Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 23
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Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^37 - 49809463975510789629375582642143499672/9317405211111424789646489158029125*t^35 + 6806277167854517122577141493848354345256/9317405211111424789646489158029125*t^33 - 517842726528494987856874555432475345116344/9317405211111424789646489158029125*t^31 + 64550863379083319227901606179277777991378984/24225253548889704453080871810875725*t^29 - 1118701615153991412102037938605976046662760236/13044367295555994705505084821240775*t^27 + 325456237581744218830534610400439092917361127473/169576774842227931171566102676130075*t^25 - 10323482778137903115670102538906087245131330901173/339153549684455862343132205352260150*t^23 + 302584777644225259691442986656671774825325161129/876932255163428215496140156049800*t^21 - 216800628191994729643923485465463319225348767610239/77520811356447054249858789794802320*t^19 + 311998869145660218403018732833136334095243156866381/19380202839111763562464697448700580*t^17 - 84572556775899769962142678088794484310670091424639/1302870779099950491594265374702560*t^15 + 1676012474689949457000917277356963430473635635939/9344360096003743279876903302170*t^13 - 230735635327243880068563654436240263324064004327757/701545804130742572396912124839840*t^11 + 428875416795723356967615694364418304034882438726469/1122473286609188115835059399743744*t^9 - 84075533332357916572366332000114003807912393518139/320706653316910890238588399926784*t^7 + 241928371312403394361155293027901613139704049285979/2565653226535287121908707199414272*t^5 - 71011801504343804759464408169161466973021180635709/5131306453070574243817414398828544*t^3 + 1990007550000125048719189418943036072754839272841/5131306453070574243817414398828544*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: 0
  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:
| (-5.4141280416357074908 - 1.3690301873473354424e-438j)  +/-  (3.4e-120, 3.4e-120j)
| (-2.3166778458612639611 - 1.7198531056427479042e-442j)  +/-  (5.83e-121, 5.83e-121j)
| (6.7300882498474260939 - 2.5570964167127117358e-442j)  +/-  (1.79e-121, 1.79e-121j)
| (5.4141280416357074908 - 5.5110117494901794041e-449j)  +/-  (3.25e-120, 3.25e-120j)
| (4.8770456620131362741 + 6.249449171716651828e-460j)  +/-  (5.52e-120, 5.52e-120j)
| (10.992060928810581455 - 1.5061180570339435557e-466j)  +/-  (9.1e-124, 9.1e-124j)
| (-3.4678350964366356194 + 1.2899994718877030953e-461j)  +/-  (4.61e-120, 4.61e-120j)
| (-10.992060928810581455 + 2.9535087255613499793e-469j)  +/-  (9.1e-124, 9.1e-124j)
| (-4.8770456620131362741 + 5.9825414836622038364e-465j)  +/-  (5.98e-120, 5.98e-120j)
| (3.0486879132310133212 - 2.7349174395941008928e-465j)  +/-  (2.98e-120, 2.98e-120j)
| (3.4678350964366356194 - 6.0883202080448954236e-471j)  +/-  (5.27e-120, 5.27e-120j)
| (-6.7300882498474260939 + 1.0268087885758534131e-476j)  +/-  (1.94e-121, 1.94e-121j)
| (6.0125220595380861421 + 2.5638192665197747343e-476j)  +/-  (1.16e-120, 1.16e-120j)
| (-3.911506869286660161 - 2.4593804985011208278e-479j)  +/-  (6.51e-120, 6.51e-120j)
| (-6.0125220595380861421 - 1.2715378292670122592e-481j)  +/-  (1.19e-120, 1.19e-120j)
| (1.6506801238857845559 - 1.1760915006526242099e-483j)  +/-  (3.65e-122, 3.65e-122j)
| (1.9934558432194148849 + 1.0435710066412408312e-482j)  +/-  (1.59e-121, 1.59e-121j)
| (4.379642388316824271 + 1.4817018622616126692e-484j)  +/-  (7.46e-120, 7.46e-120j)
| (-0.85055070809945363663 + 5.5305082968629290689e-497j)  +/-  (5.98e-124, 5.98e-124j)
| (-2.6612593529121161453 - 1.8590605544792130868e-493j)  +/-  (1.35e-120, 1.35e-120j)
| (3.911506869286660161 - 5.9886759727052968114e-492j)  +/-  (5.94e-120, 5.94e-120j)
| (1.0363502036603261655 + 2.7259414585587836625e-499j)  +/-  (2.39e-123, 2.39e-123j)
| (1.2997170475287520799 - 1.627887508388473148e-498j)  +/-  (9.26e-123, 9.26e-123j)
| (-1.2997170475287520799 - 5.4498254590315770487e-498j)  +/-  (9.23e-123, 9.23e-123j)
| (-1.0363502036603261655 + 8.9428939750594018778e-499j)  +/-  (2.42e-123, 2.42e-123j)
| (-4.379642388316824271 + 3.6758601029851236089e-495j)  +/-  (7.05e-120, 7.05e-120j)
