Starting with polynomial:
P : t
Extension levels are: 1 6 46
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 46 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^53 - 497358798350424908828226205924038373588938096455279/37328816368371875061089885084028121119367704491703*t^51 + 16779213139123763271764079492030611845404086060538694/200346427391383194491166630201322318072503860679491*t^49 - 2815030228865141493149650489035518578910875365924668438026/8524024962548385699904528805672688482849066043838486725*t^47 + 9442622520003800536051444880156400667751891903815445118801248/10305546179720998311184575326058280375764520847000730450525*t^45 - 514699059097775260230717853385490941506787335503102444581984/270650707750248440495756523714661908858462163658605042135*t^43 + 1800469196394572867531268638706687361351900659265629856650234/587510072921271004978593429526949021668369086966240213415*t^41 - 40158131398931249662863232357133647705407761650990551523870910/10222675268830115486627525673768912977029622113212579713421*t^39 + 1404070953451299249500005528294347564909799894488314276214337/344894577220989051505652013285051045108961609757509437025*t^37 - 98702116702740717749590710423389503891950874704044670317216587/28626249909342091274969117102659236744043813609873283273075*t^35 + 371497865363828920513536644882370201854777132381455057788506308/154581749510447292884833232354359878417836593493315729674605*t^33 - 512108254151135547852259558623146600023144727080480161825392156/370059339737131398118237131999831224091184572302180080130115*t^31 + 1790823813057217637811544466987252550653376559559134886397736/2716787143787616493415311536372509542827383956834692468141*t^29 - 24030238398977675410140547778034408042356873222477693971369736/92617743538214198639158347830881007141842634892091788686625*t^27 + 2548547539941198206873918278013882317931039922634328918289168868/30299723284186889502951321718154516151255407185253584054405875*t^25 - 49272856032172594542928456915136219813661861552322722966823172/2206441387874122209958506504604072458193983497592825095243915*t^23 + 8693974690541318009081893048550250365799196779514168411465387/1805270226442463626329687140130604738522350134394129623381385*t^21 - 87444186110735387422731393039229738654711341592734553908894139/104826024482092387902210499936917115150197797803819126797679089*t^19 + 205021450572295218989161631170165472217759485459485176860815238/1793076734562106635169390130499898022306014962433748221539247575*t^17 - 21805410775064497263505076440144131440319221254007919702772486/1793076734562106635169390130499898022306014962433748221539247575*t^15 + 2220840470040586843748908815772733082464029099994301959636744/2271230530445335071214560831966537494920952285749414413949713595*t^13 - 4749334942945288109966609337776615208758242154544819393272/82757387749020306238587236792302985644892998266172994840272965*t^11 + 225105553675691833066784022233135027966043901742128219754186/96144523727257281958672884896686979522758689276611924569253120811*t^9 - 11080127073698927567593474517830370089462347208330919348786198/179202709502748989428526404904658231277141890290573892738802344622725*t^7 + 56436889156108781117292142314435168514749121310083556903677/59734236500916329809508801634886077092380630096857964246267448207575*t^5 - 8089518484463856892709832714013988119266975342906963279203/1182737882718143330228274272370744326429136475917787692076095474509985*t^3 + 5843346075187578768997559019453346440006139200337170784/394245960906047776742758090790248108809712158639262564025365158169995*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:
