Starting with polynomial:
P : 16*t^5 - 20*t^3 + 5*t
Extension levels are: 5 20 26
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P1 : 16*t^5 - 20*t^3 + 5*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 16*t^25 - 100*t^23 + 275*t^21 - 875/2*t^19 + 7125/16*t^17 - 4845/16*t^15 + 8925/64*t^13 - 5525/128*t^11 + 17875/2048*t^9 - 17875/16384*t^7 + 5005/65536*t^5 - 325/131072*t^3 + 25/1048576*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^51 - 208*t^49 + 1273*t^47 - 4876*t^45 + 209715/16*t^43 - 420497/16*t^41 + 5220243/128*t^39 - 3210259/64*t^37 + 203461557/4096*t^35 - 163907965/4096*t^33 + 432375229/16384*t^31 - 29267999/2048*t^29 + 1666443037/262144*t^27 - 607545099/262144*t^25 + 1445389725/2097152*t^23 - 173996955/1048576*t^21 + 4295336595/134217728*t^19 - 654116895/134217728*t^17 + 2469143955/4294967296*t^15 - 54977475/1073741824*t^13 + 228524205/68719476736*t^11 - 10311015/68719476736*t^9 + 2408445/549755813888*t^7 - 20345/274877906944*t^5 + 10425/17592186044416*t^3 - 25/17592186044416*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:   51 out of 51
Indefinite weights: 0 out of 51
Negative weights:   0 out of 51
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (1 - 5.0901348995766189259e-891j)  +/-  (4.67e-237, 4.67e-237j)
| (-0.99802672842827156195 - 7.4281153188477673642e-886j)  +/-  (9.05e-237, 9.05e-237j)
| (-0.95105651629515357212 - 1.1023822692000943919e-903j)  +/-  (1.56e-237, 1.56e-237j)
| (-0.68454710592868867373 - 2.2740823589105644091e-924j)  +/-  (4.32e-242, 4.32e-242j)
| (0.95105651629515357212 - 1.5321467525872419305e-920j)  +/-  (1.48e-237, 1.48e-237j)
| (0.92977648588825140366 + 2.3046521699703010407e-922j)  +/-  (6.97e-238, 6.97e-238j)
| (-1 - 1.9804631415403876756e-917j)  +/-  (4.65e-237, 4.65e-237j)
| (-0.92977648588825140366 + 5.9761936103412335345e-936j)  +/-  (6.56e-238, 6.56e-238j)
| (-0.58778525229247312917 + 5.9660957033063739599e-953j)  +/-  (8.01e-244, 8.01e-244j)
| (-0.99211470131447783105 + 5.847923630594360231e-945j)  +/-  (7.08e-237, 7.08e-237j)
| (0.87630668004386358731 - 7.6255704436499901587e-965j)  +/-  (9.42e-239, 9.42e-239j)
| (0.98228725072868868109 - 7.5056163814473385118e-963j)  +/-  (5.71e-237, 5.71e-237j)
| (0.96858316112863111949 + 6.5940368868407303172e-963j)  +/-  (3e-237, 3e-237j)
| (-0.84432792550201507855 - 9.7283328031875329518e-966j)  +/-  (2.56e-239, 2.56e-239j)
| (0.99802672842827156195 - 2.2246460212892288506e-961j)  +/-  (8.06e-237, 8.06e-237j)
| (0.90482705246601952771 + 6.3448866961487504281e-966j)  +/-  (2.7e-238, 2.7e-238j)
| (0.53582679497899661827 - 4.3662093851209316059e-973j)  +/-  (6.39e-245, 6.39e-245j)
| (0.99211470131447783105 - 7.2403976378540454321e-964j)  +/-  (7.49e-237, 7.49e-237j)
| (-0.72896862742141152315 + 1.9899196507093436207e-967j)  +/-  (2.72e-241, 2.72e-241j)
| (-0.98228725072868868109 + 2.9398499446650141472e-962j)  +/-  (4.58e-237, 4.58e-237j)
| (0.84432792550201507855 - 2.8692167485523163894e-986j)  +/-  (2.98e-239, 2.98e-239j)
| (0.7705132427757892308 + 2.5458084565317680059e-987j)  +/-  (1.35e-240, 1.35e-240j)
