Starting with polynomial:
P : t
Extension levels are: 1 2 8 26
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P3 : t^11 - 149/3*t^9 + 798*t^7 - 4914*t^5 + 10605*t^3 - 5355*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 16818716006919620270534203439873/31624247009580822942848348876*t^35 + 178703928418642798214093198316599291/1423091115431137032428175699420*t^33 - 7857518111436990743742589424289629534/450645519886526726935588971483*t^31 + 3582292774564155359839204121244265208818/2253227599432633634677944857415*t^29 - 14329882756963165527527952067865243780369/142309111543113703242817569942*t^27 + 6865736973134045560284981619404421741869969/1502151732955089089785296571610*t^25 - 22716819594914183031335062408514336374577595/150215173295508908978529657161*t^23 + 551986468747729814171787768965889124751719815/150215173295508908978529657161*t^21 - 518345698913137458255400313022229316938443810/7906061752395205735712087219*t^19 + 6743336074716238968073608084779238372671888550/7906061752395205735712087219*t^17 - 63061317334489079972172707537281298422711963020/7906061752395205735712087219*t^15 + 414442341419640115954909915830010636313767030500/7906061752395205735712087219*t^13 - 3702672685663732146454581693531268299059123701275/15812123504790411471424174438*t^11 + 10709821205191533477173530157596337825647795207725/15812123504790411471424174438*t^9 - 9329870141149156706852741138743629491550190228125/7906061752395205735712087219*t^7 + 8728839098009360002688730940988136114684240146850/7906061752395205735712087219*t^5 - 14259268249997881297907747257575784666986435051375/31624247009580822942848348876*t^3 + 1571565648912690099399168797165901199642315403625/31624247009580822942848348876*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:
| (-6.8345259725630225333 - 6.4902157753985332605e-916j)  +/-  (1.29e-246, 1.29e-246j)
| (-9.119892763919752428 - 5.63441720937488497e-918j)  +/-  (8.05e-248, 8.05e-248j)
| (-10.126822855475157519 - 4.1810546221823748878e-918j)  +/-  (9.38e-249, 9.38e-249j)
| (6.1796071103126966252 - 2.576281225668021225e-914j)  +/-  (1.6e-246, 1.6e-246j)
| (10.126822855475157519 - 7.2074700093787219684e-927j)  +/-  (9.93e-249, 9.93e-249j)
| (9.119892763919752428 - 9.2613492493302770547e-944j)  +/-  (7.75e-248, 7.75e-248j)
| (2.1914496258099764306 + 4.4642370893245671164e-953j)  +/-  (7.48e-250, 7.48e-250j)
| (-8.2817083144606108527 - 1.0110090797156156018e-956j)  +/-  (3.25e-247, 3.25e-247j)
| (7.5302096335407558475 + 3.0242273191690262784e-971j)  +/-  (7.73e-247, 7.73e-247j)
| (-6.1796071103126966252 - 4.9772962921774074958e-979j)  +/-  (1.69e-246, 1.69e-246j)
| (-4.9791465117195582423 + 4.1772044688294644253e-980j)  +/-  (1.8e-246, 1.8e-246j)
| (-5.5588189137377092671 - 4.860386719133573746e-984j)  +/-  (1.69e-246, 1.69e-246j)
| (-2.6840395601585691766 + 1.4556125927564466332e-987j)  +/-  (4.25e-249, 4.25e-249j)
| (6.8345259725630225333 - 8.2265684264469537811e-988j)  +/-  (1.34e-246, 1.34e-246j)
| (5.5588189137377092671 - 5.217350272125227656e-1005j)  +/-  (1.61e-246, 1.61e-246j)
| (-7.5302096335407558475 + 5.5368962400349402695e-1019j)  +/-  (7.66e-247, 7.66e-247j)
| (8.2817083144606108527 - 3.1044338266310077961e-1022j)  +/-  (3.58e-247, 3.58e-247j)
| (4.9791465117195582423 - 4.022576062865693597e-1023j)  +/-  (1.77e-246, 1.77e-246j)
| (-1.2905154052751256639 + 3.4694209253432809488e-1034j)  +/-  (1.31e-251, 1.31e-251j)
| (-4.2292200709256479271 - 3.421440462392710009e-1029j)  +/-  (8.86e-247, 8.86e-247j)
| (-4.5347589577902597849 + 2.9678360372492167129e-1029j)  +/-  (1.62e-246, 1.62e-246j)
| (0.84628809835102169611 + 2.3150015103908537832e-1034j)  +/-  (1.1e-252, 1.1e-252j)
| (4.2292200709256479271 + 3.8011479781502268565e-1027j)  +/-  (8.37e-247, 8.37e-247j)
| (-2.1914496258099764306 - 9.8943239684025696222e-1035j)  +/-  (8.04e-250, 8.04e-250j)
| (-1.7320508075688772935 - 6.9303432371133553713e-1037j)  +/-  (9.99e-251, 9.99e-251j)
| (4.5347589577902597849 + 6.5651699670249249721e-1033j)  +/-  (1.64e-246, 1.64e-246j)
| (0.41001876842815870934 - 1.4482324207666651052e-1043j)  +/-  (9.56e-254, 9.56e-254j)
| (3.203478284763699718 + 1.5086732237793351063e-1038j)  +/-  (2.99e-248, 2.99e-248j)
