Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 35
-------------------------------------------------
Trying to find an order 35 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^37 - 39424751497470590386/30432767569864143*t^35 + 5699067168042468666530/30432767569864143*t^33 - 14756540135563165368380/922205077874671*t^31 + 832092379712635330762025/922205077874671*t^29 - 65484622160507727968341355/1844410155749342*t^27 + 927273892667110956027541845/922205077874671*t^25 - 76871587391725404901550689125/3688820311498684*t^23 + 9394213259615995788307977772125/29510562491989472*t^21 - 211497316664170316653295178631875/59021124983978944*t^19 + 1742458569663921255003905989066125/59021124983978944*t^17 - 10364529596885878961664127059674625/59021124983978944*t^15 + 174256199718272464253276435544185625/236084499935915776*t^13 - 1002798788946252280064583885264391875/472168999871831552*t^11 + 471458222116587835745741104013409375/118042249967957888*t^9 - 4324517859606154268870905166525326875/944337999743663104*t^7 + 43291886262377185803118305212480199375/15109407995898609664*t^5 - 24221373528758677519465944809673215625/30218815991797219328*t^3 + 1914744300755015576620877801000428125/30218815991797219328*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:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-5.8724427668782992986 - 3.3085479060320921356e-900j)  +/-  (1.53e-246, 1.53e-246j)
| (7.6685800922176837046 - 3.6568542868012510153e-910j)  +/-  (1.39e-248, 1.39e-248j)
| (-3.2861452844435723684 - 2.0350653033301587645e-907j)  +/-  (3.49e-247, 3.49e-247j)
| (6.3920035445984787589 - 2.1640632738960500441e-909j)  +/-  (6.34e-247, 6.34e-247j)
| (6.9716614167531237856 - 4.7021841959835675644e-911j)  +/-  (1.44e-247, 1.44e-247j)
| (-6.9716614167531237856 + 2.6959290272203699279e-909j)  +/-  (1.53e-247, 1.53e-247j)
| (-7.6685800922176837046 - 2.1086938304875306291e-916j)  +/-  (1.46e-248, 1.46e-248j)
| (-6.3920035445984787589 - 2.7574002767923296208e-924j)  +/-  (6.3e-247, 6.3e-247j)
| (-1.4216306571327068585 - 4.1879510096593175702e-933j)  +/-  (1.28e-250, 1.28e-250j)
| (5.3911937992420628153 + 1.9737924122361893301e-927j)  +/-  (2.65e-246, 2.65e-246j)
| (5.8724427668782992986 - 2.9961335174751280879e-934j)  +/-  (1.48e-246, 1.48e-246j)
| (1.0629992165455703437 - 2.2156008276557214568e-944j)  +/-  (1.36e-251, 1.36e-251j)
| (-2.1504626043751080854 + 8.9755073624891375589e-939j)  +/-  (6.93e-249, 6.93e-249j)
| (3.2861452844435723684 + 5.0763339512797918968e-942j)  +/-  (3.77e-247, 3.77e-247j)
| (-5.3911937992420628153 - 4.2652218957467276509e-956j)  +/-  (2.8e-246, 2.8e-246j)
| (4.0854860081404834989 - 2.7043820644243237987e-962j)  +/-  (1.98e-246, 1.98e-246j)
| (3.6805365164412970749 - 6.4753871664165307051e-967j)  +/-  (9.07e-247, 9.07e-247j)
| (-1.7838400837919394857 + 1.0195128055044728764e-971j)  +/-  (1.08e-249, 1.08e-249j)
| (-3.6805365164412970749 + 5.5531883142499880155e-973j)  +/-  (8.42e-247, 8.42e-247j)
| (2.5223756783398072471 + 1.5809266070617476053e-979j)  +/-  (2.84e-248, 2.84e-248j)
| (4.5032865308020214763 + 6.082178815938737826e-980j)  +/-  (2.75e-246, 2.75e-246j)
| (-4.9370476056478723363 - 1.268090048454206194e-987j)  +/-  (2.86e-246, 2.86e-246j)
| (4.9370476056478723363 + 1.3404970689330266142e-1000j)  +/-  (3.05e-246, 3.05e-246j)
| (-2.5223756783398072471 - 6.6165397930839289321e-1004j)  +/-  (2.81e-248, 2.81e-248j)
| (-4.5032865308020214763 + 1.4219018903646107203e-1003j)  +/-  (2.78e-246, 2.78e-246j)
| (-4.0854860081404834989 + 2.5942604525092841468e-1017j)  +/-  (1.67e-246, 1.67e-246j)
| (0.35307961506321626195 - 2.622576520551951761e-1031j)  +/-  (7.92e-254, 7.92e-254j)
| (2.1504626043751080854 - 6.8297558445518145661e-1027j)  +/-  (6.08e-249, 6.08e-249j)
| (2.9005557495743552111 + 8.56423651667363613e-1027j)  +/-  (1.08e-247, 1.08e-247j)
| (-1.0629992165455703437 - 5.9150421746397559655e-1031j)  +/-  (1.43e-251, 1.43e-251j)
