Starting with polynomial:
P : -t+1
Extension levels are: 1 49
-------------------------------------------------
Trying to find an order 49 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^50 + 401571337016961389622481788371450899290910119743778818094469993249/163462998886106467979177611033628493890911243768038864180010080*t^49 - 473579454770797259461071968765176091907377827145986301124567201190849/163462998886106467979177611033628493890911243768038864180010080*t^48 + 3720580155621858965442836404723403033728144444316529049013785403890188/1702739571730275708116433448266963478030325455917071501875105*t^47 - 2017106750706960935032596851012450676705940298416638856267388083735541764/1702739571730275708116433448266963478030325455917071501875105*t^46 + 837734180351644708508220704308941338264629028580849627535797657002698153156/1702739571730275708116433448266963478030325455917071501875105*t^45 - 55473442906776989578468633435685414634943028293844994149198475695374764645636/340547914346055141623286689653392695606065091183414300375021*t^44 + 15045438320955367591425181003411638768868240585546055431331208582196927721925216/340547914346055141623286689653392695606065091183414300375021*t^43 - 3408748747264387497307373093132040840663295988624765067131129518877529633916074912/340547914346055141623286689653392695606065091183414300375021*t^42 + 654663630269201269369133840462711067490896294895378822248383357022179692228028118096/340547914346055141623286689653392695606065091183414300375021*t^41 - 107787822271137333255618391440286232088601323429013050514096881694687517160649783533264/340547914346055141623286689653392695606065091183414300375021*t^40 + 15349336479130463000768783170733197633742978863434606692107712156210418626584442242122240/340547914346055141623286689653392695606065091183414300375021*t^39 - 1903841310497149535764031098863588521283995288116686737880318885446374896368267371964720640/340547914346055141623286689653392695606065091183414300375021*t^38 + 206842361303842815972677979702173745089007861511011195381689439104185108518745035383477383680/340547914346055141623286689653392695606065091183414300375021*t^37 - 19773433886654055450823493561352040684819657765074142550832284787055465868017310939089250019840/340547914346055141623286689653392695606065091183414300375021*t^36 + 1669303272556919751777020564263015912685408842369038846522473271178500121152620417616456795893760/340547914346055141623286689653392695606065091183414300375021*t^35 - 124810798450061760183658863994430562499871192871793620399998155782835924334560489585444557989990400/340547914346055141623286689653392695606065091183414300375021*t^34 + 487262260379937407487558364149895876739063084998830816452477806964271732573493913788516570177459200/20032230255650302448428628803140746800356770069612605904413*t^33 - 28754520281057480341549116975485204960457804609884472653950260943230585952429125088732921957894886400/20032230255650302448428628803140746800356770069612605904413*t^32 + 1510651893713044077411756620525228968593639347326096487075064700772930402851671222878886611270251315200/20032230255650302448428628803140746800356770069612605904413*t^31 - 70709730549353671800253521107832733528669928026402731098079745152596339780647671488874492517876747468800/20032230255650302448428628803140746800356770069612605904413*t^30 + 2949970183105524672037377282832637790703520803447993971094398489988001730183108887932220715609339396096000/20032230255650302448428628803140746800356770069612605904413*t^29 - 