Starting with polynomial:
P : 121683714103007/8388608*t^27 - 805867616040669/8388608*t^25 + 1185099435353925/4194304*t^23 - 2039660932956075/4194304*t^21 + 4556689318306125/8388608*t^19 - 3463083881912655/8388608*t^17 + 456375395290815/2097152*t^15 - 166966608033225/2097152*t^13 + 166966608033225/8388608*t^11 - 27577067392875/8388608*t^9 + 1418249180205/4194304*t^7 - 82047473235/4194304*t^5 + 4411154475/8388608*t^3 - 35102025/8388608*t
Extension levels are: 27 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 121683714103007/8388608*t^27 - 805867616040669/8388608*t^25 + 1185099435353925/4194304*t^23 - 2039660932956075/4194304*t^21 + 4556689318306125/8388608*t^19 - 3463083881912655/8388608*t^17 + 456375395290815/2097152*t^15 - 166966608033225/2097152*t^13 + 166966608033225/8388608*t^11 - 27577067392875/8388608*t^9 + 1418249180205/4194304*t^7 - 82047473235/4194304*t^5 + 4411154475/8388608*t^3 - 35102025/8388608*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 121683714103007/8388608*t^55 - 95338042040138975/478150656*t^53 + 2083352201767406772895/1608020656128*t^51 - 29592335724760699337868355/5591087821357056*t^49 + 143377025806428629742838981285/9401414171611889664*t^47 - 229620034919071485391906391023297/6966447901164410241024*t^45 + 5311968455088128921757689656663695460715/95750907459834230874983890944*t^43 - 719597522233447167175088228539904822076625/9656110744603282821315683155968*t^41 + 4869682086047966903993957118651790250916148423595/59946081801350150876444249969198628864*t^39 - 1105789403809491845940619479147256596283672786569191735/15215574428900496645609955971431965176889344*t^37 + 178813694875963581279063834843941287905720535397010308941007/3326048492285504064247108325575170427842126151680*t^35 - 1252574778120940577339881819425472282920276085856619349227235/37916952812054746332417034911556942877400238129152*t^33 + 173905346164976366488879283338240762023502579935944914599470288027861/10292764426669668688657087526904014190443312687112007974912*t^31 - 324587062474979884038127374836970948583964849236087051612300591051913/45129813255397778096419537617963754527328371012721881120768*t^29 + 9577407506742696385754678459191559348063869844831437256283779888795675683309/3766514853605611994280371245613616846400133620850603740652296470528*t^27 - 39892679164178692936729184583894080852867330096203185450424600569773818807/53654057743669686528210416604182576159546062975079825365417328640*t^25 + 7669134439353452680767766407584636592843671636719937101695735034382938735/42923246194935749222568333283346060927636850380063860292333862912*t^23 - 195818751682543731029010494155033636706029426880759117759586684095673235/5598684286295967289900217384784268816648284832182242646826156032*t^21 + 10287375739254398500003625888286460992636003545523922657750523170308875/1866228095431989096633405794928089605549428277394080882275385344*t^19 - 22552582365517409894810510657441533038005802793288917474141238422875/32740843779508580642691329735580519395604004866562822496059392*t^17 + 9855443892787526562462518223908461548112115667533678266883506742921/147333797007788612892110983810112337280218021899532701232267264*t^15 - 18575016586793373540702332331842520314997747781601072947559995495/3777789666866374689541307277182367622569692869218787211083776*t^13 + 38902576272877848697550804048898219912692347786362760247865022895/147333797007788612892110983810112337280218021899532701232267264*t^11 - 