Excited electrons in the conduction band of germanium collect into four energy minima, or valleys, in momentum space. These local minima have highly anisotropic mass tensors which cause the electrons to travel in directions which are oblique to an applied electric field at sub-Kelvin temperatures and low electric fields, in contrast to the more isotropic behavior of the holes. This experiment produces a full two-dimensional image of the oblique electron and hole propagation and the quantum transitions of electrons between valleys for electric fields oriented along the [0,0,1] direction. Charge carriers are excited with a focused laser pulse on one face of a germanium crystal and then drifted through the crystal by a uniform electric field of strength between 0.5 and 6 V/cm. The pattern of charge density arriving on the opposite face is used to reconstruct the trajectories of the carriers. Measurements of the two-dimensional pattern of charge density are compared in detail with Monte Carlo simulations developed for the Cryogenic Dark Matter Search (SuperCDMS) to model the transport of charge carriers in high-purity germanium detectors.