Starting with polynomial:
P : t^7 - 21*t^5 + 105*t^3 - 105*t
Extension levels are: 7 48
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P1 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^55 - 2157887202291549839598462728271433947220487509/1615127349649056470704171123998417232551497*t^53 + 57317307725481531923445798116803252436490128173527/69450476034909428240279358331931940999714371*t^51 - 152308754294474760926816315087646600500881547434417449/486153332244365997681955508323523586998000597*t^49 + 5691301771779020314244191543778009260550336652367946682/69450476034909428240279358331931940999714371*t^47 - 1090150118992252540991844380212441827771058450225219920546/69450476034909428240279358331931940999714371*t^45 + 335428195260988445559848886739337165969947344118292342010/146829759059005133700379193090765202959227*t^43 - 37987017815014518529817171979319713922414733018223693830970/146829759059005133700379193090765202959227*t^41 + 3401256947424589564712579595210154528511138306186304341317305/146829759059005133700379193090765202959227*t^39 - 243335479756895606875675302759914753613684028593568094639815605/146829759059005133700379193090765202959227*t^37 + 14004071357262982928026364296475476713478705242200617882516018365/146829759059005133700379193090765202959227*t^35 - 650750997918782833785399969114275505938198198966323108016387152725/146829759059005133700379193090765202959227*t^33 + 24448440970905391235047073663263592646739901800907294513300205932700/146829759059005133700379193090765202959227*t^31 - 741984029302978902312840750696198270622657599134739825266579732532300/146829759059005133700379193090765202959227*t^29 + 18138775253234927174312726847068748733794205586748598351217026094118300/146829759059005133700379193090765202959227*t^27 - 355465345950691438775086716650907128425128573061932496765053522092535900/146829759059005133700379193090765202959227*t^25 + 5545908369408775327809699973810117367618099597740158759967720352572168125/146829759059005133700379193090765202959227*t^23 - 68258110217397409377018541993995568092274350006431321902265121520987145625/146829759059005133700379193090765202959227*t^21 + 654942959944134779821228699739232281947843838786789515223243796807275885625/146829759059005133700379193090765202959227*t^19 - 4825522778307851960200220554702524780465736402114003295115725826518826110625/146829759059005133700379193090765202959227*t^17 + 26773505126036636714549904556807615420645389827772708006624810891187794416250/146829759059005133700379193090765202959227*t^15 - 109032185241443153435380831539093388212638999676268035371052072676096935881250/146829759059005133700379193090765202959227*t^13 + 314773039306709937673767991644350172894661395975897504795701173412656891106250/146829759059005133700379193090765202959227*t^11 - 613298516797805280845676119777814551046394151120068219571427537633203572706250/146829759059005133700379193090765202959227*t^9 + 749302015084157301415412441382313005114728210635485450062046019860356416659375/146829759059005133700379193090765202959227*t^7 - 510069226386900258436188119031190319211909472400547200018085529766016509821875/146829759059005133700379193090765202959227*t^5 + 156305546526520048008250012199374274085189841817616721753332490990047469546875/146829759059005133700379193090765202959227*t^3 - 13250468592817984083713901914994696499211439223242558191223105000570755671875/146829759059005133700379193090765202959227*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:   55 out of 55
