Starting with polynomial:
P : 268435456*t^28 - 1811939328*t^26 + 5452595200*t^24 - 9646899200*t^22 + 11142168576*t^20 - 8820883456*t^18 + 4889837568*t^16 - 1905131520*t^14 + 515973120*t^12 - 94595072*t^10 + 11202048*t^8 - 792064*t^6 + 29120*t^4 - 420*t^2 + 1
Extension levels are: 28 29
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P1 : 268435456*t^28 - 1811939328*t^26 + 5452595200*t^24 - 9646899200*t^22 + 11142168576*t^20 - 8820883456*t^18 + 4889837568*t^16 - 1905131520*t^14 + 515973120*t^12 - 94595072*t^10 + 11202048*t^8 - 792064*t^6 + 29120*t^4 - 420*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 268435456*t^57 - 3758096384*t^55 + 24914165760*t^53 - 104035516416*t^51 + 307049267200*t^49 - 681301770240*t^47 + 1180267970560*t^45 - 1636506009600*t^43 + 1847206158336*t^41 - 1717357199360*t^39 + 1325585088256*t^37 - 853810124544*t^35 + 460160347920*t^33 - 207662105728*t^31 + 78378960360*t^29 - 24668106904*t^27 + 51538723353/8*t^25 - 5545773675/4*t^23 + 31179571995/128*t^21 - 4418157975/128*t^19 + 7952684355/2048*t^17 - 173996955/512*t^15 + 184542225/8192*t^13 - 8940555/8192*t^11 + 9641775/262144*t^9 - 105183/131072*t^7 + 169911/16777216*t^5 - 1015/16777216*t^3 + 29/268435456*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:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.97662055571008668321 - 1.0810028627976297557e-828j)  +/-  (7.31e-236, 7.31e-236j)
| (-0.94765317118280244427 + 1.998995099268080027e-829j)  +/-  (6.18e-236, 6.18e-236j)
| (-0.90757541967095705362 - 5.7706330335530517581e-836j)  +/-  (1.92e-236, 1.92e-236j)
| (-0.98682652254152615177 + 7.0833792510111450307e-847j)  +/-  (6.59e-236, 6.59e-236j)
| (0.94765317118280244427 + 1.8294555750781401376e-854j)  +/-  (5.68e-236, 5.68e-236j)
| (0.90757541967095705362 - 6.227392380050734958e-858j)  +/-  (1.76e-236, 1.76e-236j)
| (-0.99853341385112386457 - 3.3822450533977801128e-855j)  +/-  (1.26e-236, 1.26e-236j)
| (-0.92897671981679144179 + 6.9782463677675758475e-861j)  +/-  (3.46e-236, 3.46e-236j)
| (0.99853341385112386457 - 7.2177563421952589484e-859j)  +/-  (1.15e-236, 1.15e-236j)
| (0.68769945885342329308 + 1.2255724797787159948e-873j)  +/-  (2.98e-240, 2.98e-240j)
| (0.85685717616758924452 - 1.1935885178079485929e-870j)  +/-  (2.96e-237, 2.96e-237j)
| (-0.99413795715435960896 + 9.2991121971994469963e-868j)  +/-  (4.26e-236, 4.26e-236j)
| (-0.97662055571008668321 + 2.266806750699746397e-870j)  +/-  (7.68e-236, 7.68e-236j)
| (-0.796093065705643746 + 1.1485664213027067116e-878j)  +/-  (3.17e-238, 3.17e-238j)
| (0.05413890858541752615 - 5.62635096452368075e-895j)  +/-  (1.1e-254, 1.1e-254j)
| (0.82768899815689055614 + 7.7731623534979505756e-877j)  +/-  (1.14e-237, 1.14e-237j)
| (0.92897671981679144179 - 2.3774073278027586926e-875j)  +/-  (3.45e-236, 3.45e-236j)
| (0.96354999251922296004 - 7.3835146914686014891e-891j)  +/-  (6.62e-236, 6.62e-236j)
