
\begin{eqnarray*}
A_0&=&\frac{(z-x+xz)(z+x+xz)}{(x+1)(z^2-x+x z^2)} \\
A_1&=&4 \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}
    \left( 2+3 \zeta+{\zeta}^2 \right)\\
 && +\frac{8}{x^4}\left(1+2\zeta+\zz\right) \biggr) \\
A_2&=&2 \biggl( \zeta-\frac{5}{x} \left(1+\zeta \right) +\frac{2}{x^2}
      \left( 2 {\zeta}^{-1} -3 -9 \zeta-4 {\zeta}^2 \right) +\frac{4}{x^3}
      \left({\zeta}^{-1}-3 \zeta-2 {\zeta}^2 \right) \biggr) \\
A_3&=&-4 \biggl( {\zeta}^{-1}-\zeta+\frac{1}{x}\left(3 {\zeta}^{-1}+2-3 \zeta
      -2 {\zeta}^2\right)+\frac{2}{x^2} \left({\zeta}^{-1}+1-\zeta
      -{\zeta}^2 \right) \biggr) \\
A_4&=&2 \biggl(-{\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}\left(3{\zeta}^{-1}
     +13+14 \zeta+4{\zeta}^2\right)
     +\frac{8}{x^4}\left({\zeta}^{-1}+4
     +5\zeta+2{\zeta}^2\right)\biggr) \\
A_5&=&2 \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}\left({\zeta}^{-1}+2+3\zeta
      +2{\zeta}^2\right)\biggr) \\
A_6&=&-2\left(x+1\right)\biggl(\frac{1}{x}\left({\zeta}^{-1}-\zeta\right)
      +\frac{2}{x^2}\left({\zeta}^{-1}+4+3\zeta\right)+\frac{8}{x^3}
      \left(1+\zeta\right)^2\biggr) \\
A_7&=&-2\biggl({\zeta}^{-1}-2\zeta+\frac{1}{x}\left(3{\zeta}^{-1}+1
     -6\zeta-4{\zeta}^2\right)+\frac{2}{x^2}\left({\zeta}^{-1}
     +1-2\zeta-2{\zeta}^2\right)\biggr)\\
A_8&=&-2\biggl(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}\left(3{\zeta}^{-1}+5+4\zeta+2{\zeta}^2\right)
      \biggr) \\
A_9&=&8\left(x+1\right)\left({\zeta}^{-1}+1\right)\biggl(\frac{1}{x^2}
      \left(1-\zeta\right)+\frac{4}{x^3}\left(1+\zeta\right)
      +\frac{4}{x^4}\left(1+\zeta\right)^2\biggr) \\
A_{10}&=&4\biggl(2{\zeta}^{-1}+\zeta+\frac{1}{x}\left(6{\zeta}^{-1}
         +3+3\zeta+2{\zeta}^2\right)+\frac{2}{x^2}\left(2{\zeta}^{-1}
         +2+\zeta+{\zeta}^2\right)\biggr)\\
\end{eqnarray*}

