Evaluate the line integral $\oint_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x,y) = \langle \frac{-y}{x^2+4y^2}, \frac{x}{x^2+4y^2} \rangle$ and $C$ is the ellipse $x^2 + 4y^2 = 4$ oriented counterclockwise.