Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 29
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^33 - 24829734601382932392/6594497324768119*t^31 + 63870994450621183605384/164862433119202975*t^29 - 3794935047615545395694202/164862433119202975*t^27 + 11143965705436400220238176/12681725624554075*t^25 - 23027323480469799204456729/1014538049964326*t^23 + 412904248811014011199410339/1014538049964326*t^21 - 20767152059304545103623676801/4058152199857304*t^19 + 182844481668627811772072081133/4058152199857304*t^17 - 4456613667780268932301098239043/16232608799429216*t^15 + 18373590097838079639705836580915/16232608799429216*t^13 - 197700635846725100154623754431235/64930435197716864*t^11 + 20511033998251917829099633257015/4058152199857304*t^9 - 1232193814059293061364710130163355/259721740790867456*t^7 + 564809432599814013540477808920045/259721740790867456*t^5 - 380249454835700665384917576888675/1038886963163469824*t^3 + 21319584031338563129540929715475/2077773926326939648*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: 1
  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:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (2.8657722725515873146 + 2.5809701882275031179e-412j)  +/-  (6.11e-121, 6.11e-121j)
| (5.6914140105189521994 - 8.4196698801034406666e-413j)  +/-  (2.43e-120, 2.43e-120j)
| (-5.6914140105189521994 - 2.1339093070587300627e-416j)  +/-  (2.47e-120, 2.47e-120j)
| (-3.727192228774153311 - 1.3604271781257214955e-416j)  +/-  (3.57e-120, 3.57e-120j)
| (-6.2908846922229547779 + 9.446917150981419037e-417j)  +/-  (7.75e-121, 7.75e-121j)
| (5.1528479298569710382 + 1.3502715635986248118e-414j)  +/-  (5.07e-120, 5.07e-120j)
| (6.2908846922229547779 - 4.9855185164447770191e-423j)  +/-  (7.99e-121, 7.99e-121j)
| (-7.0098779648280552845 + 1.4506390406565917122e-428j)  +/-  (1.04e-121, 1.04e-121j)
| (-2.0470294314687861555 + 3.5448149883844259077e-428j)  +/-  (4.32e-122, 4.32e-122j)
| (4.6528470857682211316 - 3.4123819072914772119e-425j)  +/-  (6.22e-120, 6.22e-120j)
| (7.0098779648280552845 + 1.1935122103869632817e-441j)  +/-  (1.04e-121, 1.04e-121j)
| (-4.179919687668116293 + 4.9229417151429617163e-441j)  +/-  (5.27e-120, 5.27e-120j)
| (-4.6528470857682211316 + 1.9464986760254536391e-442j)  +/-  (5.74e-120, 5.74e-120j)
| (-0.18613403293935899053 + 1.7006623203436426962e-447j)  +/-  (1.04e-126, 1.04e-126j)
| (-5.1528479298569710382 - 1.5209426563265573239e-442j)  +/-  (4.78e-120, 4.78e-120j)
| (3.727192228774153311 + 2.4973957686777565786e-440j)  +/-  (3.42e-120, 3.42e-120j)
| (1.2631883897240742547 - 1.4791180922981658456e-461j)  +/-  (1.12e-123, 1.12e-123j)
| (-2.8657722725515873146 + 3.6371322248869668699e-459j)  +/-  (6.17e-121, 6.17e-121j)
| (0.18613403293935899053 + 1.1452401091862341859e-464j)  +/-  (1.04e-126, 1.04e-126j)
| (-3.2901719395588685704 - 4.9496954696615621102e-459j)  +/-  (1.67e-120, 1.67e-120j)
| (4.179919687668116293 + 1.2408174886773647892e-459j)  +/-  (5.55e-120, 5.55e-120j)
| (0.88647945074449508661 + 5.3189832388402999359e-474j)  +/-  (1.22e-124, 1.22e-124j)
| (3.2901719395588685704 - 2.3919133587979650334e-471j)  +/-  (1.65e-120, 1.65e-120j)
| (-0.52464762327529031788 - 2.2256156511641658703e-479j)  +/-  (9.72e-126, 9.72e-126j)
| (0.52464762327529031788 + 4.6076836625724874036e-479j)  +/-  (9.72e-126, 9.72e-126j)
| (-2.4518531530101912582 + 1.1017484851556955219e-476j)  +/-  (2e-121, 2e-121j)
| (8.7277676816312852474e-495 - 2.5914096084664728035e-495j)  +/-  (3e-493, 3e-493j)
