Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 9 14
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Trying to find an order 9 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
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Trying to find an order 14 Kronrod extension for:
P2 : 64*t^15 - 443040/191*t^13 + 5766480/191*t^11 - 34180440/191*t^9 + 97309620/191*t^7 - 129077550/191*t^5 + 68923575/191*t^3 - 18129825/382*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^29 - 187328470189621764699453638239840/20786051549784625378492529277*t^27 + 1255248598475034717191980792235504/2309561283309402819832503253*t^25 - 42784394363125384161177822410764680/2309561283309402819832503253*t^23 + 8246118673784779029369136814255613380/20786051549784625378492529277*t^21 - 38897445323606839222495575182426277890/6928683849928208459497509759*t^19 + 372477999616173391003825685695228903775/6928683849928208459497509759*t^17 - 14584240008950923529222835020228384649275/41572103099569250756985058554*t^15 + 10744593388020327801084647828771530211425/6928683849928208459497509759*t^13 - 10524838535744497451204354912261922979225/2309561283309402819832503253*t^11 + 59653685161839252474132665315537646101200/6928683849928208459497509759*t^9 - 22900068516000015377348569889074116547875/2309561283309402819832503253*t^7 + 472986231349200693101011300856062411063125/73905961065900890234640104096*t^5 - 295071385324867457196440909017710896719875/147811922131801780469280208192*t^3 + 3809360119828670247345583114017824968125/18476490266475222558660026024*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.4812218204486349855 + 2.2924019482154266925e-436j)  +/-  (2.67e-121, 2.67e-121j)
| (-3.0701613138889128067 - 6.9935569254519903716e-435j)  +/-  (8.72e-121, 8.72e-121j)
| (5.8581679320563297418 + 3.6496476481214464793e-441j)  +/-  (1.43e-122, 1.43e-122j)
| (-3.4392360781430962446 + 7.5430515795302703014e-440j)  +/-  (8.04e-121, 8.04e-121j)
| (-5.8581679320563297418 + 1.607707457379186501e-441j)  +/-  (1.46e-122, 1.46e-122j)
| (5.1063276318948135568 + 5.4561036517774693854e-440j)  +/-  (9.43e-122, 9.43e-122j)
| (1.3358490740136969497 - 1.9192937336942731321e-443j)  +/-  (3.05e-123, 3.05e-123j)
| (-5.1063276318948135568 - 1.298623437847748011e-440j)  +/-  (9.18e-122, 9.18e-122j)
| (-4.4812218204486349855 - 4.19379432761069386e-440j)  +/-  (2.56e-121, 2.56e-121j)
| (-3.9268135162497144207 - 2.8708807626815346821e-440j)  +/-  (5.12e-121, 5.12e-121j)
| (2.0150636207329153142 + 1.9173206279867369635e-441j)  +/-  (9.35e-122, 9.35e-122j)
| (-2.0150636207329153142 - 2.6848587482183065646e-440j)  +/-  (9.01e-122, 9.01e-122j)
| (-0.95452011014285350763 - 1.5298436755015111553e-448j)  +/-  (6.46e-124, 6.46e-124j)
| (-2.3506049736744922228 + 9.1966103332480061564e-447j)  +/-  (2.28e-121, 2.28e-121j)
| (3.4392360781430962446 + 2.5233442486828542429e-455j)  +/-  (8.62e-121, 8.62e-121j)
| (0.81692802571934419604 - 3.470498876683751375e-470j)  +/-  (2.64e-124, 2.64e-124j)
| (3.0701613138889128067 + 1.7804777280331478023e-470j)  +/-  (8.74e-121, 8.74e-121j)
| (-1.7281759088743055938 - 1.0567211304002158106e-479j)  +/-  (2.64e-122, 2.64e-122j)
| (-0.81692802571934419604 + 2.364743534985985521e-482j)  +/-  (2.38e-124, 2.38e-124j)
| (-2.7463107103922855327 - 3.0798342926445877472e-478j)  +/-  (5.5e-121, 5.5e-121j)
