Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 18 28
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^21 - 12952203/68336*t^19 + 987853833/68336*t^17 - 9840668841/17084*t^15 + 222748598835/17084*t^13 - 5840004786525/34168*t^11 + 43360655152815/34168*t^9 - 85340399389245/17084*t^7 + 155352674512035/17084*t^5 - 385274669454675/68336*t^3 + 24027902323425/68336*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 209029691852685078034292233620043534153065287958186851362291556873898641262954292649377863802117162509551620439383/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^47 + 78539174037031200625375315632883296767140089912302362843876231696152132222252894098117418987114212154705411398405335/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^45 - 17873772629538376068187021905340031664213934145396042069017682343298386743975378205442736832431584987654641990411876753/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^43 + 13802436797786342284624219472017495644854596920257571068284853140584662738906180554501315954199157544112363432518452312249/1268353448192216583854340244171357955378032005174725275639691384333749344808564986021654369077439452581175273840*t^41 - 1536282712923465139573903028042646795356817643980241403364711358983204549013272249391132088922582830033458659261623895100557/1268353448192216583854340244171357955378032005174725275639691384333749344808564986021654369077439452581175273840*t^39 + 127748014165744251934444257707450307486973655182136453211490287742286611784867210799131999440323828935462565677624382252042837/1268353448192216583854340244171357955378032005174725275639691384333749344808564986021654369077439452581175273840*t^37 - 8119239091754559312852466094059471538039857204573280892573784581407835383491572926849030685949413814778669038995234962788757571/1268353448192216583854340244171357955378032005174725275639691384333749344808564986021654369077439452581175273840*t^35 + 80049452031295777147582271725983857905996025906854492174384531497468348084629721992513990572377787865470429218119551448486069883/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^33 - 1544344668845216703605692301288960666021737393801154594841712030913634542505296984589530255906130682508646757420453472132152950243/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^31 + 46870456604043510427337781365094872145483230940220922941287889727171736721352249020393570109250355529035319165518564895096153912787/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^29 - 1120595366996537792904749385091152140418615160801083126187135813595127946464843885737844054952533534203144187216200418520928482460757/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^27 + 21073378337517597799093133612080849150852317149250080009312186600231946847773332000148557768416245516116208311106949229931812399442441/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^25 - 310333366072546968741932827070798449785059467740161593366707536785496575329802840592976330595835504613649843320056903207942059793853225/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^23 + 3552079152765859509921049471717414151252155668199606457707203524755320346651600518104243524390361529345319514013518510431297722039672225/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^21 - 31258280386101701357533702891606783288848248141720095775889939324087375312711893727249351721574254210784460664638419699593266394078896375/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^19 + 