Starting with polynomial:
P : t^7 - 21*t^5 + 105*t^3 - 105*t
Extension levels are: 7 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 618919329686164932725297736088680388947/558630557983338258776060990183395474*t^47 + 11620898310487819478601791008039259222545971/20669330645383515574714256636785632538*t^45 - 3587290160116009652685329803773707724049981105/20669330645383515574714256636785632538*t^43 + 754566006881577805728427523540030427519838507245/20669330645383515574714256636785632538*t^41 - 114816613173708336043341702255574743274191315236385/20669330645383515574714256636785632538*t^39 + 18629194178896811941898566319552832254487716800635/29401608314912539935582157378073446*t^37 - 1628904071978519555372858005083050705082547523759865/29401608314912539935582157378073446*t^35 + 110740300331398404477414651172723766913523691200217475/29401608314912539935582157378073446*t^33 - 2951833813493762357485027588777914139085574543278666325/14700804157456269967791078689036723*t^31 + 123926379405155783276541004588616332380609220935454716225/14700804157456269967791078689036723*t^29 - 4100404987936772786071693094339729132828850255287673753675/14700804157456269967791078689036723*t^27 + 106676438574128400602765108870839368305867652615239935225575/14700804157456269967791078689036723*t^25 - 2170590164745459752022245188306562066634400861654936590729375/14700804157456269967791078689036723*t^23 + 34252830970270431074637366336815370217731903927319562589076875/14700804157456269967791078689036723*t^21 - 414261137137047896606953011840803981433997619897629608399155625/14700804157456269967791078689036723*t^19 + 3779289276616555652437547525034795855415286866778747360039763750/14700804157456269967791078689036723*t^17 - 50941454074775242556258277913199240311493428989106462453286413125/29401608314912539935582157378073446*t^15 + 246793086183145698452098233639677835733310496062910048243920990625/29401608314912539935582157378073446*t^13 - 828978380270059723260366054488687380665093809254175999868055696875/29401608314912539935582157378073446*t^11 + 1838651888690558583465213589380835405465503511511835490168408059375/29401608314912539935582157378073446*t^9 - 2513755927208590928536564415160273437259754310352422394836674021875/29401608314912539935582157378073446*t^7 + 1908191938479753516189023611445309823989673775857708423387268509375/29401608314912539935582157378073446*t^5 - 669657234834790036467222904613696820504949954794743203675334953125/29401608314912539935582157378073446*t^3 + 70704837806066127066053658198577652758463853983240899350262546875/29401608314912539935582157378073446*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:
| (8.9474715723683809873 - 4.7426043094942559487e-507j)  +/-  (1.12e-243, 1.12e-243j)
| (-9.5657086127015393283 + 2.4920281072177557245e-510j)  +/-  (5.97e-244, 5.97e-244j)
| (10.223519935198167141 + 1.1870064271917905731e-519j)  +/-  (2.48e-244, 2.48e-244j)
| (-7.7938556999625061135 + 1.6959504212282439364e-528j)  +/-  (1.43e-243, 1.43e-243j)
| (2.8203229732465566582 + 2.1789687578878200427e-546j)  +/-  (5.05e-248, 5.05e-248j)
| (11.739852664481176211 - 1.2415699587083556219e-543j)  +/-  (1.33e-245, 1.33e-245j)
| (6.1990932789889748456 - 1.34433608280229086e-540j)  +/-  (4.2e-244, 4.2e-244j)
| (-3.7504397177257422563 + 4.3354915315939517064e-542j)  +/-  (1.43e-246, 1.43e-246j)
| (-1.9263309730863597845 + 2.4655454952089027179e-557j)  +/-  (1.09e-249, 1.09e-249j)
| (-6.7168057081817742207 - 4.4346366059287897837e-553j)  +/-  (7.24e-244, 7.24e-244j)
| (10.937412946895443258 - 2.5424337428118360219e-565j)  +/-  (7.21e-245, 7.21e-245j)
| (-12.717765761528049175 + 1.8130867719470607541e-562j)  +/-  (8.75e-247, 8.75e-247j)
| (5.1953788442737387018 + 8.3717342326669996029e-566j)  +/-  (7.38e-245, 7.38e-245j)
