We analyse the performance of a gas time projection chamber (TPC) as a high-performance gamma-ray telescope and polarimeter in the e$^+$e$^-$ pair creation regime. We use data collected at a gamma-ray beam of known polarisation. The TPC provides two orthogonal projections $(x,z)$ and $(y,z)$ of the tracks induced by each conversion in the gas volume. We use a simple vertex finder in which vertices and pseudo-tracks exiting from them are identified. We study the various contributions to the single-photon angular resolution using Monte Carlo simulations and compare them with the experimental data and find that they are in excellent agreement. The distribution of the azimutal angle of pair
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