Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 42
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^53 - 63069332325501366950894327604172116588931432837956046688641135588015229195804/6086473267365702129997460815765956775861662767203642168363652970518867201*t^51 + 691584205402015640632614651548685408105412888093277908341786213945581084757717570/225199510892530978809906050183340400706881522386534760229455159909198086437*t^49 - 124748232133183720738742733067639866409745994106948604145051049179175820612771227314/225199510892530978809906050183340400706881522386534760229455159909198086437*t^47 + 15363094522379800363025724339352992881157304878289759464920368630977069822354959033235/225199510892530978809906050183340400706881522386534760229455159909198086437*t^45 - 1373269656610777920714164867249667074161974982434245762074108405334733815208706644412530/225199510892530978809906050183340400706881522386534760229455159909198086437*t^43 + 184919251097657171769046176243699730538408242291271049273426182563628021663515509518565735/450399021785061957619812100366680801413763044773069520458910319818396172874*t^41 - 38419260470448634277199514212340951805874203529857887322265027440125980776863115530599421875/1801596087140247830479248401466723205655052179092278081835641279273584691496*t^39 + 2224881147715211985500395836856093932859048024971369198497007083692670016404120044481073465/2562725586259243002104194027690929168783858007243638807732064408639523032*t^37 - 573929144964966403140732628991280119305534435707039647716409588853992675636997577320947449125/20501804690073944016833552221527433350270864057949110461856515269116184256*t^35 + 29507184643949478593601088125910514219904822933918704413658527166418048622568738486289559177275/41003609380147888033667104443054866700541728115898220923713030538232368512*t^33 - 303394147650032202383716714971034363869099139552137269931612100986326806083442991874620334534075/20501804690073944016833552221527433350270864057949110461856515269116184256*t^31 + 9990509566571535069772207927777847457106908362651259698827978831841887314516060954739989590137125/41003609380147888033667104443054866700541728115898220923713030538232368512*t^29 - 131504876485343772463587584664990534521510351014831067060368819690570721103151308684987616521165075/41003609380147888033667104443054866700541728115898220923713030538232368512*t^27 + 689376779883478396247057634161724350609957023131870386623673589634088298594003596020020588407430375/20501804690073944016833552221527433350270864057949110461856515269116184256*t^25 - 91555105694073396977527671084286950460836531781180710754535387061995682918401086923423149802123793125/328028875041183104269336835544438933604333824927185767389704244305858948096*t^23 + 2385863160057886703553802456629312463917108649839639423064829682212715313829651923772578683209402169375/1312115500164732417077347342177755734417335299708743069558816977223435792384*t^21 - 48227230054961722719503346358058833304230386585118466834553445495294945566136990076466750361234951284375/5248462000658929668309389368711022937669341198834972278235267908893743169536*t^19 + 372209852058176776776775450786136361523226364255206909916742824722562035559939855340148901447464700493125/10496924001317859336618778737422045875338682397669944556470535817787486339072*t^17 - 1074263969982152291758628224950542755917583329342234627127495841087224264317580559259049815560619510721875/10496924001317859336618778737422045875338682397669944556470535817787486339072*t^15 + 