Starting with polynomial:
P : t
Extension levels are: 1 28 30
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : t^29 - 29/4*t^27 + 377/16*t^25 - 725/16*t^23 + 7337/128*t^21 - 51359/1024*t^19 + 127281/4096*t^17 - 28101/2048*t^15 + 140505/32768*t^13 - 121771/131072*t^11 + 70499/524288*t^9 - 6409/524288*t^7 + 2639/4194304*t^5 - 1015/67108864*t^3 + 29/268435456*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^59 - 15*t^57 + 1709/16*t^55 - 3843/8*t^53 + 392041/256*t^51 - 942565/256*t^49 + 7101325/1024*t^47 - 2686285/256*t^45 + 425257833/32768*t^43 - 435127363/32768*t^41 + 11886493311/1048576*t^39 - 4256631275/524288*t^37 + 82123154529/16777216*t^35 - 41738903353/16777216*t^33 + 35755133261/33554432*t^31 - 805055213/2097152*t^29 + 248883578585/2147483648*t^27 - 62630270703/2147483648*t^25 + 208644329595/34359738368*t^23 - 17798864985/17179869184*t^21 + 78643211955/549755813888*t^19 - 8648672175/549755813888*t^17 + 2968493505/2199023255552*t^15 - 48370695/549755813888*t^13 + 295739535/70368744177664*t^11 - 9852141/70368744177664*t^9 + 13633335/4503599627370496*t^7 - 85463/2251799813685248*t^5 + 16269/72057594037927936*t^3 - 29/72057594037927936*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
Positive weights:   59 out of 59
Indefinite weights: 0 out of 59
Negative weights:   0 out of 59
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99413795715435960896 - 6.7927714652866244456e-796j)  +/-  (7.97e-234, 7.97e-234j)
| (-1 + 9.5521352168939241726e-794j)  +/-  (5.01e-234, 5.01e-234j)
| (-0.92897671981679144179 - 1.4798213026727260424e-815j)  +/-  (5.15e-235, 5.15e-235j)
| (-0.99413795715435960896 + 1.7518348610541540418e-831j)  +/-  (7.44e-234, 7.44e-234j)
| (0.88351204444602292283 + 1.3306796151598842534e-859j)  +/-  (7.3e-236, 7.3e-236j)
| (0.94765317118280244427 - 1.6338045294012056154e-858j)  +/-  (1.1e-234, 1.1e-234j)
| (-0.99853341385112386457 - 5.1875711822608431178e-855j)  +/-  (1.03e-233, 1.03e-233j)
| (-0.90757541967095705362 + 9.0991983073726972503e-869j)  +/-  (1.88e-235, 1.88e-235j)
| (0.98682652254152615177 + 1.5029973181543158205e-869j)  +/-  (5.29e-234, 5.29e-234j)
| (0.99853341385112386457 - 9.3341358356664695603e-869j)  +/-  (1.02e-233, 1.02e-233j)
| (0.90757541967095705362 - 2.9779773391326854462e-876j)  +/-  (1.87e-235, 1.87e-235j)
| (0.26752833852922082119 + 5.7703010149087837981e-889j)  +/-  (1.95e-249, 1.95e-249j)
| (-0.94765317118280244427 + 1.0889595654679281386e-871j)  +/-  (1.04e-234, 1.04e-234j)
| (-0.85685717616758924452 + 1.6318875480260215126e-882j)  +/-  (2.38e-236, 2.38e-236j)
| (0.92897671981679144179 - 5.0812463559171269109e-882j)  +/-  (5.46e-235, 5.46e-235j)
| (0.85685717616758924452 - 5.3096187008285603001e-884j)  +/-  (2.18e-236, 2.18e-236j)
| (0.796093065705643746 - 8.7316578407786665226e-885j)  +/-  (1.42e-237, 1.42e-237j)
| (-0.98682652254152615177 + 6.4609521533922160423e-879j)  +/-  (5.58e-234, 5.58e-234j)
