Starting with polynomial:
P : 262144*t^18 - 20054016*t^16 + 601620480*t^14 - 9124577280*t^12 + 75277762560*t^10 - 338749931520*t^8 + 790416506880*t^6 - 846874828800*t^4 + 317578060800*t^2 - 17643225600
Extension levels are: 18 27
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Trying to find an order 27 Kronrod extension for:
P1 : 262144*t^18 - 20054016*t^16 + 601620480*t^14 - 9124577280*t^12 + 75277762560*t^10 - 338749931520*t^8 + 790416506880*t^6 - 846874828800*t^4 + 317578060800*t^2 - 17643225600
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 262144*t^45 - 225459593443788744497457659904/2416372265418801343709*t^43 + 36295556663166650839325520691200/2416372265418801343709*t^41 - 3507747625061994496659862381461504/2416372265418801343709*t^39 + 227822982293057377761814105465307136/2416372265418801343709*t^37 - 10549491904788131913587540728642068480/2416372265418801343709*t^35 + 32783914568619040329262016910375690240/219670205947163758519*t^33 - 845287962573129089746973522560474890240/219670205947163758519*t^31 + 16655963458848168993762002923602095339520/219670205947163758519*t^29 - 252643193027286915978811703283250192634880/219670205947163758519*t^27 + 2957966046807717424111639674488725156761600/219670205947163758519*t^25 - 26699794738329453386773994900511200993088000/219670205947163758519*t^23 + 184898704265360067998260184458000146236208000/219670205947163758519*t^21 - 973860371412378229092277490659494029683560000/219670205947163758519*t^19 + 3850847761605773717215529183562715650943800000/219670205947163758519*t^17 - 11225554048030697176739330266455528594615240000/219670205947163758519*t^15 + 23528910270774553002206159185279205971264867500/219670205947163758519*t^13 - 34260729427931527072067886354433864906922681250/219670205947163758519*t^11 + 33016408607003353812065688818842780554127927500/219670205947163758519*t^9 - 19604772644036946450197982700603702021923706875/219670205947163758519*t^7 + 25621059462642942356182575706119494496350859375/878680823788655034076*t^5 - 7530623484111515034703313166062955126966665625/1757361647577310068152*t^3 + 315985856650052961811842870386999345319178125/1757361647577310068152*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
-------------------------------------------------
The nodes are:
| (3.2703417454357226811 + 3.4273997669834422117e-859j)  +/-  (1.66e-245, 1.66e-245j)
| (-7.7293162647260076464 - 6.9357949448789218856e-871j)  +/-  (4.9e-248, 4.9e-248j)
| (-3.5737690684862660795 + 2.4890873518259666247e-866j)  +/-  (3.3e-245, 3.3e-245j)
| (7.7293162647260076464 - 3.2837071615494425759e-870j)  +/-  (5.67e-248, 5.67e-248j)
| (5.4878264405491588638 - 1.4561288025705077102e-866j)  +/-  (1.92e-245, 1.92e-245j)
| (5.9577669110593466725 + 2.3825826716536627462e-866j)  +/-  (9.81e-246, 9.81e-246j)
| (-4.248117873568126463 + 4.2992267693601533673e-866j)  +/-  (4.29e-245, 4.29e-245j)
| (-6.4681068287923266861 - 2.5484251007203794868e-868j)  +/-  (2.79e-246, 2.79e-246j)
| (-7.0398165628119152385 - 1.4818302459406035184e-868j)  +/-  (6.2e-247, 6.2e-247j)
| (-5.9577669110593466725 + 1.4210736509050252172e-867j)  +/-  (9.82e-246, 9.82e-246j)
| (5.0483640088744667684 + 2.0228988868756139831e-865j)  +/-  (3.02e-245, 3.02e-245j)
| (3.8931174284421970828 - 5.1804630947587068964e-867j)  +/-  (3.9e-245, 3.9e-245j)
| (7.0398165628119152385 - 4.7104747726192467873e-873j)  +/-  (5.89e-247, 5.89e-247j)
