Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 10 29
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P2 : 35/8*t^14 - 436215/27784*t^12 + 12954799/583464*t^10 - 3039465/194488*t^8 + 2679105/472328*t^6 - 8846695/8974232*t^4 + 1485/22952*t^2 - 273/390184
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^43 - 10000227296659883079139015133943534348726535017424488730133384744027541918078231243115178574119104217955/212297719938719737386601898842419941615401363985081421883000980082286530737677151700432936481157531104*t^41 + 35494055504501434990250788310063746847036111405655558588128034314157881622119789169885065888545495593787243/150605329385277398700414053300680471706600823869541667442687664026499579196125281898485252845586159799747*t^39 - 117426413850339318664299475221826984424693643512062093673187589706249372352099834729984558739246391851287357883/161448913101017371406843865138329465669476083188148667498561175836407548898246302195176191050468363305328784*t^37 + 1519224392365616821517797744656749721283006724415532087875661697474060484565862738683384398274783353615872034259/980225543827605469255837752625571755850390505070902624098407139006760118310781120470712588520700777210924760*t^35 - 6359808410157845295075296605381751905800322338820058794541010456670397879693019897585405264268228302135833028311/2629310870502282905768600089395651298045753354778421156405139149335780082057154064321440825679056202401068768*t^33 + 14343005491135325960153305358220141174643089699283482302496572222652916342456911995399751047805645671359343832706/5012123846894976789121393920410460286899717332546365329397296503421330781421449935112746573950700885827037339*t^31 - 134783894271109990314566900297809824366172134854068900796970283857191039685661539146205164831794093539245416011983/51428749037704979227506476748559505552536230020910531205989651078584089757194008029852530063146322132833948348*t^29 + 10748367072316966430928240880849717908607299986225031957752096729060326558793543976739106231581292308104295712281/5714305448633886580834052972062167283615136668990059022887739008731565528577112003316947784794035792537105372*t^27 - 851509589190033604146400956646576800281168744459648358810798920426850029283159543641946847563198438346136651009689/800002762808744121316767416088703419706119133658608263204283461222419174000795680464372689871165010955194752080*t^25 + 90325437173545168419508020586565239449579337022731348535677816971419426339545763817697556393661873106909445290240/190000656167076728812732261321067062180203294243919462511017322040324553825188974110288513844401690101858753619*t^23 - 616528991222991374480407986671614952781207954451964440873321456277915942736662463401729779996104169578866343987565/3691441319817490731218798219952160065215378288167578128785479399640591331460814354142748268976947121978970070312*t^21 + 84510839437542331224981123515230803738991632625553488442332087780177023933788202430728304487601487739225743234445/1845720659908745365609399109976080032607689144083789064392739699820295665730407177071374134488473560989485035156*t^19 - 176582613325815867344653811933456100738553168620142511457064545138187432160808556214300750597921739795306568155845/18262920213833901512345633298710686638433976794092228637149213871906083429332449962600965120201738392948588768912*t^17 + 16472215423381481534054657660796961160219983429069121316160111754776319472069632282596219724749046378144743970966/10675751154410258604643219465055144027613979081840677769510018403062747298764189500196887698941457369407447111239*t^15 - 54130125484200504787556922537275781500069712633291273403487438784699219233013041799808771797864744056803947553985/298921032323487240930010145021544032773191414291538977546280515285756924365397306005512855570360806343408519114692*t^13 + 62934972873545285050745760634673980193133004618502447273836182226184958534748908138946137902648723789476888509305/4184894452528821373020142030301616458824679800081545685647927214000596941115562284077179977985051288807719267605688*t^11 - 4661640053804370337827575677957845059785436698162222675814938861552404640694003824375900842512808326522866522085/5579859270038428497360189373735488611766239733442060914197236285334129254820749712102906637313401718410292356807584*t^9 + 709491296770422110910809608892039356450753508366887588082974087159236703672227449028335215381551244172779645/24910086026957270077500845418462002731099284524294914795523376273813077030449775500459404630863400528617376592891*t^7 - 205519923224012171406123527470415496841408588431791361233334387272324811670586722024144341874509409304348081/398561376431316321240013526695392043697588552388718636728374020381009232487196408007350474093814408457878025486256*t^5 + 32230449428658236859817035842922543990096112326147487381529499055581796350032515223295049603988344043265/8664377748506876548695946232508522689078012008450405146269000443065418097547748000159792915082921922997348380136*t^3 - 376687886559678772043501607530195441648165943065488600939024117240351181637876943442081779407997478295/84168240985495372187332049115797077551043545224946792849470290018349775804749552001552274032234098680545669978464*t
-------------------------------------------------
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: 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:
| (-0.99893549269777725407 + 1.3891823894391203507e-915j)  +/-  (2.1e-240, 2.1e-240j)
| (0.97217434831073791571 + 3.8540069931885323623e-924j)  +/-  (3.99e-240, 3.99e-240j)
| (-0.92774812921769162233 + 3.2306610590575861254e-925j)  +/-  (1.06e-240, 1.06e-240j)
| (0.98588837552317212171 + 4.2671782195199531146e-928j)  +/-  (5.49e-240, 5.49e-240j)
| (0.8199768406755148703 + 1.7459946439249571488e-931j)  +/-  (2.79e-242, 2.79e-242j)
| (0.99893549269777725407 - 2.4506826521108567014e-931j)  +/-  (2.03e-240, 2.03e-240j)
| (-0.41135182402411033794 + 2.2140173603262902701e-937j)  +/-  (1.28e-248, 1.28e-248j)
| (-0.89713180012258579561 + 4.3644738841591039403e-930j)  +/-  (3.48e-241, 3.48e-241j)
| (-0.97217434831073791571 - 4.0576623222067064589e-928j)  +/-  (3.98e-240, 3.98e-240j)
| (0.48025516436971419274 + 7.7709224840334231876e-952j)  +/-  (1.77e-247, 1.77e-247j)
| (0.77389784997984473677 - 6.2777088918452247999e-948j)  +/-  (5.89e-243, 5.89e-243j)
| (-0.3399810435848562648 - 1.8129919984178039423e-954j)  +/-  (7.18e-250, 7.18e-250j)
| (-0.95280406968027788258 + 1.0253097557687713868e-943j)  +/-  (2.35e-240, 2.35e-240j)
