Three small circles $C_1$, $C_2$, and $C_3$, each with radius $0.4$ and centered at the origin are in the xy-, yz-, and xz-planes, respectively. The circles are oriented counterclockwise when viewed from the positive z-, x-, and y-axes, respectively. A vector field $\vec{F}$ has circulation around $C_1$ of $0.09 \pi$, around $C_2$ of $0.3 \pi$, and around $C_3$ of $2 \pi$. Estimate $\mathrm{curl}(\vec{F})$ at the origin.

$\mathrm{curl}(\vec{F}(0,0,0)) \approx$