Examples of distribution of eigenvalues (red dots) with respect to the complex unit circle with a magnification on the right of each panel for particular orbits from the families of the 1:2:3 resonant chain. (a) Triple instability with three pairs of real eigenvalues (S₁ family); (b) Double instability with two pairs of real eigenvalues (S₃ family); (c) u-complex instability with one pair of real and two pairs of complex eigenvalues outside the unit circle (S₅ family); (d) Complex instability with two pairs of complex eigenvalues outside the unit circle, while the rest remain on it (S₅ family). (e) Linear stability with all pairs on the unit circle (S₁ family).