Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 40
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^49 - 568606710067804714700476221573369771702597180884558110248614464086072/65703617067213487295636604494416823944702401140119109814307960999*t^47 + 140988920027455025077213440720422220659109547191467721423592878502471608/65703617067213487295636604494416823944702401140119109814307960999*t^45 - 21283089217432653424187489545297441753141791043543114192409814447994905270/65703617067213487295636604494416823944702401140119109814307960999*t^43 + 2190866337377804835732821457129749276782195289549583405267133083356091326670/65703617067213487295636604494416823944702401140119109814307960999*t^41 - 326512641058774678259835041767286700987777437693488097786365172353724125384605/131407234134426974591273208988833647889404802280238219628615921998*t^39 + 493227929090320000605583106148068082849462934213128978902934686979146222590395/3551546868498026340304681324022531024037967629195627557530160054*t^37 - 84571802597664457643962603268802089329563182035713047649233017831823366460174645/14206187473992105361218725296090124096151870516782510230120640216*t^35 + 5639455172878922191512496550325821538147144392540386318809662753952919961556355425/28412374947984210722437450592180248192303741033565020460241280432*t^33 - 147471817968208848401154044546068008924624608874015557195018700703931381457072884175/28412374947984210722437450592180248192303741033565020460241280432*t^31 + 3036912808085764712905509198069868947994890789901462946379985595225692185597283040475/28412374947984210722437450592180248192303741033565020460241280432*t^29 - 197101500567282170476054902116155405897036064597206162366551997987891029174200246451075/113649499791936842889749802368720992769214964134260081840965121728*t^27 + 2513069048121013793407268430512171841438234556243567727050010249172751787528137822051425/113649499791936842889749802368720992769214964134260081840965121728*t^25 - 100137028357814548302903702390514302169548081464775052755049360182064400801345160773450625/454597999167747371558999209474883971076859856537040327363860486912*t^23 + 772378185457984384665346731493756325386182049393163916784672874309414252213425052464344375/454597999167747371558999209474883971076859856537040327363860486912*t^21 - 18219593973584283523571783921665066258749782637321758380706327673281114720090522333219008125/1818391996670989486235996837899535884307439426148161309455441947648*t^19 + 323065995819006626062791227920677318873709028774490873010087976167189141875662334018667888125/7273567986683957944943987351598143537229757704592645237821767790592*t^17 - 2105440655924597911646331306369769824762021121286630299508007141526541990330428303860392964375/14547135973367915889887974703196287074459515409185290475643535581184*t^15 + 4896861103492076054164006875673143829058460000677563329500895232959549261596681439628747509375/14547135973367915889887974703196287074459515409185290475643535581184*t^13 - 31272534244881653502844728613574178673583694603509767212330012670958568597362697986331281896875/58188543893471663559551898812785148297838061636741161902574142324736*t^11 + 