Starting with polynomial:
P : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Extension levels are: 12 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 676039/1024*t^12 - 969969/512*t^10 + 2078505/1024*t^8 - 255255/256*t^6 + 225225/1024*t^4 - 9009/512*t^2 + 231/1024
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 676039/1024*t^39 - 4674646814067943812208069137696356038986057/736744565370451670402786637169143987200*t^37 + 62093674762666969977496801542838155450068957/2210233696111355011208359911507431961600*t^35 - 264309017502781151705650621505962078185783424981/3478465790940050516639716828730396421166080*t^33 + 2400212087488592426074609568555321177279167157843/17102456805455248373478607741257782404066560*t^31 - 8763255980037182299523963789521252839869480194149/46746715268244345554174861159437938571115264*t^29 + 12462211266430817030320258317005098133564273194733279/66614069257248192414699177152199062463839251200*t^27 - 8801641658907899851402385689310598182916886752490947/61939397730423757859281691036255268606727724800*t^25 + 132718859585211336204542981649875268793388495645779197/1600514037354149903083838896376836140797844408832*t^23 - 21972441455926643158098599581428900361811392367880809/589663066393634174820361698665150157136047940096*t^21 + 20560261219754542383902190142520255819303843997571155/1600514037354149903083838896376836140797844408832*t^19 - 66598858552802639507752287298327217298599770337311403/19795831514643433011826428455187183846710180846080*t^17 + 49443085137093121623837446472111464078951035653394631/75107713687911848780164978550563138712518039092480*t^15 - 315838835148051072958679596137274442427467400251621/3365482252682388852444550951445998565260371150592*t^13 + 1928437864956512721079114599260792323866319643260539/205294417413625719999117608038205912480882640186112*t^11 - 128293142400574456461903774613297275430881769006395/205294417413625719999117608038205912480882640186112*t^9 + 104204948777405298991755774920348605895562013478121/4105888348272514399982352160764118249617652803722240*t^7 - 2237826930410709977261458563949771364199479451657/4105888348272514399982352160764118249617652803722240*t^5 + 3817120189678816183068795600062700465566836387/821177669654502879996470432152823649923530560744448*t^3 - 5416761398348909210850392419418174462612643/821177669654502879996470432152823649923530560744448*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:
| (0.98156063424671925069 + 1.1736931368291362521e-852j)  +/-  (6.46e-242, 6.46e-242j)
| (-0.96243172765883034673 + 5.6613715402768278143e-867j)  +/-  (4.33e-242, 4.33e-242j)
| (-0.93655674136618045245 - 3.825340383097634348e-868j)  +/-  (2.59e-242, 2.59e-242j)
| (0.99927725490974903268 + 1.3247851468208789293e-865j)  +/-  (2.7e-242, 2.7e-242j)
| (0.90411725637047485668 + 8.4516595892518911076e-879j)  +/-  (1.15e-242, 1.15e-242j)
| (0.93655674136618045245 - 1.9545662270256760638e-892j)  +/-  (2.5e-242, 2.5e-242j)
| (-0.99927725490974903268 - 1.4860687036903775504e-899j)  +/-  (2.88e-242, 2.88e-242j)
| (-0.90411725637047485668 + 1.7409444043129681431e-911j)  +/-  (1.14e-242, 1.14e-242j)
