Starting with polynomial:
P : 61989816618513/8388608*t^26 - 395033145117975/8388608*t^24 + 556271163533475/4194304*t^22 - 911337863661225/4194304*t^20 + 1923935489951475/8388608*t^18 - 1369126185872445/8388608*t^16 + 166966608033225/2097152*t^14 - 55655536011075/2097152*t^12 + 49638721307175/8388608*t^10 - 7091245901025/8388608*t^8 + 300840735195/4194304*t^6 - 13233463425/4194304*t^4 + 456326325/8388608*t^2 - 1300075/8388608
Extension levels are: 26 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 61989816618513/8388608*t^26 - 395033145117975/8388608*t^24 + 556271163533475/4194304*t^22 - 911337863661225/4194304*t^20 + 1923935489951475/8388608*t^18 - 1369126185872445/8388608*t^16 + 166966608033225/2097152*t^14 - 55655536011075/2097152*t^12 + 49638721307175/8388608*t^10 - 7091245901025/8388608*t^8 + 300840735195/4194304*t^6 - 13233463425/4194304*t^4 + 456326325/8388608*t^2 - 1300075/8388608
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 61989816618513/8388608*t^53 - 45158973663286539/461373440*t^51 + 294839418254227692273/482135244800*t^49 - 3749138791942800161490921/1564528869376000*t^47 + 329406760054071326783096961321/49865446389186560000*t^45 - 37353767696682963814902997019763/2742599551405260800000*t^43 + 47918145192996646733723862016471697547/2198234679444587610112000000*t^41 - 224755736524713573046603617982499963277147/8100494793753305343262720000000*t^39 + 678025121951807412965879575042115222143500329499/23752837868879004658888975974400000000*t^37 - 131314666771363694345959288795768795594698407817851733/5472535080800378278384725619621888000000000*t^35 + 6928133922048441146671502220947600334536281948893630408063/417472338638856856966578793892855726080000000000*t^33 - 217663850080629369213666839475503225456759141924349532511589/22960978625137127133161833664107064934400000000000*t^31 + 1256814170674019562557620175420085456101991875516515487064365848419/280654423936583462925577158416623305801158144000000000000*t^29 - 2131076154156573075410056540161987348930328124531418564831637926855103/1219443472004455146411632753320228263706032135680000000000000*t^27 + 8427631131128134410921666330124927470388387632253441329817367092977/15008535040054832571220095425479732476381933977600000000000*t^25 - 96391678007647276317146376238663466528575393258933196892837844233/652545001741514459618265018499118803320953651200000000000*t^23 + 1871807320293551576098988574029658402446170763300576837253280863/59322272885592223601660456227192618483723059200000000000*t^21 - 16896272139082885007422024077117575923789521843467278938267453/3122224888715380189561076643536453604406476800000000000*t^19 + 5730624581993575059535518090035338353334339141743752766506973/7805562221788450473902691608841134011016192000000000000*t^17 - 60300907795558716156153755814452302219912129052261572593951/780556222178845047390269160884113401101619200000000000*t^15 + 9589914092221912997004412706579624146165748722407053122569/1561112444357690094780538321768226802203238400000000000*t^13 - 50578141519546014281862432419028446353983761874747098859/141919313123426372252776211069838800200294400000000000*t^11 + 313648568281758728628255882935985301340313115788353721/21833740480527134192734801703052123107737600000000000*t^9 - 