32516347475659728527717043401302002506294026499003337074506971836276366490384060663548639371875/58188543893471663559551898812785148297838061636741161902574142324736*t^9 - 81876859482016365071696571275437591729408488303762422869781462253045911862077872937481706603125/232754175573886654238207595251140593191352246546964647610296569298944*t^7 + 28063433349625435974807696102826575766373094865662590008570852411750318022394925759666924584375/232754175573886654238207595251140593191352246546964647610296569298944*t^5 - 17629554654081322429842161044166187705560806342082522980550821946313475900017682675662359390625/931016702295546616952830381004562372765408986187858590441186277195776*t^3 + 1720857074793974401419103100413461467137947217272018577471470745435319462667255339252903234375/1862033404591093233905660762009124745530817972375717180882372554391552*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:
| (-5.865589981004548738 + 4.8782648525273596454e-868j)  +/-  (1.25e-243, 1.25e-243j)
| (-8.1578322518138739613 + 1.0398752623715914056e-872j)  +/-  (1.15e-245, 1.15e-245j)
| (8.8087375538082217077 + 9.7464205179571316e-870j)  +/-  (8e-247, 8e-247j)
| (5.865589981004548738 + 7.4197388879504920011e-880j)  +/-  (1.27e-243, 1.27e-243j)
| (-8.8087375538082217077 + 6.3955121669228905846e-900j)  +/-  (9.51e-247, 9.51e-247j)
| (8.1578322518138739613 + 4.6385265107972118298e-903j)  +/-  (1.25e-245, 1.25e-245j)
| (7.6191662979117022883 + 6.2147314668080149507e-927j)  +/-  (6.79e-245, 6.79e-245j)
| (-7.1374702560082517496 + 4.7335890972128566857e-941j)  +/-  (2.36e-244, 2.36e-244j)
| (6.6912766494053209377 + 1.2134533963329932507e-944j)  +/-  (6.17e-244, 6.17e-244j)
| (4.3645886281973410867 - 4.2637018164109329786e-956j)  +/-  (3.35e-244, 3.35e-244j)
| (4.0091652680023463644 - 1.2306937634508270456e-958j)  +/-  (1.44e-244, 1.44e-244j)
| (-2.9746872378814771183 + 2.8588289784539886875e-967j)  +/-  (4.74e-246, 4.74e-246j)
| (6.269485251306835822 - 1.7756790923884277642e-963j)  +/-  (9.56e-244, 9.56e-244j)
| (3.6595069473376959347 + 6.7430426845851973869e-976j)  +/-  (5.2e-245, 5.2e-245j)
| (7.1374702560082517496 + 4.0378649443284269662e-974j)  +/-  (2.38e-244, 2.38e-244j)
| (2.3057426490156475613 - 9.483324740288650397e-981j)  +/-  (2.05e-247, 2.05e-247j)
| (-1.9764411316057930187 - 2.0240580296857921686e-981j)  +/-  (3e-248, 3e-248j)
| (-2.6384291054842239697 - 1.66838118634911046e-979j)  +/-  (1e-246, 1e-246j)
| (-6.6912766494053209377 - 6.3285809585575817226e-976j)  +/-  (5.78e-244, 5.78e-244j)
| (-6.269485251306835822 + 4.3111695228814571821e-976j)  +/-  (9.18e-244, 9.18e-244j)
| (-7.6191662979117022883 + 4.3568614612953252635e-979j)  +/-  (6.88e-245, 6.88e-245j)
| (4.7266647076018145587 + 7.3486110689572582532e-977j)  +/-  (6.47e-244, 6.47e-244j)
| (3.3148827525018539415 + 3.622159555818452203e-980j)  +/-  (1.66e-245, 1.66e-245j)
| (1.9764411316057930187 - 1.235920488946750118e-982j)  +/-  (3.4e-248, 3.4e-248j)
| (-3.3148827525018539415 - 1.5572881564217267515e-980j)  +/-  (1.63e-245, 1.63e-245j)
| (-5.4755002282562594142 - 2.1512839539902577864e-977j)  +/-  (1.18e-243, 1.18e-243j)
| (1.6506801238857845559 - 3.3669564061670955443e-985j)  +/-  (4.17e-249, 4.17e-249j)
