How to calculate $\int_{|z|=4} \frac{z^2dz}{e^{z^2}-1}$

Question

I have an integral $$\int_{|z|=4} \frac{z^2dz}{e^{z^2}-1}$$ I've tried to calculate it using the Residue theorem. So I've found the 9 poles, $z=0$ and $z_{mn}=\sqrt{2\pi n}e^{i\pi \frac{(1+2m)}{4}}$, where $m=0,1,2,3$ and $n=1,2$. But I can't understand how to find the residue of the poles. It's simple poles and I need to calculate $$\lim_{z\to z_{mn}} \frac{z^2(z-z_{mn})}{e^{z^2}-1}$$ How can I calculate it?