Starting with polynomial:
P : 33554432*t^26 - 218103808*t^24 + 627048448*t^22 - 1049624576*t^20 + 1133117440*t^18 - 825556992*t^16 + 412778496*t^14 - 141213696*t^12 + 32361472*t^10 - 4759040*t^8 + 416416*t^6 - 18928*t^4 + 338*t^2 - 1
Extension levels are: 26 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 33554432*t^26 - 218103808*t^24 + 627048448*t^22 - 1049624576*t^20 + 1133117440*t^18 - 825556992*t^16 + 412778496*t^14 - 141213696*t^12 + 32361472*t^10 - 4759040*t^8 + 416416*t^6 - 18928*t^4 + 338*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 33554432*t^53 - 452984832*t^51 + 2885681152*t^49 - 11534336000*t^47 + 32446742528*t^45 - 68295524352*t^43 + 111641198592*t^41 - 145204854784*t^39 + 152724881920*t^37 - 131318510336*t^35 + 92949332736*t^33 - 54369592576*t^31 + 26316006392*t^29 - 10529070020*t^27 + 3470860998*t^25 - 937382805*t^23 + 13165769595/64*t^21 - 4643330505/128*t^19 + 324111975/64*t^17 - 140500215/256*t^15 + 1474166715/32768*t^13 - 176498205/65536*t^11 + 14697345/131072*t^9 - 792675/262144*t^7 + 396045/8388608*t^5 - 5863/16777216*t^3 + 13/16777216*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:   53 out of 53
Indefinite weights: 0 out of 53
Negative weights:   0 out of 53
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.95472086650854562606 + 8.6680395111884405354e-900j)  +/-  (1.14e-236, 1.14e-236j)
| (0.99817555422331747084 + 1.051288618906349042e-902j)  +/-  (5.11e-236, 5.11e-236j)
| (-0.93501624268541482344 - 1.6778972078554793752e-913j)  +/-  (5.15e-237, 5.15e-237j)
| (-1 + 5.5047715360223379242e-911j)  +/-  (3.01e-236, 3.01e-236j)
| (0.91189984599209007718 + 2.9427565681616778945e-927j)  +/-  (2.03e-237, 2.03e-237j)
| (0.93501624268541482344 - 3.3142742788059820586e-925j)  +/-  (4.81e-237, 4.81e-237j)
| (-0.9927088740980539928 + 2.4556046977758718761e-921j)  +/-  (4.25e-236, 4.25e-236j)
| (-0.91189984599209007718 + 1.4125362371480038981e-932j)  +/-  (1.78e-237, 1.78e-237j)
| (-0.99817555422331747084 - 3.4694673680661554198e-931j)  +/-  (5.71e-236, 5.71e-236j)
| (1 - 9.0888046710780227193e-939j)  +/-  (2.84e-236, 2.84e-236j)
| (0.8854560256532098959 - 2.2441746422664403173e-956j)  +/-  (5.96e-238, 5.96e-238j)
| (-0.97094181742605202716 + 1.2187630334942763032e-953j)  +/-  (1.89e-236, 1.89e-236j)
| (-0.85578127230144752264 - 1.0831226215846438894e-959j)  +/-  (2.02e-238, 2.02e-238j)
| (-0.82298386589365639458 + 1.8123567620751775305e-960j)  +/-  (6.37e-239, 6.37e-239j)
| (0.95472086650854562606 + 9.7874516442994497541e-956j)  +/-  (1.27e-236, 1.27e-236j)
| (0.85578127230144752264 - 1.4140390350396864961e-967j)  +/-  (1.9e-238, 1.9e-238j)
| (0.82298386589365639458 + 1.8948357814963715545e-969j)  +/-  (5.01e-239, 5.01e-239j)
| (-0.98361990694714358842 - 4.8259709461341042821e-967j)  +/-  (2.92e-236, 2.92e-236j)
| (-0.7871834806090501818 - 2.1893769528375719804e-974j)  +/-  (1.19e-239, 1.19e-239j)
| (0.9927088740980539928 + 1.3482254164421435423e-967j)  +/-  (4.3e-236, 4.3e-236j)
| (0.7871834806090501818 + 1.7542030166966828658e-991j)  +/-  (1.45e-239, 1.45e-239j)
| (0.74851074817110109863 + 3.4507592837873970334e-992j)  +/-  (2.47e-240, 2.47e-240j)
| (0.97094181742605202716 - 1.60157076070623548e-989j)  +/-  (1.92e-236, 1.92e-236j)
| (-0.7071067811865475244 + 3.482826856641501572e-1013j)  +/-  (4.45e-241, 4.45e-241j)
| (-0.74851074817110109863 + 2.3487757562647194977e-1012j)  +/-  (3.06e-240, 3.06e-240j)
| (0.23931566428755776715 - 1.5250172846237304048e-1021j)  +/-  (1.07e-250, 1.07e-250j)
