The growth rate, in the limit |$k\rightarrow \infty$| with |$\alpha =1$| fixed, of the non-axisymmetric AMRI versus |$\omega _{A\theta }/\Omega$|⁠, in the range of small values, for different azimuthal wavenumbers |$m=1$| (solid line), 5 (dashed line), and 10 (long-dashed line) for |$Ro=-3/4$|⁠, a Keplerian rotation. The magnetic Rossby number is |$Rb=-1$|⁠.