56670167342902447162468234077603898274618674624021687454948082545/5746018083303755902792328368594381153928502854081775348058423296*t^9 + 304578016127937303524381205925362885639865372827625052502786605/1276892907400834645064961859687640256428556189795950077346316288*t^7 - 63622431434211232929405882067392575427246439172911933451911/19058103095534845448730774025188660543709793877551493691736064*t^5 + 6521178190514254092599218052364468393739247628258982867265/294667594015577225784221967620224674560436043799065402464534528*t^3 - 789491613277973939185248678692583274596306998892153665/17984407146490628803731857178699158541247270278816198272483328*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:
| (-0.99936554652297716812 - 2.8620828166619410131e-813j)  +/-  (3.01e-236, 3.01e-236j)
| (0.97992347596150122286 - 6.7187092021366578642e-814j)  +/-  (8.5e-236, 8.5e-236j)
| (-0.88427665971018918738 - 5.2394621939241423979e-827j)  +/-  (4.58e-237, 4.58e-237j)
| (0.99617926288898856694 + 5.0299303474002176685e-823j)  +/-  (7.19e-236, 7.19e-236j)
| (0.93172592245498812853 - 1.6524790578624387825e-842j)  +/-  (2.46e-236, 2.46e-236j)
| (0.95090055781470500685 - 2.9602934789201140224e-865j)  +/-  (4.53e-236, 4.53e-236j)
| (-0.99617926288898856694 - 2.8306951621916011328e-884j)  +/-  (7.6e-236, 7.6e-236j)
| (-0.9094823206774911043 + 2.8162515637912471101e-885j)  +/-  (1.07e-236, 1.07e-236j)
| (-0.9669649256262432901 + 2.4533763983364475177e-884j)  +/-  (7.1e-236, 7.1e-236j)
| (0.99936554652297716812 - 4.0260032476607102248e-881j)  +/-  (2.87e-236, 2.87e-236j)
| (0.8562079080182944903 - 7.1643118845169197341e-894j)  +/-  (1.58e-237, 1.58e-237j)
| (-0.5405515645794568949 + 1.9398593141863338253e-903j)  +/-  (1.7e-243, 1.7e-243j)
| (-0.97992347596150122286 + 4.2649047105897096754e-894j)  +/-  (8.7e-236, 8.7e-236j)
| (-0.82534390724636190138 + 1.2895545068558648713e-898j)  +/-  (4.26e-238, 4.26e-238j)
| (0.22645936543953685886 + 7.0735043650780832314e-910j)  +/-  (2.12e-250, 2.12e-250j)
| (0.82534390724636190138 - 4.2699356632031121879e-897j)  +/-  (4.42e-238, 4.42e-238j)
| (0.9094823206774911043 - 1.5501756353660065326e-894j)  +/-  (1.13e-236, 1.13e-236j)
| (0.98970960230169772503 + 3.4527750240476460615e-904j)  +/-  (1e-235, 1e-235j)
| (-0.75561835042722878432 + 1.2154624552777882881e-917j)  +/-  (2.47e-239, 2.47e-239j)
| (-0.93172592245498812853 + 3.0415831518053289357e-914j)  +/-  (2.6e-236, 2.6e-236j)
| (-0.98970960230169772503 + 2.0113304258033711814e-913j)  +/-  (9.09e-236, 9.09e-236j)
| (0.71701347373942369929 + 6.1643133238537186571e-919j)  +/-  (4.45e-240, 4.45e-240j)
| (-0.95090055781470500685 + 1.3193595333903256335e-915j)  +/-  (4.27e-236, 4.27e-236j)
| (-0.8562079080182944903 + 5.7458288058879374884e-917j)  +/-  (1.44e-237, 1.44e-237j)
| (-0.71701347373942369929 + 1.0130545955574591446e-919j)  +/-  (4.55e-240, 4.55e-240j)
| (0.88427665971018918738 + 2.1970730309484482905e-917j)  +/-  (4.34e-237, 4.34e-237j)
| (0.75561835042722878432 + 3.3680458052411290249e-922j)  +/-  (2.48e-239, 2.48e-239j)
| (0.79177163907050822714 - 2.060995080641027536e-922j)  +/-  (1.18e-238, 1.18e-238j)
| (0.9669649256262432901 + 1.3752168696725844275e-926j)  +/-  (7.16e-236, 7.16e-236j)
| (-0.63290797194649514093 + 6.4854407703699073247e-939j)  +/-  (1.12e-241, 1.12e-241j)
| (-0.79177163907050822714 - 3.0140347393347464467e-939j)  +/-  (1.14e-238, 1.14e-238j)
| (0.67606882688450432389 - 2.0223057969582254835e-942j)  +/-  (7.42e-241, 7.42e-241j)
