Starting with polynomial:
P : t
Extension levels are: 1 2 6 46
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 Kronrod extension for:
P3 : t^9 - 117/4*t^7 + 945/4*t^5 - 2205/4*t^3 + 945/4*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 1645497558074402688597526632099383720044416897631390645936527900645930019/1242040548235081892440674122108620720124460215611443254141070791435908*t^53 + 82622128944557361464299610356798202348897581224870023985927464163183769143325/101847324955276715180135278012906899050205737680138346839567804897744456*t^51 - 93237338040717301038263631407497033362152617628375153852987556451668180214194209/305541974865830145540405834038720697150617213040415040518703414693233368*t^49 + 6901521019844332164712487727277212615069692472484371832667701412738174976441258427/87297707104522898725830238296777342043033489440118583005343832769495248*t^47 - 1308673656836180611386972725815371540650193521690148573212698442833743514574115135115/87297707104522898725830238296777342043033489440118583005343832769495248*t^45 + 62810069483922789383269456873843483907419797116200307715079179711158079633751314491715/29099235701507632908610079432259114014344496480039527668447944256498416*t^43 - 171517644526137541713900740637808886075692320713390520986744399068374996120412718118135/709737456134332509966099498347783268642548694635110430937754737963376*t^41 + 15169187175710962124848005566077606806135657124052144816778325449507583980417585672054735/709737456134332509966099498347783268642548694635110430937754737963376*t^39 - 1070836391103558599850403709226083442917767824342395855220277126910009331429090990335701755/709737456134332509966099498347783268642548694635110430937754737963376*t^37 + 60732087029930600318020021008657726818371696839923951116179718742580408817152781699196536275/709737456134332509966099498347783268642548694635110430937754737963376*t^35 - 2776894271863390575013809713496902749421812662631125436316258589592213438367231382427576780275/709737456134332509966099498347783268642548694635110430937754737963376*t^33 + 51231287393260979561582584656544065610837920297178667982444390011147648305980184389161889827925/354868728067166254983049749173891634321274347317555215468877368981688*t^31 - 1523550110303124514759840072006685772444563490159509850967601442872787477873335813504588719805925/354868728067166254983049749173891634321274347317555215468877368981688*t^29 + 1254977255842028643368795233311609515434543016826374361151357254434018775480925353164240051924475/12236852691971250171829301695651435666250839562674317774788874792472*t^27 - 23949813638140019344028720226761191220163538513767680249960162445271016553639521073171075366378375/12236852691971250171829301695651435666250839562674317774788874792472*t^25 + 362360803422971347663673787471540991643607098527292327711245608621095047904789626741422281592541875/12236852691971250171829301695651435666250839562674317774788874792472*t^23 - 4303226876548030064231847604638875709171926975150706343610935016298060938622372431557120292737145625/12236852691971250171829301695651435666250839562674317774788874792472*t^21 + 19800599427693046752966666906820492596736369633746885309423197036018812142186765059228563898647174375/6118426345985625085914650847825717833125419781337158887394437396236*t^19 - 34738650274427711241897576077754055856298628025237127118091883726901944960256408742440693128462751875/1529606586496406271478662711956429458281354945334289721848609349059*t^17 + 2914981165134874586930532228277505535395913707232202146544067794298724668682326235620203032876017015625/24473705383942500343658603391302871332501679125348635549577749584944*t^15 - 