| (-1.5554767642228736527 + 4.5340360676990933304e-875j)  +/-  (7.62e-249, 7.62e-249j)
| (-3.8931174284421970828 - 7.7186854957594774721e-871j)  +/-  (4.28e-245, 4.28e-245j)
| (-4.6350308632978133027 + 6.8172763942793249104e-872j)  +/-  (4e-245, 4e-245j)
| (-1.8355316042616288923 + 3.437146997924535631e-874j)  +/-  (4.1e-248, 4.1e-248j)
| (2.1198333626376326649 - 2.1403095945032208225e-871j)  +/-  (2.55e-247, 2.55e-247j)
| (-1.3009208583896173657 + 6.9070114428708679788e-877j)  +/-  (1.33e-249, 1.33e-249j)
| (1.3009208583896173657 - 3.5384074057596093599e-877j)  +/-  (1.3e-249, 1.3e-249j)
| (4.248117873568126463 + 2.3272847650408577247e-871j)  +/-  (4.44e-245, 4.44e-245j)
| (6.4681068287923266861 - 1.3713046340545390456e-883j)  +/-  (2.93e-246, 2.93e-246j)
| (4.6350308632978133027 + 2.2104121019430192062e-882j)  +/-  (3.94e-245, 3.94e-245j)
| (3.5737690684862660795 - 3.5399932133185412482e-902j)  +/-  (2.8e-245, 2.8e-245j)
| (-2.9613775055316068448 + 1.7379773064209359145e-914j)  +/-  (6.75e-246, 6.75e-246j)
| (2.9613775055316068448 + 1.8701492053522236005e-933j)  +/-  (7.24e-246, 7.24e-246j)
| (-2.6598968089773363996 - 1.3227009911029901698e-949j)  +/-  (2.62e-246, 2.62e-246j)
| (2.6598968089773363996 + 4.9747875288097355803e-960j)  +/-  (2.59e-246, 2.59e-246j)
| (-2.3862990891666860003 - 2.6451824882881557764e-972j)  +/-  (9.11e-247, 9.11e-247j)
| (-0.77668291926741166132 - 1.4637218425143232816e-978j)  +/-  (1.33e-251, 1.33e-251j)
| (-3.2703417454357226811 - 4.7939849736700429962e-971j)  +/-  (1.61e-245, 1.61e-245j)
| (2.3862990891666860003 + 2.1272320228074809671e-974j)  +/-  (9.15e-247, 9.15e-247j)
| (1.5554767642228736527 + 3.1193743128838833219e-981j)  +/-  (7.87e-249, 7.87e-249j)
| (0.77668291926741166132 - 9.0910659089543890964e-985j)  +/-  (1.33e-251, 1.33e-251j)
| (-2.1198333626376326649 + 6.0322147434145371245e-980j)  +/-  (2.35e-247, 2.35e-247j)
| (-5.0483640088744667684 + 1.2834765634387123854e-978j)  +/-  (3.05e-245, 3.05e-245j)
| (-1.0468425106882874223 + 1.7979544605608055916e-984j)  +/-  (1.69e-250, 1.69e-250j)
| (1.0468425106882874223 + 1.4493627885960345628e-984j)  +/-  (1.77e-250, 1.77e-250j)
| (1.8355316042616288923 - 3.0379240758085817343e-986j)  +/-  (4.41e-248, 4.41e-248j)
| (-5.4878264405491588638 + 5.2078128491398894946e-991j)  +/-  (1.84e-245, 1.84e-245j)
| (-0.51203083305217269548 + 8.8500949072733607057e-999j)  +/-  (9.14e-253, 9.14e-253j)
| (-0.25826775051909675926 - 3.1041783375243593729e-1000j)  +/-  (8.9e-254, 8.9e-254j)
| (0.25826775051909675926 + 1.6886102734864402078e-999j)  +/-  (6.86e-254, 6.86e-254j)
| (0.51203083305217269548 - 3.2973493259668381707e-998j)  +/-  (9.14e-253, 9.14e-253j)
| (-9.0946313516733698919e-1122 - 1.2484372309920835732e-1121j)  +/-  (6.95e-1120, 6.95e-1120j)
-------------------------------------------------
The weights are:
| (3.9057605859413032312e-06 - 7.1492224536136513996e-864j)  +/-  (3.62e-72, 5.89e-194j)
| (5.0863515908753531125e-27 - 6.3030793320847140248e-880j)  +/-  (5.39e-89, 8.76e-211j)
| (4.8996080480733928346e-07 + 3.4624231608685054535e-866j)  +/-  (1.41e-74, 2.29e-196j)
| (5.0863515908753531125e-27 + 1.5548806474530299692e-879j)  +/-  (2.58e-89, 4.2e-211j)
| (2.1319294547649792732e-14 + 1.9204738786078906918e-871j)  +/-  (4.08e-83, 6.63e-205j)
| (1.0579203320480329715e-16 - 4.7980308642788698652e-873j)  +/-  (1.41e-84, 2.29e-206j)
