Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 34
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^40 - 141834330436042694831355286864/6416079694967971826817497*t^38 + 637037927188843320757767442224184/186066311154071182977707413*t^36 - 410378924499380771828059414467315500/1302464178078498280843951891*t^34 + 25074236396765863920464920670828632230/1302464178078498280843951891*t^32 - 1076677685353553674203343393496721217020/1302464178078498280843951891*t^30 + 1156956351907157237814478958192744706330/44912557864775802787722479*t^28 - 3806723924547664742843253641977369598685/6416079694967971826817497*t^26 + 65402061774094819452536091891521255283750/6416079694967971826817497*t^24 - 6722244714051452325752811781421330039308875/51328637559743774614539976*t^22 + 128764779972484355766026537381917154114626125/102657275119487549229079952*t^20 - 1823026149948664126133116323760498569291138375/205314550238975098458159904*t^18 + 18806952412350374415905021280841092572758618875/410629100477950196916319808*t^16 - 69224469338957311991141869115216843432055365625/410629100477950196916319808*t^14 + 353089288511251506681727414140455970308652219375/821258200955900393832639616*t^12 - 1197370402590347747234274212095992530791143200625/1642516401911800787665279232*t^10 + 5088858567810852833024963246919647865220220701875/6570065607647203150661116928*t^8 - 12397531148563865978830187740251446795638229608125/26280262430588812602644467712*t^6 + 7474538858095093525410609147763495751884995796875/52560524861177625205288935424*t^4 - 1673480434066823468291361415659708278774544365625/105121049722355250410577870848*t^2 + 58513797397030080965390135162395387659199715625/210242099444710500821155741696
-------------------------------------------------
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:
| (4.2417964851912590438 - 4.063639262952819255e-906j)  +/-  (4.81e-246, 4.81e-246j)
| (-7.7944253586693429042 - 8.5540965291902509248e-924j)  +/-  (3.06e-248, 3.06e-248j)
| (6.0105563714866933969 - 1.3065104875806218273e-950j)  +/-  (3.02e-246, 3.02e-246j)
| (5.533380626676997833 - 2.9474649067422600866e-967j)  +/-  (4.93e-246, 4.93e-246j)
| (6.5261607177494391437 - 4.5928520994508119414e-985j)  +/-  (1.23e-246, 1.23e-246j)
| (7.1018306526592276733 + 6.5528586635897925259e-990j)  +/-  (2.69e-247, 2.69e-247j)
| (5.0835406080517587749 + 1.0592428062101152549e-991j)  +/-  (6.38e-246, 6.38e-246j)
| (-6.0105563714866933969 + 2.6796729176219464031e-997j)  +/-  (3.07e-246, 3.07e-246j)
| (-7.1018306526592276733 - 4.2662064905606881712e-997j)  +/-  (3.12e-247, 3.12e-247j)
| (2.0010559231670022765 + 3.3590976244575597945e-999j)  +/-  (7.4e-249, 7.4e-249j)
| (-5.0835406080517587749 + 6.3288161814593519698e-996j)  +/-  (7.02e-246, 7.02e-246j)
| (-6.5261607177494391437 - 4.2670978076530118761e-997j)  +/-  (1.39e-246, 1.39e-246j)
| (1.3358490740136969497 + 7.3265305783541382551e-1001j)  +/-  (2.05e-250, 2.05e-250j)
