Starting with polynomial:
P : -t+1
Extension levels are: 1 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^28 + 3254014980889061538354284815345/4292420644705676598492079924*t^27 - 1145540458271874071262388934664873/4292420644705676598492079924*t^26 + 9576601285417271835553555802516277/165093101719449099942003074*t^25 - 1441435197783067977109334505927654375/165093101719449099942003074*t^24 + 79863923215853984443013332860219291000/82546550859724549971001537*t^23 - 6762487285307386841832640006115668335000/82546550859724549971001537*t^22 + 448297302585021714678871701507635602362000/82546550859724549971001537*t^21 - 23649557322049539095700497707906955301558000/82546550859724549971001537*t^20 + 1003854481737766940876808572009133245462700000/82546550859724549971001537*t^19 - 34533892722533957071092780354373149816351660000/82546550859724549971001537*t^18 + 966952629454944266799692535271470453524177400000/82546550859724549971001537*t^17 - 22077797265964742757603042106014582479566786920000/82546550859724549971001537*t^16 + 410942070926235787614132295960443107185420500480000/82546550859724549971001537*t^15 - 6221593364829176784091970912429407836327818688000000/82546550859724549971001537*t^14 + 76293138373026304558635724359795472280428689945600000/82546550859724549971001537*t^13 - 753008970561007134650086158336880580380211632512000000/82546550859724549971001537*t^12 + 5930865885658649737972933932339570224174641926835200000/82546550859724549971001537*t^11 - 36859980230538224535547545669226093691861664712780800000/82546550859724549971001537*t^10 + 178165063197274697364031180783348355491780191962880000000/82546550859724549971001537*t^9 - 657437433299610262496191722448460208683210386021632000000/82546550859724549971001537*t^8 + 1808171765791262478226459924493286331808643031142400000000/82546550859724549971001537*t^7 - 3591977712490996530307353426426000122146406033608704000000/82546550859724549971001537*t^6 + 4940865023181722317026427906428116806659013538144256000000/82546550859724549971001537*t^5 - 4436983397494717005985097841682851843706703149670400000000/82546550859724549971001537*t^4 + 2385428733338756222976639966401972488838571006148608000000/82546550859724549971001537*t^3 - 668488185789540079196359839505472237667064152637440000000/82546550859724549971001537*t^2 + 75740894934514405193281777530864979824160665993216000000/82546550859724549971001537*t - 1873089395906901539221926757466693068566692265984000000/82546550859724549971001537
-------------------------------------------------
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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   28 out of 28
Indefinite weights: 0 out of 28
Negative weights:   0 out of 28
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (94.76020581534311231 - 2.6381941111798191759e-219j)  +/-  (7.88e-218, 7.88e-218j)
| (58.222056263844702763 + 2.6133231567087262982e-214j)  +/-  (2.02e-212, 2.02e-212j)
| (73.125904610109316248 - 1.1139146933479405609e-218j)  +/-  (3.47e-217, 3.47e-217j)
