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\begin{document}

$$
   \bar{Y}_{lm} = \frac{1}{nnn}\sum_{j = 1}^{nnn} Y_{lm}( \theta( {\bf r}_{ij} ), \phi( {\bf r}_{ij} ) ) 
$$

$$
   Q_l = \sqrt{\frac{4 \pi}{2 l + 1} \sum_{m = -l}^{m = l} \bar{Y}_{lm} \bar{Y}^*_{lm}}
   $$

\end{document}
