\begin{eqnarray*}
C_1&=&\zm+\zeta-\frac{4}{x}\left(1+\zm+2\zeta\right)+\frac{8}{x^2}
      \left(2-\zz\right)+\frac{32}{x^3}\zz z^4 \\
   && +\frac{16}{x^4}\zeta z^2
      \left(1+3\zeta+2\zz\right)\\
C_2&=&\zeta-\frac{2}{x}\zeta z^2\left(2-\zeta \right)+\frac{4}{x^2}z^2
      \left(1-\zeta-3\zz\right)-\frac{16}{x^3}\zd z^4\\
C_3&=&-\zm+\zeta+\frac{4}{x}\zz z^2+\frac{4}{x^2}z^2 
      \left(1+\zz+2\zd\right)\\
C_4&=&\zeta-\frac{2}{x}\left(\zm+3+4\zeta\right)+\frac{4}{x^2}
      \left(\zm+4-\zeta-2\zz\right)\\
   && +\frac{8}{x^3}z^2\left(1+6\zeta+4\zz\right)
      +\frac{32}{x^4}\zd z^6\\
C_5&=&\zm+\zeta-\frac{2}{x}\left(\zm+1+\zeta-\zz\right)
      -\frac{4}{x^2}\left(\zm+1+4\zeta+3\zz\right)-\frac{16}{x^3}\zd z^4\\
C_6&=&-\zm+\zeta-\frac{2}{x}\zeta z^2\left(2-\zeta\right)+\frac{4}{x^2}
      z^2 \left(2-2\zeta-3\zz\right)\\
   && +\frac{8}{x^3}z^2\left(1-3\zz-2\zd\right)\\
C_7&=& \zeta\biggl(1+\frac{4}{x}\zeta z^2 +\frac{4}{x^2}\zeta z^2 \left(     
      1+2\zeta\right)\biggr)\\
C_8&=&\zeta-\frac{2}{x}\left(\zm+1+\zeta-\zz\right)-\frac{4}{x^2}
       \left(\zm+1+5\zeta+3\zz\right)-\frac{8}{x^3}\zz z^2\left(3+2\zeta
       \right)\\
C_9&=&-z^2 \biggl(1-\zeta+\frac{8}{x}\zeta-\frac{8}{x^2}\left(2-\zz\right)
       -\frac{32}{x^3}\zz z^4 -\frac{16}{x^4}\zeta z^2 \left(
       1+3 \zeta +2 \zz \right)\biggr) \\
C_{10}&=&\zm+\zeta+\frac{4}{x}\zz z^2 -\frac{4}{x^2} z^2
         \left(1-\zz-2\zd\right)\\
\end{eqnarray*}

