\begin{center}
\footnotesize
\setlength{\mylength}{\baselineskip}
\begin{longtable}{rp{0ex}p{9cm}p{0ex}RL}
\caption{Laurent polynomials and selected mutations for bucket 71.}\\

\toprule \multicolumn{1}{c}{{Node}}&& \multicolumn{1}{c}{{Laurent polynomial}} && \multicolumn{2}{c}{{Mutations from Figure~\ref{fig:71a}}} \\ \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:71a}}} \\ \midrule \endhead

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

\bottomrule \endlastfoot

117 && $x+\frac{x}{y}+y+z+\frac{3}{x}+\frac{2}{xz}+\frac{3}{x^2z}+\frac{1}{x^3z^2}$ && $563 \colon {}$ & $\left(\frac{(x+y)^2}{x^2y},z,\frac{x^3}{(x+y)^2}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
334 && $x+\frac{x}{z}+y+\frac{y}{z}+z+\frac{1}{y}+\frac{2y}{x}+\frac{2}{x}+\frac{y}{x^2}$ && $563 \colon {}$ & $\left(\frac{x+y}{xy},\frac{x+y}{x^2},z\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $1290 \colon {}$ & $\left(y,\frac{xy^2}{xy^2z+(y+1)^2},\frac{x^2y^2z}{xy^2z+(y+1)^2}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 563 && $x+y+z+\frac{1}{y}+\frac{1}{yz}+\frac{2y}{x}+\frac{2}{x}+\frac{2}{xz}+\frac{y}{x^2}+\frac{y}{x^2z}$ && $117 \colon {}$ & $\left(\frac{(xz+1)^2}{x^2z},\frac{(xz+1)^2}{x^3z^2},y\right)$ \spacer \\* 
 &&  && $334 \colon {}$ & $\left(\frac{x+y}{xy},\frac{x+y}{x^2},z\right)$ \spacer \\* 
 &&  && $617 \colon {}$ & $\left(x,y,\frac{z(x+y)}{x}\right)$ \spacer \\* 
 &&  && $812 \colon {}$ & $\left(\frac{(y+1)(xz+1)^2}{x^2yz},\frac{(y+1)(xz+1)^2}{x^3yz^2},y\right)$ \spacer \\* 
 &&  && $889 \colon {}$ & $\left(\frac{xy^2z+(y+z)^2}{xyz},\frac{xy^2z+(y+z)^2}{xy^2},\frac{x^2y^2z}{xy^2z+(y+z)^2}\right)$ \spacer \\* 
 &&  && $1239 \colon {}$ & $\left(x,\frac{x^2z}{y(1+z(x+1)^2)},z\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
617 && $x+y+z+\frac{1}{y}+\frac{1}{yz}+\frac{yz}{x}+\frac{2y}{x}+\frac{2}{x}+\frac{1}{xz}+\frac{y}{x^2}$ && $563 \colon {}$ & $\left(x,y,\frac{xz}{x+y}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 812 && $x+y+z+\frac{z}{y}+\frac{3}{x}+\frac{2}{xz}+\frac{3}{xy}+\frac{3}{x^2z}+\frac{3}{x^2yz}+\frac{1}{x^3z^2}+\frac{1}{x^3yz^2}$ && $563 \colon {}$ & $\left(\frac{(z+1)(x+y)^2}{x^2yz},z,\frac{x^3z}{(z+1)(x+y)^2}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
889 && $x+y+z+\frac{2z}{y}+\frac{y}{xz}+\frac{3}{x}+\frac{1}{xz}+\frac{3z}{xy}+\frac{2}{xy}+\frac{z^2}{xy^2}+\frac{z}{xy^2}$ && $563 \colon {}$ & $\left(\frac{x^2yz+(x+y)^2}{x^2y},\frac{x^3yz}{x^2yz+(x+y)^2},\frac{x^2y^2z}{x^2yz+(x+y)^2}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 1239 && $x+y+\frac{y}{z}+z+\frac{1}{y}+\frac{2y}{x}+\frac{2y}{xz}+\frac{2}{x}+\frac{2}{xz}+\frac{y}{x^2}+\frac{2y}{x^2z}+\frac{y}{x^2z^2}$ && $563 \colon {}$ & $\left(x,\frac{x^2z}{y(1+z(x+1)^2)},z\right)$ \spacer \\* 
 &&  && $2192 \colon {}$ & $\left(x,\frac{xyz+1}{xy^2z},\frac{xyz+1}{xy}\right)$ \spacer \\* 
 &&  && $2860 \colon {}$ & $\left(y,\frac{(xyz+1)^2}{x^3y^2z^2},\frac{(xyz+1)^2}{x^2y^2z}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
1290 && $x+y+z+\frac{2}{y}+\frac{y}{x}+\frac{1}{x}+\frac{1}{xz}+\frac{2}{xy}+\frac{1}{xy^2}+\frac{y}{x^2z}+\frac{2}{x^2z}+\frac{1}{x^2yz}$ && $334 \colon {}$ & $\left(\frac{x^2z+y(x+1)^2}{x^2},x,\frac{x^2z}{y(x^2z+y(x+1)^2)}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 1388 && $x+y+z+\frac{1}{y}+\frac{1}{yz}+\frac{2}{x}+\frac{1}{xz}+\frac{z}{xy}+\frac{3}{xy}+\frac{2}{xyz}+\frac{1}{x^2y}+\frac{1}{x^2yz}$ && $2192 \colon {}$ & $\left(x,y,\frac{xy+(x+1)^2}{x^2yz}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \rowcolor[gray]{0.95}
2192 && $x+y+z+\frac{1}{y}+\frac{1}{yz}+\frac{2}{x}+\frac{1}{xz}+\frac{3}{xy}+\frac{2}{xyz}+\frac{1}{xy^2z}+\frac{1}{x^2y}+\frac{2}{x^2yz}+\frac{2}{x^2y^2z}+\frac{1}{x^3y^2z}$ && $1239 \colon {}$ & $\left(x,\frac{xz+y}{xyz},\frac{xz^2}{xz+y}\right)$ \spacer \\* \rowcolor[gray]{0.95}
 &&  && $1388 \colon {}$ & $\left(x,y,\frac{xy+(x+1)^2}{x^2yz}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 2860 && $x+y+z+\frac{2}{y}+\frac{1}{x}+\frac{1}{xz}+\frac{4}{xy}+\frac{2}{xyz}+\frac{1}{xy^2}+\frac{2}{xy^2z}+\frac{2}{x^2yz}+\frac{5}{x^2y^2z}+\frac{2}{x^2y^3z}+\frac{1}{x^3y^2z^2}+\frac{2}{x^3y^3z^2}+\frac{1}{x^3y^4z^2}$ && $1239 \colon {}$ & $\left(\frac{(xz+y)^2}{x^2yz^2},x,\frac{x^2z^3}{(xz+y)^2}\right)$ \bottomspacer \\ \addlinespace[1.1ex]
 \end{longtable}
\end{center}
