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\begin{document}
Calculations 
\centering 
a0 
\begin{eqnarray}
8.0 i \Delta \gamma g_{1} g_{2} \cos{\left(\varphi \right)} - 8.0 i \Delta \gamma g_{1} g_{2} \cos{\left(\chi_{1L} - \chi_{2L} + \varphi \right)} + 16.0 i \gamma^{2} g_{1}^{2} \sin{\left(\chi_{1L} \right)} - 16.0 \gamma^{2} g_{1}^{2} \cos{\left(\chi_{1L} \right)} + 16.0 \gamma^{2} g_{1}^{2} + 16.0 i \gamma^{2} g_{1} g_{2} \sin{\left(\chi_{1L} + \varphi \right)} + 16.0 i \gamma^{2} g_{1} g_{2} \sin{\left(\chi_{2L} - \varphi \right)} + 16.0 \gamma^{2} g_{1} g_{2} \cos{\left(\varphi \right)} - 16.0 \gamma^{2} g_{1} g_{2} \cos{\left(\chi_{1L} + \varphi \right)} - 16.0 \gamma^{2} g_{1} g_{2} \cos{\left(\chi_{2L} - \varphi \right)} + 16.0 \gamma^{2} g_{1} g_{2} \cos{\left(\chi_{1L} - \chi_{2L} + \varphi \right)} + 16.0 i \gamma^{2} g_{2}^{2} \sin{\left(\chi_{2L} \right)} - 16.0 \gamma^{2} g_{2}^{2} \cos{\left(\chi_{2L} \right)} + 16.0 \gamma^{2} g_{2}^{2} - 4.0 g_{1}^{3} g_{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\chi_{1L} + \varphi \right)} - 4.0 g_{1}^{3} g_{2} \cos{\left(\chi_{1L} \right)} \cos{\left(\chi_{1L} + \varphi \right)} + 4.0 g_{1}^{3} g_{2} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\chi_{2L} \right)} \cos^{2}{\left(\varphi \right)} \cos{\left(\chi_{1L} - \chi_{2L} \right)} - 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\chi_{2L} \right)} \cos^{2}{\left(\varphi \right)} - 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\chi_{2L} \right)} \cos{\left(\chi_{1L} - \chi_{2L} \right)} - 16.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\varphi \right)} \cos{\left(\chi_{1L} \right)} \cos^{2}{\left(\chi_{2L} \right)} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{1L} \right)} \sin{\left(\varphi \right)} \cos{\left(\chi_{1L} \right)} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{2L} \right)} \sin{\left(\varphi \right)} \cos^{2}{\left(\chi_{1L} \right)} \cos{\left(\chi_{2L} \right)} \cos{\left(\varphi \right)} - 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{2L} \right)} \sin{\left(\varphi \right)} \cos{\left(\chi_{1L} \right)} \cos{\left(\varphi \right)} - 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{2L} \right)} \sin{\left(\varphi \right)} \cos{\left(\chi_{2L} \right)} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2} \sin{\left(\chi_{2L} \right)} \sin{\left(\chi_{1L} + \varphi \right)} \cos{\left(\chi_{1L} \right)} \cos{\left(\chi_{2L} \right)} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2} \cos^{2}{\left(\chi_{1L} \right)} \cos^{2}{\left(\chi_{2L} \right)} \cos^{2}{\left(\varphi \right)} - 4.0 g_{1}^{2} g_{2}^{2} \cos^{2}{\left(\chi_{1L} \right)} - 4.0 g_{1}^{2} g_{2}^{2} \cos^{2}{\left(\chi_{2L} \right)} - 8.0 g_{1}^{2} g_{2}^{2} \cos{\left(\chi_{2L} \right)} \cos{\left(\varphi \right)} \cos{\left(\chi_{1L} + \varphi \right)} + 8.0 g_{1}^{2} g_{2}^{2}