109694051417418935671195563328345965444544357783995272465064468305965427561808548895265793787818562748416000/20032230255650302448428628803140746800356770069612605904413*t^28 + 3634309994635878548525196967198853147235928746023886921101973953952439479024300308470961831999732936343552000/20032230255650302448428628803140746800356770069612605904413*t^27 - 107208065197850729037086100752928988646914004526687503566377732996599363917817166200834426369500677913706496000/20032230255650302448428628803140746800356770069612605904413*t^26 + 2812807994905534939279931051679293662074351648544000909091812513116796958973733532781585986967936011636834304000/20032230255650302448428628803140746800356770069612605904413*t^25 - 65545911222624667437429181225946814210003572468422397157422382836671805711771415660880026079436867607861657600000/20032230255650302448428628803140746800356770069612605904413*t^24 + 1354159907085557636673936834009990400101510554271150017643963968663742192946486282155708811713441729916541337600000/20032230255650302448428628803140746800356770069612605904413*t^23 - 24749775889718799976684204185262549857479923211496684260002969562147107931362076320803161969441065012182594355200000/20032230255650302448428628803140746800356770069612605904413*t^22 + 399143152394557290030296279562529863616681628634283207223682916664587829135949698104716552590970270109957462425600000/20032230255650302448428628803140746800356770069612605904413*t^21 - 5662749870049249220886821793714033517020158583049422527787687134740115159008821103338999860651102170588724487782400000/20032230255650302448428628803140746800356770069612605904413*t^20 + 70427037418045242301010171327211329533872222260321056895319166380784377157666859929531179331805695104013861650432000000/20032230255650302448428628803140746800356770069612605904413*t^19 - 764714586951186517827774785920703163074009253264283550825092298062745262683493842359491205571024107242970197000192000000/20032230255650302448428628803140746800356770069612605904413*t^18 + 7215619006113219614755098751643707236650402718969689025762313367487710110923846316637049980450222126557152169426944000000/20032230255650302448428628803140746800356770069612605904413*t^17 - 58846614847452985872118746643833431777425892177338140741828897281691058145391992175010492693635582474285528621514752000000/20032230255650302448428628803140746800356770069612605904413*t^16 + 412236566988387510994791525659028860659736585094830992564502900587787559116297440245804328619478139412737929529786368000000/20032230255650302448428628803140746800356770069612605904413*t^15 - 2462826122899850247566608509876903876992952242721358116001250953041467545164369789357788727462992972406171382138798080000000/20032230255650302448428628803140746800356770069612605904413*t^14 + 12444271503134232326418673430795566634407026010962281502188495145195013994242394408841699421800879037908519408768122880000000/20032230255650302448428628803140746800356770069612605904413*t^13 - 52666719006587531915928584384329155269117864299567586224711154848693651526295021034343456017466297318706915266065858560000000/20032230255650302448428628803140746800356770069612605904413*t^12 + 184575426118636485419836431100038708266057032315580014174075344676543496450667881151338181866535064500260966491257569280000000/20032230255650302448428628803140746800356770069612605904413*t^11 - 528434589574942303390561911801034696926882438101781122689458936521525214940537830643544476158990496328406224454203473920000000/20032230255650302448428628803140746800356770069612605904413*t^10 + 1215923207660998142405167364693786100851078910851055371956926720479283788092208099522660858955396152545178110420372684800000000/20032230255650302448428628803140746800356770069612605904413*t^9 - 2204321585207501163990458856392419417389731926392730944688321655980864506091805905236238773689847981965727404955323596800000000/20032230255650302448428628803140746800356770069612605904413*t^8 + 3071476707398068597665735987482314308458031983629817558371931951045692373908937850844156010261267495157002881849727385600000000/20032230255650302448428628803140746800356770069612605904413*t^7 - 3187341624611383414529245495562286048048598022118629465347116558430526729676723459110163125237641624284930762248867020800000000/20032230255650302448428628803140746800356770069612605904413*t^6 + 2363340078241752348962773458597232202069691977246878774369483482557225925272976540187831100329279194079650288495702835200000000/20032230255650302448428628803140746800356770069612605904413*t^5 - 1183047204779564112120733978665562807445926922173290204598518325201103514567703431025832445906763635180084764778430464000000000/20032230255650302448428628803140746800356770069612605904413*t^4 + 368228239657177351275028229952273622447977631147239440990391110857138761949338036260357502425089913669391608860114944000000000/20032230255650302448428628803140746800356770069612605904413*t^3 - 62571938502533159145961076955577322836336701754260096460852943686250215652212182893857524308976996231548357698387968000000000/20032230255650302448428628803140746800356770069612605904413*t^2 + 4579680168926168565539131493477823792953273279054105937633269721370360280728447672563103421489766012251901121265664000000000/20032230255650302448428628803140746800356770069612605904413*t - 81028939814135462383261460627966302189417948706229386140672921611956916286750669524797566559220034397752195547136000000000/20032230255650302448428628803140746800356770069612605904413
-------------------------------------------------
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: 0
  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:
| (178.90951503288136494 - 2.5827572805033864273e-616j)  +/-  (3.03e-238, 3.03e-238j)
| (96.038047921253654234 - 1.2875748590108916384e-619j)  +/-  (5.8e-231, 5.8e-231j)
| (141.21932987735607633 + 1.0838392108140126398e-630j)  +/-  (2.47e-234, 2.47e-234j)
| (151.57735371884902995 - 1.115604597304873566e-634j)  +/-  (2.51e-235, 2.51e-235j)
| (30.733966251611862345 - 3.1821318306256259058e-635j)  +/-  (9.81e-233, 9.81e-233j)
| (61.016168073789437643 - 9.3168243361019393924e-641j)  +/-  (2.99e-230, 2.99e-230j)
| (163.65416602268190008 - 2.3052477361264647545e-658j)  +/-  (1.33e-236, 1.33e-236j)
| (42.567143263083621295 - 1.6699190246196164037e-653j)  +/-  (3.37e-231, 3.37e-231j)
| (79.424208505917035051 - 3.1016273097715441612e-667j)  +/-  (2.37e-230, 2.37e-230j)
| (102.25778115354329376 + 4.9549375137363425029e-686j)  +/-  (2.57e-231, 2.57e-231j)
| (11.840680304999454678 + 3.4997570887671573535e-707j)  +/-  (3.08e-238, 3.08e-238j)
| (28.131666235869897614 + 8.5288063686363237525e-701j)  +/-  (3.56e-233, 3.56e-233j)
| (15.199975320342105886 - 3.8768892230191123732e-705j)  +/-  (9.01e-237, 9.01e-237j)
| (90.183287715784317875 + 4.785542694261149235e-697j)  +/-  (9.21e-231, 9.21e-231j)
| (108.89054357913412001 - 4.1310719812313626748e-706j)  +/-  (1.03e-231, 1.03e-231j)
| (10.32892129017020986 + 1.8935417429269992324e-718j)  +/-  (4.37e-239, 4.37e-239j)
| (36.355877472237096836 + 1.5324452291881574692e-709j)  +/-  (6.44e-232, 6.44e-232j)
| (132.01430633875366167 + 2.0007843990268884827e-710j)  +/-  (1.68e-233, 1.68e-233j)
| (17.051627295107432252 + 3.738152061090720811e-721j)  +/-  (4.19e-236, 4.19e-236j)
