\apphead{Explicit parametrisations of the new curves of degree $7$, $8$ and $9$.} Each sextuple of binary forms below parametrises the curve $C_D$ of the indicated class birationally (verified: the forms satisfy the three quadrics of $V$ identically, have degree exactly $d$ and no common factor, vanish on $f_D$ and on the whole ideal of $C_D$, and their intersection numbers with the $56$ lines and conics give back the class $D$ with $D^2=-2$). The coefficient lists of all $48$ curves, the forms $f_D$ and generators of the ideals are in \texttt{new\_curves.json}.
{\small
% R7a, degree 7, class (-2,0,0,2,0,0,1,1,1,1,0,0,0), form f_D = 2*x*z + 2*y*z - x*u - y*u + z*u - u^2 + x*v + y*v - z*v + 2*u*v + v^2 + x*w + y*w - 3*z*w + 2*u*w - w^2
\par\smallskip\noindent\textbf{R7a} ($d=7$, $D=(-2,0,0,2,0,0,1,1,1,1,0,0,0)$, $2H-D=\Gamma_{1}+\Gamma_{6}+\Gamma_{7}+Q_{7}+Q_{9}+Q_{10}$; $f_D=2xz + 2yz - xu - yu + zu - u^{2} + xv + yv - zv + 2uv + v^{2} + xw + yw - 3zw + 2uw - w^{2}$):
\begin{align*}
x &= 3m^{7} - 127m^{6}n - 100m^{5}n^{2} - 69m^{4}n^{3} - 24m^{3}n^{4}\\
&\quad  - 7m^{2}n^{5} - mn^{6},\\
y &= 80m^{7} + 57m^{6}n - 5m^{5}n^{2} - 36m^{4}n^{3} - 23m^{3}n^{4}\\
&\quad  - 14m^{2}n^{5} - 3mn^{6} - n^{7},\\
z &= 55m^{7} + 104m^{6}n + 83m^{5}n^{2} + 87m^{4}n^{3} + 37m^{3}n^{4}\\
&\quad  + 19m^{2}n^{5} + 4mn^{6} + n^{7},\\
u &= 32m^{7} + 129m^{6}n + 107m^{5}n^{2} + 84m^{4}n^{3} + 33m^{3}n^{4}\\
&\quad  + 16m^{2}n^{5} + 3mn^{6} + n^{7},\\
v &= -43m^{7} - 8m^{6}n - 81m^{5}n^{2} - 59m^{4}n^{3} - 37m^{3}n^{4}\\
&\quad  - 17m^{2}n^{5} - 4mn^{6} - n^{7},\\
w &= -81m^{7} - 67m^{6}n - 18m^{5}n^{2} - 23m^{4}n^{3} + 4m^{3}n^{4}\\
&\quad  - m^{2}n^{5} + mn^{6}.
\end{align*}
% R8a, degree 8, class (-3,-1,-1,4,0,2,1,1,2,3,-2,0,-1), form f_D = 3*x*y + y*z + 5*x*u + y*u + 4*z*u - 2*u^2 - 2*x*v - 5*y*v - 2*u*v + 3*v^2 + 3*x*w + 2*y*w - 6*z*w + 3*u*w - 3*v*w - 5*w^2
\par\smallskip\noindent\textbf{R8a} ($d=8$, $D=(-3,-1,-1,4,0,2,1,1,2,3,-2,0,-1)$, $2H-D=\Gamma_{1}+\Gamma_{3}+\Gamma_{15}+\Gamma_{16}+Q_{1}+Q_{9}$; $f_D=3xy + yz + 5xu + yu + 4zu - 2u^{2} - 2xv - 5yv - 2uv + 3v^{2} + 3xw + 2yw - 6zw + 3uw - 3vw - 5w^{2}$):
\begin{align*}
x &= 175m^{7}n + 95m^{6}n^{2} + 85m^{5}n^{3} + 51m^{4}n^{4} + 9m^{3}n^{5}\\
&\quad  + 17m^{2}n^{6} - mn^{7} + n^{8},\\
y &= -125m^{8} - 175m^{7}n - 115m^{6}n^{2} - 161m^{5}n^{3} - 35m^{4}n^{4}\\
&\quad  - 29m^{3}n^{5} - 5m^{2}n^{6} - 3mn^{7},\\
z &= 125m^{8} + 50m^{7}n + 30m^{6}n^{2} - 8m^{5}n^{3} + 10m^{4}n^{4}\\
&\quad  + 2m^{3}n^{5} + 6m^{2}n^{6} + n^{8},\\
u &= 125m^{8} + 125m^{7}n + 205m^{6}n^{2} + 95m^{5}n^{3} + 59m^{4}n^{4}\\
&\quad  + 35m^{3}n^{5} - m^{2}n^{6} + 5mn^{7},\\
v &= -125m^{8} - 100m^{7}n - 90m^{6}n^{2} - 78m^{5}n^{3} - 34m^{4}n^{4}\\
&\quad  + 4m^{3}n^{5} - 10m^{2}n^{6} + 2mn^{7} - n^{8},\\
w &= 25m^{7}n + 45m^{6}n^{2} + 99m^{5}n^{3} + 7m^{4}n^{4} + 35m^{3}n^{5}\\
&\quad  + 3m^{2}n^{6} + mn^{7} + n^{8}.
