On the Stone Von Neumann theorem: Why is this a (non orthogonal basis of $L^2(\mathbb R^n)$?

Question

In the proof of the Stone Von Neumann theorem of the Folland's book "Harmonic Analysis in phase space", he says that the functions: $$ \phi^{ab}(x)=e^{2\pi i bx+\pi i ab}e^{-\pi(x+a)^2} $$ are a (non orthogonal) basis of $L^2(\mathbb R^n)$.

Why is it a basis?