In this document we offer a table with all the information we extracted from the different considered models for walks in the quarter plane. You can check the papers by Bousquet-Melou and Mishna and by Dreyfus et. al for getting a precise definition of the objects used here.
The models are named using the convention and definitions presented in the previous papers. Namely, we have:

• Names with the preffix "FG-BMM": these models are the walk models with finite group and are ordered following the tables in Section 8 of the paper by Bousquet-Melou and Mishna. The numbers "X.Y" after the preffix indicates the table (X) and the index in such table (Y) that represents the model. To have an appropriate alphabetic ordering, in the table 1 we use two digits to index each model. In this way FG-BMM-1.01 would be the first model (N, E, S, W) of the first table from that paper and FG-BMM-2.4 would be the fourth model (reverse Kreweras model) of the second table from that paper.
• Names with the preffix "NE-DHRS": these models are the walks which kernel function defines a singular curve. These curves have genus zero and are rational curves. They can be all found in the paper by Dreyfus et. al.
• The other names are taken from the other paper by Dreyfus et. al that studies the cases where the kernel function described a non-singular (i.e., elliptic) curve. See Figure 1 in that paper to see each model.

These results have been obtained using the code available in our GitLab repository and the documentation can be found here.