Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 8 30
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
-------------------------------------------------
Trying to find an order 30 Kronrod extension for:
P2 : 35/8*t^12 - 87219/8284*t^10 + 102069/11336*t^8 - 891429/269230*t^6 + 24664563/47599864*t^4 - 792603/23799932*t^2 + 30429/47599864
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 35/8*t^42 - 12273981785066856558647929240429529366716346211529994546281545350477222618487300681520620859723429458631147103097/285628149246674977278685651271182401226344511628054737418082697916233716494518075757822937542599488518092144592*t^40 + 16679278308566959095598712469327418957916270079207675236612451748760942759380979995742991580349167475487737570649177/85402816624755818206327009730083537966677008976788366488006726676953881231860904651589058325237247066909551233008*t^38 - 2461924752567053884163591235891509085007437630762502793391708933132244488930399961969137703909673724721394194804338793/4517359510941031436703086567301787139816336527456437280023513700544139507264221535518263348255970173802320999430160*t^36 + 2990307278030379225223331445012771623585774311400846622184139895209283184951473481620152618867007490638118242086614931683/2861897828831508116199295443271258879311643068027901564804230046418063849168793150135337106565098970776230430505654032*t^34 - 9448598624190141983229532721781001826484248808903930473332241423092778691804537804522443704354178302519825978730457743/6474881965682145059274424079799228233736749022687560101367036304113266627078717534242844132500223915783326765849896*t^32 + 461377697018199973942771921372949039299885619645075180003147952610849203960826459367857481927970170178344354054516331019943/300373011828977550372270170273926097377164655536987256882467497665966495463495245772292660728751637565146420331159600388*t^30 - 106483403252666110422168726943872155521448057683524549196615976989594315558674728532815582773054161220468235707028272370401/85613563758017755903207439836529660605085578148223421043795083875806875518580770534131724555537906359148013524340175956*t^28 + 1594124695692411575667327324094572736281538725662291085326651353228311420572793273376571684546830272143061383907913135675053/2033322139252921702701176696117579439370782481020306249790133242050413293566293300185628458194025276029765321203079178955*t^26 - 96823173633284566316408410375147836620260249946156729107374459731774282191530703046572613920641907077409845169952135412845/250255032523436517255529439522163623307173228433268461512631783636973943823543790792077348700803110895971116455763591256*t^24 + 1984167338094651229673519959038124151498084609972507247334226314203201133736799450924766228825636681499454418565226073772895/13263516723742135414543060294674672035280181106963228460169484532759619022647820911980099481142564877486469172155470336568*t^22 - 10182411680723549502201060749473062835620845300525224932055654069275443192855003138206118971528732406598224326362433355469465/225479784303616302047232025009469424599763078818374883822881237056913523385012955503661691179423602917269975926642995721656*t^20 + 125325505268272056285994907130281707542002522215103933502093351263761914723412883451130170940793740832463704393142605931205/11867357068611384318275369737340496031566477832546046516993749318784922283421734500192720588390715943014209259296999774824*t^18 - 7749834266270112556929711186920967665402827152256295817016229969740845919606544740612249453895746493810354337872231741544/4101218986946581345286341012169142010909003368600471958078722191050671671476628834625425497458556245012263494021757275123*t^16 + 4169304492151460104971815145893944964820477636879792507436852884033481495008063808504568426829383400948720005203749245745/16404875947786325381145364048676568043636013474401887832314888764202686685906515338501701989834224980049053976087029100492*t^14 - 607564347808004759870753116879777301142406450319248964428830831221319852439898734156506621392903304340289660907083842295/24244849395828235383263934101399248679874501092282986436301709581137522221560692881615445002979222842854821179061517639516*t^12 + 1328309214237801490499254400502884282793864566332979681625589456047613489292801543125261297301428838134889239215952591395/759671947735951375342269935177176458636067700891533575004120233542309029608901710290617276760015649076117730277260886038168*t^10 - 1619119883399663678481219235720362854507444713842053195413798558783437012198169548611970464513295910581050121993932863995/19751470641134735758899018314606587924537760223179872950107126072100034769831444467556049195760406875979060987208783036992368*t^8 + 6722165281377135398910154889125662797351395474930654991542950324755140761747779038272864693700741204598647261727545583/2821638663019247965557002616372369703505394317597124707158160867442862109975920638222292742251486696568437283886969005284624*t^6 - 1373088804440289059214725880418238341787233831155065198253649680098259041406652620598893631045908603797058751718510685/36681302619250223552241034012840806145570126128762621193056091276757207429686968296889805649269327055389684690530597068700112*t^4 + 7333629604537765297779292108378135191158823485198405213713984449421717368742686978689002068597788167521345734933235/30301945641989315108373028097564144207210104193325643594263727576451606137567495549604622058092052784887130831307884535013136*t^2 - 71680516984039435982919510439003235379056923482314554963289187111028293558947116747710868388405661399629312729265/257566537956909178421170738829295225761285885643267970551241684399838652169323712171639287493782448671540612066117018547611656
-------------------------------------------------
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:
| (0.9732162594524303742 + 1.9876802874720422497e-859j)  +/-  (6.37e-242, 6.37e-242j)
| (-0.99791133541218448993 + 5.4726965488890549978e-863j)  +/-  (1.53e-242, 1.53e-242j)
| (-0.92276234388451625867 - 2.0676606120700926091e-862j)  +/-  (6.2e-242, 6.2e-242j)
| (0.99791133541218448993 - 8.7171478287262836395e-860j)  +/-  (1.48e-242, 1.48e-242j)
| (0.89156425086624165 - 2.876363419319818944e-871j)  +/-  (4.87e-242, 4.87e-242j)
| (0.92276234388451625867 + 9.7765210467939999762e-891j)  +/-  (6.51e-242, 6.51e-242j)
| (-0.18035397587349104032 - 1.0861088453890349023e-910j)  +/-  (2.74e-252, 2.74e-252j)
| (-0.89156425086624165 + 1.3093505108947182471e-901j)  +/-  (4.68e-242, 4.68e-242j)
| (-0.9732162594524303742 + 2.5654784597254338019e-903j)  +/-  (6.31e-242, 6.31e-242j)
