Starting with polynomial:
P : 2*t
Extension levels are: 1 12 26
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : 2*t^13 - 78*t^11 + 2145/2*t^9 - 6435*t^7 + 135135/8*t^5 - 135135/8*t^3 + 135135/32*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^39 - 998308440773553/1727893965901*t^37 + 257797121629388445/3455787931802*t^35 - 670600399023694791405/117496789681268*t^33 + 478667987578694698785/1654884361708*t^31 - 2416645470227816281034295/234993579362536*t^29 + 871991597314486710622727595/3289910111075504*t^27 - 33203884869265082250535203375/6579820222151008*t^25 + 235784492644841624045208450375/3289910111075504*t^23 - 156567943914214897471879382625/205619381942219*t^21 + 1193922944497128613044349375875/197889329989504*t^19 - 822635028797626470290220266625/23281097645824*t^17 + 14028622277659932081684225841875/93124390583296*t^15 - 85099063701299068989880463311875/186248781166592*t^13 + 355315925375604072207365302175625/372497562333184*t^11 - 973691552747640765860869148083125/744995124666368*t^9 + 3263757841954301373168344757095625/2979980498665472*t^7 - 2992249040222128651171112083303125/5959960997330944*t^5 + 1230875600141909941353488131903125/11919921994661888*t^3 - 144526707157778177345428818628125/23839843989323776*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:   39 out of 39
Indefinite weights: 0 out of 39
Negative weights:   0 out of 39
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.1013375961786396412 + 1.8326105747726501912e-887j)  +/-  (4.36e-246, 4.36e-246j)
| (6.5965993185583502521 - 3.5483483053273430977e-892j)  +/-  (1.18e-247, 1.18e-247j)
| (-6.5965993185583502521 - 3.419264593403306065e-892j)  +/-  (1.2e-247, 1.2e-247j)
| (-5.4826529566363255452 + 1.4337306244618495352e-889j)  +/-  (1.32e-246, 1.32e-246j)
| (7.3030144449000419082 - 9.8444132930033788553e-894j)  +/-  (1.25e-248, 1.25e-248j)
| (-6.0090448678930447846 + 3.2923953676025149939e-892j)  +/-  (5.19e-247, 5.19e-247j)
| (-4.537137677994161275 + 1.562407454792178057e-889j)  +/-  (3.28e-246, 3.28e-246j)
| (6.0090448678930447846 - 7.89587090566008705e-901j)  +/-  (4.75e-247, 4.75e-247j)
| (-7.3030144449000419082 - 1.6300487298809545322e-901j)  +/-  (1.22e-248, 1.22e-248j)
| (-4.9956418273366616879 - 1.2939234028358489581e-897j)  +/-  (2.47e-246, 2.47e-246j)
| (2.1766382333216371019 + 1.2949777197587605344e-904j)  +/-  (3.23e-248, 3.23e-248j)
| (-1.5368740138097483788 + 3.4924773821026325199e-907j)  +/-  (9.34e-250, 9.34e-250j)
| (-2.5197356856782378834 - 8.7203654713025786255e-902j)  +/-  (1.73e-247, 1.73e-247j)
| (4.9956418273366616879 + 2.2764193267835231769e-910j)  +/-  (2.4e-246, 2.4e-246j)
| (2.8834300582169392514 + 7.79578693865117126e-909j)  +/-  (8.18e-247, 8.18e-247j)
| (5.4826529566363255452 - 1.2625868999770776704e-911j)  +/-  (1.4e-246, 1.4e-246j)