4511186473705371948525056930663075034737519006485668680390828153771449799361194357539995267765551303465625/20993848002635718673237557474844091750677364795339889112941071635574972678144*t^13 - 1659384579646606182934110416853563414445293135390916039707240427066421064571066490872304064128546967409375/5248462000658929668309389368711022937669341198834972278235267908893743169536*t^11 + 12998016847816959239743437287491040990981069643979086188824883685221697864338607366696076240166748745359375/41987696005271437346475114949688183501354729590679778225882143271149945356288*t^9 - 31469298621941054344308140001781725247221874412162703326519750530756819627235062541118762304502152432565625/167950784021085749385900459798752734005418918362719112903528573084599781425152*t^7 + 5267072055183813116704136126965932384718740239849806745304548657838141772401790838482291093302106746140625/83975392010542874692950229899376367002709459181359556451764286542299890712576*t^5 - 12918673252209893224754169300657155335519160085431261363622093361927833713060258528914584046427006499234375/1343606272168685995087203678390021872043351346901752903228228584676798251401216*t^3 + 1188482173252745613881830180639479086036271425257587123484695822918877507087761617344111972337554040390625/2687212544337371990174407356780043744086702693803505806456457169353596502802432*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:
| (7.0945134715078356788 + 8.1407080418348197161e-914j)  +/-  (7.37e-244, 7.37e-244j)
| (10.424560756118196501 + 5.0637167028382522497e-927j)  +/-  (5.1e-248, 5.1e-248j)
| (7.5800095873208540355 - 3.555473133401887364e-922j)  +/-  (2.48e-244, 2.48e-244j)
| (-5.4229657974396051609 - 4.7434820361495040476e-926j)  +/-  (3.09e-243, 3.09e-243j)
| (5.813617755079217874 - 3.3980520350641612364e-931j)  +/-  (3.06e-243, 3.06e-243j)
| (-5.0445809565113964346 - 3.1453095638197961204e-936j)  +/-  (2.37e-243, 2.37e-243j)
| (-7.5800095873208540355 - 5.1871915300863619692e-940j)  +/-  (2.69e-244, 2.69e-244j)
| (-8.7652524760827822031 + 3.908859681772507113e-941j)  +/-  (5.83e-246, 5.83e-246j)
| (-5.813617755079217874 + 2.8506163999966781706e-938j)  +/-  (3.24e-243, 3.24e-243j)
| (-10.424560756118196501 + 2.5144023881387988338e-943j)  +/-  (4.6e-248, 4.6e-248j)
| (-8.1201998415065250616 - 7.1130583784138701449e-940j)  +/-  (5.14e-245, 5.14e-245j)
| (3.2759416955673464603 + 4.401340010347850211e-937j)  +/-  (6.86e-245, 6.86e-245j)
| (-6.6443315873794432436 - 2.2972410025318275076e-939j)  +/-  (1.6e-243, 1.6e-243j)
| (-1.9727710239943847613 - 6.3190167231288186247e-944j)  +/-  (1.76e-247, 1.76e-247j)
| (-7.0945134715078356788 - 8.3527769488407122977e-940j)  +/-  (7.93e-244, 7.93e-244j)
| (6.6443315873794432436 + 2.7692512177110887213e-938j)  +/-  (1.57e-243, 1.57e-243j)
| (6.2193942326250746318 - 3.9759773909971211982e-950j)  +/-  (2.42e-243, 2.42e-243j)
| (8.1201998415065250616 + 3.7776333010711818272e-960j)  +/-  (5.37e-245, 5.37e-245j)
| (-3.6175209290195820986 + 2.2116919558767531615e-961j)  +/-  (1.8e-244, 1.8e-244j)
| (1.9727710239943847613 + 3.1669544111662027309e-965j)  +/-  (1.69e-247, 1.69e-247j)
| (-4.6763396070122971181 - 1.873028668592973833e-960j)  +/-  (1.67e-243, 1.67e-243j)
| (1.6506801238857845559 - 3.253445498594652781e-966j)  +/-  (1.4e-248, 1.4e-248j)
| (5.4229657974396051609 - 3.796151762691483885e-961j)  +/-  (2.91e-243, 2.91e-243j)
| (-3.9640358271607061973 + 1.7561279411054138765e-972j)  +/-  (4.19e-244, 4.19e-244j)
| (-6.2193942326250746318 - 7.8434625729775019456e-971j)  +/-  (2.47e-243, 2.47e-243j)
| (3.6175209290195820986 + 4.3401242313089185057e-977j)  +/-  (1.85e-244, 1.85e-244j)
