Starting with polynomial:
P : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Extension levels are: 10 21
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Trying to find an order 21 Kronrod extension for:
P1 : t^10 - 45*t^8 + 630*t^6 - 3150*t^4 + 4725*t^2 - 945
Solvable: 1
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Ending with final polynomial:
P : t^31 - 19104435/55417*t^29 + 2832167295/55417*t^27 - 21673129909995/5042947*t^25 + 1149124583361375/5042947*t^23 - 63516635808019065/7924631*t^21 + 1520109287771433525/7924631*t^19 - 25009941631077915075/7924631*t^17 + 282820165145501559525/7924631*t^15 - 2177738168992190382375/7924631*t^13 + 861410447564587098975/609587*t^11 - 260064800171087659875/55417*t^9 + 527154492894880323375/55417*t^7 - 590725613789628526125/55417*t^5 + 302310908444829335625/55417*t^3 - 44538274723888425375/55417*t
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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:   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:
| (4.2053322407548003888 + 4.6934750776603389517e-277j)  +/-  (6.6e-121, 6.6e-121j)
| (7.0590920255135463775 - 7.637805453259794898e-287j)  +/-  (6.26e-121, 6.26e-121j)
| (8.9779794088140455997 - 1.7469236713976346135e-298j)  +/-  (4e-122, 4e-122j)
| (2.4843258416389545809 + 1.6567934717223660674e-305j)  +/-  (1.47e-121, 1.47e-121j)
| (-7.9320541513376066292 + 1.9245992545065188233e-308j)  +/-  (2.59e-121, 2.59e-121j)
| (-8.9779794088140455997 - 1.2053479854104181601e-309j)  +/-  (3.9e-122, 3.9e-122j)
| (-6.274512412354208506 - 1.0524895411591818017e-307j)  +/-  (1.08e-120, 1.08e-120j)
| (-3.5818234835519269228 + 2.0140625970536147041e-308j)  +/-  (3.18e-121, 3.18e-121j)
| (-7.0590920255135463775 + 8.4609913774000109966e-309j)  +/-  (7.51e-121, 7.51e-121j)
| (7.9320541513376066292 - 4.9217829926403231546e-315j)  +/-  (2.77e-121, 2.77e-121j)
| (1.4659890943911581833 - 1.3344224124784415605e-325j)  +/-  (1.43e-123, 1.43e-123j)
| (3.5818234835519269228 + 1.5485354385163220479e-335j)  +/-  (3.31e-121, 3.31e-121j)
| (5.5465177154434916105 - 1.8670084359904236333e-353j)  +/-  (1.2e-120, 1.2e-120j)
| (-2.4843258416389545809 + 1.2846571339659571471e-366j)  +/-  (1.29e-121, 1.29e-121j)
| (-1.4659890943911581833 - 9.4474313937967070556e-369j)  +/-  (1.43e-123, 1.43e-123j)
| (0.48493570751549765305 + 8.0846270815733122934e-370j)  +/-  (3.81e-126, 3.81e-126j)
| (-4.2053322407548003888 - 1.9195106634383426813e-365j)  +/-  (5.66e-121, 5.66e-121j)
| (-4.8594628283323121502 + 4.3601861346159630139e-366j)  +/-  (8.78e-121, 8.78e-121j)
| (-0.98119022590930265381 + 2.8700208253583517532e-370j)  +/-  (8.8e-125, 8.8e-125j)
| (-1.9097910332573536923 - 3.1375415224003309003e-367j)  +/-  (1.76e-122, 1.76e-122j)
| (2.2332955076097249561 - 1.6509339719850160755e-365j)  +/-  (8.13e-122, 8.13e-122j)
| (0.98119022590930265381 - 4.3642698200866560275e-369j)  +/-  (9.26e-125, 9.26e-125j)
| (6.274512412354208506 + 1.1035794886840224354e-364j)  +/-  (1.03e-120, 1.03e-120j)
| (-2.2332955076097249561 + 6.4601689105612047675e-374j)  +/-  (7.92e-122, 7.92e-122j)
| (1.9405424155717572003e-389 + 5.478875399077763357e-389j)  +/-  (1.8e-387, 1.8e-387j)
| (2.9952302297504877891 + 6.2947080204709682768e-372j)  +/-  (1.93e-121, 1.93e-121j)
