Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 6 16
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Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
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Trying to find an order 6 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
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Trying to find an order 16 Kronrod extension for:
P3 : 4*t^11 - 6923/82*t^9 + 97479/164*t^7 - 566685/328*t^5 + 1313235/656*t^3 - 418635/656*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^27 - 18602579712383878626727500047181374637/37352128661862989611625882764510142*t^25 + 192929105341891780923534882307275370184011/7395721475048871943101924787373008116*t^23 - 55950380084413613458467937165969594423074041/73957214750488719431019247873730081160*t^21 + 663864826594708668963424528982895827637682549/49304809833659146287346165249153387440*t^19 - 3801287791192870507782550586682542459572035613/24652404916829573143673082624576693720*t^17 + 2078590764950990084632582196395305710554955567/1792902175769423501358042372696486816*t^15 - 1839187122969481435753377901357387069479940493/320681689975018837641275871539209024*t^13 + 44010590698246551975681326315142359919699322615/2390536234359231335144056496928649088*t^11 - 354948968306563035285879570862895401610640869861/9562144937436925340576225987714596352*t^9 + 847268809082663823603602552646224294888980760013/19124289874873850681152451975429192704*t^7 - 1075909353398307023974063851904183537025616991035/38248579749747701362304903950858385408*t^5 + 585959156894788828875873698514534545937251754645/76497159499495402724609807901716770816*t^3 - 38989004364594468641511334375185435705024746445/76497159499495402724609807901716770816*t
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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
-------------------------------------------------
The nodes are:
| (5.7315176002685958101 + 5.1298662913992650034e-472j)  +/-  (6.3e-123, 6.3e-123j)
| (-2.3142743884833336815 - 1.787434837981487188e-471j)  +/-  (1.24e-121, 1.24e-121j)
| (-3.7487098758283944347 - 4.6738912651555937085e-482j)  +/-  (1.07e-121, 1.07e-121j)
| (-4.9662161004294137869 - 1.7862039809153132441e-482j)  +/-  (2.93e-122, 2.93e-122j)
| (4.9662161004294137869 - 7.5189465194371428503e-485j)  +/-  (3.02e-122, 3.02e-122j)
| (2.7156176269150499178 - 4.5516491313556331764e-483j)  +/-  (1.3e-121, 1.3e-121j)
| (3.2137281525534003284 + 1.0474819634547848906e-485j)  +/-  (1.34e-121, 1.34e-121j)
| (-2.1109759403485031626 + 1.0100065409132670386e-484j)  +/-  (8.64e-122, 8.64e-122j)
| (-5.7315176002685958101 - 1.0595057872596641997e-489j)  +/-  (5.85e-123, 5.85e-123j)
| (2.3142743884833336815 + 3.2961078581275985921e-487j)  +/-  (1.51e-121, 1.51e-121j)
| (1.3866480207208212553 - 7.1888314517440803606e-490j)  +/-  (3.3e-123, 3.3e-123j)
| (-3.2137281525534003284 + 7.3050178922343671135e-489j)  +/-  (1.16e-121, 1.16e-121j)
| (-4.3256200360048530098 + 4.3968794689061861868e-491j)  +/-  (7.09e-122, 7.09e-122j)
| (-1.0945422412614507352 - 4.771212543021018507e-492j)  +/-  (4.65e-124, 4.65e-124j)
| (1.7320508075688772935 + 9.6447018822482753528e-492j)  +/-  (1.51e-122, 1.51e-122j)
| (3.7487098758283944347 + 9.0275253401412558769e-493j)  +/-  (1.1e-121, 1.1e-121j)
| (-0.30858349852792099829 + 1.4757613435748921077e-497j)  +/-  (1.53e-126, 1.53e-126j)
