\begin{longtable}{@{}cll@{}}
\caption{Elimination on each factor of the first minor.}\label{resultanttable}\\
\toprule $(k,l)$ & index & polynomial\\\midrule\endfirsthead
\toprule $(k,l)$ & index & polynomial\\\midrule\endhead
\bottomrule\endfoot
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(1,-1)$ & 1 & $\bigl(u - 2\bigr)\bigl(3 u - 14\bigr)$\\*[3pt]
$(1,-1)$ & 2 & $\bigl(3 u - 17\bigr)\bigl(3 u^{2} - 12 u + 5\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(1,-1)$ & 2 & $\bigl(3 u - 13\bigr)\bigl(3 u^{2} - 12 u + 17\bigr)$\\*[3pt]
$(1,-1)$ & 4 & $\bigl(u - 2\bigr)\bigl(3 u - 14\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u - 3$; resultants in $u$}\\*
$(1,-1)$ & 1 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} + 2 a + 2\bigr)$\\*[3pt]
$(1,-1)$ & 4 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a - 1\bigr)\bigl(a^{2} + 6 a + 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} + 2 a + u^{2} - 4 u + 4$; resultants in $u$}\\*
$(1,-1)$ & 1 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(4 a - 1\bigr)\bigl(a^{2} + 10 a + 4\bigr)$\\*[3pt]
$(1,-1)$ & 4 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(a^{2} - 6 a + 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(-1,1)$ & 2 & $\bigl(3 u + 7\bigr)\bigl(u^{2} + 4 u - 1\bigr)$\\*[3pt]
$(-1,1)$ & 4 & $\bigl(3 u + 8\bigr)\bigl(3 u^{2} + 12 u - 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(-1,1)$ & 1 & $\bigl(3 u + 8\bigr)\bigl(3 u^{2} + 12 u - 4\bigr)$\\*[3pt]
$(-1,1)$ & 2 & $\bigl(3 u + 11\bigr)\bigl(3 u^{2} + 12 u - 23\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u + 1$; resultants in $u$}\\*
$(-1,1)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(a^{2} + 10 a - 2\bigr)$\\*[3pt]
$(-1,1)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(4 a + 1\bigr)\bigl(a^{2} - 2 a - 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} + 2 a + u^{2} + 4 u + 4$; resultants in $u$}\\*
$(-1,1)$ & 2 & $\bigl(a - 1\bigr)\bigl(3 a - 5\bigr)$\\*[3pt]
$(-1,1)$ & 4 & \shortstack[l]{$\bigl(a\bigr)\bigl(a + 1\bigr)\bigl(a + 2\bigr)\bigl(3 a + 1\bigr)$\\$\quad\cdot\bigl(8 a + 3\bigr)$}\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=a - 1$; specialize at $1$}\\*
$(-1,-1)$ & 3 & $\bigl(u + 2\bigr)\bigl(u + 4\bigr)\bigl(u + 6\bigr)$\\*[3pt]
$(-1,-1)$ & 4 & $\bigl(u + 1\bigr)\bigl(u + 5\bigr)\bigl(u + 7\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(-1,-1)$ & 2 & $\bigl(3 u + 16\bigr)\bigl(3 u^{2} + 18 u + 32\bigr)$\\*[3pt]
$(-1,-1)$ & 4 & $\bigl(u + 3\bigr)\bigl(3 u + 17\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(-1,-1)$ & 1 & $\bigl(u + 3\bigr)\bigl(3 u + 17\bigr)$\\*[3pt]
$(-1,-1)$ & 2 & $\bigl(3 u + 20\bigr)\bigl(3 u^{2} + 18 u + 20\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} + 6 u + 9$; resultants in $u$}\\*
$(-1,-1)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a + 1\bigr)\bigl(a^{2} - 10 a + 4\bigr)$\\*[3pt]
$(-1,-1)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} + 6 a + 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(0,-2)$ & 2 & $\bigl(3 u + 13\bigr)\bigl(3 u^{2} + 12 u + 17\bigr)$\\*[3pt]
$(0,-2)$ & 4 & $\bigl(u + 2\bigr)\bigl(3 u + 14\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(0,-2)$ & 1 & $\bigl(u + 2\bigr)$\\*[3pt]
$(0,-2)$ & 2 & $\bigl(3 u + 17\bigr)\bigl(3 u^{2} + 12 u + 5\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u + 3$; resultants in $u$}\\*
$(0,-2)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(a^{2} - 2 a + 2\bigr)$\\*[3pt]
$(0,-2)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(4 a + 1\bigr)\bigl(a^{2} - 6 a + 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} + 4 u + 4$; resultants in $u$}\\*
$(0,-2)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a + 1\bigr)$\\*[3pt]