| (-0.86113631159405257522 + 2.1582128948253470961e-956j)  +/-  (1.03e-241, 1.03e-241j)
| (0.99444997880691468328 + 1.7702812608411108905e-965j)  +/-  (5.23e-240, 5.23e-240j)
| (0.54627694908708365616 + 3.2096924260515397982e-973j)  +/-  (2.12e-246, 2.12e-246j)
| (0.89713180012258579561 + 2.0229712725979375196e-966j)  +/-  (3.41e-241, 3.41e-241j)
| (-0.98588837552317212171 - 3.7944762762288490594e-978j)  +/-  (6.71e-240, 6.71e-240j)
| (-0.72317255923281838433 + 1.5005630796652638739e-1003j)  +/-  (1.19e-243, 1.19e-243j)
| (-0.99444997880691468328 - 2.2482239683301616186e-1016j)  +/-  (5.84e-240, 5.84e-240j)
| (0.95280406968027788258 - 6.5687627143084208713e-1035j)  +/-  (2.26e-240, 2.26e-240j)
| (0.86113631159405257522 + 1.3992296279973956823e-1037j)  +/-  (1.06e-241, 1.06e-241j)
| (0.11539569344883949077 - 4.0514985607774736311e-1051j)  +/-  (1.03e-253, 1.03e-253j)
| (-0.8199768406755148703 + 3.7525745487468390827e-1039j)  +/-  (2.77e-242, 2.77e-242j)
| (-0.77389784997984473677 + 1.7501947630891917931e-1040j)  +/-  (5.93e-243, 5.93e-243j)
| (0.19155914238284693361 + 2.657174428162318136e-1050j)  +/-  (2.01e-252, 2.01e-252j)
| (0.72317255923281838433 - 4.7581176301896501083e-1040j)  +/-  (1.07e-243, 1.07e-243j)
| (0.92774812921769162233 + 6.2382983501159005678e-1044j)  +/-  (1.05e-240, 1.05e-240j)
| (-0.11539569344883949077 + 9.9896768562101789455e-1057j)  +/-  (1.06e-253, 1.06e-253j)
| (-0.6681029835901517016 + 1.8859532682355836858e-1048j)  +/-  (1.42e-244, 1.42e-244j)
| (-0.19155914238284693361 - 2.1625342891178898079e-1057j)  +/-  (2.05e-252, 2.05e-252j)
| (0.41135182402411033794 + 6.8860946755623771408e-1053j)  +/-  (1.21e-248, 1.21e-248j)
| (0.6681029835901517016 + 2.3769972748804063825e-1050j)  +/-  (1.63e-244, 1.63e-244j)
| (-8.7341584963050070879e-1067 - 2.1678949143377370696e-1066j)  +/-  (1.01e-1064, 1.01e-1064j)
| (-0.54627694908708365616 + 3.2680339294868927156e-1051j)  +/-  (2.01e-246, 2.01e-246j)
| (-0.48025516436971419274 - 1.9492256160778554985e-1052j)  +/-  (1.64e-247, 1.64e-247j)
| (0.038531374089383882299 - 6.5457102736477074919e-1061j)  +/-  (4.85e-255, 4.85e-255j)
| (0.60901913582877133643 + 7.6691972112351413229e-1054j)  +/-  (2e-245, 2e-245j)
| (0.3399810435848562648 + 1.0252485270719597782e-1057j)  +/-  (7.58e-250, 7.58e-250j)
| (-0.26657044191236231761 + 8.1479657489046877487e-1057j)  +/-  (4.47e-251, 4.47e-251j)
| (-0.60901913582877133643 - 1.9365708129057081488e-1053j)  +/-  (2.05e-245, 2.05e-245j)
| (-0.038531374089383882299 + 3.0432715915362551596e-1063j)  +/-  (6.33e-255, 6.33e-255j)
| (0.26657044191236231761 - 1.1913523702340618049e-1059j)  +/-  (4.31e-251, 4.31e-251j)
-------------------------------------------------
The weights are:
| (0.0027110959253106720995 + 1.6399336829816072846e-915j)  +/-  (1.74e-78, 9.92e-194j)
| (0.01651339050086864988 - 8.3259031770595954103e-918j)  +/-  (6.62e-79, 3.77e-194j)
| (0.027862958814293976887 - 2.2097782586262342678e-916j)  +/-  (3.38e-79, 1.92e-194j)
| (0.010990374251202506271 + 7.6882625313697258827e-918j)  +/-  (4.36e-79, 2.48e-194j)
| (0.043662364941697255251 + 8.3778492462462753005e-918j)  +/-  (7.06e-80, 4.01e-195j)
| (0.0027110959253106720995 + 1.8851095244029940275e-918j)  +/-  (1.2e-79, 6.83e-195j)