| (0.7071067811865475244 - 2.9665982233050385702e-1011j)  +/-  (4.75e-241, 4.75e-241j)
| (0.56806474673115580251 + 7.42570772138953518e-1014j)  +/-  (1.06e-243, 1.06e-243j)
| (0.98361990694714358842 - 1.022179611168519052e-1012j)  +/-  (3.22e-236, 3.22e-236j)
| (-0.66312265824079520238 - 3.4158847060158133764e-1023j)  +/-  (6.44e-242, 6.44e-242j)
| (-0.23931566428755776715 - 1.8854646943281679389e-1033j)  +/-  (1.2e-250, 1.2e-250j)
| (0.51733781417765677104 + 1.8520644515190151161e-1027j)  +/-  (7.33e-245, 7.33e-245j)
| (0.66312265824079520238 + 1.4039948196119432122e-1025j)  +/-  (6.65e-242, 6.65e-242j)
| (0.060378497422286053438 - 9.0355930143253671916e-1037j)  +/-  (9.47e-255, 9.47e-255j)
| (-0.56806474673115580251 - 6.3187654542128686114e-1025j)  +/-  (8.39e-244, 8.39e-244j)
| (-0.61671887262854305846 + 6.5849504746906716647e-1024j)  +/-  (7.86e-243, 7.86e-243j)
| (-0.8854560256532098959 + 1.5787885944198615259e-1031j)  +/-  (6.78e-238, 6.78e-238j)
| (0.61671887262854305846 - 3.5786342253143629136e-1039j)  +/-  (7.69e-243, 7.69e-243j)
| (0.29750305385520297665 - 2.3734239791745488035e-1045j)  +/-  (2.33e-249, 2.33e-249j)
| (-0.29750305385520297665 + 7.2355335334884611783e-1045j)  +/-  (2.08e-249, 2.08e-249j)
| (-0.51733781417765677104 - 3.7089234170616925029e-1040j)  +/-  (8.33e-245, 8.33e-245j)
| (1.9684848688427697967e-1068 - 6.7099032154924131663e-1069j)  +/-  (1.1e-1066, 1.1e-1066j)
| (0.35460488704253562597 - 1.7204523307678646536e-1045j)  +/-  (3.48e-248, 3.48e-248j)
| (0.41041280545275679642 + 5.8197805946835988855e-1044j)  +/-  (5.12e-247, 5.12e-247j)
| (-0.060378497422286053438 - 6.2137532086574720813e-1051j)  +/-  (9.47e-255, 9.47e-255j)
| (-0.41041280545275679642 - 1.4626451424057403627e-1043j)  +/-  (6.19e-247, 6.19e-247j)
| (-0.35460488704253562597 - 2.9907967201795523426e-1044j)  +/-  (3.38e-248, 3.38e-248j)
| (0.12053668025532305335 - 2.2313178551675489296e-1050j)  +/-  (2.41e-253, 2.41e-253j)
| (0.46472317204376854566 + 6.4387646641565503259e-1045j)  +/-  (6.78e-246, 6.78e-246j)
| (0.18025503781390574017 - 1.9559180689017561003e-1048j)  +/-  (4.41e-252, 4.41e-252j)
| (-0.18025503781390574017 + 6.9947829633413553876e-1048j)  +/-  (5.07e-252, 5.07e-252j)
| (-0.46472317204376854566 + 2.0613472694398330439e-1041j)  +/-  (6.73e-246, 6.73e-246j)
| (-0.12053668025532305335 + 7.4082435460866694019e-1049j)  +/-  (2.44e-253, 2.44e-253j)
-------------------------------------------------
The weights are:
| (0.019230769230769230769 - 8.9914784334992628242e-901j)  +/-  (2.85e-53, 2.46e-166j)
| (0.019230769230769230769 + 1.1303460086872400402e-901j)  +/-  (5.15e-55, 4.44e-168j)
| (0.019230769230769230769 - 8.4594868865673685519e-900j)  +/-  (2.21e-53, 1.9e-166j)
| (0.0096153846153846153846 + 1.8407778147737809654e-900j)  +/-  (2.55e-54, 2.2e-167j)
| (0.019230769230769230769 + 8.6958744230145688883e-902j)  +/-  (9.02e-56, 7.79e-169j)
| (0.019230769230769230769 - 8.5008692546747011801e-902j)  +/-  (8.43e-56, 7.28e-169j)
| (0.019230769230769230769 + 4.3881460419424842225e-900j)  +/-  (9.4e-55, 8.11e-168j)
| (0.019230769230769230769 + 3.8926801170173945747e-900j)  +/-  (9.56e-56, 8.25e-169j)
| (0.019230769230769230769 - 3.8361216471608939564e-900j)  +/-  (1.87e-54, 1.61e-167j)
| (0.0096153846153846153846 - 9.8044696396161722627e-902j)  +/-  (2.85e-58, 2.46e-171j)
| (0.019230769230769230769 - 8.8791775184645050693e-902j)  +/-  (2.22e-58, 1.91e-171j)
| (0.019230769230769230769 + 1.0276508065986242275e-899j)  +/-  (2.86e-55, 2.47e-168j)