| (-0.76216205512763646326 + 1.5924756312054052427e-893j)  +/-  (2.93e-238, 2.93e-238j)
| (-0.97662055571008668321 + 7.7795251298691879697e-888j)  +/-  (3.72e-234, 3.72e-234j)
| (-5.7195066902199164229e-936 - 8.3519994579935309785e-936j)  +/-  (5.97e-934, 5.97e-934j)
| (0.82768899815689055614 - 2.1214212469011019919e-898j)  +/-  (6.36e-237, 6.36e-237j)
| (1 - 1.5898940762886287483e-893j)  +/-  (5e-234, 5e-234j)
| (-0.82768899815689055614 + 1.0076832970011810394e-900j)  +/-  (5.8e-237, 5.8e-237j)
| (-0.72599549192313085814 + 6.2358619437433416947e-903j)  +/-  (5.25e-239, 5.25e-239j)
| (0.96354999251922296004 - 1.0345886969925647792e-898j)  +/-  (2.18e-234, 2.18e-234j)
| (0.68769945885342329308 - 8.0508275168517751484e-908j)  +/-  (8.65e-240, 8.65e-240j)
| (-0.05413890858541752615 + 2.6660129548524585318e-924j)  +/-  (1.4e-254, 1.4e-254j)
| (-0.88351204444602292283 + 1.4490099371223288625e-900j)  +/-  (6.19e-236, 6.19e-236j)
| (-0.64738628478182763918 - 2.2593022947558809333e-906j)  +/-  (1.12e-240, 1.12e-240j)
| (-0.96354999251922296004 + 5.980639656972088051e-904j)  +/-  (2.59e-234, 2.59e-234j)
| (0.76216205512763646326 - 6.854020205256221309e-915j)  +/-  (2.64e-238, 2.64e-238j)
| (0.60517421519376516592 + 2.0227665708665789545e-918j)  +/-  (1.63e-241, 1.63e-241j)
| (0.97662055571008668321 + 3.3825621955992748743e-915j)  +/-  (3.92e-234, 3.92e-234j)
| (-0.68769945885342329308 - 1.8994684238676964365e-919j)  +/-  (8.04e-240, 8.04e-240j)
| (-0.60517421519376516592 - 8.8912432252968894241e-922j)  +/-  (1.33e-241, 1.33e-241j)
| (0.3193015301359799732 - 1.6947989427838544946e-930j)  +/-  (4.19e-248, 4.19e-248j)
| (0.64738628478182763918 - 6.9161299726662586128e-923j)  +/-  (1.23e-240, 1.23e-240j)
| (0.72599549192313085814 - 4.6855333980075071677e-921j)  +/-  (5.56e-239, 5.56e-239j)
| (-0.3193015301359799732 + 8.9661726676612798359e-929j)  +/-  (3.73e-248, 3.73e-248j)
| (-0.56118706536238236927 - 8.428509013611171949e-923j)  +/-  (1.44e-242, 1.44e-242j)
| (-0.796093065705643746 + 2.2166282931169136227e-928j)  +/-  (1.43e-237, 1.43e-237j)
| (0.51555385717702173971 - 1.2625621066886511541e-935j)  +/-  (1.39e-243, 1.39e-243j)
| (0.56118706536238236927 + 2.6018906155503959024e-937j)  +/-  (1.41e-242, 1.41e-242j)
| (-0.10811901842394176303 - 4.1520340237608809915e-947j)  +/-  (2.21e-253, 2.21e-253j)
| (-0.51555385717702173971 + 2.9374703440627133947e-937j)  +/-  (1.28e-243, 1.28e-243j)
| (-0.37013815533991435686 + 1.4097775664260836156e-941j)  +/-  (5.96e-247, 5.96e-247j)
| (0.10811901842394176303 + 3.687590848877873031e-948j)  +/-  (2.66e-253, 2.66e-253j)
| (0.46840844069979013922 + 2.7783976933236294288e-940j)  +/-  (1.15e-244, 1.15e-244j)
| (0.16178199655276472654 + 4.6256842130023033881e-946j)  +/-  (5.33e-252, 5.33e-252j)
| (-0.21497044021102406718 + 9.5656615256447914718e-946j)  +/-  (1.07e-250, 1.07e-250j)
| (-0.46840844069979013922 - 1.2299770152737230653e-939j)  +/-  (1.37e-244, 1.37e-244j)