| (2.4518531530101912582 - 1.2519769371661958108e-475j)  +/-  (1.9e-121, 1.9e-121j)
| (-1.2631883897240742547 + 1.0158685093795889107e-479j)  +/-  (1.1e-123, 1.1e-123j)
| (-0.88647945074449508661 - 1.2741625003487138262e-480j)  +/-  (1.3e-124, 1.3e-124j)
| (-1.6506801238857845559 + 2.2504962151922121886e-478j)  +/-  (7.6e-123, 7.6e-123j)
| (2.0470294314687861555 + 5.4181940408953910758e-477j)  +/-  (4.53e-122, 4.53e-122j)
| (1.6506801238857845559 - 5.5187937519413332704e-480j)  +/-  (7.09e-123, 7.09e-123j)
-------------------------------------------------
The weights are:
| (6.4090544817749074077e-05 - 5.8501185553355062615e-416j)  +/-  (4.72e-27, 2.15e-86j)
| (2.7213569846252943046e-15 + 9.9653251202552170108e-423j)  +/-  (1e-36, 4.55e-96j)
| (2.7213569846252943046e-15 - 3.2900996007593565966e-423j)  +/-  (1.54e-37, 7.02e-97j)
| (2.3220055816809653738e-07 - 9.0740852747106060333e-419j)  +/-  (1.46e-32, 6.62e-92j)
| (2.3580864473794436155e-18 + 7.4221865823339825659e-425j)  +/-  (5.23e-39, 2.38e-98j)
| (8.5786962369386693607e-13 - 2.6605282555878665316e-421j)  +/-  (8.51e-37, 3.87e-96j)
| (2.3580864473794436155e-18 - 1.9841846314310455275e-424j)  +/-  (1.01e-39, 4.59e-99j)
| (2.131764001173272836e-22 - 5.2786334277353432955e-427j)  +/-  (7.85e-42, 3.57e-101j)
| (0.003421757906150340472 - 4.6518358959569575541e-416j)  +/-  (7.34e-29, 3.34e-88j)
| (1.084350002143718703e-10 + 4.6814364618727884331e-420j)  +/-  (1.52e-36, 6.93e-96j)
| (2.131764001173272836e-22 + 1.2579195511312413964e-426j)  +/-  (7.06e-42, 3.21e-101j)
| (6.7316513204837171923e-09 + 1.1548659877299043762e-419j)  +/-  (2.23e-36, 1.01e-95j)
| (1.084350002143718703e-10 - 1.1126367373515955089e-420j)  +/-  (1.04e-37, 4.72e-97j)
| (0.17217844693323715608 + 1.4453901433195790088e-413j)  +/-  (1.5e-30, 6.83e-90j)
| (8.5786962369386693607e-13 + 7.5876577584753762969e-422j)  +/-  (8.41e-39, 3.83e-98j)
| (2.3220055816809653738e-07 + 6.9439927324424347892e-418j)  +/-  (8.53e-38, 3.88e-97j)
| (0.04376978387650936692 - 1.2074593253678746263e-414j)  +/-  (1.04e-30, 4.72e-90j)
| (6.4090544817749074077e-05 - 2.8861412571302682459e-417j)  +/-  (1.62e-35, 7.37e-95j)
| (0.17217844693323715608 + 1.646189600085848298e-413j)  +/-  (3.53e-31, 1.61e-90j)
| (4.8288351570019947361e-06 + 5.6491361771521964604e-418j)  +/-  (4.64e-36, 2.11e-95j)
| (6.7316513204837171923e-09 - 6.1923258810722115699e-419j)  +/-  (5.42e-39, 2.47e-98j)
| (0.095172622783036758401 + 2.5547171091835225989e-414j)  +/-  (1.82e-32, 8.28e-92j)
| (4.8288351570019947361e-06 - 8.1935682630978654688e-417j)  +/-  (1.05e-37, 4.79e-97j)
| (0.15100124557079286308 - 3.9110414311060803208e-414j)  +/-  (1.21e-32, 5.51e-92j)
| (0.15100124557079286308 - 5.6639655511558935535e-414j)  +/-  (2.48e-32, 1.13e-91j)
| (0.00056567059620787937814 + 1.2449945207244743178e-416j)  +/-  (4.74e-36, 2.15e-95j)
| (0.038635891910920737163 - 2.4073750267711363507e-413j)  +/-  (3.95e-32, 1.79e-91j)
| (0.00056567059620787937814 + 1.5994202561457839081e-415j)  +/-  (5.63e-37, 2.56e-96j)
| (0.04376978387650936692 - 4.6865648629950564657e-415j)  +/-  (7.52e-35, 3.42e-94j)
| (0.095172622783036758401 + 1.3476038903231108252e-414j)  +/-  (2.91e-34, 1.32e-93j)
| (0.01450336795712543389 + 1.5443649488670252889e-415j)  +/-  (1.55e-35, 7.05e-95j)
| (0.003421757906150340472 - 2.7912678851192273292e-415j)  +/-  (2.97e-37, 1.36e-96j)
| (0.01450336795712543389 + 5.7403062230184654424e-415j)  +/-  (9.7e-37, 4.36e-96j)
