Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 30
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^34 - 4542188879693093336/686534065894227*t^32 + 3139335470420148981144/2974980952208317*t^30 - 271991763923113816217540/2974980952208317*t^28 + 14653092749850591024550590/2974980952208317*t^26 - 40396579460771031195867225/228844688631409*t^24 + 1997346214105168100431781475/457689377262818*t^22 - 69379739317743358814936512425/915378754525636*t^20 + 425860955370971355403250861625/457689377262818*t^18 - 14725783633622623307899636762125/1830757509051272*t^16 + 353893639867157573599983140314125/7323030036205088*t^14 - 2886578219842312604205524838285375/14646060072410176*t^12 + 15402614513447053825219864523071125/29292120144820352*t^10 - 50820450670033868440618845998529375/58584240289640704*t^8 + 94934265573375534203126258585180625/117168480579281408*t^6 - 86513577793018379986418608001011875/234336961158562816*t^4 + 57284128499247205673336055183414375/937347844634251264*t^2 - 2846913802557759570759470087461875/1874695689268502528
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   32 out of 34
Indefinite weights: 2 out of 34
Negative weights:   0 out of 34
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (13.397379575149501589 - 4.5230801890512554333e-408j)  +/-  (4.33e-124, 4.33e-124j)
| (-13.397379575149501589 + 9.2950188133371088668e-409j)  +/-  (3.95e-124, 3.95e-124j)
| (6.9862896483655426271 + 7.2178694346707673995e-405j)  +/-  (2.11e-121, 2.11e-121j)
| (4.6400172344676556936 + 8.7863557196138237719e-404j)  +/-  (7.74e-120, 7.74e-120j)
| (5.6741059393863508525 - 2.9065181245579953895e-411j)  +/-  (3.64e-120, 3.64e-120j)
| (4.1690618540258434828 - 3.2493329273139617683e-412j)  +/-  (7.35e-120, 7.35e-120j)
| (-6.9862896483655426271 + 3.100918567825010106e-422j)  +/-  (1.91e-121, 1.91e-121j)
| (-3.7182110212276068206 - 2.1907635772349467622e-421j)  +/-  (4.75e-120, 4.75e-120j)
| (6.2708296783085712044 + 5.4021647255342741793e-421j)  +/-  (1.26e-120, 1.26e-120j)
| (5.1378961519209729923 + 4.3343865638493871908e-424j)  +/-  (7.62e-120, 7.62e-120j)
| (-5.1378961519209729923 + 1.7078030016084390267e-428j)  +/-  (7.08e-120, 7.08e-120j)
| (3.7182110212276068206 + 6.4636115099868411007e-437j)  +/-  (4.41e-120, 4.41e-120j)
| (-5.6741059393863508525 + 5.2932007150332757914e-450j)  +/-  (4e-120, 4e-120j)
| (-3.2830117856754832816 + 9.6084095604087225788e-451j)  +/-  (1.9e-120, 1.9e-120j)
| (3.2830117856754832816 + 1.218090739099105791e-450j)  +/-  (2.1e-120, 2.1e-120j)
| (0.88868764156389208198 - 7.4027212798063434359e-461j)  +/-  (1.18e-124, 1.18e-124j)
| (-4.6400172344676556936 + 3.181237384148961234e-456j)  +/-  (8.61e-120, 8.61e-120j)
| (-6.2708296783085712044 + 4.7729548964304899603e-459j)  +/-  (1.29e-120, 1.29e-120j)
| (-1.2647304744914514339 + 1.3183910681070018521e-462j)  +/-  (1.19e-123, 1.19e-123j)
| (-4.1690618540258434828 + 6.8528136396407290125e-460j)  +/-  (7.72e-120, 7.72e-120j)
| (2.8604088483096278713 + 6.2281215423911593334e-460j)  +/-  (7.06e-121, 7.06e-121j)
| (0.52464762327529031788 + 5.4509781865063466156e-471j)  +/-  (1.17e-125, 1.17e-125j)
| (-2.8604088483096278713 - 4.2448276326498446694e-466j)  +/-  (6.98e-121, 6.98e-121j)
| (-2.0452629112581039048 - 4.2523081587605563667e-467j)  +/-  (4.7e-122, 4.7e-122j)
| (-1.6506801238857845559 - 2.7012736188548504327e-466j)  +/-  (8.95e-123, 8.95e-123j)
| (2.4482853030240403573 + 9.4145666786123341781e-467j)  +/-  (1.97e-121, 1.97e-121j)
| (-2.4482853030240403573 - 4.1820767988846144822e-470j)  +/-  (1.9e-121, 1.9e-121j)
