Starting with polynomial:
P : 2*t
Extension levels are: 1 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^31 - 465*t^29 + 94395/2*t^27 - 11044215/4*t^25 + 828316125/8*t^23 - 41912795925/16*t^21 + 1466947857375/32*t^19 - 35835440515875/64*t^17 + 609202488769875/128*t^15 - 7107362368981875/256*t^13 + 55437426478058625/512*t^11 - 277187132390293125/1024*t^9 + 831561397170879375/2048*t^7 - 1343291487737574375/4096*t^5 + 959493919812553125/8192*t^3 - 191898783962510625/16384*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:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-1.5938858604721398261 - 3.4659732976039180887e-740j)  +/-  (5.63e-251, 5.63e-251j)
| (-6.2750787049428601427 + 1.2441027941534292447e-736j)  +/-  (8.65e-249, 8.65e-249j)
| (-6.9956801237185402753 + 4.3632686865598102283e-741j)  +/-  (1.1e-249, 1.1e-249j)
| (3.7007434032314694224 - 1.1185845632261072619e-739j)  +/-  (3.64e-248, 3.64e-248j)
| (6.2750787049428601427 - 2.3779493391276620644e-749j)  +/-  (8.49e-249, 8.49e-249j)
| (6.9956801237185402753 - 4.8814714058187750648e-750j)  +/-  (1.18e-249, 1.18e-249j)
| (-4.6315595063128599421 + 3.3412681043754612314e-751j)  +/-  (6.26e-248, 6.26e-248j)
| (-3.7007434032314694224 - 1.7875815539558787972e-750j)  +/-  (3.71e-248, 3.71e-248j)
| (-2.8316804533902054557 - 1.474387688932250548e-751j)  +/-  (6.01e-249, 6.01e-249j)
| (2.0002585489356389658 + 3.1590402665057913585e-752j)  +/-  (2.88e-250, 2.88e-250j)
| (1.1918269983500464261 - 5.2970114226063765574e-756j)  +/-  (6.28e-252, 6.28e-252j)
| (2.8316804533902054557 - 2.2654144897803077425e-750j)  +/-  (5.03e-249, 5.03e-249j)
| (-2.0002585489356389658 + 9.5611112182091822347e-759j)  +/-  (2.64e-250, 2.64e-250j)
| (7.637753044015781009e-766 - 1.7722585445152649851e-765j)  +/-  (5.98e-764, 5.98e-764j)
| (-4.1562717558181451725 - 4.804038279360449025e-757j)  +/-  (6.66e-248, 6.66e-248j)
| (3.2603207323135408105 + 2.3530861047888105473e-762j)  +/-  (1.52e-248, 1.52e-248j)
| (-0.79287697691530893969 - 4.5329126770867083448e-777j)  +/-  (4.84e-253, 4.84e-253j)
| (-5.6739614446185883296 + 6.5426472286342212235e-771j)  +/-  (2.89e-248, 2.89e-248j)
| (-1.1918269983500464261 - 3.0007010330644433728e-780j)  +/-  (6.46e-252, 6.46e-252j)
| (4.1562717558181451725 + 1.7430723630229269264e-782j)  +/-  (6.37e-248, 6.37e-248j)
| (1.5938858604721398261 + 1.5297012314115047171e-795j)  +/-  (5.13e-251, 5.13e-251j)
| (-5.1335955771123807046 + 1.2901968936004858417e-791j)  +/-  (5.35e-248, 5.35e-248j)
| (-2.4123177054804201052 - 2.1932980580250837429e-795j)  +/-  (1.69e-249, 1.69e-249j)
| (-3.2603207323135408105 + 1.8266754488438140173e-795j)  +/-  (1.64e-248, 1.64e-248j)
| (5.6739614446185883296 + 9.946391926287698561e-805j)  +/-  (3.29e-248, 3.29e-248j)
| (4.6315595063128599421 - 3.4058018784145557219e-831j)  +/-  (6.02e-248, 6.02e-248j)
| (5.1335955771123807046 - 3.4413487571078387205e-860j)  +/-  (4.88e-248, 4.88e-248j)
| (0.79287697691530893969 + 6.1596333725149344883e-870j)  +/-  (5.84e-253, 5.84e-253j)
