Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 6 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P3 : t^11 - 6923/164*t^9 + 97479/164*t^7 - 566685/164*t^5 + 1313235/164*t^3 - 418635/82*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 777206413554596144125804957212332944481327551817235951123089476858988125821291274138323393/1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764*t^41 + 257748777342921895565304658506533665318135940070984369826513302588340377995361997490047998469/1056104070806118053678643966725105687591418764603133312724996323351652402389047977350764*t^39 - 664150072640571300448298807123810410422859369507395128160284527686468028741294530795170206498275/13729352920479534697822371567426373938688443939840733065424952203571481231057623705559932*t^37 + 87998855371762678816195569241718038156930711467045969969243162733491492400835456698552506786719325/13729352920479534697822371567426373938688443939840733065424952203571481231057623705559932*t^35 - 590027830922071724814884872107452636428617032664301777700572447583504320963725630311050083389451465/980668065748538192701597969101883852763460281417195218958925157397962945075544550397138*t^33 + 20290643762847229349319169281399405989116853273609230666904945461700248842214159447195408048908962535/490334032874269096350798984550941926381730140708597609479462578698981472537772275198569*t^31 - 1043359537503517343845503257635176634318065054425189970341912348558553863043368603800772373393978427305/490334032874269096350798984550941926381730140708597609479462578698981472537772275198569*t^29 + 40578006669938432189917244135968531433121747500567849544445077233479109413660512289049271538749553283925/490334032874269096350798984550941926381730140708597609479462578698981472537772275198569*t^27 - 184641797831597437466388020908090253257706572584657649664846752597999714909573664480950956599178203901525/75436005057579860977045997623221834827958483185938093766071165953689457313503426953626*t^25 + 4155600522008653395520313844784294346578727943538186438557599852802519412205562396187659838122392412388125/75436005057579860977045997623221834827958483185938093766071165953689457313503426953626*t^23 - 70899266573925847782504632878863740947846331197932963744691108422061151924199442328170926654220664793993375/75436005057579860977045997623221834827958483185938093766071165953689457313503426953626*t^21 + 909480971954310413123483631284542115865865735601785674221598315570697697432833131280143269313707329628777625/75436005057579860977045997623221834827958483185938093766071165953689457313503426953626*t^19 - 4328687106980456423427840456564269990496759347725674507153407408909152569278484933506307566688561607026457500/37718002528789930488522998811610917413979241592969046883035582976844728656751713476813*t^17 + 29995764576108099168897808476050643836213770632650497066970305221570521980839185986365847194205383218951724375/37718002528789930488522998811610917413979241592969046883035582976844728656751713476813*t^15 - 147265464134235897899469802423174862504504386477191795965819467297248642697905036033281594623785349831437800625/37718002528789930488522998811610917413979241592969046883035582976844728656751713476813*t^13 + 12027887937582578875408732329197005170190591352392963558113089059870888800015640104262522519095792595521652500/919951281189998304598121922234412619853152233974854802025258121386456796506139353093*t^11 - 4271160003602439426702072053830020150646039718239549876226393880619642772320285304844713293207224019298930814375/150872010115159721954091995246443669655916966371876187532142331907378914627006853907252*t^9 + 5546006874667759120440300722089546048357060213623786323112067849405795840011417368378899033545017264011419196875/150872010115159721954091995246443669655916966371876187532142331907378914627006853907252*t^7 - 3883562376215640774853717333279210845616952494215340612311734187169969548858850228140290179216872338380026440625/150872010115159721954091995246443669655916966371876187532142331907378914627006853907252*t^5 + 1258960391394032296385931023512289518313691475763014050440817152138439442363151069026691754804543691231675509375/150872010115159721954091995246443669655916966371876187532142331907378914627006853907252*t^3 - 69055039422845262347148530517663594466461692535445577437724367582425584715847724239266453953539164559945984375/75436005057579860977045997623221834827958483185938093766071165953689457313503426953626*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:
| (8.0070409743765106028 - 7.3708107352215753479e-603j)  +/-  (1.71e-245, 1.71e-245j)
| (9.4049996689811046528 + 6.3524501554434143722e-646j)  +/-  (3.31e-246, 3.31e-246j)
| (-11.190808228269224593 + 3.2346849438990174263e-667j)  +/-  (6.13e-248, 6.13e-248j)
| (7.3734346964032152291 + 2.465044290586494284e-683j)  +/-  (2.39e-245, 2.39e-245j)
| (-10.215557341189196396 + 2.8364155052976321081e-702j)  +/-  (6.87e-247, 6.87e-247j)
| (6.7688245544274573417 + 3.6790222407699276831e-700j)  +/-  (2.3e-245, 2.3e-245j)
| (-3.5585734899654051025 - 1.4646096378349772821e-710j)  +/-  (8.36e-247, 8.36e-247j)
| (-8.0070409743765106028 - 6.3694787150163074881e-709j)  +/-  (1.74e-245, 1.74e-245j)
| (-8.679002287120409963 - 5.6847528470045897639e-709j)  +/-  (9.7e-246, 9.7e-246j)
| (3.2728782272458314193 - 2.0950235632120240606e-708j)  +/-  (4.41e-247, 4.41e-247j)
| (-5.6241491838399473972 - 5.366939884794313067e-714j)  +/-  (1.34e-245, 1.34e-245j)
| (2.4494897427831780982 - 3.7879540610948644796e-715j)  +/-  (6.62e-249, 6.62e-249j)
| (11.190808228269224593 + 1.1449428795837175841e-717j)  +/-  (6.17e-248, 6.17e-248j)
| (10.215557341189196396 - 1.1411746180937363313e-735j)  +/-  (7.19e-247, 7.19e-247j)
| (-5.0771681611060075351 - 1.0494288945630817837e-743j)  +/-  (6.67e-246, 6.67e-246j)
| (1.961016437141193946 - 3.516103141012643592e-747j)  +/-  (6.73e-250, 6.73e-250j)
| (8.679002287120409963 + 9.4427884312006410851e-742j)  +/-  (8.87e-246, 8.87e-246j)
| (-4.5448979391212497356 - 1.6336364483360922155e-749j)  +/-  (3.65e-246, 3.65e-246j)
| (-2.9249337997859815875 - 1.1445215106287684156e-750j)  +/-  (8.66e-248, 8.66e-248j)
| (-1.4744384610486526794 + 7.5951048687807338934e-754j)  +/-  (5.7e-251, 5.7e-251j)
| (1.4744384610486526794 - 2.8889023582802297071e-753j)  +/-  (5.55e-251, 5.55e-251j)
| (4.5448979391212497356 - 1.3587985627857685803e-747j)  +/-  (3.12e-246, 3.12e-246j)
| (-2.4494897427831780982 + 1.1708540267684173829e-762j)  +/-  (6.77e-249, 6.77e-249j)
| (-9.4049996689811046528 - 7.6094390441859269611e-759j)  +/-  (3.14e-246, 3.14e-246j)
| (-4.0296969696001522128 - 2.4214448612574638795e-759j)  +/-  (1.63e-246, 1.63e-246j)
| (-3.2728782272458314193 + 1.6645999798208195854e-760j)  +/-  (4.38e-247, 4.38e-247j)
| (0.70791864763939706654 - 1.1436884306738956421e-765j)  +/-  (1.8e-252, 1.8e-252j)
| (1 + 5.7117315346551344735e-764j)  +/-  (7.15e-252, 7.15e-252j)
| (5.6241491838399473972 - 3.1341419527198023907e-757j)  +/-  (1.24e-245, 1.24e-245j)
| (4.0296969696001522128 - 1.4108837833522173125e-763j)  +/-  (1.52e-246, 1.52e-246j)
| (-6.1871137386569344401 - 2.756219495194582274e-769j)  +/-  (2e-245, 2e-245j)
| (-6.7688245544274573417 + 1.7980123783519503412e-769j)  +/-  (2.36e-245, 2.36e-245j)
| (0.46424731586597086304 + 6.3954267983505425264e-785j)  +/-  (2.23e-253, 2.23e-253j)
| (-0.70791864763939706654 - 3.8510677371667519193e-777j)  +/-  (1.64e-252, 1.64e-252j)
| (-0.46424731586597086304 - 1.3040868356968435119e-785j)  +/-  (2.23e-253, 2.23e-253j)
| (-7.3734346964032152291 - 3.186681648329623362e-770j)  +/-  (2.41e-245, 2.41e-245j)
| (5.0771681611060075351 - 3.0210133904023033323e-770j)  +/-  (7.15e-246, 7.15e-246j)
| (2.9249337997859815875 - 9.5869122509296597663e-777j)  +/-  (8.84e-248, 8.84e-248j)
| (3.5585734899654051025 - 9.5997425507953993237e-780j)  +/-  (8.34e-247, 8.34e-247j)
| (-1 - 1.1483923987844767703e-797j)  +/-  (7.02e-252, 7.02e-252j)
| (6.1871137386569344401 - 1.4958647628555510018e-804j)  +/-  (1.92e-245, 1.92e-245j)
