Starting with polynomial:
P : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Extension levels are: 7 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : 128*t^7 - 1344*t^5 + 3360*t^3 - 1680*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 128*t^49 - 19805418549957277847209527554837772446304/279315278991669129388030495091697737*t^47 + 185934372967805111657628656128628147560735536/10334665322691757787357128318392816269*t^45 - 28698321280928077221482638430189661792399848840/10334665322691757787357128318392816269*t^43 + 3018264027526311222913710094160121710079354028980/10334665322691757787357128318392816269*t^41 - 229633226347416672086683404511149486548382630472770/10334665322691757787357128318392816269*t^39 + 18629194178896811941898566319552832254487716800635/14700804157456269967791078689036723*t^37 - 1628904071978519555372858005083050705082547523759865/29401608314912539935582157378073446*t^35 + 110740300331398404477414651172723766913523691200217475/58803216629825079871164314756146892*t^33 - 2951833813493762357485027588777914139085574543278666325/58803216629825079871164314756146892*t^31 + 123926379405155783276541004588616332380609220935454716225/117606433259650159742328629512293784*t^29 - 4100404987936772786071693094339729132828850255287673753675/235212866519300319484657259024587568*t^27 + 106676438574128400602765108870839368305867652615239935225575/470425733038600638969314518049175136*t^25 - 2170590164745459752022245188306562066634400861654936590729375/940851466077201277938629036098350272*t^23 + 34252830970270431074637366336815370217731903927319562589076875/1881702932154402555877258072196700544*t^21 - 414261137137047896606953011840803981433997619897629608399155625/3763405864308805111754516144393401088*t^19 + 1889644638308277826218773762517397927707643433389373680019881875/3763405864308805111754516144393401088*t^17 - 50941454074775242556258277913199240311493428989106462453286413125/30107246914470440894036129155147208704*t^15 + 246793086183145698452098233639677835733310496062910048243920990625/60214493828940881788072258310294417408*t^13 - 828978380270059723260366054488687380665093809254175999868055696875/120428987657881763576144516620588834816*t^11 + 1838651888690558583465213589380835405465503511511835490168408059375/240857975315763527152289033241177669632*t^9 - 2513755927208590928536564415160273437259754310352422394836674021875/481715950631527054304578066482355339264*t^7 + 1908191938479753516189023611445309823989673775857708423387268509375/963431901263054108609156132964710678528*t^5 - 669657234834790036467222904613696820504949954794743203675334953125/1926863802526108217218312265929421357056*t^3 + 70704837806066127066053658198577652758463853983240899350262546875/3853727605052216434436624531858842714112*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
-------------------------------------------------
The nodes are:
| (-5.9107025009587894247 - 2.644559331705498727e-949j)  +/-  (9.31e-244, 9.31e-244j)
| (-8.301329429185597997 + 1.4619451259987482364e-958j)  +/-  (9.82e-246, 9.82e-246j)
| (-8.9928184115185802124 - 6.3028927197675619643e-961j)  +/-  (6.1e-247, 6.1e-247j)
| (-7.2291202737744768985 - 7.7887336973570637026e-957j)  +/-  (1.99e-244, 1.99e-244j)
| (-7.7339188633873081343 + 8.2500931455020958791e-959j)  +/-  (5.34e-245, 5.34e-245j)
| (8.9928184115185802124 + 2.5315316978964540543e-961j)  +/-  (6.75e-247, 6.75e-247j)
| (7.7339188633873081343 + 7.2216989500439758606e-960j)  +/-  (5.29e-245, 5.29e-245j)
| (6.3268178232955430976 - 4.84617304632708698e-958j)  +/-  (7.24e-244, 7.24e-244j)
| (-6.3268178232955430976 - 7.5671450250104070748e-957j)  +/-  (7.88e-244, 7.88e-244j)
| (4.0251819378730136215 - 8.39733313274368008e-968j)  +/-  (1.32e-244, 1.32e-244j)
| (8.301329429185597997 - 9.5915867162617750846e-971j)  +/-  (9.06e-246, 9.06e-246j)
| (-1.9942694995188460666 + 7.5746236155400170277e-971j)  +/-  (3.65e-248, 3.65e-248j)
| (6.763977426895820449 - 5.3611062264449761821e-967j)  +/-  (4.54e-244, 4.54e-244j)
| (-4.3834208947810544423 - 6.1572781857128687559e-966j)  +/-  (3.02e-244, 3.02e-244j)
| (5.9107025009587894247 - 1.5808203100496463239e-973j)  +/-  (9.13e-244, 9.13e-244j)
| (5.1247973826161375113 + 1.6075809499196874859e-974j)  +/-  (8.23e-244, 8.23e-244j)
| (3.673687611619088718 + 2.0662533798729878476e-976j)  +/-  (5.11e-245, 5.11e-245j)
| (-6.763977426895820449 + 6.5850341493268867034e-974j)  +/-  (4.27e-244, 4.27e-244j)
| (-1.0704850154804961772 - 1.6639079346173144591e-993j)  +/-  (1.17e-250, 1.17e-250j)
| (-3.3280690387312467515 - 1.4770650603533438394e-986j)  +/-  (1.65e-245, 1.65e-245j)
| (5.511088217032914005 + 3.3301296148837399316e-999j)  +/-  (9.3e-244, 9.3e-244j)
| (3.3280690387312467515 - 5.4703695716222948376e-1005j)  +/-  (1.75e-245, 1.75e-245j)
| (2.9876524519620575644 - 8.9800797808274999564e-1005j)  +/-  (4.33e-246, 4.33e-246j)
| (7.2291202737744768985 + 3.0065597711740468645e-1003j)  +/-  (1.87e-244, 1.87e-244j)
| (4.3834208947810544423 - 9.8519222516568879508e-1003j)  +/-  (2.9e-244, 2.9e-244j)
| (-5.511088217032914005 - 4.6356319968941170681e-1008j)  +/-  (9.43e-244, 9.43e-244j)
| (1.3621216938790457764 - 1.0668455955073465071e-1039j)  +/-  (8.77e-250, 8.77e-250j)
| (-5.1247973826161375113 - 3.83937596281426793e-1034j)  +/-  (7.75e-244, 7.75e-244j)
| (-2.9876524519620575644 - 3.3060314126540436016e-1047j)  +/-  (4.38e-246, 4.38e-246j)
| (-0.81628788285896466304 - 3.6207554687301908144e-1056j)  +/-  (1.94e-251, 1.94e-251j)
| (-2.6519613568352334924 - 5.3065364279260204664e-1051j)  +/-  (9.88e-247, 9.88e-247j)
| (1.673551628767471445 + 1.3996012778649915935e-1054j)  +/-  (5.63e-249, 5.63e-249j)
| (2.6519613568352334924 - 4.248269801004644734e-1052j)  +/-  (1.03e-246, 1.03e-246j)