| (4.8594628283323121502 + 4.4493118510725648652e-373j)  +/-  (9.74e-121, 9.74e-121j)
| (1.9097910332573536923 + 3.7775987837580032986e-378j)  +/-  (1.68e-122, 1.68e-122j)
| (-2.9952302297504877891 + 4.5458340115104473995e-376j)  +/-  (1.88e-121, 1.88e-121j)
| (-0.48493570751549765305 + 1.4629226742854427476e-381j)  +/-  (4e-126, 4e-126j)
| (-5.5465177154434916105 + 6.5013490417134542744e-380j)  +/-  (1.12e-120, 1.12e-120j)
-------------------------------------------------
The weights are:
| (3.6826950711473326504e-05 - 6.1222437329908119952e-281j)  +/-  (2.19e-28, 1.07e-88j)
| (4.9519053394003707587e-12 + 1.2170508623281857977e-286j)  +/-  (2.27e-35, 1.11e-95j)
| (1.5075620694644059136e-18 + 1.1359721931266714457e-290j)  +/-  (1.14e-38, 5.58e-99j)
| (0.0077100998546675577366 + 8.3146085214993674936e-279j)  +/-  (2.49e-23, 1.22e-83j)
| (8.1290809917128702351e-15 + 6.2615399864759309021e-289j)  +/-  (5.04e-39, 2.48e-99j)
| (1.5075620694644059136e-18 - 4.1124678037230501577e-291j)  +/-  (8.67e-41, 4.26e-101j)
| (8.4841424052058853863e-10 + 8.1627060151527812113e-286j)  +/-  (4.21e-37, 2.07e-97j)
| (0.0003966234959990587011 + 2.004504260774781939e-281j)  +/-  (2.68e-32, 1.31e-92j)
| (4.9519053394003707587e-12 - 3.083309652380010208e-287j)  +/-  (4.19e-38, 2.06e-98j)
| (8.1290809917128702351e-15 - 2.0392916898171244834e-288j)  +/-  (2.55e-40, 1.25e-100j)
| (0.063536013846266050929 - 1.3757355366970702642e-278j)  +/-  (2.74e-25, 1.35e-85j)
| (0.0003966234959990587011 + 2.5034751554612203686e-280j)  +/-  (1.04e-32, 5.1e-93j)
| (5.8780673908266008441e-08 + 1.0431623923596182065e-283j)  +/-  (5.93e-37, 2.91e-97j)
| (0.0077100998546675577366 + 2.1390472121884796454e-279j)  +/-  (9.28e-32, 4.56e-92j)
| (0.063536013846266050929 - 6.6450329490320024499e-279j)  +/-  (1.37e-28, 6.74e-89j)
| (0.17429978199070572253 - 1.1777764098211140467e-278j)  +/-  (7.53e-29, 3.7e-89j)
| (3.6826950711473326504e-05 - 2.0550858464319767416e-282j)  +/-  (7.59e-36, 3.73e-96j)
| (1.9907335741441219582e-06 + 1.8930186897646980258e-283j)  +/-  (3.33e-37, 1.64e-97j)
| (0.1224786781252728551 + 7.6796033715315518019e-279j)  +/-  (1.74e-29, 8.52e-90j)
| (0.027104366679879095305 + 6.3915376907619590977e-279j)  +/-  (4.94e-31, 2.43e-91j)
| (0.0059490058752018684094 - 1.6975946964316006725e-278j)  +/-  (2.24e-32, 1.1e-92j)
| (0.1224786781252728551 + 1.2353809242311383819e-278j)  +/-  (1.06e-30, 5.2e-91j)
| (8.4841424052058853863e-10 - 4.1341924769168797339e-285j)  +/-  (4.04e-40, 1.98e-100j)
| (0.0059490058752018684094 - 5.1994294905536309453e-279j)  +/-  (1.61e-32, 7.92e-93j)
| (0.19192450375947925747 + 1.0952592881948266755e-278j)  +/-  (1.38e-30, 6.77e-91j)
| (0.0025243009339343603983 - 1.168289469092907466e-279j)  +/-  (9.5e-35, 4.67e-95j)
| (1.9907335741441219582e-06 - 2.6233028711037277539e-282j)  +/-  (5.19e-38, 2.55e-98j)
| (0.027104366679879095305 + 1.7026503711568799395e-278j)  +/-  (4.22e-33, 2.08e-93j)
| (0.0025243009339343603983 - 1.9633875017053164411e-280j)  +/-  (1.25e-35, 6.16e-96j)
| (0.17429978199070572253 - 9.3423133184644183074e-279j)  +/-  (9.22e-34, 4.87e-94j)
| (5.8780673908266008441e-08 - 1.4346757329694576015e-284j)  +/-  (6.14e-40, 2.99e-100j)