11134868109408269883317511954556486865298367817206824604208357394228581035173546587539664513811870365625/24473705383942500343658603391302871332501679125348635549577749584944*t^13 + 29955230562361677500116632120136890197313181673145873111167621870269527960723076987434382327837906321875/24473705383942500343658603391302871332501679125348635549577749584944*t^11 - 54190822487551331257879324045101666689030902681422279060289288252136137627836913499357343685039431009375/24473705383942500343658603391302871332501679125348635549577749584944*t^9 + 61571962903981613433604771824251883145382626294357098214058450063258088844540956247118412208602982809375/24473705383942500343658603391302871332501679125348635549577749584944*t^7 - 39312822969957584570531057194495880361551136014999373591512727096723175147049869187689084490808446671875/24473705383942500343658603391302871332501679125348635549577749584944*t^5 + 11473603177450517814594605799316417956628835479498074113279585837530534843547725119852972777810103734375/24473705383942500343658603391302871332501679125348635549577749584944*t^3 - 943903009182802754004932083792782045701244177630584131450687129825184586713402292425028357001724109375/24473705383942500343658603391302871332501679125348635549577749584944*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: 0
  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
Positive weights:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.865451836358424749 + 3.4464799379147361506e-628j)  +/-  (2.55e-243, 2.55e-243j)
| (-8.0010938485083247848 + 1.1184332495194749892e-627j)  +/-  (2.39e-242, 2.39e-242j)
| (-12.316080251450683627 + 1.7148224265595418114e-629j)  +/-  (8.44e-245, 8.44e-245j)
| (-13.240243025565495471 + 4.9602689269207096987e-630j)  +/-  (5.37e-246, 5.37e-246j)
| (-8.5272859185516515355 - 1.8881842965691534199e-626j)  +/-  (2.92e-242, 2.92e-242j)
| (-11.550002399274391179 + 3.4959491579094066058e-628j)  +/-  (5.66e-244, 5.66e-244j)
| (-5.0926888252123037806 + 4.4133011966984112218e-629j)  +/-  (5.11e-244, 5.11e-244j)
| (-7.489964075029995321 + 6.7674033085262571248e-628j)  +/-  (2e-242, 2e-242j)
| (-6.0257378505565082345 + 7.8233642189247860456e-628j)  +/-  (3.35e-243, 3.35e-243j)
| (-6.5039601760656038509 - 4.0091741017699496634e-627j)  +/-  (7.67e-243, 7.67e-243j)
| (-4.6360179025987323904 + 4.1819223491320486449e-629j)  +/-  (1.32e-244, 1.32e-244j)
| (-5.5556503671530191771 - 1.7260273500470332685e-628j)  +/-  (1.33e-243, 1.33e-243j)
| (-3.7389768076762027897 - 1.0792663151401462898e-630j)  +/-  (8.51e-246, 8.51e-246j)
| (-10.233226218187384855 + 6.7010672529790583017e-628j)  +/-  (6.76e-243, 6.76e-243j)
| (-9.6382895098820749093 + 5.0323933078758497946e-627j)  +/-  (1.29e-242, 1.29e-242j)
| (-9.0716241400918925323 + 9.4544421369653798875e-627j)  +/-  (2.14e-242, 2.14e-242j)
| (-4.1849560176727318607 - 6.3400578615421445332e-630j)  +/-  (3.81e-245, 3.81e-245j)
| (-6.9915380529935432666 - 8.365896807716616079e-627j)  +/-  (1.35e-242, 1.35e-242j)
| (10.865451836358424749 - 7.7425649370456029093e-627j)  +/-  (2.25e-243, 2.25e-243j)
| (13.240243025565495471 + 3.3224552665145949262e-636j)  +/-  (5.28e-246, 5.28e-246j)
| (11.550002399274391179 - 6.7378959741487799083e-640j)  +/-  (5.69e-244, 5.69e-244j)
| (8.0010938485083247848 - 9.7702840157585570532e-665j)  +/-  (2.45e-242, 2.45e-242j)
| (1.5367529171254680708 + 3.1320952279086426496e-692j)  +/-  (1.27e-249, 1.27e-249j)
| (4.6360179025987323904 - 2.4365138965059395082e-691j)  +/-  (1.35e-244, 1.35e-244j)
| (10.233226218187384855 + 6.0642442682163830441e-702j)  +/-  (6.79e-243, 6.79e-243j)
| (-1.7320508075688772935 + 8.1074617934006657677e-718j)  +/-  (5.41e-249, 5.41e-249j)
