Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 7 18
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^9 - 173/5*t^7 + 1743/5*t^5 - 1113*t^3 + 798*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 23713059798960210194599/80267486778947466790*t^25 + 38490928736959356647640159/1043477328126317068270*t^23 - 2669596356929556607160822889/1043477328126317068270*t^21 + 1251302066060699168832390282579/11478250609389487750970*t^19 - 17120091141427130568943443496242/5739125304694743875485*t^17 + 305729943623714833393266252893961/5739125304694743875485*t^15 - 54678536972190494062088435867835/88294235456842213469*t^13 + 406108271543059496773949642304984/88294235456842213469*t^11 - 337716694675472793580850976022851/16053497355789493358*t^9 + 893850191374390231079302957672731/16053497355789493358*t^7 - 1231431587235049993945122648792933/16053497355789493358*t^5 + 723505001219868112063866791914905/16053497355789493358*t^3 - 56456117968234496017092998491395/8026748677894746679*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:
| (5.8741551179286637647 - 2.3186344033636075867e-268j)  +/-  (2.72e-121, 2.72e-121j)
| (-5.1296283468100778728 + 7.2958764101115075034e-275j)  +/-  (2.68e-121, 2.68e-121j)
| (-5.8741551179286637647 + 3.0017526596717173444e-275j)  +/-  (2.59e-121, 2.59e-121j)
| (6.6777802338765819173 - 5.1377524306840423013e-275j)  +/-  (1.86e-121, 1.86e-121j)
| (-3.1397980296785904718 + 1.9474371700079872288e-278j)  +/-  (2.98e-122, 2.98e-122j)
| (8.6474647718653274221 - 1.0260542373804458879e-279j)  +/-  (1.42e-122, 1.42e-122j)
| (-4.4288667337963182986 - 3.2252706560744905179e-278j)  +/-  (1.54e-121, 1.54e-121j)
| (3.7653170801120690939 - 5.0042512681429803232e-285j)  +/-  (7.47e-122, 7.47e-122j)
| (-1.5210893971982421578 + 2.0398676089216326056e-290j)  +/-  (3.85e-124, 3.85e-124j)
| (7.5730280378398728682 - 1.8458610474383024791e-295j)  +/-  (8.11e-122, 8.11e-122j)
| (-8.6474647718653274221 + 2.1275494053065567882e-300j)  +/-  (1.52e-122, 1.52e-122j)
| (-7.5730280378398728682 + 1.4004422619062950483e-300j)  +/-  (8.6e-122, 8.6e-122j)
| (0.48578750800440925497 + 7.7953637376900243768e-310j)  +/-  (3.33e-126, 3.33e-126j)
| (-2.3240847980372237438e-320 + 7.3121715584504488538e-321j)  +/-  (6.58e-319, 6.58e-319j)
| (5.1296283468100778728 + 5.917992126241737933e-327j)  +/-  (2.52e-121, 2.52e-121j)
| (4.4288667337963182986 + 2.2491159417808284323e-337j)  +/-  (1.59e-121, 1.59e-121j)
| (1 + 2.9803100106223349186e-345j)  +/-  (4.33e-125, 4.33e-125j)
| (-2.5607064282994026938 + 1.1478186311434321494e-352j)  +/-  (9.69e-123, 9.69e-123j)
| (-1 - 1.7371237963121743973e-353j)  +/-  (4.14e-125, 4.14e-125j)
| (2.5607064282994026938 - 2.0420415473423253949e-351j)  +/-  (9.8e-123, 9.8e-123j)
| (3.1397980296785904718 - 7.7445636075341802703e-361j)  +/-  (3e-122, 3e-122j)
| (2.0314545988278380851 - 5.3482757528758301843e-366j)  +/-  (2.3e-123, 2.3e-123j)