| (1.7281759088743055938 + 4.8337172612001624317e-479j)  +/-  (2.42e-122, 2.42e-122j)
| (0.95452011014285350763 + 6.8466576815349034247e-482j)  +/-  (8.4e-124, 8.4e-124j)
| (2.7463107103922855327 - 7.1907922540537572113e-478j)  +/-  (6.04e-121, 6.04e-121j)
| (-1.3358490740136969497 - 5.6296918963728928469e-486j)  +/-  (3.14e-123, 3.14e-123j)
| (-0.43607741192761650868 - 1.4393699905133298893e-488j)  +/-  (5.57e-126, 5.57e-126j)
| (2.3506049736744922228 + 6.7266385186162410578e-487j)  +/-  (2.11e-121, 2.11e-121j)
| (0.43607741192761650868 + 9.2713316482852283233e-494j)  +/-  (4.7e-126, 4.7e-126j)
| (3.9268135162497144207 + 5.1930575474806655531e-499j)  +/-  (5.61e-121, 5.61e-121j)
| (-7.2043510565184357639e-564 - 1.9213381624829617802e-565j)  +/-  (2.09e-562, 2.09e-562j)
-------------------------------------------------
The weights are:
| (6.2784510264571781781e-10 + 1.249752216530721562e-444j)  +/-  (2.8e-41, 8.79e-101j)
| (1.386786080265369202e-05 - 5.3710921903282178383e-439j)  +/-  (3.23e-37, 1.02e-96j)
| (6.0880983466646053087e-16 + 2.3656920031251701108e-448j)  +/-  (5.45e-45, 1.71e-104j)
| (1.8153896955021721349e-06 - 2.9517337295388006865e-440j)  +/-  (9.37e-39, 2.94e-98j)
| (6.0880983466646053087e-16 - 7.183482520276539553e-448j)  +/-  (5.45e-46, 1.71e-105j)
| (1.7987734464733139055e-12 - 4.1824943377331776966e-446j)  +/-  (5.01e-44, 1.57e-103j)
| (0.03943204590198260876 + 7.0337187410195252581e-438j)  +/-  (8.82e-32, 2.77e-91j)
| (1.7987734464733139055e-12 + 1.5087405516947345388e-445j)  +/-  (2.05e-44, 6.45e-104j)
| (6.2784510264571781781e-10 - 1.1590307924662721709e-443j)  +/-  (3.77e-43, 1.18e-102j)
| (5.9450421025892773649e-08 + 5.9521624467354844603e-442j)  +/-  (8.34e-42, 2.62e-101j)
| (0.0026332138376991789718 + 1.4177682215473141034e-438j)  +/-  (6.33e-39, 1.99e-98j)
| (0.0026332138376991789718 + 6.9495809834980685272e-438j)  +/-  (3.02e-38, 9.49e-98j)
| (0.056361707824534927646 - 6.0188939248952450291e-437j)  +/-  (1.34e-36, 4.19e-96j)
| (0.00088167117870531143763 - 2.7762638730565300373e-438j)  +/-  (4.6e-39, 1.44e-98j)
| (1.8153896955021721349e-06 + 1.5808734723842237257e-441j)  +/-  (2.39e-44, 7.52e-104j)
| (0.066069237518347228315 + 3.6283623337632073654e-437j)  +/-  (3.32e-38, 1.04e-97j)
| (1.386786080265369202e-05 - 1.5189256184552388614e-440j)  +/-  (1.41e-43, 4.42e-103j)
| (0.0098414704891443031864 - 1.0993658988936746106e-437j)  +/-  (4.08e-39, 1.28e-98j)
| (0.066069237518347228315 + 6.2947072068361515575e-437j)  +/-  (9.21e-38, 2.88e-97j)
| (0.0001112953649127647007 + 1.301015433063793324e-438j)  +/-  (7.33e-41, 2.3e-100j)
| (0.0098414704891443031864 - 3.0332967235325553956e-438j)  +/-  (1.02e-40, 3.21e-100j)
| (0.056361707824534927646 - 3.1429091700713648509e-437j)  +/-  (3.39e-39, 1.06e-98j)
| (0.0001112953649127647007 + 7.0325489720879528148e-440j)  +/-  (1.68e-43, 5.24e-103j)
| (0.03943204590198260876 + 1.8044759691947371165e-437j)  +/-  (6.59e-40, 1.86e-99j)
| (0.20109430586613203423 - 2.303925987939165814e-437j)  +/-  (4.33e-40, 1.25e-99j)
| (0.00088167117870531143763 - 3.6058893556970888609e-439j)  +/-  (7.31e-43, 2.3e-102j)
| (0.20109430586613203423 - 1.7257679907868484624e-437j)  +/-  (6.37e-41, 1.62e-100j)
| (5.9450421025892773649e-08 - 6.4710332684443422941e-443j)  +/-  (9.69e-47, 3.26e-106j)
| (0.24711861737595595219 + 1.5610629956348005095e-437j)  +/-  (4.68e-41, 1.07e-100j)