| (-0.97926804762290628805 - 1.6114108247814973096e-873j)  +/-  (2.1e-236, 2.1e-236j)
| (0.99578622164257325157 + 3.9571274275879755784e-880j)  +/-  (1.87e-236, 1.87e-236j)
| (-0.94910791234275852453 + 8.8671882602036202419e-890j)  +/-  (9.12e-237, 9.12e-237j)
| (-0.99922980310880762556 - 2.1466020183411644409e-889j)  +/-  (7.16e-237, 7.16e-237j)
| (0.96589964414193507946 - 6.5688706308784780767e-893j)  +/-  (1.47e-236, 1.47e-236j)
| (0.92893581812780978774 - 3.4736356645282080391e-906j)  +/-  (4.84e-237, 4.84e-237j)
| (-0.9892068248842597406 + 4.3527928074376757199e-911j)  +/-  (2.39e-236, 2.39e-236j)
| (-0.87872467137552887135 - 2.7568473672405391034e-912j)  +/-  (7.53e-238, 7.53e-238j)
| (-0.99578622164257325157 + 3.9358362027552305841e-911j)  +/-  (1.82e-236, 1.82e-236j)
| (0.99922980310880762556 + 2.7838752091278083015e-908j)  +/-  (7.23e-237, 7.23e-237j)
| (0.87872467137552887135 - 4.7290061785669314876e-923j)  +/-  (8.15e-238, 8.15e-238j)
| (0.94910791234275852453 - 1.0844209734317289154e-937j)  +/-  (1.02e-236, 1.02e-236j)
| (-0.92893581812780978774 + 2.377051156983032161e-956j)  +/-  (4.79e-237, 4.79e-237j)
| (-0.84885986332950034662 + 5.2990210524574926864e-960j)  +/-  (2.52e-238, 2.52e-238j)
| (0.97926804762290628805 - 5.6975248438864810096e-956j)  +/-  (2.16e-236, 2.16e-236j)
| (0.90544792852686475006 - 2.6710311010741329231e-970j)  +/-  (2.11e-237, 2.11e-237j)
| (0.84885986332950034662 - 6.7219958757251309563e-974j)  +/-  (2.57e-238, 2.57e-238j)
| (-0.96589964414193507946 - 8.7882943724730273738e-975j)  +/-  (1.53e-236, 1.53e-236j)
| (-0.74153118559939443986 + 1.4478467291733894e-980j)  +/-  (3.58e-240, 3.58e-240j)
| (-0.90544792852686475006 - 2.0883411008834404911e-977j)  +/-  (2.08e-237, 2.08e-237j)
| (0.81595942993114102612 - 1.6605919191528899242e-978j)  +/-  (7.2e-239, 7.2e-239j)
| (0.78014058408954629057 - 4.2714570865014741418e-982j)  +/-  (1.67e-239, 1.67e-239j)
| (0.9892068248842597406 + 1.6198120009927285944e-984j)  +/-  (2.49e-236, 2.49e-236j)
| (-0.81595942993114102612 - 1.2876067704967681875e-997j)  +/-  (7.59e-239, 7.59e-239j)
| (-0.78014058408954629057 - 1.4031458932863379753e-1001j)  +/-  (1.65e-239, 1.65e-239j)
| (0.29410973989288452854 - 3.1761414653510825868e-1011j)  +/-  (3.76e-249, 3.76e-249j)
| (0.74153118559939443986 - 4.4160881937550507152e-1002j)  +/-  (3.37e-240, 3.37e-240j)
| (0.70026916917185830928 + 1.6071718206507532175e-1003j)  +/-  (6.42e-241, 6.42e-241j)
| (-0.40584515137739716691 + 5.8070516911455638379e-1009j)  +/-  (9.44e-247, 9.44e-247j)
| (-0.61038608075005898237 + 4.312142614898179918e-1004j)  +/-  (1.26e-242, 1.26e-242j)
| (-0.70026916917185830928 + 9.537525440462660118e-1003j)  +/-  (6.57e-241, 6.57e-241j)
| (0.65650199231085992828 - 9.7959153801652571854e-1005j)  +/-  (9.99e-242, 9.99e-242j)
| (0.45963266211036751021 + 1.2497048741010328894e-1010j)  +/-  (1.28e-245, 1.28e-245j)