\end{align*}
% R8b, degree 8, class (-3,-1,-1,4,0,2,1,2,2,2,-2,0,-1), form f_D = 3*x*y - 2*x*z - 6*y*z - 2*x*u - y*u + u^2 - 3*x*v - 6*y*v + 6*z*v + u*v + 5*v^2 - 2*y*w + 3*z*w + 2*u*w + 2*v*w - w^2
\par\smallskip\noindent\textbf{R8b} ($d=8$, $D=(-3,-1,-1,4,0,2,1,2,2,2,-2,0,-1)$, $2H-D=\Gamma_{1}+\Gamma_{6}+Q_{1}+Q_{3}+Q_{6}$; $f_D=3xy - 2xz - 6yz - 2xu - yu + u^{2} - 3xv - 6yv + 6zv + uv + 5v^{2} - 2yw + 3zw + 2uw + 2vw - w^{2}$):
\begin{align*}
x &= 12m^{8} - 46m^{7}n + 97m^{6}n^{2} - 109m^{5}n^{3} + 84m^{4}n^{4}\\
&\quad  - 34m^{3}n^{5} - m^{2}n^{6} + 7mn^{7} - 4n^{8},\\
y &= 4m^{8} + 20m^{7}n - 35m^{6}n^{2} + 89m^{5}n^{3} - 100m^{4}n^{4}\\
&\quad  + 98m^{3}n^{5} - 50m^{2}n^{6} + 20mn^{7} - 2n^{8},\\
z &= -16m^{8} + 28m^{7}n - 43m^{6}n^{2} + 31m^{5}n^{3} - 43m^{4}n^{4}\\
&\quad  + 29m^{3}n^{5} - 31m^{2}n^{6} + 13mn^{7} - 6n^{8},\\
u &= -4m^{8} + 50m^{7}n - 79m^{6}n^{2} + 99m^{5}n^{3} - 42m^{4}n^{4}\\
&\quad  + 6m^{3}n^{5} + 22m^{2}n^{6} - 12mn^{7} + 6n^{8},\\
v &= 16m^{8} - 36m^{7}n + 89m^{6}n^{2} - 99m^{5}n^{3} + 90m^{4}n^{4}\\
&\quad  - 48m^{3}n^{5} + 23m^{2}n^{6} - 7mn^{7} + 2n^{8},\\
w &= -12m^{8} + 12m^{7}n + 29m^{6}n^{2} - 81m^{5}n^{3} + 121m^{4}n^{4}\\
&\quad  - 91m^{3}n^{5} + 53m^{2}n^{6} - 15mn^{7} + 4n^{8}.
