% orbit 11, S = (1,-1,1,0), degree 11
\begin{align*}
x &= 729m^{11} - 4374m^{10}n + 12393m^{9}n^{2} - 20034m^{8}n^{3} + 18684m^{7}n^{4} - 7218m^{6}n^{5}\\
&\quad  - 4888m^{5}n^{6} + 9158m^{4}n^{7} - 6389m^{3}n^{8} + 2464m^{2}n^{9} - 497mn^{10} + 36n^{11},\\
y &= -729m^{11} + 5103m^{10}n - 16119m^{9}n^{2} + 31995m^{8}n^{3} - 44514m^{7}n^{4} + 45354m^{6}n^{5}\\
&\quad  - 33474m^{5}n^{6} + 16986m^{4}n^{7} - 5245m^{3}n^{8} + 631m^{2}n^{9} + 113mn^{10} - 37n^{11},\\
z &= 1215m^{10}n - 6480m^{9}n^{2} + 16119m^{8}n^{3} - 24876m^{7}n^{4} + 26658m^{6}n^{5} - 21448m^{5}n^{6}\\
&\quad  + 13470m^{4}n^{7} - 6636m^{3}n^{8} + 2439m^{2}n^{9} - 592mn^{10} + 67n^{11},\\
u &= 729m^{10}n - 2916m^{9}n^{2} + 4293m^{8}n^{3} - 378m^{7}n^{4} - 8640m^{6}n^{5} + 15054m^{5}n^{6}\\
&\quad  - 13636m^{4}n^{7} + 7618m^{3}n^{8} - 2713m^{2}n^{9} + 590mn^{10} - 65n^{11},\\
v &= 729m^{11} - 4860m^{10}n + 14337m^{9}n^{2} - 25272m^{8}n^{3} + 28890m^{7}n^{4} - 22440m^{6}n^{5}\\
&\quad  + 12598m^{5}n^{6} - 6028m^{4}n^{7} + 3013m^{3}n^{8} - 1380m^{2}n^{9} + 401mn^{10} - 52n^{11},\\
w &= 729m^{11} - 4617m^{10}n + 14985m^{9}n^{2} - 31347m^{8}n^{3} + 45558m^{7}n^{4} - 46542m^{6}n^{5}\\
&\quad  + 33278m^{5}n^{6} - 16310m^{4}n^{7} + 5313m^{3}n^{8} - 1137m^{2}n^{9} + 169mn^{10} - 15n^{11}.
\end{align*}