Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^50 - 11302091699750257223815425123794855953588394/10283796262563126106561632595159527911147*t^48 + 148166764371858755719569584110402424641304250503/267378702826641278770602447474147725689822*t^46 - 865077759713359389774222492534474969892277782274795/5080195353706184296641446502008806788106618*t^44 + 181522366476741794835734554009488547936334961292034915/5080195353706184296641446502008806788106618*t^42 - 27620965516647967658771148153929696016983129359985783805/5080195353706184296641446502008806788106618*t^40 + 243033971583649335721651675243508877354044070047360875215/390784257977398792049342038616062060623586*t^38 - 1125320657397994934447253074161189753108226478183972502995/20567592525126252213123265190319055822294*t^36 + 77275683253277674347754373243734564608959365136122836486225/20567592525126252213123265190319055822294*t^34 - 4180573004581893996440079315963961989130139966859880756455825/20567592525126252213123265190319055822294*t^32 + 89553727629345549566981456876066296772859972679497520159822575/10283796262563126106561632595159527911147*t^30 - 3044371152392251160574408502621661566391562923499712243438093425/10283796262563126106561632595159527911147*t^28 + 6311674854109002093840310078435222026191601739555872891331526325/791061250966394315889356353473809839319*t^26 - 134409007435010528837492151395489656906260411855779409313528111875/791061250966394315889356353473809839319*t^24 + 2248012864469671204005828133917522838220235231095132053870871945625/791061250966394315889356353473809839319*t^22 - 380524233050354946543944155782354295277567364989623923696327985801875/10283796262563126106561632595159527911147*t^20 + 3811314544216725427232601718154896461562454177948443687404329675707500/10283796262563126106561632595159527911147*t^18 - 28897829495887660775820151991764808629334664045803356367822182967836875/10283796262563126106561632595159527911147*t^16 + 324734879624759312968613877930689988086689246857847835099916874504959375/20567592525126252213123265190319055822294*t^14 - 101056829246688293283558015039078676287157822026585893032890846113353125/1582122501932788631778712706947619678638*t^12 + 282840025339085177346743262196640573889117645943509535340666997587128125/1582122501932788631778712706947619678638*t^10 - 516906107792559986213377237959640538088629134834152397991756657023621875/1582122501932788631778712706947619678638*t^8 + 564524036859985806619198623084241954382865335848226076810412839474103125/1582122501932788631778712706947619678638*t^6 - 317497322877416021493557276788038777134390548449147437488603855263421875/1582122501932788631778712706947619678638*t^4 + 68529262256641426691379188887060772100110756054251100895191535012703125/1582122501932788631778712706947619678638*t^2 - 2351031588067984580369362913622700342502865269030033732515346147015625/1582122501932788631778712706947619678638
-------------------------------------------------
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:   50 out of 50
