Top panel: zoomed Nyquist contours in the complex plane of obtained via the matrix method for a truncated Mestel disc with ν_t = 6 and q = 6, looking for m_φ = 2 modes. Each contour corresponds to a fixed value of η. For a growth rate of η ≃ 0.20, one can note that the contour crosses the origin, which corresponds to the presence of an unstable mode. Bottom panel: illustration of the function for the same truncated Mestel disc. Each line corresponds to a fixed value of η. Such a representation allows us to determine the pattern speed ω₀ = m_φΩ_p ≃ 0.94 of the unstable mode.