208338682983905540018647959488559237110788520959199209463129961323144555710669207706646798769963914395590152816981587362409070819685657875/126835344819221658385434024417135795537803200517472527563969138433374934480856498602165436907743945258117527384*t^17 - 2061408193478679097126969047921258757751233936681972031805194446989801274851771907626832842094848594431971520287120503218978122583039773875/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^15 + 7366670386867589818013719607572721873563357567577853440432518404724579324798371233915920990679747308999089421250402525320070498308661401875/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^13 - 18318221633220581618145501257165529916213894402371429850720897897163255977168521790260399205704624324944054517967988319007179331200819667125/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^11 + 30046879367004143161021907144002955783685578377769250938303514909511624790311884417074889454928970325151480968970739325207866408139967837625/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^9 - 29969941108026587513899181179444863646151457360252542703968219075648129870129061818526934060754750522589742065734891256572907027063447355125/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^7 + 15866679447394958265681328554603097519397139463373046330676490867583126902591356549176288264252983842429309107019270772566512390448757284125/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^5 - 3446892634364763186423430350661686974852850588203105864916585556020146848936572174155526686570131278441454253812648212274007474007519466875/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*t^3 + 173062571740404057416726132494134604500392201631009462106263720853821522066728509795998794387665212830463845524279411963073988063059229375/253670689638443316770868048834271591075606401034945055127938276866749868961712997204330873815487890516235054768*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
Positive weights:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.2290295042495264728 - 3.5340382500485591114e-909j)  +/-  (1.36e-244, 1.36e-244j)
| (9.5999153873671106502 + 5.8961677675662521748e-913j)  +/-  (1.68e-245, 1.68e-245j)
| (11.366367925845271679 + 9.0982639358848678513e-917j)  +/-  (2.27e-247, 2.27e-247j)
| (-7.6160439823731721235 + 6.4252487669265645979e-913j)  +/-  (2.59e-244, 2.59e-244j)
| (10.400430448598917261 + 5.1764941099219783263e-915j)  +/-  (2.82e-246, 2.82e-246j)
| (-9.5999153873671106502 + 1.4664920571532595713e-914j)  +/-  (1.63e-245, 1.63e-245j)
| (3.5379555964245162312 + 4.2248467565547848961e-914j)  +/-  (9.83e-246, 9.83e-246j)
| (-3.5379555964245162312 + 1.071076901421392599e-915j)  +/-  (9.18e-246, 9.18e-246j)
| (-11.366367925845271679 + 1.0049838491637263986e-916j)  +/-  (2.23e-247, 2.23e-247j)
| (5.5746342077876410169 + 2.4116387555531284868e-912j)  +/-  (4.39e-244, 4.39e-244j)
| (5.1481977652724566272 + 1.6543035524033856397e-923j)  +/-  (3.11e-244, 3.11e-244j)
| (2.4493260905130791576 + 1.8345829309709610827e-942j)  +/-  (7.88e-248, 7.88e-248j)
| (-10.400430448598917261 - 9.3032080534127772528e-941j)  +/-  (2.98e-246, 2.98e-246j)
| (7.6160439823731721235 - 1.6928534725327492713e-941j)  +/-  (2.58e-244, 2.58e-244j)
| (-5.5746342077876410169 + 1.4792400581867848889e-955j)  +/-  (4.77e-244, 4.77e-244j)
| (-7.041587556711086616 - 2.2750162174159515197e-955j)  +/-  (4e-244, 4e-244j)
| (8.8858352807964073612 + 6.1102534456848924202e-957j)  +/-  (5.51e-245, 5.51e-245j)
| (-5.1481977652724566272 + 9.1620790110724325065e-966j)  +/-  (3.12e-244, 3.12e-244j)