| (-1.3866480207208212553 - 5.6931419763238137832e-494j)  +/-  (3.37e-123, 3.37e-123j)
| (-0.7071067811865475244 + 6.3186823885301374322e-499j)  +/-  (2.85e-125, 2.85e-125j)
| (1.5883385918466600591e-500 - 5.4913175304323809541e-501j)  +/-  (4.54e-499, 4.54e-499j)
| (2.1109759403485031626 - 1.7213303964605315299e-498j)  +/-  (8.66e-122, 8.66e-122j)
| (0.7071067811865475244 + 3.0242728810273737258e-500j)  +/-  (2.59e-125, 2.59e-125j)
| (0.30858349852792099829 - 3.2969337037656684436e-501j)  +/-  (1.53e-126, 1.53e-126j)
| (-1.7320508075688772935 + 1.7727616115727883807e-504j)  +/-  (1.48e-122, 1.48e-122j)
| (4.3256200360048530098 + 1.1472476284742901256e-515j)  +/-  (7.14e-122, 7.14e-122j)
| (-2.7156176269150499178 - 1.1944187860318536382e-520j)  +/-  (1.28e-121, 1.28e-121j)
| (1.0945422412614507352 - 5.4584886532565413783e-538j)  +/-  (5.89e-124, 5.89e-124j)
-------------------------------------------------
The weights are:
| (2.6835292923650413121e-15 - 4.0934364189896494228e-484j)  +/-  (2.79e-50, 1.33e-110j)
| (0.0006971013750211989649 - 9.3970721037655726685e-474j)  +/-  (1.8e-40, 8.58e-101j)
| (2.4643553511255249536e-07 - 2.5178526631572411676e-478j)  +/-  (5.3e-46, 2.53e-106j)
| (7.5300734092034141422e-12 - 1.4221991069125759411e-481j)  +/-  (2.54e-49, 1.21e-109j)
| (7.5300734092034141422e-12 + 5.2020293508686966977e-482j)  +/-  (9.8e-50, 4.67e-110j)
| (0.000167875563269929339 + 2.0133591198615202926e-476j)  +/-  (1.54e-44, 7.33e-105j)
| (9.543402580773294287e-06 - 1.138207597828245172e-477j)  +/-  (4.57e-46, 2.18e-106j)
| (0.0018700307591674720403 + 1.4040211500468957991e-473j)  +/-  (1.95e-42, 9.29e-103j)
| (2.6835292923650413121e-15 + 9.4200550828027459277e-484j)  +/-  (1.67e-52, 7.94e-113j)
| (0.0006971013750211989649 - 2.6935979010668590439e-475j)  +/-  (3.63e-44, 1.73e-104j)
| (0.023332068581095853866 + 3.8721295620653228149e-474j)  +/-  (2.9e-41, 1.38e-101j)
| (9.543402580773294287e-06 + 6.9885112791725508545e-477j)  +/-  (5.56e-47, 2.65e-107j)
| (2.5465529869010766443e-09 + 7.6353777689822376471e-480j)  +/-  (2.11e-49, 1e-109j)
| (0.058400603298841288783 - 1.701022105423498432e-473j)  +/-  (9.5e-42, 4.51e-102j)
| (0.011199772111725564284 - 1.5111017215339353402e-474j)  +/-  (7.31e-44, 3.47e-104j)
| (2.4643553511255249536e-07 + 5.9651373781960711357e-479j)  +/-  (2.72e-49, 1.3e-109j)
| (0.18916701354179256298 - 1.9739742133189403019e-473j)  +/-  (9.27e-42, 4.41e-102j)
| (0.023332068581095853866 + 1.5443752252888152254e-473j)  +/-  (2.26e-43, 1.08e-103j)
| (0.14030513762584780822 + 1.5784539241187748684e-473j)  +/-  (4.86e-42, 2.31e-102j)
| (0.14970120950207338367 + 2.1651828532352343918e-473j)  +/-  (2.56e-42, 1.22e-102j)
| (0.0018700307591674720403 + 6.4534503255708597555e-475j)  +/-  (4.38e-45, 2.06e-105j)
| (0.14030513762584780822 + 8.3975551616779101497e-474j)  +/-  (1.13e-43, 5.37e-104j)
| (0.18916701354179256298 - 1.5095894904910004467e-473j)  +/-  (3.74e-43, 1.8e-103j)
| (0.011199772111725564284 - 1.0497631981598437311e-473j)  +/-  (5.2e-45, 2.53e-105j)
| (2.5465529869010766443e-09 - 2.3177647898737220954e-480j)  +/-  (4.03e-51, 1.92e-111j)
| (0.000167875563269929339 - 2.5214219852339987676e-475j)  +/-  (4.49e-47, 2.25e-107j)
| (0.058400603298841288783 - 6.0879923842685484177e-474j)  +/-  (1.01e-44, 4.01e-105j)
