Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 7 16
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Trying to find an order 7 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : 4*t^9 - 346/5*t^7 + 1743/5*t^5 - 1113/2*t^3 + 399/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^25 - 3996542237238873402/8668431607928285*t^23 + 1110940457535288120331/50276903325984053*t^21 - 3193129745837663521251159/5530459365858245830*t^19 + 125410447049968218592107248/13826148414645614575*t^17 - 4933242633342244128706595251/55304593658582458300*t^15 + 12278462268531611687762578533/22121837463432983320*t^13 - 95665691290200967625369237103/44243674926865966640*t^11 + 16445562475294184528223386277/3217721812862979392*t^9 - 222571687427214277786313843709/32177218128629793920*t^7 + 312026495095950148930485331899/64354436257259587840*t^5 - 1300279447112577931849497921/887647396651856384*t^3 + 3218976882263878499935860507/25741774502903835136*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
-------------------------------------------------
The nodes are:
| (3.6527029017403973465 + 4.2658424376067536271e-489j)  +/-  (6.77e-122, 6.77e-122j)
| (-3.6527029017403973465 + 5.9935613377389273121e-496j)  +/-  (6.5e-122, 6.5e-122j)
| (5.620436371311244372 + 5.4694856140754841333e-498j)  +/-  (3.75e-123, 3.75e-123j)
| (-1.8237120088249817235 - 2.4989733508135229975e-498j)  +/-  (5.26e-123, 5.26e-123j)
| (-5.620436371311244372 + 3.6455109197694377081e-499j)  +/-  (3.63e-123, 3.63e-123j)
| (1.8237120088249817235 - 2.1877942456301936533e-497j)  +/-  (5.08e-123, 5.08e-123j)
| (3.1316817004388926669 + 6.5374599556657180563e-503j)  +/-  (5.54e-122, 5.54e-122j)
| (-2.6533869991500808333 + 6.6355812825569825698e-510j)  +/-  (3.69e-122, 3.69e-122j)
| (-4.857308021359547327 + 8.7359523381758402921e-512j)  +/-  (2.11e-122, 2.11e-122j)
| (-3.1316817004388926669 + 1.6764989056761092952e-511j)  +/-  (5.28e-122, 5.28e-122j)
| (1.0558727165941354008 - 7.6317215518760207332e-514j)  +/-  (1.75e-124, 1.75e-124j)
| (4.221333835316177546 + 1.2170037529422273346e-511j)  +/-  (4.58e-122, 4.58e-122j)
| (-4.221333835316177546 - 1.0108543364224197574e-516j)  +/-  (4.3e-122, 4.3e-122j)
| (-2.2201724783418921227 - 4.8579700357687885557e-519j)  +/-  (1.59e-122, 1.59e-122j)
| (2.2201724783418921227 + 1.6957289692201910093e-516j)  +/-  (1.56e-122, 1.56e-122j)
| (1.4364553225037617879 - 7.1936345305684536515e-525j)  +/-  (1.24e-123, 1.24e-123j)
| (2.6533869991500808333 - 1.0316311107014982988e-533j)  +/-  (3.34e-122, 3.34e-122j)
| (4.857308021359547327 + 1.4068522919220544406e-545j)  +/-  (1.98e-122, 1.98e-122j)
| (-0.7071067811865475244 - 2.4981450065462881878e-551j)  +/-  (3.07e-125, 3.07e-125j)
| (-1.4364553225037617879 - 4.6691443994964509926e-551j)  +/-  (1.23e-123, 1.23e-123j)
| (0.36810361851285660272 + 3.8237928145583113384e-554j)  +/-  (2.18e-126, 2.18e-126j)
| (0.7071067811865475244 + 1.4811603181229609752e-554j)  +/-  (3.1e-125, 3.1e-125j)
| (-3.1730270348374803938e-555 - 2.9175688347751484757e-554j)  +/-  (7.34e-553, 7.34e-553j)
| (-1.0558727165941354008 - 1.2108625450034802139e-555j)  +/-  (1.8e-124, 1.8e-124j)
| (-0.36810361851285660272 - 9.8729929036193820455e-560j)  +/-  (2.05e-126, 2.05e-126j)
-------------------------------------------------
The weights are:
| (4.918268049132682992e-07 - 1.0190025197498291261e-494j)  +/-  (7.14e-45, 5.33e-105j)
| (4.918268049132682992e-07 - 2.871907577750462166e-496j)  +/-  (2.2e-45, 1.64e-105j)
| (9.4575638266566189924e-15 - 2.3251077199317178363e-500j)  +/-  (8.58e-50, 6.4e-110j)
| (0.0078586825637522553702 - 6.9954747230759427369e-493j)  +/-  (2.86e-39, 2.13e-99j)
| (9.4575638266566189924e-15 + 4.9338145784335151076e-501j)  +/-  (3.05e-50, 2.27e-110j)
| (0.0078586825637522553702 - 2.0946045359653041473e-492j)  +/-  (2.36e-40, 1.76e-100j)
| (1.5518305760138097596e-05 + 4.4678632413298755998e-494j)  +/-  (1.73e-44, 1.29e-104j)
| (0.00022538916494692615419 - 2.9061335135061516182e-494j)  +/-  (1.33e-43, 9.94e-104j)
| (2.1845618237296597331e-11 - 4.7865915590912687647e-499j)  +/-  (3.96e-49, 2.96e-109j)
| (1.5518305760138097596e-05 + 3.4311837082295638618e-495j)  +/-  (3.43e-45, 2.56e-105j)
| (0.068077547275039627752 - 1.0241072119136097316e-491j)  +/-  (4.01e-40, 3e-100j)
| (6.1458425088199552694e-09 - 2.1939064171435721747e-496j)  +/-  (4.54e-49, 3.39e-109j)
| (6.1458425088199552694e-09 + 1.5843530202538085956e-497j)  +/-  (5.78e-48, 4.31e-108j)
| (0.0016777607854465190957 + 1.7194378678596719458e-493j)  +/-  (7.26e-44, 5.42e-104j)
| (0.0016777607854465190957 + 7.0491018606501500906e-493j)  +/-  (3.23e-45, 2.41e-105j)
| (0.027763539503184092054 + 4.9976917675873814414e-492j)  +/-  (9.01e-44, 6.72e-104j)
| (0.00022538916494692615419 - 1.8338903521150884946e-493j)  +/-  (2.89e-46, 2.15e-106j)
| (2.1845618237296597331e-11 + 3.3815155122744435776e-498j)  +/-  (2.9e-51, 2.17e-111j)
| (0.11412012223317357634 + 1.1075885333913776173e-491j)  +/-  (2.79e-44, 2.06e-104j)
| (0.027763539503184092054 + 2.1764153665931136485e-492j)  +/-  (2.95e-45, 2.2e-105j)
| (0.17418455338153802063 - 1.909334587347762574e-491j)  +/-  (2.81e-44, 2.07e-104j)
| (0.11412012223317357634 + 1.6393542408942611848e-491j)  +/-  (1.88e-44, 1.4e-104j)
| (0.21215277758531269322 + 1.8028626110601912474e-491j)  +/-  (1.26e-44, 9.34e-105j)
| (0.068077547275039627752 - 5.6480612071465502609e-492j)  +/-  (1.44e-45, 1.13e-105j)
| (0.17418455338153802063 - 1.5597365319703872593e-491j)  +/-  (4.72e-45, 3.32e-105j)