| (-3.203478284763699718 - 3.1855248565221796601e-1039j)  +/-  (2.73e-248, 2.73e-248j)
| (-0.84628809835102169611 - 9.6204740814550548178e-1044j)  +/-  (1.08e-252, 1.08e-252j)
| (3.7355715460409572598 + 2.5137829838673613199e-1041j)  +/-  (1.49e-247, 1.49e-247j)
| (1.7320508075688772935 + 2.0662881344682799548e-1045j)  +/-  (1.04e-250, 1.04e-250j)
| (1.2905154052751256639 - 4.6866790123519367832e-1046j)  +/-  (1.34e-251, 1.34e-251j)
| (-3.7355715460409572598 + 2.4477422386416958381e-1044j)  +/-  (1.53e-247, 1.53e-247j)
| (-3.8219942997158413385e-1059 + 3.0114943574265642151e-1059j)  +/-  (1.8e-1057, 1.8e-1057j)
| (-0.41001876842815870934 + 8.4917661355414427076e-1050j)  +/-  (7.66e-254, 7.66e-254j)
| (2.6840395601585691766 - 2.3115797199107932168e-1047j)  +/-  (4.37e-249, 4.37e-249j)
-------------------------------------------------
The weights are:
| (1.93278130276958879e-11 - 2.1289401572130233834e-925j)  +/-  (8.89e-86, 8.08e-210j)
| (3.1233047790880202694e-19 + 2.9076023316797801319e-930j)  +/-  (1.57e-90, 1.43e-214j)
| (2.4907710528739964531e-23 - 1.3743253867287500126e-932j)  +/-  (2.66e-92, 2.42e-216j)
| (1.2971963533788100134e-09 + 1.4194378992405983227e-922j)  +/-  (3.84e-87, 3.49e-211j)
| (2.4907710528739964531e-23 + 5.8459671774847934202e-932j)  +/-  (6.76e-95, 6.15e-219j)
| (3.1233047790880202694e-19 - 1.5755514979837546984e-929j)  +/-  (2.6e-93, 2.36e-217j)
| (0.017197000418961522298 + 8.4686103479840543447e-919j)  +/-  (3.93e-75, 3.57e-199j)
| (4.0158250719394416354e-16 - 1.8780926462553344998e-928j)  +/-  (2.42e-91, 2.2e-215j)
| (1.3971283600988779725e-13 - 7.0393251982103717899e-926j)  +/-  (5.41e-91, 4.92e-215j)
| (1.2971963533788100134e-09 + 3.0151008881641870207e-924j)  +/-  (3.41e-88, 3.1e-212j)
| (8.9985393354514834234e-07 + 5.4108218437746226621e-922j)  +/-  (7.94e-87, 7.22e-211j)
| (4.6959581333746291364e-08 - 4.0941132820466911046e-923j)  +/-  (1.42e-87, 1.29e-211j)
| (0.0055259021546119642176 - 1.4907291338596151586e-919j)  +/-  (6.65e-82, 6.04e-206j)
| (1.93278130276958879e-11 + 3.1408676908946853531e-924j)  +/-  (6.17e-92, 5.61e-216j)
| (4.6959581333746291364e-08 - 7.3325539804289644206e-922j)  +/-  (2.18e-90, 1.98e-214j)
| (1.3971283600988779725e-13 + 6.1050325738614109054e-927j)  +/-  (2.03e-92, 1.84e-216j)
| (4.0158250719394416354e-16 + 1.3746771596115177156e-927j)  +/-  (8.05e-95, 7.32e-219j)
| (8.9985393354514834234e-07 + 4.8546872661997367343e-921j)  +/-  (5.02e-90, 4.56e-214j)
| (0.076619335328470511968 + 1.7883047006808143522e-918j)  +/-  (1.79e-80, 1.62e-204j)
| (2.147662883442546077e-05 + 9.2595441796046571913e-921j)  +/-  (1.36e-88, 1.24e-212j)
| (4.1441005031928805136e-06 - 4.0015729699283036385e-921j)  +/-  (9.29e-89, 8.44e-213j)
| (0.12395995385809593359 - 3.847849733081142546e-918j)  +/-  (5.64e-83, 5.12e-207j)
| (2.147662883442546077e-05 + 4.8293186247993260692e-920j)  +/-  (1.14e-90, 1.03e-214j)
| (0.017197000418961522298 + 4.0680220679042583667e-919j)  +/-  (4.38e-86, 3.97e-210j)
| (0.039685772651746155269 - 9.4353864848469025708e-919j)  +/-  (5.32e-85, 4.83e-209j)
| (4.1441005031928805136e-06 - 2.5368284170695832832e-920j)  +/-  (5.72e-91, 5.2e-215j)
| (0.15538166841428428759 + 4.9001411041085731579e-918j)  +/-  (3.28e-86, 2.98e-210j)
| (0.0012466046174997762851 + 1.6061191358962904554e-919j)  +/-  (1.2e-90, 1.08e-214j)
| (0.0012466046174997762851 + 5.165210901282702333e-920j)  +/-  (6.66e-90, 6.11e-214j)
| (0.12395995385809593359 - 2.9293739515521126411e-918j)  +/-  (4.15e-87, 3.77e-211j)
| (0.00019728639521785036136 - 7.6614144942358271655e-920j)  +/-  (6e-91, 5.5e-215j)
| (0.039685772651746155269 - 1.6679849434699056803e-918j)  +/-  (2.96e-89, 2.83e-213j)
| (0.076619335328470511968 + 2.7200594082514803218e-918j)  +/-  (9.35e-89, 9.24e-213j)
| (0.00019728639521785036136 - 1.9226216769282934582e-920j)  +/-  (3.02e-91, 2.88e-215j)
| (0.1603198146031904401 - 5.1960632237532183739e-918j)  +/-  (8.8e-89, 9.01e-213j)
| (0.15538166841428428759 + 4.2963178058930846392e-918j)  +/-  (5.36e-89, 5.92e-213j)
| (0.0055259021546119642176 - 3.7397877764358789563e-919j)  +/-  (1.05e-90, 8.33e-215j)
