Starting with polynomial:
P : t
Extension levels are: 1 6 20
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 1301488437/4381822*t^25 + 329506387725/8763644*t^23 - 163952800339575/61345508*t^21 + 1037180455957125/8763644*t^19 - 30017405619954675/8763644*t^17 + 289699766277482025/4381822*t^15 - 3735739069226884125/4381822*t^13 + 31703548135043932875/4381822*t^11 - 85537131923390647500/2190911*t^9 + 1103512337933439344625/8763644*t^7 - 1910682259733299177125/8763644*t^5 + 1454477359576101485625/8763644*t^3 - 306293411468461291875/8763644*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:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.7998686649362950686 - 2.0057814688263196556e-456j)  +/-  (4.14e-121, 4.14e-121j)
| (-5.0560504680630166662 + 8.4887518196703612471e-456j)  +/-  (4.42e-121, 4.42e-121j)
| (6.6003938101214660308 - 1.8775247109184772362e-462j)  +/-  (2.6e-121, 2.6e-121j)
| (-5.7998686649362950686 - 3.0097725533311843758e-461j)  +/-  (4.06e-121, 4.06e-121j)
| (8.5530293529089886832 + 8.9506658703209879078e-466j)  +/-  (1.69e-122, 1.69e-122j)
| (-7.4895580986385039061 - 4.7243293563464644671e-465j)  +/-  (9.73e-122, 9.73e-122j)
| (3.7504397177257422563 + 6.0129245368875420837e-463j)  +/-  (6.93e-121, 6.93e-121j)
| (-6.6003938101214660308 - 7.5590721178626845135e-470j)  +/-  (2.87e-121, 2.87e-121j)
| (-3.7504397177257422563 + 5.8900082530358255771e-477j)  +/-  (8.67e-121, 8.67e-121j)
| (5.0560504680630166662 + 1.3962963059803776323e-485j)  +/-  (5.26e-121, 5.26e-121j)
| (7.4895580986385039061 - 3.3184156547017336486e-488j)  +/-  (9.57e-122, 9.57e-122j)
| (-8.5530293529089886832 - 4.2320604118198331038e-490j)  +/-  (1.72e-122, 1.72e-122j)
| (-1.1544053947399681272 - 7.6924935346617010602e-491j)  +/-  (4.69e-125, 4.69e-125j)
| (4.3555542742307012392 - 3.333235153364832759e-487j)  +/-  (4.85e-121, 4.85e-121j)
| (1.1544053947399681272 - 4.9657681790856002064e-494j)  +/-  (5.13e-125, 5.13e-125j)
| (-4.3555542742307012392 + 9.8539602072862389941e-490j)  +/-  (4.81e-121, 4.81e-121j)
| (2.3667594107345412886 - 5.2356974137859223673e-498j)  +/-  (6.1e-123, 6.1e-123j)
| (2.9943401400162375974 + 3.0328456230523332104e-498j)  +/-  (4.93e-122, 4.93e-122j)
| (-0.57198427649553482556 + 7.4835917082847410327e-503j)  +/-  (3.74e-126, 3.74e-126j)
| (3.5594438741290223058 - 2.7111277603396536732e-497j)  +/-  (5.91e-121, 5.91e-121j)
| (1.7524492428832058996 + 4.0013222240386049127e-505j)  +/-  (6.28e-124, 6.28e-124j)
| (-1.867380600597457171e-504 + 4.6490117322431829419e-505j)  +/-  (5.2e-503, 5.2e-503j)
| (-3.5594438741290223058 + 6.02750459185025705e-501j)  +/-  (5.9e-121, 5.9e-121j)
| (-2.3667594107345412886 - 1.0400392095047168975e-509j)  +/-  (6.06e-123, 6.06e-123j)
| (-2.9943401400162375974 + 4.8025032540814801563e-515j)  +/-  (5.18e-122, 5.18e-122j)
| (-1.7524492428832058996 - 2.7415547888065219989e-522j)  +/-  (6.13e-124, 6.13e-124j)
| (0.57198427649553482556 + 2.9651336197416005989e-526j)  +/-  (4.11e-126, 4.11e-126j)
-------------------------------------------------
The weights are:
| (1.5211932191571769754e-08 + 6.4159118936439182972e-464j)  +/-  (6.34e-41, 2.1e-100j)
| (8.0886563430968495738e-07 + 2.4130137204084463276e-461j)  +/-  (4.9e-40, 1.63e-99j)
| (1.1579724106364961183e-10 + 4.2427448591196047686e-465j)  +/-  (1.1e-42, 3.66e-102j)
| (1.5211932191571769754e-08 + 6.7997758052908158157e-463j)  +/-  (8.34e-42, 2.77e-101j)
| (6.3508929056755576049e-17 + 7.3748652152919059511e-469j)  +/-  (1.8e-46, 5.98e-106j)
| (2.5088428225441960657e-13 + 3.1975169970047369635e-466j)  +/-  (2.06e-45, 6.84e-105j)
| (0.00013548201932480794815 + 1.0520300912058973373e-460j)  +/-  (2e-39, 6.63e-99j)
| (1.1579724106364961183e-10 - 1.7145682216339327238e-464j)  +/-  (8.24e-44, 2.74e-103j)
| (0.00013548201932480794815 + 9.5128921392047970426e-460j)  +/-  (7.55e-40, 2.5e-99j)
| (8.0886563430968495738e-07 + 1.1997595535583353434e-463j)  +/-  (4.93e-42, 1.64e-101j)
| (2.5088428225441960657e-13 - 8.8925596817388558565e-467j)  +/-  (1e-45, 3.32e-105j)
| (6.3508929056755576049e-17 - 2.2414215839661840437e-468j)  +/-  (4.93e-48, 1.63e-107j)
| (0.12085544844482172293 - 1.6268210744535920159e-459j)  +/-  (7.26e-35, 2.41e-94j)
| (2.0556078807406430869e-05 - 5.4142249640586988936e-462j)  +/-  (2.24e-41, 7.44e-101j)
| (0.12085544844482172293 - 9.7232147344028598107e-460j)  +/-  (4.43e-36, 1.47e-95j)
| (2.0556078807406430869e-05 - 1.1966153645435186611e-460j)  +/-  (3.14e-42, 1.04e-101j)
| (0.015077371440022784028 - 3.1059096216920962508e-460j)  +/-  (7.61e-40, 2.52e-99j)
| (0.0028398025902361611888 + 1.7842881312413379436e-460j)  +/-  (1.02e-40, 3.39e-100j)
| (0.19505668069615854297 + 1.8366891835762244869e-459j)  +/-  (1.04e-38, 3.44e-98j)
| (0.00023112896829255611227 - 1.7099883403158147284e-460j)  +/-  (7.73e-41, 2.56e-100j)
| (0.052086648283233455594 + 5.7416389215309316836e-460j)  +/-  (2.14e-40, 7.1e-100j)
| (0.22739211457097574536 - 1.7701369271133943867e-459j)  +/-  (9.64e-40, 3.2e-99j)
| (0.00023112896829255611227 - 1.2708070012899879922e-459j)  +/-  (9.65e-43, 3.2e-102j)
| (0.015077371440022784028 - 9.6676447969430477818e-460j)  +/-  (6.24e-43, 2.07e-102j)
| (0.0028398025902361611888 + 8.3127890528310738343e-460j)  +/-  (3.29e-43, 1.09e-102j)
| (0.052086648283233455594 + 1.282632710337802491e-459j)  +/-  (1.29e-42, 4.27e-102j)
| (0.19505668069615854297 + 1.4288492098516196365e-459j)  +/-  (3.91e-42, 1.21e-101j)