| (-0.76216205512763646326 - 1.5737756993712382808e-904j)  +/-  (7.54e-239, 7.54e-239j)
| (-0.96354999251922296004 - 3.6486281880956703008e-901j)  +/-  (7.46e-236, 7.46e-236j)
| (0.98682652254152615177 - 2.1997720802958948548e-912j)  +/-  (7.51e-236, 7.51e-236j)
| (0.72599549192313085814 - 1.9315131127258721407e-930j)  +/-  (1.43e-239, 1.43e-239j)
| (-0.88351204444602292283 + 2.5751838062375879284e-929j)  +/-  (7.81e-237, 7.81e-237j)
| (-0.68769945885342329308 + 1.0473743084745633163e-932j)  +/-  (3.25e-240, 3.25e-240j)
| (-0.72599549192313085814 - 8.4092491711461029982e-932j)  +/-  (1.48e-239, 1.48e-239j)
| (0.3193015301359799732 - 3.1994560672104348738e-941j)  +/-  (2.97e-248, 2.97e-248j)
| (0.76216205512763646326 + 9.4292986212852947217e-930j)  +/-  (7.32e-239, 7.32e-239j)
| (0.796093065705643746 - 2.7751047539016651449e-929j)  +/-  (2.99e-238, 2.99e-238j)
| (-0.82768899815689055614 - 8.4514783742044252989e-930j)  +/-  (9.7e-238, 9.7e-238j)
| (-0.64738628478182763918 - 1.7700489997406196054e-935j)  +/-  (4.34e-241, 4.34e-241j)
| (-0.16178199655276472654 - 1.1334079838460729096e-944j)  +/-  (4.21e-252, 4.21e-252j)
| (0.88351204444602292283 - 1.7349831123404610049e-929j)  +/-  (8.2e-237, 8.2e-237j)
| (0.64738628478182763918 + 4.2474783450928766709e-945j)  +/-  (4.5e-241, 4.5e-241j)
| (0.21497044021102406718 + 6.5195018785288697381e-955j)  +/-  (9.78e-251, 9.78e-251j)
| (-0.60517421519376516592 - 1.8588138040426561571e-946j)  +/-  (5.87e-242, 5.87e-242j)
| (-0.51555385717702173971 - 4.1316842074997584412e-948j)  +/-  (8.75e-244, 8.75e-244j)
| (0.26752833852922082119 - 1.6185469754096656057e-953j)  +/-  (1.65e-249, 1.65e-249j)
| (0.60517421519376516592 + 1.4294422054625407434e-945j)  +/-  (6.02e-242, 6.02e-242j)
| (0.99413795715435960896 + 9.2249275763774423795e-947j)  +/-  (4.06e-236, 4.06e-236j)
| (-0.21497044021102406718 - 1.2412342910067232809e-962j)  +/-  (1.09e-250, 1.09e-250j)
| (-0.56118706536238236927 - 9.2583568064419853088e-953j)  +/-  (8.12e-243, 8.12e-243j)
| (-0.85685717616758924452 + 2.0256467133902425684e-958j)  +/-  (3.06e-237, 3.06e-237j)
| (0.56118706536238236927 - 2.1962791468318559891e-964j)  +/-  (8.89e-243, 8.89e-243j)
| (0.51555385717702173971 + 8.1712434999835523059e-968j)  +/-  (9.13e-244, 9.13e-244j)
| (-0.10811901842394176303 + 3.5386913905368747954e-978j)  +/-  (2.18e-253, 2.18e-253j)
| (-0.46840844069979013922 - 3.5510512906074083579e-969j)  +/-  (8.32e-245, 8.32e-245j)
| (-0.3193015301359799732 + 1.2185136657910650712e-973j)  +/-  (3.59e-248, 3.59e-248j)
| (0.10811901842394176303 - 1.5522707440370527737e-978j)  +/-  (2.11e-253, 2.11e-253j)
| (0.46840844069979013922 - 1.6776149282593832832e-970j)  +/-  (7.56e-245, 7.56e-245j)
| (0.16178199655276472654 - 9.8076681523129845532e-980j)  +/-  (4.91e-252, 4.91e-252j)
