Is there a closed formula that evaluates the integral, $$ I = \int_{-\infty}^{\infty} dx_1 .. \int_{-\infty}^{\infty} dx_D \exp\left(-\sum_{\mu=1}^D \sum_{\nu=1}^D a_{\mu\nu} x_{\mu} x_{\nu} \right), $$ where $a_{\mu\nu} \in \mathbb{C}$ ($\mu=1,\dots,D$, $\nu=1,\dots,D$) do not constitute a Hermitian or complex-symmetric matrix?
Edit (2015-9-9):
I realized that the quadratic form in the exponent can always be expressed with a complex symmetric matrix, $a'_{\mu\nu} := (a_{\mu\nu}+a_{\nu\mu})/2$. That is, $$ \sum_{\mu=1}^D \sum_{\nu=1}^D a_{\mu\nu} x_{\mu} x_{\nu} = \sum_{\mu=1}^D \sum_{\nu=1}^D a'_{\mu\nu} x_{\mu} x_{\nu}. $$ I also realized that I do not know a formula for $I$ even in the case where $a_{\mu\nu}$ is complex symmetric. Therefore, I would like to change my question to the following: Is there a closed formula that evaluates the integral $I$ above if $a_{\mu\nu}$ constitute a complex symmetric matrix?