\begin{equation*}
\vec{\mu}^{(eq)} = 
\begin{pmatrix}\rho \\
\rho \ou  \\
\rho \ov  \\
\rho \ow  \\
\rho \ou \ov  \\
\rho \ou \ow  \\
\rho \ov \ow  \\
\rho \ou \ov \ow  \\
\rho \left( \ou^2 + c_s^2 \right)\\
\rho \left( \ov^2 + c_s^2 \right)\\
\rho \left( \ow^2 + c_s^2 \right)\\
\rho \left( \ou^2 \ov + \ov c_s^2 \right)\\
\rho \left( \ou^2 \ow + \ow c_s^2 \right)\\
\rho \left( \ou^2 \ov \ow  +  \ov \ow c_s^2\right)\\
\rho \left( \ou \ov^2 + \ou c_s^2 \right)\\
\rho \left( \ov^2 \ow + \ow c_s^2 \right)\\
\rho \left( \ou \ov^2 \ow + \ou \ow c_s^2 \right)\\
\rho \left( \ou \ow^2 + \ou c_s^2 \right)\\
\rho \left( \ov \ow^2 + \ov c_s^2 \right)\\
\rho \left( \ou \ov \ow^2  + \ou \ov c_s^2 \right)\\
\rho \left( \ou^2 \ov^2  + \ov^2 c_s^2 + \ou^2 c_s^2 + c_s^4 \right)\\
\rho \left( \ou^2 \ow^2 + \ow^2 c_s^2 + \ou^2 c_s^2 + c_s^4\right)\\
\rho \left( \ov^2 \ow^2 + \ow^2 c_s^2 + \ov^2 c_s^2 + c_s^4 \right)\\
\rho \left( \ou^2 \ov^2 \ow + \ov^2 \ow c_s^2 + \ou^2 \ow c_s^2 + \ow c_s^4 \right)\\
\rho \left( \ou^2 \ov \ow^2 + \ov \ow^2 c_s^2 + \ou^2 \ov c_s^2 + \ov c_s^4 \right)\\
\rho \left( \ou \ov^2 \ow^2 + \ou \ow^2 c_s^2 + \ou \ov^2 c_s^2 + \ou c_s^4 \right)\\
\rho \left( \ou^2 \ov^2 \ow^2 + \ov^2 \ow^2 c_s^2 + \ou^2 \ow^2 c_s^2 + \ow^2 c_s^4 + \ou^2 \ov^2 c_s^2 + \ov^2 c_s^4 + \ou^2 c_s^4 + c_s^6 \right)\end{pmatrix}.
\end{equation*}