| (-0.35307961506321626195 - 1.3612916040711427623e-1032j)  +/-  (7.92e-254, 7.92e-254j)
| (1.4216306571327068585 + 1.824720339785641106e-1030j)  +/-  (1.33e-250, 1.33e-250j)
| (1.7838400837919394857 - 3.9192469487768814966e-1029j)  +/-  (1.05e-249, 1.05e-249j)
| (3.9307140659250956019e-1039 - 2.913538480806636186e-1039j)  +/-  (1.81e-1037, 1.81e-1037j)
| (-2.9005557495743552111 + 1.6475963105998841085e-1030j)  +/-  (1.14e-247, 1.14e-247j)
| (-0.7071067811865475244 - 4.8392353500856971859e-1038j)  +/-  (1.09e-252, 1.09e-252j)
| (0.7071067811865475244 + 9.8178922268678376358e-1036j)  +/-  (1.09e-252, 1.09e-252j)
-------------------------------------------------
The weights are:
| (2.9630077619784795154e-16 - 5.8870597205052277579e-915j)  +/-  (1.97e-88, 6.6e-212j)
| (1.3081357732527324533e-26 + 3.8781397281284243796e-922j)  +/-  (6.49e-93, 2.17e-216j)
| (4.4911111112033092688e-06 - 7.2223591534966919468e-911j)  +/-  (1.05e-80, 3.52e-204j)
| (5.5353806094116645608e-19 + 3.2479103402663624453e-918j)  +/-  (1.35e-90, 4.53e-214j)
| (2.7370920704845757405e-22 - 6.4162535896899329571e-920j)  +/-  (1.21e-91, 4.07e-215j)
| (2.7370920704845757405e-22 + 7.4608801204003490323e-919j)  +/-  (4.05e-93, 1.36e-216j)
| (1.3081357732527324533e-26 - 2.9114352404998927832e-921j)  +/-  (4.86e-95, 1.63e-218j)
| (5.5353806094116645608e-19 - 7.6239565813901433525e-917j)  +/-  (8.18e-92, 2.74e-215j)
| (0.026936684953905086072 + 4.2088692718949856345e-909j)  +/-  (1.56e-75, 5.21e-199j)
| (6.2710959826873730871e-14 + 1.3621141250634373068e-915j)  +/-  (2.45e-91, 8.21e-215j)
| (2.9630077619784795154e-16 - 8.4015933112693202529e-917j)  +/-  (5.57e-92, 1.87e-215j)
| (0.065087945073671223034 - 4.3602146694290508754e-909j)  +/-  (4.19e-75, 1.4e-198j)
| (0.0020426639798191643396 + 1.2531890568698271354e-909j)  +/-  (3.14e-82, 1.05e-205j)
| (4.4911111112033092688e-06 - 1.9643540232952847194e-911j)  +/-  (1.55e-87, 5.21e-211j)
| (6.2710959826873730871e-14 + 3.163291546808894005e-914j)  +/-  (2.46e-92, 8.26e-216j)
| (1.3070906597076646258e-08 - 8.5591045461444397457e-913j)  +/-  (6.91e-90, 2.32e-213j)
| (2.9489213816229726276e-07 + 4.5229682744861570131e-912j)  +/-  (6.47e-89, 2.17e-212j)
| (0.0085288853193579436007 - 2.4573475683756052716e-909j)  +/-  (2.37e-83, 7.94e-207j)
| (2.9489213816229726276e-07 + 1.9018472245954074907e-911j)  +/-  (4.22e-90, 1.41e-213j)
| (0.00036489041767745422945 - 2.1920105766343943847e-910j)  +/-  (1.57e-87, 5.25e-211j)
| (3.7383396003562932081e-10 + 1.3014650102089747661e-913j)  +/-  (2.3e-91, 7.7e-215j)
| (6.4895246930151583787e-12 - 1.7647170190304320336e-913j)  +/-  (1.48e-93, 4.96e-217j)
| (6.4895246930151583787e-12 - 1.5418315920483817891e-914j)  +/-  (1.42e-92, 4.75e-216j)
| (0.00036489041767745422945 - 5.5749308501729682409e-910j)  +/-  (7e-89, 2.35e-212j)
| (3.7383396003562932081e-10 + 9.7396093843115204282e-913j)  +/-  (3.49e-93, 1.17e-216j)
| (1.3070906597076646258e-08 - 4.6826951147074074209e-912j)  +/-  (2.06e-92, 6.92e-216j)
| (0.17601377698218117666 - 8.4169720185396699658e-909j)  +/-  (2.61e-88, 8.74e-212j)
| (0.0020426639798191643396 + 5.7610789476277980773e-910j)  +/-  (7.26e-91, 2.43e-214j)
| (4.7786382978924042734e-05 + 7.1312438103473546213e-911j)  +/-  (1.43e-91, 4.78e-215j)
| (0.065087945073671223034 - 6.3057796527907912954e-909j)  +/-  (2.29e-89, 7.67e-213j)
| (0.17601377698218117666 - 9.5020966418668129479e-909j)  +/-  (1.72e-89, 5.76e-213j)
| (0.026936684953905086072 + 2.5573584526497088167e-909j)  +/-  (1.26e-90, 4.21e-214j)
| (0.0085288853193579436007 - 1.3042489139394708621e-909j)  +/-  (5.89e-91, 1.97e-214j)
| (0.1991141080104398512 + 9.5590478072608164979e-909j)  +/-  (2.51e-90, 8.43e-214j)
| (4.7786382978924042734e-05 + 2.172393993892496642e-910j)  +/-  (1.28e-92, 4.38e-216j)
| (0.1214155134306466472 + 8.2713413301698767409e-909j)  +/-  (1.47e-90, 5.22e-214j)
| (0.1214155134306466472 + 6.4818130842749065852e-909j)  +/-  (1.02e-90, 2.92e-214j)
