Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^30 - 44415116660718776/14034565486637*t^28 + 41787292089133003284/154380220353007*t^26 - 2037902437254525232950/154380220353007*t^24 + 2736181514635588869525/6712183493609*t^22 - 10219444445714530223925/1220396998838*t^20 + 285672334235558196305925/2440793997676*t^18 - 5466076290997159029376275/4881587995352*t^16 + 71094019363512913815854625/9763175990704*t^14 - 616457662947059781468859875/19526351981408*t^12 + 3444381417064654515554980875/39052703962816*t^10 - 11747550342411579500016337125/78105407925632*t^8 + 22435126401148897969032625125/156210815851264*t^6 - 20712361223497629609450174375/312421631702528*t^4 + 6902164669750959186681114375/624843263405056*t^2 - 344707237908050990670140625/1249686526810112
-------------------------------------------------
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:   30 out of 30
Indefinite weights: 0 out of 30
Negative weights:   0 out of 30
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (4.7679083427559449884 + 2.1878285939131315873e-275j)  +/-  (1.29e-120, 1.29e-120j)
| (-1.262506471817959365 + 1.3004021601741530924e-279j)  +/-  (8.6e-124, 8.6e-124j)
| (3.7844729202429740017 + 2.9876082609899761642e-276j)  +/-  (1.2e-120, 1.2e-120j)
| (-5.9199139135296215841 + 1.7943590098322443934e-282j)  +/-  (2.96e-121, 2.96e-121j)
| (-6.6478855427506000907 - 3.8461570652447280132e-294j)  +/-  (4.1e-122, 4.1e-122j)
| (-3.7844729202429740017 - 1.6729339488913030711e-307j)  +/-  (1.32e-120, 1.32e-120j)
| (-4.2622181192321594918 + 6.4859702821924243203e-320j)  +/-  (1.56e-120, 1.56e-120j)
| (5.3129863581021106794 + 7.8417223991654119501e-327j)  +/-  (8.02e-121, 8.02e-121j)
| (-5.3129863581021106794 - 9.4906333221695604245e-331j)  +/-  (7.58e-121, 7.58e-121j)
| (4.2622181192321594918 - 2.0945652855040096353e-338j)  +/-  (1.55e-120, 1.55e-120j)
| (6.6478855427506000907 + 6.4114979121214735396e-344j)  +/-  (4.11e-122, 4.11e-122j)
| (-2.8884834542446347376 - 5.7208927875003390817e-349j)  +/-  (3.38e-121, 3.38e-121j)
| (-1.6506801238857845559 + 1.5128980903037294669e-362j)  +/-  (5.91e-123, 5.91e-123j)
| (-4.7679083427559449884 - 7.2593594203362394682e-368j)  +/-  (1.46e-120, 1.46e-120j)
| (-3.3279654340381046883 - 2.3622896018292888734e-380j)  +/-  (6.98e-121, 6.98e-121j)
| (1.6506801238857845559 - 3.4570002894350305163e-387j)  +/-  (5.57e-123, 5.57e-123j)
| (3.3279654340381046883 - 9.4854927364905205429e-385j)  +/-  (7.27e-121, 7.27e-121j)
| (-2.0509826281355495698 - 9.749019370089310507e-387j)  +/-  (2.28e-122, 2.28e-122j)
| (-0.17334337719571430791 + 6.4598076669616511464e-406j)  +/-  (7.64e-127, 7.64e-127j)
| (-2.4633506340977978266 - 5.9413775101209809112e-393j)  +/-  (1.03e-121, 1.03e-121j)
| (2.8884834542446347376 - 1.5274856801181736749e-394j)  +/-  (3.39e-121, 3.39e-121j)
| (0.88705319480172758621 - 5.4328174746011372607e-400j)  +/-  (1.03e-124, 1.03e-124j)
| (0.17334337719571430791 - 4.2590277450984517094e-409j)  +/-  (7.64e-127, 7.64e-127j)
| (-0.52464762327529031788 - 3.9591398221398476217e-401j)  +/-  (8.88e-126, 8.88e-126j)
| (5.9199139135296215841 + 5.2108712603587124136e-397j)  +/-  (2.61e-121, 2.61e-121j)
