
\begin{eqnarray*}
A_0&=&\frac{(z-x+xz)(z+x+xz)}{(x+1)(z^2-x+x z^2)} \\
A_1&=&2 \biggl( {\zeta}^{-1}+\frac{1}{x} \left(1-{\zeta}^{-1}-2 \zeta\right)
    -\frac{2}{x^2} \left( {\zeta}^{-1}-4-3 \zeta \right) + \frac{8}{x^3}
    \zeta z^2 \left(2+\zeta\right) \\
 && +\frac{8}{x^4} \zz z^4 \biggr) \\
A_2&=& \zeta-\frac{5}{x} \zeta z^2 +\frac{2}{x^2}
      z^2 \left( 2 -5 \zeta -4 \zz \right) +\frac{4}{x^3}
      z^2 \left(1-\zeta-2 \zz \right) \\
A_3&=&-2\biggl( {\zeta}^{-1}-\zeta+\frac{1}{x} z^2 \left(3-\zeta-2\zz
      \right)+\frac{2}{x^2} z^2 \left(1 -\zz
      \right) \biggr) \\
A_4&=& -{\zeta}^{-1}-\frac{1}{x}\left(5 {\zeta}^{-1}+1+4\zeta\right)
     +\frac{4}{x^2}\left(5+3\zeta\right)\\
   &&+\frac{4}{x^3} z^2 \left(3+10 \zeta+4 \zz \right)
     +\frac{8}{x^4}z^2 \left(1+3\zeta+2\zz \right) \\
A_5&=& \left(x+1\right) \biggl(\frac{1}{x}\left(3{\zeta}^{-1}
      +\zeta\right)-\frac{2}{x^2}\left(1+3\zeta\right)
      -\frac{4}{x^3}z^2\left(1+\zeta+2 \zz \right)\biggr) \\
A_6&=&-\left(x+1\right)\biggl(\frac{1}{x}\left({\zeta}^{-1}-\zeta\right)
      +\frac{2}{x^2}z^2\left(1+3\zeta\right)+\frac{8}{x^3}\zz z^4\biggr) \\
A_7&=&-{\zeta}^{-1}+2\zeta-\frac{1}{x}z^2\left(3-2 \zeta-4\zz
     \right)-\frac{2}{x^2}z^2\left(1-2\zz\right)\\
A_8&=&-2{\zeta}^{-1}+\zeta-\frac{1}{x}\left(12{\zeta}^{-1}+9+5\zeta
      \right)-\frac{2}{x^2}\left(11{\zeta}^{-1}+14+11\zeta+4{\zeta}^2
      \right)\\
      &&-\frac{4}{x^3}z^2\left(3+2\zeta+2\zz\right)\\
A_9&=&4\left(x+1\right)z^2\biggl(\frac{1}{x^2}
      \left(1-\zeta\right)+\frac{4}{x^3}\zeta z^2
      +\frac{4}{x^4}\zz z^4 \biggr) \\
A_{10}&=&2\biggl(2{\zeta}^{-1}+\zeta+\frac{1}{x}\left(6{\zeta}^{-1}
         +3+3\zeta+2{\zeta}^2\right)+\frac{2}{x^2}z^2\left(2+\zz
         \right)\biggr)\\
\end{eqnarray*}