| (-0.26752833852922082119 - 7.6822881619334796775e-975j)  +/-  (1.92e-249, 1.92e-249j)
| (-0.41988910156026457697 + 2.3776782131015379703e-970j)  +/-  (6.48e-246, 6.48e-246j)
| (-0.05413890858541752615 + 5.1370352962775483019e-982j)  +/-  (1.1e-254, 1.1e-254j)
| (0.37013815533991435686 + 3.9835398340198019454e-975j)  +/-  (5.11e-247, 5.11e-247j)
| (0.41988910156026457697 + 1.3523618577429617804e-971j)  +/-  (6.4e-246, 6.4e-246j)
| (2.5675206470919015185e-1002 - 2.5595510972807833656e-1002j)  +/-  (2.07e-1000, 2.07e-1000j)
| (-0.37013815533991435686 - 1.3089561952306177296e-972j)  +/-  (4.5e-247, 4.5e-247j)
-------------------------------------------------
The weights are:
| (0.00079676362352623229638 + 2.7386122399786624831e-830j)  +/-  (2.24e-55, 9.56e-168j)
| (0.0017578183990892780517 + 5.8866869676162961459e-831j)  +/-  (1.1e-55, 4.69e-168j)
| (0.0030397734070532100071 + 1.6905739703636599477e-830j)  +/-  (6.66e-56, 2.84e-168j)
| (0.00045126576566549617005 + 2.0543340687467745363e-831j)  +/-  (2e-56, 8.54e-169j)
| (0.0017578183990892780517 + 6.5783544566587339876e-830j)  +/-  (2.23e-57, 9.53e-170j)
| (0.0030397734070532100071 + 4.7919643907413344641e-830j)  +/-  (8.92e-58, 3.81e-170j)
| (5.0534852117589577972e-05 + 1.7088474665291772193e-832j)  +/-  (3.78e-57, 1.61e-169j)
| (0.0023621078282488719126 - 2.6622306990424738294e-830j)  +/-  (1.31e-56, 5.57e-169j)
| (5.0534852117589577972e-05 + 2.4877895174722316067e-831j)  +/-  (3.59e-59, 1.53e-171j)
| (0.0090874043843570476392 - 3.5111478190753061967e-830j)  +/-  (2.07e-59, 8.83e-172j)
| (0.0045826858560362919033 + 4.1871693479110352363e-830j)  +/-  (1.42e-58, 6.05e-171j)
| (0.00020154693353373548958 - 7.5616364406416338028e-832j)  +/-  (4.66e-57, 1.99e-169j)
| (0.00079676362352623229638 - 5.0573824720837248454e-831j)  +/-  (2.51e-57, 1.07e-169j)
| (0.006314410874748096369 + 1.2178895376776155502e-830j)  +/-  (2.29e-60, 9.77e-173j)
| (0.017190844458227238008 + 2.3575248861527709325e-830j)  +/-  (5.35e-62, 2.28e-174j)
| (0.005429843488449014165 - 4.0023292622658378806e-830j)  +/-  (4.59e-60, 1.96e-172j)
| (0.0023621078282488719126 - 5.3846065798896726275e-830j)  +/-  (1.33e-59, 5.7e-172j)
| (0.0012339898606242306507 - 1.0218638135401157536e-829j)  +/-  (7.46e-60, 3.19e-172j)
| (0.0072260172710968558057 - 1.2279731823560194658e-830j)  +/-  (2.32e-62, 9.9e-175j)
| (0.0012339898606242306507 + 1.4829646040656882128e-830j)  +/-  (2.52e-59, 1.08e-171j)
| (0.00045126576566549617005 + 4.7750857180330563424e-830j)  +/-  (3.85e-61, 1.65e-173j)
| (0.008153974925987779947 + 3.6143852295608789512e-830j)  +/-  (4.61e-63, 1.97e-175j)
| (0.0037828701261863588856 - 1.3987911345545638611e-830j)  +/-  (3.73e-61, 1.59e-173j)
| (0.0090874043843570476392 - 1.2890457117338158213e-830j)  +/-  (2.07e-64, 8.83e-177j)
