Starting with polynomial:
P : t^18 - 153*t^16 + 9180*t^14 - 278460*t^12 + 4594590*t^10 - 41351310*t^8 + 192972780*t^6 - 413513100*t^4 + 310134825*t^2 - 34459425
Extension levels are: 18 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : t^18 - 153*t^16 + 9180*t^14 - 278460*t^12 + 4594590*t^10 - 41351310*t^8 + 192972780*t^6 - 413513100*t^4 + 310134825*t^2 - 34459425
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 1720120189237890201549207/2416372265418801343709*t^43 + 553826243029276288441856700/2416372265418801343709*t^41 - 107047962190612625020137401778/2416372265418801343709*t^39 + 13905211321597740341907599210529/2416372265418801343709*t^37 - 1287779773533707508982854092851815/2416372265418801343709*t^35 + 8003885392729257892886234597259690/219670205947163758519*t^33 - 412738262975160688353014415312731880/219670205947163758519*t^31 + 16265589315281415032970705980080171230/219670205947163758519*t^29 - 493443736381419757771116607975098032490/219670205947163758519*t^27 + 11554554870342646187936092478471582643600/219670205947163758519*t^25 - 208592146393198854584171835160243757758500/219670205947163758519*t^23 + 2889042254146251062472815382156252284940750/219670205947163758519*t^21 - 30433136606636819659133671583109188427611250/219670205947163758519*t^19 + 240677985100360857325970573972669728183987500/219670205947163758519*t^17 - 1403194256003837147092416283306941074326905000/219670205947163758519*t^15 + 5882227567693638250551539796319801492816216875/219670205947163758519*t^13 - 17130364713965763536033943177216932453461340625/219670205947163758519*t^11 + 33016408607003353812065688818842780554127927500/219670205947163758519*t^9 - 39209545288073892900395965401207404043847413750/219670205947163758519*t^7 + 25621059462642942356182575706119494496350859375/219670205947163758519*t^5 - 7530623484111515034703313166062955126966665625/219670205947163758519*t^3 + 631971713300105923623685740773998690638356250/219670205947163758519*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: 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:   45 out of 45
Indefinite weights: 0 out of 45
Negative weights:   0 out of 45
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.5549235088936426837 - 6.845530806019622367e-855j)  +/-  (5.83e-245, 5.83e-245j)
| (-9.147284400156139114 - 3.0219154136272136143e-856j)  +/-  (4.13e-246, 4.13e-246j)
| (9.9558040597473560895 + 4.9268685635687753108e-857j)  +/-  (8.78e-247, 8.78e-247j)
| (9.147284400156139114 + 1.5657693930509890262e-855j)  +/-  (4.55e-246, 4.55e-246j)
| (-7.7609585801742880666 + 9.5546763800240654933e-858j)  +/-  (2.65e-245, 2.65e-245j)
| (6.5549235088936426837 - 1.4457425480109918456e-855j)  +/-  (6.06e-245, 6.06e-245j)
| (7.7609585801742880666 - 2.8174888359177038905e-862j)  +/-  (2.59e-245, 2.59e-245j)
| (-0.36524575550769759592 + 3.253787269574675619e-873j)  +/-  (9.61e-254, 9.61e-254j)
| (-7.1394648491464788756 - 4.1708755867779666537e-863j)  +/-  (4.29e-245, 4.29e-245j)
| (-10.930903889446471857 - 9.5825124961702727202e-867j)  +/-  (7.85e-248, 7.85e-248j)
| (10.930903889446471857 + 1.5914704347689699561e-866j)  +/-  (7.56e-248, 7.56e-248j)
| (-4.1880202316294037045 + 1.3856803024262816114e-864j)  +/-  (1.06e-245, 1.06e-245j)
| (7.1394648491464788756 + 2.6929321395205562913e-862j)  +/-  (4.57e-245, 4.57e-245j)
| (-1.0983955180915012277 + 1.1723927129903675168e-871j)  +/-  (2.05e-251, 2.05e-251j)