| (82.582412524026447145 - 1.5907902574424805164e-222j)  +/-  (6.6e-221, 6.6e-221j)
| (65.164851881924186055 - 4.8243388260492089995e-221j)  +/-  (3.78e-219, 3.78e-219j)
| (3.547639674183864955 + 4.1077101843196035445e-240j)  +/-  (1.37e-238, 1.37e-238j)
| (13.864653006114726269 - 1.8641510858859596815e-225j)  +/-  (3.78e-223, 3.78e-223j)
| (52.047839298141516876 + 8.6058544983002581478e-231j)  +/-  (2.46e-229, 2.46e-229j)
| (1.6674305593006918488 + 3.258981667033441315e-254j)  +/-  (9.48e-250, 9.48e-250j)
| (4.7673066304535590768 + 1.5458770161346366261e-251j)  +/-  (8.89e-247, 8.89e-247j)
| (2.5155754275820032715 - 1.0311753731687978931e-254j)  +/-  (1.18e-248, 1.18e-248j)
| (28.793184540110814238 + 4.2525425871094504156e-245j)  +/-  (3.32e-241, 3.32e-241j)
| (22.017040822075553519 + 4.9021284900061389306e-266j)  +/-  (8.27e-242, 8.27e-242j)
| (41.449258771425285268 + 5.0664314989086302777e-294j)  +/-  (5.11e-241, 5.11e-241j)
| (7.7877639432184149325 - 1.5899994084044043516e-311j)  +/-  (3.36e-245, 3.36e-245j)
| (1 - 1.0291631239082147745e-328j)  +/-  (7.55e-251, 7.55e-251j)
| (32.647304639723025089 + 4.1551816690108245763e-322j)  +/-  (4.53e-241, 4.53e-241j)
| (0.19239448076312373664 - 9.4744825540969908473e-357j)  +/-  (1.89e-253, 1.89e-253j)
| (25.258276625394778082 - 2.4669813119470662295e-343j)  +/-  (1.71e-241, 1.71e-241j)
| (16.335974166316745697 + 5.4383184080295131534e-355j)  +/-  (1.34e-242, 1.34e-242j)
| (11.622681869956703042 + 4.3208887366296194373e-361j)  +/-  (9.31e-244, 9.31e-244j)
| (0.510034045077433086 + 1.0417088269247790672e-390j)  +/-  (3.84e-252, 3.84e-252j)
| (9.5999153874253640383 + 8.6645487485570707047e-366j)  +/-  (2.13e-244, 2.13e-244j)
| (0.033543934947520504023 - 5.384835846437190862e-392j)  +/-  (6.05e-255, 6.05e-255j)
| (46.490551284852078982 + 1.9374163765172059173e-381j)  +/-  (4.24e-241, 4.24e-241j)
| (19.04866514298373574 + 2.1408143837293283223e-405j)  +/-  (3.36e-242, 3.36e-242j)
| (6.1789482234423837516 + 1.658205084226385159e-417j)  +/-  (6.76e-246, 6.76e-246j)
| (36.85248599096773134 - 6.3240090238780466876e-422j)  +/-  (4.72e-241, 4.72e-241j)
-------------------------------------------------
The weights are:
| (1.0207527747279829559e-40 + 4.239947313608505941e-248j)  +/-  (1.29e-101, 1.82e-191j)
| (3.3823505034677563662e-25 - 4.4156932548760832342e-239j)  +/-  (2.08e-96, 2.92e-186j)
| (1.5003959252875198697e-31 + 3.9695790122623848463e-243j)  +/-  (4.23e-99, 5.94e-189j)
| (1.430785696867535107e-35 - 2.3764081791509192091e-245j)  +/-  (1.25e-100, 1.75e-190j)
| (3.7015617637637506569e-28 - 4.2228917194999144331e-241j)  +/-  (4.7e-98, 6.6e-188j)
| (0.032397325597475881724 + 5.3750951058830311519e-229j)  +/-  (2.78e-73, 3.9e-163j)
| (2.2418873453472537322e-06 + 7.1947231580064810327e-231j)  +/-  (3.16e-86, 4.44e-176j)
| (1.4546052056610639335e-22 + 2.9595226933534616091e-238j)  +/-  (9.14e-97, 1.28e-186j)
| (0.14292193309970170234 + 1.0528356858378191217e-228j)  +/-  (3.96e-69, 5.57e-159j)
| (0.01118059381316447126 - 3.2799630430483464392e-229j)  +/-  (1.67e-77, 2.35e-167j)
