Evaluating multiple polylogarithm values at sixth roots of unity up to weight six

We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form G(a1,…,aw;1) where the indices ai are equal to zero or a sixth root of unity, with a1≠1. For w≤6, we construct bases of the linear spaces generated by the real and imaginary parts of G(a1,…,aw;1) and obtain a table for expressing them as linear combinations of the elements of the bases.