Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 44
-------------------------------------------------
Trying to find an order 44 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^46 - 652618759244694300136298254/328554527712538859293821*t^44 + 147843161308428442702882534487/328554527712538859293821*t^42 - 1931673809424984673454917269341/31290907401194177075602*t^40 + 359350760788782222844235780635135/62581814802388354151204*t^38 - 48088733100800756271685634741077765/125163629604776708302408*t^36 + 4793538669643366861204530466109832645/250327259209553416604816*t^34 - 363669080576741295726834409793149497195/500654518419106833209632*t^32 + 10638278566648275608891163502015826036205/500654518419106833209632*t^30 - 483469422378515934095438914521460853535975/1001309036838213666419264*t^28 + 17114153390549405080171026219639526359173175/2002618073676427332838528*t^26 - 471343440903367731977154543442685958888464625/4005236147352854665677056*t^24 + 10051953136613388127832888908199421423885783375/8010472294705709331354112*t^22 - 164596511353522504235705583559780169096986105125/16020944589411418662708224*t^20 + 2043552433628788824141758728595832027718485313125/32041889178822837325416448*t^18 - 18903609717232533926149205139151118529031452406875/64083778357645674650832896*t^16 + 254444769171771327690787068699371255630015319298125/256335113430582698603331584*t^14 - 1206207101484704284148798911079075984266756210404375/512670226861165397206663168*t^12 + 3851416510085025553983783077951054730002382119094375/1025340453722330794413326336*t^10 - 7768595482246110156525718773028809910326295579040625/2050680907444661588826652672*t^8 + 8981581027375602654009994990221907328379413226421875/4101361814889323177653305344*t^6 - 5062234556861893634917131213002486273072866172990625/8202723629778646355306610688*t^4 + 1011560207500850556576228390815270305758041309990625/16405447259557292710613221376*t^2 - 27935260452304471699310794304065169594696878659375/32810894519114585421226442752
-------------------------------------------------
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:   46 out of 46
Indefinite weights: 0 out of 46
Negative weights:   0 out of 46
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.6603627677188145289 + 1.2210434848880184243e-941j)  +/-  (3.14e-247, 3.14e-247j)
| (6.4689493095518454199 - 5.2668767483259245281e-938j)  +/-  (1.66e-244, 1.66e-244j)
| (7.9882640762673609758 - 7.3178501722933521136e-950j)  +/-  (4.25e-246, 4.25e-246j)
| (-6.0336694422589309095 + 2.8798931769651071267e-952j)  +/-  (2.57e-244, 2.57e-244j)
| (-6.4689493095518454199 + 1.2497416973858959672e-969j)  +/-  (1.68e-244, 1.68e-244j)
| (4.8323431634415850791 - 6.2479330160325668739e-979j)  +/-  (2.24e-244, 2.24e-244j)
| (-8.6603627677188145289 - 1.8018311051230525035e-982j)  +/-  (3.03e-247, 3.03e-247j)
| (-7.9882640762673609758 + 1.3942258850270322955e-980j)  +/-  (4.09e-246, 4.09e-246j)
| (6.9308416005017414599 + 4.0421221808754604671e-984j)  +/-  (7.33e-245, 7.33e-245j)
| (7.4302331911338007592 + 4.1790656963209827671e-984j)  +/-  (2.25e-245, 2.25e-245j)
| (1.024075050557459816 - 1.2437189561919506914e-990j)  +/-  (2.76e-251, 2.76e-251j)
| (4.4561397413983689238 + 1.4512625866584853708e-982j)  +/-  (1.36e-244, 1.36e-244j)
| (-2.0084319718887430012 + 7.1518517532500720071e-990j)  +/-  (1.66e-248, 1.66e-248j)
| (-2.6833333162856042637 + 2.0108524405632401307e-987j)  +/-  (6.1e-247, 6.1e-247j)