\end{align*}
% R8c, degree 8, class (-3,-1,-1,4,0,3,0,1,2,3,-2,0,-1), form f_D = x*y + 4*x*z + y*z - 3*x*u - y*u - 2*u^2 - 2*x*v + 3*y*v - 4*z*v - 2*u*v - v^2 + 5*x*w + 2*y*w + 6*z*w + u*w - 3*v*w + 7*w^2
\par\smallskip\noindent\textbf{R8c} ($d=8$, $D=(-3,-1,-1,4,0,3,0,1,2,3,-2,0,-1)$, $2H-D=\Gamma_{1}+\Gamma_{4}+\Gamma_{15}+\Gamma_{16}+Q_{3}+Q_{11}$; $f_D=xy + 4xz + yz - 3xu - yu - 2u^{2} - 2xv + 3yv - 4zv - 2uv - v^{2} + 5xw + 2yw + 6zw + uw - 3vw + 7w^{2}$):
\begin{align*}
x &= 3m^{8} - m^{7}n + 29m^{6}n^{2} + 5m^{5}n^{3} + 119m^{4}n^{4}\\
&\quad  + 65m^{3}n^{5} + 55m^{2}n^{6} - 25mn^{7} - 250n^{8},\\
y &= -2m^{8} - 11m^{7}n - 37m^{6}n^{2} - 69m^{5}n^{3} - 223m^{4}n^{4}\\
&\quad  - 257m^{3}n^{5} - 595m^{2}n^{6} - 375mn^{7} - 375n^{8},\\
z &= -m^{8} + 10m^{7}n + 12m^{6}n^{2} + 148m^{5}n^{3} + 164m^{4}n^{4}\\
&\quad  + 526m^{3}n^{5} + 360m^{2}n^{6} + 600mn^{7} + 125n^{8},\\
u &= 2m^{8} - 5m^{7}n - 23m^{6}n^{2} - 87m^{5}n^{3} - 231m^{4}n^{4}\\
&\quad  - 355m^{3}n^{5} - 545m^{2}n^{6} - 325mn^{7} - 375n^{8},\\
v &= m^{8} + 16m^{7}n + 12m^{6}n^{2} + 94m^{5}n^{3} - 12m^{4}n^{4}\\
&\quad  + 164m^{3}n^{5} - 200m^{2}n^{6} + 50mn^{7} - 125n^{8},\\
w &= -3m^{8} - m^{7}n - 51m^{6}n^{2} - 75m^{5}n^{3} - 291m^{4}n^{4}\\
&\quad  - 323m^{3}n^{5} - 525m^{2}n^{6} - 425mn^{7} - 250n^{8}.
\end{align*}
% R8d, degree 8, class (-2,-2,-2,3,1,1,1,2,2,2,-1,0,-1), form f_D = 7*x*y + 2*x*z + 6*y*z + 2*x*u - 3*y*u + 4*z*u - 3*u^2 - x*v + 10*y*v - 2*z*v + 7*u*v - 3*v^2 - 2*x*w + 4*y*w - z*w + 6*u*w + 2*v*w + 5*w^2
\par\smallskip\noindent\textbf{R8d} ($d=8$, $D=(-2,-2,-2,3,1,1,1,2,2,2,-1,0,-1)$, $2H-D=\Gamma_{2}+\Gamma_{3}+\Gamma_{5}+\Gamma_{7}+Q_{3}+Q_{6}$; $f_D=7xy + 2xz + 6yz + 2xu - 3yu + 4zu - 3u^{2} - xv + 10yv - 2zv + 7uv - 3v^{2} - 2xw + 4yw - zw + 6uw + 2vw + 5w^{2}$):
\begin{align*}
x &= m^{8} - 10m^{7}n + 13m^{6}n^{2} - 50m^{5}n^{3} - 137m^{4}n^{4}\\
&\quad  - 118m^{3}n^{5} - 245m^{2}n^{6} - 750mn^{7},\\
y &= -3m^{8} - m^{7}n - 32m^{6}n^{2} - 51m^{5}n^{3} - 116m^{4}n^{4}\\
&\quad  - 379m^{3}n^{5} - 60m^{2}n^{6} - 825mn^{7} - 1125n^{8},\\
z &= 2m^{8} + 6m^{7}n + 5m^{6}n^{2} + 138m^{5}n^{3} + 117m^{4}n^{4}\\
&\quad  + 430m^{3}n^{5} + 1015m^{2}n^{6} + 1050mn^{7} + 1125n^{8},\\
u &= 2m^{8} - 2m^{7}n + 41m^{6}n^{2} + 50m^{5}n^{3} + 161m^{4}n^{4}\\
&\quad  + 586m^{3}n^{5} + 575m^{2}n^{6} + 1350mn^{7} + 1125n^{8},\\
v &= m^{8} + 3m^{7}n + 4m^{6}n^{2} + 57m^{5}n^{3} - 48m^{4}n^{4}\\
&\quad  + 137m^{3}n^{5} + 200m^{2}n^{6} - 525mn^{7} - 1125n^{8},\\
w &= -3m^{8} - 2m^{7}n - 31m^{6}n^{2} - 54m^{5}n^{3} - 217m^{4}n^{4}\\
&\quad  - 170m^{3}n^{5} - 765m^{2}n^{6} - 1350mn^{7}.