| (0.63290797194649514093 + 4.1866518476709438758e-945j)  +/-  (1.18e-241, 1.18e-241j)
| (-0.11397258560952996693 - 1.2914783189373888966e-955j)  +/-  (4.39e-253, 4.39e-253j)
| (-0.67606882688450432389 + 3.1476271326833470238e-946j)  +/-  (7.57e-241, 7.57e-241j)
| (-0.44114825175002688059 + 7.4345929556120668131e-953j)  +/-  (1.36e-245, 1.36e-245j)
| (0.057082916723187490812 - 5.9667581069047243902e-962j)  +/-  (1.89e-254, 1.89e-254j)
| (0.58768341187210822029 - 1.7527354638993763541e-951j)  +/-  (1.43e-242, 1.43e-242j)
| (0.28168978132000734802 + 7.7319687235048977443e-958j)  +/-  (3.74e-249, 3.74e-249j)
| (-0.33599390363850889973 - 3.1219170434408853941e-956j)  +/-  (5.99e-248, 5.99e-248j)
| (-0.58768341187210822029 + 2.722206364628954568e-953j)  +/-  (1.47e-242, 1.47e-242j)
| (-0.17049043085087520581 + 2.3284614098312078e-963j)  +/-  (9.81e-252, 9.81e-252j)
| (0.5405515645794568949 + 2.3287090604026969774e-954j)  +/-  (1.6e-243, 1.6e-243j)
| (0.49165606141217095241 + 7.2571476960324040952e-955j)  +/-  (1.53e-244, 1.53e-244j)
| (1.432883272852044867e-979 + 2.8393029092243743695e-979j)  +/-  (1.75e-977, 1.75e-977j)
| (-0.49165606141217095241 - 3.0039683365877314922e-957j)  +/-  (1.59e-244, 1.59e-244j)
| (-0.28168978132000734802 - 4.1471046618973593603e-961j)  +/-  (4.22e-249, 4.22e-249j)
| (0.11397258560952996693 + 2.6419961350791526173e-964j)  +/-  (4.36e-253, 4.36e-253j)
| (0.44114825175002688059 + 1.7001674410252200879e-955j)  +/-  (1.31e-245, 1.31e-245j)
| (0.17049043085087520581 + 3.174611276559964104e-963j)  +/-  (1.02e-251, 1.02e-251j)
| (-0.22645936543953685886 + 1.3362562752416348562e-961j)  +/-  (2.03e-250, 2.03e-250j)
| (-0.38920185274720471495 + 1.4107345021822381464e-958j)  +/-  (9.43e-247, 9.43e-247j)
| (-0.057082916723187490812 - 5.5449193770323376196e-965j)  +/-  (1.89e-254, 1.89e-254j)
| (0.33599390363850889973 + 1.5868377600522639359e-958j)  +/-  (5.96e-248, 5.96e-248j)
| (0.38920185274720471495 - 1.7874528036970529706e-957j)  +/-  (9.69e-247, 9.69e-247j)
-------------------------------------------------
The weights are:
| (0.0017088604963509650263 - 3.0406462951545008542e-813j)  +/-  (1.41e-51, 3.28e-164j)
| (0.011393506344486885997 + 1.1322762205044506823e-814j)  +/-  (5.82e-52, 1.35e-164j)
| (0.026650092713661029661 - 6.7243723467454417456e-814j)  +/-  (2.38e-52, 5.52e-165j)
| (0.004783536555319381045 - 2.0195151305577283252e-814j)  +/-  (2.4e-52, 5.57e-165j)
| (0.020723383186119052609 - 3.2217505080186962473e-814j)  +/-  (1.28e-52, 2.96e-165j)
| (0.017619253477651071545 + 4.3883017911618020299e-814j)  +/-  (1.97e-52, 4.56e-165j)
| (0.004783536555319381045 + 4.5068625327136394312e-813j)  +/-  (1.32e-53, 3.05e-166j)
| (0.023744293821437958856 + 7.6332871120217155019e-814j)  +/-  (3.7e-54, 8.58e-167j)
| (0.014512882774771543816 - 1.2870369313336628226e-813j)  +/-  (1.76e-54, 4.08e-167j)
| (0.0017088604963509650263 + 5.7134105232915855821e-815j)  +/-  (5.93e-54, 1.38e-166j)
| (0.029477308245351115913 + 2.0718277859917961956e-814j)  +/-  (9.9e-56, 2.3e-168j)
| (0.048037222658882904512 + 3.2116801170432879417e-814j)  +/-  (4.64e-57, 1.08e-169j)
| (0.011393506344486885997 + 1.6663170504883564018e-813j)  +/-  (9.26e-55, 2.15e-167j)
| (0.032236632791665027205 - 5.4229109698508747035e-814j)  +/-  (3.48e-56, 8.06e-169j)
| (0.055631999803508207492 + 1.7990386507372071893e-814j)  +/-  (4.48e-58, 1.04e-170j)
