The numerical approximation of Helmholtz solutions using propagative plane waves, namely $\mathbf{x} \mapsto e^{i\kappa \mathbf{d} \cdot \mathbf{x}} $ with real-valued $\mathbf{d} $ and for a wavenumber $ \kappa > 0$, is known to be unstable despite provably good error estimates. This instability arises from the presence of exponentially large coefficients in discrete representations, which are sensitive to finite precision arithmetic. The use of evanescent plane waves, namely $ \mathbf{x} \mapsto e^{i\kappa \mathbf{d} \cdot \mathbf{x}} $ with complex-valued $ \mathbf{d} $, addresses this issue by ensuring stability through bounded coefficients and enabling accurate numerical computations.

Building on this, we develop a Trefftz Continuous Galerkin method, with basis functions formed by simple linear combinations of evanescent plane waves. This approach retains the conforming property of classical finite element methods while achieving the spectral accuracy typical of Trefftz formulations, ensuring stability even in high-resolution Trefftz spaces.