| (1.0171426846361271854 - 5.1897053042751615711e-986j)  +/-  (6.16e-251, 6.16e-251j)
| (5.4755002282562594142 + 1.219961311139840507e-977j)  +/-  (1.19e-243, 1.19e-243j)
| (-2.3057426490156475613 - 4.1404305203770046647e-989j)  +/-  (1.83e-247, 1.83e-247j)
| (-4.7266647076018145587 + 9.7089412769492731102e-985j)  +/-  (5.98e-244, 5.98e-244j)
| (6.8663692164221356642e-1005 - 2.0337509972642452367e-1004j)  +/-  (1.05e-1002, 1.05e-1002j)
| (1.3295002292819626982 + 1.6082318992509774281e-991j)  +/-  (5.39e-250, 5.39e-250j)
| (-3.6595069473376959347 - 5.318397709606242913e-985j)  +/-  (5.74e-245, 5.74e-245j)
| (-0.52464762327529031788 - 1.651027028778089864e-995j)  +/-  (1.47e-252, 1.47e-252j)
| (-4.3645886281973410867 + 7.0725900195401005527e-986j)  +/-  (3.43e-244, 3.43e-244j)
| (5.0964958137239483231 + 4.9008680829067287244e-988j)  +/-  (1.02e-243, 1.02e-243j)
| (2.9746872378814771183 - 9.4558817191701503897e-994j)  +/-  (4.25e-246, 4.25e-246j)
| (-4.0091652680023463644 + 2.4970686311036246964e-990j)  +/-  (1.42e-244, 1.42e-244j)
| (-1.6506801238857845559 + 2.4434279929146296988e-995j)  +/-  (4.54e-249, 4.54e-249j)
| (-0.73395630342256598469 - 6.3816829231579159054e-999j)  +/-  (9.58e-252, 9.58e-252j)
| (-1.3295002292819626982 - 2.4024490978491093421e-996j)  +/-  (5.44e-250, 5.44e-250j)
| (0.73395630342256598469 - 5.0159873850626868446e-999j)  +/-  (9.73e-252, 9.73e-252j)
| (0.2903588150065040993 + 1.4587578897514322788e-1002j)  +/-  (9.67e-254, 9.67e-254j)
| (-5.0964958137239483231 + 1.4886671861496065372e-995j)  +/-  (9.82e-244, 9.82e-244j)
| (-1.0171426846361271854 + 7.265876217775536229e-1003j)  +/-  (6.82e-251, 6.82e-251j)
| (-0.2903588150065040993 - 8.769434164080164463e-1005j)  +/-  (1.25e-253, 1.25e-253j)
| (2.6384291054842239697 + 4.3695228940284785839e-1001j)  +/-  (1.03e-246, 1.03e-246j)
| (0.52464762327529031788 + 3.1079163693875309614e-1007j)  +/-  (1.46e-252, 1.46e-252j)
-------------------------------------------------
The weights are:
| (2.5565117574460031095e-16 + 7.6762676998786806214e-883j)  +/-  (2.01e-76, 5.22e-197j)
| (4.0961593948351655378e-30 + 3.0553259965917118391e-891j)  +/-  (2.19e-83, 5.69e-204j)
| (8.5002445053887271497e-35 + 1.6286715342646233267e-894j)  +/-  (4.45e-86, 1.16e-206j)
| (2.5565117574460031095e-16 + 1.0630935241513115537e-884j)  +/-  (1.9e-78, 4.94e-199j)
| (8.5002445053887271497e-35 - 8.1204421664998935121e-894j)  +/-  (3.78e-86, 9.83e-207j)
| (4.0961593948351655378e-30 - 4.9941785094545766517e-892j)  +/-  (8.18e-85, 2.13e-205j)
| (1.7512163610504201184e-26 + 4.253203538732105999e-890j)  +/-  (9.34e-84, 2.43e-204j)
| (1.9550281249421738882e-23 + 1.8104700568026478738e-887j)  +/-  (6.19e-84, 1.61e-204j)
| (8.7658380208593874648e-21 + 4.5261916294766597477e-887j)  +/-  (6.95e-82, 1.81e-202j)
| (1.0786187512965404212e-09 + 4.0095055847992564708e-881j)  +/-  (3.96e-76, 1.03e-196j)
| (2.0791146827009086623e-08 - 2.0952853575716014765e-880j)  +/-  (5.13e-75, 1.33e-195j)
| (2.7388664278638900768e-05 + 4.3836847673548061666e-878j)  +/-  (3.55e-73, 9.24e-194j)
| (1.9758641671896790136e-18 - 8.02285559783036257e-886j)  +/-  (2.44e-81, 6.34e-202j)