| (0.070207278649980500164 - 4.2384098273029527331e-917j)  +/-  (2.23e-80, 1.27e-195j)
| (0.033339226748802724798 + 1.5101489514412475523e-916j)  +/-  (3.98e-80, 2.26e-195j)
| (0.01651339050086864988 - 6.1324996777000242155e-916j)  +/-  (1.63e-80, 9.3e-196j)
| (0.067530340164449415457 + 1.4665726594383785946e-917j)  +/-  (7.51e-82, 4.27e-197j)
| (0.048450083564559851818 - 8.7378887858706481049e-918j)  +/-  (4.7e-81, 2.67e-196j)
| (0.072462980496812817144 + 4.5103204094322919578e-917j)  +/-  (1.91e-81, 1.08e-196j)
| (0.022226829962448139194 + 3.5098560434855736721e-916j)  +/-  (1.66e-80, 9.43e-196j)
| (0.038615831070142865659 - 1.1033103187460720968e-916j)  +/-  (1.64e-81, 9.3e-197j)
| (0.0063424688265891806734 - 5.4330022279999333361e-918j)  +/-  (9.36e-81, 5.32e-196j)
| (0.064446834101244487656 - 1.2594178541300205354e-917j)  +/-  (4.23e-83, 2.41e-198j)
| (0.033339226748802724798 + 8.1082963357310968975e-918j)  +/-  (2.85e-82, 1.62e-197j)
| (0.010990374251202506271 + 1.1695959612583238245e-915j)  +/-  (2.21e-81, 1.26e-196j)
| (0.052950149760615670639 + 5.7957809342761450052e-917j)  +/-  (1.59e-84, 9.04e-200j)
| (0.0063424688265891806734 - 2.4144550069355813651e-915j)  +/-  (1.76e-81, 1e-196j)
| (0.022226829962448139194 + 8.2959181632655155727e-918j)  +/-  (6.81e-83, 3.87e-198j)
| (0.038615831070142865659 - 8.1736236201645000768e-918j)  +/-  (1.72e-83, 9.77e-199j)
| (0.076588348999320960767 - 7.6695777975757475241e-917j)  +/-  (9.03e-87, 5.13e-202j)
| (0.043662364941697255251 + 8.5151360066948595101e-917j)  +/-  (4.18e-84, 2.38e-199j)
| (0.048450083564559851818 - 6.883657269082384669e-917j)  +/-  (1.16e-84, 6.57e-200j)
| (0.075662778839347529475 + 4.3478018631924265652e-917j)  +/-  (6.34e-88, 3.6e-203j)
| (0.052950149760615670639 + 9.2808438616721851879e-918j)  +/-  (2.25e-86, 1.28e-201j)
| (0.027862958814293976887 - 8.1647195536891151287e-918j)  +/-  (1.29e-84, 7.36e-200j)
| (0.076588348999320960767 - 9.6729651741858392285e-917j)  +/-  (6.74e-89, 3.83e-204j)
| (0.057133964075054827482 - 5.0645151188686750593e-917j)  +/-  (1.22e-87, 6.92e-203j)
| (0.075662778839347529475 + 6.4109318705238786422e-917j)  +/-  (7.42e-89, 4.22e-204j)
| (0.070207278649980500164 - 1.765895776303031887e-917j)  +/-  (5.09e-89, 2.9e-204j)
| (0.057133964075054827482 - 1.0050795482831522305e-917j)  +/-  (4.92e-88, 2.8e-203j)
| (-6.2125869769811469408e-05 - 4.0134079586107364507e-916j)  +/-  (1.33e-89, 7.56e-205j)
| (0.064446834101244487656 - 4.2991966898523640296e-917j)  +/-  (4.22e-90, 2.4e-205j)
| (0.067530340164449415457 + 4.18242303562810097e-917j)  +/-  (4.96e-90, 2.82e-205j)
| (0.077074402921833759359 + 2.4611903160468463177e-916j)  +/-  (4.79e-90, 2.72e-205j)
| (0.06097435570102146184 + 1.1117837432967932982e-917j)  +/-  (2.66e-90, 1.51e-205j)
| (0.072462980496812817144 + 2.2197766917593661276e-917j)  +/-  (3.34e-91, 1.9e-206j)
| (0.074285004619287653222 - 5.1199704031367357451e-917j)  +/-  (2.41e-91, 1.38e-206j)
| (0.06097435570102146184 + 4.5848237841172489748e-917j)  +/-  (1.64e-91, 9.36e-207j)
| (0.077074402921833759359 + 2.6586760246850040102e-916j)  +/-  (7.18e-91, 4.16e-206j)
| (0.074285004619287653222 - 2.9629947196200056958e-917j)  +/-  (9.31e-92, 5.16e-207j)