| (25.662810912485229738 - 5.4070870461418482674e-715j)  +/-  (1.01e-233, 1.01e-233j)
| (5.3610113703874399951 + 4.8287741329904422258e-730j)  +/-  (1.15e-242, 1.15e-242j)
| (13.463710367874350345 + 8.7035225727969507731e-726j)  +/-  (1.67e-237, 1.67e-237j)
| (49.415327828875332495 + 2.9523021033596127707e-717j)  +/-  (9.4e-231, 9.4e-231j)
| (69.754100574285808948 - 3.0940018300694798373e-738j)  +/-  (3.03e-230, 3.03e-230j)
| (84.65555321371241067 - 2.0022347310853075372e-754j)  +/-  (1.64e-230, 1.64e-230j)
| (3.5047775454220619898 - 3.0634619313379105083e-779j)  +/-  (1.12e-244, 1.12e-244j)
| (19.021024722287073171 + 3.9507683740557851037e-770j)  +/-  (2e-235, 2e-235j)
| (33.473847905093539532 + 4.9240012667214595572e-766j)  +/-  (2.69e-232, 2.69e-232j)
| (6.4441179431938160183 + 3.4225085814697112082e-776j)  +/-  (9.87e-242, 9.87e-242j)
| (123.6671384184031586 + 1.8335296819366329563e-764j)  +/-  (8.24e-233, 8.24e-233j)
| (2.7293492741008550995 - 1.9279246024082740281e-791j)  +/-  (1.09e-245, 1.09e-245j)
| (8.9266413560965881911 + 2.8897318331196731878e-787j)  +/-  (6.49e-240, 6.49e-240j)
| (1.4782203138430168634 + 2.6381962435315901714e-794j)  +/-  (5.52e-248, 5.52e-248j)
| (7.632204985029612635 - 1.1116249745394769228e-787j)  +/-  (8.29e-241, 8.29e-241j)
| (56.959885862142329682 - 2.0205930715596068898e-776j)  +/-  (2.26e-230, 2.26e-230j)
| (74.464066058828127076 - 7.6316207026961750411e-797j)  +/-  (2.81e-230, 2.81e-230j)
| (65.276534044294032472 + 1.050915398815795538e-810j)  +/-  (3.07e-230, 3.07e-230j)
| (1 - 8.0558754625783873334e-835j)  +/-  (3.45e-249, 3.45e-249j)
| (4.381623627599818905 - 3.9679514713014754106e-829j)  +/-  (1.24e-243, 1.24e-243j)
| (53.096273602572570275 + 7.8730527205621827479e-815j)  +/-  (1.45e-230, 1.45e-230j)
| (0.13320901377990397875 + 2.8601790617760218277e-841j)  +/-  (3.39e-253, 3.39e-253j)
| (39.385107287146253794 + 2.080283172643631167e-819j)  +/-  (1.41e-231, 1.41e-231j)
| (21.11075247171910365 + 2.933345054481111849e-824j)  +/-  (7.95e-235, 7.95e-235j)
| (0.61791274394612926264 - 8.9902830731787775134e-841j)  +/-  (1.98e-250, 1.98e-250j)
| (45.908225844366416868 + 1.5249814114295198311e-819j)  +/-  (5.83e-231, 5.83e-231j)
| (115.99888870126915461 + 2.3432867613812723411e-835j)  +/-  (3.11e-232, 3.11e-232j)
| (0.025160056574757086692 + 2.3921750938725372523e-891j)  +/-  (1.14e-254, 1.14e-254j)
| (2.0542226838949691498 + 2.1425797137864015966e-867j)  +/-  (7.47e-247, 7.47e-247j)
| (0.32985142260645409311 - 2.0502745835023798715e-873j)  +/-  (8.23e-252, 8.23e-252j)
| (23.323644686030310245 - 3.5925485496574278945e-854j)  +/-  (3.06e-234, 3.06e-234j)
-------------------------------------------------
The weights are:
| (3.6060254728118575427e-77 + 3.2567844870257867157e-680j)  +/-  (2.25e-72, 2.09e-183j)
| (1.1790628910300783999e-41 + 7.5839689056003447756e-661j)  +/-  (7.4e-60, 6.88e-171j)
| (4.5372651055759364065e-61 - 6.6705873187049200021e-672j)  +/-  (7.92e-68, 7.35e-179j)
| (1.6426642224523640769e-65 + 3.2700506367727862004e-674j)  +/-  (2.39e-69, 2.22e-180j)
| (1.1994414441570905051e-13 + 4.2253617409399536171e-648j)  +/-  (2.65e-40, 2.47e-151j)
| (1.317409623625441048e-26 - 1.40251924559926058e-654j)  +/-  (2.48e-53, 2.3e-164j)
| (1.1190613280160702231e-70 - 7.0209411628879863674e-677j)  +/-  (2.89e-71, 2.68e-182j)
| (1.0631723683921184557e-18 + 7.5052617193115953721e-651j)  +/-  (2.02e-47, 1.87e-158j)
| (1.6345069747228106324e-34 - 3.3692752020357409783e-658j)  +/-  (1.74e-58, 1.62e-169j)
