  As part of our ongoing Deep Ecliptic Survey (DES) of the Kuiper belt, we
report on the occupation of the 1:1 (Trojan), 4:3, 3:2, 7:4, 2:1, and 5:2
Neptunian mean-motion resonances (MMRs). The occupation of the 1:1 and 5:2 MMRs
is not easily understood within the standard model of resonance sweeping by a
migratory Neptune over an initially dynamically cold belt. Our dynamically hot,
5:2 resonant objects can librate with modest amplitudes of 90 deg within the
resonance for at least 1 Gyr. Their trajectories cannot be explained by close
encounters with Neptune alone, given the latter's current orbit. The hot orbits
of such 5:2 resonant KBOs, unlike hot orbits of previously known resonant KBOs,
may imply that these objects were pre-heated to large inclination and large
eccentricity prior to resonance capture by a migratory Neptune. Our first
discovered Neptunian Trojan, 2001QR322, may not owe its existence to Neptune's
migration at all. The trajectory of 2001QR322 is remarkably stable; the object
can undergo tadpole-type libration about Neptune's leading Lagrange (L4) point
for at least 1 Gyr with a libration amplitude of 24 deg. Trojan capture
probably occurred while Neptune accreted the bulk of its mass. For an assumed
albedo of 12--4%, our Trojan is 130--230 km in diameter. Model-dependent
estimates place the total number of Neptune Trojans resembling 2001QR322 at
20--60. Their existence might rule out violent orbital histories for Neptune.