| (-10.937412946895443258 - 3.977694174232403805e-563j)  +/-  (7.01e-245, 7.01e-245j)
| (-11.739852664481176211 + 5.1449727902337577029e-572j)  +/-  (1.35e-245, 1.35e-245j)
| (9.5657086127015393283 + 2.0061026023772382186e-582j)  +/-  (6.1e-244, 6.1e-244j)
| (3.2820642585673753459 + 4.3355453873750471086e-594j)  +/-  (3.15e-247, 3.15e-247j)
| (-8.3589956400084918456 + 9.5018331547301970527e-609j)  +/-  (1.4e-243, 1.4e-243j)
| (-2.8203229732465566582 + 3.0490783374137047978e-632j)  +/-  (4.78e-248, 4.78e-248j)
| (-8.9474715723683809873 - 4.4848898417717769132e-642j)  +/-  (1.08e-243, 1.08e-243j)
| (-6.1990932789889748456 - 1.1711812059143726447e-663j)  +/-  (4.06e-244, 4.06e-244j)
| (1.1544053947399681272 - 9.2391133689499595379e-683j)  +/-  (2.62e-251, 2.62e-251j)
| (12.717765761528049175 + 4.5850833032441942394e-679j)  +/-  (8.99e-247, 8.99e-247j)
| (-3.2820642585673753459 + 4.9434422049060333323e-679j)  +/-  (2.88e-247, 2.88e-247j)
| (4.2251786172219736544 + 1.55272404469576682e-677j)  +/-  (6.37e-246, 6.37e-246j)
| (3.7504397177257422563 - 8.820829195393110862e-679j)  +/-  (1.51e-246, 1.51e-246j)
| (1.5138944272096902994 - 2.163391570422731932e-682j)  +/-  (1.72e-250, 1.72e-250j)
| (-10.223519935198167141 - 5.6031920355670584888e-674j)  +/-  (2.83e-244, 2.83e-244j)
| (-7.2475579629098812381 - 4.8440854216984380879e-686j)  +/-  (1.06e-243, 1.06e-243j)
| (-0.81022737168930255753 + 5.6002185999139320237e-703j)  +/-  (2.87e-252, 2.87e-252j)
| (7.7938556999625061135 + 3.0546346164220430277e-694j)  +/-  (1.31e-243, 1.31e-243j)
| (8.3589956400084918456 - 1.0483685668452827483e-696j)  +/-  (1.29e-243, 1.29e-243j)
| (-5.1953788442737387018 + 9.8219598495800452899e-703j)  +/-  (7.43e-245, 7.43e-245j)
| (7.2475579629098812381 - 1.0701890296959857037e-716j)  +/-  (1.14e-243, 1.14e-243j)
| (-1.5138944272096902994 - 5.6560336937356521468e-723j)  +/-  (1.58e-250, 1.58e-250j)
| (-4.2251786172219736544 + 6.5345572159732907221e-716j)  +/-  (6.08e-246, 6.08e-246j)
| (6.7168057081817742207 + 1.2294891413363773741e-724j)  +/-  (7.44e-244, 7.44e-244j)
| (0.81022737168930255753 + 3.0404722620813976808e-738j)  +/-  (2.63e-252, 2.63e-252j)
| (4.7066003710877185095 + 8.3700891833449679497e-730j)  +/-  (2.15e-245, 2.15e-245j)
| (-4.7066003710877185095 + 3.3932450148266445792e-732j)  +/-  (2.5e-245, 2.5e-245j)
| (-0.41879336373834164514 + 2.6385545033788620077e-753j)  +/-  (1.47e-253, 1.47e-253j)
| (-1.1544053947399681272 - 1.5897222506825662052e-752j)  +/-  (2.66e-251, 2.66e-251j)
| (2.3667594107345412886 + 2.4966402589791433891e-749j)  +/-  (7.84e-249, 7.84e-249j)
| (1.9263309730863597845 - 3.0538742506832393927e-750j)  +/-  (1.11e-249, 1.11e-249j)
| (-5.6924668875592327488 + 2.8163021721218015246e-743j)  +/-  (1.88e-244, 1.88e-244j)
| (-2.3667594107345412886 - 3.2786918721193322368e-759j)  +/-  (7.68e-249, 7.68e-249j)
| (-7.0752353957765322e-775 + 1.7229408305567684294e-774j)  +/-  (9.13e-773, 9.13e-773j)
| (5.6924668875592327488 - 1.0232508894494203189e-754j)  +/-  (1.82e-244, 1.82e-244j)
| (0.41879336373834164514 - 4.2085725197744627017e-775j)  +/-  (1.5e-253, 1.5e-253j)
-------------------------------------------------
The weights are:
| (9.9162337245501076523e-19 + 2.1802030592207101859e-524j)  +/-  (4.13e-78, 1.64e-198j)
| (3.4259790312919653708e-21 - 1.3571943444439914496e-527j)  +/-  (1.7e-80, 6.74e-201j)
| (5.4771038180730054232e-24 - 7.2846110074093354253e-528j)  +/-  (3.94e-81, 1.56e-201j)
| (1.4283629793630439678e-14 + 4.1795604101006471236e-524j)  +/-  (7.92e-77, 3.14e-197j)
| (0.0034246339786544481092 + 4.1145850172977974514e-517j)  +/-  (1.63e-57, 6.47e-178j)
| (4.0785201099155257021e-31 - 8.1539374212039512631e-532j)  +/-  (1.44e-84, 5.7e-205j)
