Compute the spectrum of a compact operator

Question

For operator $T:C([0,1])\rightarrow C([0,1])$, $$T(f)(x)=\int_0^x\dfrac{f(t)}{\sqrt{x-t}}dt$$ Now, I want to find $\sigma(T)$, which is spectrum of $T$.

I proved $T$ is a compact operator, so $0\in\sigma(T)$, but how can I proceed?

Many thanks