Indefinite weights: 0 out of 55
Negative weights:   0 out of 55
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (9.6702684626926102923 - 2.31787483748280208e-537j)  +/-  (1.51e-242, 1.51e-242j)
| (13.279467766861315918 + 6.4830489824115690201e-544j)  +/-  (6.26e-246, 6.26e-246j)
| (-13.279467766861315918 + 9.8088803131740847727e-543j)  +/-  (5.79e-246, 5.79e-246j)
| (-8.5563578986629578895 - 1.4300254514557561438e-538j)  +/-  (3.01e-242, 3.01e-242j)
| (-12.353732521818776209 - 4.2789057524810800765e-542j)  +/-  (1.06e-244, 1.06e-244j)
| (11.586209302409767188 + 1.7773203097867617608e-545j)  +/-  (6.88e-244, 6.88e-244j)
| (7.0159800678485146855 - 3.5929985885988729489e-545j)  +/-  (1.53e-242, 1.53e-242j)
| (8.5563578986629578895 - 2.3484329434233262355e-545j)  +/-  (2.93e-242, 2.93e-242j)
| (-11.586209302409767188 - 7.1419023026512916741e-549j)  +/-  (6.76e-244, 6.76e-244j)
| (-7.5159912559500918768 + 1.4934832430284839845e-558j)  +/-  (2.3e-242, 2.3e-242j)
| (-10.26662137264236816 + 9.3459359428904884476e-575j)  +/-  (7.61e-243, 7.61e-243j)
| (-9.6702684626926102923 - 2.7733306732139075122e-594j)  +/-  (1.44e-242, 1.44e-242j)
| (-6.5267693261374909927 - 5.6818979028590697972e-613j)  +/-  (8.54e-243, 8.54e-243j)
| (-2.8674866764033146541 + 1.8400195864173948527e-629j)  +/-  (7.42e-247, 7.42e-247j)
| (-2.4369524902066244737 - 4.4434666502919773166e-632j)  +/-  (7.59e-247, 7.59e-247j)
| (10.26662137264236816 + 9.3380819300251503809e-637j)  +/-  (7.05e-243, 7.05e-243j)
| (2.8674866764033146541 - 7.8711431356075709002e-659j)  +/-  (7.06e-247, 7.06e-247j)
| (9.1021643282647796552 + 1.4168862154297641915e-656j)  +/-  (2.24e-242, 2.24e-242j)
| (12.353732521818776209 - 1.6443977278670341943e-667j)  +/-  (9.99e-245, 9.99e-245j)
| (-5.5750274498292971425 - 2.4867919047180036562e-676j)  +/-  (1.78e-243, 1.78e-243j)
| (10.900250723923995227 - 8.5402218871365251684e-676j)  +/-  (2.84e-243, 2.84e-243j)
| (1.5730767703710473301 - 4.8782812463975738393e-690j)  +/-  (6.4e-250, 6.4e-250j)
| (4.6516749916850779166 + 6.0443596690837462103e-684j)  +/-  (1.76e-244, 1.76e-244j)
| (-5.1102492234943523974 - 4.9943174997088570301e-684j)  +/-  (6.28e-244, 6.28e-244j)
| (-2.3667594107345412886 - 1.5973177522635557532e-687j)  +/-  (5.45e-247, 5.45e-247j)
| (-4.1985964504457850824 + 3.8391422675191544355e-686j)  +/-  (4.67e-245, 4.67e-245j)
| (1.9987287623870007419 + 3.1597865951972321594e-688j)  +/-  (1.55e-248, 1.55e-248j)
| (7.5159912559500918768 - 6.3971764037335127618e-681j)  +/-  (2.4e-242, 2.4e-242j)
| (-3.7504397177257422563 - 2.1041997546804040192e-693j)  +/-  (1.17e-245, 1.17e-245j)
| (-1.1544053947399681272 - 4.9929775408097078275e-699j)  +/-  (2.9e-251, 2.9e-251j)
| (4.1985964504457850824 - 2.7701751540673048383e-692j)  +/-  (5.16e-245, 5.16e-245j)
| (6.5267693261374909927 + 1.4118006689611701454e-688j)  +/-  (8.56e-243, 8.56e-243j)
| (5.1102492234943523974 + 4.2419088834892274894e-696j)  +/-  (5.89e-244, 5.89e-244j)
| (3.7504397177257422563 - 3.1779444437654112507e-704j)  +/-  (1.23e-245, 1.23e-245j)
| (-10.900250723923995227 + 6.2164651487987742744e-708j)  +/-  (2.77e-243, 2.77e-243j)