| (-1.6763873721464086419 + 3.6801264621709296898e-990j)  +/-  (2.6e-249, 2.6e-249j)
| (3.3750363392157269927 + 1.8999300333121010114e-986j)  +/-  (1.01e-245, 1.01e-245j)
| (2.344009637805236127 + 1.2152565346516113577e-989j)  +/-  (1.09e-247, 1.09e-247j)
| (-5.2190390030403462372 + 1.8893209329930342515e-984j)  +/-  (3.18e-244, 3.18e-244j)
| (-1.024075050557459816 + 3.551479016421540739e-1009j)  +/-  (2.92e-251, 2.92e-251j)
| (-7.4302331911338007592 - 4.0656017754081749424e-1002j)  +/-  (2.38e-245, 2.38e-245j)
| (6.0336694422589309095 - 4.1627623499460629882e-1006j)  +/-  (2.64e-244, 2.64e-244j)
| (4.0887114434886806193 + 1.3355882275482672685e-1008j)  +/-  (6.35e-245, 6.35e-245j)
| (-2.344009637805236127 + 3.9188346015646385757e-1012j)  +/-  (1.11e-247, 1.11e-247j)
| (-5.618469340983665912 + 1.4355637779951668861e-1007j)  +/-  (2.99e-244, 2.99e-244j)
| (-3.3750363392157269927 + 5.7731585525310061195e-1014j)  +/-  (9.2e-246, 9.2e-246j)
| (-6.9308416005017414599 + 2.1777178877214832115e-1013j)  +/-  (7.9e-245, 7.9e-245j)
| (0.7071067811865475244 - 7.0920557204053188136e-1021j)  +/-  (2.73e-252, 2.73e-252j)
| (-4.0887114434886806193 - 2.8921440365010488066e-1013j)  +/-  (6.09e-245, 6.09e-245j)
| (-1.3479981296140842947 - 5.042747550331917978e-1026j)  +/-  (3.09e-250, 3.09e-250j)
| (-3.0268185358315165097 - 4.3431010501909171977e-1021j)  +/-  (2.84e-246, 2.84e-246j)
| (3.0268185358315165097 + 4.4397009757609126345e-1022j)  +/-  (2.6e-246, 2.6e-246j)
| (5.618469340983665912 + 1.8473995915306716013e-1020j)  +/-  (3.49e-244, 3.49e-244j)
| (0.40393277113026404256 - 2.9704859997485407179e-1029j)  +/-  (2.1e-253, 2.1e-253j)
| (-4.4561397413983689238 - 1.4085330871967105944e-1019j)  +/-  (1.31e-244, 1.31e-244j)
| (1.6763873721464086419 - 1.0000097005822967987e-1037j)  +/-  (2.46e-249, 2.46e-249j)
| (1.3479981296140842947 - 9.6408647325381568109e-1039j)  +/-  (2.78e-250, 2.78e-250j)
| (-3.7287059254999456137 + 2.668850767715728028e-1033j)  +/-  (2.54e-245, 2.54e-245j)
| (2.0084319718887430012 - 5.4467244853605249527e-1044j)  +/-  (1.82e-248, 1.82e-248j)
| (5.2190390030403462372 - 1.0414249511646238364e-1041j)  +/-  (2.91e-244, 2.91e-244j)
| (-0.7071067811865475244 + 4.3384400097501182253e-1058j)  +/-  (2.51e-252, 2.51e-252j)
| (-0.40393277113026404256 + 1.0883826753626915391e-1059j)  +/-  (2.1e-253, 2.1e-253j)
| (-4.8323431634415850791 - 4.2991135866382895544e-1053j)  +/-  (2.24e-244, 2.24e-244j)
| (0.12777029749292425659 - 3.9481325118798108295e-1072j)  +/-  (2.08e-254, 2.08e-254j)
| (3.7287059254999456137 - 4.4526114727278348834e-1065j)  +/-  (2.47e-245, 2.47e-245j)
| (2.6833333162856042637 + 6.6549277572644432906e-1071j)  +/-  (5.98e-247, 5.98e-247j)
| (-0.12777029749292425659 - 1.0759377580944495247e-1078j)  +/-  (2.08e-254, 2.08e-254j)
-------------------------------------------------
The weights are:
| (1.1695338935605936521e-33 - 2.5260873203728155032e-964j)  +/-  (4.43e-87, 1.47e-209j)
| (1.6900890380169289759e-19 + 5.8954159378946191587e-956j)  +/-  (4.77e-82, 1.58e-204j)
| (6.5500930983947089003e-29 + 9.3464362799075988607e-962j)  +/-  (1.31e-85, 4.34e-208j)
| (3.7035368359093888161e-17 + 1.1296546587416083991e-956j)  +/-  (6.11e-83, 2.02e-205j)
| (1.6900890380169289759e-19 - 6.8801672657813856015e-958j)  +/-  (2.43e-84, 8.03e-207j)
| (1.5525617346298829982e-11 + 6.968181432525241401e-953j)  +/-  (2e-79, 6.61e-202j)
| (1.1695338935605936521e-33 - 3.658924952584630789e-965j)  +/-  (6.67e-91, 2.21e-213j)
