  We report results of the first search to date for continuous gravitational
waves from unstable r-modes from the pulsar J0537-6910. We use data from the
first two observing runs of the Advanced LIGO network. We find no significant
signal candidate and set upper limits on the amplitude of gravitational wave
signals, which are within an order of magnitude of the spin-down values. We
highlight the importance of having timing information at the time of the
gravitational wave observations, i.e. rotation frequency and
frequency-derivative values, and glitch occurrence times, such as those that a
NICER campaign could provide.
