Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 6 46
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P2 : 8*t^9 - 117*t^7 + 945/2*t^5 - 2205/4*t^3 + 945/8*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^55 - 1645497558074402688597526632099383720044416897631390645936527900645930019/310510137058770473110168530527155180031115053902860813535267697858977*t^53 + 82622128944557361464299610356798202348897581224870023985927464163183769143325/50923662477638357590067639006453449525102868840069173419783902448872228*t^51 - 93237338040717301038263631407497033362152617628375153852987556451668180214194209/305541974865830145540405834038720697150617213040415040518703414693233368*t^49 + 6901521019844332164712487727277212615069692472484371832667701412738174976441258427/174595414209045797451660476593554684086066978880237166010687665538990496*t^47 - 1308673656836180611386972725815371540650193521690148573212698442833743514574115135115/349190828418091594903320953187109368172133957760474332021375331077980992*t^45 + 62810069483922789383269456873843483907419797116200307715079179711158079633751314491715/232793885612061063268880635458072912114755971840316221347583554051987328*t^43 - 171517644526137541713900740637808886075692320713390520986744399068374996120412718118135/11355799298149320159457591973564532298280779114161766895004075807414016*t^41 + 15169187175710962124848005566077606806135657124052144816778325449507583980417585672054735/22711598596298640318915183947129064596561558228323533790008151614828032*t^39 - 1070836391103558599850403709226083442917767824342395855220277126910009331429090990335701755/45423197192597280637830367894258129193123116456647067580016303229656064*t^37 + 60732087029930600318020021008657726818371696839923951116179718742580408817152781699196536275/90846394385194561275660735788516258386246232913294135160032606459312128*t^35 - 2776894271863390575013809713496902749421812662631125436316258589592213438367231382427576780275/181692788770389122551321471577032516772492465826588270320065212918624256*t^33 + 51231287393260979561582584656544065610837920297178667982444390011147648305980184389161889827925/181692788770389122551321471577032516772492465826588270320065212918624256*t^31 - 1523550110303124514759840072006685772444563490159509850967601442872787477873335813504588719805925/363385577540778245102642943154065033544984931653176540640130425837248512*t^29 + 1254977255842028643368795233311609515434543016826374361151357254434018775480925353164240051924475/25061074313157120351906409872694140244481719424357002802767615574982656*t^27 - 23949813638140019344028720226761191220163538513767680249960162445271016553639521073171075366378375/50122148626314240703812819745388280488963438848714005605535231149965312*t^25 + 362360803422971347663673787471540991643607098527292327711245608621095047904789626741422281592541875/100244297252628481407625639490776560977926877697428011211070462299930624*t^23 - 4303226876548030064231847604638875709171926975150706343610935016298060938622372431557120292737145625/200488594505256962815251278981553121955853755394856022422140924599861248*t^21 + 19800599427693046752966666906820492596736369633746885309423197036018812142186765059228563898647174375/200488594505256962815251278981553121955853755394856022422140924599861248*t^19 - 34738650274427711241897576077754055856298628025237127118091883726901944960256408742440693128462751875/100244297252628481407625639490776560977926877697428011211070462299930624*t^17 + 2914981165134874586930532228277505535395913707232202146544067794298724668682326235620203032876017015625/3207817512084111405044020463704849951293660086317696358754254793597779968*t^15 - 