$(0,-2)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} + 6 a + 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(-2,0)$ & 2 & $\bigl(3 u + 19\bigr)\bigl(3 u^{2} + 24 u + 53\bigr)$\\*[3pt]
$(-2,0)$ & 4 & $\bigl(u + 4\bigr)\bigl(3 u + 20\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(-2,0)$ & 1 & $\bigl(u + 4\bigr)\bigl(3 u + 20\bigr)$\\*[3pt]
$(-2,0)$ & 2 & $\bigl(3 u + 23\bigr)\bigl(3 u^{2} + 24 u + 41\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u + 5$; resultants in $u$}\\*
$(-2,0)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(a^{2} - 2 a + 2\bigr)$\\*[3pt]
$(-2,0)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(4 a + 1\bigr)\bigl(a^{2} - 6 a + 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} + 8 u + 16$; resultants in $u$}\\*
$(-2,0)$ & 1 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a + 1\bigr)\bigl(a^{2} - 10 a + 4\bigr)$\\*[3pt]
$(-2,0)$ & 4 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} + 6 a + 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(1,1)$ & 1 & $\bigl(3 u - 11\bigr)\bigl(3 u^{2} - 18 u + 11\bigr)$\\*[3pt]
$(1,1)$ & 2 & $\bigl(3 u - 14\bigr)\bigl(3 u^{2} - 18 u - 8\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(1,1)$ & 2 & $\bigl(3 u - 10\bigr)\bigl(u^{2} - 6 u + 4\bigr)$\\*[3pt]
$(1,1)$ & 4 & $\bigl(3 u - 11\bigr)\bigl(3 u^{2} - 18 u + 11\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u - 2$; resultants in $u$}\\*
$(1,1)$ & 1 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} - 10 a - 2\bigr)$\\*[3pt]
$(1,1)$ & 4 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a - 1\bigr)\bigl(a^{2} + 2 a - 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} - 6 u + 9$; resultants in $u$}\\*
$(1,1)$ & 2 & $\bigl(a + 1\bigr)\bigl(3 a + 5\bigr)$\\*[3pt]
$(1,1)$ & 4 & \shortstack[l]{$\bigl(a - 2\bigr)\bigl(a - 1\bigr)\bigl(a\bigr)\bigl(3 a - 1\bigr)$\\$\quad\cdot\bigl(8 a - 3\bigr)$}\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(2,0)$ & 1 & $\bigl(3 u - 14\bigr)\bigl(3 u^{2} - 24 u + 32\bigr)$\\*[3pt]
$(2,0)$ & 2 & $\bigl(3 u - 17\bigr)\bigl(3 u^{2} - 24 u + 13\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(2,0)$ & 2 & $\bigl(3 u - 13\bigr)\bigl(u^{2} - 8 u + 11\bigr)$\\*[3pt]
$(2,0)$ & 4 & $\bigl(3 u - 14\bigr)\bigl(3 u^{2} - 24 u + 32\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u - 3$; resultants in $u$}\\*
$(2,0)$ & 1 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} - 10 a - 2\bigr)$\\*[3pt]
$(2,0)$ & 4 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a - 1\bigr)\bigl(a^{2} + 2 a - 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} - 8 u + 16$; resultants in $u$}\\*
$(2,0)$ & 2 & $\bigl(a + 1\bigr)\bigl(3 a + 5\bigr)$\\*[3pt]
$(2,0)$ & 4 & \shortstack[l]{$\bigl(a - 2\bigr)\bigl(a - 1\bigr)\bigl(a\bigr)\bigl(3 a - 1\bigr)$\\$\quad\cdot\bigl(8 a - 3\bigr)$}\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a - 1$; specialize at $\frac{1}{3}$}\\*
$(0,2)$ & 1 & $\bigl(3 u - 8\bigr)\bigl(3 u^{2} - 12 u - 4\bigr)$\\*[3pt]
$(0,2)$ & 2 & $\bigl(3 u - 11\bigr)\bigl(3 u^{2} - 12 u - 23\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=3 a + 1$; specialize at $- \frac{1}{3}$}\\*
$(0,2)$ & 2 & $\bigl(3 u - 7\bigr)\bigl(u^{2} - 4 u - 1\bigr)$\\*[3pt]
$(0,2)$ & 4 & $\bigl(3 u - 8\bigr)\bigl(3 u^{2} - 12 u - 4\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 2 a + u - 1$; resultants in $u$}\\*
$(0,2)$ & 1 & $\bigl(a + 1\bigr)\bigl(3 a + 1\bigr)\bigl(a^{2} - 10 a - 2\bigr)$\\*[3pt]
$(0,2)$ & 4 & $\bigl(a - 1\bigr)\bigl(3 a - 1\bigr)\bigl(4 a - 1\bigr)\bigl(a^{2} + 2 a - 2\bigr)$\\[3pt]
\multicolumn{3}{@{}l}{\rule{0pt}{15pt}$g=- 3 a^{2} - 2 a + u^{2} - 4 u + 4$; resultants in $u$}\\*
$(0,2)$ & 2 & $\bigl(a + 1\bigr)\bigl(3 a + 5\bigr)$\\*[3pt]
$(0,2)$ & 4 & \shortstack[l]{$\bigl(a - 2\bigr)\bigl(a - 1\bigr)\bigl(a\bigr)\bigl(3 a - 1\bigr)$\\$\quad\cdot\bigl(8 a - 3\bigr)$}\\[3pt]
\end{longtable}