Indefinite weights: 0 out of 50
Negative weights:   0 out of 50
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.8883912474120303293 + 2.8474839009931985495e-951j)  +/-  (1.34e-243, 1.34e-243j)
| (10.142640977705775046 + 1.2283948437914033971e-952j)  +/-  (3.62e-244, 3.62e-244j)
| (-10.8414945277759442 - 6.9230014994516639945e-951j)  +/-  (9.92e-245, 9.92e-245j)
| (-5.1876850108301378979 + 7.1493517079644596287e-954j)  +/-  (1.65e-244, 1.65e-244j)
| (6.6884352765945244108 + 1.5424179851412655569e-955j)  +/-  (1.13e-243, 1.13e-243j)
| (-8.8883912474120303293 + 3.5007940641490708916e-954j)  +/-  (1.39e-243, 1.39e-243j)
| (10.8414945277759442 + 1.8577184774539160337e-965j)  +/-  (1.06e-244, 1.06e-244j)
| (-1.4616606440824023397 + 3.3125915952693125851e-971j)  +/-  (1.46e-250, 1.46e-250j)
| (-10.142640977705775046 - 2.5504978406777148087e-964j)  +/-  (3.63e-244, 3.63e-244j)
| (7.7512867268225031744 - 3.3113021132197509188e-969j)  +/-  (1.86e-243, 1.86e-243j)
| (6.1774944790008462567 + 4.0807131904740557787e-971j)  +/-  (6.79e-244, 6.79e-244j)
| (-9.4966933233186196389 + 5.0113547997648234365e-974j)  +/-  (7.97e-244, 7.97e-244j)
| (12.564677203011667177 - 3.5585116625157766479e-984j)  +/-  (1.28e-246, 1.28e-246j)
| (-11.622911308531963874 + 4.9227944104531645979e-981j)  +/-  (1.63e-245, 1.63e-245j)
| (8.3085932485238087347 - 4.6605650560493764239e-980j)  +/-  (1.76e-243, 1.76e-243j)
| (9.4966933233186196389 - 2.8179037294031341222e-981j)  +/-  (8.27e-244, 8.27e-244j)
| (5.1876850108301378979 + 2.1312108640565785175e-983j)  +/-  (1.61e-244, 1.61e-244j)
| (7.2122606938930550032 - 5.1105534210469142715e-991j)  +/-  (1.65e-243, 1.65e-243j)
| (2.3007521037946006035 + 1.1152021183112661854e-999j)  +/-  (2.78e-248, 2.78e-248j)
| (-7.7512867268225031744 - 7.6316672628858094145e-997j)  +/-  (1.99e-243, 1.99e-243j)
| (-12.564677203011667177 + 2.0251428674923955916e-1008j)  +/-  (1.33e-246, 1.33e-246j)
| (-4.2343312875995918938 - 1.3477748067431233248e-1004j)  +/-  (1.83e-245, 1.83e-245j)
| (-4.7066523654551996558 - 5.132571615074200473e-1007j)  +/-  (5.31e-245, 5.31e-245j)
| (11.622911308531963874 - 6.893635044211303968e-1010j)  +/-  (1.77e-245, 1.77e-245j)
| (-1.8891758777537106755 - 3.8119007063717850585e-1015j)  +/-  (1.82e-249, 1.82e-249j)
| (5.6776795041055335516 + 5.9001357551583045381e-1009j)  +/-  (3.48e-244, 3.48e-244j)
| (2.6269238091101833296 - 6.2104288025217799553e-1016j)  +/-  (1.71e-247, 1.71e-247j)
| (2.9195878684581467755 + 1.0417491950417398219e-1014j)  +/-  (5.74e-247, 5.74e-247j)
| (1.0358869572653216056 - 1.5304821492103446327e-1020j)  +/-  (9.08e-252, 9.08e-252j)
| (-1.0358869572653216056 - 1.1289040917300790778e-1020j)  +/-  (9e-252, 9e-252j)
| (1.8891758777537106755 - 1.3377047957979379757e-1018j)  +/-  (1.93e-249, 1.93e-249j)
| (4.2343312875995918938 - 1.100443021467923258e-1012j)  +/-  (1.92e-245, 1.92e-245j)
| (1.4616606440824023397 + 2.6588162059882999247e-1022j)  +/-  (1.42e-250, 1.42e-250j)
