Show that the set $\{e^{\pm i (n-1/4)t}: n=\pm 1,\pm2,\pm3,\ldots\}$ is not a basis for $L^2[\pi,\pi]$

Question

Show that the set $\{e^{\pm i (n-1/4)t}: n=\pm 1,\pm2,\pm3,\ldots\}$ is not a basis for $L^2[\pi,\pi]$.

(HINT: The series $$\sum_n c_n e^{i\lambda_n t}$$ with $\lambda_n=n-1/4$, diverges in $L^2[\pi,\pi]$.)

Besides the suggestion in brackets, have you other tips that can help me?

Thanks.