\end{eqnarray}
a1 
\begin{eqnarray}
\gamma \left(4.0 \Delta^{2} + 16.0 \gamma^{2} + 8.0 i g_{1}^{2} \sin{\left(\chi_{1L} \right)} - 8.0 g_{1}^{2} \cos{\left(\chi_{1L} \right)} + 16.0 g_{1}^{2} + 8.0 i g_{1} g_{2} \sin{\left(\chi_{1L} + \varphi \right)} + 8.0 i g_{1} g_{2} \sin{\left(\chi_{2L} - \varphi \right)} + 16.0 g_{1} g_{2} \cos{\left(\varphi \right)} - 8.0 g_{1} g_{2} \cos{\left(\chi_{1L} + \varphi \right)} - 8.0 g_{1} g_{2} \cos{\left(\chi_{2L} - \varphi \right)} + 16.0 g_{1} g_{2} \cos{\left(\chi_{1L} - \chi_{2L} + \varphi \right)} + 8.0 i g_{2}^{2} \sin{\left(\chi_{2L} \right)} - 8.0 g_{2}^{2} \cos{\left(\chi_{2L} \right)} + 16.0 g_{2}^{2}\right)
\end{eqnarray}
a2 
\begin{eqnarray}
1.0 \Delta^{2} + 20.0 \gamma^{2} + 4.0 g_{1}^{2} + 4.0 g_{1} g_{2} \cos{\left(\varphi \right)} + 4.0 g_{1} g_{2} \cos{\left(\chi_{1L} - \chi_{2L} + \varphi \right)} + 4.0 g_{2}^{2}
\end{eqnarray}
Correlation  12 
\begin{eqnarray}
\frac{\tau g_{1}^{2} \left(0.00048828125 \tau^{2} g_{1}^{2} \left(\tau^{2} \left(1.0 \Delta^{2} + 8.0 g_{1}^{2} \cos{\left(\varphi \right)} + 8.0 g_{1}^{2}\right) + 20.0\right) \left(\tau^{2} \left(4.0 \Delta^{2} + 16.0 g_{1}^{2} \cos{\left(\varphi \right)} + 16.0 g_{1}^{2}\right) + 16.0\right) \left(- 8.0 \Delta \tau \sin{\left(\varphi \right)} + 16.0 \cos{\left(\varphi \right)} + 16.0\right) \left(8.0 \Delta \tau \sin{\left(\varphi \right)} + 16.0 \cos{\left(\varphi \right)} + 16.0\right) + i \tau^{2} g_{1}^{2} \left(0.25 \Delta^{2} \tau^{2} + 1.0 \tau^{2} g_{1}^{2} \cos{\left(\varphi \right)} + 1.0 \tau^{2} g_{1}^{2} + 1.0\right)^{2} \left(8.0 \Delta \tau \sin^{2}{\left(\varphi \right)} - 16.0 i \sin^{2}{\left(\varphi \right)} + 32.0 i \cos{\left(\varphi \right)} + 32.0 i\right) + \left(\tau^{2} \left(0.25 \Delta^{2} + 1.0 g_{1}^{2} \cos{\left(\varphi \right)} + 1.0 g_{1}^{2}\right) + 1\right)^{3} \left(8.0 i \Delta \tau \cos{\left(\varphi \right)} + 8.0 \tau^{2} g_{1}^{2} \sin^{2}{\left(\varphi \right)} - 16.0 \cos{\left(\varphi \right)}\right)\right)}{\left(\tau^{2} \left(0.25 \Delta^{2} + 1.0 g_{1}^{2} \cos{\left(\varphi \right)} + 1.0 g_{1}^{2}\right) + 1\right)^{3} \left(\tau^{2} \left(4.0 \Delta^{2} + 16.0 g_{1}^{2} \cos{\left(\varphi \right)} + 16.0 g_{1}^{2}\right) + 16.0\right)}
\end{eqnarray}
Correlation 0th order 
\begin{eqnarray}
0
\end{eqnarray}
Correlation 1th order 
\begin{eqnarray}
0
\end{eqnarray}
Correlation 2th order 
\begin{eqnarray}
0
\end{eqnarray}

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