Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 37
-------------------------------------------------
Trying to find an order 37 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^40 + 8148763327054863743494950442836706903698900446327970969848437724691811984841145853766113031152202641/27066379837767945636124854807435125048119820632224435394180682521055983598797236795516229308029820*t^39 - 2273511908275836381682766498769994451885926153862875775025596579788266823400188818831921974484627902817/9022126612589315212041618269145041682706606877408145131393560840351994532932412265172076436009940*t^38 + 10041007457766770835514974141727020940284073059528199112951976886112516413274001292599998584115154689285147/76688076207009179302353755287732854303006158457969233616845267142991953529925504253962649706084490*t^37 - 3653195763332514256639588156466239949503077208432663170796696215018354666936380846016491457662906404683124379/76688076207009179302353755287732854303006158457969233616845267142991953529925504253962649706084490*t^36 + 497024292850909570846562037944636005213475121446482980912073277468618371043246982087065296057195981661044037682/38344038103504589651176877643866427151503079228984616808422633571495976764962752126981324853042245*t^35 - 430241268559438195784665769892556919279743756777502263598875529071564511129212912899397949528066624228010669174/156506277973488121025211745485169090414298282567284150238459728863248884754950008681556427971601*t^34 + 4302247519076631391701288418329557932434597648091305639270570129842979337694781752383582833042418728598886076972/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^33 - 4186424049357716234864470733986522250460430008840995364932052217538835003312056507462384415938145896632154701867044/64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071*t^32 + 482971151893964691940586223172016403418039779805861547987626881779570804536675664892985715291683775780987104718734848/64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071*t^31 - 46758329939951663040723919525656585517942216662767344339688404928886969837598626035410363973379198821934077234724684288/64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071*t^30 + 3831232906817086784018393461512522900545582818678283478888332571097695552755463836684483640031523491882029002223205309440/64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071*t^29 - 267405341016161728512321786271122362694775421547456501732255341963362287411942175797229211610655152078691079507625036119040/64443761518495108657440130493893154876475763410058179509954006002514246663802944751229117400071*t^28 + 2282341152461768587093337189270780656987201014379206660817028179980615837628831639259530089652840865575266953344945032990720/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^27 - 117147887808024895358332043177090729969664722347666090019899240444126475524339311464602968126375758947275382290251429204029440/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^26 + 5178873596274173981584225937849878851980486870337022850477702067547171467307351683421016273297313917776238745459687300166410240/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^25 - 197506281629379525219708379878610539026430912182180114628307424076736693663637219581223905853464437869397369683799062317624320000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^24 + 6502928195896254992140066421277369079252084030109680700932242436653745348349633674881396190393398380259852319567845691880017920000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^23 - 184852780549841021913823121436532184511376939800244632404383125236239836479469906416218479596978948845819603938731348199469854720000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^22 + 