Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 6 26
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^35 - 290697708258522989004080931821/599634363318125150367149292*t^33 + 3765175490117101671802713294925/36341476564734857598009048*t^31 - 5163604061077454135245186661266739/399756242212083433578099528*t^29 + 1256805400737228573606089585726811031/1199268726636250300734298584*t^27 - 2596188494765740681609590180974264125/44417360245787048175344392*t^25 + 102526940774678510281832126147751403275/44417360245787048175344392*t^23 - 264506466412973194947735213321176239525/4037941840526095288667672*t^21 + 13310989224423175302394787916432742725/9921233023405639529896*t^19 - 79724345682880297261467398447163295305975/4037941840526095288667672*t^17 + 831694491688574974955376740619163680561375/4037941840526095288667672*t^15 - 6006479197812439372482655158331641183061875/4037941840526095288667672*t^13 + 2631069359300418656618132235241130357742375/367085621866008662606152*t^11 - 8003658380864455962810141255411397948065375/367085621866008662606152*t^9 + 155676040108256963714564075056674000041554875/4037941840526095288667672*t^7 - 141080780245798380617120080422583950881784375/4037941840526095288667672*t^5 + 53751834892663314539541725817696059768255625/4037941840526095288667672*t^3 - 6038866703595855320517922290826257435001875/4037941840526095288667672*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:
| (-4.1177241122665281454 + 7.5330135417673856322e-975j)  +/-  (1.81e-246, 1.81e-246j)
| (8.0277645155482722887 + 1.2315066566808641532e-983j)  +/-  (1.31e-247, 1.31e-247j)
| (9.8967295584200285873 - 2.3977884640018155366e-990j)  +/-  (4.34e-249, 4.34e-249j)
| (8.8778121614584294694 - 5.9376420766789067345e-994j)  +/-  (3.82e-248, 3.82e-248j)
| (-8.8778121614584294694 - 4.6666510100629285712e-995j)  +/-  (3.49e-248, 3.49e-248j)
| (-7.2634562219137210033 + 2.5928575183831148299e-993j)  +/-  (3.12e-247, 3.12e-247j)
| (1.7320508075688772935 - 4.0590255060251727804e-997j)  +/-  (3.82e-251, 3.82e-251j)
| (-5.2309986748047412569 + 1.0515413668333888832e-993j)  +/-  (5.11e-247, 5.11e-247j)
| (-9.8967295584200285873 + 2.5915056434318754427e-995j)  +/-  (4.62e-249, 4.62e-249j)
| (4.5832178550799577262 - 4.5949769641730717306e-991j)  +/-  (8.18e-247, 8.18e-247j)
| (-5.8794563174935402792 - 5.649489353502917766e-997j)  +/-  (5.31e-247, 5.31e-247j)
| (-4.5832178550799577262 - 1.5657610440207356721e-996j)  +/-  (7.34e-247, 7.34e-247j)
| (-6.5529890884439704496 - 6.3217085582267685645e-998j)  +/-  (4.85e-247, 4.85e-247j)
| (-3.4470934073717645935 + 9.8377099862242518473e-999j)  +/-  (2.97e-248, 2.97e-248j)
| (6.5529890884439704496 - 2.9462250594073896039e-996j)  +/-  (4.91e-247, 4.91e-247j)
| (7.2634562219137210033 - 1.5470888359838114562e-1004j)  +/-  (3.46e-247, 3.46e-247j)
| (5.8794563174935402792 - 2.6758637972781664572e-1020j)  +/-  (4.91e-247, 4.91e-247j)
| (4.1177241122665281454 - 2.7820824640949360045e-1034j)  +/-  (1.68e-246, 1.68e-246j)
| (-1.1951357186449846156 - 4.9847373456412698596e-1062j)  +/-  (5.2e-252, 5.2e-252j)
| (-2.2902796089096094026 - 7.3161591623340884516e-1059j)  +/-  (3.5e-250, 3.5e-250j)
| (2.2902796089096094026 + 1.085667372026191871e-1057j)  +/-  (3.53e-250, 3.53e-250j)
| (5.2309986748047412569 + 2.5969069459095773423e-1057j)  +/-  (5.02e-247, 5.02e-247j)
| (-8.0277645155482722887 - 6.528992152505635512e-1069j)  +/-  (1.26e-247, 1.26e-247j)
| (-0.43274138130451967893 - 1.5341191262881697222e-1073j)  +/-  (1.13e-253, 1.13e-253j)
| (0.43274138130451967893 + 2.1907152260653400874e-1073j)  +/-  (1.06e-253, 1.06e-253j)
| (3.4470934073717645935 + 2.8554675938823273855e-1066j)  +/-  (3.29e-248, 3.29e-248j)
| (0.74109534999454084186 + 3.4221363340250044406e-1085j)  +/-  (7.49e-253, 7.49e-253j)
