Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 18
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 8054880965040595537504108712022329/2616420482506284892722222867462*t^25 + 38318532686490862474726678493408987389/54944830132631982747166680216702*t^23 - 3709235259758805845518111914465376906699/54944830132631982747166680216702*t^21 + 65453924789021995893651495904258813923893/18314943377543994249055560072234*t^19 - 346045948455444559426569734061408230412088/3052490562923999041509260012039*t^17 + 6823477816157005987362812950159827283444729/3052490562923999041509260012039*t^15 - 12043632963166837691018952653624243452039725/436070080417714148787037144577*t^13 + 92084416354677522990744585382536526442292570/436070080417714148787037144577*t^11 - 844353751622751312357970658347724980970739555/872140160835428297574074289154*t^9 + 2195390217545643743067297557248776952554001455/872140160835428297574074289154*t^7 - 2933303286161246373455525132291856194622316065/872140160835428297574074289154*t^5 + 1644110385427518271189164617717505558924272025/872140160835428297574074289154*t^3 - 111889442686943409393747161516766198799180725/436070080417714148787037144577*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:
| (1.5093152835436173382 - 3.0950057574202503082e-273j)  +/-  (4.47e-124, 4.47e-124j)
| (-6.1010688419859005636 + 1.9464508357762524904e-273j)  +/-  (6.64e-122, 6.64e-122j)
| (-53.304307202012995798 + 1.9314014153045520641e-283j)  +/-  (8e-125, 8e-125j)
| (8.093377131087349119 - 8.6513029648275216332e-282j)  +/-  (7.66e-123, 7.66e-123j)
| (4.5173668061815881253 + 3.4818030450642686822e-280j)  +/-  (5.9e-122, 5.9e-122j)
| (-7.0094102363920008218 - 1.7069341885280404326e-279j)  +/-  (3.28e-122, 3.28e-122j)
| (-2.4494897427831780982 + 6.4985012283616136982e-297j)  +/-  (3.96e-123, 3.96e-123j)
| (-3.7932353000477464006 + 5.6916362400911601889e-318j)  +/-  (3.35e-122, 3.35e-122j)
| (53.304307202012995798 - 2.090897961908610521e-337j)  +/-  (8e-125, 8e-125j)
| (6.1010688419859005636 - 1.395232020820067664e-333j)  +/-  (6.94e-122, 6.94e-122j)
| (-5.2813190319494233748 - 8.0842313880868100938e-347j)  +/-  (7.59e-122, 7.59e-122j)
| (7.0094102363920008218 - 1.0622126969066931525e-358j)  +/-  (3.53e-122, 3.53e-122j)
| (-8.093377131087349119 - 6.9692565074610038199e-359j)  +/-  (6.44e-123, 6.44e-123j)
| (-4.5173668061815881253 + 2.4660806031497295927e-362j)  +/-  (6.18e-122, 6.18e-122j)
| (3.101982937842391518 + 1.789681918599873272e-366j)  +/-  (1.27e-122, 1.27e-122j)
| (2.4494897427831780982 - 1.0038834746498322029e-366j)  +/-  (4.22e-123, 4.22e-123j)
| (5.2813190319494233748 + 8.1530036704833405688e-369j)  +/-  (7.7e-122, 7.7e-122j)
| (0.44097761024700514913 + 3.5918177256716282178e-372j)  +/-  (2.61e-126, 2.61e-126j)
| (-1.5093152835436173382 - 8.6659205237941397718e-375j)  +/-  (4.43e-124, 4.43e-124j)
| (1.8970896005796689968 + 4.3573412231921566352e-378j)  +/-  (1.35e-123, 1.35e-123j)