| (-3.7717517330651896976 + 1.4775729967685109815e-1016j)  +/-  (5.59e-246, 5.59e-246j)
| (-7.2122606938930550032 - 8.7149892498175631149e-1023j)  +/-  (1.76e-243, 1.76e-243j)
| (-2.9195878684581467755 + 1.9485145551119374966e-1037j)  +/-  (5.34e-247, 5.34e-247j)
| (-5.6776795041055335516 + 3.6658389355130068524e-1042j)  +/-  (3.63e-244, 3.63e-244j)
| (3.3242574335521189524 - 6.0806488907121906531e-1057j)  +/-  (1.67e-246, 1.67e-246j)
| (-8.3085932485238087347 - 1.2550473724069895685e-1060j)  +/-  (1.9e-243, 1.9e-243j)
| (-6.6884352765945244108 + 4.0434468609959048921e-1067j)  +/-  (1.15e-243, 1.15e-243j)
| (-0.61670659019259415219 + 5.0394549770139281125e-1082j)  +/-  (5.51e-253, 5.51e-253j)
| (-6.1774944790008462567 - 3.6993762906324281977e-1076j)  +/-  (7e-244, 7e-244j)
| (-3.3242574335521189524 - 6.2149725721444334583e-1079j)  +/-  (1.75e-246, 1.75e-246j)
| (0.61670659019259415219 + 3.0927305105941620818e-1085j)  +/-  (5.06e-253, 5.06e-253j)
| (-2.6269238091101833296 - 1.9942686915055456265e-1080j)  +/-  (1.81e-247, 1.81e-247j)
| (-2.3007521037946006035 - 1.8201558140091884575e-1080j)  +/-  (2.68e-248, 2.68e-248j)
| (0.20453592226750995163 - 6.0151093905867551757e-1087j)  +/-  (3.88e-254, 3.88e-254j)
| (4.7066523654551996558 + 5.201492105699626666e-1077j)  +/-  (5.84e-245, 5.84e-245j)
| (-0.20453592226750995163 + 2.458196312911059835e-1087j)  +/-  (3.88e-254, 3.88e-254j)
| (3.7717517330651896976 - 9.5359851752130717545e-1083j)  +/-  (5.89e-246, 5.89e-246j)
-------------------------------------------------
The weights are:
| (1.6537185828575344832e-18 + 3.4499165986630027466e-968j)  +/-  (1.06e-67, 1.7e-188j)
| (1.2239705811867524647e-23 + 1.00771171794587649e-970j)  +/-  (1.41e-70, 2.27e-191j)
| (8.7714201647827364852e-27 - 5.5406316108868013085e-972j)  +/-  (1.67e-73, 2.69e-194j)
| (2.7741957673009694755e-07 + 6.5302596848666485664e-960j)  +/-  (6.02e-59, 9.68e-180j)
| (3.9840371523075322625e-11 + 7.8124442069825016285e-964j)  +/-  (1.29e-63, 2.08e-184j)
| (1.6537185828575344832e-18 + 2.1667749843688425133e-967j)  +/-  (6.58e-70, 1.06e-190j)
| (8.7714201647827364852e-27 - 2.0493974616501114411e-972j)  +/-  (3.34e-73, 5.38e-194j)
| (0.058661696802104975079 - 2.5012466710475811323e-957j)  +/-  (1.26e-37, 2.02e-158j)
| (1.2239705811867524647e-23 + 2.9064097281271864583e-970j)  +/-  (1.7e-72, 2.74e-193j)
| (1.9616248423856651879e-14 + 9.822639915975065294e-966j)  +/-  (5.97e-67, 9.6e-188j)
| (1.0414958309917377063e-09 - 5.5776229442496450983e-963j)  +/-  (1.54e-63, 2.48e-184j)
| (6.5021331183287754157e-21 - 9.4671954212227219763e-969j)  +/-  (8.41e-72, 1.35e-192j)
| (2.2687044447003512647e-35 - 5.8461756746656836599e-977j)  +/-  (4.42e-78, 7.12e-199j)
| (1.5508870538932460682e-30 + 5.2163094295299805063e-974j)  +/-  (8.77e-77, 1.41e-197j)
| (2.316257000470181315e-16 - 7.5563090928862102767e-967j)  +/-  (1.65e-68, 2.65e-189j)
| (6.5021331183287754157e-21 - 3.1766807781747635526e-969j)  +/-  (4.75e-71, 7.64e-192j)
