  We build two families of inspiral waveforms for precessing binaries on
eccentric orbits in the Fourier domain. To achieve this, we use a small
eccentricity expansion of the waveform amplitudes in order to separate the
periastron precession timescale from the orbital timescale, and use a shifted
uniform asymptotics transformation to compute the Fourier transform in the
presence of spin-induced precession. We show that the resulting waveforms can
yield a median faithfulness above 0.993 when compared to an equivalent time
domain waveform with an initial eccentricity of $e_0 \approx 0.3$. We also show
that when the spins are large, using a circular waveform can potentially lead
to significant biases in the recovery of the parameters, even when the system
has fully circularized, particularly when the accumulated number of cycles is
large. This is an effect of the residual eccentricity present when the objects
forming the binary have nonvanishing spin components in the orbital plane.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics