Table D.1

Secular average of the semi-major axes (⟨a_k⟩), mean mean motions (N_k), and mean longitudes at the origin (λ_0k) in the full solution LaX13b in the La2004 invariant reference frame (see Sec. D.2) derived by frequency analysis. The secular average of the action-like variable is also provided because it cannot be directly obtained from ⟨a_k⟩: due to the contribution of the short-period terms, the average ⟨f(x)⟩ of f(x) is not f(⟨x⟩).

k	⟨ak⟩ (au)		Nk (rad yr−1)	λ0k (rad)
1	+ 3.8709826346795750e-1	+ 6.2217220269433726e-1	+ 2.6087903147673952e+1	− 1.9409256207851238e+0
2	+ 7.2332656745540558e-1	+ 8.5048604874990819e-1	+ 1.0213285580208819e+1	+ 3.1147692710442865e+0
3	+ 9.9999548642649372e-1	+ 9.9999769746809641e-1	+ 6.2830757971490190e+0	+ 1.6916552864570649e+0
4	+ 1.5236795439419937e+0	+ 1.2343740652952826e+0	+ 3.3406125732385012e+0	− 1.4103263138988523e-1
5	+ 5.1927031282775076e+0	+ 2.2787503028934468e+0	+ 5.2968797602323869e-1	+ 5.4918813383105469e-1
6	+ 9.5493731166789555e+0	+ 3.0902059273326929e+0	+ 2.1329780126024636e-1	+ 8.2272979387628475e-1
7	+ 1.9216488649834947e+1	+ 4.3836614414294299e+0	+ 7.4781213910514538e-2	− 8.6189037349800601e-1
8	+ 3.0106792749722608e+1	+ 5.4869659219790110e+0	+ 3.8132752280987267e-2	− 1.0322632668252640e+0