Starting with polynomial:
P : t
Extension levels are: 1 6 38
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^7 - 21/13*t^5 + 105/143*t^3 - 35/429*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 2186967021800587663549575801481231033005196689/195135190394750335560135443022699379846719529*t^43 + 125816522611504796386300222556941107606628264572/2146487094342253691161489873249693178313914819*t^41 - 9085730119350444824504858713689152554833785783975123/47819439487756727731695671396256664626477394337682*t^39 + 40369372972408026052101566988085611961532281434277547/94412739501468411162578633269532389134327163179526*t^37 - 1673851233333849025938244062491476437292103606189469017/2360318487536710279064465831738309728358179079488150*t^35 + 780215435077711034272371376842076689375069464541906463/868755880286621094311122717900319042874691123374630*t^33 - 118533570477326590360381243604466718514418109394757266/133510102814610601073787257512819593169054263548915*t^31 + 179885971085737771800028501706000253426175053194499248/258977428351232611721442752524866921689370318450305*t^29 - 7623281164073610471604956902502512475618370391024210828/17586921725306432814174339648734144591087238898397985*t^27 + 1558836886182240308191320713380852556190828136788144626034/7200867395306022768914715733953924757572941704510730525*t^25 - 174350161143548083647035970483938998918156565590554374415/2016242870685686375296120405507098932120423677263004547*t^23 + 13373986121779682647035136314257118167722328634512807657/486129703999315687324361046387087094305714799656297539*t^21 - 311693745377284652613092390736139247275226409290193791973/45071168270793697296215759872174217743486986425276728973*t^19 + 16224389258066407297175461186649831982140048159279375163/11957656888169756425526630170168670013578180072012193401*t^17 - 6580123265288589256655116615563588027061748221421831980466/32225885313617493566794268308604565686593195294072861215695*t^15 + 148290192453666094652024104287932721130484679214093681593/6445177062723498713358853661720913137318639058814572243139*t^13 - 930752488383714019178442211962856072928272848263266185/495782850978730670258373358593916395178356850678044018703*t^11 + 11915642425577966456946142011618290292043837448027968562/112632849508713449543243183920563370140973979076766545703527*t^9 - 10717594569263325055405958976263054599201027493816442447/2791725652997066694648942996478839353444439620698760849228714*t^7 + 975262250650241485994680699062855574636752957743611119/12145819399402822632563583166498846537712821726416686811579470*t^5 - 3028833432764914187919663805093802936697682348871013/3817257525526601398805697566613923197566886828302387283639262*t^3 + 62613002724321761509737313622703641996480220520101/26720802678686209791639882966297462382968207798116710985474834*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:
| (0.40584515137739716691 - 4.0346385668466682283e-934j)  +/-  (3.69e-248, 3.69e-248j)
| (0.99311871465402599022 + 1.5131809450040851213e-924j)  +/-  (9.22e-240, 9.22e-240j)
| (-0.94910791234275852453 - 1.6695348567200702016e-931j)  +/-  (7.55e-240, 7.55e-240j)
| (0.98302717551808456035 - 4.3265082025439592913e-936j)  +/-  (1.19e-239, 1.19e-239j)
| (0.89695444033183137638 + 5.044852797403011051e-941j)  +/-  (2.11e-240, 2.11e-240j)
| (0.92527990983272503848 - 5.6773916476855897165e-942j)  +/-  (4.45e-240, 4.45e-240j)
| (-0.99311871465402599022 + 2.2677852294791105885e-947j)  +/-  (8.89e-240, 8.89e-240j)
| (-0.82731650802680986417 + 1.9650184796501508586e-964j)  +/-  (2.36e-241, 2.36e-241j)
