sequences and series - How do I evaluate this sum :$sum_{n=1}^{infty}frac{{(-1)}^{n²}}{{(ipi)}^{n}}$?

I'm interesting to know how do i evaluate this sum : $$\sum_{n=1}^{\infty}\frac{{(-1)}^{n²}}{{(i\pi)}^{n}}$$ , I have tried to evaluate it using two partial sum for odd integer $n$ and even integer $n$ ,but i can't since it's alternating series ,and i would like to know if it's well know series also what about it's values :real or complex ? .

Note : wolfram alpha showed that is a convergent series by the root test

Thank you for any help