Is there an $F \in L^2({\mathbb{T}})$ s,t $\hat{F} = 1/\sqrt{n}$ for $n \geq 1$?

Question

I am unsure of where to start with this. Is it a matter of showing:

$$\int_{\mathbb{T}}|F(n)|^2\mathrm d\lambda < \infty$$

So must I derive $\hat{F} = 1/\sqrt{n}$ ? Or should I be using Bessel's inequality?