| (-2.0123794485666877403 + 3.7550373168081557496e-717j)  +/-  (1.48e-248, 1.48e-248j)
| (-3.297748672781599548 - 3.1493179246894487466e-715j)  +/-  (1.79e-246, 1.79e-246j)
| (3.7389768076762027897 + 7.0949922016668345574e-711j)  +/-  (8.81e-246, 8.81e-246j)
| (7.489964075029995321 + 1.7074392906574649631e-724j)  +/-  (2.07e-242, 2.07e-242j)
| (-1.1415617753905223547 - 1.4083415224160366806e-754j)  +/-  (4.26e-251, 4.26e-251j)
| (9.6382895098820749093 + 8.3381425372258702954e-743j)  +/-  (1.32e-242, 1.32e-242j)
| (3.297748672781599548 - 1.7650385306340277136e-756j)  +/-  (1.86e-246, 1.86e-246j)
| (-2.8612795760570581173 + 5.0834709005813807352e-773j)  +/-  (3.4e-247, 3.4e-247j)
| (2.8612795760570581173 - 6.4623669156573033463e-767j)  +/-  (3.62e-247, 3.62e-247j)
| (5.5556503671530191771 - 2.7462860831708913316e-785j)  +/-  (1.29e-243, 1.29e-243j)
| (5.0926888252123037806 + 1.9237772999362200256e-810j)  +/-  (4.59e-244, 4.59e-244j)
| (12.316080251450683627 + 2.8875783302530331689e-820j)  +/-  (9.37e-245, 9.37e-245j)
| (-0.74109534999454084186 - 6.2597490697292204162e-829j)  +/-  (2.08e-252, 2.08e-252j)
| (1.7320508075688772935 + 7.627052715480746142e-826j)  +/-  (5.68e-249, 5.68e-249j)
| (2.4305264143398318338 + 6.2017428668588242424e-824j)  +/-  (6.35e-248, 6.35e-248j)
| (8.5272859185516515355 + 2.2071264188720816539e-817j)  +/-  (2.57e-242, 2.57e-242j)
| (6.9915380529935432666 + 4.6222359895950586444e-819j)  +/-  (1.33e-242, 1.33e-242j)
| (6.0257378505565082345 - 4.801593345320473463e-828j)  +/-  (3.44e-243, 3.44e-243j)
| (-1.5367529171254680708 - 3.1248509686777112101e-843j)  +/-  (1.4e-249, 1.4e-249j)
| (9.0716241400918925323 - 1.1915624673076616289e-834j)  +/-  (2.16e-242, 2.16e-242j)
| (1.1415617753905223547 + 2.0136574563711541e-856j)  +/-  (4.56e-251, 4.56e-251j)
| (-2.4305264143398318338 + 2.6212672843733490363e-851j)  +/-  (6e-248, 6e-248j)
| (0.74109534999454084186 + 5.5665249007050092444e-855j)  +/-  (2.08e-252, 2.08e-252j)
| (0.35910385988980628011 - 1.7616062054957278017e-871j)  +/-  (9.81e-254, 9.81e-254j)
| (6.5039601760656038509 + 4.8009047937052994448e-844j)  +/-  (7.68e-243, 7.68e-243j)
| (-0.35910385988980628011 - 3.4264437726264776654e-872j)  +/-  (1.2e-253, 1.2e-253j)
| (2.0123794485666877403 + 7.0069104556014880396e-866j)  +/-  (1.51e-248, 1.51e-248j)
| (4.1849560176727318607 + 3.4555887261146489126e-861j)  +/-  (3.77e-245, 3.77e-245j)
| (2.9818451386433569793e-894 + 1.0576442288534562572e-894j)  +/-  (1.74e-892, 1.74e-892j)
-------------------------------------------------
The weights are:
| (6.0430726187810894282e-27 + 1.5854605610403875332e-646j)  +/-  (4.04e-42, 4.48e-164j)
| (2.5953582843639517036e-15 - 6.0134764974352799813e-640j)  +/-  (1.43e-35, 1.59e-157j)
| (3.7920273246832601227e-34 + 1.9724029694545617147e-650j)  +/-  (1.56e-45, 1.74e-167j)
| (3.6499943613112614766e-39 - 4.1315863897207675918e-653j)  +/-  (1.08e-47, 1.2e-169j)
| (3.4611827927408944168e-17 + 4.7459649441478587997e-641j)  +/-  (4.56e-38, 5.06e-160j)
| (3.0854784123172266898e-30 - 2.5375276604067724532e-648j)  +/-  (4.26e-44, 4.73e-166j)
| (4.2811207933713545973e-07 + 2.9613306440689290802e-634j)  +/-  (1.17e-29, 1.29e-151j)
| (1.3238781005892112343e-13 + 5.7249679808441224176e-639j)  +/-  (3.87e-36, 4.3e-158j)
| (2.4668923624361347998e-09 + 9.2230593058156894423e-636j)  +/-  (4.08e-33, 4.53e-155j)
| (1.2557771580230303577e-10 - 5.0523141738112610296e-637j)  +/-  (1.73e-34, 1.92e-156j)
| (3.896449514972316835e-06 - 1.1357917992246831798e-634j)  +/-  (6.36e-30, 7.05e-152j)
| (3.6926508143962167737e-08 - 5.428984207232581957e-635j)  +/-  (3.99e-32, 4.43e-154j)
| (0.00016299115478504650482 - 1.3586985522822013927e-634j)  +/-  (7.33e-28, 8.14e-150j)