| (1.853107651601512142 - 2.7209692023793354518e-913j)  +/-  (6.43e-249, 6.43e-249j)
| (-1.853107651601512142 - 3.6959086343326228961e-911j)  +/-  (5.81e-249, 5.81e-249j)
| (3.2466089783724099881 - 7.0234932720200076209e-910j)  +/-  (6.42e-246, 6.42e-246j)
| (-2.1766382333216371019 + 2.2479397027996554493e-910j)  +/-  (3.14e-248, 3.14e-248j)
| (3.6873605262774233741 - 1.8240735145697551381e-913j)  +/-  (5.52e-246, 5.52e-246j)
| (3.3752537601454316441 - 3.12813039894329752e-915j)  +/-  (9.75e-246, 9.75e-246j)
| (-3.3752537601454316441 + 1.3083160119520253185e-919j)  +/-  (9.3e-246, 9.3e-246j)
| (-2.8834300582169392514 + 1.9127498233769666542e-946j)  +/-  (8.25e-247, 8.25e-247j)
| (-1.2200550365907484262 + 1.4482185077456871446e-968j)  +/-  (1.23e-250, 1.23e-250j)
| (-4.1013375961786396412 - 8.1601746390447955703e-966j)  +/-  (4.18e-246, 4.18e-246j)
| (4.537137677994161275 + 9.8925355550202752489e-983j)  +/-  (3.78e-246, 3.78e-246j)
| (2.5197356856782378834 + 6.5637504933902858694e-983j)  +/-  (1.64e-247, 1.64e-247j)
| (0.30552184523686539698 + 1.3776634474782583406e-994j)  +/-  (6.32e-254, 6.32e-254j)
| (-0.90807862556293763753 + 3.5976261248285039142e-993j)  +/-  (1.31e-251, 1.31e-251j)
| (-3.2466089783724099881 - 6.3546313492158083435e-990j)  +/-  (6.74e-246, 6.74e-246j)
| (1.2200550365907484262 - 6.0360287841287812757e-1012j)  +/-  (1.25e-250, 1.25e-250j)
| (0.90807862556293763753 + 7.7284007175194194029e-1013j)  +/-  (1.22e-251, 1.22e-251j)
| (-3.6873605262774233741 - 8.4454068987609173679e-1013j)  +/-  (6.05e-246, 6.05e-246j)
| (-0.60576387917106011308 + 6.3174870530128773209e-1023j)  +/-  (9.08e-253, 9.08e-253j)
| (-0.30552184523686539698 - 4.6397200490022597889e-1024j)  +/-  (6.8e-254, 6.8e-254j)
| (-1.7914824344398183277e-1041 + 3.3091996245348564768e-1042j)  +/-  (7.1e-1040, 7.1e-1040j)
| (0.60576387917106011308 - 1.0911364173575429613e-1022j)  +/-  (8.85e-253, 8.85e-253j)
| (1.5368740138097483788 - 4.4251223033973629029e-1020j)  +/-  (9.83e-250, 9.83e-250j)
-------------------------------------------------
The weights are:
| (1.1884272443741244748e-08 - 1.4388098393290033747e-894j)  +/-  (2.19e-84, 3.88e-206j)
| (4.5008488891243231881e-20 - 4.0097998857090881774e-903j)  +/-  (2.52e-92, 4.48e-214j)
| (4.5008488891243231881e-20 + 9.1822907641855356213e-904j)  +/-  (2.97e-93, 5.27e-215j)
| (2.5086742999285877097e-14 + 2.8045731548621037098e-900j)  +/-  (1.12e-90, 1.99e-212j)
| (3.1580233298266404617e-24 + 1.3209874178002481391e-905j)  +/-  (1.21e-95, 2.15e-217j)
| (6.4783247520340071955e-17 - 6.9843423561757260914e-902j)  +/-  (4.72e-92, 8.38e-214j)
| (2.89086932638706746e-10 + 1.8227493012907421228e-897j)  +/-  (4.82e-89, 8.55e-211j)