5848145424093768446230388334584359596576261735467186817/15611124443576900947805383217682268022032384000000000000*t^7 + 194028746252352207188048652951458423629532057498315841/34344473775869182085171843078900989648471244800000000000*t^5 - 18010516018046587649227079144059829945789475778209741/446478159086299367107233960025712865430126182400000000000*t^3 + 19235142105841871015829076877578412153216564803203/223239079543149683553616980012856432715063091200000000000*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:
| (0.9993170647600717767 + 2.2503969068927205518e-869j)  +/-  (4.84e-237, 4.84e-237j)
| (-0.9644411182393125503 - 1.915490200529569184e-883j)  +/-  (1.06e-236, 1.06e-236j)
| (-0.92654057077036118681 - 2.8713471711010808385e-884j)  +/-  (3.55e-237, 3.55e-237j)
| (-0.9993170647600717767 - 2.0112292080919694227e-882j)  +/-  (4.72e-237, 4.72e-237j)
| (0.92654057077036118681 - 2.1976421297638883357e-883j)  +/-  (3.71e-237, 3.71e-237j)
| (0.90263786198430707422 - 8.482222615620196729e-894j)  +/-  (1.6e-237, 1.6e-237j)
| (-0.995885701145616929 - 9.1230673029974182125e-898j)  +/-  (1.18e-236, 1.18e-236j)
| (-0.90263786198430707422 + 1.7423599817641500485e-902j)  +/-  (1.66e-237, 1.66e-237j)
| (-0.98891914482443501839 - 3.242997480769097897e-899j)  +/-  (1.53e-236, 1.53e-236j)
| (0.995885701145616929 + 1.9218162762329197991e-897j)  +/-  (1.24e-236, 1.24e-236j)
| (0.87556963516367067168 + 1.2747605293282042956e-911j)  +/-  (5.95e-238, 5.95e-238j)
| (-0.34813819710369490173 + 2.7227831946509496587e-923j)  +/-  (5.89e-248, 5.89e-248j)
| (-0.94715906666171425014 + 1.5102976931536887615e-911j)  +/-  (6.46e-237, 6.46e-237j)
| (-0.81234972708512833937 - 1.2418020185922618279e-913j)  +/-  (5.98e-239, 5.98e-239j)
| (0.94715906666171425014 + 6.5910699064385563672e-910j)  +/-  (6.53e-237, 6.53e-237j)
| (0.8454459427884980188 - 4.0823813986664284528e-922j)  +/-  (2.18e-238, 2.18e-238j)
| (0.81234972708512833937 + 1.8366778936529974364e-922j)  +/-  (5.83e-239, 5.83e-239j)
| (-0.9783854459564709911 + 2.095098028092499e-921j)  +/-  (1.54e-236, 1.54e-236j)
| (-0.77638594882067885619 + 1.6901802261513653003e-923j)  +/-  (1.44e-239, 1.44e-239j)
| (0.98891914482443501839 - 1.7203275991365622548e-918j)  +/-  (1.53e-236, 1.53e-236j)
| (0.059230093429313207094 - 9.9651906847251934852e-953j)  +/-  (2.07e-254, 2.07e-254j)
| (0.73769697950761261046 - 1.2459731574496973905e-938j)  +/-  (3.43e-240, 3.43e-240j)
| (0.9783854459564709911 - 8.2912109960746202566e-934j)  +/-  (1.36e-236, 1.36e-236j)
| (-0.8454459427884980188 - 7.0399963198857661506e-962j)  +/-  (2.01e-238, 2.01e-238j)
| (-0.69642726041995726486 - 9.6069498710716361076e-968j)  +/-  (5.43e-241, 5.43e-241j)
| (0.9644411182393125503 + 3.9436369004519591969e-966j)  +/-  (1.01e-236, 1.01e-236j)
| (0.69642726041995726486 - 9.746453147859929543e-985j)  +/-  (5.68e-241, 5.68e-241j)
| (0.55854453098081558341 + 1.3368962113405806973e-987j)  +/-  (1.41e-243, 1.41e-243j)
| (-0.73769697950761261046 - 4.3804796349058802405e-982j)  +/-  (3.02e-240, 3.02e-240j)
| (-0.65271000950691347845 - 3.3260510151587554428e-984j)  +/-  (8.73e-242, 8.73e-242j)
| (-0.87556963516367067168 + 2.6249604937660587151e-986j)  +/-  (5.99e-238, 5.99e-238j)
| (0.40305175512348630648 + 2.2837221805475447805e-994j)  +/-  (8.37e-247, 8.37e-247j)
