The complex wavenumber eigenvalues of Laplace's tidal equations are determined for an ocean of constant depth bounded by meridians. A Galerkin method is used to expand the tide height and velocities in series of associated Legendre functions. A homogeneous system of equations results from the continuity and momentum equations. The frequency and depth are fixed, so that the meridional wavenumbers are the eigenvalues. This gives rise to a generalized eigenvalue problem that must be solved numerically by iteration. The eigenvalues are not integers and represent inertia-gravity wave solutions at the specified tidal forcing frequency that can be excited by the presence of meridional boundaries. Those complex eigenvalues represent solutions that decay away from meridional boundaries. The eigenvalue spectrum is investigated for the semi-diurnal, fortnightly, and monthly tides. One complex wavenumber for the semi-diurnal tide explains the amphidromic systems within 20 degrees of a north-south coastline. The fortnightly and monthly tides have only real wavenumber eigenvalues. The basin scale deviation of these tides from equilibrium is attributed to low wavenumber divergent inertia-gravity waves.