In my research I encounter some elements in a root lattice and I would like to verify that these elements are imaginary roots. Consider the root system $J_{6, 11}$ with the following Dynkin diagram: \begin{align} \circ - \circ - \circ - \circ - \circ - & \circ - \circ - \circ - \circ - \circ \\ & \ | \\ & \ \bullet \end{align} where the $\circ$'s corresponds to the simple roots $\alpha_1, \ldots, \alpha_{10}$ (from left to right) and $\bullet$ corresponds to the simple root $\alpha_{11}$.

Let $\gamma = \alpha_1+2\alpha_2+3\alpha_3+4\alpha_4+5\alpha_5+6\alpha_6+5\alpha_7+4\alpha_8+3\alpha_9+2\alpha_{10}+2\alpha_{11}$. I would like to verify that $\gamma$ is an imaginary root in $J_{6,11}$. Are there some method to do this? Thank you very much.