stepsize at 400 d
we adopt gas' f and g functionsthe syplectic ap together with the third-order halley thod (danby 1992) as a solver for kepler equations the nuber of axiu iterations we sethalley's thod is 15， but they never reached the axiuany of our tegrations
the terval of the data output is 200 000 d (～547 yr) for the calcutions of all ne ps (n±1，2，3)， and about 8000 000 d (～21 903 yr) for the tegration of the outer five ps (f±)
although no output filterg was done when the nurical tegrations wereprocess， we applied a low-pass filter to the raw orbital data after we had pleted all the calcutions see section 41 for ore detail
24 error estiation
241 retive errorstotal energy and angur ontu
aordg to one of the basic properties of syplectic tegrators， which nserve the
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