  We report the discovery of 854 ultra diffuse galaxies (UDGs) in the Coma
cluster using deep R band images, with partial B, i, and Halpha band coverage,
obtained with the Subaru telescope. Many of them (332) are Milky Way-sized with
very large effective radii of r_e>1.5kpc. This study was motivated by the
recent discovery of 47 UDGs by van-Dokkum et al. (2015); our discovery suggests
>1,000 UDGs after accounting for the smaller Subaru field. The new UDGs show a
distribution concentrated around the cluster center, strongly suggesting that
the great majority are (likely longtime) cluster members. They are a passively
evolving population, lying along the red sequence in the CM diagram with no
Halpha signature. Star formation was, therefore, quenched in the past. They
have exponential light profiles, effective radii re ~ 800 pc- 5 kpc, effective
surface brightnesses mu_e(R)=25-28 mag arcsec-2, and stellar masses ~1x10^7 -
5x10^8Msun. There is also a population of nucleated UDGs. Some MW-sized UDGs
appear closer to the cluster center than previously reported; their survival in
the strong tidal field, despite their large sizes, possibly indicates a large
dark matter fraction protecting the diffuse stellar component. The indicated
baryon fraction ~<1% is less than the cosmic average, and thus the gas must
have been removed from the possibly massive dark halo. The UDG population
appears to be elevated in the Coma cluster compared to the field, indicating
that the gas removal mechanism is related primarily to the cluster environment.