| (-1.7320508075688772935 + 9.974830853234774146e-974j)  +/-  (2.5e-249, 2.5e-249j)
| (-2.8507128874867724365 + 3.6837791501629084318e-971j)  +/-  (7.17e-247, 7.17e-247j)
| (2.8507128874867724365 - 1.5236773497808946917e-969j)  +/-  (6.65e-247, 6.65e-247j)
| (1.0205995233277591225 - 4.8357106528349303206e-977j)  +/-  (1.23e-251, 1.23e-251j)
| (-6.5070736248349749985 + 1.1104183855300979963e-968j)  +/-  (4.8e-244, 4.8e-244j)
| (-1.0205995233277591225 + 1.2915155409772592244e-978j)  +/-  (1.23e-251, 1.23e-251j)
| (6.5070736248349749985 + 1.4331611691888609352e-970j)  +/-  (4.86e-244, 4.86e-244j)
| (-4.331905305784102388 - 2.459631867724372248e-985j)  +/-  (7.95e-245, 7.95e-245j)
| (1.7320508075688772935 + 3.9811535154424075352e-991j)  +/-  (2.45e-249, 2.45e-249j)
| (7.041587556711086616 - 6.9570667808929922467e-987j)  +/-  (3.92e-244, 3.92e-244j)
| (-2.4493260905130791576 - 1.9019153131298689592e-999j)  +/-  (7.82e-248, 7.82e-248j)
| (-3.1818251743752155138 - 1.4370894671290685519e-996j)  +/-  (2.92e-246, 2.92e-246j)
| (-8.8858352807964073612 - 5.0713622872849448873e-996j)  +/-  (5.43e-245, 5.43e-245j)
| (-8.2290295042495264728 - 1.4821306145505520423e-995j)  +/-  (1.32e-244, 1.32e-244j)
| (4.7297437340900698938 + 1.9273946248344151444e-994j)  +/-  (1.67e-244, 1.67e-244j)
| (4.331905305784102388 + 4.8297544070570555616e-1004j)  +/-  (8.07e-245, 8.07e-245j)
| (-1.6809825272698164793e-1039 - 4.4583987372182187e-1039j)  +/-  (2.33e-1037, 2.33e-1037j)
| (-0.2645038383451557269 + 3.005163484772497843e-1021j)  +/-  (6.78e-254, 6.78e-254j)
| (0.2645038383451557269 - 3.2105833043276873006e-1021j)  +/-  (6.78e-254, 6.78e-254j)
| (1.4413941089583441416 + 7.5005807626087575688e-1018j)  +/-  (3.14e-250, 3.14e-250j)
| (2.0300538192074472479 + 1.1379270670603486907e-1015j)  +/-  (1.2e-248, 1.2e-248j)
| (-1.4413941089583441416 - 4.6225765910803476528e-1018j)  +/-  (3.06e-250, 3.06e-250j)
| (-0.60175639427798112939 + 8.7634682891451001399e-1022j)  +/-  (6.49e-253, 6.49e-253j)
| (-3.938157784076607613 + 5.8085385528919208835e-1013j)  +/-  (3.4e-245, 3.4e-245j)
| (3.938157784076607613 + 2.3507193414317495933e-1011j)  +/-  (3.14e-245, 3.14e-245j)
| (0.60175639427798112939 - 6.5847807309207488319e-1028j)  +/-  (6.49e-253, 6.49e-253j)
| (6.0190000588018053598 + 4.1185582021655279058e-1020j)  +/-  (5.38e-244, 5.38e-244j)
| (-4.7297437340900698938 + 1.1738751251187434858e-1028j)  +/-  (1.7e-244, 1.7e-244j)
| (-2.0300538192074472479 - 5.4179070907915540216e-1035j)  +/-  (1.13e-248, 1.13e-248j)
| (3.1818251743752155138 - 8.7444389475528590114e-1034j)  +/-  (3.09e-246, 3.09e-246j)
| (-6.0190000588018053598 + 4.6284586906593415567e-1037j)  +/-  (5.04e-244, 5.04e-244j)
-------------------------------------------------
The weights are:
| (4.9896618340942612516e-16 + 9.9112031296577391975e-924j)  +/-  (2.55e-79, 5.64e-201j)
| (2.9122203008380525809e-21 - 4.9028420655001268243e-928j)  +/-  (9.74e-83, 2.15e-204j)
| (3.9262183874518687473e-29 - 3.6660422195922259023e-933j)  +/-  (6.52e-87, 1.44e-208j)
| (6.009248140659015698e-14 - 3.1753340797472503308e-924j)  +/-  (2.32e-81, 5.12e-203j)
| (1.1160408446740455685e-24 + 2.4163647266115690134e-930j)  +/-  (7.98e-85, 1.76e-206j)
| (2.9122203008380525809e-21 + 3.8810416000028826204e-929j)  +/-  (2.72e-86, 6.01e-208j)
| (0.00029759088981702077197 + 1.8575272753056254243e-915j)  +/-  (1.89e-67, 4.17e-189j)
| (0.00029759088981702077197 + 7.3545020739142264331e-916j)  +/-  (1.49e-68, 3.3e-190j)
| (3.9262183874518687473e-29 + 5.9893006340849955038e-934j)  +/-  (4.63e-90, 1.02e-211j)
