Starting with polynomial:
P : t
Extension levels are: 1 28 30
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^29 - 406/57*t^27 + 23751/1045*t^25 - 475020/11077*t^23 + 910455/17119*t^21 - 780390/17119*t^19 + 1170585/42347*t^17 - 208104/17437*t^15 + 390195/107113*t^13 - 3381690/4391633*t^11 + 476905/4391633*t^9 - 1560780/162490421*t^7 + 78039/162490421*t^5 - 20010/1787394631*t^3 + 30015/387864634927*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 51271/3477*t^57 + 147829338/1432585*t^55 - 1497374879278/3284188089*t^53 + 129062239636450733/90411777149967*t^51 - 8380660773522778343/2487210261596151*t^49 + 286966408259803665730816228/46072304388995221528737*t^47 - 1816217692874009582848316056916/196429759893378882256084335*t^45 + 20073610403677007096341507198448571/1789965459510785829821967554227*t^43 - 411053438719128103440679858339889956121/36542394618534950034768466033621539*t^41 + 97600373741932032572289204772074403484503498/10372589907198258950862961203065697668415*t^39 - 3061149960753848401053335548288497629572958/463757362582882083399649441083165540255*t^37 + 27014919160026088915268866807029631932833205213388403581/6933771385386260550016988851822514001853897618402575*t^35 - 10585651097981429166855632271089488068145360552380346793/5462889158036220151539803741181495376020311509136745*t^33 + 1924303619245004915262411666256766314540750431668170562887534088/2370498997063731624541507692685850284866418700761737419951535*t^31 - 2365734269905430162420543099641492539625334632042572331535420958376/8275187693468044511615306954438393285516981399578938200907845529*t^29 + 92814656365494289689533221528966172530426335285038509575946760243/1100640727702646314352774816600180387728859595017888332140452361*t^27 - 30864357814703900601975611839093953275490503295054917057767627477/1489471070252868943924695264629873744077516545964378797056167725*t^25 + 2759434615431199728337642249488190272024715455590750739293628506/655367270911262335326865916437144447394107280224326670704713799*t^23 - 288568511949897217872403175763730786060905006557124843117025306/411871130730793325363524429697652044014478488362323876055531597*t^21 + 31437540690010232381602978560442078017268390141790006317155433/333419486782070787199043585945718321345054014388547899664001769*t^19 - 3575845056896453487167363317762592715470012005245164630388199/354064656242260928821275386933069300994902560171120525030193829*t^17 + 210536611046723343494318949795081851416082768142433537954109684/249615582650793954818999147787813857201406304920639970146286649445*t^15 - 127099138548945857631190379558702514213804120634383159222076/2377291263340894807799991883693465306680060046863237810917015709*t^13 + 214645118288264453920048949906615313787388982920781645426307/86496828273864864929953550845154545389205261705100883427980648489*t^11 - 3027520198930321945038066852128739582128111593842538479881911/37720480475429977915362471218564214021092512763578994345820288254703*t^9 + 7055124680283557916754162309289887475721422186753418325382/4191164497269997546151385690951579335676945862619888260646698694967*t^7 - 31905774522448489419792136792378611672984208583837962466/1560091412464687215368222037879360517304295743631145529616980399535*t^5 + 4985828139369957294528073056209359138403063512940783987963/42334952586924245213675146864301902869672830158323491320792303517861667*t^3 - 31508626907381284670042457929888179531604624192365687217/155228159485388899116808871835773643855467043913852801509571779565492779*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.99105540572280567469 + 6.4303020420989505566e-870j)  +/-  (3.06e-234, 3.06e-234j)