| (0.11913321609243148322 + 7.9809607147240150347e-1019j)  +/-  (4.8e-253, 4.8e-253j)
| (-0.65650199231085992828 + 2.4526534209795315033e-1007j)  +/-  (9.84e-242, 9.84e-242j)
| (-0.45963266211036751021 - 1.6137346930970586198e-1011j)  +/-  (1.27e-245, 1.27e-245j)
| (0.059673455694931269713 - 2.4058239499322136292e-1021j)  +/-  (2.61e-254, 2.61e-254j)
| (0.56208626068936942579 - 7.9280996926533326041e-1008j)  +/-  (1.46e-243, 1.46e-243j)
| (0.35060498230371059528 - 3.4960236219820194653e-1013j)  +/-  (5.56e-248, 5.56e-248j)
| (-0.11913321609243148322 + 2.3864881992103970834e-1019j)  +/-  (5.06e-253, 5.06e-253j)
| (-0.56208626068936942579 + 1.9978956071910842748e-1010j)  +/-  (1.47e-243, 1.47e-243j)
| (-0.17816636694744912322 + 6.0527106531611836144e-1018j)  +/-  (9.47e-252, 9.47e-252j)
| (0.40584515137739716691 + 9.9637017707934010614e-1012j)  +/-  (9.07e-247, 9.07e-247j)
| (0.61038608075005898237 + 2.2984147546415945334e-1011j)  +/-  (1.29e-242, 1.29e-242j)
| (-3.6020039229928310698e-1034 - 3.7390843416281659128e-1033j)  +/-  (1.99e-1031, 1.99e-1031j)
| (-0.51177517236857447879 - 5.989426387941844061e-1016j)  +/-  (1.42e-244, 1.42e-244j)
| (-0.29410973989288452854 - 6.443241417751895974e-1020j)  +/-  (3.71e-249, 3.71e-249j)
| (0.17816636694744912322 + 1.6569472796261851895e-1022j)  +/-  (1.01e-251, 1.01e-251j)
| (0.51177517236857447879 - 3.5744481598214219527e-1015j)  +/-  (1.47e-244, 1.47e-244j)
| (0.23656155175711493063 + 3.3698895026575302071e-1021j)  +/-  (2.11e-250, 2.11e-250j)
| (-0.23656155175711493063 + 1.3765843545315892523e-1022j)  +/-  (1.86e-250, 1.86e-250j)
| (-0.35060498230371059528 - 6.2415008021982497763e-1020j)  +/-  (5.31e-248, 5.31e-248j)
| (-0.059673455694931269713 + 1.4150940223219204418e-1025j)  +/-  (2.39e-254, 2.39e-254j)
-------------------------------------------------
The weights are:
| (0.011650229637211595332 - 1.1603454588345703779e-874j)  +/-  (1.18e-54, 5.28e-167j)
| (0.0049574636138990276423 - 4.3821013306520537222e-876j)  +/-  (2.42e-56, 1.08e-168j)
| (0.018491154559841565159 - 8.5182636993342281823e-874j)  +/-  (5.96e-55, 2.66e-167j)
| (0.0019981523994904915778 - 1.4106837864021511824e-874j)  +/-  (2.19e-55, 9.75e-168j)
| (0.015084931561958256769 + 1.1580613382852360566e-875j)  +/-  (5.98e-57, 2.67e-169j)
| (0.021842189012479065973 + 1.4900784386029519196e-875j)  +/-  (4.48e-57, 2e-169j)
| (0.008237600805851949382 - 1.4288675069837782063e-873j)  +/-  (1.55e-55, 6.92e-168j)
| (0.028310709902792539688 + 3.2852267467974989125e-874j)  +/-  (6.57e-58, 2.93e-170j)
| (0.0049574636138990276423 + 5.2394406467244023664e-874j)  +/-  (1.77e-55, 7.91e-168j)
| (0.0019981523994904915778 + 1.4231027628988098009e-876j)  +/-  (1.69e-58, 7.55e-171j)
| (0.028310709902792539688 + 1.7777732378015903142e-875j)  +/-  (1.19e-59, 5.29e-172j)
| (0.018491154559841565159 - 1.3322837233067972277e-875j)  +/-  (1.05e-58, 4.7e-171j)
| (0.021842189012479065973 + 5.6491736712234758464e-874j)  +/-  (1.6e-58, 7.14e-171j)
| (0.03140123880767673995 - 2.6836223859594576368e-874j)  +/-  (7.2e-60, 3.21e-172j)
| (0.011650229637211595332 - 9.5856342615578664122e-876j)  +/-  (7.56e-59, 3.37e-171j)
| (0.025120148425688430391 - 1.6372705840522581005e-875j)  +/-  (1.02e-59, 4.54e-172j)