| (9.2338051465212786913e-10 - 9.6751605293128066501e-521j)  +/-  (1.23e-72, 4.87e-193j)
| (0.00016598940120223277655 + 2.3803132411347213317e-518j)  +/-  (8.54e-65, 3.39e-185j)
| (0.026846682675970332453 + 1.5557710621626981391e-516j)  +/-  (3.06e-53, 1.22e-173j)
| (3.3375606404733468671e-11 + 2.7900541551108057893e-522j)  +/-  (3.55e-75, 1.41e-195j)
| (3.1593376394818849423e-27 + 1.0504488632819768152e-529j)  +/-  (3.53e-83, 1.4e-203j)
| (3.4347039691684478073e-36 - 3.0872882076161576298e-535j)  +/-  (1.01e-88, 4e-209j)
| (2.7058810594991048397e-07 - 1.6934703991180228616e-519j)  +/-  (2.57e-72, 1.02e-192j)
| (3.1593376394818849423e-27 - 1.0517291447534107176e-530j)  +/-  (1.25e-85, 4.95e-206j)
| (4.0785201099155257021e-31 + 1.1009707295448536047e-532j)  +/-  (4.1e-87, 1.63e-207j)
| (3.4259790312919653708e-21 + 4.0767159652687468943e-526j)  +/-  (6.61e-83, 2.62e-203j)
| (0.00085001665391007754062 - 1.5973238647358329397e-517j)  +/-  (6.19e-68, 2.46e-188j)
| (1.5438054496891727745e-16 - 3.7552823494136741877e-525j)  +/-  (3.75e-81, 1.49e-201j)
| (0.0034246339786544481092 + 2.1422541247765092347e-517j)  +/-  (8.92e-68, 3.54e-188j)
| (9.9162337245501076523e-19 + 2.62547137859738947e-526j)  +/-  (2.57e-82, 1.02e-202j)
| (9.2338051465212786913e-10 - 1.7553224714642409378e-521j)  +/-  (5.26e-78, 2.09e-198j)
| (0.068843752568781771557 + 9.2625651565874530519e-516j)  +/-  (9.65e-60, 3.83e-180j)
| (3.4347039691684478073e-36 + 1.7736452888011796319e-534j)  +/-  (1.05e-91, 4.18e-212j)
| (0.00085001665391007754062 - 7.3993232317251414541e-518j)  +/-  (7.53e-71, 2.99e-191j)
| (2.5339042559967449701e-05 - 1.9597945134783208979e-518j)  +/-  (4.52e-75, 1.79e-195j)
| (0.00016598940120223277655 + 5.8161741946052906284e-518j)  +/-  (1.63e-73, 6.48e-194j)
| (0.049343945288308104833 - 5.3903904028252101589e-516j)  +/-  (1.23e-65, 4.87e-186j)
| (5.4771038180730054232e-24 + 4.8535165131769519009e-529j)  +/-  (7.44e-86, 2.95e-206j)
| (8.4259687726753412514e-13 - 3.7518057337051221523e-523j)  +/-  (1.65e-80, 6.56e-201j)
| (0.10523859041113114637 - 9.1462455318500673832e-516j)  +/-  (2.18e-65, 8.64e-186j)
| (1.4283629793630439678e-14 + 6.0673258042038850677e-523j)  +/-  (2.31e-84, 9.16e-205j)
| (1.5438054496891727745e-16 - 1.1049251839018856519e-523j)  +/-  (3.93e-85, 1.56e-205j)
| (2.7058810594991048397e-07 - 4.4923165754052265668e-520j)  +/-  (1.2e-80, 4.74e-201j)
| (8.4259687726753412514e-13 - 3.5751686902450275726e-522j)  +/-  (5.98e-84, 2.37e-204j)
| (0.049343945288308104833 - 3.8301910114748951401e-516j)  +/-  (2.2e-73, 8.61e-194j)
| (2.5339042559967449701e-05 - 7.0252058420083402138e-519j)  +/-  (2.25e-79, 8.8e-200j)
| (3.3375606404733468671e-11 + 1.9595996580517303426e-521j)  +/-  (2.2e-83, 8.75e-204j)
| (0.10523859041113114637 - 1.0967755978998612931e-515j)  +/-  (1.2e-73, 4.69e-194j)
| (2.9947087118533065309e-06 + 6.0465783256392384367e-519j)  +/-  (1.82e-80, 7.11e-201j)
| (2.9947087118533065309e-06 + 1.8778703684125569392e-519j)  +/-  (1.12e-80, 4.32e-201j)
| (0.15009178731802404315 + 9.368995482918905593e-516j)  +/-  (9.23e-75, 3.58e-195j)
| (0.068843752568781771557 + 7.1454665654283327615e-516j)  +/-  (7.12e-75, 2.77e-195j)
| (0.010867625170329637723 - 1.0112830146689784615e-516j)  +/-  (8.06e-78, 3.13e-198j)
| (0.026846682675970332453 + 2.40952487574527504e-516j)  +/-  (3.24e-77, 1.25e-197j)
| (1.8399824703135909623e-08 + 9.5035307850495619263e-521j)  +/-  (1.91e-82, 7.22e-203j)
| (0.010867625170329637723 - 5.8817364276419865519e-517j)  +/-  (2e-78, 7.51e-199j)
| (0.16859670567374514949 - 9.5509600334661210174e-516j)  +/-  (5.23e-77, 1.75e-197j)
| (1.8399824703135909623e-08 + 4.2748914382158095127e-520j)  +/-  (8.87e-83, 3.85e-203j)
| (0.15009178731802404315 + 1.0289167495715329333e-515j)  +/-  (3.39e-77, 1.02e-197j)
