Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 9 16
-------------------------------------------------
Trying to find an order 9 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P2 : t^15 - 13845/191*t^13 + 360405/191*t^11 - 4272555/191*t^9 + 24327405/191*t^7 - 64538775/191*t^5 + 68923575/191*t^3 - 18129825/191*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^31 - 57010117328160707221839485390631909655/127678172195960946379309627115979517*t^29 + 10257982309944094849354605018951121519195/127678172195960946379309627115979517*t^27 - 3027010787425551134847140550639714279302615/383034516587882839137928881347938551*t^25 + 183741273049907803609459804404965766302791475/383034516587882839137928881347938551*t^23 - 7313260173914925160739443947925733717284228625/383034516587882839137928881347938551*t^21 + 197042092115289485868836481827746087311830959525/383034516587882839137928881347938551*t^19 - 3646561598011138324056834849627177832302053512075/383034516587882839137928881347938551*t^17 + 46446025834352566579721941475075622655427691161125/383034516587882839137928881347938551*t^15 - 134489432478225917549691005099173615145785246235125/127678172195960946379309627115979517*t^13 + 780492772593427554317977809703175091245115100816625/127678172195960946379309627115979517*t^11 - 265690651878126795786194982639169187580326050571125/11607106563269176943573602465089047*t^9 + 608079922581907564869728793471397218483337468364625/11607106563269176943573602465089047*t^7 - 781520970338406505246184963233696013614138600216875/11607106563269176943573602465089047*t^5 + 486096311613285833355945554098452142978708378284375/11607106563269176943573602465089047*t^3 - 100252484253233875494515769323786003044777611875625/11607106563269176943573602465089047*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
Positive weights:   31 out of 31
Indefinite weights: 0 out of 31
Negative weights:   0 out of 31
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (3.8796403220018030492 - 3.1710764229543662432e-366j)  +/-  (1.11e-120, 1.11e-120j)
| (-8.2615823390255012477 - 4.8993555836836961477e-367j)  +/-  (4.86e-122, 4.86e-122j)
| (-12.864132707639172954 + 3.4058172563377753056e-369j)  +/-  (8.67e-124, 8.67e-124j)
| (2.8523776395080470908 + 4.2885458510936729949e-367j)  +/-  (1.54e-121, 1.54e-121j)
| (4.3418637687749014379 + 3.6822537800689622395e-366j)  +/-  (1.97e-120, 1.97e-120j)
| (12.864132707639172954 - 3.4531464907756385641e-370j)  +/-  (8.67e-124, 8.67e-124j)
| (-4.3418637687749014379 + 9.7234768687721161196e-365j)  +/-  (1.97e-120, 1.97e-120j)
| (-5.5533529315903281928 - 1.2734314358728595425e-369j)  +/-  (1.14e-120, 1.14e-120j)
| (7.2094666581229529422 + 1.1545468211793502151e-374j)  +/-  (2.5e-121, 2.5e-121j)
| (-1.8891758777537106755 - 3.7982028841680670053e-376j)  +/-  (4.9e-123, 4.9e-123j)
| (8.2615823390255012477 + 2.486590440824302664e-375j)  +/-  (4.91e-122, 4.91e-122j)
| (6.3323533291181535762 + 4.4025203030713527679e-374j)  +/-  (6.7e-121, 6.7e-121j)
| (-6.3323533291181535762 - 5.2828586335974810996e-373j)  +/-  (6.29e-121, 6.29e-121j)
| (-1.3498952853218839149 - 9.7863081825432947116e-378j)  +/-  (1e-123, 1e-123j)
| (-4.8675088466804980907 + 4.1863218769177361522e-375j)  +/-  (1.72e-120, 1.72e-120j)
| (2.4440098084964929991 - 2.3243690050557694253e-381j)  +/-  (3.45e-122, 3.45e-122j)
| (4.8675088466804980907 - 1.9676223496631201744e-379j)  +/-  (1.8e-120, 1.8e-120j)
| (-3.8796403220018030492 - 5.1488486075045916765e-387j)  +/-  (1.05e-120, 1.05e-120j)
| (-2.0846549594537907181e-405 + 3.6038383201079733174e-406j)  +/-  (6.56e-404, 6.56e-404j)
| (-7.2094666581229529422 - 7.6932727265319736584e-396j)  +/-  (2.3e-121, 2.3e-121j)
