  In complex vector spaces maximal sets of equiangular lines, known as SICs,
are related to real quadratic number fields in a dimension dependent way. If
the dimension is of the form $n^2+3$ the base field has a fundamental unit of
negative norm, and there exists a SIC with anti-unitary symmetry. We give eight
examples of exact solutions of this kind, for which we have endeavoured to make
them as simple as we can---as a belated reply to the referee of an earlier
publication, who claimed that our exact solution in dimension 28 was too
complicated to be fit to print. An interesting feature of the simplified
solutions is that the components of the fiducial vectors largely consist of
algebraic units.