| (-0.16178199655276472654 - 1.4610884889229550605e-947j)  +/-  (5.24e-252, 5.24e-252j)
| (0.41988910156026457697 + 3.8429797255755179821e-940j)  +/-  (8.89e-246, 8.89e-246j)
| (0.37013815533991435686 + 2.7893042312486436615e-942j)  +/-  (6.46e-247, 6.46e-247j)
| (0.05413890858541752615 - 1.0450396190078281231e-948j)  +/-  (1.21e-254, 1.21e-254j)
| (-0.41988910156026457697 + 9.7450697370388013996e-940j)  +/-  (8.58e-246, 8.58e-246j)
| (-0.26752833852922082119 - 2.5326586463021337051e-945j)  +/-  (2.44e-249, 2.44e-249j)
| (0.21497044021102406718 - 4.5115527662004790112e-945j)  +/-  (1.18e-250, 1.18e-250j)
-------------------------------------------------
The weights are:
| (0.017241379310344827586 + 3.2787815350980669824e-796j)  +/-  (2.99e-50, 6.28e-161j)
| (0.0086206896551724137931 + 9.2351325081424941299e-793j)  +/-  (1.48e-50, 3.12e-161j)
| (0.017241379310344827586 - 2.3194541128734464988e-794j)  +/-  (1.98e-51, 4.15e-162j)
| (0.017241379310344827586 + 2.8095229563028544271e-793j)  +/-  (3.18e-51, 6.67e-162j)
| (0.017241379310344827586 - 9.802551279572598506e-796j)  +/-  (5.57e-53, 1.17e-163j)
| (0.017241379310344827586 + 1.0975383712073079383e-795j)  +/-  (4.86e-53, 1.02e-163j)
| (0.017241379310344827586 - 1.1229674342138709786e-792j)  +/-  (9.63e-51, 2.02e-161j)
| (0.017241379310344827586 + 1.7825226304382231851e-794j)  +/-  (1.47e-52, 3.09e-163j)
| (0.017241379310344827586 - 2.4307497606904468991e-795j)  +/-  (1.84e-53, 3.87e-164j)
| (0.017241379310344827586 + 1.8404313668240610166e-795j)  +/-  (1.29e-53, 2.71e-164j)
| (0.017241379310344827586 + 9.9865493678077556303e-796j)  +/-  (3.66e-54, 7.69e-165j)
| (0.017241379310344827586 + 1.3154342605134625768e-795j)  +/-  (5.13e-57, 1.08e-167j)
| (0.017241379310344827586 + 3.146772451506740426e-794j)  +/-  (2.04e-54, 4.27e-165j)
| (0.017241379310344827586 + 1.1511758107499721427e-794j)  +/-  (1.01e-55, 2.13e-166j)
| (0.017241379310344827586 - 1.0335127974463720034e-795j)  +/-  (2.41e-54, 5.05e-165j)
| (0.017241379310344827586 + 9.722512726489730586e-796j)  +/-  (1.14e-55, 2.4e-166j)
| (0.017241379310344827586 + 9.7608219446976720362e-796j)  +/-  (3.5e-57, 7.34e-168j)
| (0.017241379310344827586 - 1.2502376484783413374e-793j)  +/-  (6.88e-55, 1.44e-165j)
| (0.017241379310344827586 - 6.9312146955125069856e-795j)  +/-  (2.78e-59, 5.83e-170j)
| (0.017241379310344827586 + 7.0449014191889335497e-794j)  +/-  (2.13e-55, 4.47e-166j)
| (0.017241379310344827586 - 1.658700599089956046e-795j)  +/-  (4.03e-62, 8.47e-173j)
| (0.017241379310344827586 - 9.7145611006601407862e-796j)  +/-  (2.7e-57, 5.66e-168j)
| (0.0086206896551724137931 - 5.8721146497076852217e-796j)  +/-  (5.11e-56, 1.07e-166j)
| (0.017241379310344827586 - 9.564262028180541901e-795j)  +/-  (9.11e-59, 1.91e-169j)
| (0.017241379310344827586 + 6.0173661359075457265e-795j)  +/-  (2.58e-60, 5.41e-171j)