| (0.96243172765883034673 - 7.8219468908250298682e-919j)  +/-  (4.69e-242, 4.69e-242j)
| (-0.99381860753331415898 + 2.4022254385914173396e-929j)  +/-  (6.62e-242, 6.62e-242j)
| (0.86534088064385613748 - 2.1224305194608058342e-937j)  +/-  (4.4e-243, 4.4e-243j)
| (0.99381860753331415898 + 9.9265576050347698422e-948j)  +/-  (5.98e-242, 5.98e-242j)
| (-0.82049846747331434717 + 4.7134061944585860018e-960j)  +/-  (1.25e-243, 1.25e-243j)
| (-0.86534088064385613748 - 1.6238393830366653361e-960j)  +/-  (3.97e-243, 3.97e-243j)
| (-0.98156063424671925069 - 3.8811885056314432335e-964j)  +/-  (6.28e-242, 6.28e-242j)
| (0.82049846747331434717 - 3.945594395820670932e-967j)  +/-  (1.23e-243, 1.23e-243j)
| (0.76990267419430468704 + 5.0116320381942164934e-974j)  +/-  (2.86e-244, 2.86e-244j)
| (-0.2888027818544233386 - 4.5978875602131241465e-982j)  +/-  (4.1e-251, 4.1e-251j)
| (-0.65290241370592929634 + 2.9698016401228094754e-979j)  +/-  (8.42e-246, 8.42e-246j)
| (-0.51761410214626703923 + 9.2797254544615336583e-982j)  +/-  (1.1e-247, 1.1e-247j)
| (0.2888027818544233386 + 1.8528863052668906957e-981j)  +/-  (4.3e-251, 4.3e-251j)
| (0.71390667945292835568 - 1.2745042166059797676e-978j)  +/-  (5.9e-245, 5.9e-245j)
| (0.041835281993367161313 + 1.298373781287550652e-980j)  +/-  (4.1e-255, 4.1e-255j)
| (-0.71390667945292835568 + 1.0463943185502861353e-979j)  +/-  (5.79e-245, 5.79e-245j)
| (-0.76990267419430468704 + 4.1590983319246044369e-984j)  +/-  (2.83e-244, 2.83e-244j)
| (-7.715352537560820391e-988 + 4.2263973117760862838e-988j)  +/-  (3.43e-986, 3.43e-986j)
| (0.65290241370592929634 - 3.5837457610338227428e-984j)  +/-  (7.86e-246, 7.86e-246j)
| (0.36783149899818019375 - 8.806126064687063453e-988j)  +/-  (6.47e-250, 6.47e-250j)
| (-0.20774760048786754486 + 4.1751695858780944421e-989j)  +/-  (2.37e-252, 2.37e-252j)
| (-0.5873179542866174473 - 6.0901306752512528415e-988j)  +/-  (1.06e-246, 1.06e-246j)
| (-0.12523340851146891547 - 1.0263942192704258329e-988j)  +/-  (1.14e-253, 1.14e-253j)
| (0.44428046687251340275 - 8.8526787869589869067e-987j)  +/-  (8.58e-249, 8.58e-249j)
| (0.5873179542866174473 + 7.9754490650584530736e-988j)  +/-  (1.05e-246, 1.05e-246j)
| (-0.041835281993367161313 - 4.6900248691930564054e-994j)  +/-  (6.54e-255, 6.54e-255j)
| (-0.44428046687251340275 - 2.0197671131234219146e-991j)  +/-  (8.39e-249, 8.39e-249j)
| (-0.36783149899818019375 - 4.7574233032376363442e-993j)  +/-  (7.34e-250, 7.34e-250j)
| (0.12523340851146891547 + 1.3947886539109213958e-991j)  +/-  (1.09e-253, 1.09e-253j)
| (0.51761410214626703923 - 2.6049442836174436661e-991j)  +/-  (1.01e-247, 1.01e-247j)
| (0.20774760048786754486 + 3.6344648952325654756e-998j)  +/-  (2.37e-252, 2.37e-252j)
-------------------------------------------------
The weights are:
| (0.015708142111668729614 - 3.8399171066086119407e-854j)  +/-  (4.67e-77, 7.28e-194j)
| (0.022528130553608176662 + 1.1706647199053062106e-854j)  +/-  (1.82e-77, 2.84e-194j)
| (0.029191468722889114938 - 1.394795649173107973e-854j)  +/-  (1.81e-77, 2.82e-194j)