| (-4.7494988641678432088 + 1.8726446057424209252e-1049j)  +/-  (5.34e-244, 5.34e-244j)
| (-3.673687611619088718 - 1.6205017055044423209e-1059j)  +/-  (4.98e-245, 4.98e-245j)
| (-2.3207698935229894148 - 1.1623659909552679196e-1068j)  +/-  (2.24e-247, 2.24e-247j)
| (1.9942694995188460666 - 1.5567159765987847407e-1068j)  +/-  (3.59e-248, 3.59e-248j)
| (2.3207698935229894148 - 1.5058328999786704863e-1067j)  +/-  (2.02e-247, 2.02e-247j)
| (0.81628788285896466304 - 1.4749408054385906505e-1072j)  +/-  (1.87e-251, 1.87e-251j)
| (4.7494988641678432088 + 2.1502789435386677373e-1069j)  +/-  (5.07e-244, 5.07e-244j)
| (-0.57291726882445917398 + 1.2593150049935630475e-1076j)  +/-  (2.05e-252, 2.05e-252j)
| (0.57291726882445917398 - 3.3336956122531938716e-1076j)  +/-  (1.74e-252, 1.74e-252j)
| (0.29613162741530575221 + 1.0501108538909621377e-1077j)  +/-  (8.81e-254, 8.81e-254j)
| (1.0704850154804961772 + 2.0929812150783134664e-1075j)  +/-  (1.27e-250, 1.27e-250j)
| (-0.29613162741530575221 - 1.9159361226726983699e-1077j)  +/-  (1.01e-253, 1.01e-253j)
| (-1.673551628767471445 + 7.5317984203464198046e-1073j)  +/-  (5.59e-249, 5.59e-249j)
| (-1.3621216938790457764 - 1.5294778067289933074e-1075j)  +/-  (8.97e-250, 8.97e-250j)
| (-4.0251819378730136215 - 4.9544400631681436099e-1079j)  +/-  (1.33e-244, 1.33e-244j)
| (-1.0121550462681070285e-1216 + 1.128923800481939047e-1216j)  +/-  (7.43e-1215, 7.43e-1215j)
-------------------------------------------------
The weights are:
| (1.5438054496891727745e-16 - 2.5210162435203672929e-964j)  +/-  (6.68e-66, 2.97e-187j)
| (4.0785201099155257021e-31 - 5.9801509956387773294e-973j)  +/-  (2.7e-73, 1.2e-194j)
| (3.4347039691684478073e-36 + 1.3623050744067301966e-975j)  +/-  (2.67e-75, 1.18e-196j)
| (5.4771038180730054232e-24 - 4.426936832070516465e-969j)  +/-  (3.77e-71, 1.67e-192j)
| (3.1593376394818849423e-27 + 7.1987879670038962403e-971j)  +/-  (3.34e-72, 1.48e-193j)
| (3.4347039691684478073e-36 - 2.8173088546132143714e-976j)  +/-  (1.99e-80, 8.85e-202j)
| (3.1593376394818849423e-27 - 9.6191368388314276618e-972j)  +/-  (1.1e-77, 4.89e-199j)
| (9.9162337245501076523e-19 + 2.4129818117309289385e-967j)  +/-  (1.61e-74, 7.13e-196j)
| (9.9162337245501076523e-19 - 7.0963293755082195689e-966j)  +/-  (3.93e-72, 1.75e-193j)
| (1.8399824703135909623e-08 + 8.7934062517374507734e-962j)  +/-  (1.01e-67, 4.49e-189j)
| (4.0785201099155257021e-31 + 1.0059300505210901083e-973j)  +/-  (1.91e-79, 8.49e-201j)
| (0.0034246339786544481092 + 4.0418933731967262003e-958j)  +/-  (1.55e-57, 6.88e-179j)
| (3.4259790312919653708e-21 - 1.2485669066506118014e-968j)  +/-  (6.96e-76, 3.09e-197j)
| (9.2338051465212786913e-10 - 1.0932058716816723669e-961j)  +/-  (3.56e-70, 1.58e-191j)
| (1.5438054496891727745e-16 - 3.4536378006488134486e-966j)  +/-  (3.37e-74, 1.5e-195j)
| (8.4259687726753412514e-13 - 3.4579339169193343454e-964j)  +/-  (4.54e-73, 2.02e-194j)