| (0.008153974925987779947 + 1.2530584737000722028e-830j)  +/-  (1.22e-63, 5.2e-176j)
| (0.015483560911255549534 - 2.7906686927576739025e-830j)  +/-  (1.32e-67, 5.66e-180j)
| (0.0072260172710968558057 - 3.7268389966281695845e-830j)  +/-  (1.58e-64, 6.75e-177j)
| (0.006314410874748096369 + 3.8534712027574643628e-830j)  +/-  (2.95e-64, 1.26e-176j)
| (0.005429843488449014165 - 1.2301032148027624565e-830j)  +/-  (5.06e-64, 2.16e-176j)
| (0.010015362039247971781 + 1.3334238440871895129e-830j)  +/-  (1.47e-66, 6.28e-179j)
| (0.016790113544679331416 + 2.0214380487787135891e-830j)  +/-  (5.8e-70, 2.48e-182j)
| (0.0037828701261863588856 - 4.4332609884903164589e-830j)  +/-  (1.44e-64, 6.14e-177j)
| (0.010015362039247971781 + 3.4139471720649890106e-830j)  +/-  (2.39e-67, 1.02e-179j)
| (0.01644461568681859529 - 2.6167146928308520415e-830j)  +/-  (3.17e-70, 1.35e-182j)
| (0.010926968435596731217 - 1.3845415338492711108e-830j)  +/-  (2.34e-68, 9.98e-181j)
| (0.012658693454308535683 - 1.5026779396680132026e-830j)  +/-  (3.38e-70, 1.44e-182j)
| (0.016007389449720596936 + 2.7036322722859800324e-830j)  +/-  (2.34e-70, 9.97e-183j)
| (0.010926968435596731217 - 3.320690039078349454e-830j)  +/-  (3.12e-69, 1.33e-181j)
| (0.00020154693353373548958 - 1.2416759084712982593e-830j)  +/-  (3.06e-67, 1.31e-179j)
| (0.01644461568681859529 - 1.9405059046351265308e-830j)  +/-  (2.92e-72, 1.25e-184j)
| (0.011811535821895813421 + 1.4412439142678327834e-830j)  +/-  (1.1e-69, 4.68e-182j)
| (0.0045826858560362919033 + 1.2791302340472032464e-830j)  +/-  (2.07e-67, 8.82e-180j)
| (0.011811535821895813421 + 3.229975060194845596e-830j)  +/-  (1.39e-70, 5.94e-183j)
| (0.012658693454308535683 - 3.1408582058717563564e-830j)  +/-  (2.2e-71, 9.4e-184j)
| (0.017039832376811092097 - 2.1038446884886331236e-830j)  +/-  (1.92e-73, 8.21e-186j)
| (0.013458509184158468701 + 1.5681819310846607933e-830j)  +/-  (1.14e-72, 4.85e-185j)
| (0.015483560911255549534 - 1.7841558355416354722e-830j)  +/-  (6.15e-74, 2.62e-186j)
| (0.017039832376811092097 - 2.443538182595749196e-830j)  +/-  (2.78e-74, 1.19e-186j)
| (0.013458509184158468701 + 3.0527075318331437837e-830j)  +/-  (5.72e-74, 2.44e-186j)
| (0.016790113544679331416 + 2.5299812429974710423e-830j)  +/-  (2.93e-74, 1.25e-186j)
| (0.016007389449720596936 + 1.8613155359310670472e-830j)  +/-  (7.82e-75, 3.34e-187j)
| (0.014201605903291617579 - 1.6372199728242671311e-830j)  +/-  (6.89e-75, 2.94e-187j)
| (0.017190844458227238008 + 2.1874778608834045957e-830j)  +/-  (1.69e-75, 7.23e-188j)
| (0.014879271482095955674 + 2.8778103562490207348e-830j)  +/-  (8.17e-76, 3.49e-188j)
| (0.014201605903291617579 - 2.9651100745162258612e-830j)  +/-  (8.14e-76, 3.47e-188j)
| (0.017241379310344827586 - 2.2721081043281123487e-830j)  +/-  (3.72e-76, 1.6e-188j)
| (0.014879271482095955674 + 1.7093415189565320897e-830j)  +/-  (2.57e-76, 1.07e-188j)