| (-1.961016437141193946 - 2.3631572698373243122e-829j)  +/-  (6.17e-250, 6.17e-250j)
| (3.0974826088377307009e-830 + 6.8658531603540111156e-831j)  +/-  (1.36e-828, 1.36e-828j)
-------------------------------------------------
The weights are:
| (3.1080720643274200065e-15 + 1.0650095202070769056e-616j)  +/-  (4.51e-84, 1.4e-206j)
| (1.8828566986133637754e-20 - 1.7679085453828859637e-620j)  +/-  (3.32e-87, 1.03e-209j)
| (2.8680305969316895827e-28 + 6.5836467687782621162e-626j)  +/-  (6.98e-92, 2.16e-214j)
| (3.8552666147553833134e-13 - 6.1802623686924189875e-616j)  +/-  (4.06e-83, 1.26e-205j)
| (7.5866178838425793837e-24 - 1.788989433039908823e-623j)  +/-  (2.03e-90, 6.29e-213j)
| (2.6573266358750340883e-11 + 4.121452115067381597e-615j)  +/-  (2.63e-82, 8.16e-205j)
| (0.00029061128595811491371 + 1.2315294891675744526e-610j)  +/-  (1.58e-74, 4.88e-197j)
| (3.1080720643274200065e-15 + 1.4305541217347586223e-618j)  +/-  (3.22e-87, 9.99e-210j)
| (1.2207332485464347084e-17 - 5.6842891107555041565e-620j)  +/-  (2.34e-88, 7.26e-211j)
| (0.00043080566507499020554 - 7.7357152358924149538e-610j)  +/-  (2.49e-75, 7.73e-198j)
| (2.9943924920534081433e-08 + 3.4596915990445932903e-614j)  +/-  (6.36e-83, 1.97e-205j)
| (0.0096692100294743085842 - 1.5468370055157601493e-609j)  +/-  (9.76e-72, 3.03e-194j)
| (2.8680305969316895827e-28 - 3.9698837192308800645e-625j)  +/-  (3.24e-94, 1e-216j)
| (7.5866178838425793837e-24 + 1.4761056933495140069e-622j)  +/-  (4e-92, 1.24e-214j)
| (5.4377654475689170919e-07 - 2.7873649745382225445e-613j)  +/-  (2.24e-83, 6.93e-206j)
| (0.028492078760360070538 + 2.938909141966725116e-609j)  +/-  (2.58e-72, 7.99e-195j)
| (1.2207332485464347084e-17 + 1.4115142079477300516e-618j)  +/-  (4.21e-89, 1.3e-211j)
| (6.8458490611804894508e-06 + 2.0765785403804991352e-612j)  +/-  (2.2e-82, 6.83e-205j)
| (0.002492529641159706201 + 4.9822450650396984403e-610j)  +/-  (1.83e-78, 5.67e-201j)
| (0.065066805538170161206 - 4.7197623343474425836e-609j)  +/-  (1.51e-72, 4.69e-195j)
| (0.065066805538170161206 - 6.8503065083034868219e-609j)  +/-  (2.17e-72, 6.73e-195j)
| (6.8458490611804894508e-06 + 7.5285991140497783102e-612j)  +/-  (5.18e-84, 1.61e-206j)
| (0.0096692100294743085842 - 8.2212983805142590837e-610j)  +/-  (1.51e-77, 4.67e-200j)
| (1.8828566986133637754e-20 + 1.4193988935045274747e-621j)  +/-  (3.03e-93, 9.4e-216j)
| (5.97582288912229944e-05 - 1.5524835007348292822e-611j)  +/-  (5.8e-82, 1.8e-204j)
| (0.00043080566507499020554 - 3.2466664199957994167e-610j)  +/-  (6.37e-80, 1.98e-202j)
| (0.033684050042526229432 - 4.9924370747448496521e-608j)  +/-  (6.84e-75, 2.12e-197j)
| (0.10981366573047444022 + 2.3877031141595598349e-608j)  +/-  (6.56e-75, 2.03e-197j)
| (2.9943924920534081433e-08 + 1.9790959145795588017e-613j)  +/-  (5.42e-88, 1.68e-210j)
| (5.97582288912229944e-05 - 4.6983205471419565783e-611j)  +/-  (1.22e-84, 3.78e-207j)
| (1.1108456558316799546e-09 - 3.7694314798650185688e-615j)  +/-  (2.25e-88, 6.97e-211j)
| (2.6573266358750340883e-11 + 3.4537737724818541779e-616j)  +/-  (5.49e-90, 1.7e-212j)
| (0.15553898369041559496 + 4.4916767546401914291e-608j)  +/-  (1.23e-79, 3.8e-202j)
| (0.033684050042526229432 - 4.1813629090195387778e-608j)  +/-  (3.54e-80, 1.1e-202j)
| (0.15553898369041559496 + 3.9993670124534818646e-608j)  +/-  (5.25e-80, 1.63e-202j)
| (3.8552666147553833134e-13 - 2.545989552042968995e-617j)  +/-  (3.39e-91, 1.05e-213j)
| (5.4377654475689170919e-07 - 1.244779845001750945e-612j)  +/-  (4.93e-89, 1.53e-211j)
| (0.002492529641159706201 + 1.0717164258563263451e-609j)  +/-  (1.94e-85, 6.01e-208j)
| (0.00029061128595811491371 + 3.2018656589249344054e-610j)  +/-  (1.94e-86, 6.01e-209j)
| (0.10981366573047444022 + 1.8575172027260121526e-608j)  +/-  (2.46e-84, 7.75e-207j)
| (1.1108456558316799546e-09 - 2.9398919118998691896e-614j)  +/-  (2.68e-91, 8.33e-214j)
| (0.028492078760360070538 + 1.782565654618416043e-609j)  +/-  (1.56e-85, 4.6e-208j)
| (0.18890816136031346736 - 2.7267899285699783319e-608j)  +/-  (2.97e-84, 1.04e-206j)
