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A_{1,-1} & = & \frac{50\sqrt{3}}{\sqrt{2\pi}}\int_{-\pi/4}^{\pi/4}\int_0^{\pi}e^{-i\varphi}\sin\theta d\theta d\varphi\\

& = & \frac{100\sqrt{3}}{\sqrt{2\pi}}\int_{-\pi/4}^{\pi/4}e^{-i\varphi}d\varphi\\

& = & \frac{100\sqrt{3}}{\sqrt{\pi}}\\

\end{alignat*}

Is this correct?