Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 38
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^42 - 32367057756501387767271185768/5151895684408414257614025*t^40 + 97507240530938716238452566235408/87582226634943042379438425*t^38 - 10342099639862360125510871105004032/87582226634943042379438425*t^36 + 6993083893890325790949689527087983/834116444142314689327985*t^34 - 41434643274003584747363943829412943/98131346369684081097410*t^32 + 33277162902879147022596246825265752/2133290138471393067335*t^30 - 21160668227866393409073547270094489778/49065673184842040548705*t^28 + 3542824764995802554384970640785531656541/392525385478736324389640*t^26 - 1736132561206550994824849549047000679865/12077704168576502288912*t^24 + 457667971765786010535696012757511211615/262558786273402223672*t^22 - 4210031745963006900953294784742127140095/262558786273402223672*t^20 + 466433748041870287259939897369291850158385/4200940580374435578752*t^18 - 4804053862734541224215125826432587980700905/8401881160748871157504*t^16 + 565131444356370737972723357829688145601075/262558786273402223672*t^14 - 24286269700167102552018969433317954912965325/4200940580374435578752*t^12 + 1438933380059224246865362547936364112519732275/134430098571981938520064*t^10 - 18270911670714842390722255008176392046555025/1407645011224941764608*t^8 + 1277641035952745447270866565233136734600815675/134430098571981938520064*t^6 - 245291429071364164255073727580914972477307125/67215049285990969260032*t^4 + 1186701471380143445471422752077936261452171125/2150881577151711016321024*t^2 - 58966886019780348627966223500001232220043125/4301763154303422032642048
-------------------------------------------------
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:
| (6.8396592683983631633 - 2.0942558474257653531e-256j)  +/-  (1.25e-118, 1.25e-118j)
| (-5.4058938408026921308 - 2.8272742865330118994e-256j)  +/-  (8.34e-118, 8.34e-118j)
| (-8.0982816839480572246 - 6.1800518055372021131e-259j)  +/-  (2.52e-120, 2.52e-120j)
| (6.3276237737581348981 - 5.5289640924397904175e-255j)  +/-  (3.24e-118, 3.24e-118j)
| (7.4110540457803254327 + 2.3715589296499112795e-260j)  +/-  (2.78e-119, 2.78e-119j)
| (-4.9784193179451938001 - 1.4821395487793250939e-261j)  +/-  (9.22e-118, 9.22e-118j)
| (4.9784193179451938001 - 1.0870820357830294249e-260j)  +/-  (1.02e-117, 1.02e-117j)
| (-7.4110540457803254327 - 7.7462946633145825739e-274j)  +/-  (2.98e-119, 2.98e-119j)
| (-4.5665619502128693515 - 8.6724825597318861962e-273j)  +/-  (8.09e-118, 8.09e-118j)
| (5.8534035514221029558 + 6.1703851383698553681e-272j)  +/-  (6.46e-118, 6.46e-118j)
| (2.2904400041330501608 - 3.00795746198729848e-283j)  +/-  (3.09e-120, 3.09e-120j)
| (3.3971138885789312059 - 3.0929290946120496449e-301j)  +/-  (1.07e-118, 1.07e-118j)
| (8.0982816839480572246 - 1.0334843564335189657e-318j)  +/-  (2.45e-120, 2.45e-120j)
| (-0.87560849309255521627 - 2.6889367739374900875e-323j)  +/-  (3.94e-124, 3.94e-124j)
| (-2.2904400041330501608 - 3.6181191382128899542e-319j)  +/-  (3.05e-120, 3.05e-120j)