| (2.0509826281355495698 - 1.9078722418479383162e-396j)  +/-  (2.43e-122, 2.43e-122j)
| (0.52464762327529031788 + 6.2884956022189201144e-402j)  +/-  (8.88e-126, 8.88e-126j)
| (1.262506471817959365 - 3.284243532116797787e-400j)  +/-  (8.84e-124, 8.84e-124j)
| (2.4633506340977978266 - 8.6890878250775770128e-397j)  +/-  (9.45e-122, 9.45e-122j)
| (-0.88705319480172758621 - 1.944554701637353727e-403j)  +/-  (9.51e-125, 9.51e-125j)
-------------------------------------------------
The weights are:
| (3.9540244420170023822e-11 + 5.634833932561921706e-286j)  +/-  (4.24e-34, 1.88e-93j)
| (0.043770329845233304175 + 3.5566976804489684389e-280j)  +/-  (2.43e-18, 1.08e-77j)
| (1.5848443824820115628e-07 - 2.0951161237857789372e-282j)  +/-  (2.47e-31, 1.1e-90j)
| (2.2143567116954878825e-16 + 8.5365725684530805228e-289j)  +/-  (6.96e-38, 3.09e-97j)
| (3.028691333127769107e-20 - 7.5273322188631269146e-291j)  +/-  (1.91e-39, 8.46e-99j)
| (1.5848443824820115628e-07 + 6.2268651742315394063e-284j)  +/-  (1.32e-33, 5.87e-93j)
| (3.5668721245466323631e-09 - 7.2721245677863721022e-285j)  +/-  (6.9e-35, 3.06e-94j)
| (1.7728179975787436202e-13 - 2.6391604026117479957e-286j)  +/-  (1.1e-38, 4.89e-98j)
| (1.7728179975787436202e-13 - 3.120846856040565031e-287j)  +/-  (1.49e-37, 6.61e-97j)
| (3.5668721245466323631e-09 - 1.0047362335944556495e-283j)  +/-  (3.6e-36, 1.59e-95j)
| (3.028691333127769107e-20 - 3.2332630331447781339e-290j)  +/-  (2.92e-42, 1.29e-101j)
| (5.799699361112612378e-05 + 1.978081368896193116e-282j)  +/-  (1.99e-33, 8.84e-93j)
| (0.014585317840073117674 - 3.5801005617774692721e-281j)  +/-  (6.57e-30, 2.91e-89j)
| (3.9540244420170023822e-11 + 5.9757740632835813828e-286j)  +/-  (4.38e-37, 1.94e-96j)
| (3.9101729410229565783e-06 - 3.9858262442769105577e-283j)  +/-  (2.42e-34, 1.07e-93j)
| (0.014585317840073117674 + 2.5882016284922358804e-280j)  +/-  (2.89e-33, 1.28e-92j)
| (3.9101729410229565783e-06 + 6.7821306768913020447e-282j)  +/-  (4.61e-37, 2.04e-96j)
| (0.0034149519107210465573 + 2.3048296714512055379e-281j)  +/-  (4.57e-33, 2.02e-92j)
| (0.19026190192168223102 - 1.3539468748255686836e-279j)  +/-  (4.69e-32, 2.08e-91j)
| (0.00054682304371572400951 - 7.7257317848170717212e-282j)  +/-  (9.43e-34, 4.18e-93j)
| (5.799699361112612378e-05 - 1.724475976679567908e-281j)  +/-  (2.35e-37, 1.04e-96j)
| (0.094751619820247469906 + 8.4593362907708008245e-280j)  +/-  (1.03e-33, 4.56e-93j)
| (0.19026190192168223102 + 1.4151636045535507048e-279j)  +/-  (1.58e-33, 6.99e-93j)
| (0.15260698636074683714 + 1.0735608341829172289e-279j)  +/-  (1.86e-33, 8.21e-93j)
| (2.2143567116954878825e-16 + 4.8372996785845576494e-288j)  +/-  (2.8e-43, 1.24e-102j)
| (0.0034149519107210465573 - 1.1654025338606695386e-280j)  +/-  (1.26e-36, 5.57e-96j)
| (0.15260698636074683714 - 1.2037576425062864365e-279j)  +/-  (1.01e-34, 4.47e-94j)
| (0.043770329845233304175 - 5.0343921925009519091e-280j)  +/-  (1.36e-35, 5.99e-95j)
| (0.00054682304371572400951 + 4.6673087417346824143e-281j)  +/-  (2.6e-37, 1.15e-96j)
| (0.094751619820247469906 - 7.8663580349089946374e-280j)  +/-  (2.64e-35, 1.09e-94j)