| (4.4466997442141940363e-24 - 6.0842871867107641705e-645j)  +/-  (7.16e-45, 7.95e-167j)
| (1.5552611614077902065e-21 + 1.6282793283779718318e-643j)  +/-  (7.8e-44, 8.66e-166j)
| (2.9851357253780928266e-19 - 3.2752980537194814013e-642j)  +/-  (1.52e-42, 1.69e-164j)
| (2.8153687409599122192e-05 - 7.060506527050053103e-634j)  +/-  (4.56e-32, 5.06e-154j)
| (4.7754089820916923858e-12 - 3.83739494975597793e-637j)  +/-  (6.99e-38, 7.76e-160j)
| (6.0430726187810894282e-27 - 4.1620957166933760909e-647j)  +/-  (2.05e-61, 2.28e-183j)
| (3.6499943613112614766e-39 + 1.438376968225487641e-653j)  +/-  (4.85e-66, 5.38e-188j)
| (3.0854784123172266898e-30 + 7.3404174116690164232e-649j)  +/-  (6.73e-63, 7.47e-185j)
| (2.5953582843639517036e-15 + 9.1384545765862959948e-641j)  +/-  (2e-57, 2.22e-179j)
| (0.044050129943622889414 - 3.3996210673668649949e-631j)  +/-  (8.01e-32, 8.89e-154j)
| (3.896449514972316835e-06 - 2.8213485379229903243e-635j)  +/-  (3.8e-49, 4.22e-171j)
| (4.4466997442141940363e-24 + 1.4366232389172305729e-645j)  +/-  (4.56e-61, 5.06e-183j)
| (0.010053164551112199665 + 4.7807824471087201746e-631j)  +/-  (7.41e-33, 8.23e-155j)
| (0.021126155840174655693 - 1.6765868822119141675e-631j)  +/-  (1.71e-34, 1.9e-156j)
| (0.00076165934527924007927 + 3.0851278205260405824e-633j)  +/-  (1.1e-38, 1.22e-160j)
| (0.00016299115478504650482 - 4.1689224206167510821e-634j)  +/-  (2.84e-47, 3.15e-169j)
| (1.3238781005892112343e-13 - 8.420986834824717649e-640j)  +/-  (3.17e-57, 3.51e-179j)
| (0.084176119992467656935 + 3.2991442114804273155e-631j)  +/-  (6.88e-34, 7.63e-156j)
| (1.5552611614077902065e-21 - 3.4108265914227870228e-644j)  +/-  (7.08e-61, 7.86e-183j)
| (0.00076165934527924007927 + 1.4860374801106783601e-633j)  +/-  (1.23e-46, 1.37e-168j)
| (0.0028877187689196625932 - 1.047456330064904584e-632j)  +/-  (7.11e-41, 7.89e-163j)
| (0.0028877187689196625932 - 5.2590052020301145726e-633j)  +/-  (1.91e-45, 2.12e-167j)
| (3.6926508143962167737e-08 - 1.3856159214873621454e-636j)  +/-  (3.95e-54, 4.38e-176j)
| (4.2811207933713545973e-07 + 6.5534591981659119971e-636j)  +/-  (9.08e-53, 1.01e-174j)
| (3.7920273246832601227e-34 - 6.2554839027414463814e-651j)  +/-  (1.53e-67, 1.7e-189j)
| (0.11924828652658106429 - 3.3734808392784680553e-631j)  +/-  (1.26e-41, 1.4e-163j)
| (0.010053164551112199665 + 3.0289708880682874633e-631j)  +/-  (5.92e-44, 6.57e-166j)
| (0.0088804912809191327129 + 1.9892900109320155758e-632j)  +/-  (1.15e-46, 1.28e-168j)
| (3.4611827927408944168e-17 - 8.2381944864457186743e-642j)  +/-  (1.57e-60, 1.74e-182j)
| (4.7754089820916923858e-12 + 6.5859058154527045682e-639j)  +/-  (3.76e-58, 4.18e-180j)
| (2.4668923624361347998e-09 + 2.6343470833509032321e-637j)  +/-  (8.67e-57, 9.62e-179j)
| (0.044050129943622889414 - 5.1064560532935804963e-631j)  +/-  (8.31e-48, 9.24e-170j)
| (2.9851357253780928266e-19 + 6.0033773348269701699e-643j)  +/-  (2.58e-62, 2.86e-184j)
| (0.084176119992467656935 + 2.4341752938698984434e-631j)  +/-  (1.48e-49, 1.68e-171j)
| (0.0088804912809191327129 + 3.689525806449717135e-632j)  +/-  (2.13e-50, 2.39e-172j)
| (0.11924828652658106429 - 2.7674501281256133988e-631j)  +/-  (2.28e-49, 2.66e-171j)
| (0.13814587068730866168 + 3.4628920643768882906e-631j)  +/-  (1.27e-49, 1.52e-171j)
| (1.2557771580230303577e-10 - 4.4487177739187681842e-638j)  +/-  (9.33e-58, 1.04e-179j)
| (0.13814587068730866168 + 3.812144511858120875e-631j)  +/-  (4.14e-50, 5.07e-172j)
| (0.021126155840174655693 - 9.9178604455167597263e-632j)  +/-  (2.8e-51, 3.21e-173j)
| (2.8153687409599122192e-05 + 1.1203097563290655815e-634j)  +/-  (2.06e-54, 2.27e-176j)
| (0.14094978827187446517 - 3.9486559582255173221e-631j)  +/-  (1.91e-51, 5.58e-173j)