| (-0.96858316112863111949 + 8.5878561566698256019e-984j)  +/-  (2.84e-237, 2.84e-237j)
| (-0.87630668004386358731 - 8.316019448867095408e-1000j)  +/-  (9.2e-239, 9.2e-239j)
| (-0.7705132427757892308 + 2.2684150304513351802e-1002j)  +/-  (1.5e-240, 1.5e-240j)
| (0.18738131458572463054 + 1.4202515996441005633e-1016j)  +/-  (5.3e-252, 5.3e-252j)
| (0.72896862742141152315 - 9.8344972702610859709e-1004j)  +/-  (2.66e-241, 2.66e-241j)
| (0.8090169943749474241 - 1.1097805615472273407e-1003j)  +/-  (6.93e-240, 6.93e-240j)
| (-0.8090169943749474241 + 3.6913575935267900804e-1006j)  +/-  (6.69e-240, 6.69e-240j)
| (-0.63742398974868971018 + 2.3757371429411347067e-1009j)  +/-  (5.8e-243, 5.8e-243j)
| (-0.42577929156507264886 + 5.0622732250932622896e-1013j)  +/-  (4.99e-247, 4.99e-247j)
| (0.42577929156507264886 - 1.7894915985052573722e-1012j)  +/-  (4.7e-247, 4.7e-247j)
| (0.68454710592868867373 - 2.8205853682032873561e-1010j)  +/-  (4.3e-242, 4.3e-242j)
| (0.12533323356430424537 + 1.8327236701003275433e-1022j)  +/-  (2.95e-253, 2.95e-253j)
| (-0.53582679497899661827 + 7.7387707091784201963e-1012j)  +/-  (7.25e-245, 7.25e-245j)
| (-0.90482705246601952771 - 7.1738412317323261755e-1016j)  +/-  (2.79e-238, 2.79e-238j)
| (-0.062790519529313376076 + 8.3019301339193409514e-1034j)  +/-  (1.29e-254, 1.29e-254j)
| (0.63742398974868971018 - 4.3341710366073654132e-1022j)  +/-  (6.38e-243, 6.38e-243j)
| (0.58778525229247312917 + 6.6534246344789225213e-1027j)  +/-  (7.18e-244, 7.18e-244j)
| (-0.24868988716485478824 + 1.0557778083743629716e-1033j)  +/-  (9.89e-251, 9.89e-251j)
| (-0.48175367410171527499 - 7.8730766747513517069e-1029j)  +/-  (6.85e-246, 6.85e-246j)
| (-0.18738131458572463054 + 1.4485978670102394843e-1035j)  +/-  (4.35e-252, 4.35e-252j)
| (0.3090169943749474241 - 3.0331448999503837989e-1033j)  +/-  (1.85e-249, 1.85e-249j)
| (0.36812455268467795916 - 2.8380131904134608386e-1031j)  +/-  (3.58e-248, 3.58e-248j)
| (-5.1056893363025673025e-1054 + 6.0115711113945370796e-1054j)  +/-  (4.02e-1052, 4.02e-1052j)
| (-0.3090169943749474241 + 1.0355433079556529801e-1032j)  +/-  (1.77e-249, 1.77e-249j)
| (-0.36812455268467795916 + 1.5153852721928940745e-1031j)  +/-  (3.62e-248, 3.62e-248j)
| (0.062790519529313376076 - 1.5904645667624094936e-1037j)  +/-  (1.29e-254, 1.29e-254j)
| (0.48175367410171527499 + 3.7451446296902848413e-1029j)  +/-  (5.67e-246, 5.67e-246j)
| (0.24868988716485478824 + 2.9434153639947784483e-1035j)  +/-  (9.81e-251, 9.81e-251j)
| (-0.12533323356430424537 + 3.2522785988339495831e-1037j)  +/-  (2.12e-253, 2.12e-253j)
-------------------------------------------------
The weights are:
| (0.01 + 3.7601519750301354926e-888j)  +/-  (4.93e-57, 1.09e-169j)
| (0.02 + 1.8803238088582997837e-885j)  +/-  (2.27e-57, 5.02e-170j)
| (0.02 - 3.1629052571477951635e-886j)  +/-  (7.89e-58, 1.75e-170j)
| (0.02 - 4.739143636781507387e-887j)  +/-  (8.19e-59, 1.81e-171j)
| (0.02 - 7.6242432338923027109e-888j)  +/-  (1.9e-58, 4.19e-171j)
| (0.02 + 7.7077500725159251632e-888j)  +/-  (1.76e-58, 3.9e-171j)