| (2.4966422206054607743e-44 + 1.125996476847540174e-662j)  +/-  (5.66e-63, 5.26e-174j)
| (1.1291447670840136284e-05 - 1.8931997178761369938e-644j)  +/-  (3.71e-29, 3.44e-140j)
| (1.5365160091368381532e-12 - 1.3211738363313171946e-647j)  +/-  (2.37e-42, 2.2e-153j)
| (4.4921693917762726203e-07 - 4.0352120253660771059e-645j)  +/-  (1.85e-33, 1.71e-144j)
| (3.8785784587541493568e-39 - 4.6896532034693393846e-660j)  +/-  (5.86e-61, 5.44e-172j)
| (3.5129722549552303499e-47 - 2.0485976205808316725e-664j)  +/-  (8.83e-65, 8.21e-176j)
| (4.7597795866624098571e-05 + 3.7744432723305959651e-644j)  +/-  (1.97e-30, 1.83e-141j)
| (4.8013446561847738697e-16 + 1.1787852944448647207e-649j)  +/-  (4.27e-48, 3.96e-159j)
| (4.058747433750830054e-57 + 7.9106944664494931257e-670j)  +/-  (5.04e-69, 4.68e-180j)
| (7.5098545515898794066e-08 + 1.7158379267811203987e-645j)  +/-  (3.24e-38, 3.01e-149j)
| (1.7203289698714983718e-11 + 3.4674878167855379616e-647j)  +/-  (1.76e-43, 1.64e-154j)
| (0.0048419452656327873949 + 3.4078454943660161972e-643j)  +/-  (1.01e-26, 9.39e-138j)
| (2.3873411444701576635e-06 + 8.9846940197234250146e-645j)  +/-  (2.96e-35, 2.75e-146j)
| (1.2433968136075075824e-21 + 3.1181108270070529479e-652j)  +/-  (7.71e-54, 7.17e-165j)
| (2.3339407146731179019e-30 - 2.5211615933131140669e-656j)  +/-  (3.98e-59, 3.7e-170j)
| (9.2243093285548648124e-37 + 3.7080626346119449213e-659j)  +/-  (2.04e-61, 1.9e-172j)
| (0.024822724284201123571 + 7.2307115412000155249e-643j)  +/-  (1.69e-28, 1.57e-139j)
| (1.1132171867675329855e-08 - 6.9149704218734177577e-646j)  +/-  (1.18e-42, 1.09e-153j)
| (8.1512274897049146001e-15 - 2.6820379224785937678e-649j)  +/-  (1.06e-48, 9.86e-160j)
| (0.0018050769092040725989 - 2.14043258541280689e-643j)  +/-  (8.81e-35, 8.18e-146j)
| (1.5641068218072683458e-53 - 6.3835183500164733466e-668j)  +/-  (1.29e-69, 1.19e-180j)
| (0.047320578397508756453 - 9.5831124562788186468e-643j)  +/-  (3.39e-30, 3.15e-141j)
| (0.000179031863841924009 - 7.1185320596996342026e-644j)  +/-  (1.9e-37, 1.76e-148j)
| (0.12014851169257130541 - 1.3553431896308176462e-642j)  +/-  (3.05e-28, 2.83e-139j)
| (0.00060138910376382448526 + 1.2696409254295156256e-643j)  +/-  (1.39e-36, 1.29e-147j)
| (7.2465357043242223797e-25 + 9.2360861373615149484e-654j)  +/-  (3.02e-57, 2.81e-168j)
| (2.2119744153402018654e-32 + 3.0054301510395136088e-657j)  +/-  (1.07e-60, 9.91e-172j)
| (1.9539208323725299538e-28 + 1.9590938443947670103e-655j)  +/-  (4.52e-59, 4.2e-170j)
| (0.15813124514451859227 + 1.4138837229605577408e-642j)  +/-  (4.53e-37, 4.21e-148j)
| (0.011603755290500599069 - 5.1170370464647390641e-643j)  +/-  (1.11e-39, 1.03e-150j)
| (3.2885564187143246111e-23 - 5.5947562480288238394e-653j)  +/-  (5.14e-57, 4.78e-168j)
| (0.13294199062500671185 - 6.196506475514651361e-643j)  +/-  (1.46e-39, 1.36e-150j)
| (2.4393700914281451986e-17 - 3.1941879227917908645e-650j)  +/-  (2.85e-54, 2.65e-165j)
| (1.4598891196355912806e-09 + 2.6480480146968316784e-646j)  +/-  (3.95e-50, 3.69e-161j)
| (0.18041494009134483663 - 1.3122268217374187911e-642j)  +/-  (3.8e-43, 3.53e-154j)
| (3.9509399653568718331e-20 - 1.5979458342462321785e-651j)  +/-  (5.61e-56, 5.2e-167j)
| (3.0896073396920539166e-50 + 3.9197806828898025673e-666j)  +/-  (2.41e-71, 2.23e-182j)
| (0.0630398861397947286 + 1.9454004983530058949e-643j)  +/-  (8.43e-46, 7.53e-157j)
| (0.080166250057842201795 + 1.1849378954034019981e-642j)  +/-  (7.59e-46, 6.93e-157j)
| (0.17392086145422800008 + 1.0333031473502773927e-642j)  +/-  (1.56e-45, 1.37e-156j)
| (1.6894451384360110532e-10 - 9.6998947313302285199e-647j)  +/-  (4.89e-51, 4.58e-162j)