| (-6.6777802338765819173 - 1.5342343773508546061e-369j)  +/-  (1.88e-121, 1.88e-121j)
| (-0.48578750800440925497 - 9.3364977071829720161e-373j)  +/-  (3.33e-126, 3.33e-126j)
| (-3.7653170801120690939 + 2.5275601527732907668e-374j)  +/-  (7.9e-122, 7.9e-122j)
| (-2.0314545988278380851 + 5.0216468576528105731e-378j)  +/-  (2.7e-123, 2.7e-123j)
| (1.5210893971982421578 + 4.5359634475906838378e-382j)  +/-  (3.71e-124, 3.71e-124j)
-------------------------------------------------
The weights are:
| (9.8832215076674869394e-09 + 7.8548507048421078725e-276j)  +/-  (4.97e-41, 7.46e-101j)
| (5.5589672450307278045e-07 - 2.3236159751974748563e-276j)  +/-  (6.19e-40, 9.3e-100j)
| (9.8832215076674869394e-09 + 1.9506013460001230081e-277j)  +/-  (1.73e-41, 2.6e-101j)
| (6.9642078277768414493e-11 + 1.6660432363499311618e-277j)  +/-  (3.16e-43, 4.74e-103j)
| (0.0017433044574893640728 + 7.1129688291783644842e-274j)  +/-  (1.96e-36, 2.95e-96j)
| (2.8541324863367743767e-17 + 1.5856704808944207785e-281j)  +/-  (7.04e-47, 1.06e-106j)
| (1.4968037093525062101e-05 + 2.0058787021945466189e-275j)  +/-  (1.1e-39, 1.65e-99j)
| (0.00021481447658721927718 - 6.1175462897969361159e-274j)  +/-  (9.94e-40, 1.49e-99j)
| (0.064616713007727776208 - 1.9418459859606300463e-272j)  +/-  (1.7e-32, 2.55e-92j)
| (1.3492009003117934119e-13 - 2.4733565476703086991e-279j)  +/-  (3.48e-45, 5.23e-105j)
| (2.8541324863367743767e-17 - 3.0282983815494410324e-282j)  +/-  (2.86e-48, 4.3e-108j)
| (1.3492009003117934119e-13 + 3.124780890144587656e-280j)  +/-  (1.52e-46, 2.29e-106j)
| (0.17740053584341527688 - 6.462813072607452393e-272j)  +/-  (1.02e-34, 1.54e-94j)
| (0.19034964838266794687 + 6.8142713720812213093e-272j)  +/-  (8.02e-35, 1.2e-94j)
| (5.5589672450307278045e-07 - 3.4343854575091451948e-275j)  +/-  (5.05e-43, 7.59e-103j)
| (1.4968037093525062101e-05 + 1.4299618766085492416e-274j)  +/-  (2.7e-42, 4.05e-102j)
| (0.12659263371237718764 + 4.9578315141951180061e-272j)  +/-  (3.71e-36, 5.56e-96j)
| (0.0083069578315009462832 - 2.9387885895549560269e-273j)  +/-  (2.55e-40, 3.83e-100j)
| (0.12659263371237718764 + 3.5153714860859642527e-272j)  +/-  (2.54e-37, 3.82e-97j)
| (0.0083069578315009462832 - 7.4811415255944688189e-273j)  +/-  (8.71e-41, 1.31e-100j)
| (0.0017433044574893640728 + 2.3448423734259024546e-273j)  +/-  (1.86e-41, 2.79e-101j)
| (0.025934682592751693492 + 1.8095447506920317691e-272j)  +/-  (2.03e-40, 3.04e-100j)
| (6.9642078277768414493e-11 - 1.0666788663854341069e-278j)  +/-  (2.31e-47, 3.49e-107j)
| (0.17740053584341527688 - 5.4755197716806802843e-272j)  +/-  (9.29e-40, 1.42e-99j)
| (0.00021481447658721927718 - 1.338328491333581187e-274j)  +/-  (1.92e-43, 2.89e-103j)
| (0.025934682592751693492 + 8.7956756881660895721e-273j)  +/-  (1.96e-41, 3e-101j)
| (0.064616713007727776208 - 3.2989291483759950529e-272j)  +/-  (3.52e-41, 4.43e-101j)