| (-4.624961649990098928 + 5.0460623662807016843e-865j)  +/-  (2.66e-245, 2.66e-245j)
| (-5.5056994672140224846 - 1.00505711251832595e-865j)  +/-  (6.13e-245, 6.13e-245j)
| (4.1880202316294037045 + 6.4322704704279868141e-865j)  +/-  (9.69e-246, 9.69e-246j)
| (2.5958336889112403291 - 2.9756551172246606394e-867j)  +/-  (6.57e-248, 6.57e-248j)
| (-1.8397799215086454897 - 1.1577585043594567386e-869j)  +/-  (2.08e-249, 2.08e-249j)
| (-2.1997763359202049895 + 1.5317453944156747529e-868j)  +/-  (1.23e-248, 1.23e-248j)
| (4.624961649990098928 - 4.9187009120303065394e-864j)  +/-  (2.35e-245, 2.35e-245j)
| (1.4804588762840777849 - 4.2247445170702282978e-878j)  +/-  (2.62e-250, 2.62e-250j)
| (3.3747365357780909953 + 4.6897778169122220447e-873j)  +/-  (1.38e-246, 1.38e-246j)
| (-9.9558040597473560895 - 2.4804333116387184425e-875j)  +/-  (8.85e-247, 8.85e-247j)
| (2.1997763359202049895 - 4.1853750180594035163e-876j)  +/-  (1.16e-248, 1.16e-248j)
| (3.7616621417686668167 + 2.1148930358054962384e-872j)  +/-  (3.77e-246, 3.77e-246j)
| (8.4255547670777891876 + 1.2113106561686148115e-875j)  +/-  (1.38e-245, 1.38e-245j)
| (5.0540726854427398454 + 8.0591468848254557041e-890j)  +/-  (3.76e-245, 3.76e-245j)
| (-2.9978970914131035381 - 1.1641471875011920428e-915j)  +/-  (3.33e-247, 3.33e-247j)
| (-0.72412094845557664816 - 4.708374242159164504e-934j)  +/-  (1.73e-252, 1.73e-252j)
| (1.8397799215086454897 - 5.8993692384961044565e-930j)  +/-  (1.89e-249, 1.89e-249j)
| (5.5056994672140224846 - 5.5125297268446770349e-944j)  +/-  (6.01e-245, 6.01e-245j)
| (1.0983955180915012277 - 8.5384583951455105501e-975j)  +/-  (1.92e-251, 1.92e-251j)
| (6.0077459113595975203 + 7.7110226094408479637e-967j)  +/-  (6.05e-245, 6.05e-245j)
| (0.36524575550769759592 + 1.0954989007842478331e-983j)  +/-  (1.19e-253, 1.19e-253j)
| (-6.0077459113595975203 + 1.5103039010558915326e-974j)  +/-  (6.39e-245, 6.39e-245j)
| (-2.5958336889112403291 + 1.1485892634589944704e-978j)  +/-  (6.19e-248, 6.19e-248j)
| (-1.2679182546710405457e-1001 - 1.1086419152243095624e-1001j)  +/-  (7.58e-1000, 7.58e-1000j)
| (-3.7616621417686668167 - 8.0327595775306264224e-977j)  +/-  (4.04e-246, 4.04e-246j)
| (-5.0540726854427398454 + 7.7913703590436657408e-979j)  +/-  (4.12e-245, 4.12e-245j)
| (-3.3747365357780909953 - 7.3414501179363612528e-980j)  +/-  (1.35e-246, 1.35e-246j)
| (-8.4255547670777891876 - 3.7011517704546219631e-983j)  +/-  (1.39e-245, 1.39e-245j)
| (2.9978970914131035381 - 2.006558841031443666e-988j)  +/-  (3.61e-247, 3.61e-247j)
| (0.72412094845557664816 + 1.7241199998595469468e-992j)  +/-  (1.57e-252, 1.57e-252j)
| (-1.4804588762840777849 + 1.2933996865381819808e-990j)  +/-  (2.34e-250, 2.34e-250j)
-------------------------------------------------
The weights are:
| (1.0567165239914133855e-10 - 3.6045277486859434396e-864j)  +/-  (4.65e-79, 4.33e-200j)
| (2.0478452909708065568e-19 + 3.8466815985462503939e-871j)  +/-  (1.64e-85, 1.53e-206j)
| (1.0405615988877967079e-22 + 1.1574369280179491954e-873j)  +/-  (3.39e-88, 3.15e-209j)
| (2.0478452909708065568e-19 - 1.4184460705661268078e-871j)  +/-  (1.04e-86, 9.68e-208j)
| (2.1319294547649792732e-14 + 1.3934668829819107634e-867j)  +/-  (9.1e-84, 8.46e-205j)
| (1.0567165239914133855e-10 + 7.0846076801308587911e-865j)  +/-  (7.67e-82, 7.13e-203j)
| (2.1319294547649792732e-14 - 4.0459968477253463097e-868j)  +/-  (1.86e-84, 1.73e-205j)
