\begin{table}%t1
\caption{\label{t:poisson1}Non-zero values of the coefficients in Eqs. (\protect\ref{Mup})$-$(\protect\ref{mup}).}
\small%\centering
\par
\begin{tabular}{@{}cccc@{}}
\hline\hline\noalign{\smallskip}
\multicolumn{1}{c}{$(i,j)$} & \multicolumn{1}{c}{$M^*_{i,j}$} & \multicolumn{1}{c}{$\Lambda^*_{i,j}$} & \multicolumn{1}{c}{$\nu^*_{i,j}$}  \\[0.5ex]
\noalign{\smallskip}\hline\noalign{\smallskip}
$(2,-2)$ & $(\Lambda +M)^2(M^2-N^2)$
         & $(\Lambda+M)^2(M^2-N^2)$
         & $-(M+\Lambda)^2$ \vphantom{$\displaystyle K^{2^3}$}
\\ \noalign{\smallskip}
$(2,-1)$ & $2N(M+\Lambda)\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}$
         & $4N~(M+\Lambda)\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}$
         & $-2\frac{M+\Lambda}{N}~\frac{\sqrt{M^2-\Lambda ^2}}{\sqrt{M^2-N^2}}~(2N^2-M^2)$\\ 
\noalign{\smallskip}\\ 
$(2,0)$ & -- 
        & $-2(M^2-\Lambda^2)~(M^2-3N^2)$
        & $6 \left(M^2-\Lambda ^2\right)$
\\[1ex]
$(2,1)$ & $2N(M-\Lambda ) \sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}$
        & $-4N~(M-\Lambda)\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}$
        & $2\frac{M-\Lambda}{N}~\frac{\sqrt{M^2-\Lambda ^2}}{\sqrt{M^2-N^2}}~(2N^2-M^2)$
\\[1ex]
$(2,2)$ & $-(M-\Lambda )^2(M^2-N^2)$
        & $(M-\Lambda)^2(M^2-N^2)$
        & $-(M-\Lambda)^2$
\\[1ex]
$(0,2)$ & $-2(M^2-\Lambda ^2)~(M^2-N^2)$
        & -- 
        & $-2 \left(M^2-\Lambda ^2\right)$
\\[1ex]
$(0,1)$ & $4 N~\Lambda  \sqrt{M^2-\Lambda ^2}\sqrt{M^2-N^2}$ 
        & -- 
        & $4\frac{\Lambda}{N}~\frac{\sqrt{M^2-\Lambda ^2}}{\sqrt{M^2-N^2}}~(2N^2-M^2)$ \\[2ex]
\hline
\end{tabular}\\[1ex]
\par
\begin{tabular}{@{}ccc@{}}
\multicolumn{1}{c}{$(i,j)$} & \multicolumn{1}{c}{$\lambda^*_{i,j}$} & \multicolumn{1}{c}{$\mu^*_{i,j}$}  \\[0.5ex]
\hline\noalign{\smallskip}
$(2,-2)$ & $(M+\Lambda)~(M^2-N^2)$
         & $(M+\Lambda)\left[M~N^2-\Lambda~(M^2-2N^2)\right]$ \vphantom{$\displaystyle K^{K^K}$}
\\[1ex]
$(2,-1)$ & $2N~\frac{\sqrt{M^2-N^2}}{\sqrt{M^2-\Lambda^2}}~(M^2-2\Lambda^2-M~\Lambda) $
         & $-2N~\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}\left[M+2\Lambda-\left(\frac{\Lambda^2}{M^2-\Lambda^2}+\frac{N^2}{M^2-N^2}\right)(M+\Lambda)\right]$ 
\\[1ex]
$(2,0)$ & $2\Lambda~(M^2-3N^2)$
        & $-6M^2N^2-2\Lambda^2(M^2-6N^2)$
\\[1ex]
$(2,1)$ & $2N~\frac{\sqrt{M^2-N^2}}{\sqrt{M^2-\Lambda^2}}~(M^2-2\Lambda^2+M~\Lambda) $
        & $2N~\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}\left[M-2\Lambda-\left(\frac{\Lambda^2}{M^2-\Lambda^2}+\frac{N^2}{M^2-N^2}\right)(M-\Lambda)\right]$
\\[1ex]
$(2,2)$ & $-(M-\Lambda )~(M^2-N^2)$
        & $(M-\Lambda)\left[M~N^2+(M^2-2N^2)~\Lambda\right]$
\\[1ex]
$(0,2)$ & $-2\Lambda~(M^2-N^2)$
        & $2M^2N^2+2\Lambda^2(M^2-2N^2)$
\\[1ex]
$(0,1)$ & $-4N~\frac{\sqrt{M^2-N^2}}{\sqrt{M^2-\Lambda^2}}~(M^2-2\Lambda^2)$
        & $4N~\Lambda~\sqrt{M^2-\Lambda^2}\sqrt{M^2-N^2}\left(2-\frac{\Lambda^2}{M^2-\Lambda^2}-\frac{N^2}{M^2-N^2}\right)$
\\
\noalign{\smallskip}\hline
\end{tabular}
\vspace*{4mm}
\end{table}