  We derive analytic expressions that provide Fourier domain gravitational wave
(GW) response function for compact binaries inspiraling along moderately
eccentric orbits. These expressions include amplitude corrections to the two GW
polarization states that are accurate to the first post-Newtonian (PN) order.
Additionally, our fully 3PN accurate GW phase evolution incorporates
eccentricity effects up to sixth order at each PN order. Further, we develop a
prescription to incorporate analytically the effects of 3PN accurate periastron
advance in the GW phase evolution. This is how we provide a ready-to-use and
efficient inspiral template family for compact binaries in moderately eccentric
orbits. Preliminary GW data analysis explorations suggest that our template
family should be required to construct analytic inspiral-merger-ringdown
templates to model moderately eccentric compact binary coalescence.
