Complex Langevin as an approach to finite density lattice QCD has been known for a long time, but has seen a resurgence due to advances in theory, computational power and numerical methods. Here, we explore the application of this method to the analysis of Bose Einstein condensates. While they are typically well described by semiclassical Bogoliubov theory, in situations not well described by mean field theory, or when doing precision measurements, higher order corrections should be taken into account. We calculate the nonuniversal shift of the polar to easy plane transition in the spin-1 Bose gas due to quantum corrections. Additionally, we extract entanglement measures at the critical point using field theoretical methods. To this end, we adapt methods known from Hamiltonian Monte Carlo to complex Langevin, specifically Fourier acceleration, histogram reweighting and the replica trick. We demonstrate their applicability and show that they greatly enhance the effectiveness of complex Langevin for the task at hand.