\end{align*}
% R8e, degree 8, class (-2,-2,-1,4,0,1,0,1,2,2,0,0,-1), form f_D = 2*x*y - 6*x*z + 5*y*z + 5*x*u - 2*y*u - 4*z*u + 5*u^2 + 4*x*v - 4*y*v - 3*z*v + 6*u*v - 3*v^2 + 2*x*w + 7*y*w + 4*z*w - 2*u*w + 5*v*w - 3*w^2
\par\smallskip\noindent\textbf{R8e} ($d=8$, $D=(-2,-2,-1,4,0,1,0,1,2,2,0,0,-1)$, $2H-D=\Gamma_{1}+\Gamma_{2}+\Gamma_{7}+\Gamma_{8}+Q_{7}+Q_{11}$; $f_D=2xy - 6xz + 5yz + 5xu - 2yu - 4zu + 5u^{2} + 4xv - 4yv - 3zv + 6uv - 3v^{2} + 2xw + 7yw + 4zw - 2uw + 5vw - 3w^{2}$):
\begin{align*}
x &= 4500m^{8} + 8950m^{7}n + 5735m^{6}n^{2} + 3930m^{5}n^{3} + 443m^{4}n^{4}\\
&\quad  + 94m^{3}n^{5} - 243m^{2}n^{6} - 54mn^{7} - 27n^{8},\\
y &= -4625m^{8} + 3050m^{7}n + 3025m^{6}n^{2} + 5386m^{5}n^{3} + 2791m^{4}n^{4}\\
&\quad  + 1478m^{3}n^{5} + 439m^{2}n^{6} + 102mn^{7} + 18n^{8},\\
z &= 8375m^{8} + 7175m^{7}n + 10200m^{6}n^{2} + 4893m^{5}n^{3} + 3388m^{4}n^{4}\\
&\quad  + 669m^{3}n^{5} + 292m^{2}n^{6} - 9mn^{7} + 9n^{8},\\
u &= -8125m^{8} - 8350m^{7}n - 9915m^{6}n^{2} - 5130m^{5}n^{3} - 2657m^{4}n^{4}\\
&\quad  - 726m^{3}n^{5} - 113m^{2}n^{6} + 6mn^{7} + 18n^{8},\\
v &= -6500m^{8} - 850m^{7}n - 3005m^{6}n^{2} + 298m^{5}n^{3} - 953m^{4}n^{4}\\
&\quad  - 214m^{3}n^{5} - 347m^{2}n^{6} - 66mn^{7} - 27n^{8},\\
w &= -1875m^{8} - 6875m^{7}n - 4660m^{6}n^{2} - 5529m^{5}n^{3} - 2296m^{4}n^{4}\\
&\quad  - 1553m^{3}n^{5} - 384m^{2}n^{6} - 147mn^{7} - 9n^{8}.
