Let $\kappa>0$ and $\mu,\hbar>0$. For the self-adjoint Coulomb Hamiltonian without spin on $L^2(\mathbb R^3)$, the negative point spectrum is \begin{align*} E_n=-\frac{\mu\kappa^2}{2\hbar^2n^2},\qquad n=1,2,3,\dots. \end{align*} For fixed $n$, the allowed angular momentum quantum numbers are \begin{align*} l=0,1,\dots,n-1, \end{align*} and for each $l$ the magnetic quantum number satisfies $m=-l,\dots,l$.