Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 40
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 71075838758475589337559527696671221462824647610569763781076808010759/65703617067213487295636604494416823944702401140119109814307960999*t^47 + 35247230006863756269303360180105555164777386797866930355898219625617902/65703617067213487295636604494416823944702401140119109814307960999*t^45 - 10641544608716326712093744772648720876570895521771557096204907223997452635/65703617067213487295636604494416823944702401140119109814307960999*t^43 + 2190866337377804835732821457129749276782195289549583405267133083356091326670/65703617067213487295636604494416823944702401140119109814307960999*t^41 - 326512641058774678259835041767286700987777437693488097786365172353724125384605/65703617067213487295636604494416823944702401140119109814307960999*t^39 + 986455858180640001211166212296136165698925868426257957805869373958292445180790/1775773434249013170152340662011265512018983814597813778765080027*t^37 - 84571802597664457643962603268802089329563182035713047649233017831823366460174645/1775773434249013170152340662011265512018983814597813778765080027*t^35 + 5639455172878922191512496550325821538147144392540386318809662753952919961556355425/1775773434249013170152340662011265512018983814597813778765080027*t^33 - 294943635936417696802308089092136017849249217748031114390037401407862762914145768350/1775773434249013170152340662011265512018983814597813778765080027*t^31 + 12147651232343058851622036792279475791979563159605851785519942380902768742389132161900/1775773434249013170152340662011265512018983814597813778765080027*t^29 - 394203001134564340952109804232310811794072129194412324733103995975782058348400492902150/1775773434249013170152340662011265512018983814597813778765080027*t^27 + 10052276192484055173629073722048687365752938224974270908200040996691007150112551288205700/1775773434249013170152340662011265512018983814597813778765080027*t^25 - 200274056715629096605807404781028604339096162929550105510098720364128801602690321546901250/1775773434249013170152340662011265512018983814597813778765080027*t^23 + 3089512741831937538661386925975025301544728197572655667138691497237657008853700209857377500/1775773434249013170152340662011265512018983814597813778765080027*t^21 - 36439187947168567047143567843330132517499565274643516761412655346562229440181044666438016250/1775773434249013170152340662011265512018983814597813778765080027*t^19 + 323065995819006626062791227920677318873709028774490873010087976167189141875662334018667888125/1775773434249013170152340662011265512018983814597813778765080027*t^17 - 2105440655924597911646331306369769824762021121286630299508007141526541990330428303860392964375/1775773434249013170152340662011265512018983814597813778765080027*t^15 + 9793722206984152108328013751346287658116920001355126659001790465919098523193362879257495018750/1775773434249013170152340662011265512018983814597813778765080027*t^13 - 31272534244881653502844728613574178673583694603509767212330012670958568597362697986331281896875/1775773434249013170152340662011265512018983814597813778765080027*t^11 + 