4533406476311432672632569644480277292191148157367594945113961713397937989335810316918031359296071080288446523094420451559887216640000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^21 - 95783604078968125742219464955639286974852228536085208447300310729405552762535750947229596115486165853754148410959904752036050903040000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^20 + 1739817912247697316397717574974021677841904345427680989989800574461302703009301533920193678049687820486829088567873181070270253465600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^19 - 27090863491262335977760859778132117781112912914407260928759115206211410324575761400585202884779103742770960315912236393896936040857600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^18 + 360306264338615759161941487260679851380286528193454455728539057019838328422817767264051637010198362610073959178658044550770718161305600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^17 - 4074822780772494784093336879792160241592616764386231810360571767515013783160818246505610944539703995710466724601933423553017185522483200000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^16 + 38975005092716478588387497064274986322975193301621800849667176779372580954028682284590245797847199987502239254219482929479746523181875200000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^15 - 313254627783132631495064621653153623601372387419793418629626098028704263920434630640738007120259120352746381347565125789715442455386521600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^14 + 2099448740964660345126868923995946570422256956386418349937678064731164378803774022996167266626379841041579109937497651101184145427110297600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^13 - 11626442468458204239517932802818708417636766169588879229021601639133946345973668237406683217068638583573799595330193286332813965432822169600000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^12 + 52626957946889334953219162375333771646105922026617200559352489728310576087121396340401784276988429047821246405350856689136143321275773747200000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^11 - 192200360008199232107300788111972625890673351132828270901716915483699323980538968596833169417794303704483568671454485003249928159725040435200000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^10 + 557562433672975098167503609125445982889961476670014992418707998329764938579011650838627426586385452500770057944666950427550298891551244288000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^9 - 1260512967236050289905257578262462767242009145756791180176360648382754224643634269289760503965873119750174600924295063592210808364322521088000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^8 + 2169010315574555755048539971627061273461718058546536778301322721787843157297669233828890063721260556842695265621824757113664818296251219968000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^7 - 2757130040173329590402276325772509787143765530862872862036443427122560819174862020154902409568101423579328927686552530042194426445279789056000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^6 + 2490028052962415682410134842928481151730065351621711049093374120744379119185039843661764888088452826949985852795014502538784378576422567936000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^5 - 1515159810200614467896931230750882321328711899706885140056854447831899084295331636156058334728986649803328256972931960414769910917030215680000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^4 + 575235466954992595717133023085664872796896464178562916467536185697227802664792339901411934654637962894721830326626693133004665191797882880000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^3 - 120580560979983871802951313687557729390660929170209488201042467538065851873660734557034751273884169732036233253901399681144416784749690880000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t^2 + 11128413564917128354275472347326575202043217660100243666625545339589098869228574540281978897721045212899737357424130858375599793907957760000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153*t - 257191607956165021276410726824683546309504642050741990951457227013931294452444360726711831874662848504170302217688180201095462607912960000000/9206251645499301236777161499127593553782251915722597072850572286073463809114706393032731057153