| (0.99869716983629779653 + 1.552741525832596249e-966j)  +/-  (3.06e-240, 3.06e-240j)
| (-0.99869716983629779653 + 3.5231564012921695006e-969j)  +/-  (3.09e-240, 3.09e-240j)
| (0.86424872654774620284 + 1.4878425577134060927e-987j)  +/-  (7.93e-241, 7.93e-241j)
| (-0.2075060231037000142 - 1.9826837958797266427e-996j)  +/-  (8.59e-252, 8.59e-252j)
| (-0.92527990983272503848 - 5.9402051590388088509e-984j)  +/-  (4.39e-240, 4.39e-240j)
| (-0.78634138223211167125 + 2.7008081427389692054e-998j)  +/-  (6.66e-242, 6.66e-242j)
| (-0.98302717551808456035 + 2.2789611124653011223e-1009j)  +/-  (1.2e-239, 1.2e-239j)
| (0.78634138223211167125 - 1.277056273586038418e-1031j)  +/-  (6.49e-242, 6.49e-242j)
| (0.82731650802680986417 - 6.6221111947390692799e-1031j)  +/-  (2.37e-241, 2.37e-241j)
| (-0.96836499411155083244 + 2.9997421624204314041e-1029j)  +/-  (1.12e-239, 1.12e-239j)
| (-0.86424872654774620284 - 1.1700224709204207054e-1036j)  +/-  (7.47e-241, 7.47e-241j)
| (-0.89695444033183137638 + 2.1359324536634216461e-1037j)  +/-  (2.05e-240, 2.05e-240j)
| (0.94910791234275852453 - 6.1536070633590247756e-1039j)  +/-  (8.58e-240, 8.58e-240j)
| (0.74153118559939443986 - 9.6584391935362196938e-1044j)  +/-  (1.44e-242, 1.44e-242j)
| (0.2075060231037000142 - 1.6340219288024465915e-1054j)  +/-  (1.01e-251, 1.01e-251j)
| (-0.74153118559939443986 + 2.9711133437831782389e-1045j)  +/-  (1.34e-242, 1.34e-242j)
| (-0.69311334988001176448 - 1.0664597640750095425e-1046j)  +/-  (2.63e-243, 2.63e-243j)
| (7.7807973244183839548e-1061 - 1.0939675467331201407e-1060j)  +/-  (6.04e-1059, 6.04e-1059j)
| (0.69311334988001176448 - 6.3654603054616454329e-1045j)  +/-  (2.52e-243, 2.52e-243j)
| (0.96836499411155083244 - 1.360810497105417166e-1050j)  +/-  (1.19e-239, 1.19e-239j)
| (-0.4684154515856345436 - 5.8533281516781329487e-1059j)  +/-  (5.18e-247, 5.18e-247j)
| (-0.64133115028343268629 + 1.6754260825143420368e-1056j)  +/-  (4.17e-244, 4.17e-244j)
| (-0.27507723855088058796 - 4.2916378350871176651e-1063j)  +/-  (1.74e-250, 1.74e-250j)
| (0.4684154515856345436 - 4.6261720612282492713e-1059j)  +/-  (5.08e-247, 5.08e-247j)
| (0.64133115028343268629 + 4.774943116866201734e-1056j)  +/-  (4.35e-244, 4.35e-244j)
| (0.0696281261216648487 - 3.3544682129981372487e-1068j)  +/-  (2.4e-254, 2.4e-254j)
| (-0.58644085221929352121 + 7.5279113651584481569e-1059j)  +/-  (4.99e-245, 4.99e-245j)
| (-0.40584515137739716691 - 3.0472140568680012711e-1062j)  +/-  (4.07e-248, 4.07e-248j)
| (0.13891088318625219794 - 1.0143501156100243107e-1065j)  +/-  (5.05e-253, 5.05e-253j)
| (0.58644085221929352121 - 9.4827769776922023659e-1059j)  +/-  (5.64e-245, 5.64e-245j)
| (0.27507723855088058796 + 4.5424390650509277921e-1066j)  +/-  (1.89e-250, 1.89e-250j)
| (-0.34129641748462589504 + 8.2424076245814140354e-1066j)  +/-  (2.54e-249, 2.54e-249j)
| (-0.52870980256015580703 - 6.2828850760344773895e-1065j)  +/-  (5.2e-246, 5.2e-246j)
| (-0.13891088318625219794 - 1.9060148807655985294e-1069j)  +/-  (4.67e-253, 4.67e-253j)
| (0.34129641748462589504 - 3.5369985896600513351e-1064j)  +/-  (2.73e-249, 2.73e-249j)
| (0.52870980256015580703 + 4.4300433653140953242e-1062j)  +/-  (5.4e-246, 5.4e-246j)
| (-0.0696281261216648487 - 2.337740884046330582e-1072j)  +/-  (2.4e-254, 2.4e-254j)
-------------------------------------------------
The weights are:
| (0.063609968775742402781 + 2.3138264215385653673e-925j)  +/-  (1.06e-71, 6.15e-187j)
| (0.0078238329722524496142 - 7.8671703237173745684e-925j)  +/-  (4.9e-72, 2.85e-187j)
| (0.021550788606607373572 + 2.2380922129787462979e-926j)  +/-  (1.03e-73, 5.97e-189j)
| (0.012369281814680291637 + 2.1857381936879253993e-924j)  +/-  (3.65e-72, 2.12e-187j)