| (0.0023539256069539227963 + 2.8644002143817884158e-853j)  +/-  (5.06e-78, 7.9e-195j)
| (0.035649527156843355705 + 3.9663343283125425842e-853j)  +/-  (1.53e-78, 2.39e-195j)
| (0.029191468722889114938 - 5.9447785488441142947e-853j)  +/-  (2.07e-78, 3.22e-195j)
| (0.0023539256069539227963 - 2.5619205035965875673e-855j)  +/-  (5.45e-80, 8.5e-197j)
| (0.035649527156843355705 + 1.6289437856778241066e-854j)  +/-  (5.47e-80, 8.54e-197j)
| (0.022528130553608176662 + 1.1896985660900464672e-852j)  +/-  (7.16e-79, 1.12e-195j)
| (0.0088047464350396065079 + 6.6565602483581133297e-855j)  +/-  (5.66e-80, 8.83e-197j)
| (0.041858060233696003973 - 2.9979144246333221843e-853j)  +/-  (1.61e-80, 2.5e-197j)
| (0.0088047464350396065079 - 1.0727084020199918937e-852j)  +/-  (8.25e-79, 1.29e-195j)
| (0.047774636723547921912 + 2.1811269491758577225e-854j)  +/-  (3.16e-82, 4.94e-199j)
| (0.041858060233696003973 - 1.8864940709848307278e-854j)  +/-  (1.07e-81, 1.67e-198j)
| (0.015708142111668729614 - 9.3914415195253277441e-855j)  +/-  (1.53e-80, 2.39e-197j)
| (0.047774636723547921912 + 2.4403742663530954317e-853j)  +/-  (7.46e-83, 1.16e-199j)
| (0.053358058110358998119 - 2.093108591898781329e-853j)  +/-  (1.01e-83, 1.58e-200j)
| (0.080135470380747332411 + 1.1412190504057737663e-853j)  +/-  (1.06e-86, 1.65e-203j)
| (0.063368561203459245841 - 3.4859723369464527422e-854j)  +/-  (6.89e-86, 1.08e-202j)
| (0.071602544663105747657 - 5.0982804324882224567e-854j)  +/-  (1.39e-86, 2.17e-203j)
| (0.080135470380747332411 + 2.0927412462907663974e-853j)  +/-  (3.3e-88, 5.15e-205j)
| (0.058568566149893602893 + 1.8710575686756680111e-853j)  +/-  (2.65e-86, 4.13e-203j)
| (0.083653861758430443944 - 1.0881962773459809787e-852j)  +/-  (1.69e-88, 2.63e-205j)
| (0.058568566149893602893 + 2.9537340758881507271e-854j)  +/-  (1.26e-86, 1.97e-203j)
| (0.053358058110358998119 - 2.5294454790710887638e-854j)  +/-  (2.48e-86, 3.87e-203j)
| (-3.9896471980255712853e-05 + 1.6368624065500593686e-852j)  +/-  (8.65e-89, 1.35e-205j)
| (0.063368561203459245841 - 1.7336225339346967542e-853j)  +/-  (1.03e-88, 1.61e-205j)
| (0.077829693205145505974 - 1.8276968017141829586e-853j)  +/-  (1.01e-89, 1.58e-206j)
| (0.081880242400274573541 - 1.7129653812517845495e-853j)  +/-  (1.52e-89, 2.37e-206j)
| (0.06772349107732482134 + 4.1747279502240086743e-854j)  +/-  (1.18e-88, 1.84e-205j)
| (0.083051899473796595177 + 3.0751687908392291306e-853j)  +/-  (9.05e-90, 1.41e-206j)
| (0.074978922269206428852 + 1.696332106452537924e-853j)  +/-  (7e-91, 1.09e-207j)
| (0.06772349107732482134 + 1.6613222329760901771e-853j)  +/-  (1.17e-90, 1.82e-207j)
| (0.083653861758430443944 - 9.9922778059028190307e-853j)  +/-  (4.18e-90, 6.52e-207j)
| (0.074978922269206428852 + 6.3920558704728959019e-854j)  +/-  (3.97e-91, 6.19e-208j)
| (0.077829693205145505974 - 8.3127117016399673457e-854j)  +/-  (2.95e-91, 4.6e-208j)
| (0.083051899473796595177 + 3.9746237137963285167e-853j)  +/-  (9.59e-92, 1.5e-208j)
| (0.071602544663105747657 - 1.6474340672036781076e-853j)  +/-  (1.49e-92, 2.39e-209j)
| (0.081880242400274573541 - 2.6327339355373089e-853j)  +/-  (3.46e-92, 5.35e-209j)
