  We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC)
simulations of the harmonically perturbed uniform electron gas (UEG) for
different densities and temperatures. This allows us to study the linear
response of the UEG with respect to different contributions to the total energy
for different wave numbers. We find that the induced change in the interaction
energy exhibits a non-monotonic behaviour, and becomes negative for
intermediate wave numbers. This effect is strongly dependent on the coupling
strength and can be traced back to the spatial alignment of electrons
introduced in earlier works [T.~Dornheim \emph{et al.}, Communications Physics
\textbf{5}, 304 (2022)]. The observed quadratic dependence on the perturbation
amplitude in the limit of weak perturbations and the quartic dependence of the
perturbation amplitude corrections are consistent with linear and non-linear
versions of the density stifness theorem. All PIMC simulation results are
freely available online and can be used to benchmark new methods, or as input
for other calculations.