| (-4.1671937509505656197 - 3.3743124339778863993e-316j)  +/-  (5e-118, 5e-118j)
| (-5.8534035514221029558 + 1.1725858370986212359e-318j)  +/-  (6.09e-118, 6.09e-118j)
| (-2.6546739192663197361 + 2.2388966870194042488e-318j)  +/-  (1.09e-119, 1.09e-119j)
| (5.4058938408026921308 + 1.7418800528745737707e-321j)  +/-  (8.63e-118, 8.63e-118j)
| (3.7779829715511411049 + 1.4868193364628003638e-335j)  +/-  (2.62e-118, 2.62e-118j)
| (1.9269745503978767464 + 4.1569972520126597026e-348j)  +/-  (1.12e-120, 1.12e-120j)
| (1.6053478034130488758 + 1.7458673299672420621e-348j)  +/-  (1.01e-120, 1.01e-120j)
| (-3.7779829715511411049 + 6.1407830147309372936e-347j)  +/-  (2.31e-118, 2.31e-118j)
| (-3.3971138885789312059 - 5.6777095390694073629e-347j)  +/-  (1.04e-118, 1.04e-118j)
| (-1.6506801238857845559 + 2.2660847184879817078e-349j)  +/-  (1.41e-120, 1.41e-120j)
| (4.5665619502128693515 - 4.8535271169416545787e-345j)  +/-  (8.11e-118, 8.11e-118j)
| (1.2290262221385897052 - 3.2738271234816641522e-357j)  +/-  (8.22e-123, 8.22e-123j)
| (2.6546739192663197361 + 6.6668881587814605092e-353j)  +/-  (1.02e-119, 1.02e-119j)
| (-1.9269745503978767464 - 3.1673067106945378496e-362j)  +/-  (1.11e-120, 1.11e-120j)
| (-1.2290262221385897052 + 2.6934455954319009409e-363j)  +/-  (9.13e-123, 9.13e-123j)
| (-6.8396592683983631633 - 2.8170587700341972959e-359j)  +/-  (1.36e-118, 1.36e-118j)
| (1.6506801238857845559 + 1.3789303737084510701e-360j)  +/-  (1.39e-120, 1.39e-120j)
| (0.17477192763441092128 + 1.0749659171868160739e-366j)  +/-  (1.06e-126, 1.06e-126j)
| (4.1671937509505656197 - 4.655466097707751104e-357j)  +/-  (4.53e-118, 4.53e-118j)
| (-3.0231078217169608504 + 9.2218767229692228308e-371j)  +/-  (3.64e-119, 3.64e-119j)
| (-6.3276237737581348981 - 1.8151977414820487336e-370j)  +/-  (3.41e-118, 3.41e-118j)
| (3.0231078217169608504 - 9.4633915434242433485e-373j)  +/-  (3.67e-119, 3.67e-119j)
| (0.52464762327529031788 + 1.3028138448808624838e-383j)  +/-  (1.9e-125, 1.9e-125j)
| (0.87560849309255521627 - 2.3575862330107357222e-382j)  +/-  (4.27e-124, 4.27e-124j)
| (-0.17477192763441092128 - 2.1422858896561905205e-384j)  +/-  (1.06e-126, 1.06e-126j)
| (-0.52464762327529031788 + 4.7652448721221470067e-383j)  +/-  (1.6e-125, 1.6e-125j)
| (-1.6053478034130488758 + 6.8157020696547068418e-379j)  +/-  (9.51e-121, 9.51e-121j)
-------------------------------------------------
The weights are:
| (1.4602488077300143253e-21 + 2.5494165151028429651e-274j)  +/-  (5.18e-31, 1.9e-89j)
| (5.0099581765195337028e-14 - 8.2526479473871076977e-269j)  +/-  (1.49e-27, 5.45e-86j)
| (1.4733313651753866001e-29 - 3.7045340352913275926e-278j)  +/-  (8.72e-35, 3.19e-93j)
| (1.1314115866943745641e-18 + 4.5769612672843797859e-272j)  +/-  (3.99e-30, 1.46e-88j)
| (4.858761290988438263e-25 - 9.4767404411642564484e-277j)  +/-  (5.05e-33, 1.85e-91j)
| (4.0724839116636452148e-12 + 3.6080852325650512323e-268j)  +/-  (2.58e-27, 9.44e-86j)
| (4.0724839116636452148e-12 - 2.9422819973946200517e-269j)  +/-  (8.94e-28, 3.27e-86j)