| (2.7741957673009694755e-07 - 1.8718498774898836067e-961j)  +/-  (3.44e-64, 5.54e-185j)
| (1.07326880311692897e-12 - 9.8955548797763212416e-965j)  +/-  (1.05e-66, 1.69e-187j)
| (0.010937144823513650447 + 9.2194996831230504904e-958j)  +/-  (1.99e-55, 3.2e-176j)
| (1.9616248423856651879e-14 + 5.2759685869904591649e-965j)  +/-  (5.54e-73, 8.91e-194j)
| (2.2687044447003512647e-35 - 1.3685605042849043864e-976j)  +/-  (1.75e-81, 2.81e-202j)
| (2.3857022099754340344e-05 + 4.2160489556016320451e-959j)  +/-  (6.89e-66, 1.11e-186j)
| (2.9429854381374346202e-06 - 1.9283766823256338518e-959j)  +/-  (6.54e-67, 1.05e-187j)
| (1.5508870538932460682e-30 + 2.0690819386002563234e-974j)  +/-  (2.09e-78, 3.37e-199j)
| (0.028453302069352038501 + 2.3155310700098801351e-957j)  +/-  (7.91e-58, 1.27e-178j)
| (1.9738030479770587481e-08 + 3.4381210874908364745e-962j)  +/-  (4.69e-67, 7.55e-188j)
| (0.0033659108289750805932 - 7.1616026517113388674e-958j)  +/-  (1.7e-61, 2.74e-182j)
| (0.0020035791532031195833 + 3.3711842202148391622e-958j)  +/-  (9.35e-63, 1.5e-183j)
| (0.098655360293697799866 - 1.8651618658849245972e-957j)  +/-  (8.85e-56, 1.42e-176j)
| (0.098655360293697799866 + 2.8030656046859840111e-957j)  +/-  (2.3e-56, 3.7e-177j)
| (0.028453302069352038501 - 1.0740431629959293163e-957j)  +/-  (1.11e-59, 1.79e-180j)
| (2.3857022099754340344e-05 - 4.2069622508382087343e-960j)  +/-  (1.34e-66, 2.16e-187j)
| (0.058661696802104975079 + 1.3964587463587723427e-957j)  +/-  (1.04e-58, 1.67e-179j)
| (0.00014836577910296507644 - 1.1771079069043465038e-958j)  +/-  (1.45e-68, 2.33e-189j)
| (1.07326880311692897e-12 - 6.2456241857911710185e-964j)  +/-  (6.07e-76, 9.76e-197j)
| (0.0020035791532031195833 - 1.2148213155295113396e-957j)  +/-  (9.64e-68, 1.55e-188j)
| (1.9738030479770587481e-08 + 7.8339675625904573344e-961j)  +/-  (2.08e-73, 3.35e-194j)
| (0.00069134551778413865217 - 8.0608459277718103253e-959j)  +/-  (7.14e-68, 1.15e-188j)
| (2.316257000470181315e-16 - 3.7681390672034156654e-966j)  +/-  (5.47e-78, 8.8e-199j)
| (3.9840371523075322625e-11 + 6.5823045020191293821e-963j)  +/-  (8.1e-76, 1.3e-196j)
| (0.13701765758414856607 - 3.0617812153997754873e-957j)  +/-  (4.87e-67, 7.84e-188j)
| (1.0414958309917377063e-09 - 6.6637736765073247518e-962j)  +/-  (4.77e-75, 7.68e-196j)
| (0.00069134551778413865217 + 3.7177002376816660513e-958j)  +/-  (1.85e-71, 2.97e-192j)
| (0.13701765758414856607 + 2.4075226851293778969e-957j)  +/-  (7.6e-69, 1.22e-189j)
| (0.0033659108289750805932 + 2.2010552193813572368e-957j)  +/-  (5.95e-71, 9.58e-192j)
| (0.010937144823513650447 - 2.4059944729202833508e-957j)  +/-  (8.79e-71, 1.41e-191j)
| (0.16003853890054324364 - 2.8800429817105209256e-957j)  +/-  (5.66e-71, 1.01e-191j)
| (2.9429854381374346202e-06 + 9.2176742691427812274e-961j)  +/-  (2.65e-75, 4.28e-196j)
| (0.16003853890054324364 + 3.1180233998660910259e-957j)  +/-  (1.46e-71, 3.33e-192j)
| (0.00014836577910296507644 + 1.8389197552588394942e-959j)  +/-  (5.55e-74, 8.76e-195j)