| (1.0362802085752798674 - 6.4627796675161849804e-991j)  +/-  (1.24e-250, 1.24e-250j)
| (8.7652524760827822031 - 1.8654803672220066351e-984j)  +/-  (5.98e-246, 5.98e-246j)
| (-4.3165988392019924112 + 1.9572445939982311756e-984j)  +/-  (9.3e-244, 9.3e-244j)
| (-0.52464762327529031788 + 1.8181864177775179648e-998j)  +/-  (1.37e-252, 1.37e-252j)
| (4.3165988392019924112 - 1.0831881143521490325e-988j)  +/-  (9.18e-244, 9.18e-244j)
| (2.3862793919737297977 - 1.3049269845194019596e-1001j)  +/-  (2.43e-245, 2.43e-245j)
| (2.5925512579525993678 + 2.3420676441923476812e-1002j)  +/-  (1.66e-245, 1.66e-245j)
| (4.6763396070122971181 + 4.089133253954037293e-1007j)  +/-  (1.61e-243, 1.61e-243j)
| (-2.3321485292078624061 + 4.1042756655162091095e-1021j)  +/-  (1.62e-245, 1.62e-245j)
| (-1.0362802085752798674 + 9.9655366917557894356e-1026j)  +/-  (1.3e-250, 1.3e-250j)
| (2.3321485292078624061 - 1.9707368453773840211e-1019j)  +/-  (1.46e-245, 1.46e-245j)
| (0.76230747769843339458 + 4.0695304498721299661e-1028j)  +/-  (1.34e-251, 1.34e-251j)
| (3.9640358271607061973 + 3.4264232477999828941e-1022j)  +/-  (4.18e-244, 4.18e-244j)
| (-2.3862793919737297977 - 2.5637992531760797402e-1032j)  +/-  (2.42e-245, 2.42e-245j)
| (-0.76230747769843339458 - 6.1007784319410664084e-1040j)  +/-  (1.26e-251, 1.26e-251j)
| (5.0445809565113964346 - 1.5435535292629095069e-1033j)  +/-  (2.36e-243, 2.36e-243j)
| (1.3372181387845985925 - 8.3547471222411266073e-1046j)  +/-  (1.36e-249, 1.36e-249j)
| (-0.27640828571199568205 + 8.8727751520341665568e-1049j)  +/-  (1.16e-253, 1.16e-253j)
| (-1.6506801238857845559 + 3.6828962747257020099e-1044j)  +/-  (1.31e-248, 1.31e-248j)
| (-3.2759416955673464603 + 2.3856382886312157397e-1040j)  +/-  (6.79e-245, 6.79e-245j)
| (-2.9375877618940839119 + 3.6523636258920536297e-1041j)  +/-  (2.59e-245, 2.59e-245j)
| (2.9375877618940839119 - 5.6666361682803021811e-1043j)  +/-  (2.7e-245, 2.7e-245j)
| (0.52464762327529031788 + 3.5339898791144129371e-1050j)  +/-  (1.37e-252, 1.37e-252j)
| (0.27640828571199568205 - 2.2611012118873383956e-1050j)  +/-  (1.16e-253, 1.16e-253j)
| (-2.5925512579525993678 - 5.3361279626867501748e-1047j)  +/-  (1.79e-245, 1.79e-245j)
| (-1.3372181387845985925 - 3.7285253986128981782e-1050j)  +/-  (1.3e-249, 1.3e-249j)
| (5.1555811911226838914e-1183 - 6.7280033013156860383e-1183j)  +/-  (4.49e-1181, 4.49e-1181j)
-------------------------------------------------
The weights are:
| (3.6352485522501728868e-23 - 2.2431910165906919841e-935j)  +/-  (1.16e-69, 1.78e-190j)
| (9.8013693316204496703e-46 + 4.4882009739573815179e-948j)  +/-  (4.47e-79, 6.84e-200j)
| (3.1952231088705036431e-26 - 1.4513888338381758829e-937j)  +/-  (2.93e-71, 4.48e-192j)
| (3.6636223238077396973e-14 - 2.0980697955314526894e-932j)  +/-  (1.57e-66, 2.4e-187j)
| (4.7052799530441290694e-16 + 1.7504482525244297913e-932j)  +/-  (7.72e-67, 1.18e-187j)
| (1.8676806947368095799e-12 + 2.0978411811062070492e-931j)  +/-  (4.1e-65, 6.28e-186j)
| (3.1952231088705036431e-26 + 4.8018160967972531389e-939j)  +/-  (8.75e-75, 1.34e-195j)
| (1.791900431102503319e-34 + 2.2597320295052022484e-943j)  +/-  (1.54e-78, 2.36e-199j)
| (4.7052799530441290694e-16 + 1.7369990568629174687e-933j)  +/-  (2.07e-69, 3.17e-190j)
| (9.8013693316204496703e-46 - 8.5312277040498736846e-949j)  +/-  (1.81e-83, 2.77e-204j)
| (7.5476753569619103477e-30 - 5.8017436680895485406e-941j)  +/-  (8.27e-77, 1.27e-197j)
| (4.1838608025781330308e-06 - 8.8575958752547856135e-927j)  +/-  (4.01e-64, 6.13e-185j)
