For the self-adjoint Coulomb Hamiltonian without spin on $L^2(\mathbb R^3)$, the point spectrum below zero consists exactly of the eigenvalues \begin{align*} E_n=-\frac{\mu\kappa^2}{2\hbar^2n^2},\qquad n\ge 1, \end{align*} with finite multiplicities as above, accumulating only at $0$ from below. The essential spectrum is $[0,\infty)$, and its spectral subspace is continuous. There are no positive square-integrable eigenfunctions.