  We implement a search for exoplanets in campaigns zero through eight (C0-8)
of the K2 extension of the Kepler spacecraft. We apply a modified version of
the QATS planet search algorithm to K2 light curves produced by the EVEREST
pipeline, carrying out the C0-8 search on $1.5 \times 10^5$ target stars with
magnitudes in the range of Kp = 9-15. We detect 818 transiting planet
candidates, of which 374 were undiscovered by prior searches, with
{64,15,5,2,1} in {2,3,4,5,6}-planet multi-planet candidate systems,
respectively. Of the new planets detected, 100 orbit M dwarfs, including one
which is potentially rocky and in the habitable zone. 154 of our candidates
reciprocally transit with our Solar System: they are geometrically aligned to
see at least one Solar System planet transit. We find candidates which display
transit timing variations and dozens of candidates on both period extremes with
single transits or ultra-short periods. We point to evidence that our
candidates display similar patterns in frequency and size-period relation as
confirmed planets, such as tentative evidence for the radius gap. Confirmation
of these planet candidates with follow-up studies will increase the number of
K2 planets by up to 50%, and characterization of their host stars will improve
statistical studies of planet properties. Our sample includes many planets
orbiting bright stars amenable for radial velocity follow-up and future
characterization with JWST. We also list the 579 eclipsing binary systems
detected as part of this search.
