Hatcher and Oertel gave in their paper Boundary slopes of Montesinos knots an algorithm for computing the boundary slopes of a given Montesinos knot. At the end of their paper, they provided a table which gave the boundary slopes for each knot of 10 or fewer crossings which is a Montesinos knot. Unfortunately, this table contains several errors. In the late 1990s, I wrote a new implementation of their algorithm and published a short paper in Topology correcting this table, which you can also find on the arXiv. This program itself had some bugs that were fixed in 2008 with the arXiv version of the paper updated to match in 2010.
The 2020 version of the program, which now works with Python 3.6 or newer, is available here on GitHub. You can get Python from its homepage, but it is already installed on most Linux and macOS computers. To run the program, download the zip file and:
On Linux or macOS, open a terminal, go to the directory where you unpacked the files, and type:
python3 bdry_run.py
and then answer the questions it asks.
On Windows, double-click the file bdry_run.py.
The files two_bridge_bdry.py and montesinos_bdry.py offer a purely command-line version of bdry_run.py.
The old Python 2 version of the code is here if you need it.
Copyright 1998-present by Nathan M. Dunfield. This code is in the public domain.