  We present examples of Legendrian knots in $\mathbb{R}^3$ that have
linearized Legendrian contact homology over $\mathbb{Z}$ containing torsion. As
a consequence, we show that there exist augmentations of Legendrian knots over
$\mathbb{Z}$ that are not induced by exact Lagrangian fillings, even though
their mod $2$ reductions are.
