\begin{center}
\footnotesize
\setlength{\mylength}{\baselineskip}
\begin{longtable}{rp{0ex}p{9cm}p{0ex}RL}
\caption{Laurent polynomials and selected mutations for bucket 82.}\\

\toprule \multicolumn{1}{c}{{Node}}&& \multicolumn{1}{c}{{Laurent polynomial}} && \multicolumn{2}{c}{{Mutations from Figure~\ref{fig:82a}}} \\ \midrule \endfirsthead

\multicolumn{6}{c}{{\tablename\ \thetable{} -- continued from previous page}} \\ \addlinespace[1.7ex] \midrule \multicolumn{1}{c}{{Node}}&& \multicolumn{1}{c}{{Laurent polynomial}} && \multicolumn{2}{c}{{Mutations from Figure~\ref{fig:82a}}} \\ \midrule \endhead

\midrule \multicolumn{6}{c}{{Continued on next page}} \endfoot

\bottomrule \endlastfoot

340 && $x+y+z+\frac{z}{y}+\frac{2}{y}+\frac{1}{yz}+\frac{y}{x}+\frac{2}{x}+\frac{1}{xy}$ && $658 \colon {}$ & $\left(\frac{xz+y+1}{x},y,\frac{x^2z}{xz+y+1}\right)$ \spacer \\* 
 &&  && $968 \colon {}$ & $\left(y,\frac{z+y(z+1)^2}{xyz},z\right)$ \spacer \\* 
 &&  && $1256 \colon {}$ & $\left(\frac{x^2y^2z}{xy^2z+y+1},y,\frac{xy}{xy^2z+y+1}\right)$ \spacer \\* 
 &&  && $1351 \colon {}$ & $\left(\frac{x^2yz}{xyz+1},y,\frac{xyz+1}{xy}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
407 && $x+\frac{x}{y}+y+z+\frac{1}{y}+\frac{y}{x}+\frac{2}{x}+\frac{1}{xz}+\frac{1}{x^2z}$ && $1044 \colon {}$ & $\left(\frac{xy}{y+1},\frac{x}{y+1},\frac{y+1}{xyz}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 658 && $x+\frac{x}{y}+y+z+\frac{2}{y}+\frac{y}{x}+\frac{1}{x}+\frac{1}{xy}+\frac{1}{x^2z}+\frac{1}{x^2yz}$ && $340 \colon {}$ & $\left(\frac{xz+y+1}{x},y,\frac{x^2z}{xz+y+1}\right)$ \spacer \\* 
 &&  && $939 \colon {}$ & $\left(x,\frac{xz+(x+1)^2}{xy},\frac{1}{x^2z}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
939 && $x+\frac{x}{y}+y+z+\frac{z}{y}+\frac{3}{y}+\frac{1}{x}+\frac{z}{xy}+\frac{3}{xy}+\frac{1}{x^2z}+\frac{1}{x^2y}$ && $658 \colon {}$ & $\left(x,\frac{1+xz(x+1)^2}{x^2yz},\frac{1}{x^2z}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 968 && $x+y+z+\frac{2}{y}+\frac{z}{x}+\frac{2}{x}+\frac{1}{xz}+\frac{z}{xy}+\frac{3}{xy}+\frac{1}{xyz}+\frac{1}{xy^2}$ && $340 \colon {}$ & $\left(\frac{z+x(z+1)^2}{xyz},x,z\right)$ \spacer \\* 
 &&  && $1890 \colon {}$ & $\left(\frac{x^2y}{xy+1},\frac{xy+1}{x},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
1044 && $x+y+z+\frac{1}{y}+\frac{y}{x}+\frac{z}{x}+\frac{3}{x}+\frac{1}{xz}+\frac{z}{xy}+\frac{2}{xy}+\frac{1}{xyz}$ && $407 \colon {}$ & $\left(x+y,\frac{x}{y},\frac{1}{xz}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $1890 \colon {}$ & $\left(x,\frac{xz+(z+1)^2}{xyz},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 1256 && $x+y+z+\frac{2}{y}+\frac{y}{x}+\frac{2}{x}+\frac{2}{xy}+\frac{1}{xy^2}+\frac{1}{x^2z}+\frac{3}{x^2yz}+\frac{3}{x^2y^2z}+\frac{1}{x^2y^3z}$ && $340 \colon {}$ & $\left(\frac{xy+yz+z}{y},y,\frac{x}{z(xy+yz+z)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
1351 && $x+y+z+\frac{z}{y}+\frac{2}{y}+\frac{y}{x}+\frac{2}{x}+\frac{2}{xy}+\frac{1}{xy^2}+\frac{1}{x^2z}+\frac{2}{x^2yz}+\frac{1}{x^2y^2z}$ && $340 \colon {}$ & $\left(\frac{xyz+1}{yz},y,\frac{xyz^2}{xyz+1}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 1890 && $x+y+z+\frac{1}{y}+\frac{z}{x}+\frac{3}{x}+\frac{1}{xz}+\frac{z}{xy}+\frac{3}{xy}+\frac{1}{xyz}+\frac{z}{x^2y}+\frac{2}{x^2y}+\frac{1}{x^2yz}$ && $968 \colon {}$ & $\left(\frac{xy+1}{y},\frac{xy^2}{xy+1},z\right)$ \spacer \\* 
 &&  && $1044 \colon {}$ & $\left(x,\frac{xz+(z+1)^2}{xyz},z\right)$ \spacer \\* 
 &&  && $2608 \colon {}$ & $\left(\frac{(xy+1)(xyz+(z+1)^2)}{x^2yz},\frac{x^3y^2z}{(xy+1)(xyz+(z+1)^2)},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
2608 && $x+y+z+\frac{z}{x}+\frac{4}{x}+\frac{1}{xz}+\frac{z}{xy}+\frac{3}{xy}+\frac{1}{xyz}+\frac{2z}{x^2y}+\frac{5}{x^2y}+\frac{2}{x^2yz}+\frac{z}{x^3y^2}+\frac{2}{x^3y^2}+\frac{1}{x^3y^2z}$ && $1890 \colon {}$ & $\left(\frac{(xy+1)(xyz+(z+1)^2)}{x^2yz},\frac{x^3y^2z}{(xy+1)(xyz+(z+1)^2)},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \end{longtable}
\end{center}
