Starting with polynomial:
P : t
Extension levels are: 1 10 34
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^11 - 55/21*t^9 + 330/133*t^7 - 330/323*t^5 + 55/323*t^3 - 33/4199*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 16634372675715074333808519308001980730561855853693795/1515260311995642701509797231793347989411216181878586*t^43 + 305862931420013864247081145688211359502879920798151555101/5441299780376352941121681859369912629975677309126002326*t^41 - 56282818979412213773921991005040109306021466527592102921609273/315663403509083174996821568866697056446463979895672209937075*t^39 + 2440764757575182530668275294180984505302226079142023402250284/6219548841069654999937375041098214607447198524260208184995*t^37 - 56646025350379453859379892373001397140957213448230848280753934553453/89037381930566092172253477997100943802270083329707590120178471350*t^35 + 8126806584311345359389420876073371558053913260710507592384501443031/10325343450771530016614268876974731298078379411344241543348427770*t^33 - 7962275911003280826680324834922303886984441722339867819927682096748/10481788048510492592623575981171318135928051826667639142490070615*t^31 + 395044800758045956741371124360698308859599266292903590239650902068058/681316223153182018520532438776135678835323368733396544261854589975*t^29 - 432628489122256854857918698604692148148890649426140510448979149889469/1226369201675727633336958389797044221903582063720113779671338261955*t^27 + 1280312004943824375135480267306956677523626480886882168854613813728373/7459539161189967228417111573266921406735463549978469856405433587675*t^25 - 1174814926349222447740312214850513895518377956498629720011219035905922/17604512420408322659064383312909934519895693977949188861116823266913*t^23 + 900748945247506337305500583339535313387593587327538658304663870161716/43628574259272799633333471688515924679741502467091468047115605487567*t^21 - 52363894999628715089269869942290679559702316738256238652513227656749/10387755776017333246031778973456172542795595825497968582646572735135*t^19 + 104887561944380736508779156121947889920652651662624740051393902343/109344797642287718379281883931117605713637850794715458764700765633*t^17 - 12146822549925916591632483081524265848046184274284262317576455198748/86929114125618736111529097725238496542342091381798789717937108678235*t^15 + 6781634910192722205063278725740432796065826219143490543710264060001/446236119178176178705849368322890948917356069093233787218743824548273*t^13 - 26915387570320277428378590530299791161650823973181726949370289396663/22586412801479994276034529565881711106740022574103679383841033580981818*t^11 + 76968764450001190634261413909593682049350253859430108404588420693413/1201186498987799695589109072367345545222083018713695676322454967715851230*t^9 - 552094122387079102750050929663762955748992336945093661594703213/251821068970188615427486178693363845958507970380229701535105863252799*t^7 + 6860283323993904421097621973287784194307241017269305272696471592/162064845101528530357260747859086303720439772366133543630807416279122785*t^5 - 17827044653752198042000632421235548335827376077227202323719772579/48036020088093056397892085665433180422738348529321982332171318185131993474*t^3 + 14338846722924764823572358128415658386032423261165278096576133/16012006696031018799297361888477726807579449509773994110723772728377331158*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:
| (0.51909612920681181593 + 6.7428704134305470924e-849j)  +/-  (7.23e-246, 7.23e-246j)
| (0.9782286581460569928 + 2.1890396107397691496e-850j)  +/-  (3.24e-240, 3.24e-240j)
| (-0.88706259976809529908 + 1.6798822977652281379e-866j)  +/-  (2.04e-240, 2.04e-240j)
| (0.99830447999694790041 + 3.7390822411985613714e-869j)  +/-  (6.85e-241, 6.85e-241j)