| (0.13422081050506088619 + 7.9086893960291757071e-858j)  +/-  (2.46e-60, 2.29e-181j)
| (2.0533464348154024856e-12 - 6.7782892602423608876e-866j)  +/-  (8.11e-83, 7.54e-204j)
| (5.0863515908753531125e-27 + 6.4627887320123484073e-876j)  +/-  (9.84e-92, 9.15e-213j)
| (5.0863515908753531125e-27 - 2.8277148355132978375e-876j)  +/-  (1.93e-91, 1.8e-212j)
| (2.713055173079856165e-05 + 1.0505512307560553203e-860j)  +/-  (8.73e-77, 8.12e-198j)
| (2.0533464348154024856e-12 + 1.7059835177175052453e-866j)  +/-  (4.68e-84, 4.35e-205j)
| (0.083681090562836417675 + 5.4836184952258469733e-858j)  +/-  (2.46e-60, 2.29e-181j)
| (3.9057605859413032312e-06 - 2.589535049846016257e-861j)  +/-  (3.13e-78, 2.91e-199j)
| (4.9674941340504285497e-08 - 1.1133215230599867508e-862j)  +/-  (1.4e-80, 1.31e-201j)
| (2.713055173079856165e-05 + 1.0215844778095546307e-862j)  +/-  (1.44e-79, 1.34e-200j)
| (0.0055867075824956810251 + 1.6428514696106597812e-859j)  +/-  (4.51e-74, 4.2e-195j)
| (0.025656834468251718334 + 2.7675340294024601271e-858j)  +/-  (1.28e-69, 1.19e-190j)
| (0.01343811304009347425 - 1.4986509923989455176e-858j)  +/-  (7.92e-72, 7.37e-193j)
| (3.9057605859413032312e-06 + 1.0329676903729424615e-862j)  +/-  (3.65e-81, 3.4e-202j)
| (0.049853666318840028841 - 1.9777542138147929212e-858j)  +/-  (1.1e-69, 1.02e-190j)
| (0.00049806518333288799201 + 1.4700488534600418942e-860j)  +/-  (4.19e-78, 3.89e-199j)
| (1.0405615988877967079e-22 - 2.9051086349716898863e-873j)  +/-  (2.1e-93, 1.95e-214j)
| (0.01343811304009347425 - 4.7964300790881758454e-859j)  +/-  (1.5e-74, 1.39e-195j)
| (0.00013792151443861805275 - 2.5781875918932698907e-861j)  +/-  (3.03e-79, 2.82e-200j)
| (1.0579203320480329715e-16 + 8.9984620605327220336e-870j)  +/-  (3.75e-90, 3.49e-211j)
| (4.8996080480733928346e-07 - 5.0041444959995611892e-863j)  +/-  (1.73e-83, 1.61e-204j)
| (0.0017411954828563019764 - 3.0049642869231241224e-859j)  +/-  (7.17e-82, 6.66e-203j)
| (0.11157870147232638221 - 7.0491519488232964313e-858j)  +/-  (3.95e-74, 3.67e-195j)
| (0.025656834468251718334 + 1.1009922667840370878e-858j)  +/-  (2.33e-76, 2.16e-197j)
| (4.9674941340504285497e-08 + 1.4076135634195710389e-863j)  +/-  (5.64e-85, 5.25e-206j)
| (0.083681090562836417675 + 3.2399744201348151457e-858j)  +/-  (5.53e-77, 5.14e-198j)
| (3.0534231324471660655e-09 - 3.2523949597356072393e-864j)  +/-  (3.85e-86, 3.58e-207j)
| (0.13422081050506088619 + 6.662516915152187869e-858j)  +/-  (1.68e-77, 1.56e-198j)
| (3.0534231324471660655e-09 + 1.9228726062277354212e-863j)  +/-  (1.89e-89, 1.76e-210j)
| (0.0055867075824956810251 + 6.7356394423367050123e-859j)  +/-  (7.55e-83, 7.02e-204j)
| (0.14715062952047031836 - 7.6665701148945912589e-858j)  +/-  (5.76e-79, 5.35e-200j)
| (0.00013792151443861805275 - 4.0706587174762862688e-860j)  +/-  (8.73e-86, 8.12e-207j)
| (4.8996080480733928346e-07 + 5.9506137191031432374e-862j)  +/-  (3.77e-88, 3.51e-209j)
| (0.00049806518333288799201 + 1.2547201908106672504e-859j)  +/-  (2.85e-85, 2.64e-206j)
| (1.0579203320480329715e-16 - 2.7397713557498891725e-869j)  +/-  (1.01e-95, 9.49e-217j)
| (0.0017411954828563019764 - 5.2613894470763115775e-860j)  +/-  (4.28e-85, 4e-206j)
| (0.11157870147232638221 - 5.0052699478058926672e-858j)  +/-  (4.55e-83, 4.49e-204j)
| (0.049853666318840028841 - 4.0764940248594432642e-858j)  +/-  (1.26e-83, 1.01e-204j)