| (-3.3067835418331311817 - 4.0905376189360413971e-724j)  +/-  (2.9e-246, 2.9e-246j)
| (-8.0286629605110423859 + 2.6809136405904778543e-722j)  +/-  (2.91e-242, 2.91e-242j)
| (2.4369524902066244737 - 4.1658541707414593211e-735j)  +/-  (7.18e-247, 7.18e-247j)
| (5.5750274498292971425 - 1.078914420051012722e-731j)  +/-  (1.75e-243, 1.75e-243j)
| (-7.0159800678485146855 - 1.1755179029375135307e-736j)  +/-  (1.56e-242, 1.56e-242j)
| (-1.9987287623870007419 + 6.4154338958741405229e-751j)  +/-  (1.32e-248, 1.32e-248j)
| (3.3067835418331311817 + 2.8713674849923003387e-748j)  +/-  (3.12e-246, 3.12e-246j)
| (8.0286629605110423859 - 7.4607526997310700585e-745j)  +/-  (2.93e-242, 2.93e-242j)
| (0.74791742049367699555 - 1.0037247938468554518e-759j)  +/-  (1.55e-252, 1.55e-252j)
| (-6.046861070612816037 - 5.4175932363681503009e-749j)  +/-  (3.9e-243, 3.9e-243j)
| (-0.74791742049367699555 + 1.4279588995818976534e-766j)  +/-  (1.55e-252, 1.55e-252j)
| (-9.1021643282647796552 + 2.4782998689503395322e-755j)  +/-  (2.15e-242, 2.15e-242j)
| (6.046861070612816037 + 1.0577591069168821022e-768j)  +/-  (4.1e-243, 4.1e-243j)
| (0.36224063360743618138 - 8.1726241950308186554e-790j)  +/-  (1.27e-253, 1.27e-253j)
| (1.1326441344796843443e-801 + 4.2511762263131365592e-802j)  +/-  (6.65e-800, 6.65e-800j)
| (-4.6516749916850779166 - 1.2618336984800105557e-778j)  +/-  (1.81e-244, 1.81e-244j)
| (-0.36224063360743618138 - 8.8671529835883245701e-793j)  +/-  (1.27e-253, 1.27e-253j)
| (-1.5730767703710473301 - 3.7019903946005611075e-791j)  +/-  (5.42e-250, 5.42e-250j)
| (1.1544053947399681272 + 3.4672429108637031006e-791j)  +/-  (2.95e-251, 2.95e-251j)
| (2.3667594107345412886 - 8.5019781475175764922e-788j)  +/-  (5.1e-247, 5.1e-247j)
-------------------------------------------------
The weights are:
| (1.1449571619808186931e-21 + 1.2748524303533620428e-557j)  +/-  (4.28e-65, 1.56e-187j)
| (2.1732314072909069522e-39 + 7.8620061378072489119e-568j)  +/-  (1.32e-72, 4.8e-195j)
| (2.1732314072909069522e-39 - 1.936894248505802503e-567j)  +/-  (1.05e-73, 3.83e-196j)
| (2.7075814603887060469e-17 - 1.796172034866359701e-554j)  +/-  (1.93e-64, 7e-187j)
| (2.3875373317420968647e-34 + 9.9169319112171966762e-565j)  +/-  (3.9e-72, 1.42e-194j)
| (2.0336543140369021379e-30 + 5.3792227698494205046e-563j)  +/-  (5.78e-71, 2.1e-193j)
| (4.0372034680231287173e-12 + 1.7216706460971275609e-554j)  +/-  (3.88e-61, 1.41e-183j)
| (2.7075814603887060469e-17 + 3.119406952798341443e-556j)  +/-  (9.53e-65, 3.46e-187j)
| (2.0336543140369021379e-30 - 1.3912287276444462309e-562j)  +/-  (6.94e-72, 2.52e-194j)
| (1.092400387839618032e-13 - 3.538875787482371439e-553j)  +/-  (2.82e-64, 1.02e-186j)
| (3.165032421699447327e-24 - 4.4321292287383785155e-559j)  +/-  (4.01e-70, 1.46e-192j)
| (1.1449571619808186931e-21 + 1.5528166497642586552e-557j)  +/-  (5.2e-69, 1.89e-191j)
| (1.0860797263074948618e-10 - 8.9572297810480399414e-552j)  +/-  (4.11e-63, 1.49e-185j)
| (0.0028567620134387483661 - 4.9185396390699436057e-547j)  +/-  (3.45e-50, 1.25e-172j)
| (0.0081434754222234443023 + 7.1113935280589636879e-546j)  +/-  (1.52e-47, 5.53e-170j)
| (3.165032421699447327e-24 + 2.3391241519548073427e-559j)  +/-  (2.75e-73, 1e-195j)
| (0.0028567620134387483661 - 1.9498840289508188406e-547j)  +/-  (8.43e-54, 3.06e-176j)