| (0.93697730750483150689 + 1.3256453428842619159e-879j)  +/-  (3.57e-240, 3.57e-240j)
| (0.91132177238465617417 + 1.8668039886011881681e-888j)  +/-  (2.9e-240, 2.9e-240j)
| (-0.99109155573433854993 + 1.2622516807262179018e-894j)  +/-  (2.16e-240, 2.16e-240j)
| (-0.91132177238465617417 - 1.8355407584480808193e-895j)  +/-  (2.94e-240, 2.94e-240j)
| (-0.9782286581460569928 + 3.4864255639193078012e-895j)  +/-  (3.44e-240, 3.44e-240j)
| (-0.99830447999694790041 - 1.2830812867405204269e-898j)  +/-  (6.96e-241, 6.96e-241j)
| (0.85923913977231152766 - 1.3081749582819642573e-896j)  +/-  (8.04e-241, 8.04e-241j)
| (-0.19849655580992875252 + 2.5598631469055450961e-914j)  +/-  (5.71e-252, 5.71e-252j)
| (-0.85923913977231152766 - 5.7565518729652688422e-906j)  +/-  (8.07e-241, 8.07e-241j)
| (-0.82223694657126440006 - 2.2775207763839944925e-909j)  +/-  (1.89e-241, 1.89e-241j)
| (0.99109155573433854993 + 7.2313349298382434862e-908j)  +/-  (2.05e-240, 2.05e-240j)
| (0.88706259976809529908 + 1.4210560949545113167e-920j)  +/-  (1.94e-240, 1.94e-240j)
| (0.77862462538017224309 - 3.6969733132201831911e-928j)  +/-  (4.37e-242, 4.37e-242j)
| (-0.95997212101126122796 + 1.2946834658325754847e-924j)  +/-  (3.56e-240, 3.56e-240j)
| (-0.77862462538017224309 + 4.233760932190135345e-930j)  +/-  (4.27e-242, 4.27e-242j)
| (-0.93697730750483150689 + 1.4559574880856346592e-928j)  +/-  (3.68e-240, 3.68e-240j)
| (0.82223694657126440006 + 7.3060344817053422452e-929j)  +/-  (2.04e-241, 2.04e-241j)
| (0.73015200557404932409 + 1.7409541923516330264e-934j)  +/-  (7.98e-243, 7.98e-243j)
| (0.19849655580992875252 + 1.4406918717646808788e-946j)  +/-  (6.01e-252, 6.01e-252j)
| (-0.4057855931856229671 - 1.4418555148168016686e-943j)  +/-  (4.94e-248, 4.94e-248j)
| (-0.73015200557404932409 - 8.4167094068970158178e-938j)  +/-  (7.98e-243, 7.98e-243j)
| (3.7651692411797500689e-947 + 8.189026773466100782e-948j)  +/-  (1.73e-945, 1.73e-945j)
| (0.67792099987124251142 - 1.8478201819333752691e-938j)  +/-  (1.42e-243, 1.42e-243j)
| (0.95997212101126122796 + 2.5860641868084434214e-950j)  +/-  (3.86e-240, 3.86e-240j)
| (-0.67792099987124251142 + 8.262535895586691204e-971j)  +/-  (1.48e-243, 1.48e-243j)
| (-0.62339896593674833591 - 2.4239070792152334105e-972j)  +/-  (2.66e-244, 2.66e-244j)
| (-0.33922312700371203653 + 2.9778371771626800961e-977j)  +/-  (2.51e-249, 2.51e-249j)
| (0.26954315595234497233 - 5.421046234424077539e-978j)  +/-  (1.2e-250, 1.2e-250j)
| (0.62339896593674833591 + 3.8022045848059947181e-973j)  +/-  (2.65e-244, 2.65e-244j)
| (0.060951189834873209916 - 1.0247327020344389748e-980j)  +/-  (2.02e-254, 2.02e-254j)
| (-0.5694667156699958151 + 1.0445424500625176757e-977j)  +/-  (4.48e-245, 4.48e-245j)
| (-0.46653541464058167468 - 2.9853719209731525253e-979j)  +/-  (8.36e-247, 8.36e-247j)
| (0.12795563599012561477 - 9.117452251432402961e-983j)  +/-  (2.61e-253, 2.61e-253j)
| (0.5694667156699958151 + 2.1187370112557872012e-979j)  +/-  (4.51e-245, 4.51e-245j)
| (0.33922312700371203653 - 1.0504587427667722992e-984j)  +/-  (2.56e-249, 2.56e-249j)
| (-0.26954315595234497233 + 4.0938631505393352276e-982j)  +/-  (1.17e-250, 1.17e-250j)
| (-0.51909612920681181593 + 1.202753395153195396e-982j)  +/-  (7.55e-246, 7.55e-246j)
| (-0.12795563599012561477 - 2.1376255914564471071e-985j)  +/-  (2.72e-253, 2.72e-253j)
| (0.46653541464058167468 - 5.0061758897577231807e-983j)  +/-  (8.45e-247, 8.45e-247j)
| (0.4057855931856229671 + 3.0475127188936305434e-985j)  +/-  (4.94e-248, 4.94e-248j)
| (-0.060951189834873209916 + 1.7465071843492979758e-992j)  +/-  (1.25e-254, 1.25e-254j)
-------------------------------------------------
The weights are:
| (0.049655818517784974747 - 5.9749420832001074979e-850j)  +/-  (3.86e-73, 3.36e-189j)
| (0.015621842720756917589 - 1.0918368223791499019e-850j)  +/-  (1.79e-73, 1.56e-189j)
