Time series of the unwrapped phase (top) and the norm (bottom) of the bisymmetric fluctuations probed by A₂(t) from Equation (B.6) over ten independent realisations of the unstable Zang ν​ = ​4 disc (Zang 1976). Each simulation is performed with N​ = ​2​ × ​10⁸ particles using the Plummer softening kernel (Equation G.2) and for varying softening lengths, ε. For each ε, the same ten initial conditions are used and shown in the same colour. The frequency Ω_M (resp. growth rate γ_M) of the mode are estimated by a linear fit of the phase (resp. log of the norm) of such time series, only using t​ ≥ ​T_min​ = ​10 t_dyn. The growth of the phase is generically more regular than the growth of the norm. The Plummer softening kernel introduces a strong gravity bias when compared with (non-softened) theoretical predictions.