The H$\alpha$ Dots Survey. IV. A Fourth List of Faint Emission-Line
  Objects
  We present the fourth catalog of serendipitously discovered compact
extragalactic emission-line sources -- H$\alpha$ Dots. A total of 454 newly
discovered objects are included in the current survey list. These objects have
been detected in searches of moderately deep narrow-band images acquired for
the ALFALFA H$\alpha$ project (Van Sistine et al. 2016). The catalog of H-alpha
Dots presented in the current paper was derived from searches carried out using
ALFALFA H$\alpha$ images obtained with the KPNO 2.1 m telescope. This results
in a substantially deeper sample of Dots compared to our previous lists, which
were all discovered in images taken with the WIYN 0.9 m telescope. The median
R-band magnitude of the current catalog is 21.59, more than 1.6 magnitudes
fainter than the median for the 0.9~m sample (factor of 4.4x fainter).
Likewise, the median emission-line flux of the detected sources is a factor of
4.3x fainter. The line-flux completeness limit of the current sample is
approximately 3 x 10$^{-16}$ erg/s/cm$^2$. We present accurate coordinates,
apparent magnitudes and narrow-band line fluxes for each object in the sample.
Unlike our previous lists of H$\alpha$ Dots, the current sample does not
include follow-up spectroscopy.