| (0.024047657693986275365 - 1.06293770177671656e-850j)  +/-  (6.13e-75, 5.34e-191j)
| (0.0043484687017863568108 + 2.1134466208812511532e-851j)  +/-  (6.65e-74, 5.79e-190j)
| (0.024897732978640612178 - 2.6999763454570580119e-850j)  +/-  (7.89e-74, 6.87e-190j)
| (0.025489860348945247282 + 2.6274544701430107313e-850j)  +/-  (5.41e-74, 4.71e-190j)
| (0.010064055861765659916 + 3.1791367812040701246e-852j)  +/-  (2.9e-76, 2.52e-192j)
| (0.025489860348945247282 + 6.9728714193591104197e-851j)  +/-  (5.91e-76, 5.14e-192j)
| (0.015621842720756917589 - 7.4542022372093114276e-852j)  +/-  (1.51e-76, 1.31e-192j)
| (0.0043484687017863568108 - 8.2675917963859088693e-853j)  +/-  (9.49e-77, 8.27e-193j)
| (0.032667321235025227611 + 4.9315209428506705607e-851j)  +/-  (1.96e-77, 1.71e-193j)
| (0.07116935939761053691 + 4.3662052049945373232e-850j)  +/-  (3.91e-79, 3.4e-195j)
| (0.032667321235025227611 + 1.0980295207635700856e-850j)  +/-  (2.98e-77, 2.59e-193j)
| (0.040725064643368438171 - 9.8266044415800009935e-851j)  +/-  (4.5e-78, 3.92e-194j)
| (0.010064055861765659916 - 1.2208832797809906361e-850j)  +/-  (2.22e-77, 1.93e-193j)
| (0.024047657693986275365 - 1.9204359020198157841e-850j)  +/-  (1.82e-77, 1.58e-193j)
| (0.04623829606701329131 - 1.8319018574353753583e-850j)  +/-  (2.26e-79, 1.97e-195j)
| (0.020795099747321867428 + 1.5631566272092306817e-851j)  +/-  (4.28e-78, 3.73e-194j)
| (0.04623829606701329131 + 9.8969917083860873844e-851j)  +/-  (6.64e-80, 5.78e-196j)
| (0.024897732978640612178 - 3.3088175338580262125e-851j)  +/-  (2.88e-78, 2.51e-194j)
| (0.040725064643368438171 + 7.4429234410757055991e-851j)  +/-  (2.56e-79, 2.23e-195j)
| (0.050537089627728197919 + 3.4442727411315166251e-850j)  +/-  (8.78e-81, 7.64e-197j)
| (0.07116935939761053691 + 9.1482229570183249513e-850j)  +/-  (1.65e-83, 1.43e-199j)
| (0.064230869222785943511 - 3.599588016272239065e-850j)  +/-  (1.3e-83, 1.13e-199j)
| (0.050537089627728197919 - 1.1405754958963558513e-850j)  +/-  (1.33e-81, 1.16e-197j)
| (0.05915901028721546568 - 1.0367437644449079008e-849j)  +/-  (1.59e-84, 1.38e-200j)
| (0.053698091493877539686 - 6.8332117301387168066e-850j)  +/-  (3.39e-82, 2.96e-198j)
| (0.020795099747321867428 + 3.4809934395454383557e-850j)  +/-  (2.04e-80, 1.78e-196j)
| (0.053698091493877539686 + 1.4828035032678203082e-850j)  +/-  (8.32e-83, 7.25e-199j)
| (0.05488064513678228137 - 2.1472097669212735012e-850j)  +/-  (1.26e-83, 1.1e-199j)
| (0.068455722182776895358 + 3.3990772272987281556e-850j)  +/-  (3.66e-85, 3.19e-201j)
| (0.070630460481985317414 - 1.0424826467811367566e-849j)  +/-  (7.28e-86, 6.34e-202j)
| (0.05488064513678228137 + 1.6143634599524528017e-849j)  +/-  (1.08e-84, 9.4e-201j)
| (0.063952411561030172604 + 1.035569937849327647e-849j)  +/-  (5.76e-86, 5.01e-202j)
| (0.052247348987882012614 + 3.2282455802245542869e-850j)  +/-  (3.52e-85, 3.07e-201j)
| (0.056655474446016639406 + 4.0842035611164060423e-850j)  +/-  (8.12e-86, 7.08e-202j)
| (0.069411803801521861962 - 9.3516408277867106332e-850j)  +/-  (2.9e-86, 2.52e-202j)
| (0.052247348987882012614 - 5.1755670350725330248e-849j)  +/-  (2.05e-86, 1.78e-202j)
| (0.068455722182776895358 + 1.4314530343334778026e-849j)  +/-  (2.66e-87, 2.32e-203j)
| (0.070630460481985317414 - 3.6226809737255373327e-850j)  +/-  (3.15e-87, 2.77e-203j)
| (0.049655818517784974747 - 4.120036131705974339e-850j)  +/-  (1.72e-86, 1.5e-202j)
| (0.069411803801521861962 - 5.891729055846362654e-850j)  +/-  (5.99e-88, 5.25e-204j)
| (0.056655474446016639406 + 6.2634657465672754517e-849j)  +/-  (4.16e-88, 3.55e-204j)
| (0.064230869222785943511 - 2.5017586462495594068e-849j)  +/-  (3.04e-88, 2.59e-204j)
| (0.063952411561030172604 + 8.3395462912185463906e-850j)  +/-  (2.58e-88, 2.36e-204j)