11134868109408269883317511954556486865298367817206824604208357394228581035173546587539664513811870365625/6415635024168222810088040927409699902587320172635392717508509587195559936*t^13 + 29955230562361677500116632120136890197313181673145873111167621870269527960723076987434382327837906321875/12831270048336445620176081854819399805174640345270785435017019174391119872*t^11 - 54190822487551331257879324045101666689030902681422279060289288252136137627836913499357343685039431009375/25662540096672891240352163709638799610349280690541570870034038348782239744*t^9 + 61571962903981613433604771824251883145382626294357098214058450063258088844540956247118412208602982809375/51325080193345782480704327419277599220698561381083141740068076697564479488*t^7 - 39312822969957584570531057194495880361551136014999373591512727096723175147049869187689084490808446671875/102650160386691564961408654838555198441397122762166283480136153395128958976*t^5 + 11473603177450517814594605799316417956628835479498074113279585837530534843547725119852972777810103734375/205300320773383129922817309677110396882794245524332566960272306790257917952*t^3 - 943903009182802754004932083792782045701244177630584131450687129825184586713402292425028357001724109375/410600641546766259845634619354220793765588491048665133920544613580515835904*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:
| (7.6830346741448676282 + 1.2042731313012876589e-934j)  +/-  (1.55e-243, 1.55e-243j)
| (8.167085019247815837 + 3.5820390814481111619e-935j)  +/-  (3.81e-244, 3.81e-244j)
| (-7.6830346741448676282 + 4.1281314410671164891e-933j)  +/-  (1.61e-243, 1.61e-243j)
| (-8.7087838634384977609 - 3.7979807712905006376e-937j)  +/-  (5.94e-245, 5.94e-245j)
| (6.8152998714767807262 + 1.3849460786057312427e-936j)  +/-  (9.36e-243, 9.36e-243j)
| (7.2359836522962683774 + 5.0279224060191398214e-937j)  +/-  (4.88e-243, 4.88e-243j)
| (-4.5989943450632400534 - 3.3745221152659738264e-940j)  +/-  (5e-243, 5e-243j)
| (-8.167085019247815837 + 1.8985536139735132068e-952j)  +/-  (3.87e-244, 3.87e-244j)
| (-9.3622656279352527663 - 1.2800956067648096899e-956j)  +/-  (3.73e-246, 3.73e-246j)
| (5.2962043882973367259 - 2.2097744037220739163e-951j)  +/-  (1.45e-242, 1.45e-242j)
| (6.0297016981244305775 - 7.0464532828934403043e-953j)  +/-  (1.72e-242, 1.72e-242j)
| (1.4229671544019500361 - 1.6373147138677240905e-961j)  +/-  (1.08e-248, 1.08e-248j)
| (-2.3318604491728060235 + 1.9880351064682500809e-958j)  +/-  (1.28e-246, 1.28e-246j)
| (-3.9284380485154323472 - 7.2344801395767697525e-955j)  +/-  (9.01e-244, 9.01e-244j)
| (-5.2962043882973367259 + 1.1178985943065980607e-964j)  +/-  (1.36e-242, 1.36e-242j)
| (2.3318604491728060235 + 1.2620324242106899454e-983j)  +/-  (1.36e-246, 1.36e-246j)
| (-7.2359836522962683774 - 5.2286530576019633371e-977j)  +/-  (5.05e-243, 5.05e-243j)
| (-5.6576277171902074402 - 1.2847509828499930063e-984j)  +/-  (1.61e-242, 1.61e-242j)
| (4.5989943450632400534 + 1.4247055464320590767e-993j)  +/-  (4.96e-243, 4.96e-243j)
| (-6.8152998714767807262 - 5.0478435293525911894e-992j)  +/-  (9.23e-243, 9.23e-243j)
| (5.6576277171902074402 + 2.2990457732431175615e-999j)  +/-  (1.65e-242, 1.65e-242j)
| (8.7087838634384977609 - 7.9504586039756401366e-1002j)  +/-  (6.71e-245, 6.71e-245j)
| (3.6010748027805722608 + 5.0403148751066514228e-1000j)  +/-  (3.34e-244, 3.34e-244j)
| (-3.6010748027805722608 - 2.0135756074233670702e-998j)  +/-  (3.07e-244, 3.07e-244j)
| (9.3622656279352527663 - 1.2421575175589582504e-1005j)  +/-  (3.79e-246, 3.79e-246j)
| (2.9592107790638377223 - 3.5343713925479245658e-1004j)  +/-  (2.63e-245, 2.63e-245j)
| (2.0232301911005156592 + 2.3465780274336645579e-1006j)  +/-  (2.38e-247, 2.38e-247j)