| (0.98903089924147443685 + 5.1221393391536203054e-916j)  +/-  (4.55e-242, 4.55e-242j)
| (0.86113631159405257522 + 2.408108712246483431e-934j)  +/-  (2.72e-242, 2.72e-242j)
| (-0.98903089924147443685 + 3.2381539116230467297e-942j)  +/-  (4.29e-242, 4.29e-242j)
| (-0.95082892736674805085 + 1.3634430074107154594e-944j)  +/-  (7.39e-242, 7.39e-242j)
| (-0.78041081606004642435 - 6.0705170944003191638e-950j)  +/-  (1.95e-243, 1.95e-243j)
| (0.95082892736674805085 - 2.413192214709756351e-952j)  +/-  (7.06e-242, 7.06e-242j)
| (0.82592388681481513624 - 5.176329995714764434e-968j)  +/-  (9.18e-243, 9.18e-243j)
| (0.78041081606004642435 - 1.7638547455692117172e-977j)  +/-  (1.92e-243, 1.92e-243j)
| (-0.35241611849142175407 + 1.3971886959928125866e-983j)  +/-  (9.6e-248, 9.6e-248j)
| (-0.72698793312645016103 - 2.4764862350233056669e-979j)  +/-  (3.36e-244, 3.36e-244j)
| (-0.86113631159405257522 + 3.9747241564125946199e-977j)  +/-  (2.75e-242, 2.75e-242j)
| (0.46004775847492141355 + 3.5110873145678455767e-986j)  +/-  (1.28e-247, 1.28e-247j)
| (0.72698793312645016103 + 2.5188152207616114015e-983j)  +/-  (3.29e-244, 3.29e-244j)
| (0.18035397587349104032 + 1.0415092959388702077e-991j)  +/-  (2.76e-252, 2.76e-252j)
| (-0.82592388681481513624 - 1.4801513868195870099e-983j)  +/-  (9.01e-243, 9.01e-243j)
| (-0.60281098604335596895 - 1.5927728340769848001e-986j)  +/-  (6.76e-246, 6.76e-246j)
| (0.24939306577124368718 - 1.0052406432628418635e-995j)  +/-  (6.18e-251, 6.18e-251j)
| (0.6674742407002819824 + 8.1275798342241983608e-988j)  +/-  (4.96e-245, 4.96e-245j)
| (0.35241611849142175407 + 1.5033225721697471031e-991j)  +/-  (9.51e-248, 9.51e-248j)
| (-0.11168445537822003281 + 6.6815342846134137757e-997j)  +/-  (1.14e-253, 1.14e-253j)
| (-0.6674742407002819824 - 6.9143238415404534591e-989j)  +/-  (5.39e-245, 5.39e-245j)
| (-0.24939306577124368718 - 1.094971290661894622e-995j)  +/-  (6.02e-251, 6.02e-251j)
| (0.36816873917250407949 - 7.2412095244080716033e-991j)  +/-  (7.4e-248, 7.4e-248j)
| (0.60281098604335596895 - 3.6550346241011472764e-991j)  +/-  (6.98e-246, 6.98e-246j)
| (0.038004420322129332558 + 1.2734885830709041958e-1001j)  +/-  (6.78e-255, 6.78e-255j)
| (-0.5336240989298893725 - 2.0343273114667111009e-994j)  +/-  (8.73e-247, 8.73e-247j)
| (-0.36816873917250407949 - 3.44610122788698768e-994j)  +/-  (7.36e-248, 7.36e-248j)
| (0.11168445537822003281 - 4.5429453057490969974e-1000j)  +/-  (1.34e-253, 1.34e-253j)
| (0.5336240989298893725 + 9.0009764665103886368e-995j)  +/-  (8.43e-247, 8.43e-247j)
| (0.3399810435848562648 + 2.0633621995697784996e-996j)  +/-  (3.19e-248, 3.19e-248j)
| (-0.3399810435848562648 + 1.3820632250939264937e-994j)  +/-  (3.78e-248, 3.78e-248j)
| (-0.46004775847492141355 - 1.4264852708544917507e-995j)  +/-  (1.15e-247, 1.15e-247j)
| (-0.038004420322129332558 - 1.6521099497200080263e-1002j)  +/-  (6.78e-255, 6.78e-255j)
-------------------------------------------------
The weights are:
| (0.019187943501667792274 + 5.2725219327257914366e-860j)  +/-  (3.44e-78, 6.86e-195j)
| (0.0053562054882901399605 + 5.2277676621220971118e-863j)  +/-  (9.2e-79, 1.83e-195j)
| (0.030297186047189900319 - 9.8903281969650573246e-862j)  +/-  (8.42e-79, 1.68e-195j)
| (0.0053562054882901399605 + 1.3401859707750208022e-859j)  +/-  (5.42e-79, 1.08e-195j)