| (0.019230769230769230769 + 1.6846873050249414611e-900j)  +/-  (9.01e-58, 7.77e-171j)
| (0.019230769230769230769 - 1.265236359805348846e-900j)  +/-  (1.94e-58, 1.67e-171j)
| (0.019230769230769230769 + 8.2646920850461658061e-902j)  +/-  (2.92e-59, 2.52e-172j)
| (0.019230769230769230769 + 9.0650278501454592453e-902j)  +/-  (5.62e-60, 4.85e-173j)
| (0.019230769230769230769 - 9.2614705078768374075e-902j)  +/-  (8.78e-61, 7.57e-174j)
| (0.019230769230769230769 - 5.7682197436868040044e-900j)  +/-  (4.87e-57, 4.2e-170j)
| (0.019230769230769230769 + 9.9484717987539957101e-901j)  +/-  (1.19e-60, 1.03e-173j)
| (0.019230769230769230769 - 4.8614058974835472641e-902j)  +/-  (4.33e-60, 3.73e-173j)
| (0.019230769230769230769 + 9.4737687073388212024e-902j)  +/-  (4.76e-62, 4.11e-175j)
| (0.019230769230769230769 - 9.7058932838199504177e-902j)  +/-  (4.82e-63, 4.16e-176j)
| (0.019230769230769230769 - 7.9140455884850137574e-902j)  +/-  (1.35e-60, 1.16e-173j)
| (0.019230769230769230769 + 6.7307847714589124417e-901j)  +/-  (1.19e-64, 1.03e-177j)
| (0.019230769230769230769 - 8.0824937687377239205e-901j)  +/-  (9.68e-64, 8.35e-177j)
| (0.019230769230769230769 - 1.3933824903921729062e-901j)  +/-  (2.73e-68, 2.36e-181j)
| (0.019230769230769230769 + 9.9612492043567223398e-902j)  +/-  (7.86e-65, 6.78e-178j)
| (0.019230769230769230769 - 1.0899583647834311214e-901j)  +/-  (3.28e-67, 2.83e-180j)
| (0.019230769230769230769 + 7.2108297594429119659e-902j)  +/-  (3.87e-62, 3.34e-175j)
| (0.019230769230769230769 - 5.7153156944289965051e-901j)  +/-  (4.51e-67, 3.89e-180j)
| (0.019230769230769230769 - 2.3284173798393898201e-901j)  +/-  (2.07e-70, 1.79e-183j)
| (0.019230769230769230769 + 1.1281760332223995325e-901j)  +/-  (4.5e-68, 3.88e-181j)
| (0.019230769230769230769 - 1.0243070998203678946e-901j)  +/-  (3.01e-66, 2.6e-179j)
| (0.019230769230769230769 + 1.6399796676871060238e-901j)  +/-  (4.73e-71, 4.08e-184j)
| (0.019230769230769230769 - 4.3098543972408406074e-901j)  +/-  (6.03e-70, 5.21e-183j)
| (0.019230769230769230769 + 4.9304665533868652581e-901j)  +/-  (3.62e-69, 3.12e-182j)
| (0.019230769230769230769 - 2.4064970227658103162e-900j)  +/-  (7.84e-67, 6.76e-180j)
| (0.019230769230769230769 + 1.0554665576995651931e-901j)  +/-  (2.45e-68, 2.11e-181j)
| (0.019230769230769230769 + 1.3282908127783838255e-901j)  +/-  (7.67e-72, 6.62e-185j)
| (0.019230769230769230769 + 2.5347839863305880026e-901j)  +/-  (6.83e-73, 5.89e-186j)
| (0.019230769230769230769 + 3.80981200184212537e-901j)  +/-  (1.91e-71, 1.65e-184j)
| (0.019230769230769230769 - 1.7439620710591191871e-901j)  +/-  (1.95e-73, 1.69e-186j)
| (0.019230769230769230769 - 1.2699800358675855614e-901j)  +/-  (2.05e-72, 1.77e-185j)
| (0.019230769230769230769 + 1.2176353879266406797e-901j)  +/-  (2.22e-72, 1.92e-185j)
| (0.019230769230769230769 + 1.8619520310596763443e-901j)  +/-  (2.11e-74, 1.82e-187j)
| (0.019230769230769230769 + 3.0610412811214714732e-901j)  +/-  (1.44e-74, 1.25e-187j)
| (0.019230769230769230769 - 2.7761863846749321553e-901j)  +/-  (1.38e-74, 1.19e-187j)
| (0.019230769230769230769 - 1.5479581998566524035e-901j)  +/-  (3.71e-75, 3.2e-188j)
| (0.019230769230769230769 - 1.1705647693517871422e-901j)  +/-  (2.36e-74, 2.04e-187j)
| (0.019230769230769230769 + 1.4662208007904904291e-901j)  +/-  (3.23e-75, 2.79e-188j)
| (0.019230769230769230769 + 2.1506462187167538084e-901j)  +/-  (2.5e-76, 2.17e-189j)
| (0.019230769230769230769 - 3.400533355512988699e-901j)  +/-  (2.78e-76, 2.53e-189j)
| (0.019230769230769230769 - 1.9964693478755338294e-901j)  +/-  (2.37e-76, 2.03e-189j)