| (3.066645715924690037e-08 - 1.2877768007154904066e-918j)  +/-  (7.08e-76, 1.56e-197j)
| (2.9737392093782296455e-07 + 6.8807859206328747581e-918j)  +/-  (1.34e-74, 2.95e-196j)
| (0.0084463112484661029573 - 2.2378927757732712512e-914j)  +/-  (8.91e-64, 1.97e-185j)
| (1.1160408446740455685e-24 - 2.8851462916815049742e-931j)  +/-  (7.64e-89, 1.69e-210j)
| (6.009248140659015698e-14 - 8.3988145179244711414e-923j)  +/-  (2e-81, 4.43e-203j)
| (3.066645715924690037e-08 - 1.8412942168707013643e-919j)  +/-  (2.97e-79, 6.57e-201j)
| (3.7879655010963945353e-12 + 7.8075788220088701121e-923j)  +/-  (9.06e-83, 2e-204j)
| (1.9470101081005090722e-18 + 6.5839191089593140061e-926j)  +/-  (5.51e-85, 1.22e-206j)
| (2.9737392093782296455e-07 + 1.3397466881642403649e-918j)  +/-  (1.66e-78, 3.67e-200j)
| (0.019575756450692364201 - 8.3477850636338084013e-914j)  +/-  (1.92e-65, 4.25e-187j)
| (0.0025026763179032799717 + 5.357990893347414175e-915j)  +/-  (1.57e-71, 3.47e-193j)
| (0.0025026763179032799717 + 1.115885739873377519e-914j)  +/-  (2.7e-71, 5.97e-193j)
| (0.10255873813385394478 - 1.6231008166411768477e-913j)  +/-  (4.89e-61, 1.08e-182j)
| (1.306522850401533586e-10 - 1.4430732032922261677e-921j)  +/-  (5.1e-82, 1.13e-203j)
| (0.10255873813385394478 - 1.2594678421882018516e-913j)  +/-  (4.77e-62, 1.05e-183j)
| (1.306522850401533586e-10 - 1.1399445719234810903e-920j)  +/-  (5.87e-82, 1.3e-203j)
| (1.3101182982283476426e-05 + 4.1219085790363829076e-917j)  +/-  (1.13e-77, 2.5e-199j)
| (0.019575756450692364201 - 1.2895234127239716788e-913j)  +/-  (6.45e-69, 1.43e-190j)
| (3.7879655010963945353e-12 + 9.6648537268978014813e-922j)  +/-  (7.04e-83, 1.56e-204j)
| (0.0084463112484661029573 - 1.1985425223163663887e-914j)  +/-  (2.36e-72, 5.21e-194j)
| (0.00081321410069666649114 - 2.4225237826768824695e-915j)  +/-  (1.96e-74, 4.34e-196j)
| (1.9470101081005090722e-18 - 2.6208516940868671835e-927j)  +/-  (4.45e-89, 9.83e-211j)
| (4.9896618340942612516e-16 + 1.1286828233102639195e-925j)  +/-  (1.52e-87, 3.36e-209j)
| (2.2648666001269540758e-06 - 3.3541316577552558538e-917j)  +/-  (2.34e-81, 5.17e-203j)
| (1.3101182982283476426e-05 + 1.4173209378487073012e-916j)  +/-  (6.62e-81, 1.46e-202j)
| (0.10577551057987557538 + 7.1435078948843259602e-913j)  +/-  (7.2e-71, 1.59e-192j)
| (0.10784141634270339713 - 5.2559162729207287344e-913j)  +/-  (3.57e-71, 7.88e-193j)
| (0.10784141634270339713 - 5.6111917894128261745e-913j)  +/-  (3.19e-71, 7.05e-193j)
| (0.054557246393840920568 + 1.4758090550978856129e-913j)  +/-  (5.05e-74, 1.12e-195j)
| (0.019883420850007722102 + 6.4376517681639547709e-914j)  +/-  (1.02e-75, 2.24e-197j)
| (0.054557246393840920568 + 1.0294751645777929126e-913j)  +/-  (4.33e-75, 9.55e-197j)
| (0.13055166995745470443 + 2.5145624365304768129e-913j)  +/-  (2.97e-73, 6.56e-195j)
| (6.8507287321471633042e-05 - 1.7492252318965314389e-916j)  +/-  (8.68e-81, 1.91e-202j)
| (6.8507287321471633042e-05 - 5.2588732931796673493e-916j)  +/-  (1.03e-80, 2.28e-202j)
| (0.13055166995745470443 + 2.9186754037256568711e-913j)  +/-  (1.76e-75, 3.88e-197j)
| (2.5128432658393458849e-09 + 1.0443666929590100425e-919j)  +/-  (1.01e-84, 2.24e-206j)
| (2.2648666001269540758e-06 - 8.2807252465162859832e-918j)  +/-  (4.77e-83, 1.05e-204j)
| (0.019883420850007722102 + 3.8555550025204821871e-914j)  +/-  (7.78e-79, 1.77e-200j)
| (0.00081321410069666649114 - 5.507328182712637345e-915j)  +/-  (1.79e-80, 4.28e-202j)
| (2.5128432658393458849e-09 + 1.9534813249142297125e-920j)  +/-  (8.08e-86, 1.76e-207j)