| (0.03140123880767673995 - 1.9143480168804157368e-875j)  +/-  (3.42e-61, 1.53e-173j)
| (0.015084931561958256769 + 1.6850106858772348047e-873j)  +/-  (2.68e-59, 1.2e-171j)
| (0.039959508484213774659 + 1.6786619800334304073e-874j)  +/-  (6.48e-64, 2.89e-176j)
| (0.025120148425688430391 - 4.180127991455049965e-874j)  +/-  (7.14e-61, 3.19e-173j)
| (0.034380082064445884432 + 2.04905841952600134e-875j)  +/-  (1.01e-62, 4.5e-175j)
| (0.037236290223478981836 - 2.1835384967545038396e-875j)  +/-  (9.74e-64, 4.35e-176j)
| (0.008237600805851949382 + 7.2148032875942133192e-876j)  +/-  (1.81e-60, 8.07e-173j)
| (0.034380082064445884432 + 2.2524945597036218877e-874j)  +/-  (2.03e-63, 9.06e-176j)
| (0.037236290223478981836 - 1.9292815785641368851e-874j)  +/-  (3.71e-64, 1.66e-176j)
| (0.057055746030597882031 - 3.7821539174375103081e-875j)  +/-  (1.12e-69, 5.02e-182j)
| (0.039959508484213774659 + 2.3191574221777626112e-875j)  +/-  (6e-66, 2.68e-178j)
| (0.042539938900946265301 - 2.4571253043086431258e-875j)  +/-  (5.09e-67, 2.27e-179j)
| (0.054546356807835868008 - 8.2051386823639936572e-875j)  +/-  (1.47e-70, 6.56e-183j)
| (0.047236007906149524055 - 1.1827377139653741308e-874j)  +/-  (3.56e-69, 1.59e-181j)
| (0.042539938900946265301 - 1.4791558501315335529e-874j)  +/-  (1.06e-67, 4.74e-180j)
| (0.044968334414771128196 + 2.5985652305123521442e-875j)  +/-  (6.56e-69, 2.92e-181j)
| (0.052996596336984927451 + 3.2211048665838636344e-875j)  +/-  (2.01e-71, 8.99e-184j)
| (0.059281837297994393468 + 4.4720800840905022893e-875j)  +/-  (4.57e-73, 2.04e-185j)
| (0.044968334414771128196 + 1.3169447728219867344e-874j)  +/-  (2.15e-69, 9.59e-182j)
| (0.052996596336984927451 + 8.9194226634313454056e-875j)  +/-  (5.09e-72, 2.27e-184j)
| (0.059602184834616330268 - 4.7411391316100683529e-875j)  +/-  (1.04e-73, 4.65e-186j)
| (0.049334848712608548022 + 2.8962207269329332343e-875j)  +/-  (3.23e-72, 1.44e-184j)
| (0.055901038830899770216 + 3.5833277679025397266e-875j)  +/-  (3.56e-73, 1.59e-185j)
| (0.059281837297994393468 + 5.7108928735924946555e-875j)  +/-  (4.12e-75, 1.84e-187j)
| (0.049334848712608548022 + 1.0700608487488173315e-874j)  +/-  (6.37e-73, 2.84e-185j)
| (0.058749225516755480268 - 6.1033128099937897449e-875j)  +/-  (2.6e-75, 1.16e-187j)
| (0.054546356807835868008 - 3.3968461627536643302e-875j)  +/-  (4.74e-74, 2.12e-186j)
| (0.047236007906149524055 - 2.7445655732768920576e-875j)  +/-  (3.14e-73, 1.4e-185j)
| (0.059709097644347000639 + 5.0346824776893930456e-875j)  +/-  (1.14e-75, 5.06e-188j)
| (0.051257343027373283756 - 9.7426834256978534478e-875j)  +/-  (1.21e-74, 5.41e-187j)
| (0.057055746030597882031 - 7.029192132452617821e-875j)  +/-  (2.1e-76, 9.38e-189j)
| (0.058749225516755480268 - 4.2243213963810853353e-875j)  +/-  (3.12e-76, 1.39e-188j)
| (0.051257343027373283756 - 3.0546652749938995614e-875j)  +/-  (1.71e-75, 7.62e-188j)
| (0.05800629306126479585 + 3.9951327675545751831e-875j)  +/-  (2.34e-76, 1.04e-188j)
| (0.05800629306126479585 + 6.5401334169765428255e-875j)  +/-  (4.33e-77, 1.93e-189j)
| (0.055901038830899770216 + 7.5801641557896701349e-875j)  +/-  (4.27e-77, 1.9e-189j)
| (0.059602184834616330268 - 5.35645380442704774e-875j)  +/-  (4.04e-77, 1.8e-189j)