| (1.653320356183165976e-20 + 5.7989795538582250974e-936j)  +/-  (2.7e-73, 4.13e-194j)
| (0.0037691867256882447994 + 7.9046525600454070585e-925j)  +/-  (2.77e-56, 4.25e-177j)
| (3.6352485522501728868e-23 - 2.0856606717687651418e-937j)  +/-  (2.31e-74, 3.53e-195j)
| (1.653320356183165976e-20 + 1.769757743320145118e-934j)  +/-  (3.85e-77, 5.9e-198j)
| (3.7163729897564537688e-18 - 1.7484955721046116073e-933j)  +/-  (3.45e-76, 5.27e-197j)
| (7.5476753569619103477e-30 + 8.6061268309101932414e-940j)  +/-  (5.67e-82, 8.67e-203j)
| (4.0217564053342919982e-07 + 5.46636890631656737e-928j)  +/-  (1.27e-68, 1.94e-189j)
| (0.0037691867256882447994 + 1.3994013446818740707e-924j)  +/-  (3.99e-62, 6.11e-183j)
| (6.5314299606799617006e-11 - 1.7867671666262272025e-930j)  +/-  (2.48e-71, 3.79e-192j)
| (0.01175443796477297362 - 2.0926340370582220818e-924j)  +/-  (3.89e-60, 5.95e-181j)
| (3.6636223238077396973e-14 - 1.5711506253984199036e-931j)  +/-  (1.01e-75, 1.55e-196j)
| (2.9537744402830089234e-08 - 8.8689607828467305676e-929j)  +/-  (3.51e-70, 5.37e-191j)
| (3.7163729897564537688e-18 - 1.1492808710326471109e-934j)  +/-  (3.8e-75, 5.81e-196j)
| (4.0217564053342919982e-07 + 1.684097072519333501e-927j)  +/-  (8.26e-72, 1.26e-192j)
| (0.056093934061562650282 - 7.2471784917104000455e-924j)  +/-  (3.33e-59, 5.1e-180j)
| (1.791900431102503319e-34 - 2.1450880175795151781e-942j)  +/-  (9.95e-86, 1.52e-206j)
| (1.6240372016448792901e-09 + 1.3296585425259975612e-929j)  +/-  (1.34e-71, 2.05e-192j)
| (0.099706808890770860186 - 1.6192805243935753837e-923j)  +/-  (2.45e-60, 3.75e-181j)
| (1.6240372016448792901e-09 + 5.4619684060966426029e-929j)  +/-  (1.74e-74, 2.66e-195j)
| (-0.00072622367899343512757 + 4.275618850186569421e-924j)  +/-  (1.85e-68, 2.83e-189j)
| (0.00025286725993809680904 - 5.2470712332241624592e-925j)  +/-  (1.72e-69, 2.63e-190j)
| (6.5314299606799617006e-11 - 8.6973777822553592661e-930j)  +/-  (5.55e-76, 8.5e-197j)
| (0.0015722299288428408655 - 2.2269772010006816415e-924j)  +/-  (1.61e-71, 2.46e-192j)
| (0.056093934061562650282 - 5.3998539127330563461e-924j)  +/-  (5.99e-67, 9.16e-188j)
| (0.0015722299288428408655 - 4.4080958248616713878e-924j)  +/-  (1.02e-68, 1.56e-189j)
| (0.079969867443172082165 + 1.3481176283355086163e-923j)  +/-  (1.19e-66, 1.82e-187j)
| (2.9537744402830089234e-08 - 3.1329990654243936344e-928j)  +/-  (2.63e-74, 4.02e-195j)
| (-0.00072622367899343512757 + 2.1233049816756653511e-924j)  +/-  (5.39e-72, 8.23e-193j)
| (0.079969867443172082165 + 1.0865156046075514573e-923j)  +/-  (2.26e-68, 3.46e-189j)
| (1.8676806947368095799e-12 + 1.2422792766311829231e-930j)  +/-  (3.55e-77, 5.43e-198j)
| (0.029117214107713100573 + 3.741740106963989611e-924j)  +/-  (4.96e-69, 7.6e-190j)
| (0.13903597780269829238 + 1.783633314823979146e-923j)  +/-  (1.23e-68, 1.88e-189j)
| (0.01175443796477297362 - 1.302652816983255566e-924j)  +/-  (2.32e-71, 3.56e-192j)
| (4.1838608025781330308e-06 - 3.2615122528566240701e-927j)  +/-  (2.01e-75, 3.07e-196j)
| (3.4086372599384002436e-05 + 2.0874076331174765367e-926j)  +/-  (5.8e-75, 8.94e-196j)
| (3.4086372599384002436e-05 + 5.037637346211992448e-926j)  +/-  (3.5e-74, 5.67e-195j)
| (0.099706808890770860186 - 1.8779012267798977332e-923j)  +/-  (2.35e-71, 3.87e-192j)
| (0.13903597780269829238 + 1.9282515051240216275e-923j)  +/-  (1.13e-71, 1.84e-192j)
| (0.00025286725993809680904 - 2.4385216297086685891e-925j)  +/-  (4.05e-74, 6.04e-195j)
| (0.029117214107713100573 + 2.5549085315580433248e-924j)  +/-  (4.45e-73, 6.08e-194j)
| (0.15882999171158220523 - 1.7993869327350177233e-923j)  +/-  (1.34e-72, 3.47e-193j)