\end{align*}
% R9a, degree 9, class (-3,-1,-1,5,-1,3,1,1,3,3,-2,0,-2), form f_D = 2*x*y*u + 2*x*z*u - x*u^2 + 2*y*u^2 + 2*z*u^2 - u^3 + 2*x*y*v + 2*x*z*v - 2*y*z*v - 5*x*u*v + 3*y*u*v - 3*u^2*v - x*v^2 + 2*y*v^2 - 2*u*v^2 - v^3 + 2*y*z*w - 2*x*u*w - 2*y*u*w - z*u*w + 2*y*v*w - 2*v^2*w + x*w^2 + v*w^2
\par\smallskip\noindent\textbf{R9a} ($d=9$, $D=(-3,-1,-1,5,-1,3,1,1,3,3,-2,0,-2)$, $3H-D=\Gamma_{1}+\Gamma_{29}+\Gamma_{30}+Q_{1}+Q_{2}+Q_{3}+Q_{11}+Q_{23}+Q_{24}$; $f_D=2xyu + 2xzu - xu^{2} + 2yu^{2} + 2zu^{2} - u^{3} + 2xyv + 2xzv - 2yzv - 5xuv + 3yuv - 3u^{2}v - xv^{2} + 2yv^{2} - 2uv^{2} - v^{3} + 2yzw - 2xuw - 2yuw - zuw + 2yvw - 2v^{2}w + xw^{2} + vw^{2}$):
\begin{align*}
x &= 3m^{9} + 4m^{8}n + 29m^{7}n^{2} + 34m^{6}n^{3} + 105m^{5}n^{4}\\
&\quad  + 92m^{4}n^{5} + 166m^{3}n^{6} + 86m^{2}n^{7} + 96mn^{8} + 10n^{9},\\
y &= 2m^{9} + 6m^{8}n + 16m^{7}n^{2} + 50m^{6}n^{3} + 45m^{5}n^{4}\\
&\quad  + 148m^{4}n^{5} + 59m^{3}n^{6} + 184m^{2}n^{7} + 35mn^{8} + 80n^{9},\\
z &= m^{9} - 2m^{8}n + 12m^{7}n^{2} + 2m^{6}n^{3} + 55m^{5}n^{4}\\
&\quad  + 64m^{4}n^{5} + 112m^{3}n^{6} + 168m^{2}n^{7} + 83mn^{8} + 130n^{9},\\
u &= 2m^{9} + 6m^{8}n + 24m^{7}n^{2} + 38m^{6}n^{3} + 105m^{5}n^{4}\\
&\quad  + 78m^{4}n^{5} + 199m^{3}n^{6} + 46m^{2}n^{7} + 137mn^{8} - 10n^{9},\\
v &= -m^{9} + 2m^{8}n + m^{7}n^{2} + 20m^{6}n^{3} + 35m^{5}n^{4}\\
&\quad  + 86m^{4}n^{5} + 98m^{3}n^{6} + 174m^{2}n^{7} + 80mn^{8} + 130n^{9},\\
w &= 3m^{9} + 4m^{8}n + 28m^{7}n^{2} + 26m^{6}n^{3} + 95m^{5}n^{4}\\
&\quad  + 72m^{4}n^{5} + 136m^{3}n^{6} + 112m^{2}n^{7} + 69mn^{8} + 80n^{9}.
\end{align*}
% R9b, degree 9, class (-2,-3,-1,5,0,1,1,2,2,3,-1,0,-2), form f_D = x*y*z - 5*x*y*u + 4*y*z*u + 2*x*u^2 - y*u^2 - 2*z*u^2 - 7*u^3 + 3*x*y*v - x*z*v - y*z*v + 7*x*u*v + 8*y*u*v - 6*z*u*v + 3*u^2*v - 3*x*v^2 - 3*y*v^2 + z*v^2 + u*v^2 + 3*v^3 - x*y*w + 9*x*z*w + y*z*w + 8*x*u*w + 4*y*u*w - 5*z*u*w - 6*u^2*w - x*v*w - 5*y*v*w - 3*z*v*w - 4*u*v*w + 5*v^2*w + 6*x*w^2 + 2*y*w^2 - 10*z*w^2 + 2*u*w^2 - 6*w^3