| (3.7932353000477464006 + 5.5804821662630763265e-379j)  +/-  (3.18e-122, 3.18e-122j)
| (-1 + 4.0473937773725387983e-384j)  +/-  (3.29e-125, 3.29e-125j)
| (-3.101982937842391518 + 3.4773420532246450406e-389j)  +/-  (1.25e-122, 1.25e-122j)
| (-0.44097761024700514913 - 1.9364463770834512949e-394j)  +/-  (2e-126, 2e-126j)
| (-1.8970896005796689968 + 4.1245608753763042022e-395j)  +/-  (1.36e-123, 1.36e-123j)
| (-2.2187537812786329213e-399 - 2.709439713676792125e-399j)  +/-  (9.46e-398, 9.46e-398j)
| (1 + 3.6865447442783439307e-398j)  +/-  (3.29e-125, 3.29e-125j)
-------------------------------------------------
The weights are:
| (0.053003966905533439969 + 9.2182127160252898108e-275j)  +/-  (8.37e-24, 7.38e-85j)
| (2.822641293439896717e-09 - 2.603361498690971375e-281j)  +/-  (6.35e-40, 5.6e-101j)
| (5.8660790842740262777e-56 + 1.5254760238285013883e-306j)  +/-  (1.23e-64, 1.08e-125j)
| (2.9659995857988814657e-15 + 2.2710371581342723894e-284j)  +/-  (8.37e-44, 7.38e-105j)
| (1.0969829399561777188e-05 + 1.8904544187280326514e-278j)  +/-  (1.19e-37, 1.05e-98j)
| (8.3170036595688753649e-12 + 1.649048220612616098e-282j)  +/-  (4.96e-42, 4.37e-103j)
| (0.012369489487987247135 + 4.350285080031101995e-276j)  +/-  (6.24e-33, 5.5e-94j)
| (0.00021184727145440471032 + 8.1090779237773894272e-278j)  +/-  (9e-37, 7.94e-98j)
| (5.8660790842740262777e-56 - 1.6071225878410013697e-306j)  +/-  (6.9e-66, 6.08e-127j)
| (2.822641293439896717e-09 + 7.6056662439835488381e-281j)  +/-  (3.65e-42, 3.22e-103j)
| (2.7595062565327185381e-07 + 6.9324520634631541934e-280j)  +/-  (3.49e-40, 3.07e-101j)
| (8.3170036595688753649e-12 - 2.2387807122818711354e-282j)  +/-  (1.33e-43, 1.17e-104j)
| (2.9659995857988814657e-15 - 1.6636927456097021497e-284j)  +/-  (5.92e-45, 5.22e-106j)
| (1.0969829399561777188e-05 - 8.8278578632590033332e-279j)  +/-  (2.72e-39, 2.4e-100j)
| (0.0021906887213644710218 + 1.8408111231174023287e-276j)  +/-  (5.5e-39, 4.85e-100j)
| (0.012369489487987247135 - 1.8670000832498647102e-275j)  +/-  (6.17e-38, 5.44e-99j)
| (2.7595062565327185381e-07 - 1.4438609365428336601e-279j)  +/-  (2.86e-42, 2.52e-103j)
| (0.18867004994440842309 + 3.4119676983616352454e-274j)  +/-  (8.6e-37, 7.6e-98j)
| (0.053003966905533439969 + 5.3779639660936659818e-275j)  +/-  (1.32e-37, 1.16e-98j)
| (0.029618303265473400068 + 2.1262986112542467031e-274j)  +/-  (1.21e-37, 1.07e-98j)
| (0.00021184727145440471032 - 1.9608518819742370095e-277j)  +/-  (2.29e-40, 2.02e-101j)
| (0.13739520919768364555 - 9.1207620135720969229e-275j)  +/-  (1.29e-37, 1.14e-98j)
| (0.0021906887213644710218 - 6.1862151806094627709e-277j)  +/-  (1.78e-40, 1.58e-101j)
| (0.18867004994440842309 + 1.8636431253963171291e-274j)  +/-  (3.1e-38, 2.83e-99j)
| (0.029618303265473400068 - 2.3876401715941040953e-275j)  +/-  (3.58e-39, 3.11e-100j)
| (0.15305839319021698062 - 3.0548846367796250544e-274j)  +/-  (1.61e-38, 1.59e-99j)
| (0.13739520919768364555 - 4.5237707974639644139e-274j)  +/-  (1.01e-38, 7.91e-100j)