| (0.017241379310344827586 - 1.2216311516720222382e-795j)  +/-  (6.28e-57, 1.32e-167j)
| (0.017241379310344827586 - 1.0140558508475368209e-795j)  +/-  (2.65e-61, 5.55e-172j)
| (0.017241379310344827586 + 1.752358072560355553e-795j)  +/-  (2.18e-63, 4.58e-174j)
| (0.017241379310344827586 - 1.414435029279812399e-794j)  +/-  (2.27e-58, 4.77e-169j)
| (0.017241379310344827586 + 4.6777410056809778726e-795j)  +/-  (1.26e-62, 2.64e-173j)
| (0.017241379310344827586 - 4.518895982182193667e-794j)  +/-  (2.07e-57, 4.35e-168j)
| (0.017241379310344827586 - 9.8508842221107829398e-796j)  +/-  (6.42e-61, 1.35e-171j)
| (0.017241379310344827586 - 1.0561168677365162761e-795j)  +/-  (1.21e-63, 2.55e-174j)
| (0.017241379310344827586 + 1.5017735662158861058e-795j)  +/-  (4.37e-58, 9.18e-169j)
| (0.017241379310344827586 - 5.2804731010101668486e-795j)  +/-  (2.25e-62, 4.71e-173j)
| (0.017241379310344827586 - 4.1785800622534576919e-795j)  +/-  (6.09e-64, 1.28e-174j)
| (0.017241379310344827586 - 1.2656819441197007843e-795j)  +/-  (4.69e-66, 9.85e-177j)
| (0.017241379310344827586 + 1.0334922685289110316e-795j)  +/-  (1.27e-63, 2.67e-174j)
| (0.017241379310344827586 + 9.9786255773070830264e-796j)  +/-  (1.86e-62, 3.91e-173j)
| (0.017241379310344827586 - 2.4283726041668892485e-795j)  +/-  (1.05e-68, 2.21e-179j)
| (0.017241379310344827586 + 3.7606552086110832864e-795j)  +/-  (1.99e-66, 4.18e-177j)
| (0.017241379310344827586 + 8.0833632656024396827e-795j)  +/-  (1.82e-63, 3.82e-174j)
| (0.017241379310344827586 - 1.1111500566775961807e-795j)  +/-  (3.71e-67, 7.79e-178j)
| (0.017241379310344827586 + 1.0819659518135911922e-795j)  +/-  (2.58e-66, 5.41e-177j)
| (0.017241379310344827586 - 1.8571942804769339476e-795j)  +/-  (9.46e-70, 1.98e-180j)
| (0.017241379310344827586 - 3.4073509669230307059e-795j)  +/-  (1.96e-68, 4.12e-179j)
| (0.017241379310344827586 + 2.6233164455571927183e-795j)  +/-  (8.31e-70, 1.74e-180j)
| (0.017241379310344827586 - 1.499448435129587511e-795j)  +/-  (5.68e-71, 1.19e-181j)
| (0.017241379310344827586 + 1.1438449610320531732e-795j)  +/-  (1.11e-69, 2.32e-180j)
| (0.017241379310344827586 + 1.4316513235793215498e-795j)  +/-  (3.15e-71, 6.61e-182j)
| (0.017241379310344827586 - 2.1075942983723564032e-795j)  +/-  (1.99e-71, 4.17e-182j)
| (0.017241379310344827586 + 3.1061003079225189032e-795j)  +/-  (8.64e-71, 1.82e-181j)
| (0.017241379310344827586 + 1.9749189424423508643e-795j)  +/-  (2.7e-71, 5.66e-182j)
| (0.017241379310344827586 - 1.1802880793766190566e-795j)  +/-  (1.61e-71, 3.38e-182j)
| (0.017241379310344827586 + 1.2207787894297872201e-795j)  +/-  (8.77e-72, 1.84e-182j)
| (0.017241379310344827586 + 1.5747959044639231322e-795j)  +/-  (1.98e-72, 4.21e-183j)
| (0.017241379310344827586 - 2.8472566818314421592e-795j)  +/-  (1.07e-72, 2.29e-183j)
| (0.017241379310344827586 + 2.2577244550074854658e-795j)  +/-  (7.44e-73, 1.63e-183j)
| (0.017241379310344827586 - 1.3705535896353961627e-795j)  +/-  (6.23e-73, 1.21e-183j)
