  This note explores the use of Newton polytopes in the study of Lagrangian
fillings of Legendrian submanifolds. In particular, we show that Newton
polytopes associated to augmented values of Reeb chords can distinguish
infinitely many distinct Lagrangian fillings, both for Legendrian links and
higher-dimensional Legendrian spheres. The computations we perform work in
finite characteristic, which significantly simplifies arguments and also allows
us to show that there exist Legendrian links with infinitely many
non-orientable exact Lagrangian fillings.