| (0.01 - 3.7643654198698066073e-885j)  +/-  (9.62e-58, 2.13e-170j)
| (0.02 + 2.1767298818655007878e-886j)  +/-  (4.86e-59, 1.08e-171j)
| (0.02 - 3.6213444532086134592e-887j)  +/-  (2.72e-60, 6.01e-173j)
| (0.02 + 2.5128827479757019553e-885j)  +/-  (4.07e-58, 9e-171j)
| (0.02 + 7.9269638975868770163e-888j)  +/-  (5.91e-61, 1.31e-173j)
| (0.02 - 7.5077045863695307654e-888j)  +/-  (6.73e-61, 1.49e-173j)
| (0.02 + 7.5574740534946020111e-888j)  +/-  (6.77e-61, 1.5e-173j)
| (0.02 - 9.6658131609828246438e-887j)  +/-  (2.94e-63, 6.51e-176j)
| (0.02 - 7.4943928081839900794e-888j)  +/-  (3.63e-61, 8.02e-174j)
| (0.02 - 7.8084118672252583864e-888j)  +/-  (8.44e-63, 1.87e-175j)
| (0.02 + 9.6857795196835181196e-888j)  +/-  (3.11e-67, 6.89e-180j)
| (0.02 + 7.4778224413932465777e-888j)  +/-  (2.32e-61, 5.13e-174j)
| (0.02 + 5.5215756092834686505e-887j)  +/-  (8.44e-66, 1.87e-178j)
| (0.02 - 9.4388338225535105302e-886j)  +/-  (3.26e-64, 7.22e-177j)
| (0.02 - 8.0643731786432136037e-888j)  +/-  (7.3e-65, 1.62e-177j)
| (0.02 - 8.4007234341417525879e-888j)  +/-  (1.72e-66, 3.8e-179j)
| (0.02 + 5.0456631185829330754e-886j)  +/-  (1.48e-64, 3.27e-177j)
| (0.02 + 1.2205250851476390452e-886j)  +/-  (2.09e-66, 4.63e-179j)
| (0.02 - 6.5298299469510301215e-887j)  +/-  (2.79e-67, 6.18e-180j)
| (0.02 + 1.2532713296490537164e-887j)  +/-  (9.15e-72, 2.03e-184j)
| (0.02 + 8.6027326407957101617e-888j)  +/-  (6.95e-69, 1.54e-181j)
| (0.02 + 8.2218231287728386268e-888j)  +/-  (2.39e-67, 5.28e-180j)
| (0.02 + 7.8600403035617616619e-887j)  +/-  (6.38e-68, 1.41e-180j)
| (0.02 + 4.1198392202062850242e-887j)  +/-  (1.09e-69, 2.42e-182j)
| (0.02 + 2.596127223989555183e-887j)  +/-  (7.09e-73, 1.57e-185j)
| (0.02 + 1.0434344885073589422e-887j)  +/-  (2.33e-73, 5.15e-186j)
| (0.02 - 8.8297900116903678771e-888j)  +/-  (3.87e-71, 8.56e-184j)
| (0.02 - 1.3224934026942829021e-887j)  +/-  (1.52e-74, 3.36e-187j)
| (0.02 + 3.214249981361067299e-887j)  +/-  (1.97e-72, 4.35e-185j)
| (0.02 - 1.5940222393832114858e-886j)  +/-  (2.19e-69, 4.84e-182j)
| (0.02 + 1.588509948700233855e-887j)  +/-  (7.78e-76, 1.72e-188j)
| (0.02 + 9.0841562317575457773e-888j)  +/-  (1.44e-72, 3.19e-185j)
| (0.02 - 9.3684638902259465433e-888j)  +/-  (4.44e-73, 9.83e-186j)
| (0.02 - 1.9825919281222586645e-887j)  +/-  (2.39e-76, 5.29e-189j)
| (0.02 - 2.877598585345646275e-887j)  +/-  (1.49e-74, 3.3e-187j)
| (0.02 + 1.8326508589875380362e-887j)  +/-  (1.4e-76, 3.09e-189j)
| (0.02 + 1.1366431700470997798e-887j)  +/-  (3.34e-77, 7.38e-190j)
| (0.02 - 1.0874674676523766321e-887j)  +/-  (6.57e-77, 1.45e-189j)
| (0.02 - 1.4885705779549054268e-887j)  +/-  (6.03e-78, 1.34e-190j)
| (0.02 + 2.1561791492872757603e-887j)  +/-  (1.09e-77, 2.41e-190j)
| (0.02 - 2.3585055078484170873e-887j)  +/-  (1.61e-77, 3.56e-190j)
| (0.02 + 1.4004623223904690965e-887j)  +/-  (1.2e-78, 2.67e-191j)
| (0.02 - 1.0039679736101149707e-887j)  +/-  (1.16e-78, 2.58e-191j)
| (0.02 - 1.1916420606156662254e-887j)  +/-  (6.11e-79, 1.36e-191j)
| (0.02 - 1.7023513608043972969e-887j)  +/-  (5.26e-79, 1.14e-191j)
