Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 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 4 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^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^25 - 348014751929152618870273276746/733464270055645672977186689*t^23 + 153951172651106060050334095501747/6601178430500811056794680201*t^21 - 24632777273882457889865235837261211/39607070583004866340768081206*t^19 + 588513253829657275685895530373650731/59410605874507299511152121809*t^17 - 23269302317304109655434464829755368705/237642423498029198044608487236*t^15 + 7383949727826985973919839506480381205/12186790948616881951005563448*t^13 - 56517883464854813075798130791547873535/24373581897233763902011126896*t^11 + 518594847574714663638285824411403957695/97494327588935055608044507584*t^9 - 149887996532323417856644169086966276615/21665406130874456801787668352*t^7 + 200323274179145436469215778597849666625/43330812261748913603575336704*t^5 - 112297857423043112018826691186454021075/86661624523497827207150673408*t^3 + 2547611754963744844507275162055738625/28887208174499275735716891136*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:
| (4.9564214419954260363 + 2.8938478364131726731e-391j)  +/-  (1.97e-122, 1.97e-122j)
| (-5.7229165279589903882 - 2.4467734006469601199e-396j)  +/-  (3.76e-123, 3.76e-123j)
| (5.7229165279589903882 + 3.7051140066939681816e-395j)  +/-  (3.57e-123, 3.57e-123j)
| (-0.7071067811865475244 - 3.020017454512819348e-394j)  +/-  (3e-125, 3e-125j)
| (-3.734461892066996592 - 1.4824688726297081195e-396j)  +/-  (4.81e-122, 4.81e-122j)
| (-4.9564214419954260363 + 8.704768857426371107e-403j)  +/-  (1.75e-122, 1.75e-122j)
| (3.1942626038546491957 - 8.1222278546615575652e-410j)  +/-  (4.06e-122, 4.06e-122j)
| (-1.0672470719421885588 - 6.5719688024287212516e-418j)  +/-  (2.58e-124, 2.58e-124j)
| (-1.3414467590878960693 - 4.4110690295667918432e-419j)  +/-  (8.93e-124, 8.93e-124j)
| (0.31182031325788265436 + 3.5707793537173210496e-419j)  +/-  (1.86e-126, 1.86e-126j)
| (0.7071067811865475244 + 1.9493816942421862764e-420j)  +/-  (2.6e-125, 2.6e-125j)
| (3.734461892066996592 + 3.1640746329197478873e-420j)  +/-  (4.92e-122, 4.92e-122j)
| (2.1934325427598809165 - 1.8422724887541991989e-425j)  +/-  (8.88e-123, 8.88e-123j)
| (-4.3141181931579130425 - 1.3645515430253017482e-427j)  +/-  (4.31e-122, 4.31e-122j)
| (-3.1942626038546491957 + 3.588932123213438552e-429j)  +/-  (3.69e-122, 3.69e-122j)
| (1.3414467590878960693 - 1.0518558391598588957e-431j)  +/-  (9.13e-124, 9.13e-124j)
| (1.7320508075688772935 + 1.8407477185297530674e-432j)  +/-  (2.94e-123, 2.94e-123j)
| (4.3141181931579130425 + 1.2900224773021493338e-434j)  +/-  (3.97e-122, 3.97e-122j)
| (-2.6822224032999497583 - 1.76926683074779618e-436j)  +/-  (1.99e-122, 1.99e-122j)
| (2.6822224032999497583 - 3.9626539626351386864e-443j)  +/-  (1.97e-122, 1.97e-122j)
| (1.576522671149282472e-447 + 2.204212253180941234e-447j)  +/-  (6.77e-446, 6.77e-446j)
| (1.0672470719421885588 + 6.1126747087385373625e-448j)  +/-  (2.59e-124, 2.59e-124j)
| (-1.7320508075688772935 - 3.4212731578760470312e-449j)  +/-  (2.71e-123, 2.71e-123j)
| (-2.1934325427598809165 - 7.2664837157120193569e-456j)  +/-  (8.16e-123, 8.16e-123j)
| (-0.31182031325788265436 - 1.7340853630909551097e-463j)  +/-  (1.86e-126, 1.86e-126j)
-------------------------------------------------
The weights are:
| (8.315495083621511987e-12 - 1.306414998184255224e-401j)  +/-  (3.85e-51, 1.81e-111j)
| (2.9648891649656180409e-15 + 7.9143890783672872291e-405j)  +/-  (3.42e-53, 1.61e-113j)
| (2.9648891649656180409e-15 - 4.1928944950176243442e-404j)  +/-  (5.93e-53, 2.79e-113j)
| (0.13739459664090088616 - 2.4811967447879572923e-395j)  +/-  (1.18e-40, 5.58e-101j)
| (2.7594171590299776598e-07 - 4.4431999335840272004e-400j)  +/-  (1.54e-49, 7.24e-110j)
| (8.315495083621511987e-12 - 7.5100063437702180008e-403j)  +/-  (6.18e-52, 2.91e-112j)
| (1.0969750954910715367e-05 + 3.7937851145979068814e-399j)  +/-  (6.49e-49, 3.06e-109j)
| (0.053004441932920119316 - 8.7355412343764255595e-395j)  +/-  (9.29e-41, 4.38e-101j)
| (0.029618061245413510546 + 2.5960785068858581724e-395j)  +/-  (9.44e-43, 4.45e-103j)
| (0.18866904339664570246 + 4.8778699307993582509e-395j)  +/-  (1.58e-41, 7.46e-102j)
| (0.13739459664090088616 - 1.8472382958885156601e-395j)  +/-  (8.8e-42, 4.15e-102j)
| (2.7594171590299776598e-07 - 6.6161958632980473001e-400j)  +/-  (3.16e-50, 1.49e-110j)
| (0.002190694902967108127 + 3.0400144847643664086e-398j)  +/-  (6.05e-47, 2.85e-107j)
| (2.8224051156123765114e-09 + 2.444500566460199048e-401j)  +/-  (1.27e-51, 6e-112j)
| (1.0969750954910715367e-05 + 5.4549043716064774012e-399j)  +/-  (7.76e-50, 3.66e-110j)
| (0.029618061245413510546 - 2.6696926239648765184e-396j)  +/-  (1.14e-45, 5.37e-106j)
| (0.012369450855440736234 + 2.0405338490633105975e-397j)  +/-  (8.25e-47, 3.9e-107j)
| (2.8224051156123765114e-09 + 9.4511645650835723268e-401j)  +/-  (2.36e-52, 1.11e-112j)
| (0.00021184779334027693017 - 5.2115168159728755464e-398j)  +/-  (5.13e-50, 2.4e-110j)
| (0.00021184779334027693017 - 1.5517135529064463685e-398j)  +/-  (2.21e-49, 1.05e-109j)
| (0.15306122941795454186 - 9.9091265132780603514e-395j)  +/-  (3.9e-46, 1.91e-106j)
| (0.053004441932920119316 + 8.1831837416363737829e-396j)  +/-  (1.95e-46, 9.4e-107j)
| (0.012369450855440736234 - 3.5940174863890381349e-396j)  +/-  (9.2e-49, 4.38e-109j)
| (0.002190694902967108127 + 4.3452155624928922076e-397j)  +/-  (1.3e-49, 5.94e-110j)
| (0.18866904339664570246 + 1.5246247923546783502e-394j)  +/-  (2.36e-47, 1.49e-107j)