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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:
| (362.35024106871380022 - 7.3247492910397003264e-557j)  +/-  (1.21e-247, 1.21e-247j)
| (85.055166795313084497 + 3.0309885208245146506e-544j)  +/-  (7.31e-237, 7.31e-237j)
| (78.38945572569035159 - 4.1183748711543800621e-559j)  +/-  (1.81e-236, 1.81e-236j)
| (72.257066840006992149 - 2.2202819605273009095e-582j)  +/-  (3.44e-236, 3.44e-236j)
| (100.48097474498165405 - 9.3101910186024443065e-597j)  +/-  (5.27e-238, 5.27e-238j)
| (120.47521345413333075 + 2.1808413952740843259e-614j)  +/-  (6.86e-240, 6.86e-240j)
| (47.450948762728838789 + 4.2045422476880271592e-645j)  +/-  (9.46e-236, 9.46e-236j)
| (51.768015963857398219 - 2.8680371970932638878e-684j)  +/-  (1.03e-235, 1.03e-235j)
| (66.580170753905852065 + 6.7090680835528504461e-705j)  +/-  (6.23e-236, 6.23e-236j)
| (109.67790834667199166 + 7.0179017432601103267e-716j)  +/-  (7.74e-239, 7.74e-239j)
| (134.21305167028985641 + 2.3281443574152335702e-721j)  +/-  (2.62e-241, 2.62e-241j)
| (92.364011056744960444 + 2.2665141389678703892e-716j)  +/-  (2.39e-237, 2.39e-237j)
| (7.6365028252698677246 - 7.7530937139501378226e-729j)  +/-  (9.28e-243, 9.28e-243j)
| (56.375306989273960561 + 5.1357663529323932448e-721j)  +/-  (1.06e-235, 1.06e-235j)
| (9.125153831612906719 - 7.7145561265894823927e-738j)  +/-  (5.97e-242, 5.97e-242j)
| (39.598750605634248462 - 7.696658375865529693e-731j)  +/-  (5.68e-236, 5.68e-236j)
| (2.2942803602790417198 + 7.0031612030401404025e-750j)  +/-  (2.57e-247, 2.57e-247j)
| (12.539840421758880575 + 1.7490487757520782811e-742j)  +/-  (1.69e-240, 1.69e-240j)
| (14.472654135692662713 + 7.4631854926643024377e-742j)  +/-  (8.69e-240, 8.69e-240j)
| (5.0833616221631849166 - 3.0883184879746692119e-747j)  +/-  (1.69e-244, 1.69e-244j)
| (21.224664676291763358 + 4.1234810815652450532e-739j)  +/-  (4.15e-238, 4.15e-238j)
| (0.7379496200907535497 + 8.1338752311028748762e-753j)  +/-  (2.23e-250, 2.23e-250j)
| (10.758551764034145248 + 3.793521369885649146e-743j)  +/-  (3.21e-241, 3.21e-241j)
| (4.0152978662397656555 - 6.7855980941323914546e-748j)  +/-  (1.89e-245, 1.89e-245j)
| (23.811107477774379559 + 4.5009314497351417804e-738j)  +/-  (1.27e-237, 1.27e-237j)
| (6.2899450829374791969 - 7.4049422955370966791e-751j)  +/-  (1.23e-243, 1.23e-243j)
| (1.6450466479456830663 + 4.5507072257299672642e-756j)  +/-  (2.7e-248, 2.7e-248j)
| (18.810032378294138631 - 4.1273747636967131884e-743j)  +/-  (1.28e-238, 1.28e-238j)
| (61.301030475400501162 + 1.8130198318613232852e-744j)  +/-  (8.44e-236, 8.44e-236j)
| (36.028083568300484881 + 5.4761638315082692231e-762j)  +/-  (3.37e-236, 3.37e-236j)
| (43.400953976589364242 - 1.2415621640058022996e-775j)  +/-  (8.02e-236, 8.02e-236j)
| (0.41577455678347908331 - 1.3972193256565989846e-797j)  +/-  (1.21e-251, 1.21e-251j)
| (0.17405942884392781865 + 9.67112511947308528e-800j)  +/-  (4.61e-253, 4.61e-253j)
| (0.033477401740240545328 - 3.5417834261423990293e-800j)  +/-  (8.3e-255, 8.3e-255j)
| (3.0852615701792661758 + 1.4087864814952264648e-793j)  +/-  (2.16e-246, 2.16e-246j)
| (16.561145378418001833 - 1.0901046519279837636e-784j)  +/-  (3.37e-239, 3.37e-239j)
| (29.527926894647967142 + 7.7993659060563089348e-782j)  +/-  (7.59e-237, 7.59e-237j)