| (0.65271000950691347845 - 1.75064812006534673e-989j)  +/-  (9.1e-242, 9.1e-242j)
| (0.11825166289205722204 - 6.0746602219282844996e-1003j)  +/-  (4.36e-253, 4.36e-253j)
| (-0.60669229301761806323 + 9.5735642937210780865e-994j)  +/-  (1.12e-242, 1.12e-242j)
| (-0.5084407148245057177 + 3.0661667305070545344e-995j)  +/-  (1.31e-244, 1.31e-244j)
| (0.17685882035689018397 - 2.8902435848179629411e-1001j)  +/-  (8.72e-252, 8.72e-252j)
| (0.60669229301761806323 + 4.7454010817097951152e-994j)  +/-  (1.26e-242, 1.26e-242j)
| (0.29200483948595689514 + 1.0570829971990968631e-1000j)  +/-  (3.4e-249, 3.4e-249j)
| (-0.29200483948595689514 - 3.9125393675659731328e-1000j)  +/-  (3.44e-249, 3.44e-249j)
| (-0.55854453098081558341 - 2.2359332003708249861e-997j)  +/-  (1.4e-243, 1.4e-243j)
| (-0.11825166289205722204 - 4.139363969125616909e-1006j)  +/-  (4.51e-253, 4.51e-253j)
| (0.34813819710369490173 - 1.1747991286356355154e-999j)  +/-  (5.8e-248, 5.8e-248j)
| (0.45655021602829963383 - 2.8770608878269128432e-998j)  +/-  (1.24e-245, 1.24e-245j)
| (1.8723959410168910616e-1008 - 1.7558358229119656476e-1008j)  +/-  (1.36e-1006, 1.36e-1006j)
| (-0.45655021602829963383 + 1.2448392790166425895e-999j)  +/-  (1.23e-245, 1.23e-245j)
| (-0.23484525515245750134 + 4.9106797630662855883e-1004j)  +/-  (1.86e-250, 1.86e-250j)
| (0.77638594882067885619 - 3.2543211795793899306e-1002j)  +/-  (1.47e-239, 1.47e-239j)
| (0.5084407148245057177 - 1.2078053532049412612e-1012j)  +/-  (1.34e-244, 1.34e-244j)
| (0.23484525515245750134 + 1.750985941155278328e-1017j)  +/-  (1.89e-250, 1.89e-250j)
| (-0.17685882035689018397 - 2.4966442089414355538e-1018j)  +/-  (9.27e-252, 9.27e-252j)
| (-0.40305175512348630648 - 1.0714360452119580132e-1013j)  +/-  (8.99e-247, 8.99e-247j)
| (-0.059230093429313207094 + 1.379247731223379601e-1021j)  +/-  (2.07e-254, 2.07e-254j)
-------------------------------------------------
The weights are:
| (0.001839811851460777305 - 2.3896147838639316727e-869j)  +/-  (1.43e-57, 1.42e-170j)
| (0.015615240928537467071 - 1.7894509716298816077e-871j)  +/-  (7.07e-58, 7e-171j)
| (0.022276973597308167473 - 2.603101680703699594e-871j)  +/-  (4.52e-58, 4.47e-171j)
| (0.001839811851460777305 - 2.0715681970319349902e-872j)  +/-  (1.16e-58, 1.15e-171j)
| (0.022276973597308167473 - 6.888492386758976037e-870j)  +/-  (6.33e-60, 6.27e-173j)
| (0.025506915123408240046 + 5.9283853229370772752e-870j)  +/-  (5.97e-60, 5.91e-173j)
| (0.0051517359460188982774 + 6.0902710600447264689e-872j)  +/-  (8.96e-59, 8.87e-172j)
| (0.025506915123408240046 + 3.0134865906176232963e-871j)  +/-  (3.52e-60, 3.48e-173j)
| (0.0087752767072997680498 - 9.93234881467367466e-872j)  +/-  (4.27e-59, 4.23e-172j)
| (0.0051517359460188982774 + 3.5412526997442123858e-869j)  +/-  (6.04e-62, 5.98e-175j)
| (0.028610883257247265841 - 5.2030044903210963397e-870j)  +/-  (3.25e-62, 3.22e-175j)
| (0.055555692444225008774 - 9.278405151935356334e-871j)  +/-  (7.65e-64, 7.58e-177j)
| (0.01895143714509108693 + 2.1979295672304658674e-871j)  +/-  (6.73e-60, 6.67e-173j)
| (0.034551368778581017719 - 4.2918650260797097824e-871j)  +/-  (1.47e-62, 1.46e-175j)
| (0.01895143714509108693 + 8.2024187988866571828e-870j)  +/-  (1.74e-62, 1.73e-175j)