| (-6.0297016981244305775 - 4.4322190501326692959e-1000j)  +/-  (1.8e-242, 1.8e-242j)
| (-6.4146069458345601984 + 1.4164214159064604986e-1011j)  +/-  (1.47e-242, 1.47e-242j)
| (-1.4229671544019500361 - 3.961048658278770883e-1030j)  +/-  (1e-248, 1e-248j)
| (-0.80720607252199280332 - 2.1086853361444634611e-1032j)  +/-  (3.49e-251, 3.49e-251j)
| (1.7186417094327194137 - 4.6670414837413961426e-1029j)  +/-  (5.2e-248, 5.2e-248j)
| (4.260840095780958075 + 3.8942410848337167919e-1024j)  +/-  (2.39e-243, 2.39e-243j)
| (-4.9437639681955259086 - 1.3816442130878256833e-1025j)  +/-  (8.9e-243, 8.9e-243j)
| (-1.086648408707626953 - 1.407931103112415766e-1044j)  +/-  (8.91e-250, 8.91e-250j)
| (-0.52403354748695764515 + 1.1527123091662317993e-1047j)  +/-  (1.62e-252, 1.62e-252j)
| (3.9284380485154323472 + 3.8808680699275003188e-1039j)  +/-  (9.79e-244, 9.79e-244j)
| (0.52403354748695764515 - 1.5205690525161892709e-1048j)  +/-  (1.64e-252, 1.64e-252j)
| (3.278159696629798858 - 1.8660534453028038996e-1040j)  +/-  (9.4e-245, 9.4e-245j)
| (-0.25392477447834586951 - 3.7869538309131890114e-1049j)  +/-  (7.64e-254, 7.64e-254j)
| (-1.7186417094327194137 - 1.7862079848393095059e-1043j)  +/-  (4.55e-248, 4.55e-248j)
| (-2.6438558554070727122 + 1.2839817664367631502e-1039j)  +/-  (6.16e-246, 6.16e-246j)
| (0.80720607252199280332 - 1.0831630213895039671e-1046j)  +/-  (2.9e-251, 2.9e-251j)
| (1.086648408707626953 + 5.755733731769622085e-1045j)  +/-  (9.36e-250, 9.36e-250j)
| (2.6438558554070727122 - 1.8237596730619096119e-1041j)  +/-  (6.52e-246, 6.52e-246j)
| (-2.9592107790638377223 + 5.2976261740206572695e-1038j)  +/-  (2.66e-245, 2.66e-245j)
| (6.4146069458345601984 - 6.5396827291697408074e-1041j)  +/-  (1.42e-242, 1.42e-242j)
| (-2.0232301911005156592 - 1.1705527697466701986e-1044j)  +/-  (2.43e-247, 2.43e-247j)
| (0.25392477447834586951 - 7.7513621558346006285e-1053j)  +/-  (7.64e-254, 7.64e-254j)
| (-4.260840095780958075 - 2.6927770261716774564e-1042j)  +/-  (2.48e-243, 2.48e-243j)
| (-2.0778443709350027246e-1073 - 5.1870104202741009533e-1074j)  +/-  (1.18e-1071, 1.18e-1071j)
| (-1.2247448713915890491 - 2.7613689361658365069e-1056j)  +/-  (4.01e-249, 4.01e-249j)
| (-3.278159696629798858 + 2.7380162086232647138e-1056j)  +/-  (9.98e-245, 9.98e-245j)
| (4.9437639681955259086 - 1.4265146851110311179e-1061j)  +/-  (8.82e-243, 8.82e-243j)
| (1.2247448713915890491 + 1.4674133155131163704e-1069j)  +/-  (3.74e-249, 3.74e-249j)
-------------------------------------------------
The weights are:
| (6.0430726187810894282e-27 - 5.4638703206320633107e-960j)  +/-  (1.68e-76, 3.86e-198j)
| (3.0854784123172266898e-30 - 1.8676747607190136887e-962j)  +/-  (5.35e-78, 1.23e-199j)
| (6.0430726187810894282e-27 + 2.196161581082223918e-958j)  +/-  (1.76e-78, 4.04e-200j)
| (3.7920273246832601227e-34 - 1.9069050762327583487e-963j)  +/-  (1.69e-81, 3.88e-203j)
| (1.5552611614077902065e-21 - 1.8469276211991958088e-956j)  +/-  (2.89e-75, 6.65e-197j)
| (4.4466997442141940363e-24 - 9.4251899342876130746e-959j)  +/-  (3.72e-76, 8.56e-198j)
| (1.2557771580230303577e-10 - 2.1915032771783017498e-949j)  +/-  (1.23e-69, 2.83e-191j)
| (3.0854784123172266898e-30 + 6.7792953871840236136e-961j)  +/-  (1.22e-80, 2.81e-202j)
| (3.6499943613112614766e-39 + 1.5714453489707873059e-966j)  +/-  (2.5e-84, 5.74e-206j)
| (1.3238781005892112343e-13 - 9.0454834541126867544e-953j)  +/-  (2.91e-73, 6.7e-195j)
| (3.4611827927408944168e-17 - 1.2214674299735817088e-954j)  +/-  (3.7e-75, 8.5e-197j)
| (0.021126155840174655693 - 7.9188174366704939443e-945j)  +/-  (2.6e-50, 5.98e-172j)
| (0.00076165934527924007927 + 3.870744834297702849e-946j)  +/-  (5.08e-60, 1.17e-181j)
