Wave frequency (normalized by rotation frequency) vs dimensionless reduced gravity, gH/Ω²R² computed from Eq. (16) at the latitude 45⁰ of the solar tachocline for the magnetic field strength of 10 kG and the wavelength of k_xR = 1. The dashed lines correspond to the solutions with α_z/Ω= 0, while the solid lines show the solutions for the dynamo coefficient of α_z/Ω= 0.3. The blue and green lines show the fast and slow magneto-Rossby waves, respectively. The red lines correspond to the modified dynamo waves. The Rossby waves have very low frequency for the lower value of reduced gravity. The frequency of slow magneto-Rossby waves remains low, but that of fast magneto-Rossby waves increases for the larger value of reduced gravity. When approaching the dynamo wave solution (for the reduced gravity of ∼0.5), the two waves do not cross, but rather switch properties (called the avoided crossing). High frequency inertia gravity waves are not shown in the plot.