| (0.032236632791665027205 - 1.9192867195346785824e-814j)  +/-  (1.89e-56, 4.39e-169j)
| (0.023744293821437958856 + 2.636612222887775895e-814j)  +/-  (1.31e-55, 3.04e-168j)
| (0.0081507848991812207039 + 5.5286171273905030793e-814j)  +/-  (1.46e-54, 3.38e-167j)
| (0.0373987947325034857 - 4.5374434578351403419e-814j)  +/-  (6.74e-58, 1.56e-170j)
| (0.020723383186119052609 - 8.8423150565790410181e-814j)  +/-  (3.43e-56, 7.96e-169j)
| (0.0081507848991812207039 - 2.418749258957180479e-813j)  +/-  (7.54e-56, 1.75e-168j)
| (0.039793035290743862212 + 1.6903448808370741313e-814j)  +/-  (6.34e-61, 1.47e-173j)
| (0.017619253477651071545 + 1.0501625219265434987e-813j)  +/-  (3.09e-56, 7.17e-169j)
| (0.029477308245351115913 + 6.0079721785409878194e-814j)  +/-  (7.67e-58, 1.78e-170j)
| (0.039793035290743862212 + 4.1945904048036751308e-814j)  +/-  (2.9e-60, 6.72e-173j)
| (0.026650092713661029661 - 2.2936745927430456475e-814j)  +/-  (1.14e-59, 2.65e-172j)
| (0.0373987947325034857 - 1.7401310240719190758e-814j)  +/-  (5.37e-62, 1.24e-174j)
| (0.034885782764645987104 + 1.8131150205452184325e-814j)  +/-  (1.9e-61, 4.4e-174j)
| (0.014512882774771543816 - 7.8029889417502579795e-814j)  +/-  (1.14e-59, 2.64e-172j)
| (0.044219641308865595579 + 3.6381397116111996941e-814j)  +/-  (1.82e-64, 4.22e-177j)
| (0.034885782764645987104 + 4.9399325324280046833e-814j)  +/-  (1.01e-61, 2.34e-174j)
| (0.042076049883697133524 - 1.6574409957970028885e-814j)  +/-  (1.25e-64, 2.9e-177j)
| (0.044219641308865595579 + 1.6385595019275517e-814j)  +/-  (1.17e-65, 2.7e-178j)
| (0.056732581852837114168 + 2.1859047904194268377e-814j)  +/-  (6.66e-70, 1.54e-182j)
| (0.042076049883697133524 - 3.897145537092379935e-814j)  +/-  (4.13e-65, 9.58e-178j)
| (0.051257312049126774322 + 2.8718320232030708265e-814j)  +/-  (1.03e-68, 2.4e-181j)
| (0.057017310146644013037 - 1.9635046282217877797e-814j)  +/-  (2.58e-70, 5.98e-183j)
| (0.046203032841401990932 - 1.631703231462573807e-814j)  +/-  (4.65e-68, 1.08e-180j)
| (0.054797154957272254207 - 1.7562440415378146851e-814j)  +/-  (3.29e-70, 7.62e-183j)
| (0.053783094025116511898 + 2.5980804088250981773e-814j)  +/-  (2.44e-70, 5.65e-183j)
| (0.046203032841401990932 - 3.4119037168569673177e-814j)  +/-  (9.29e-68, 2.15e-180j)
| (0.056273933611951210319 - 2.2747104449491778996e-814j)  +/-  (6.06e-71, 1.41e-183j)
| (0.048037222658882904512 + 1.6344260292463153709e-814j)  +/-  (8.22e-70, 1.91e-182j)
| (0.049728898953217361222 - 1.6449602413298848273e-814j)  +/-  (1.34e-70, 3.1e-183j)
| (0.057115970127565464439 + 2.030453046587052394e-814j)  +/-  (7.76e-72, 1.8e-184j)
| (0.049728898953217361222 - 3.0324106504809186964e-814j)  +/-  (4.37e-70, 1.01e-182j)
| (0.054797154957272254207 - 2.4797303883809360593e-814j)  +/-  (1.14e-71, 2.65e-184j)
| (0.056732581852837114168 + 1.9029150209853528719e-814j)  +/-  (1.44e-72, 3.34e-185j)
| (0.051257312049126774322 + 1.6628842463302606615e-814j)  +/-  (6.16e-73, 1.43e-185j)
| (0.056273933611951210319 - 1.8480274148958510471e-814j)  +/-  (7.84e-73, 1.82e-185j)
| (0.055631999803508207492 + 2.3721665101082028809e-814j)  +/-  (7.82e-73, 1.81e-185j)
| (0.052605634749807609177 - 2.7280176494753889579e-814j)  +/-  (1.22e-72, 2.84e-185j)
| (0.057017310146644013037 - 2.1045487871120966898e-814j)  +/-  (3.01e-73, 6.98e-186j)
| (0.053783094025116511898 + 1.719299050642072684e-814j)  +/-  (1.52e-74, 3.55e-187j)
| (0.052605634749807609177 - 1.6879571586606088701e-814j)  +/-  (1.43e-74, 3.31e-187j)