65032694951319457055434086802604005012588052998006674149013943672552732980768121327097278743750/1775773434249013170152340662011265512018983814597813778765080027*t^9 - 81876859482016365071696571275437591729408488303762422869781462253045911862077872937481706603125/1775773434249013170152340662011265512018983814597813778765080027*t^7 + 56126866699250871949615392205653151532746189731325180017141704823500636044789851519333849168750/1775773434249013170152340662011265512018983814597813778765080027*t^5 - 17629554654081322429842161044166187705560806342082522980550821946313475900017682675662359390625/1775773434249013170152340662011265512018983814597813778765080027*t^3 + 1720857074793974401419103100413461467137947217272018577471470745435319462667255339252903234375/1775773434249013170152340662011265512018983814597813778765080027*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:
| (10.093907237081436422 + 3.5336816236909825679e-521j)  +/-  (3.14e-244, 3.14e-244j)
| (9.4628941871794062932 + 3.8140967492809656996e-531j)  +/-  (8.25e-244, 8.25e-244j)
| (-10.093907237081436422 + 1.5821616238432513796e-536j)  +/-  (3.59e-244, 3.59e-244j)
| (-7.2075335003461107971 + 7.4557031338453387424e-538j)  +/-  (1.36e-243, 1.36e-243j)
| (10.775128312482734876 - 5.860481958928879913e-543j)  +/-  (1.05e-244, 1.05e-244j)
| (-12.457436115980788254 - 4.7127716759905966763e-551j)  +/-  (1.25e-246, 1.25e-246j)
| (6.6845133342807458445 - 1.9689008966094131748e-560j)  +/-  (8.72e-244, 8.72e-244j)
| (-11.536917010079826478 - 1.2418007473532714499e-572j)  +/-  (1.67e-245, 1.67e-245j)
| (-2.7951098535489397252 - 7.9304294984968271262e-578j)  +/-  (4.3e-248, 4.3e-248j)
| (-4.2068430356301461695 + 5.0206229333549031106e-575j)  +/-  (6.08e-246, 6.08e-246j)
| (5.1753243565235333078 + 9.4097932639046476171e-572j)  +/-  (7.77e-245, 7.77e-245j)
| (-8.2951969024563777892 - 4.0631039517195520085e-578j)  +/-  (1.72e-243, 1.72e-243j)
| (11.536917010079826478 - 6.5049860680559366946e-579j)  +/-  (1.8e-245, 1.8e-245j)
| (-8.8663910714962193486 - 2.8868613180865218066e-581j)  +/-  (1.39e-243, 1.39e-243j)
| (-7.7435266835769796999 + 9.2107222806716457872e-580j)  +/-  (1.63e-243, 1.63e-243j)
| (12.457436115980788254 - 1.1723531815478114606e-581j)  +/-  (1.23e-246, 1.23e-246j)
| (4.6879521462647776165 + 1.1114973925544011113e-580j)  +/-  (2.52e-245, 2.52e-245j)
| (-10.775128312482734876 + 3.0474557393571568924e-584j)  +/-  (1.01e-244, 1.01e-244j)
| (-1.8801972554286911227 + 6.1897215105416787368e-591j)  +/-  (7.46e-250, 7.46e-250j)
| (-5.1753243565235333078 + 2.6938715821832878799e-586j)  +/-  (7.66e-245, 7.66e-245j)
| (3.7313022243357029508 + 8.7886296422470964064e-586j)  +/-  (1.47e-246, 1.47e-246j)
| (-6.1724604321760617844 - 6.4826692562681533981e-585j)  +/-  (4.66e-244, 4.66e-244j)
| (-4.6879521462647776165 + 3.1507986433254266555e-588j)  +/-  (2.39e-245, 2.39e-245j)
| (-1.0379709584894152952 - 1.1245496096077970397e-601j)  +/-  (1.45e-251, 1.45e-251j)
| (-2.3344142183389772393 - 1.0845408316891874145e-597j)  +/-  (6.22e-249, 6.22e-249j)
| (-5.6698158958040825877 + 5.1867623803730000887e-593j)  +/-  (2.11e-244, 2.11e-244j)
| (7.2075335003461107971 + 3.6331012717242398225e-606j)  +/-  (1.33e-243, 1.33e-243j)
