homework and exercises - What is $langle G_{munu}ranglelangle G_{munu}rangle$ for the Dirac gamma matrices?

Given the following 16 matrix multiplications of the Dirac gamma matrices

$$\begin{align} G_{\mu\nu} = \dfrac{1}{2} \begin{pmatrix} I && \gamma_{0} && i\gamma_{123} && i\gamma_{0123} \\ i\gamma_{23} && i\gamma_{023} && i\gamma_{1} && \gamma_{01} \\ i\gamma_{31} && i\gamma_{031} && i\gamma_{2} && \gamma_{02} \\ i\gamma_{12} && i\gamma_{012} && i\gamma_{3} && \gamma_{03} \end{pmatrix}, \end{align}$$ where $\gamma_{01} = \gamma_{0}\gamma_{1}$:

What is

$$\begin{align} \sum_{\mu=0}^{3}\sum_{\nu=0}^{3} \langle G_{\mu\nu} \rangle^2 = ? \end{align}$$ The Bra-Ket notation is used in this question: $$\begin{align} \langle G_{\mu\nu} \rangle = \langle \Psi | G_{\mu\nu} | \Psi \rangle , \end{align}$$ where $\Psi$ is the Dirac bi-spinor of four complex components.