\begin{center}
\footnotesize
\setlength{\mylength}{\baselineskip}
\begin{longtable}{rp{0ex}p{9cm}p{0ex}RL}
\caption{Laurent polynomials and selected mutations for bucket 31.}\\

\toprule \multicolumn{1}{c}{{Node}}&& \multicolumn{1}{c}{{Laurent polynomial}} && \multicolumn{2}{c}{{Mutations from Figure~\ref{fig:31a}}} \\ \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:31a}}} \\ \midrule \endhead

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

\bottomrule \endlastfoot

78 && $x+y+z+\frac{1}{y}+\frac{y}{x}+\frac{1}{x}+\frac{1}{xyz}$ && $79 \colon {}$ & $\left(\frac{x+yz}{xyz},\frac{x+yz}{xy},\frac{x^2}{x+yz}\right)$ \spacer \\* 
 &&  && $207 \colon {}$ & $\left(y,\frac{xz+1}{x},\frac{x^2z}{xz+1}\right)$ \spacer \\* 
 &&  && $377 \colon {}$ & $\left(\frac{(xz+1)(xz+y)}{x^2yz},\frac{(xz+1)(xz+y)}{x^2z},\frac{xy}{(xz+1)(xz+y)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
79 && $x+y+z+\frac{1}{y}+\frac{1}{yz}+\frac{z}{x}+\frac{1}{x}$ && $78 \colon {}$ & $\left(\frac{yz+1}{xyz},\frac{yz+1}{y},\frac{y}{x}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $169 \colon {}$ & $\left(\frac{x^2y}{xyz+xy+z},\frac{xyz+xy+z}{xz},\frac{x^2yz}{xyz+xy+z}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 169 && $x+y+\frac{y}{z}+z+\frac{z}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{z}{x^2y}$ && $79 \colon {}$ & $\left(\frac{xy+yz+1}{y},\frac{y^2z}{xy+yz+1},\frac{z}{x}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
207 && $x+y+z+\frac{z}{y}+\frac{1}{y}+\frac{1}{x}+\frac{1}{xy}+\frac{1}{xyz}$ && $78 \colon {}$ & $\left(\frac{yz+1}{y},x,\frac{y^2z}{yz+1}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $379 \colon {}$ & $\left(\frac{x^2y}{xy+z+1},\frac{xy+z+1}{x},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 315 && $x+y+z+\frac{y}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{y}{x^2z}+\frac{2}{x^2z}+\frac{1}{x^2yz}$ && $377 \colon {}$ & $\left(x,y,\frac{z(y+1)}{y}\right)$ \spacer \\* 
 &&  && $584 \colon {}$ & $\left(x,\frac{xz}{y(x^2z+xz+1)},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
377 && $x+y+z+\frac{z}{y}+\frac{y}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{y}{x^2z}+\frac{1}{x^2z}$ && $78 \colon {}$ & $\left(\frac{(yz+1)(xz+1)}{xyz},\frac{y}{x},\frac{y}{(yz+1)(xz+1)}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $315 \colon {}$ & $\left(x,y,\frac{yz}{y+1}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $634 \colon {}$ & $\left(x,\frac{xz}{y(x^2z+xz+1)},\frac{1}{xy(x^2z+xz+1)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 379 && $x+y+z+\frac{z}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{1}{xyz}+\frac{z}{x^2y}+\frac{1}{x^2y}$ && $207 \colon {}$ & $\left(\frac{xy+z+1}{y},\frac{xy^2}{xy+z+1},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
584 && $x+y+z+\frac{y}{x}+\frac{y}{xz}+\frac{2}{x}+\frac{1}{xy}+\frac{2y}{x^2z}+\frac{2}{x^2z}+\frac{y}{x^3z^2}$ && $315 \colon {}$ & $\left(x,\frac{xz}{y(x^2z+xz+1)},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 634 && $xyz+x+yz+y+z+\frac{2y}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{y}{x^2z}+\frac{1}{x^2z}$ && $377 \colon {}$ & $\left(x,\frac{1}{xy+xz+y},\frac{y}{x^2z}\right)$ \spacer \\* 
 &&  && $995 \colon {}$ & $\left(x,y,\frac{1}{x^2z(xy+y+1)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
995 && $xy^2z+xyz+x+y^2z+2yz+y+z+\frac{2y}{x}+\frac{2}{x}+\frac{1}{xy}+\frac{1}{x^2z}$ && $634 \colon {}$ & $\left(x,y,\frac{1}{x^2z(xy+y+1)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \end{longtable}
\end{center}