\par\smallskip\noindent\textbf{R9b} ($d=9$, $D=(-2,-3,-1,5,0,1,1,2,2,3,-1,0,-2)$, $3H-D=\Gamma_{1}+\Gamma_{2}+\Gamma_{7}+\Gamma_{31}+\Gamma_{32}+Q_{1}+Q_{9}+Q_{11}+Q_{13}+Q_{14}$; $f_D=xyz - 5xyu + 4yzu + 2xu^{2} - yu^{2} - 2zu^{2} - 7u^{3} + 3xyv - xzv - yzv + 7xuv + 8yuv - 6zuv + 3u^{2}v - 3xv^{2} - 3yv^{2} + zv^{2} + uv^{2} + 3v^{3} - xyw + 9xzw + yzw + 8xuw + 4yuw - 5zuw - 6u^{2}w - xvw - 5yvw - 3zvw - 4uvw + 5v^{2}w + 6xw^{2} + 2yw^{2} - 10zw^{2} + 2uw^{2} - 6w^{3}$):
\begin{align*}
x &= 4m^{9} - 10m^{8}n + 7m^{7}n^{2} - 46m^{6}n^{3} + 98m^{5}n^{4}\\
&\quad  - 92m^{4}n^{5} + 60m^{3}n^{6} - 46m^{2}n^{7} + 13mn^{8} - 4n^{9},\\
y &= 8m^{9} - 24m^{8}n + 63m^{7}n^{2} - 113m^{6}n^{3} + 97m^{5}n^{4}\\
&\quad  - 59m^{4}n^{5} + 37m^{3}n^{6} - 24m^{2}n^{7} + 9mn^{8} - 6n^{9},\\
z &= -12m^{9} + 36m^{8}n - 43m^{7}n^{2} + 8m^{6}n^{3} - m^{5}n^{4}\\
&\quad  + 6m^{4}n^{5} + 22m^{3}n^{6} - 16m^{2}n^{7} + 6mn^{8} - 2n^{9},\\
u &= -12m^{9} + 34m^{8}n - 31m^{7}n^{2} - 10m^{6}n^{3} + 77m^{5}n^{4}\\
&\quad  - 84m^{4}n^{5} + 58m^{3}n^{6} - 32m^{2}n^{7} + 10mn^{8} - 6n^{9},\\
v &= 4m^{9} + 16m^{8}n - 71m^{7}n^{2} + 105m^{6}n^{3} - 87m^{5}n^{4}\\
&\quad  + 43m^{4}n^{5} + 7m^{3}n^{6} - 2m^{2}n^{7} + 5mn^{8} - 4n^{9},\\
w &= 8m^{9} - 40m^{8}n + 55m^{7}n^{2} - 58m^{6}n^{3} + 84m^{5}n^{4}\\
&\quad  - 94m^{4}n^{5} + 70m^{3}n^{6} - 30m^{2}n^{7} + 19mn^{8} - 2n^{9}.
\end{align*}
% R9c, degree 9, class (-2,-2,-2,4,0,3,2,1,3,3,-2,0,-2), form f_D = x*y*u - 2*x*z*u + y*u^2 - 2*z*u^2 - u^3 + x*y*v + 2*y*z*v - 3*x*u*v + y*u*v - u^2*v + y*v^2 - v^3 + x*z*w - 2*x*u*w - 2*z*u*w - 2*u^2*w + 2*y*v*w + 2*z*v*w + x*w^2 - y*w^2 + 2*z*w^2 - u*w^2 + v*w^2 + 2*w^3
\par\smallskip\noindent\textbf{R9c} ($d=9$, $D=(-2,-2,-2,4,0,3,2,1,3,3,-2,0,-2)$, $3H-D=\Gamma_{2}+\Gamma_{3}+\Gamma_{5}+Q_{1}+Q_{3}+Q_{7}+Q_{8}+Q_{9}+Q_{11}$; $f_D=xyu - 2xzu + yu^{2} - 2zu^{2} - u^{3} + xyv + 2yzv - 3xuv + yuv - u^{2}v + yv^{2} - v^{3} + xzw - 2xuw - 2zuw - 2u^{2}w + 2yvw + 2zvw + xw^{2} - yw^{2} + 2zw^{2} - uw^{2} + vw^{2} + 2w^{3}$):
\begin{align*}
x &= 25m^{9} - 29m^{8}n + 15m^{7}n^{2} + 19m^{6}n^{3} - 45m^{5}n^{4}\\
&\quad  + 45m^{4}n^{5} - 28m^{3}n^{6} + 10m^{2}n^{7} - 2mn^{8},\\
y &= -15m^{9} + 29m^{8}n - 73m^{7}n^{2} + 73m^{6}n^{3} - 56m^{5}n^{4}\\