| (5.6698158958040825877 - 6.3947176966051589685e-626j)  +/-  (2.11e-244, 2.11e-244j)
| (4.2068430356301461695 - 2.7343009749188693902e-647j)  +/-  (5.88e-246, 5.88e-246j)
| (-1.4384569794809910003 - 8.2729479367134601031e-662j)  +/-  (8.35e-251, 8.35e-251j)
| (8.8663910714962193486 + 1.4493807930203802157e-671j)  +/-  (1.37e-243, 1.37e-243j)
| (-6.6845133342807458445 - 5.3204567210333442116e-693j)  +/-  (8.88e-244, 8.88e-244j)
| (8.2951969024563777892 - 5.577584831843203696e-710j)  +/-  (1.7e-243, 1.7e-243j)
| (2.7951098535489397252 + 3.318176231173921105e-726j)  +/-  (4.3e-248, 4.3e-248j)
| (-9.4628941871794062932 + 5.3420725468770479842e-723j)  +/-  (8.15e-244, 8.15e-244j)
| (7.7435266835769796999 + 7.3754491390342210507e-728j)  +/-  (1.75e-243, 1.75e-243j)
| (1.8801972554286911227 + 3.6516680751589855873e-745j)  +/-  (7.61e-250, 7.61e-250j)
| (0.74196378430272585765 - 1.5601509484992992944e-748j)  +/-  (2.24e-252, 2.24e-252j)
| (-1.8366624532562592274e-760 + 3.2781146497454005323e-760j)  +/-  (1.84e-758, 1.84e-758j)
| (-3.7313022243357029508 + 4.3055423126918722973e-742j)  +/-  (1.46e-246, 1.46e-246j)
| (-0.74196378430272585765 + 8.9205083632364730794e-750j)  +/-  (2.3e-252, 2.3e-252j)
| (-3.2608125255799958976 - 4.3462654460530029279e-744j)  +/-  (2.61e-247, 2.61e-247j)
| (2.3344142183389772393 - 3.3955423022186487509e-744j)  +/-  (5.93e-249, 5.93e-249j)
| (1.4384569794809910003 - 8.950677344592851635e-747j)  +/-  (8.34e-251, 8.34e-251j)
| (-0.41062937413677865169 - 3.748187593855509833e-750j)  +/-  (1.54e-253, 1.54e-253j)
| (6.1724604321760617844 - 1.404270649241437801e-746j)  +/-  (4.54e-244, 4.54e-244j)
| (1.0379709584894152952 - 4.0735553193262070096e-756j)  +/-  (1.35e-251, 1.35e-251j)
| (3.2608125255799958976 + 2.3830281327428398303e-753j)  +/-  (2.57e-247, 2.57e-247j)
| (0.41062937413677865169 - 6.291050247749526401e-761j)  +/-  (1.69e-253, 1.69e-253j)
-------------------------------------------------
The weights are:
| (1.9550281249421738882e-23 - 3.6632996676514285588e-543j)  +/-  (1.02e-76, 2.9e-197j)
| (8.7658380208593874648e-21 + 2.7022076810704146764e-542j)  +/-  (2.01e-75, 5.69e-196j)
| (1.9550281249421738882e-23 - 3.422087593303570703e-545j)  +/-  (1.38e-78, 3.91e-199j)
| (1.1065891336285023501e-12 + 1.7837049311311094635e-539j)  +/-  (3.23e-72, 9.13e-193j)
| (1.7512163610504201184e-26 - 2.5258877181365818932e-545j)  +/-  (3.87e-79, 1.09e-199j)
| (8.5002445053887271497e-35 + 3.1795242901052355639e-551j)  +/-  (1.75e-83, 4.94e-204j)
| (4.0914556194245348778e-11 - 6.1931297153021191632e-538j)  +/-  (4.96e-72, 1.4e-192j)
| (4.0961593948351655378e-30 - 9.7137707962155936084e-549j)  +/-  (9.27e-82, 2.62e-202j)
| (0.0037177281718024126008 - 7.6131349940749572677e-534j)  +/-  (5.84e-58, 1.65e-178j)
| (2.7388664278638900768e-05 + 2.6586233993633387604e-535j)  +/-  (5.22e-65, 1.48e-185j)
| (2.9903703994754045681e-07 + 5.5840288566397556319e-536j)  +/-  (2.21e-69, 6.27e-190j)
| (2.5565117574460031095e-16 + 2.034676858837516161e-541j)  +/-  (2.28e-76, 6.45e-197j)
| (4.0961593948351655378e-30 + 1.4561014966242387318e-547j)  +/-  (1.25e-83, 3.54e-204j)