| (0.075930226186991533878 - 7.9501050052298008433e-229j)  +/-  (1.73e-72, 2.43e-162j)
| (1.1541999153341092236e-12 - 5.3388076145519132834e-234j)  +/-  (2.86e-93, 4.01e-183j)
| (8.5058221352236533376e-10 - 1.1213580427856868751e-232j)  +/-  (1.7e-91, 2.38e-181j)
| (4.7958300686505529532e-18 + 1.9609991720376187452e-236j)  +/-  (1.61e-96, 2.26e-186j)
| (0.00070901099261875709433 - 9.168041555554588283e-230j)  +/-  (1.67e-85, 2.35e-175j)
| (0.21267195515018990868 - 1.2283699975114924887e-228j)  +/-  (4.69e-77, 6.58e-167j)
| (2.667368385045819155e-14 + 9.4513947886752778222e-235j)  +/-  (9.64e-95, 1.35e-184j)
| (0.19361373297266094634 - 9.0981857290422444311e-229j)  +/-  (3.53e-78, 4.96e-168j)
| (3.6302167254265503909e-11 + 2.6248076786579546044e-233j)  +/-  (6.62e-93, 9.3e-183j)
| (2.0827992574647179701e-07 - 1.1340143673173867646e-231j)  +/-  (5.27e-91, 7.4e-181j)
| (1.9093234651670950661e-05 - 1.9603992383847236232e-230j)  +/-  (1.34e-89, 1.88e-179j)
| (0.24174704035555044845 + 1.2146965855829943449e-228j)  +/-  (8.79e-83, 1.23e-172j)
| (0.00012978897506115561201 + 4.2791684704371393251e-230j)  +/-  (6.01e-89, 8.44e-179j)
| (0.08554867599117438935 + 3.367060416856508675e-229j)  +/-  (1.09e-83, 1.53e-173j)
| (3.4079092429535879033e-20 - 2.3748976112316427572e-237j)  +/-  (1.17e-98, 1.64e-188j)
| (1.5145083081145661234e-08 + 4.0969944662544093625e-232j)  +/-  (1.17e-92, 1.64e-182j)
| (0.0031281574303392657602 + 1.8156027603996020421e-229j)  +/-  (1.62e-89, 2.25e-179j)
| (4.344739841249658373e-16 - 1.4558433223184434184e-235j)  +/-  (1.03e-96, 1.44e-186j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^28 + 3254014980889061538354284815345/4292420644705676598492079924*t^27 - 1145540458271874071262388934664873/4292420644705676598492079924*t^26 + 9576601285417271835553555802516277/165093101719449099942003074*t^25 - 1441435197783067977109334505927654375/165093101719449099942003074*t^24 + 79863923215853984443013332860219291000/82546550859724549971001537*t^23 - 6762487285307386841832640006115668335000/82546550859724549971001537*t^22 + 448297302585021714678871701507635602362000/82546550859724549971001537*t^21 - 23649557322049539095700497707906955301558000/82546550859724549971001537*t^20 + 1003854481737766940876808572009133245462700000/82546550859724549971001537*t^19 - 34533892722533957071092780354373149816351660000/82546550859724549971001537*t^18 + 966952629454944266799692535271470453524177400000/82546550859724549971001537*t^17 - 22077797265964742757603042106014582479566786920000/82546550859724549971001537*t^16 + 410942070926235787614132295960443107185420500480000/82546550859724549971001537*t^15 - 6221593364829176784091970912429407836327818688000000/82546550859724549971001537*t^14 + 76293138373026304558635724359795472280428689945600000/82546550859724549971001537*t^13 - 753008970561007134650086158336880580380211632512000000/82546550859724549971001537*t^12 + 5930865885658649737972933932339570224174641926835200000/82546550859724549971001537*t^11 - 36859980230538224535547545669226093691861664712780800000/82546550859724549971001537*t^10 + 178165063197274697364031180783348355491780191962880000000/82546550859724549971001537*t^9 - 657437433299610262496191722448460208683210386021632000000/82546550859724549971001537*t^8 + 1808171765791262478226459924493286331808643031142400000000/82546550859724549971001537*t^7 - 3591977712490996530307353426426000122146406033608704000000/82546550859724549971001537*t^6 + 4940865023181722317026427906428116806659013538144256000000/82546550859724549971001537*t^5 - 4436983397494717005985097841682851843706703149670400000000/82546550859724549971001537*t^4 + 2385428733338756222976639966401972488838571006148608000000/82546550859724549971001537*t^3 - 668488185789540079196359839505472237667064152637440000000/82546550859724549971001537*t^2 + 75740894934514405193281777530864979824160665993216000000/82546550859724549971001537*t - 1873089395906901539221926757466693068566692265984000000/82546550859724549971001537
-------------------------------------------------
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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   28 out of 28
Indefinite weights: 0 out of 28
Negative weights:   0 out of 28
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (94.76020581534311231 - 2.6381941111798191759e-219j)  +/-  (7.88e-218, 7.88e-218j)
| (58.222056263844702763 + 2.6133231567087262982e-214j)  +/-  (2.02e-212, 2.02e-212j)
| (73.125904610109316248 - 1.1139146933479405609e-218j)  +/-  (3.47e-217, 3.47e-217j)
| (82.582412524026447145 - 1.5907902574424805164e-222j)  +/-  (6.6e-221, 6.6e-221j)
| (65.164851881924186055 - 4.8243388260492089995e-221j)  +/-  (3.78e-219, 3.78e-219j)
| (3.547639674183864955 + 4.1077101843196035445e-240j)  +/-  (1.37e-238, 1.37e-238j)
| (13.864653006114726269 - 1.8641510858859596815e-225j)  +/-  (3.78e-223, 3.78e-223j)
| (52.047839298141516876 + 8.6058544983002581478e-231j)  +/-  (2.46e-229, 2.46e-229j)
| (1.6674305593006918488 + 3.258981667033441315e-254j)  +/-  (9.48e-250, 9.48e-250j)
| (4.7673066304535590768 + 1.5458770161346366261e-251j)  +/-  (8.89e-247, 8.89e-247j)
| (2.5155754275820032715 - 1.0311753731687978931e-254j)  +/-  (1.18e-248, 1.18e-248j)
| (28.793184540110814238 + 4.2525425871094504156e-245j)  +/-  (3.32e-241, 3.32e-241j)
| (22.017040822075553519 + 4.9021284900061389306e-266j)  +/-  (8.27e-242, 8.27e-242j)
| (41.449258771425285268 + 5.0664314989086302777e-294j)  +/-  (5.11e-241, 5.11e-241j)
| (7.7877639432184149325 - 1.5899994084044043516e-311j)  +/-  (3.36e-245, 3.36e-245j)
| (1 - 1.0291631239082147745e-328j)  +/-  (7.55e-251, 7.55e-251j)
| (32.647304639723025089 + 4.1551816690108245763e-322j)  +/-  (4.53e-241, 4.53e-241j)
| (0.19239448076312373664 - 9.4744825540969908473e-357j)  +/-  (1.89e-253, 1.89e-253j)
| (25.258276625394778082 - 2.4669813119470662295e-343j)  +/-  (1.71e-241, 1.71e-241j)
| (16.335974166316745697 + 5.4383184080295131534e-355j)  +/-  (1.34e-242, 1.34e-242j)
| (11.622681869956703042 + 4.3208887366296194373e-361j)  +/-  (9.31e-244, 9.31e-244j)
| (0.510034045077433086 + 1.0417088269247790672e-390j)  +/-  (3.84e-252, 3.84e-252j)