| (2.0452629112581039048 - 5.2120545224838845259e-472j)  +/-  (4.59e-122, 4.59e-122j)
| (-0.52464762327529031788 + 5.0976986398561503643e-477j)  +/-  (1.17e-125, 1.17e-125j)
| (-0.17294424547674053872 + 9.8194213133900004392e-476j)  +/-  (5.39e-127, 5.39e-127j)
| (-0.88868764156389208198 - 1.2651217018080612252e-474j)  +/-  (1.1e-124, 1.1e-124j)
| (1.6506801238857845559 - 1.8555732444839942054e-473j)  +/-  (8.02e-123, 8.02e-123j)
| (1.2647304744914514339 + 1.1604518352388979569e-472j)  +/-  (1.17e-123, 1.17e-123j)
| (0.17294424547674053872 - 1.7373054845049783093e-476j)  +/-  (9.35e-127, 9.35e-127j)
-------------------------------------------------
The weights are:
| (3.6033334012823187704e-45 - 2.6547153442595621328e-431j)  +/-  (4.63e-43, 7.11e-103j)
| (3.6033334012823187704e-45 - 1.2888945414786019684e-431j)  +/-  (1.66e-43, 2.55e-103j)
| (2.9504187551881139157e-22 + 5.2350903889101908373e-420j)  +/-  (4.27e-34, 6.57e-94j)
| (1.2165270530400172516e-10 - 5.1496414969186496584e-413j)  +/-  (4.12e-29, 6.33e-89j)
| (3.2981905953020591084e-15 + 4.5869539768420680623e-416j)  +/-  (7.88e-32, 1.21e-91j)
| (7.3398190148629160359e-09 + 1.9278172604050848159e-412j)  +/-  (2.23e-28, 3.42e-88j)
| (2.9504187551881139157e-22 + 1.0564821206206960777e-420j)  +/-  (5.12e-38, 7.87e-98j)
| (2.4722851157261270397e-07 + 6.9493482322220615844e-413j)  +/-  (1.86e-30, 2.86e-90j)
| (3.0193716617947713301e-18 - 8.1812261875188522467e-418j)  +/-  (1.34e-33, 2.06e-93j)
| (9.9626139428145311821e-13 - 1.7886160939348964806e-414j)  +/-  (6e-31, 9.23e-91j)
| (9.9626139428145311821e-13 - 9.1074075595223803095e-416j)  +/-  (4.36e-35, 6.7e-95j)
| (2.4722851157261270397e-07 - 6.3011329717630230857e-412j)  +/-  (1.65e-29, 2.53e-89j)
| (3.2981905953020591084e-15 + 4.5988578707696286126e-417j)  +/-  (2.22e-36, 3.41e-96j)
| (5.0403133149294789422e-06 - 3.6836137883262626256e-412j)  +/-  (1.27e-31, 1.95e-91j)
| (5.0403133149294789422e-06 + 2.1507192385274206817e-411j)  +/-  (2.5e-30, 3.85e-90j)
| (0.094863340857176337189 + 2.729485077679455918e-409j)  +/-  (1.53e-27, 2.36e-87j)
| (1.2165270530400172516e-10 + 1.1518105066711945218e-414j)  +/-  (1.28e-34, 1.97e-94j)
| (3.0193716617947713301e-18 - 1.2228246674939845472e-418j)  +/-  (2.97e-38, 4.57e-98j)
| (0.043453578522491344138 + 9.6679886765367422881e-410j)  +/-  (1.13e-27, 1.74e-87j)
| (7.3398190148629160359e-09 - 1.0306593642214914378e-413j)  +/-  (6.6e-34, 1.01e-93j)
| (6.5806501951966052737e-05 - 6.6691748111970399589e-411j)  +/-  (5.54e-33, 8.51e-93j)
| (0.15317237511522942352 - 3.7873381956942414339e-409j)  +/-  (3.99e-28, 6.12e-88j)
| (6.5806501951966052737e-05 + 1.5823794381446865558e-411j)  +/-  (1.68e-32, 2.59e-92j)
| (0.003431115176272817064 + 1.6942589016313231897e-410j)  +/-  (9.13e-32, 1.4e-91j)
| (0.014440183793204234257 - 4.3568462334322013798e-410j)  +/-  (2.82e-31, 4.33e-91j)
| (0.000573115577186552944 + 1.8227971508456266549e-410j)  +/-  (2.78e-33, 4.28e-93j)
| (0.000573115577186552944 - 5.6361630494434442514e-411j)  +/-  (1.79e-32, 2.75e-92j)
| (0.003431115176272817064 - 4.3651897664886087431e-410j)  +/-  (3.58e-33, 5.49e-93j)
| (0.15317237511522942352 + 3.0178718411214805117e-409j)  +/-  (1.14e-31, 1.77e-91j)
| (0.18999518945218953997 - 4.0536232547867399758e-409j)  +/-  (9.21e-32, 1.42e-91j)
| (0.094863340857176337189 - 1.8520066661829397487e-409j)  +/-  (5.49e-32, 8.52e-92j)
| (0.014440183793204234257 + 9.1684541943087776424e-410j)  +/-  (2.56e-33, 3.94e-93j)
| (0.043453578522491344138 - 1.6913239353431691701e-409j)  +/-  (5.38e-33, 8.21e-93j)
| (0.18999518945218953997 + 4.3674980409220350393e-409j)  +/-  (2.23e-32, 3.42e-92j)