| (0.39594273647142311095 - 1.2908535868962240251e-869j)  +/-  (4.53e-254, 4.53e-254j)
| (-0.39594273647142311095 + 1.6307040889621821075e-869j)  +/-  (4.53e-254, 4.53e-254j)
| (2.4123177054804201052 - 8.0147298558506205556e-869j)  +/-  (1.33e-249, 1.33e-249j)
-------------------------------------------------
The weights are:
| (0.017967875843441640652 - 9.9411581366286706713e-742j)  +/-  (8e-79, 1.27e-203j)
| (2.8833523678578342821e-18 + 1.6773502970789214955e-750j)  +/-  (5.73e-97, 9.11e-222j)
| (2.6059738548930083167e-22 - 1.3789404130342981658e-752j)  +/-  (2.02e-98, 3.22e-223j)
| (2.8456100881628338026e-07 + 5.8587149574649500097e-745j)  +/-  (3.41e-92, 5.42e-217j)
| (2.8833523678578342821e-18 - 9.6316001461838503024e-751j)  +/-  (5.13e-99, 8.14e-224j)
| (2.6059738548930083167e-22 + 8.4388692800341422212e-753j)  +/-  (1.87e-100, 2.97e-225j)
| (1.3272514835897104702e-10 - 1.7539106918205012629e-746j)  +/-  (1.05e-95, 1.67e-220j)
| (2.8456100881628338026e-07 - 1.1720649058056513752e-744j)  +/-  (1.11e-93, 1.76e-218j)
| (7.8716240696022419012e-05 - 3.3220493683185965763e-743j)  +/-  (2.03e-91, 3.23e-216j)
| (0.0042217177672707051766 + 8.62673548688325243e-743j)  +/-  (2.27e-89, 3.61e-214j)
| (0.054567258894474982276 + 3.9513502448209334732e-742j)  +/-  (5.3e-85, 8.42e-210j)
| (7.8716240696022419012e-05 + 9.92297703078929634e-744j)  +/-  (1.07e-92, 1.71e-217j)
| (0.0042217177672707051766 - 7.4216038631931637111e-742j)  +/-  (2.71e-89, 4.3e-214j)
| (0.2232941387424068185 - 1.3849872088973091531e-741j)  +/-  (1.33e-86, 2.11e-211j)
| (8.2439316191197409886e-09 + 1.6394467233446380993e-745j)  +/-  (3.41e-95, 5.42e-220j)
| (5.9232023176863260452e-06 - 2.6590250332082429301e-744j)  +/-  (1.06e-94, 1.68e-219j)
| (0.11968310969585459495 - 2.0111429687273345154e-741j)  +/-  (1.03e-87, 1.64e-212j)
| (3.3284683241484067845e-15 - 6.5347344256383227194e-749j)  +/-  (3.18e-99, 5.05e-224j)
| (0.054567258894474982276 + 2.7021321404217695561e-741j)  +/-  (7.09e-89, 1.13e-213j)
| (8.2439316191197409886e-09 - 6.1464986227087514918e-746j)  +/-  (4.23e-98, 6.71e-223j)
| (0.017967875843441640652 - 1.9915237249168523739e-742j)  +/-  (1.14e-91, 1.81e-216j)
| (1.0496033623113593945e-12 + 1.3379485249928988531e-747j)  +/-  (4.65e-98, 7.38e-223j)
| (0.00069603127137929193123 + 1.4950723495079886859e-742j)  +/-  (3.63e-93, 5.77e-218j)
| (5.9232023176863260452e-06 + 6.7645219249035714167e-744j)  +/-  (1.25e-94, 1.98e-219j)
| (3.3284683241484067845e-15 + 3.5134271367794421359e-749j)  +/-  (9.49e-103, 1.51e-227j)
| (1.3272514835897104702e-10 + 7.8588950558628760947e-747j)  +/-  (7.06e-101, 1.12e-225j)
| (1.0496033623113593945e-12 - 6.6482821134129125007e-748j)  +/-  (6.23e-102, 9.88e-227j)
| (0.11968310969585459495 - 6.8050051966353103617e-742j)  +/-  (3.42e-96, 5.29e-221j)
| (0.19113200477464314855 + 1.0286421052108221272e-741j)  +/-  (4.38e-96, 6.67e-221j)
| (0.19113200477464314855 + 1.701876686505825972e-741j)  +/-  (3.3e-96, 4.64e-221j)
| (0.00069603127137929193123 - 3.1816506597664062663e-743j)  +/-  (4.5e-98, 8.24e-223j)
