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We build two families of inspiral waveforms for precessing binaries oneccentric orbits in the Fourier domain. To achieve this, we use a smalleccentricity expansion of the waveform amplitudes in order to separate theperiastron precession timescale from the orbital timescale, and use a shifteduniform asymptotics transformation to compute the Fourier transform in thepresence of spin-induced precession. We show that the resulting waveforms canyield a median faithfulness above 0.993 when compared to an equivalent timedomain waveform with an initial eccentricity of $e_0 \approx 0.3$. We also showthat when the spins are large, using a circular waveform can potentially leadto significant biases in the recovery of the parameters, even when the systemhas fully circularized, particularly when the accumulated number of cycles islarge. This is an effect of the residual eccentricity present when the objectsforming the binary have nonvanishing spin components in the orbital plane.

Fourier domain gravitational waveforms for precessing eccentric binaries