| (3.0776918571932592579 - 1.7292482613399186061e-995j)  +/-  (4.44e-247, 4.44e-247j)
| (7.7944253586693429042 - 4.0554239961659232205e-1001j)  +/-  (2.84e-248, 2.84e-248j)
| (-3.0776918571932592579 + 1.1288411354861646055e-998j)  +/-  (4.41e-247, 4.41e-247j)
| (-5.533380626676997833 + 1.5726814338301905936e-997j)  +/-  (5.54e-246, 5.54e-246j)
| (-3.842697061156837085 - 7.4657370591711497351e-998j)  +/-  (2.66e-246, 2.66e-246j)
| (-1.024277673614671176 + 3.4137816047985235948e-1003j)  +/-  (2.8e-251, 2.8e-251j)
| (3.842697061156837085 - 4.2046820066789700365e-997j)  +/-  (2.9e-246, 2.9e-246j)
| (-3.4551175387746972283 - 2.3056352354014064577e-1002j)  +/-  (1.24e-246, 1.24e-246j)
| (3.4551175387746972283 - 7.3369738292081305336e-1003j)  +/-  (1.09e-246, 1.09e-246j)
| (1.6621300311087156205 - 2.8696231040980852479e-1010j)  +/-  (1.37e-249, 1.37e-249j)
| (-1.6621300311087156205 - 2.2968375906146347182e-1011j)  +/-  (1.34e-249, 1.34e-249j)
| (-1.3358490740136969497 - 1.0096427359198553253e-1011j)  +/-  (2.08e-250, 2.08e-250j)
| (-2.7096083027365413158 + 3.6623830828523180893e-1009j)  +/-  (1.33e-247, 1.33e-247j)
| (4.6544388468208750531 - 4.7892141659377325816e-1007j)  +/-  (6.99e-246, 6.99e-246j)
| (2.7096083027365413158 - 8.4479034490964627051e-1016j)  +/-  (1.46e-247, 1.46e-247j)
| (-4.6544388468208750531 - 5.1847077645105511932e-1014j)  +/-  (6.14e-246, 6.14e-246j)
| (-0.72652871521944923837 + 5.0995122543956006161e-1025j)  +/-  (2.58e-252, 2.58e-252j)
| (-2.0010559231670022765 + 9.6451096998826106183e-1022j)  +/-  (7.69e-249, 7.69e-249j)
| (0.72652871521944923837 - 2.2986162627416713015e-1025j)  +/-  (2.96e-252, 2.96e-252j)
| (1.024277673614671176 + 5.8518515865255514203e-1025j)  +/-  (2.98e-251, 2.98e-251j)
| (2.3506049736744922228 + 2.1939877302764131335e-1020j)  +/-  (3.39e-248, 3.39e-248j)
| (-2.3506049736744922228 - 2.0563573605489476261e-1027j)  +/-  (3.28e-248, 3.28e-248j)
| (-0.14573118174035497438 - 5.2432366907996897616e-1034j)  +/-  (1.44e-254, 1.44e-254j)
| (-4.2417964851912590438 - 5.5530683245395570177e-1032j)  +/-  (5.08e-246, 5.08e-246j)
| (0.43607741192761650868 + 2.29650361128088152e-1044j)  +/-  (2.7e-253, 2.7e-253j)
| (0.14573118174035497438 - 1.7778137923963214477e-1046j)  +/-  (1.44e-254, 1.44e-254j)
| (-0.43607741192761650868 + 7.7882827799046737369e-1045j)  +/-  (2.74e-253, 2.74e-253j)
-------------------------------------------------
The weights are:
| (3.5090840890901716997e-09 + 6.9965376416951142654e-914j)  +/-  (6.69e-80, 1.32e-202j)
| (1.8576956633418347021e-27 + 1.4833452884257627888e-925j)  +/-  (5.11e-91, 1.01e-213j)
| (5.6946793326286716931e-17 - 3.7807041952517435394e-919j)  +/-  (3.39e-86, 6.71e-209j)
| (1.3147362229615900633e-14 + 9.998229010741365402e-918j)  +/-  (5.62e-85, 1.11e-207j)
| (9.7125186902487119255e-20 + 9.5122673138637149057e-921j)  +/-  (3.82e-88, 7.55e-211j)
| (4.3534862870649734747e-23 - 1.256064083893302006e-922j)  +/-  (3.65e-90, 7.22e-213j)