| (0.030538410380891620391 + 6.5948888499923234022e-925j)  +/-  (7.41e-73, 4.31e-188j)
| (0.026092866333498725576 - 7.9138972986948505896e-925j)  +/-  (8.88e-73, 5.17e-188j)
| (0.0078238329722524496142 - 5.9604753306388536398e-927j)  +/-  (1.14e-74, 6.64e-190j)
| (0.038986461793849319807 + 4.4801157952603985824e-926j)  +/-  (3.65e-75, 2.13e-190j)
| (0.0033455310841379611872 - 6.2612225647594351956e-925j)  +/-  (2.43e-73, 1.41e-188j)
| (0.0033455310841379611872 + 1.7535790259992758134e-927j)  +/-  (5.2e-75, 3.03e-190j)
| (0.034847282343399086061 - 5.6408639596124796612e-925j)  +/-  (2.28e-74, 1.32e-189j)
| (0.068138609566801942177 - 1.210596472597752511e-925j)  +/-  (6.11e-77, 3.56e-192j)
| (0.026092866333498725576 - 2.798509921075767183e-926j)  +/-  (1.46e-75, 8.49e-191j)
| (0.042929073222169761631 - 5.0600480743682673062e-926j)  +/-  (1.84e-76, 1.07e-191j)
| (0.012369281814680291637 + 1.1161913204477773797e-926j)  +/-  (2.89e-75, 1.68e-190j)
| (0.042929073222169761631 - 4.3545206753853206938e-925j)  +/-  (3.17e-77, 1.84e-192j)
| (0.038986461793849319807 + 4.9189759205852951861e-925j)  +/-  (1.33e-76, 7.75e-192j)
| (0.016959377319530801351 - 1.673758326774805317e-926j)  +/-  (6.6e-76, 3.84e-191j)
| (0.034847282343399086061 - 3.9138015602169179491e-926j)  +/-  (1.78e-77, 1.04e-192j)
| (0.030538410380891620391 + 3.35537700948195451e-926j)  +/-  (3.48e-77, 2.02e-192j)
| (0.021550788606607373572 + 9.8768629677220541948e-925j)  +/-  (5.46e-78, 3.18e-193j)
| (0.046653352176882474059 + 3.9010715587497553629e-925j)  +/-  (1.3e-79, 7.55e-195j)
| (0.068138609566801942177 - 1.8501129140104401353e-925j)  +/-  (3.3e-82, 1.92e-197j)
| (0.046653352176882474059 + 5.6579733329820033844e-926j)  +/-  (7.86e-80, 4.57e-195j)
| (0.050141725686281849706 - 6.2767288970282565874e-926j)  +/-  (8.86e-81, 5.15e-196j)
| (0.069685793869027812112 + 1.4939757996347545067e-925j)  +/-  (9.15e-84, 5.32e-199j)
| (0.050141725686281849706 - 3.5279459551978576071e-925j)  +/-  (1e-81, 5.84e-197j)
| (0.016959377319530801351 - 1.3262741661240130326e-924j)  +/-  (2.09e-79, 1.22e-194j)
| (0.061481051900040578212 - 8.97840356775654648e-926j)  +/-  (5.91e-84, 3.44e-199j)
| (0.053379930790552600576 + 6.9177752276625145844e-926j)  +/-  (1.22e-82, 7.12e-198j)
| (0.066949110723434202543 + 1.1271174835094098306e-925j)  +/-  (2.68e-84, 1.56e-199j)
| (0.061481051900040578212 - 2.5008890494148346594e-925j)  +/-  (1.33e-84, 7.72e-200j)
| (0.053379930790552600576 + 3.2140879008042773432e-925j)  +/-  (1.01e-83, 5.85e-199j)
| (0.069512844117742296176 - 1.6030302757325336733e-925j)  +/-  (3.09e-85, 1.8e-200j)
| (0.056356091583401177051 - 7.5816048231669465825e-926j)  +/-  (3.64e-84, 2.12e-199j)
| (0.063609968775742402781 + 9.7132519280566995121e-926j)  +/-  (4.15e-85, 2.41e-200j)
| (0.06899558101916209623 + 1.7213316992967095631e-925j)  +/-  (7.41e-86, 4.31e-201j)
| (0.056356091583401177051 - 2.9447387189971051263e-925j)  +/-  (6.18e-86, 3.6e-201j)
| (0.066949110723434202543 + 1.9907011407231624368e-925j)  +/-  (2.4e-86, 1.4e-201j)
| (0.065436167422632908619 - 1.0475880525954044548e-925j)  +/-  (3.1e-86, 1.8e-201j)
| (0.059059763431794174985 + 8.2683351766090405788e-926j)  +/-  (6.32e-86, 3.67e-201j)
| (0.06899558101916209623 + 1.298883833150732432e-925j)  +/-  (3.18e-87, 1.86e-202j)
| (0.065436167422632908619 - 2.1446298377305307853e-925j)  +/-  (1.2e-87, 7.23e-203j)
| (0.059059763431794174985 + 2.709463872044864562e-925j)  +/-  (9.65e-88, 6.02e-203j)
| (0.069512844117742296176 - 1.3929783452078751576e-925j)  +/-  (1.28e-87, 7.19e-203j)