| (-0.99667944226059658616 + 1.6008891029295135789e-875j)  +/-  (2.25e-234, 2.25e-234j)
| (-0.94057891600297289495 + 1.6968385958676958681e-889j)  +/-  (9.45e-235, 9.45e-235j)
| (0.99667944226059658616 - 2.0065445958329668508e-893j)  +/-  (2.4e-234, 2.4e-234j)
| (0.92118023295305878509 + 1.8840216145043507459e-901j)  +/-  (4.8e-235, 4.8e-235j)
| (0.94057891600297289495 - 1.7773798581188976668e-901j)  +/-  (8.58e-235, 8.58e-235j)
| (-0.99105540572280567469 - 6.5436396375708476424e-899j)  +/-  (2.86e-234, 2.86e-234j)
| (-0.89917427059277965375 + 5.2272057758778640837e-907j)  +/-  (2.05e-235, 2.05e-235j)
| (-0.98254550526141317487 - 8.1716079324714106872e-915j)  +/-  (2.89e-234, 2.89e-234j)
| (0.99944866788205071899 + 4.9319894485610570308e-922j)  +/-  (8.96e-235, 8.96e-235j)
| (0.84761991976097683151 - 2.6551587595107084397e-928j)  +/-  (2.4e-236, 2.4e-236j)
| (0.971271237101307077 - 2.1684348009209300684e-924j)  +/-  (2.32e-234, 2.32e-234j)
| (-0.92118023295305878509 - 4.7772942675026560164e-929j)  +/-  (4.34e-235, 4.34e-235j)
| (-0.87463780492010279042 + 5.6185947772590808949e-938j)  +/-  (7.11e-236, 7.11e-236j)
| (0.9572855957780877258 + 3.2561994237824666561e-936j)  +/-  (1.53e-234, 1.53e-234j)
| (0.81818548761525244499 - 2.2730185586597295237e-940j)  +/-  (6.42e-237, 6.42e-237j)
| (0.89917427059277965375 + 1.2280596049526546628e-938j)  +/-  (1.95e-235, 1.95e-235j)
| (-0.71635866532758255758 + 3.9581550634481011692e-941j)  +/-  (6.26e-239, 6.26e-239j)
| (-0.78643319958049546222 + 8.935153839180054809e-940j)  +/-  (1.74e-237, 1.74e-237j)
| (-0.9572855957780877258 - 9.7363627416184382761e-936j)  +/-  (1.56e-234, 1.56e-234j)
| (-0.59628179713822782038 + 7.6542094618989937756e-947j)  +/-  (2e-241, 2e-241j)
| (0.71635866532758255758 + 1.0409453098167795865e-944j)  +/-  (6.87e-239, 6.87e-239j)
| (-0.99944866788205071899 - 2.8861388798287509633e-938j)  +/-  (9.04e-235, 9.04e-235j)
| (-0.84761991976097683151 - 5.0453355468139653141e-948j)  +/-  (2.28e-236, 2.28e-236j)
| (-0.81818548761525244499 + 1.1136792090204953667e-948j)  +/-  (6.74e-237, 6.74e-237j)
| (0.87463780492010279042 - 1.1142838673974635593e-947j)  +/-  (7.11e-236, 7.11e-236j)
| (0.75246285173447713391 + 2.9187576758860588447e-952j)  +/-  (3.38e-238, 3.38e-238j)
| (0.78643319958049546222 + 6.8766284803024145394e-950j)  +/-  (1.6e-237, 1.6e-237j)
| (-0.971271237101307077 - 2.3604860549020186386e-950j)  +/-  (2.25e-234, 2.25e-234j)
| (-0.67821453760268651516 - 1.3221871229016668265e-967j)  +/-  (1.07e-239, 1.07e-239j)
| (-0.053211772204649315908 - 2.5583030337697709625e-981j)  +/-  (2.02e-254, 2.02e-254j)
| (0.67821453760268651516 + 1.311811753209217447e-966j)  +/-  (1.09e-239, 1.09e-239j)
| (0.63814856847884718007 - 5.8359493529617615866e-968j)  +/-  (1.51e-240, 1.51e-240j)
| (0.10627823013267923017 - 8.4570844114867779966e-981j)  +/-  (5.05e-253, 5.05e-253j)
| (-0.63814856847884718007 + 2.9433911167848238335e-968j)  +/-  (1.6e-240, 1.6e-240j)
| (-0.75246285173447713391 - 1.6773824545805004981e-970j)  +/-  (3.27e-238, 3.27e-238j)
| (0.98254550526141317487 - 5.2557255175296356263e-979j)  +/-  (2.94e-234, 2.94e-234j)
| (0.59628179713822782038 - 6.4294449598801119703e-1005j)  +/-  (2.06e-241, 2.06e-241j)
| (0.41315288817400866389 + 9.6582522677364996706e-1011j)  +/-  (1.57e-245, 1.57e-245j)