| (2.2676520340508187448e-19 - 6.2956381030420121105e-557j)  +/-  (4.56e-71, 1.66e-193j)
| (2.3875373317420968647e-34 - 3.8696949235003547441e-565j)  +/-  (2.63e-78, 9.55e-201j)
| (3.3278036697573961064e-08 - 1.7911017705061828733e-550j)  +/-  (4.84e-65, 1.76e-187j)
| (4.146810903410601335e-27 - 3.9856647702198026606e-561j)  +/-  (6.16e-75, 2.24e-197j)
| (0.048943274988886487305 - 1.3991243472592306364e-546j)  +/-  (1.12e-48, 4.06e-171j)
| (3.6388007702942076118e-06 - 4.9079149880079860692e-550j)  +/-  (3.66e-64, 1.33e-186j)
| (3.9300879322083482635e-07 + 7.1635807334904262273e-550j)  +/-  (2.44e-64, 8.88e-187j)
| (0.00094331228837086503309 - 8.2545098657349848523e-546j)  +/-  (7.89e-54, 2.87e-176j)
| (2.6712801961289924187e-05 + 9.5351151365327653099e-549j)  +/-  (2.78e-62, 1.01e-184j)
| (0.023157919512848026195 + 1.4143788863508737239e-546j)  +/-  (1.99e-54, 7.25e-177j)
| (1.092400387839618032e-13 + 3.619863062562116537e-555j)  +/-  (5.18e-71, 1.89e-193j)
| (0.00015694630226962217038 - 3.3012152752707101552e-548j)  +/-  (1.8e-61, 6.55e-184j)
| (0.084771535888632944779 + 2.6148828308981743438e-546j)  +/-  (2.5e-50, 9.11e-173j)
| (2.6712801961289924187e-05 + 2.1893737183788100423e-549j)  +/-  (1.09e-64, 3.96e-187j)
| (1.0860797263074948618e-10 - 3.1814256955095827016e-553j)  +/-  (5.79e-70, 2.1e-192j)
| (3.9300879322083482635e-07 + 1.0052459000352017124e-550j)  +/-  (2.27e-67, 8.25e-190j)
| (0.00015694630226962217038 - 9.2584323730170497167e-549j)  +/-  (3.33e-64, 1.21e-186j)
| (4.146810903410601335e-27 + 9.7634044472920176243e-561j)  +/-  (5.41e-80, 1.97e-202j)
| (0.00074365062450278301418 + 1.171430444693005567e-547j)  +/-  (1.2e-63, 4.35e-186j)
| (2.0869290100203963789e-15 + 7.8464564246220015661e-554j)  +/-  (1.11e-74, 4.05e-197j)
| (0.0081434754222234443023 + 3.2846111571874274391e-546j)  +/-  (4.43e-63, 1.61e-185j)
| (3.3278036697573961064e-08 - 1.817190846760289291e-551j)  +/-  (6.1e-70, 2.22e-192j)
| (4.0372034680231287173e-12 + 1.8058374615526422296e-552j)  +/-  (4.68e-73, 1.7e-195j)
| (0.023157919512848026195 + 2.6407591363647921416e-546j)  +/-  (4.84e-63, 1.76e-185j)
| (0.00074365062450278301418 + 3.9349473572331300123e-548j)  +/-  (4.1e-66, 1.49e-188j)
| (2.0869290100203963789e-15 - 1.4164569565362550169e-555j)  +/-  (1.5e-74, 5.44e-197j)
| (0.11995136334935790869 - 2.5893110686873483814e-546j)  +/-  (4.71e-63, 1.71e-185j)
| (2.1794317943049601562e-09 + 4.1592504807379217534e-551j)  +/-  (1.09e-71, 3.97e-194j)
| (0.11995136334935790869 - 3.2522781359612422438e-546j)  +/-  (4.76e-64, 1.73e-186j)
| (2.2676520340508187448e-19 - 5.3672280155365042413e-556j)  +/-  (2.24e-77, 8.16e-200j)
| (2.1794317943049601562e-09 + 2.7621606887505004791e-552j)  +/-  (1.27e-71, 4.63e-194j)
| (0.13921190870491268766 + 3.5359636186100454416e-546j)  +/-  (6.18e-65, 2.25e-187j)
| (0.14217814144561331053 - 4.1459680410051370195e-546j)  +/-  (3.37e-65, 1.23e-187j)
| (3.6388007702942076118e-06 - 2.6819886058027416717e-549j)  +/-  (8.55e-70, 3.1e-192j)
| (0.13921190870491268766 + 3.947447113140227878e-546j)  +/-  (1.29e-65, 4.69e-188j)
| (0.048943274988886487305 - 2.2747032758313730215e-546j)  +/-  (3.28e-66, 1.19e-188j)
| (0.084771535888632944779 + 1.8357431963544449794e-546j)  +/-  (8.9e-67, 3.09e-189j)
| (0.00094331228837086503309 - 3.9058722188339267138e-546j)  +/-  (1.19e-66, 4.46e-189j)