| (9.5999153874253640383 + 8.6645487485570707047e-366j)  +/-  (2.13e-244, 2.13e-244j)
| (0.033543934947520504023 - 5.384835846437190862e-392j)  +/-  (6.05e-255, 6.05e-255j)
| (46.490551284852078982 + 1.9374163765172059173e-381j)  +/-  (4.24e-241, 4.24e-241j)
| (19.04866514298373574 + 2.1408143837293283223e-405j)  +/-  (3.36e-242, 3.36e-242j)
| (6.1789482234423837516 + 1.658205084226385159e-417j)  +/-  (6.76e-246, 6.76e-246j)
| (36.85248599096773134 - 6.3240090238780466876e-422j)  +/-  (4.72e-241, 4.72e-241j)
-------------------------------------------------
The weights are:
| (1.0207527747279829559e-40 + 4.239947313608505941e-248j)  +/-  (1.29e-101, 1.82e-191j)
| (3.3823505034677563662e-25 - 4.4156932548760832342e-239j)  +/-  (2.08e-96, 2.92e-186j)
| (1.5003959252875198697e-31 + 3.9695790122623848463e-243j)  +/-  (4.23e-99, 5.94e-189j)
| (1.430785696867535107e-35 - 2.3764081791509192091e-245j)  +/-  (1.25e-100, 1.75e-190j)
| (3.7015617637637506569e-28 - 4.2228917194999144331e-241j)  +/-  (4.7e-98, 6.6e-188j)
| (0.032397325597475881724 + 5.3750951058830311519e-229j)  +/-  (2.78e-73, 3.9e-163j)
| (2.2418873453472537322e-06 + 7.1947231580064810327e-231j)  +/-  (3.16e-86, 4.44e-176j)
| (1.4546052056610639335e-22 + 2.9595226933534616091e-238j)  +/-  (9.14e-97, 1.28e-186j)
| (0.14292193309970170234 + 1.0528356858378191217e-228j)  +/-  (3.96e-69, 5.57e-159j)
| (0.01118059381316447126 - 3.2799630430483464392e-229j)  +/-  (1.67e-77, 2.35e-167j)
| (0.075930226186991533878 - 7.9501050052298008433e-229j)  +/-  (1.73e-72, 2.43e-162j)
| (1.1541999153341092236e-12 - 5.3388076145519132834e-234j)  +/-  (2.86e-93, 4.01e-183j)
| (8.5058221352236533376e-10 - 1.1213580427856868751e-232j)  +/-  (1.7e-91, 2.38e-181j)
| (4.7958300686505529532e-18 + 1.9609991720376187452e-236j)  +/-  (1.61e-96, 2.26e-186j)
| (0.00070901099261875709433 - 9.168041555554588283e-230j)  +/-  (1.67e-85, 2.35e-175j)
| (0.21267195515018990868 - 1.2283699975114924887e-228j)  +/-  (4.69e-77, 6.58e-167j)
| (2.667368385045819155e-14 + 9.4513947886752778222e-235j)  +/-  (9.64e-95, 1.35e-184j)
| (0.19361373297266094634 - 9.0981857290422444311e-229j)  +/-  (3.53e-78, 4.96e-168j)
| (3.6302167254265503909e-11 + 2.6248076786579546044e-233j)  +/-  (6.62e-93, 9.3e-183j)
| (2.0827992574647179701e-07 - 1.1340143673173867646e-231j)  +/-  (5.27e-91, 7.4e-181j)
| (1.9093234651670950661e-05 - 1.9603992383847236232e-230j)  +/-  (1.34e-89, 1.88e-179j)
| (0.24174704035555044845 + 1.2146965855829943449e-228j)  +/-  (8.79e-83, 1.23e-172j)
| (0.00012978897506115561201 + 4.2791684704371393251e-230j)  +/-  (6.01e-89, 8.44e-179j)
| (0.08554867599117438935 + 3.367060416856508675e-229j)  +/-  (1.09e-83, 1.53e-173j)
| (3.4079092429535879033e-20 - 2.3748976112316427572e-237j)  +/-  (1.17e-98, 1.64e-188j)
| (1.5145083081145661234e-08 + 4.0969944662544093625e-232j)  +/-  (1.17e-92, 1.64e-182j)
| (0.0031281574303392657602 + 1.8156027603996020421e-229j)  +/-  (1.62e-89, 2.25e-179j)
| (4.344739841249658373e-16 - 1.4558433223184434184e-235j)  +/-  (1.03e-96, 1.44e-186j)