&\quad  + 16m^{4}n^{5} + m^{3}n^{6} - 7m^{2}n^{7} + 3mn^{8} - n^{9},\\
z &= 5m^{9} + 17m^{8}n - 36m^{7}n^{2} + 58m^{6}n^{3} - 53m^{5}n^{4}\\
&\quad  + 47m^{4}n^{5} - 30m^{3}n^{6} + 16m^{2}n^{7} - 5mn^{8} + n^{9},\\
u &= -15m^{9} + 3m^{8}n + 25m^{7}n^{2} - 55m^{6}n^{3} + 62m^{5}n^{4}\\
&\quad  - 50m^{4}n^{5} + 31m^{3}n^{6} - 15m^{2}n^{7} + 5mn^{8} - n^{9},\\
v &= 25m^{9} - 31m^{8}n + 21m^{7}n^{2} + 3m^{6}n^{3} + m^{5}n^{4}\\
&\quad  - 7m^{4}n^{5} + 12m^{3}n^{6} - 6m^{2}n^{7} + 2mn^{8},\\
w &= 5m^{9} - 51m^{8}n + 68m^{7}n^{2} - 70m^{6}n^{3} + 35m^{5}n^{4}\\
&\quad  - 21m^{4}n^{5} + 10m^{3}n^{6} - 8m^{2}n^{7} + 3mn^{8} - n^{9}.
\end{align*}
% R9d, degree 9, class (-2,-1,-1,4,-1,1,1,1,1,2,0,0,0), form f_D = x*y - 4*x*z + 2*y*z + 17*x*u - 3*y*u + 7*z*u - 5*u^2 - x*v + 9*y*v + z*v - 2*u*v + 11*v^2 - 3*x*w - y*w - 2*z*w - u*w - 3*v*w - 5*w^2
\par\smallskip\noindent\textbf{R9d} ($d=9$, $D=(-2,-1,-1,4,-1,1,1,1,1,2,0,0,0)$, $2H-D=\Gamma_{1}+\Gamma_{3}+\Gamma_{6}+\Gamma_{15}+\Gamma_{16}+\Gamma_{19}+\Gamma_{20}$; $f_D=xy - 4xz + 2yz + 17xu - 3yu + 7zu - 5u^{2} - xv + 9yv + zv - 2uv + 11v^{2} - 3xw - yw - 2zw - uw - 3vw - 5w^{2}$):
\begin{align*}
x &= 74m^{9} + 157m^{8}n + 126m^{7}n^{2} + 845m^{6}n^{3} - 91m^{5}n^{4}\\
&\quad  + 1231m^{4}n^{5} - 291m^{3}n^{6} + 825m^{2}n^{7} - 160mn^{8} + 200n^{9},\\
y &= 72m^{9} - 55m^{8}n + 200m^{7}n^{2} - 394m^{6}n^{3} + 858m^{5}n^{4}\\
&\quad  - 540m^{4}n^{5} + 636m^{3}n^{6} + 25m^{2}n^{7} + 70mn^{8} + 100n^{9},\\
z &= 134m^{9} + 138m^{8}n + 496m^{7}n^{2} + 82m^{6}n^{3} + 370m^{5}n^{4}\\
&\quad  + 557m^{4}n^{5} - 298m^{3}n^{6} + 545m^{2}n^{7} - 180mn^{8} + 100n^{9},\\
u &= -104m^{9} + 95m^{8}n + 48m^{7}n^{2} + 565m^{6}n^{3} - 23m^{5}n^{4}\\
&\quad  + 977m^{4}n^{5} - 219m^{3}n^{6} + 585m^{2}n^{7} - 80mn^{8} + 100n^{9},\\
v &= 130m^{9} + 198m^{8}n + 248m^{7}n^{2} + 518m^{6}n^{3} - 184m^{5}n^{4}\\
&\quad  + 415m^{4}n^{5} - 188m^{3}n^{6} - 95m^{2}n^{7} + 30mn^{8} - 100n^{9},\\
w &= 30m^{9} + 343m^{8}n + 112m^{7}n^{2} + 724m^{6}n^{3} + 1146m^{4}n^{5}\\
&\quad  - 324m^{3}n^{6} + 845m^{2}n^{7} - 160mn^{8} + 200n^{9}.
\end{align*}
}