| (0.031160396523872417323 + 5.9866931635345562715e-860j)  +/-  (4.26e-79, 8.48e-196j)
| (0.030297186047189900319 - 8.3997542660066037498e-860j)  +/-  (5.9e-79, 1.18e-195j)
| (0.067218234261147852732 - 1.390074832320312477e-859j)  +/-  (8.16e-81, 1.63e-197j)
| (0.031160396523872417323 + 2.2862306105658936891e-861j)  +/-  (3.67e-80, 7.31e-197j)
| (0.019187943501667792274 - 8.005053979333199726e-863j)  +/-  (1.29e-80, 2.57e-197j)
| (0.012384884639530629017 - 3.0523313810949523941e-859j)  +/-  (3.78e-80, 7.53e-197j)
| (0.030891224464474242631 - 3.8361201999364705729e-860j)  +/-  (2.71e-81, 5.41e-198j)
| (0.012384884639530629017 - 4.5995692321003909216e-863j)  +/-  (1.07e-80, 2.13e-197j)
| (0.02545388916284700393 + 2.3874631445617669281e-862j)  +/-  (8.06e-81, 1.61e-197j)
| (0.049897680181411460503 - 3.6075559143082519254e-861j)  +/-  (7.23e-83, 1.44e-199j)
| (0.02545388916284700393 + 1.6858047793447162449e-859j)  +/-  (5.47e-81, 1.09e-197j)
| (0.040550489730334658635 + 1.5003690459842308866e-860j)  +/-  (1.61e-82, 3.21e-199j)
| (0.049897680181411460503 - 9.6218553278512629784e-862j)  +/-  (1.59e-83, 3.16e-200j)
| (-0.54360523573251509546 + 2.6311997579237861271e-858j)  +/-  (7.93e-86, 1.58e-202j)
| (0.056667037120624252934 + 4.0742815221881535552e-861j)  +/-  (7.7e-85, 1.53e-201j)
| (0.030891224464474242631 - 3.3121829352159263104e-861j)  +/-  (1.02e-83, 2.03e-200j)
| (0.0762183498826158786 - 7.1153508163908918637e-860j)  +/-  (5.5e-87, 1.1e-203j)
| (0.056667037120624252934 - 5.7769733179907811948e-861j)  +/-  (3.69e-85, 7.35e-202j)
| (0.067218234261147852732 + 1.8177283540011249883e-859j)  +/-  (7.52e-88, 1.5e-204j)
| (0.040550489730334658635 + 3.6138425647861333843e-861j)  +/-  (8.77e-85, 1.75e-201j)
| (0.067009535519066754692 + 8.1187194134919188433e-861j)  +/-  (3.37e-87, 6.71e-204j)
| (0.072482727396266886883 - 2.2484003594563967015e-859j)  +/-  (6.01e-88, 1.2e-204j)
| (0.062211896808444197705 + 1.0853819032478178679e-860j)  +/-  (3.36e-87, 6.7e-204j)
| (-0.54360523573251509546 - 4.423127386947100874e-858j)  +/-  (2.65e-88, 5.27e-205j)
| (0.071138733438145983502 + 1.2541928385336396967e-859j)  +/-  (2.58e-89, 5.14e-206j)
| (0.062211896808444197705 - 5.3347552582564714002e-861j)  +/-  (1.76e-88, 3.51e-205j)
| (0.072482727396266886883 + 1.5526966595364204934e-859j)  +/-  (2.2e-89, 4.39e-206j)
| (0.30608945922388359386 + 1.8602530048654725522e-858j)  +/-  (1.69e-88, 3.37e-205j)
| (0.067009535519066754692 - 1.7632048480117911314e-860j)  +/-  (2.39e-89, 4.75e-206j)
| (0.075610166141593441604 + 1.2208184280018687652e-859j)  +/-  (2.2e-90, 4.37e-207j)
| (0.071313991283683945466 - 1.4831836622883064842e-860j)  +/-  (6.76e-91, 1.33e-207j)
| (0.30608945922388359386 - 1.0823513914859419257e-858j)  +/-  (2.51e-90, 5.01e-207j)
| (0.071138733438145983502 - 1.4810083307694987238e-859j)  +/-  (6.18e-91, 1.27e-207j)
| (0.071313991283683945466 + 3.1144816853395192881e-860j)  +/-  (2.61e-91, 5.27e-208j)
| (0.3724652049174240629 + 2.7397093396373584673e-858j)  +/-  (6.33e-90, 1.31e-206j)
| (0.3724652049174240629 - 1.6588228911390140206e-858j)  +/-  (1.81e-90, 3.48e-207j)
| (0.0762183498826158786 + 3.6650663679131109265e-860j)  +/-  (4.45e-92, 8.17e-209j)
| (0.075610166141593441604 - 1.1536601466257512282e-859j)  +/-  (7.96e-92, 1.79e-208j)