| (2.9903703994754045681e-07 + 9.6111508999285368553e-880j)  +/-  (1.26e-74, 3.29e-195j)
| (1.9550281249421738882e-23 - 1.770891706366356749e-888j)  +/-  (1.5e-83, 3.91e-204j)
| (0.00091690863057790415095 + 1.4588167915087452833e-877j)  +/-  (5.42e-70, 1.41e-190j)
| (0.0037177281718024126008 - 8.4098048267130938037e-877j)  +/-  (1.5e-69, 3.91e-190j)
| (0.00017883974709810318935 - 1.2563302244177181569e-877j)  +/-  (2.1e-73, 5.47e-194j)
| (8.7658380208593874648e-21 - 6.8833356309436804199e-886j)  +/-  (1.97e-87, 5.14e-208j)
| (1.9758641671896790136e-18 + 2.4104752748695434504e-884j)  +/-  (1.28e-86, 3.34e-207j)
| (1.7512163610504201184e-26 - 3.2706539541493328736e-889j)  +/-  (6.61e-90, 1.72e-210j)
| (4.0914556194245348778e-11 - 6.6444049610014144966e-882j)  +/-  (1.97e-81, 5.12e-202j)
| (3.2631216814655570157e-06 - 3.9162751940099682571e-879j)  +/-  (7.69e-78, 2e-198j)
| (0.0037177281718024126008 - 4.1707285134189431244e-877j)  +/-  (9.91e-74, 2.58e-194j)
| (3.2631216814655570157e-06 - 1.4095407436737843123e-878j)  +/-  (1.55e-80, 4.04e-201j)
| (2.0669323157183775427e-14 - 3.2184817495148319822e-882j)  +/-  (1.76e-86, 4.59e-207j)
| (0.011976372785855122773 + 1.138160580515127342e-876j)  +/-  (4.02e-74, 1.05e-194j)
| (0.060976010354627605248 + 8.5534040765838822287e-876j)  +/-  (1.93e-72, 5.02e-193j)
| (2.0669323157183775427e-14 - 1.1070335624879676464e-883j)  +/-  (3.32e-84, 8.65e-205j)
| (0.00091690863057790415095 + 3.3485922677054451374e-877j)  +/-  (1.05e-77, 2.73e-198j)
| (4.0914556194245348778e-11 - 6.1794422559625588174e-881j)  +/-  (9.82e-86, 2.55e-206j)
| (0.16774352873895517551 + 3.7095095917681471721e-875j)  +/-  (2.38e-74, 6.2e-195j)
| (0.030635705071379199652 - 3.0638875057493138143e-876j)  +/-  (2.75e-75, 7.16e-196j)
| (2.9903703994754045681e-07 + 4.1497596656020219244e-879j)  +/-  (3.66e-83, 9.52e-204j)
| (0.083079601348420323218 + 4.6733348593580519745e-875j)  +/-  (1.64e-75, 4.26e-196j)
| (1.0786187512965404212e-09 + 2.7327062826431376913e-880j)  +/-  (2.44e-85, 6.35e-206j)
| (1.1065891336285023501e-12 + 9.3835946169939875526e-883j)  +/-  (5.23e-86, 1.36e-206j)
| (2.7388664278638900768e-05 + 1.4335304204296217273e-878j)  +/-  (3.24e-82, 8.42e-203j)
| (2.0791146827009086623e-08 - 1.1145310628280765812e-879j)  +/-  (1.14e-84, 2.97e-205j)
| (0.011976372785855122773 + 2.0296335238714431561e-876j)  +/-  (1.15e-80, 2.99e-201j)
| (0.082314164097107943158 - 3.0738643971210725625e-875j)  +/-  (3.92e-79, 1.02e-199j)
| (0.030635705071379199652 - 4.8599009731018532023e-876j)  +/-  (1.38e-80, 3.6e-201j)
| (0.082314164097107943158 - 2.3901561381027686659e-875j)  +/-  (1.58e-79, 4.1e-200j)
| (0.14230193268884609566 - 3.9579221636630988712e-875j)  +/-  (1.44e-79, 3.74e-200j)
| (1.1065891336285023501e-12 + 1.3374665111694008115e-881j)  +/-  (1.43e-87, 3.7e-208j)
| (0.060976010354627605248 + 1.2142195231308087999e-875j)  +/-  (1.93e-80, 5.04e-201j)
| (0.14230193268884609566 - 4.3701804378633079139e-875j)  +/-  (7.8e-80, 2.04e-200j)
| (0.00017883974709810318935 - 4.7676042416733937968e-878j)  +/-  (2.03e-83, 5.11e-204j)
| (0.083079601348420323218 + 3.9059599419730087352e-875j)  +/-  (3.9e-80, 1e-200j)