| (-0.31403163786763993495 - 6.9827916111136185272e-1013j)  +/-  (6.61e-248, 6.61e-248j)
| (-0.55272435770131951698 + 5.4001217064918363794e-1008j)  +/-  (2.35e-242, 2.35e-242j)
| (-0.15904347800452204528 - 1.0179487324935330922e-1017j)  +/-  (9.85e-252, 9.85e-252j)
| (0.46102304538823387703 - 3.21405632718667425e-1008j)  +/-  (2.13e-244, 2.13e-244j)
| (0.55272435770131951698 - 2.2952010733670438302e-1007j)  +/-  (2.22e-242, 2.22e-242j)
| (-0.10627823013267923017 + 5.6160811414211122232e-1020j)  +/-  (4.38e-253, 4.38e-253j)
| (-0.5075929551242276421 - 1.8619710426634074201e-1011j)  +/-  (2.43e-243, 2.43e-243j)
| (-0.3641113787133778382 + 7.1489531215710626655e-1015j)  +/-  (1.05e-246, 1.05e-246j)
| (0.15904347800452204528 + 6.8483681274897429664e-1019j)  +/-  (1.04e-251, 1.04e-251j)
| (0.5075929551242276421 - 3.1746540607423212287e-1012j)  +/-  (2.26e-243, 2.26e-243j)
| (0.21135228616600107451 - 7.1692192884911213865e-1020j)  +/-  (1.94e-250, 1.94e-250j)
| (-0.21135228616600107451 + 2.0587734069614943174e-1019j)  +/-  (1.75e-250, 1.75e-250j)
| (-0.46102304538823387703 + 6.1600464004094193235e-1014j)  +/-  (2.05e-244, 2.05e-244j)
| (0.053211772204649315908 + 3.8165850800755837455e-1023j)  +/-  (2.64e-254, 2.64e-254j)
| (0.3641113787133778382 + 6.1999363893086490838e-1017j)  +/-  (1.04e-246, 1.04e-246j)
| (0.31403163786763993495 + 8.2724285842276181423e-1019j)  +/-  (6.66e-248, 6.66e-248j)
| (-3.9319419546095855136e-1030 + 2.083877302088312242e-1030j)  +/-  (2.63e-1028, 2.63e-1028j)
| (-0.41315288817400866389 - 6.489574415689770454e-1015j)  +/-  (1.57e-245, 1.57e-245j)
| (-0.2630618962952171376 + 1.1189575494683139965e-1018j)  +/-  (3.35e-249, 3.35e-249j)
| (0.2630618962952171376 - 2.6339451157562802132e-1018j)  +/-  (3.43e-249, 3.43e-249j)
-------------------------------------------------
The weights are:
| (0.0070863645879019408142 - 1.1322214700668280258e-870j)  +/-  (3.31e-42, 2.25e-153j)
| (0.0041577424473933126925 + 1.4106577578268008135e-872j)  +/-  (7.65e-43, 5.2e-154j)
| (0.01806382614654310456 - 6.0138378050997966697e-872j)  +/-  (7.26e-43, 4.94e-154j)
| (0.0041577424473933126925 - 4.984093591448325273e-870j)  +/-  (1.28e-42, 8.72e-154j)
| (0.020717940357934998911 + 1.9034681304399635276e-870j)  +/-  (2.12e-43, 1.44e-154j)
| (0.01806382614654310456 - 2.3011874635026314289e-870j)  +/-  (2.6e-43, 1.77e-154j)
| (0.0070863645879019408142 - 2.3008602251183776404e-872j)  +/-  (2.59e-44, 1.76e-155j)
| (0.023280815016891586368 - 7.9201784586274611592e-872j)  +/-  (1.54e-45, 1.05e-156j)
| (0.0099097535578796565065 + 3.2013311480262589105e-872j)  +/-  (1.38e-44, 9.36e-156j)
| (0.0014850323041236489082 + 1.1377228521245148707e-870j)  +/-  (1.54e-44, 1.05e-155j)
| (0.028240351564686208758 - 1.2660327578930714805e-870j)  +/-  (7.78e-47, 5.29e-158j)
| (0.012630296294620668202 - 4.1051319137140552265e-870j)  +/-  (2.16e-45, 1.46e-156j)
| (0.020717940357934998911 + 6.9558975671673091639e-872j)  +/-  (5.78e-47, 3.93e-158j)
| (0.025784977378141956107 + 8.8959509435968369537e-872j)  +/-  (7.82e-48, 5.31e-159j)
| (0.015344904173766641986 + 2.9315618110588799374e-870j)  +/-  (1.74e-45, 1.18e-156j)
| (0.030611279042093365703 + 1.1379344384858347045e-870j)  +/-  (1.77e-48, 1.2e-159j)
| (0.023280815016891586368 - 1.6293082291704621579e-870j)  +/-  (7.04e-47, 4.78e-158j)
| (0.037142080202205204433 - 1.3988302695069060295e-871j)  +/-  (1.68e-51, 1.14e-162j)
| (0.032876304939190425453 - 1.1893680453240244372e-871j)  +/-  (5.28e-51, 3.59e-162j)
