Thanks to Bartek's answer I realized the results are still applicable, but I'd need to compute the p-values myself for different significance levels. I'll just hard-code these for my usage.
Here are my results. If anyone notices an error in them please point them out.
For $d.f.=4095$:
\begin{array}{|c|c|} \hline \texttt{Significant} & X^2 \\\ \hline .99 & 3887.41 \\\ \hline .95 & 3947.29 \\\ \hline .90 & 3979.46 \\\ \hline .75 & 4033.60 \\\ \hline .50 & 4094.33 \\\ \hline .25 & 4155.67 \\\ \hline .10 & 4211.40 \\\ \hline .05 & 4244.99 \\\ \hline .025 & 4274.26 \\\ \hline .01 & 4308.47 \\\ \hline \end{array}