| (0.031623859191524403531 + 4.6289051724209802093e-870j)  +/-  (2.85e-63, 2.82e-176j)
| (0.034551368778581017719 - 4.1587099862014182334e-870j)  +/-  (4.8e-64, 4.75e-177j)
| (0.012261815863355242371 + 1.3832163296555751052e-871j)  +/-  (3.82e-61, 3.79e-174j)
| (0.037351607543368433363 + 4.7312549959657268053e-871j)  +/-  (5.66e-65, 5.6e-178j)
| (0.0087752767072997680498 - 1.8992121194887656927e-869j)  +/-  (1.85e-63, 1.83e-176j)
| (0.059160335809234664946 + 1.4162084393035654687e-870j)  +/-  (1.55e-68, 1.53e-181j)
| (0.04000199418960095307 - 3.4408812269497769487e-870j)  +/-  (2.09e-66, 2.07e-179j)
| (0.012261815863355242371 + 1.3069177466263316064e-869j)  +/-  (7.48e-64, 7.41e-177j)
| (0.031623859191524403531 + 3.8609557404763961362e-871j)  +/-  (1.01e-65, 1e-178j)
| (0.042515857138908215675 + 5.6440975615585507317e-871j)  +/-  (4.52e-68, 4.47e-181j)
| (0.015615240928537467071 - 1.0075852669704323756e-869j)  +/-  (4.57e-64, 4.52e-177j)
| (0.042515857138908215675 + 3.1598773790427428059e-870j)  +/-  (2.67e-68, 2.65e-181j)
| (0.049154139945867922638 - 2.5096011211658846153e-870j)  +/-  (3.01e-70, 2.98e-183j)
| (0.04000199418960095307 - 5.1824776138658154904e-871j)  +/-  (4.21e-68, 4.17e-181j)
| (0.044894328775394569946 - 6.11552075549656515e-871j)  +/-  (9.23e-70, 9.13e-183j)
| (0.028610883257247265841 - 3.4341191490823344256e-871j)  +/-  (1.09e-66, 1.08e-179j)
| (0.054238795536809337444 + 2.0468384581225371385e-870j)  +/-  (4.09e-73, 4.05e-186j)
| (0.044894328775394569946 - 2.9148298363223541762e-870j)  +/-  (8.65e-71, 8.56e-184j)
| (0.05884857693065948853 - 1.503096764655867106e-870j)  +/-  (7.46e-74, 7.38e-187j)
| (0.047112219991656234496 + 6.6000394236930632088e-871j)  +/-  (1.23e-71, 1.22e-184j)
| (0.051025613706689455014 + 7.6169885338479828814e-871j)  +/-  (2.58e-73, 2.56e-186j)
| (0.058331355353784363838 + 1.5959910476462838936e-870j)  +/-  (2.24e-74, 2.22e-187j)
| (0.047112219991656234496 + 2.6997086885545828862e-870j)  +/-  (1.23e-72, 1.22e-185j)
| (0.056678955775362942993 + 1.8034317801217496664e-870j)  +/-  (1.01e-74, 1e-187j)
| (0.056678955775362942993 + 9.8781670266247203869e-871j)  +/-  (1.36e-75, 1.35e-188j)
| (0.049154139945867922638 - 7.1005232298947732583e-871j)  +/-  (1.84e-73, 1.82e-186j)
| (0.05884857693065948853 - 1.1850068118677057873e-870j)  +/-  (1.53e-76, 1.51e-189j)
| (0.055555692444225008774 - 1.9199388162999389285e-870j)  +/-  (1.81e-75, 1.79e-188j)
| (0.052725696310872361126 - 2.1860904763988668957e-870j)  +/-  (1.21e-75, 1.2e-188j)
| (0.059265028660038683918 - 1.3346098239150196062e-870j)  +/-  (1.35e-76, 1.33e-189j)
| (0.052725696310872361126 - 8.1500384999057127845e-871j)  +/-  (2.86e-76, 2.84e-189j)
| (0.057606997827714371576 - 1.0504178229657156865e-870j)  +/-  (3.55e-77, 3.52e-190j)
| (0.037351607543368433363 + 3.7685648855912183637e-870j)  +/-  (6.54e-76, 6.47e-189j)
| (0.051025613706689455014 + 2.3396062410462738256e-870j)  +/-  (2.49e-76, 2.46e-189j)
| (0.057606997827714371576 - 1.6957932012353887573e-870j)  +/-  (5.83e-77, 5.77e-190j)
| (0.058331355353784363838 + 1.1160201562880380233e-870j)  +/-  (3.66e-78, 3.65e-191j)
| (0.054238795536809337444 + 8.7028372971817738519e-871j)  +/-  (3.15e-78, 3.3e-191j)
| (0.059160335809234664946 + 1.2577229953129657147e-870j)  +/-  (3.72e-78, 3.59e-191j)