| (2.8612795760570581173 + 2.3708479871114018682e-1079j)  +/-  (3.2e-249, 3.2e-249j)
| (1.119772254851495693e-1092 - 7.6747859920630545481e-1093j)  +/-  (4.75e-1091, 4.75e-1091j)
| (-1.7320508075688772935 - 3.0670595243108739953e-1089j)  +/-  (4.17e-251, 4.17e-251j)
| (-2.8612795760570581173 - 2.1567043903197969464e-1090j)  +/-  (3.42e-249, 3.42e-249j)
| (4.1849560176727318607 - 1.4192349850899720717e-1092j)  +/-  (2.26e-246, 2.26e-246j)
| (1.1951357186449846156 + 2.7036408526222168434e-1103j)  +/-  (4.73e-252, 4.73e-252j)
| (-4.1849560176727318607 - 3.3458323700843333349e-1100j)  +/-  (2.08e-246, 2.08e-246j)
| (-0.74109534999454084186 + 1.8415887902817401367e-1111j)  +/-  (7.49e-253, 7.49e-253j)
-------------------------------------------------
The weights are:
| (0.00013419580653569417939 - 1.3401670186916649965e-977j)  +/-  (8.55e-84, 6.69e-205j)
| (3.2344547438137483459e-15 - 1.7273967318349189165e-987j)  +/-  (5.79e-94, 4.53e-215j)
| (2.5206930227669382445e-22 - 1.5943866317920537502e-991j)  +/-  (1.74e-97, 1.36e-218j)
| (2.7945234817478016139e-18 + 2.9600953846057427954e-989j)  +/-  (1.27e-95, 9.95e-217j)
| (2.7945234817478016139e-18 - 8.0813687788729674538e-989j)  +/-  (4.97e-98, 3.89e-219j)
| (1.0239418363555538088e-12 - 1.9396027581499989437e-985j)  +/-  (2.49e-95, 1.95e-216j)
| (0.04900738654460969911 + 1.0068618183062344931e-978j)  +/-  (1.3e-78, 1.01e-199j)
| (2.9200953023317313234e-07 + 2.1195960527088659306e-981j)  +/-  (2e-91, 1.56e-212j)
| (2.5206930227669382445e-22 + 3.8664884110099954691e-991j)  +/-  (2.36e-100, 1.85e-221j)
| (7.5952910672124218751e-06 + 5.8832633329055025745e-981j)  +/-  (3.73e-92, 2.92e-213j)
| (8.1942839338835597637e-09 - 9.9703221492297441676e-983j)  +/-  (3.5e-93, 2.73e-214j)
| (7.5952910672124218751e-06 - 1.0996911049456567949e-979j)  +/-  (9.25e-91, 7.24e-212j)
| (1.3031218253409162963e-10 + 4.848688063920807499e-984j)  +/-  (1.23e-94, 9.6e-216j)
| (0.00062595633386444252 - 5.7686986430554287952e-979j)  +/-  (2.7e-89, 2.11e-210j)
| (1.3031218253409162963e-10 - 1.1065652314463561692e-984j)  +/-  (2.31e-98, 1.8e-219j)
| (1.0239418363555538088e-12 + 5.3610174843847243841e-986j)  +/-  (2.39e-99, 1.87e-220j)
| (8.1942839338835597637e-09 + 1.7569991609491441762e-983j)  +/-  (9.51e-98, 7.43e-219j)
| (0.00013419580653569417939 + 1.227497035163670592e-979j)  +/-  (1.61e-95, 1.26e-216j)
| (0.10079998887025106139 - 6.0007444494235129715e-978j)  +/-  (4.4e-88, 3.47e-209j)
| (0.016362625292532630859 - 1.2069451679656582409e-978j)  +/-  (3.57e-92, 2.81e-213j)
| (0.016362625292532630859 - 3.4419850690273102435e-979j)  +/-  (7.04e-93, 5.55e-214j)
| (2.9200953023317313234e-07 - 2.5240799434291178026e-982j)  +/-  (1.59e-97, 1.25e-218j)
| (3.2344547438137483459e-15 + 5.3656932399922474243e-987j)  +/-  (2.14e-102, 1.69e-223j)
| (0.12624633923209595158 - 1.8862684703071556633e-977j)  +/-  (1.8e-90, 1.42e-211j)
| (0.12624633923209595158 - 1.527506746037832716e-977j)  +/-  (8.95e-91, 7.09e-212j)
| (0.00062595633386444252 - 5.1140247960857735069e-980j)  +/-  (1.13e-95, 8.93e-217j)
| (0.10824852053183729943 + 1.0309635750981717846e-977j)  +/-  (2e-91, 1.59e-212j)
| (0.003842428125723104143 + 1.2526496067921374487e-979j)  +/-  (5.45e-95, 4.33e-216j)
| (0.1895932991656172421 + 1.5858638364856555768e-977j)  +/-  (1.6e-91, 1.28e-212j)
| (0.04900738654460969911 + 2.4688690613514184501e-978j)  +/-  (6.34e-94, 5.06e-215j)
| (0.003842428125723104143 + 6.9579245036419440281e-979j)  +/-  (7.83e-96, 6.22e-217j)
| (-7.1985946479245359385e-05 - 1.1184043222332634115e-979j)  +/-  (7e-96, 5.41e-217j)
| (0.10079998887025106139 - 3.3009916766391525793e-978j)  +/-  (5.13e-94, 3.86e-215j)
| (-7.1985946479245359385e-05 + 1.381152785616168598e-977j)  +/-  (3.41e-96, 2.79e-217j)
| (0.10824852053183729943 + 1.4835109916543062328e-977j)  +/-  (8.68e-94, 5.95e-215j)