| (3.0534231324471660655e-09 + 3.6453602467357928245e-868j)  +/-  (4.74e-80, 7.71e-202j)
| (2.0478452909708065568e-19 - 2.5567498684446466095e-875j)  +/-  (7.58e-88, 1.23e-209j)
| (1.0405615988877967079e-22 + 2.3700437079926019874e-877j)  +/-  (1.77e-89, 2.88e-211j)
| (1.0579203320480329715e-16 + 1.3972900600371906379e-873j)  +/-  (9.89e-87, 1.61e-208j)
| (2.0533464348154024856e-12 - 5.6994568297897033424e-870j)  +/-  (4.03e-85, 6.56e-207j)
| (4.9674941340504285497e-08 + 4.9315898821554434377e-866j)  +/-  (6.86e-82, 1.12e-203j)
| (1.0405615988877967079e-22 - 6.4824764997929675702e-877j)  +/-  (3.35e-91, 5.46e-213j)
| (0.01343811304009347425 - 3.9000890191491988084e-862j)  +/-  (3.76e-71, 6.11e-193j)
| (4.9674941340504285497e-08 - 4.2874166308256133514e-867j)  +/-  (5.52e-82, 8.98e-204j)
| (1.0567165239914133855e-10 - 2.3616315630038877195e-869j)  +/-  (1.15e-84, 1.88e-206j)
| (0.0055867075824956810251 + 1.4834118077343496328e-862j)  +/-  (3.09e-74, 5.03e-196j)
| (0.0017411954828563019764 - 2.6022950265594533819e-862j)  +/-  (2.86e-77, 4.65e-199j)
| (0.025656834468251718334 + 8.3583012709563823635e-862j)  +/-  (2.26e-71, 3.67e-193j)
| (0.025656834468251718334 + 1.9400619381637320945e-861j)  +/-  (3.83e-72, 6.23e-194j)
| (3.0534231324471660655e-09 - 2.803038562453341425e-867j)  +/-  (1.14e-84, 1.86e-206j)
| (2.0478452909708065568e-19 + 7.7863081484687748007e-875j)  +/-  (3.06e-91, 4.98e-213j)
| (1.0567165239914133855e-10 + 1.3680482538335829551e-868j)  +/-  (6.76e-86, 1.1e-207j)
| (4.8996080480733928346e-07 - 7.8098260786757404229e-865j)  +/-  (2.32e-83, 3.77e-205j)
| (2.713055173079856165e-05 + 1.0800639741814518061e-864j)  +/-  (6.79e-84, 1.1e-205j)
| (2.713055173079856165e-05 + 2.1784561916583750436e-863j)  +/-  (7.57e-83, 1.23e-204j)
| (0.00013792151443861805275 - 5.2485245618395407038e-864j)  +/-  (2.74e-83, 4.46e-205j)
| (0.00013792151443861805275 - 5.0987379787251395001e-863j)  +/-  (1.12e-82, 1.82e-204j)
| (0.00049806518333288799201 + 1.9525977912627641277e-863j)  +/-  (8.52e-83, 1.39e-204j)
| (0.083681090562836417675 + 2.2461094292298641573e-861j)  +/-  (5.1e-80, 8.3e-202j)
| (3.9057605859413032312e-06 - 2.0466701282922795282e-865j)  +/-  (4.12e-85, 6.7e-207j)
| (0.00049806518333288799201 + 1.2493899913567788315e-862j)  +/-  (5.1e-83, 8.29e-205j)
| (0.01343811304009347425 - 1.0975277270072127562e-861j)  +/-  (8.21e-82, 1.33e-203j)
| (0.083681090562836417675 + 3.6452699589245773949e-861j)  +/-  (1.92e-81, 3.12e-203j)
| (0.0017411954828563019764 - 5.5544820134386517033e-863j)  +/-  (7.6e-83, 1.24e-204j)
| (2.0533464348154024856e-12 + 1.218188021615740066e-870j)  +/-  (4.64e-92, 7.55e-214j)
| (0.049853666318840028841 - 1.4267997017602744446e-861j)  +/-  (2.94e-82, 4.77e-204j)
| (0.049853666318840028841 - 2.7702984979573043872e-861j)  +/-  (7.19e-83, 1.17e-204j)
| (0.0055867075824956810251 + 5.2788246894217689559e-862j)  +/-  (1.24e-83, 2.02e-205j)
| (2.1319294547649792732e-14 - 4.8624549037854555141e-872j)  +/-  (1.51e-93, 2.46e-215j)
| (0.11157870147232638221 - 3.3751181857832098955e-861j)  +/-  (2.86e-83, 4.66e-205j)
| (0.13422081050506088619 + 4.4134713333283418252e-861j)  +/-  (6.56e-84, 1.07e-205j)
| (0.13422081050506088619 + 5.1703299870546711994e-861j)  +/-  (2.8e-84, 4.52e-206j)
| (0.11157870147232638221 - 4.6281780013064115549e-861j)  +/-  (2.63e-84, 4.2e-206j)
| (0.14715062952047031836 - 5.0266272345670178922e-861j)  +/-  (2.07e-84, 3.39e-206j)
