% orbit 9, S = (-2,0,1,0), degree 10
\begin{align*}
x &= 585m^{10} - 3606m^{9}n + 11770m^{8}n^{2} - 23192m^{7}n^{3} + 28046m^{6}n^{4} - 16020m^{5}n^{5}\\
&\quad  - 6048m^{4}n^{6} + 19656m^{3}n^{7} - 16767m^{2}n^{8} + 7290mn^{9} - 1458n^{10},\\
y &= 135m^{10} - 2145m^{9}n + 9443m^{8}n^{2} - 23460m^{7}n^{3} + 39530m^{6}n^{4} - 50022m^{5}n^{5}\\
&\quad  + 50994m^{4}n^{6} - 41796m^{3}n^{7} + 25839m^{2}n^{8} - 10449mn^{9} + 2187n^{10},\\
z &= -468m^{10} + 2190m^{9}n - 2703m^{8}n^{2} - 4684m^{7}n^{3} + 23172m^{6}n^{4} - 41448m^{5}n^{5}\\
&\quad  + 44622m^{4}n^{6} - 31428m^{3}n^{7} + 14904m^{2}n^{8} - 4374mn^{9} + 729n^{10},\\
u &= 324m^{10} - 3186m^{9}n + 11061m^{8}n^{2} - 20200m^{7}n^{3} + 18900m^{6}n^{4} - 1404m^{5}n^{5}\\
&\quad  - 20898m^{4}n^{6} + 30456m^{3}n^{7} - 23328m^{2}n^{8} + 10206mn^{9} - 2187n^{10},\\
v &= 333m^{10} - 783m^{9}n - 1799m^{8}n^{2} + 13668m^{7}n^{3} - 33674m^{6}n^{4} + 47526m^{5}n^{5}\\
&\quad  - 41202m^{4}n^{6} + 21060m^{3}n^{7} - 4131m^{2}n^{8} - 1215mn^{9} + 729n^{10},\\
w &= -603m^{10} + 3534m^{9}n - 9974m^{8}n^{2} + 20044m^{7}n^{3} - 33442m^{6}n^{4} + 48336m^{5}n^{5}\\
&\quad  - 55584m^{4}n^{6} + 46980m^{3}n^{7} - 26811m^{2}n^{8} + 9234mn^{9} - 1458n^{10}.
\end{align*}