| (1.4801201251341265242e-12 - 2.0781673483162393638e-916j)  +/-  (1.71e-84, 3.38e-207j)
| (5.6946793326286716931e-17 - 6.522559275897738419e-920j)  +/-  (1.05e-91, 2.08e-214j)
| (4.3534862870649734747e-23 - 3.1668761259592325928e-923j)  +/-  (2.91e-94, 5.74e-217j)
| (0.0035449517751410064352 + 4.5910959037400215396e-911j)  +/-  (1.1e-77, 2.18e-200j)
| (1.4801201251341265242e-12 - 1.8758411993849381402e-917j)  +/-  (1.8e-90, 3.55e-213j)
| (9.7125186902487119255e-20 + 2.0179763731219406138e-921j)  +/-  (3.81e-93, 7.53e-216j)
| (0.03023070565921465298 + 2.3741463619136684943e-910j)  +/-  (8.69e-75, 1.72e-197j)
| (1.6181681227914892982e-05 - 2.0135106849999353098e-912j)  +/-  (1.07e-83, 2.12e-206j)
| (1.8576956633418347021e-27 + 5.0255384388233682495e-925j)  +/-  (1.12e-95, 2.2e-218j)
| (1.6181681227914892982e-05 + 3.2023237107421192665e-913j)  +/-  (2.07e-86, 4.08e-209j)
| (1.3147362229615900633e-14 + 1.3210557604667402646e-918j)  +/-  (1.21e-91, 2.39e-214j)
| (8.5694874903123409489e-08 + 1.1497292836682307207e-914j)  +/-  (6.85e-89, 1.35e-211j)
| (0.060079805633816397325 + 2.7302450366925718096e-910j)  +/-  (2.08e-77, 4.1e-200j)
| (8.5694874903123409489e-08 - 2.3289883207302116727e-913j)  +/-  (1.31e-87, 2.58e-210j)
| (1.4103224744449310301e-06 - 6.5711719813958707017e-914j)  +/-  (3.31e-88, 6.55e-211j)
| (1.4103224744449310301e-06 + 6.4292741032268755014e-913j)  +/-  (7.84e-87, 1.55e-209j)
| (0.011859130167415163045 - 1.1009533054097208142e-910j)  +/-  (4.49e-82, 8.87e-205j)
| (0.011859130167415163045 + 4.8105143274321314784e-911j)  +/-  (5.52e-84, 1.09e-206j)
| (0.03023070565921465298 - 1.2369277324862973807e-910j)  +/-  (1.51e-82, 2.99e-205j)
| (0.00013286394585787853575 - 1.3525335105987215067e-912j)  +/-  (2.98e-87, 5.89e-210j)
| (9.2578155115984122646e-11 + 4.3144276135570323919e-915j)  +/-  (2.38e-90, 4.71e-213j)
| (0.00013286394585787853575 + 6.1363271359695504173e-912j)  +/-  (7.77e-87, 1.53e-209j)
| (9.2578155115984122646e-11 + 2.0012011070929411361e-916j)  +/-  (3.21e-92, 6.34e-215j)
| (0.097390577068606133582 - 5.0001787824878296331e-910j)  +/-  (3.2e-84, 6.33e-207j)
| (0.0035449517751410064352 - 1.647877307155346129e-911j)  +/-  (9.06e-87, 1.79e-209j)
| (0.097390577068606133582 + 7.0670332609661876598e-910j)  +/-  (6.6e-85, 1.31e-207j)
| (0.060079805633816397325 - 4.4685590596096080568e-910j)  +/-  (5.54e-85, 1.1e-207j)
| (0.0007966930170406082902 - 1.7483468763427499566e-911j)  +/-  (6.8e-87, 1.35e-209j)
| (0.0007966930170406082902 + 5.0155604029235689249e-912j)  +/-  (7.55e-88, 1.49e-210j)
| (0.16084564295047514779 - 9.3912996503211325965e-910j)  +/-  (4.38e-86, 8.71e-209j)
| (3.5090840890901716997e-09 - 1.6808505466035925022e-915j)  +/-  (7.44e-92, 1.47e-214j)
| (0.13510194848070018033 - 9.2196901906948521362e-910j)  +/-  (2.85e-86, 5.74e-209j)
| (0.16084564295047514779 + 1.0059553252120909352e-909j)  +/-  (1.92e-86, 3.9e-209j)
| (0.13510194848070018033 + 7.5007474720341852971e-910j)  +/-  (1.16e-86, 2.11e-209j)