| (1.3498952853218839149 - 2.2179204152249675694e-399j)  +/-  (1.01e-123, 1.01e-123j)
| (1.1542189542438079954 + 2.3115490913542698563e-401j)  +/-  (3.55e-124, 3.55e-124j)
| (-1.1542189542438079954 - 1.8865324039849403829e-400j)  +/-  (3.46e-124, 3.46e-124j)
| (-2.8523776395080470908 - 1.2685068364522565555e-401j)  +/-  (1.39e-121, 1.39e-121j)
| (3.3242574335521189524 - 3.4902471639030218317e-411j)  +/-  (3.77e-121, 3.77e-121j)
| (5.5533529315903281928 + 1.9088739925974020037e-413j)  +/-  (1.21e-120, 1.21e-120j)
| (0.61670659019259415219 - 9.3655522066127487577e-421j)  +/-  (7.44e-126, 7.44e-126j)
| (1.8891758777537106755 + 3.0981389994841402194e-418j)  +/-  (4.46e-123, 4.46e-123j)
| (-2.4440098084964929991 - 2.7952620070479136297e-419j)  +/-  (4.5e-122, 4.5e-122j)
| (-0.61670659019259415219 - 5.02556997653596333e-430j)  +/-  (7.44e-126, 7.44e-126j)
| (-3.3242574335521189524 - 2.4001624548641858356e-431j)  +/-  (3.83e-121, 3.83e-121j)
-------------------------------------------------
The weights are:
| (0.00011258756003930748774 + 7.2638801634280924354e-370j)  +/-  (1.06e-31, 1.48e-91j)
| (7.2800734358633311592e-16 + 1.2441034957474175042e-377j)  +/-  (5.49e-42, 7.64e-102j)
| (3.2905401909146598397e-28 - 1.2059128116606747874e-384j)  +/-  (9.17e-48, 1.28e-107j)
| (0.0026195598259236324481 - 8.2320670480172624165e-369j)  +/-  (4.66e-29, 6.48e-89j)
| (1.4157759110993614805e-05 + 1.2558100315458830634e-370j)  +/-  (6.9e-34, 9.6e-94j)
| (3.2905401909146598397e-28 + 6.7079864883375949011e-385j)  +/-  (6.99e-49, 9.72e-109j)
| (1.4157759110993614805e-05 + 5.2836772952667118065e-369j)  +/-  (3.94e-36, 5.49e-96j)
| (5.909066538854108414e-08 - 6.7539879121619264307e-372j)  +/-  (9.49e-39, 1.32e-98j)
| (1.9437026168870552438e-12 + 6.9735473152510674858e-376j)  +/-  (4.65e-42, 6.47e-102j)
| (0.039394271031786253877 - 1.598720817250711735e-367j)  +/-  (5.82e-30, 8.1e-90j)
| (7.2800734358633311592e-16 - 4.77450805906404737e-378j)  +/-  (5.26e-44, 7.31e-104j)
| (6.4375282105519273713e-10 - 3.8184011767896361071e-374j)  +/-  (9.15e-41, 1.27e-100j)
| (6.4375282105519273713e-10 + 1.4568240655521851266e-373j)  +/-  (7.74e-42, 1.08e-101j)
| (0.056721656032873121616 + 5.197386715752625892e-367j)  +/-  (5.11e-30, 7.11e-90j)
| (1.7772237638594821766e-06 + 3.0465969272149715735e-370j)  +/-  (3.29e-39, 4.58e-99j)
| (0.0098723629195113989633 + 2.2065845277185845899e-368j)  +/-  (6.64e-35, 9.24e-95j)
| (1.7772237638594821766e-06 - 3.7530435865824498381e-371j)  +/-  (3.02e-39, 4.2e-99j)
| (0.00011258756003930748774 - 1.2839207381648886831e-368j)  +/-  (3.02e-38, 4.2e-98j)
| (0.24714650662959283198 - 1.2877129957364153325e-367j)  +/-  (8.69e-33, 1.21e-92j)
| (1.9437026168870552438e-12 - 2.1580833554252827634e-375j)  +/-  (8.16e-44, 1.14e-103j)
| (0.056721656032873121616 + 2.3964372492837641496e-367j)  +/-  (6.66e-34, 9.27e-94j)
| (0.065776673463915747378 - 2.8086907848860460894e-367j)  +/-  (1.79e-33, 2.5e-93j)
| (0.065776673463915747378 - 5.4007180738172999279e-367j)  +/-  (6.65e-34, 9.27e-94j)
| (0.0026195598259236324481 - 6.4416538677433833698e-368j)  +/-  (1.35e-37, 1.88e-97j)
| (0.00087467731670125053947 - 1.0725128078338726054e-369j)  +/-  (1.14e-37, 1.59e-97j)
| (5.909066538854108414e-08 + 1.3262976512431028901e-372j)  +/-  (1.54e-41, 2.14e-101j)
| (0.20103896381521537838 + 1.3855609331812170986e-367j)  +/-  (1.78e-35, 2.49e-95j)
| (0.039394271031786253877 - 5.1535747469772459116e-368j)  +/-  (2.96e-36, 4.14e-96j)
| (0.0098723629195113989633 + 9.9614618038203598415e-368j)  +/-  (7.19e-38, 1.02e-97j)
| (0.20103896381521537838 + 1.9490089326617131006e-367j)  +/-  (4.84e-37, 7.92e-97j)
| (0.00087467731670125053947 + 2.676304022374060176e-368j)  +/-  (7.44e-39, 1.02e-98j)
