This dataset supports a paper in preparation for the AGU journal "Radio Science", provisionally entitled "Efficient storage of embedded element patterns for low frequency radio telescopes", by DB Davidson and AT Sutinjo, Curtin University, Perth, Western Australia. The main script is SphModes_demo.m, which calls other MATLAB functions and scripts as needed. It imports the spherical modes from the appropriate .sph file and computes the far fields from this. (The .sph files are industry-standard .sph files, exported from FEKO.) Verification data is included to check correct operation of the script; for some examples, plots are generated. Documentation is contained in the header of this script. This script runs in MATLAB R2024a, but should also run in earlier releases.