  How magnetic fields contribute to the differentiation of the rotation rates
of the Ap stars and affect the occurrence of non-radial pulsation in some of
them are important open questions. Valuable insight can be gained into these
questions by studying some of the most extreme examples of the processes at
play. The super-slowly rotating rapidly oscillating Ap (roAp) star HD 166473 is
such an example. We performed the first accurate determination of its rotation
period, (3836 +/- 30)d, from the analysis of 56 measurements of the mean
magnetic field modulus <B> based on high-resolution spectra acquired between
1992 and 2019 at various observatories and with various instrumental
configurations. We complemented this analysis with the consideration of an
inhomogeneous set of 21 determinations of the mean longitudinal magnetic field
<B_z> spanning the same time interval. This makes HD 166473 one of only four Ap
stars with a period longer than 10 years for which magnetic field measurements
have been obtained over more than a full cycle. The variation curves of <B> and
of <B_z> are well approximated by cosine waves. The magnetic field of HD 166473
only seems to deviate slightly from axisymmetry, but it definitely involves a
considerable non-dipolar component. Among the stars with rotation periods
longer than 1000 d for which magnetic field measurements with full phase
coverage are available, HD 166473 has the strongest field. Its magnetic field
is also one of the strongest known among roAp stars. Overall, the magnetic
properties of HD 166473 do not seem fundamentally distinct from those of the
faster-rotating Ap stars. However, considering as a group the eight Ap stars
that have accuractely determined periods longer than 1000 d and whose magnetic
variations have been characterised over a full cycle suggests that the angles
between their magnetic and rotation axes tend to be systematically large.