| (1.1355096713849043874 - 7.7102056199155599533e-797j)  +/-  (2.55e-249, 2.55e-249j)
| (26.576247738956842554 - 7.1815919155460025192e-783j)  +/-  (3.25e-237, 3.25e-237j)
| (32.675107432540119127 + 8.6722501538478042224e-782j)  +/-  (1.72e-236, 1.72e-236j)
-------------------------------------------------
The weights are:
| (6.2475829669965773747e-102 + 1.7122037769951982474e-614j)  +/-  (1.11e-101, 4.66e-217j)
| (8.0160185068225331691e-37 - 1.2249968151661296686e-580j)  +/-  (2.04e-77, 8.61e-193j)
| (5.7674034381502466742e-34 + 1.007209314344323187e-579j)  +/-  (2.99e-76, 1.26e-191j)
| (2.4520957428894465925e-31 - 1.1156330394697833474e-578j)  +/-  (2.32e-75, 9.75e-191j)
| (1.9773378766301902014e-43 + 7.3951393717320737206e-585j)  +/-  (2.3e-81, 9.67e-197j)
| (5.6762971342785313019e-52 + 1.6373837270896000644e-589j)  +/-  (4.1e-85, 1.73e-200j)
| (1.0315587360526965488e-20 + 9.2754939863140777231e-574j)  +/-  (6.43e-72, 2.71e-187j)
| (1.4674763593007343408e-22 - 1.2032097588913686882e-574j)  +/-  (5.39e-73, 2.27e-188j)
| (6.6460116864209810752e-29 + 1.3138808247935497497e-577j)  +/-  (7.39e-76, 3.11e-191j)
| (2.3017931144597665744e-47 - 4.8672713862266549002e-587j)  +/-  (4.94e-84, 2.08e-199j)
| (8.4046877565765956031e-58 - 1.3993831490445915732e-592j)  +/-  (8.24e-89, 3.47e-204j)
| (5.9173046604535632036e-40 - 8.7769979397529680232e-583j)  +/-  (6.95e-81, 2.93e-196j)
| (0.00068381933803710204676 - 2.9561744581604566118e-565j)  +/-  (3.68e-57, 1.55e-172j)
| (1.5640178168885304312e-24 + 1.3902126649581495303e-575j)  +/-  (1.25e-75, 5.25e-191j)
| (0.00016993043532548454479 + 1.356034905298917268e-565j)  +/-  (1.13e-59, 4.75e-175j)
| (2.3377291036143347599e-17 + 3.9622433112009047595e-572j)  +/-  (7.84e-74, 3.3e-189j)
| (0.072662425737554179853 + 6.245295312993107115e-564j)  +/-  (7.65e-48, 3.22e-163j)
| (6.6479676151834872585e-06 + 2.3548779356086968516e-566j)  +/-  (7.95e-64, 3.34e-179j)
| (1.0417988947124045271e-06 - 8.869222444273650761e-567j)  +/-  (1.55e-65, 6.52e-181j)
| (0.0070492174034517025195 - 1.1763276759749185277e-564j)  +/-  (4.02e-57, 1.69e-172j)
| (1.5138812626548279853e-09 + 3.0668545687807492782e-568j)  +/-  (3.88e-70, 1.63e-185j)
| (0.17056650364581255302 - 1.2095192262976100546e-563j)  +/-  (3.91e-53, 1.65e-168j)
| (3.6290890496810913525e-05 - 5.8398068549161999402e-566j)  +/-  (3.03e-63, 1.28e-178j)
| (0.01802083503281008133 + 2.1614843409707435353e-564j)  +/-  (2.65e-57, 1.11e-172j)
| (1.2196107284623351971e-10 - 8.565260511388267481e-569j)  +/-  (1.35e-71, 5.67e-187j)
| (0.0023672979269672107758 + 6.0676421289760044097e-565j)  +/-  (1.44e-60, 6.06e-176j)
| (0.11150485359515461498 - 9.5286882685910284619e-564j)  +/-  (5.05e-55, 2.13e-170j)
| (1.5791155065013538629e-08 - 1.0148150974156083676e-567j)  +/-  (2.78e-69, 1.17e-184j)
| (1.2148533789275865225e-26 - 1.4286194127036671456e-576j)  +/-  (1.18e-79, 4.95e-195j)
| (7.8025986102647874344e-16 - 2.2170531778025297305e-571j)  +/-  (4.21e-76, 1.77e-191j)
| (5.5570123312927095472e-19 - 6.3949393761739837393e-573j)  +/-  (4.15e-77, 1.75e-192j)
| (0.18854282400227143905 + 8.7002043888134740047e-564j)  +/-  (3.47e-60, 1.46e-175j)
| (0.16290175082529829452 - 4.5374588053871234566e-564j)  +/-  (1.62e-60, 6.81e-176j)
| (0.082845069271109694442 + 1.2924881533808693472e-564j)  +/-  (7.62e-61, 3.21e-176j)
| (0.039356009335569416905 - 3.774516932795822647e-564j)  +/-  (1.04e-63, 4.36e-179j)
| (1.391924575726292699e-07 + 3.1121651079296802163e-567j)  +/-  (2.09e-70, 8.81e-186j)
| (4.5727289005251840594e-13 - 5.2070952984569372286e-570j)  +/-  (1.56e-75, 6.58e-191j)
| (0.14328532616549410796 + 1.2307343850919615173e-563j)  +/-  (1.15e-65, 4.85e-181j)
| (8.2034184741331511882e-12 + 2.2039008814817403921e-569j)  +/-  (7.66e-75, 3.22e-190j)
| (2.0942531055920460427e-14 + 1.1255552930128785667e-570j)  +/-  (2.86e-76, 1.2e-191j)