| (1.9758641671896790136e-18 - 1.5405263488136257998e-542j)  +/-  (9.89e-78, 2.8e-198j)
| (2.0669323157183775427e-14 - 2.1116700658848764332e-540j)  +/-  (1.7e-75, 4.8e-196j)
| (8.5002445053887271497e-35 - 3.033707124976113964e-550j)  +/-  (1.71e-86, 4.84e-207j)
| (3.2631216814655570157e-06 - 1.9953021079553031759e-535j)  +/-  (3.92e-71, 1.11e-191j)
| (1.7512163610504201184e-26 + 8.2451723360716790286e-547j)  +/-  (1.16e-81, 3.29e-202j)
| (0.030635705071379199652 - 5.5234301139824127893e-533j)  +/-  (9.24e-60, 2.62e-180j)
| (2.9903703994754045681e-07 + 1.79874858643440117e-536j)  +/-  (3.93e-72, 1.11e-192j)
| (0.00017883974709810318935 - 1.9117553248831676158e-534j)  +/-  (9.6e-71, 2.72e-191j)
| (1.0786187512965404212e-09 + 7.565302579330162293e-538j)  +/-  (1.81e-74, 5.13e-195j)
| (3.2631216814655570157e-06 - 7.2971290759121936221e-536j)  +/-  (1.37e-71, 3.87e-192j)
| (0.082314164097107943158 - 4.2512314884570959695e-532j)  +/-  (5.66e-59, 1.6e-179j)
| (0.011976372785855122773 + 2.06507718683153601e-533j)  +/-  (1.58e-65, 4.46e-186j)
| (2.0791146827009086623e-08 - 3.9377992135158907814e-537j)  +/-  (1.52e-73, 4.3e-194j)
| (1.1065891336285023501e-12 + 1.0691846570725369907e-538j)  +/-  (2.29e-81, 6.47e-202j)
| (2.0791146827009086623e-08 - 1.4030988908113109006e-536j)  +/-  (2.87e-78, 8.13e-199j)
| (2.7388664278638900768e-05 + 6.4582800520791274065e-535j)  +/-  (2.25e-75, 6.37e-196j)
| (0.060976010354627605248 + 1.5315260522493572429e-532j)  +/-  (1.36e-66, 3.85e-187j)
| (1.9758641671896790136e-18 - 2.3795074873079147731e-541j)  +/-  (9.21e-85, 2.61e-205j)
| (4.0914556194245348778e-11 - 1.2584509138021070996e-538j)  +/-  (5.92e-79, 1.67e-199j)
| (2.5565117574460031095e-16 + 2.080150644152197108e-540j)  +/-  (3.7e-84, 1.05e-204j)
| (0.0037177281718024126008 - 1.344410892463196617e-533j)  +/-  (3.18e-76, 9e-197j)
| (8.7658380208593874648e-21 + 8.7188506969227395261e-544j)  +/-  (2.04e-85, 5.77e-206j)
| (2.0669323157183775427e-14 - 1.6025819812567106455e-539j)  +/-  (2.52e-83, 7.13e-204j)
| (0.030635705071379199652 - 8.0521627237657994353e-533j)  +/-  (2.92e-75, 8.26e-196j)
| (0.083079601348420323218 + 8.0072938695738358626e-532j)  +/-  (1.72e-72, 4.9e-193j)
| (0.16774352873895517551 + 6.4671321982988666846e-532j)  +/-  (6.96e-73, 1.98e-193j)
| (0.00017883974709810318935 - 8.798234883013265437e-535j)  +/-  (8.62e-77, 2.44e-197j)
| (0.083079601348420323218 + 6.9107282037503848688e-532j)  +/-  (1.44e-73, 4.16e-194j)
| (0.00091690863057790415095 + 2.6779453639400918539e-534j)  +/-  (3.14e-76, 8.88e-197j)
| (0.011976372785855122773 + 3.3076185575942338745e-533j)  +/-  (4.88e-77, 1.39e-197j)
| (0.060976010354627605248 + 2.0405774067522951484e-532j)  +/-  (5.75e-76, 1.69e-196j)
| (0.14230193268884609566 - 6.958701332839365152e-532j)  +/-  (1.9e-74, 5.9e-195j)
| (1.0786187512965404212e-09 + 3.1381273128331340662e-537j)  +/-  (4.53e-82, 1.29e-202j)
| (0.082314164097107943158 - 5.2257645872674198335e-532j)  +/-  (5.17e-76, 1.85e-196j)
| (0.00091690863057790415095 + 5.2338232354695530913e-534j)  +/-  (1.93e-78, 5.25e-199j)
| (0.14230193268884609566 - 7.5488831314224585235e-532j)  +/-  (7.72e-76, 3.34e-196j)
