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In the integration of the outer five planets (F±)， we fixed the stepsize at 400 d.
We adopt Gauss' f and g functions in the symplectic map together with the third-order Halley method (Danby 1992) as a solver for Kepler equations. The number of maximum iterations we set in Halley's method is 15， but they never reached the maximum in any of our integrations.
The interval of the data output is 200 000 d (∼547 yr) for the calculations of all nine planets (N±1，2，3)， and about 8000 000 d (∼21 903 yr) for the integration of the outer five planets (F±).
Although no output filtering was done when the numerical integrations were in process， we applied a low-pass filter to the raw orbital data after we had completed all the calculations. See Section for more detail.
Error estimation
Relative errors in total energy and angular momentum
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