| (4.858761290988438263e-25 + 1.0939375113537079585e-275j)  +/-  (2.07e-34, 7.59e-93j)
| (2.006814101096888414e-10 - 1.5788811180127315715e-267j)  +/-  (1.58e-26, 5.8e-85j)
| (3.4178839620079310029e-16 - 3.5874612060545904993e-271j)  +/-  (7.93e-30, 2.91e-88j)
| (0.0010782211916278024152 + 3.6461614763508605248e-264j)  +/-  (3.29e-19, 1.2e-77j)
| (2.0705512504297230204e-06 - 4.3510748005634252583e-266j)  +/-  (3.51e-24, 1.28e-82j)
| (1.4733313651753866001e-29 - 3.4842012367126498559e-281j)  +/-  (4.67e-36, 1.71e-94j)
| (0.092214587118267086783 + 5.9781723106274094851e-263j)  +/-  (7.52e-20, 2.75e-78j)
| (0.0010782211916278024152 - 7.554686724448174191e-264j)  +/-  (3.69e-21, 1.35e-79j)
| (6.3844690469024448017e-09 + 7.5191265363942026385e-267j)  +/-  (1.55e-27, 5.67e-86j)
| (3.4178839620079310029e-16 - 2.1850824001007525201e-270j)  +/-  (4.59e-32, 1.68e-90j)
| (0.00017963449082399562618 + 1.9953157876780875221e-264j)  +/-  (2.31e-23, 8.47e-82j)
| (5.0099581765195337028e-14 + 3.330188070007758199e-270j)  +/-  (1.71e-30, 6.26e-89j)
| (1.3736436333597067853e-07 + 8.6399270696810244671e-267j)  +/-  (1.77e-27, 6.5e-86j)
| (0.0050656371475360588678 - 2.1859086294600397062e-263j)  +/-  (9.05e-22, 3.31e-80j)
| (0.024767606194947539392 - 2.5141318203927085194e-262j)  +/-  (1.39e-20, 5.1e-79j)
| (1.3736436333597067853e-07 - 3.3878761936493438556e-266j)  +/-  (2.52e-28, 9.22e-87j)
| (2.0705512504297230204e-06 + 1.4074044868964802634e-265j)  +/-  (1.07e-27, 3.93e-86j)
| (-0.0090236930289538090475 - 4.0705758780508628925e-262j)  +/-  (2.84e-23, 1.04e-81j)
| (2.006814101096888414e-10 + 2.2811181030970839964e-268j)  +/-  (9.6e-31, 3.51e-89j)
| (0.044318410385160739313 + 4.8395130939970689464e-263j)  +/-  (1.29e-22, 4.72e-81j)
| (0.00017963449082399562618 - 8.4219235542356029756e-265j)  +/-  (1.83e-26, 6.7e-85j)
| (0.0050656371475360588678 + 3.9932343940302644572e-263j)  +/-  (7.52e-25, 2.76e-83j)
| (0.044318410385160739313 - 7.0461236685993452807e-263j)  +/-  (1.71e-23, 6.27e-82j)
| (1.4602488077300143253e-21 - 9.9889849973923746371e-274j)  +/-  (5.43e-38, 1.99e-96j)
| (-0.0090236930289538090475 + 2.4423856563861464843e-262j)  +/-  (1.9e-24, 6.96e-83j)
| (0.19130593337551237022 - 5.2984265113480168762e-263j)  +/-  (2.4e-25, 8.8e-84j)
| (6.3844690469024448017e-09 - 1.5103161408114784445e-267j)  +/-  (7.86e-31, 2.88e-89j)
| (2.2475903785468445024e-05 - 5.4234264911660647628e-265j)  +/-  (8.34e-29, 3.05e-87j)
| (1.1314115866943745641e-18 + 5.1325139810154034696e-272j)  +/-  (1.55e-36, 5.67e-95j)
| (2.2475903785468445024e-05 + 1.9770252124149005876e-265j)  +/-  (5.01e-29, 1.83e-87j)
| (0.15006897271640559887 + 4.9100540649089942088e-263j)  +/-  (5.09e-27, 1.87e-85j)
| (0.092214587118267086783 - 4.5833304164962502871e-263j)  +/-  (3.56e-27, 1.3e-85j)
| (0.19130593337551237022 + 5.5849108781197655349e-263j)  +/-  (1.22e-27, 4.49e-86j)
| (0.15006897271640559887 - 5.7530442910931610347e-263j)  +/-  (6.11e-28, 2.17e-86j)
| (0.024767606194947539392 + 4.1286483525374431184e-262j)  +/-  (1.63e-27, 6.75e-86j)