| (0.85055070809945363663 + 2.5293756278781501474e-500j)  +/-  (5.88e-124, 5.88e-124j)
| (2.6612593529121161453 - 7.1927744058252730743e-497j)  +/-  (1.33e-120, 1.33e-120j)
| (-3.0486879132310133212 - 2.3049626735197732399e-498j)  +/-  (2.71e-120, 2.71e-120j)
| (-0.52464762327529031788 - 1.7937714941953905128e-507j)  +/-  (2.37e-125, 2.37e-125j)
| (-1.9934558432194148849 - 3.6990065601809842001e-503j)  +/-  (1.63e-121, 1.63e-121j)
| (0.18980675578014987883 + 9.0715847854849871336e-508j)  +/-  (1.16e-126, 1.16e-126j)
| (0.52464762327529031788 - 4.169387659012938002e-506j)  +/-  (2.27e-125, 2.27e-125j)
| (-3.3016846350242873648e-517 - 1.3093055431777117945e-516j)  +/-  (5e-515, 5e-515j)
| (-0.18980675578014987883 + 3.2847191880413623664e-507j)  +/-  (1.16e-126, 1.16e-126j)
| (-1.6506801238857845559 - 8.4037940789652065403e-505j)  +/-  (4.31e-122, 4.31e-122j)
| (2.3166778458612639611 + 6.9215116736176326286e-505j)  +/-  (5.57e-121, 5.57e-121j)
-------------------------------------------------
The weights are:
| (5.9054254528635485708e-14 - 5.2977139693570717604e-451j)  +/-  (4.54e-32, 2.78e-93j)
| (0.00085715504425765891454 + 2.3791740438168806693e-445j)  +/-  (4.96e-19, 3.04e-80j)
| (9.9363310638063447158e-21 - 7.0809175628749271e-457j)  +/-  (4.02e-36, 2.46e-97j)
| (5.9054254528635485708e-14 - 6.9326199501092638013e-453j)  +/-  (5.26e-33, 3.22e-94j)
| (1.3589136147015022226e-11 + 2.1032812593467866218e-451j)  +/-  (1.12e-31, 6.86e-93j)
| (1.0357815592198300837e-37 + 6.1882845310667863399e-466j)  +/-  (6.2e-45, 3.8e-106j)
| (1.4589155149651045309e-06 - 4.0228353855508123416e-447j)  +/-  (1.52e-28, 9.3e-90j)
| (1.0357815592198300837e-37 - 1.8785953184365161649e-465j)  +/-  (2.44e-46, 1.49e-107j)
| (1.3589136147015022226e-11 + 4.3940816521730523383e-450j)  +/-  (2.63e-33, 1.61e-94j)
| (2.1018612183796994376e-05 + 7.4200560781151927867e-447j)  +/-  (2.09e-28, 1.28e-89j)
| (1.4589155149651045309e-06 - 7.4791610794121811506e-448j)  +/-  (8.34e-30, 5.11e-91j)
| (9.9363310638063447158e-21 + 6.9085589181589892551e-456j)  +/-  (3e-39, 1.84e-100j)
| (7.230985853717059309e-17 + 1.2294971085874839626e-454j)  +/-  (7.73e-37, 4.73e-98j)
| (5.8242216760878342386e-08 + 4.4266276684657318804e-448j)  +/-  (2.8e-32, 1.72e-93j)
| (7.230985853717059309e-17 - 2.503679764522197505e-453j)  +/-  (2.68e-37, 1.64e-98j)
| (0.013048284595671165157 + 5.3596334923722115714e-444j)  +/-  (9.8e-26, 6e-87j)
| (0.0035006165684144058781 - 1.3889131360537505637e-444j)  +/-  (2.32e-27, 1.42e-88j)
| (1.2699190635734279014e-09 - 4.2209490791593202446e-450j)  +/-  (3.21e-34, 1.96e-95j)
| (0.077007403194591314308 - 1.7071959955620706299e-442j)  +/-  (7.67e-26, 4.7e-87j)
| (0.00017390901214626988832 - 2.6972866079864948927e-445j)  +/-  (2.36e-31, 1.45e-92j)
| (5.8242216760878342386e-08 + 6.2853362024712295167e-449j)  +/-  (3.49e-33, 2.14e-94j)
| (0.030489897905075539007 + 9.3372578439336723323e-443j)  +/-  (2.86e-26, 1.75e-87j)
| (0.035256567595909779768 - 2.6201532628476671713e-443j)  +/-  (1.92e-26, 1.18e-87j)
| (0.035256567595909779768 - 3.7478785797439948464e-443j)  +/-  (1.55e-27, 9.5e-89j)
| (0.030489897905075539007 + 1.2593819334219304682e-442j)  +/-  (1.86e-26, 1.14e-87j)
| (1.2699190635734279014e-09 - 4.428909951831258384e-449j)  +/-  (1.74e-35, 1.07e-96j)
| (0.077007403194591314308 - 1.3292369496654515315e-442j)  +/-  (6.25e-27, 3.83e-88j)
| (0.00017390901214626988832 - 5.9912186194920301363e-446j)  +/-  (2.21e-31, 1.35e-92j)
| (2.1018612183796994376e-05 + 3.3631313431929217905e-446j)  +/-  (1.16e-32, 7.13e-94j)
| (0.14633025836694990441 + 1.8392287684784863571e-442j)  +/-  (4.08e-28, 2.5e-89j)
| (0.0035006165684144058781 - 1.5163714059706054794e-444j)  +/-  (5.89e-31, 3.61e-92j)
| (0.17202095335611782958 - 3.8416510161241081778e-442j)  +/-  (8.88e-29, 5.43e-90j)
| (0.14633025836694990441 + 1.5715675762329286441e-442j)  +/-  (6.16e-29, 3.77e-90j)
| (0.042584834614766567629 + 5.8732555811844842109e-442j)  +/-  (4.55e-29, 2.78e-90j)
| (0.17202095335611782958 - 4.0684403003175267847e-442j)  +/-  (2.62e-29, 1.6e-90j)
| (0.013048284595671165157 + 7.8755544538766723986e-444j)  +/-  (1.5e-31, 9.34e-93j)
| (0.00085715504425765891454 + 3.4185857067193719253e-445j)  +/-  (6.19e-33, 3.6e-94j)
