  We report on quasi-simultaneous observations from radio to X-ray frequencies
of the neutron star X-ray binary Aql X-1 over accretion state transitions
during its 2016 outburst. All the observations show radio to millimetre spectra
consistent with emission from a jet, with a spectral break from optically thick
to optically thin synchrotron emission that decreases from ~100 GHz to <5.5 GHz
during the transition from a hard to a soft accretion state. The 5.5 GHz radio
flux density as the source reaches the soft state, 0.82$\pm$0.03 mJy, is the
highest recorded to date for this source. During the decay of the outburst, the
jet spectral break is detected again at a frequency of ~30-100 GHz. The flux
density is 0.75$\pm$0.03 mJy at 97.5 GHz at this stage. This is the first time
that a change in the frequency of the jet break of a neutron star X-ray binary
has been measured, indicating that the processes at play in black holes are
also present in neutron stars, thus supporting the idea that the internal
properties of the jet rely most critically on the conditions of the accretion
disc and corona around the compact object, rather than the black hole mass or
spin or the neutron star surface or magnetic field.