| (0.015344904173766641986 + 5.0817545570723845729e-872j)  +/-  (2.81e-49, 1.91e-160j)
| (0.042730138674852857755 + 1.7314992676151290116e-871j)  +/-  (1.98e-53, 1.35e-164j)
| (0.037142080202205204433 - 8.6944928713486659454e-871j)  +/-  (1.88e-54, 1.27e-165j)
| (0.0014850323041236489082 - 4.7891926227127819144e-873j)  +/-  (1.79e-49, 1.21e-160j)
| (0.028240351564686208758 - 9.8766381881075612971e-872j)  +/-  (1.03e-50, 6.99e-162j)
| (0.030611279042093365703 + 1.087303101206579308e-871j)  +/-  (3.23e-51, 2.2e-162j)
| (0.025784977378141956107 + 1.4256018976142301116e-870j)  +/-  (2.91e-52, 1.98e-163j)
| (0.035050966880031063782 + 9.4508925261777097601e-871j)  +/-  (6.74e-55, 4.58e-166j)
| (0.032876304939190425453 - 1.033146071383860228e-870j)  +/-  (2.99e-54, 2.04e-165j)
| (0.012630296294620668202 - 4.1395511231618328049e-872j)  +/-  (1.38e-51, 9.35e-163j)
| (0.039125979732499542715 + 1.5066906269265936915e-871j)  +/-  (5.11e-56, 3.47e-167j)
| (0.053164222816562782182 - 3.2737111370895818646e-871j)  +/-  (4.32e-61, 2.94e-172j)
| (0.039125979732499542715 + 8.03936903892579682e-871j)  +/-  (2.5e-57, 1.7e-168j)
| (0.040985473885519458795 - 7.4679514166956169275e-871j)  +/-  (1.97e-58, 1.34e-169j)
| (0.052942446335892923789 + 3.8470746455228872319e-871j)  +/-  (1.71e-62, 1.16e-173j)
| (0.040985473885519458795 - 1.6176723379488685317e-871j)  +/-  (1.95e-58, 1.33e-169j)
| (0.035050966880031063782 + 1.2933332196823427804e-871j)  +/-  (8.29e-57, 5.64e-168j)
| (0.0099097535578796565065 + 7.4220091319189874682e-870j)  +/-  (2.26e-55, 1.54e-166j)
| (0.042730138674852857755 + 6.9620888749094931643e-871j)  +/-  (5.26e-60, 3.58e-171j)
| (0.048476941720340296566 + 5.3951255974546370873e-871j)  +/-  (8.55e-63, 5.81e-174j)
| (0.050550314528831236503 + 2.4902178772170391281e-871j)  +/-  (5.66e-64, 3.84e-175j)
| (0.044365570750096334647 - 1.8479732834228180786e-871j)  +/-  (1.84e-61, 1.25e-172j)
| (0.052561898412751483765 - 2.938790650480070846e-871j)  +/-  (1.93e-64, 1.31e-175j)
| (0.047242220937602114124 - 5.7313861339589627908e-871j)  +/-  (2.09e-63, 1.42e-174j)
| (0.044365570750096334647 - 6.5084189935174773758e-871j)  +/-  (2.71e-62, 1.84e-173j)
| (0.052942446335892923789 + 3.101889165869033722e-871j)  +/-  (7.27e-65, 4.94e-176j)
| (0.045874275756911573124 + 1.9678944810122557319e-871j)  +/-  (8.29e-64, 5.63e-175j)
| (0.049584147152819733354 - 2.352792795171563901e-871j)  +/-  (4.88e-65, 3.32e-176j)
| (0.052561898412751483765 - 4.0623150849212272291e-871j)  +/-  (1.45e-66, 9.88e-178j)
| (0.045874275756911573124 + 6.1000862155135165203e-871j)  +/-  (1.18e-64, 8e-176j)
| (0.052032173184001801295 + 4.2918994848774015149e-871j)  +/-  (5.77e-67, 3.92e-178j)
| (0.052032173184001801295 + 2.7830946836339840286e-871j)  +/-  (8.25e-67, 5.62e-178j)
| (0.047242220937602114124 - 2.0920612450420411635e-871j)  +/-  (3.27e-66, 2.22e-177j)
| (0.053164222816562782182 - 3.6451997269616684335e-871j)  +/-  (2.44e-67, 1.66e-178j)
| (0.049584147152819733354 - 5.0856436583213213736e-871j)  +/-  (1.4e-67, 9.46e-179j)
| (0.050550314528831236503 + 4.800334159616250253e-871j)  +/-  (4.67e-68, 3.18e-179j)
| (0.053235357903011630523 + 3.4546601683157916378e-871j)  +/-  (3.87e-68, 2.68e-179j)
| (0.048476941720340296566 + 2.2203767489978377123e-871j)  +/-  (1.58e-68, 1.1e-179j)
| (0.05136388226640826294 - 2.6336182207912247596e-871j)  +/-  (1.19e-68, 8.35e-180j)
| (0.05136388226640826294 - 4.536932348734335676e-871j)  +/-  (1.03e-68, 6.7e-180j)
