e-933j)  +/-  (2.44e-82, 2.54e-205j)
| (9.0134181288993150632e-13 + 2.3080759090377406629e-941j)  +/-  (3.54e-94, 3.69e-217j)
| (0.075173440492336461678 - 7.4545695107418572313e-932j)  +/-  (6.3e-82, 6.56e-205j)
| (0.00027586372853494393916 + 1.9982466685123137867e-933j)  +/-  (8.69e-86, 9.06e-209j)
| (0.0033947409163929450149 - 1.6625636578661487071e-933j)  +/-  (1.06e-84, 1.1e-207j)
| (0.0097716559971146063693 + 4.0014701178453549405e-933j)  +/-  (3.74e-84, 3.9e-207j)
| (2.8888656258934507779e-09 + 7.2196930550209082282e-939j)  +/-  (3.2e-92, 3.33e-215j)
| (0.14583822139078647823 - 8.5154381621804700475e-932j)  +/-  (1.83e-84, 1.9e-207j)
| (6.7746851628926766637e-08 - 9.0819430413034881745e-938j)  +/-  (4.34e-91, 4.53e-214j)
| (0.15244777659214605955 + 8.0317995748489626323e-932j)  +/-  (8.78e-85, 9.11e-208j)
| (0.047797536036386561922 + 1.9224858848562634584e-932j)  +/-  (1.08e-85, 1.12e-208j)
| (1.3891914008439135864e-17 + 1.9735435730441198384e-944j)  +/-  (6.16e-98, 6.42e-221j)
| (2.8888656258934507779e-09 - 2.3103602686150180257e-938j)  +/-  (9.55e-93, 9.99e-216j)
| (0.11528860466903793687 + 8.3415172663097076768e-932j)  +/-  (5.67e-86, 5.95e-209j)
| (0.0097716559971146063693 + 2.797780683292016528e-932j)  +/-  (2.87e-87, 2.97e-210j)
| (0.11528860466903793687 + 5.0286127293509587745e-932j)  +/-  (3.29e-86, 3.21e-209j)