| (3.6926508143962167737e-08 - 1.6809810407503458505e-948j)  +/-  (2.8e-69, 6.44e-191j)
| (1.3238781005892112343e-13 + 1.4021816777492254083e-951j)  +/-  (7.06e-75, 1.62e-196j)
| (0.00076165934527924007927 + 1.1973756542089016972e-946j)  +/-  (1.98e-62, 4.55e-184j)
| (4.4466997442141940363e-24 - 2.5136413504413038207e-957j)  +/-  (1.29e-80, 2.97e-202j)
| (2.5953582843639517036e-15 - 1.1363406327338655524e-952j)  +/-  (1.17e-76, 2.69e-198j)
| (1.2557771580230303577e-10 - 4.166996153305228925e-951j)  +/-  (3.16e-75, 7.27e-197j)
| (1.5552611614077902065e-21 + 3.9847458493036586033e-956j)  +/-  (4.87e-80, 1.12e-201j)
| (2.5953582843639517036e-15 + 1.1071381061987211152e-953j)  +/-  (1.05e-77, 2.42e-199j)
| (3.7920273246832601227e-34 - 4.7693906007649457029e-965j)  +/-  (1.31e-87, 3.01e-209j)
| (4.2811207933713545973e-07 + 5.5638235014134181438e-949j)  +/-  (1.16e-73, 2.67e-195j)
| (4.2811207933713545973e-07 + 4.9804374289867722119e-948j)  +/-  (1e-73, 2.3e-195j)
| (3.6499943613112614766e-39 + 3.158390259755554245e-967j)  +/-  (3.57e-90, 8.2e-212j)
| (2.8153687409599122192e-05 + 9.1989423536417540638e-948j)  +/-  (1.85e-71, 4.25e-193j)
| (0.0028877187689196625932 - 4.2149458361346047758e-946j)  +/-  (4.67e-67, 1.07e-188j)
| (3.4611827927408944168e-17 + 8.8648063048791573793e-954j)  +/-  (1.88e-80, 4.33e-202j)
| (2.9851357253780928266e-19 - 6.2730493528820214859e-955j)  +/-  (2.03e-81, 4.66e-203j)
| (0.021126155840174655693 - 1.5531660087501005725e-944j)  +/-  (4.49e-67, 1.03e-188j)
| (0.084176119992467656935 + 2.8383219119538633297e-944j)  +/-  (1.33e-65, 3.06e-187j)
| (0.0088804912809191327129 + 1.5896246283822638123e-945j)  +/-  (2.6e-67, 5.99e-189j)
| (2.4668923624361347998e-09 + 2.3660237927008667069e-950j)  +/-  (4.62e-77, 1.06e-198j)
| (4.7754089820916923858e-12 - 1.9951544154121305488e-950j)  +/-  (8.72e-79, 2.01e-200j)
| (0.044050129943622889414 - 4.5156899186047897158e-944j)  +/-  (1.44e-66, 3.3e-188j)
| (0.11924828652658106429 - 2.8416514856703593515e-944j)  +/-  (2.23e-66, 5.13e-188j)
| (3.6926508143962167737e-08 - 1.2055016532287181251e-949j)  +/-  (2.83e-76, 6.51e-198j)
| (0.11924828652658106429 - 2.2324360187964034028e-944j)  +/-  (3.23e-68, 7.43e-190j)
| (3.896449514972316835e-06 - 2.3504821963173956151e-948j)  +/-  (1.31e-74, 3.02e-196j)
| (0.13814587068730866168 + 3.1616306744782131202e-944j)  +/-  (4.49e-68, 1.03e-189j)
| (0.0088804912809191327129 + 3.6324689618194639864e-945j)  +/-  (8.39e-72, 1.93e-193j)
| (0.00016299115478504650482 - 1.3364140944874980802e-946j)  +/-  (2.05e-75, 4.71e-197j)
| (0.084176119992467656935 + 1.9530075489373431291e-944j)  +/-  (4.12e-69, 9.48e-191j)
| (0.044050129943622889414 - 2.7185573875248369479e-944j)  +/-  (1.12e-69, 2.58e-191j)
| (0.00016299115478504650482 - 3.3858827918014589543e-947j)  +/-  (5.49e-74, 1.26e-195j)
| (2.8153687409599122192e-05 + 4.5518860314452100777e-947j)  +/-  (1.1e-76, 2.52e-198j)
| (2.9851357253780928266e-19 + 1.3672046897709463709e-955j)  +/-  (1.06e-84, 2.44e-206j)
| (0.0028877187689196625932 - 1.1373413606756155362e-945j)  +/-  (1.55e-74, 3.57e-196j)
| (0.13814587068730866168 + 2.8138144562076058937e-944j)  +/-  (4.66e-72, 1.07e-193j)
| (2.4668923624361347998e-09 + 6.8335888115710176677e-949j)  +/-  (1.02e-79, 2.34e-201j)
| (0.14094978827187446517 - 3.237509132814569951e-944j)  +/-  (1.67e-72, 3.84e-194j)
| (0.010053164551112199665 + 4.2998554239783815263e-944j)  +/-  (5.55e-73, 1.28e-194j)
| (3.896449514972316835e-06 - 1.516136013516596494e-947j)  +/-  (9.83e-78, 2.26e-199j)
| (4.7754089820916923858e-12 + 6.5297328931678559573e-952j)  +/-  (7.45e-82, 1.76e-203j)
| (0.010053164551112199665 + 2.4198640476860561462e-944j)  +/-  (4.6e-74, 9.68e-196j)
