Starting with polynomial:
P : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Extension levels are: 7 13
-------------------------------------------------
Trying to find an order 13 Kronrod extension for:
P1 : -1/5040*t^7 + 7/720*t^6 - 7/40*t^5 + 35/24*t^4 - 35/6*t^3 + 21/2*t^2 - 7*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/5040*t^20 + 99500877068637043370825957/1421876558706119868637222560*t^19 - 15375224266994843260464236723/1421876558706119868637222560*t^18 + 1603792293969362038671102952/1645690461465416514626415*t^17 - 151195968834239082352704262063/2633104738344666423402264*t^16 + 61802785901079124212858617915791/26331047383446664234022640*t^15 - 51812766244054232665876150397455/752315639527047549543504*t^14 + 11691158508333244832759252775750835/7899314215033999270206792*t^13 - 186019990097246850867736139525822035/7899314215033999270206792*t^12 + 61129148370784011837992606765489775/219425394862055535283522*t^11 - 1610815573457098361631951842238561635/658276184586166605850566*t^10 + 5217967953159533687656251869485946905/329138092293083302925283*t^9 - 8211252714671828648604121731880365015/109712697431027767641761*t^8 + 469974862693706328255686560880983560/1859537244593690976979*t^7 - 9315559026635610065210610021664702200/15673242490146823948823*t^6 + 14684939012313682451075285133378496560/15673242490146823948823*t^5 - 14684214920740026942035682533926004400/15673242490146823948823*t^4 + 8582849228779052447900425448767521600/15673242490146823948823*t^3 - 2593330654780898434586820682235217600/15673242490146823948823*t^2 + 338248593053810606177694047933712000/15673242490146823948823*t - 13498080248464191937306955985436800/15673242490146823948823
-------------------------------------------------
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:
| (50.89876876122816857 - 9.3948369091207706185e-262j)  +/-  (6.47e-120, 6.47e-120j)
| (41.490565681697413998 + 3.4145586567658460726e-274j)  +/-  (4.4e-119, 4.4e-119j)
| (28.522543666512504675 + 1.2746277540051327866e-297j)  +/-  (2.3e-118, 2.3e-118j)
| (86.496084255711238255 - 3.9454564074813898032e-314j)  +/-  (1.28e-121, 1.28e-121j)
| (23.601044499589777387 - 4.2400399299781631635e-325j)  +/-  (3.03e-118, 3.03e-118j)
| (34.358062912036370753 + 4.541442779539238959e-343j)  +/-  (1.32e-118, 1.32e-118j)
| (19.395727862262540312 + 2.1892648880804570922e-356j)  +/-  (3e-118, 3e-118j)
| (12.734180291797813758 - 1.9530310682611707961e-363j)  +/-  (1.56e-118, 1.56e-118j)
| (6.4762198342779186243 + 1.355320654350260111e-367j)  +/-  (1.33e-119, 1.33e-119j)
| (4.9003530845264845681 - 3.1522003643889836982e-368j)  +/-  (3.12e-120, 3.12e-120j)
| (0.19304367656036241384 - 1.2012597859168839336e-375j)  +/-  (7.38e-126, 7.38e-126j)
| (1.0266648953391919503 + 1.0645688432207229883e-371j)  +/-  (9.7e-124, 9.7e-124j)
| (2.5678767449507462069 - 3.3351100506354490134e-369j)  +/-  (1.21e-121, 1.21e-121j)
| (8.1821534445628607911 + 3.4357198627146867884e-366j)  +/-  (3.72e-119, 3.72e-119j)
| (1.7886359595082123208 - 4.4973349776429159133e-375j)  +/-  (1.64e-122, 1.64e-122j)
| (0.44631636500091612787 - 1.4766443808962153995e-375j)  +/-  (6.57e-125, 6.57e-125j)
| (3.547875450319378852 + 1.4092779965649031584e-373j)  +/-  (6.78e-121, 6.78e-121j)
| (0.06896586581680091274 - 5.3182294139441021477e-375j)  +/-  (8.11e-127, 8.11e-127j)
| (10.203436488132110362 - 1.1516910368687916466e-370j)  +/-  (8.29e-119, 8.29e-119j)
| (15.793433267870370394 - 8.6208770697024294228e-378j)  +/-  (2.23e-118, 2.23e-118j)
-------------------------------------------------
The weights are:
| (8.9073720510911004857e-22 + 4.5195887753783893921e-283j)  +/-  (1.44e-50, 1.35e-109j)
| (7.6628531675746416792e-18 - 1.2926951499817483869e-281j)  +/-  (5.12e-49, 4.81e-108j)
| (2.1876897663982126293e-12 - 7.4568470534271112216e-279j)  +/-  (8.27e-47, 7.77e-106j)
| (5.995797126382857969e-33 + 6.4623391977212362472e-290j)  +/-  (2.32e-56, 2.18e-115j)
| (2.5537267185125891527e-10 + 1.1148833518695958194e-277j)  +/-  (4.28e-46, 4.02e-105j)
| (7.6614779351352952016e-15 + 3.6769413527989908604e-280j)  +/-  (3.03e-48, 2.85e-107j)
| (1.467152939475136833e-08 - 1.3032191569106294159e-276j)  +/-  (1.39e-45, 1.31e-104j)
| (8.2441788357348921126e-06 - 1.0041503174788488732e-274j)  +/-  (2.22e-44, 2.08e-103j)
| (0.0025206216600597228748 + 9.9241065081836405695e-273j)  +/-  (4.22e-42, 3.97e-101j)
| (0.011110998094858051552 - 2.8804733556113369255e-272j)  +/-  (2.73e-41, 2.56e-100j)
| (0.068461715959769469421 - 5.0359541366388792389e-271j)  +/-  (3e-37, 2.81e-96j)
| (0.24900102115517136914 - 2.8791477366655609458e-271j)  +/-  (2.87e-37, 2.7e-96j)
| (0.062016279715359773486 - 1.7832853050395788959e-271j)  +/-  (1.05e-39, 9.9e-99j)
| (0.00050701268949788052512 - 3.0177444220878377749e-273j)  +/-  (2.1e-43, 1.97e-102j)
| (0.13226728314579638472 + 2.4648990075812014586e-271j)  +/-  (1.15e-39, 1.08e-98j)
| (0.28715552367093238142 + 4.398886438218917948e-271j)  +/-  (6.74e-39, 6.33e-98j)
| (0.034026949068100307013 + 8.293017669652347375e-272j)  +/-  (4.24e-41, 3.98e-100j)
| (0.15283999490008538793 + 2.2186329003720527687e-271j)  +/-  (3.6e-39, 3.38e-98j)
| (8.3880841156507438158e-05 + 6.5420995271911554945e-274j)  +/-  (1e-44, 9.4e-104j)
| (4.5999127960408291667e-07 + 1.2481902157186964987e-275j)  +/-  (1.09e-46, 1.03e-105j)
