FastDF (Fast Distribution Function) integrates relativistic particles along geodesics in a comoving periodic volume with forces determined by cosmological linear perturbation theory. Its main application is to set up accurate particle realizations of the linear phase-space distribution of massive relic neutrinos by starting with an analytical solution deep in radiation domination. Such particle realizations are useful for Monte Carlo experiments and provide consistent initial conditions for cosmological N-body simulations. Gravitational forces are calculated from three-dimensional potential grids, which are obtained by convolving random phases with linear transfer functions using Fast Fourier Transforms. The equations of motion are solved using a symplectic leapfrog integration scheme to conserve phase-space density and prevent the build-up of errors. Particles can be exported in different gauges and snapshots are provided in the HDF5 format, compatible with N-body codes like SWIFT (ascl:1805.020) and Gadget-4 (ascl:2204.014). The code has an interface with CLASS (ascl:1106.020) for calculating transfer functions and with monofonIC (ascl:2008.024) for setting up initial conditions with dark matter, baryons, and neutrinos.