| (2.7058810594991048397e-07 - 4.1626917538655795972e-961j)  +/-  (2.58e-69, 1.15e-190j)
| (3.4259790312919653708e-21 + 1.8546409210596707554e-967j)  +/-  (2.97e-77, 1.32e-198j)
| (0.049343945288308104833 - 5.198127051682221652e-957j)  +/-  (3.68e-56, 1.63e-177j)
| (2.9947087118533065309e-06 + 6.2343357322191557363e-960j)  +/-  (1.51e-69, 6.7e-191j)
| (1.4283629793630439678e-14 + 3.8477703363252615108e-965j)  +/-  (6.09e-74, 2.71e-195j)
| (2.9947087118533065309e-06 + 1.742764610105581331e-960j)  +/-  (3.4e-69, 1.51e-190j)
| (2.5339042559967449701e-05 - 6.5304423222022440622e-960j)  +/-  (1.09e-68, 4.82e-190j)
| (5.4771038180730054232e-24 + 4.441880451278787916e-970j)  +/-  (3.58e-79, 1.59e-200j)
| (9.2338051465212786913e-10 - 1.6219285081895381193e-962j)  +/-  (3.48e-72, 1.55e-193j)
| (1.4283629793630439678e-14 + 1.0997711852038675414e-963j)  +/-  (9.35e-78, 4.15e-199j)
| (0.026846682675970332453 + 1.4605916235997290292e-957j)  +/-  (2.65e-65, 1.18e-186j)
| (8.4259687726753412514e-13 - 4.8555516970860827194e-963j)  +/-  (2.27e-77, 1.01e-198j)
| (2.5339042559967449701e-05 - 1.9879985904492697719e-959j)  +/-  (3.41e-73, 1.51e-194j)
| (0.068843752568781771557 + 8.8969237776829207981e-957j)  +/-  (4.78e-66, 2.12e-187j)
| (0.00016598940120223277655 + 5.8241490993582126659e-959j)  +/-  (1.74e-72, 7.71e-194j)
| (0.010867625170329637723 - 5.5096583297158277867e-958j)  +/-  (1.29e-69, 5.75e-191j)
| (0.00016598940120223277655 + 2.2165291803603075632e-959j)  +/-  (3.64e-72, 1.62e-193j)
| (3.3375606404733468671e-11 + 2.3636290956673096669e-962j)  +/-  (1.92e-77, 8.52e-199j)
| (2.7058810594991048397e-07 - 1.7834866395989068139e-960j)  +/-  (1.36e-75, 6.04e-197j)
| (0.00085001665391007754062 - 1.5828076237782618213e-958j)  +/-  (1.04e-72, 4.63e-194j)
| (0.0034246339786544481092 + 2.0025124182294159798e-958j)  +/-  (1.64e-72, 7.26e-194j)
| (0.00085001665391007754062 - 6.9029845795443422396e-959j)  +/-  (3.44e-73, 1.53e-194j)
| (0.068843752568781771557 + 6.7377260802871700523e-957j)  +/-  (3.06e-71, 1.36e-192j)
| (3.3375606404733468671e-11 + 2.5746743511603853981e-963j)  +/-  (5.53e-78, 2.45e-199j)
| (0.10523859041113114637 - 1.049855174917415124e-956j)  +/-  (3.37e-71, 1.49e-192j)
| (0.10523859041113114637 - 8.6431679334755447291e-957j)  +/-  (1.42e-71, 6.26e-193j)
| (0.15009178731802404315 + 8.8774496055826742683e-957j)  +/-  (7.42e-72, 3.28e-193j)
| (0.049343945288308104833 - 3.6039807538942357367e-957j)  +/-  (2.87e-72, 1.28e-193j)
| (0.15009178731802404315 + 9.8139035778738196306e-957j)  +/-  (3.41e-72, 1.53e-193j)
| (0.010867625170329637723 - 9.8619686193603258665e-958j)  +/-  (1.15e-74, 5.13e-196j)
| (0.026846682675970332453 + 2.335371525478274426e-957j)  +/-  (2.97e-74, 1.34e-195j)
| (1.8399824703135909623e-08 + 4.6337478372866280595e-961j)  +/-  (5.42e-79, 2.9e-200j)
| (0.16859670567374514949 - 9.0783273320398614248e-957j)  +/-  (3.25e-73, 1.22e-194j)