| (6.5500930983947089003e-29 + 9.8222100456813456605e-963j)  +/-  (3.47e-89, 1.15e-211j)
| (3.7076071195605595679e-22 + 8.4268822203368656288e-958j)  +/-  (7.79e-86, 2.58e-208j)
| (3.1179337271444248619e-25 - 1.0955152131210491252e-959j)  +/-  (4.82e-87, 1.59e-209j)
| (0.063474098527958547491 - 5.911785553290492809e-948j)  +/-  (6.84e-61, 2.26e-183j)
| (4.9841896914186670841e-10 - 3.4791774328913705271e-952j)  +/-  (3.04e-80, 1e-202j)
| (0.0033346542634805130808 - 4.6691485289500934297e-949j)  +/-  (6.34e-71, 2.1e-193j)
| (0.00014373013875087056475 - 6.7767871722531456192e-950j)  +/-  (1.87e-75, 6.18e-198j)
| (0.011215446010593466121 + 1.0590779409889050087e-948j)  +/-  (1.21e-68, 3.99e-191j)
| (2.2361767976549615595e-06 + 1.9959028381357573783e-950j)  +/-  (2.79e-78, 9.24e-201j)
| (0.00078232158000807534266 - 4.0024828461612732744e-949j)  +/-  (5.29e-74, 1.75e-196j)
| (3.2805059995471478005e-13 + 1.3138476619992348866e-954j)  +/-  (8.15e-86, 2.7e-208j)
| (0.063474098527958547491 + 4.2958527073690295524e-948j)  +/-  (7.47e-66, 2.47e-188j)
| (3.1179337271444248619e-25 - 7.576712632585788011e-961j)  +/-  (6.29e-91, 2.08e-213j)
| (3.7035368359093888161e-17 - 3.2447265726893760527e-955j)  +/-  (2.39e-86, 7.89e-209j)
| (1.1261707964813590369e-08 + 1.5230530204925364472e-951j)  +/-  (1.69e-81, 5.58e-204j)
| (0.00078232158000807534266 + 1.8733776449176033926e-949j)  +/-  (2.69e-76, 8.9e-199j)
| (4.4798696800336294297e-15 - 1.3796136649016771922e-955j)  +/-  (5.16e-87, 1.71e-209j)
| (2.2361767976549615595e-06 - 6.2730177579815176472e-951j)  +/-  (4.15e-82, 1.37e-204j)
| (3.7076071195605595679e-22 + 2.9047557236721708612e-959j)  +/-  (2.36e-90, 7.8e-213j)
| (0.10669558084671118552 + 9.8097482888282355072e-948j)  +/-  (6.99e-74, 2.31e-196j)
| (1.1261707964813590369e-08 - 3.4337421481617906267e-952j)  +/-  (8.73e-85, 2.89e-207j)
| (0.029922171732288241808 - 2.2098198324144789189e-948j)  +/-  (4.61e-76, 1.53e-198j)
| (2.048021068869610163e-05 + 2.1908029544450933831e-950j)  +/-  (3.38e-81, 1.12e-203j)
| (2.048021068869610163e-05 - 6.0437437209887412442e-950j)  +/-  (1e-83, 3.31e-206j)
| (4.4798696800336294297e-15 + 1.9607713949980775402e-954j)  +/-  (2.63e-89, 8.7e-212j)
| (0.13996183568318843408 - 1.5281832429338681037e-947j)  +/-  (8.26e-78, 2.73e-200j)
| (4.9841896914186670841e-10 + 6.4099446636161715677e-953j)  +/-  (3.61e-86, 1.2e-208j)
| (0.011215446010593466121 - 1.7999864194152494658e-948j)  +/-  (3.99e-81, 1.32e-203j)
| (0.029922171732288241808 + 3.3732103418051121687e-948j)  +/-  (4.7e-80, 1.56e-202j)
| (1.8432906008939506749e-07 + 1.5756066169023104733e-951j)  +/-  (1.49e-84, 4.94e-207j)
| (0.0033346542634805130808 + 8.8738927221493049126e-949j)  +/-  (2.46e-82, 8.15e-205j)
| (3.2805059995471478005e-13 - 1.2285870464582462451e-953j)  +/-  (6.31e-89, 2.08e-211j)
| (0.10669558084671118552 - 7.876502659451025627e-948j)  +/-  (1.42e-80, 4.67e-203j)
| (0.13996183568318843408 + 1.3485545850085809154e-947j)  +/-  (8.02e-81, 2.64e-203j)
| (1.5525617346298829982e-11 - 1.0091030372695827924e-953j)  +/-  (1.11e-87, 3.66e-210j)
| (0.14444724872448910655 + 2.0162419048990071571e-947j)  +/-  (1.23e-81, 4.04e-204j)
| (1.8432906008939506749e-07 - 5.863527728541944435e-951j)  +/-  (1.83e-86, 6.08e-209j)
| (0.00014373013875087056475 + 1.6383878239684749236e-949j)  +/-  (7.89e-85, 2.62e-207j)
| (0.14444724872448910655 - 1.9381376823903765032e-947j)  +/-  (7.14e-82, 2.3e-204j)