| (6.4783247520340071955e-17 + 3.79782508181041721e-901j)  +/-  (8.12e-94, 1.44e-215j)
| (3.1580233298266404617e-24 - 3.6567781146813346493e-906j)  +/-  (2.2e-96, 3.9e-218j)
| (3.8585552962993312986e-12 - 7.1224147260800093926e-899j)  +/-  (4.59e-90, 8.14e-212j)
| (0.0016406785980255262493 - 5.1890210678977339031e-892j)  +/-  (9.21e-83, 1.63e-204j)
| (0.01682864675876060769 - 9.1726048356159043873e-892j)  +/-  (1.13e-78, 2.01e-200j)
| (0.00034940706979373584276 + 5.3647417432786522248e-893j)  +/-  (3.01e-84, 5.34e-206j)
| (3.8585552962993312986e-12 + 7.7491598909547088748e-898j)  +/-  (1.23e-92, 2.18e-214j)
| (5.1350292296219335767e-05 - 1.0387667851389079749e-892j)  +/-  (4.71e-87, 8.35e-209j)
| (2.5086742999285877097e-14 - 1.9971029560743265751e-899j)  +/-  (8.8e-94, 1.56e-215j)
| (0.005777209741387757663 + 1.095546762038207638e-891j)  +/-  (1.66e-83, 2.94e-205j)
| (0.005777209741387757663 + 4.163546406586006879e-892j)  +/-  (3.59e-84, 6.37e-206j)
| (4.6339888313855082895e-06 + 9.7740055350692041225e-893j)  +/-  (1.08e-88, 1.92e-210j)
| (0.0016406785980255262493 - 1.6040765355225571846e-892j)  +/-  (1.41e-86, 2.5e-208j)
| (2.8071882207863676135e-07 + 9.4381594525894192198e-894j)  +/-  (1.61e-90, 2.86e-212j)
| (6.995033314055429034e-07 - 6.8265415635617591356e-893j)  +/-  (2.8e-89, 4.96e-211j)
| (6.995033314055429034e-07 - 6.776200235860757614e-894j)  +/-  (1.21e-92, 2.15e-214j)
| (5.1350292296219335767e-05 - 1.8369709457169496611e-893j)  +/-  (2.71e-91, 4.82e-213j)
| (0.040225303341331917178 + 1.7917974353434723827e-891j)  +/-  (2.78e-87, 4.93e-209j)
| (1.1884272443741244748e-08 - 2.8279770889396267659e-896j)  +/-  (6.97e-95, 1.24e-216j)
| (2.89086932638706746e-10 - 3.0322915377061342911e-896j)  +/-  (1.73e-95, 3.06e-217j)
| (0.00034940706979373584276 + 2.2220553592990170385e-892j)  +/-  (4.74e-91, 8.41e-213j)
| (0.15560799119154123475 - 7.1346400211205410396e-891j)  +/-  (3.82e-89, 6.77e-211j)
| (0.075929577910496021752 - 3.1462631532836001459e-891j)  +/-  (2.63e-89, 4.67e-211j)
| (4.6339888313855082895e-06 + 1.159091928764804499e-893j)  +/-  (9.68e-93, 1.72e-214j)
| (0.040225303341331917178 + 3.2964774671866483385e-891j)  +/-  (8.22e-91, 1.46e-212j)
| (0.075929577910496021752 - 4.9219841773142487973e-891j)  +/-  (2.01e-90, 3.57e-212j)
| (2.8071882207863676135e-07 + 5.1755172795662680077e-895j)  +/-  (3.64e-94, 6.47e-216j)
| (0.11696133829293969351 + 4.7745183225878535773e-891j)  +/-  (2.68e-90, 4.75e-212j)
| (0.15560799119154123475 - 6.1509200022999702422e-891j)  +/-  (9.51e-91, 1.69e-212j)
| (0.17324574083039866619 + 6.9680925295145040084e-891j)  +/-  (6.42e-91, 1.14e-212j)
| (0.11696133829293969351 + 6.4176629496453859881e-891j)  +/-  (1.35e-91, 2.48e-213j)
| (0.01682864675876060769 - 2.006429241447676889e-891j)  +/-  (2.25e-92, 3.74e-214j)
