  The minor planets on orbits that are dynamically stable in Neptune's 1:1
resonance on Gyr timescales were likely emplaced by Neptune's outward
migration. We explore the intrinsic libration amplitude, eccentricity, and
inclination distribution of Neptune's stable Trojans, using the detections and
survey efficiency of the Outer Solar System Origins Survey (OSSOS) and
Pan-STARRS1. We find that the libration amplitude of the stable Neptunian
Trojan population can be well modeled as a Rayleigh distribution with a
libration amplitude width $\sigma_{A_phi}$ of 15$^\circ$. When taken as a
whole, the Neptune Trojan population can be acceptably modeled with a Rayleigh
eccentricity distribution of width $\sigma_e$ of 0.045 and a typical sin(i) x
Gaussian inclination distribution with a width $\sigma_i$ of 14 +/- 2 degrees.
However, these distributions are only marginally acceptable. This is likely
because, even after accounting for survey detection biases, the known large Hr
< 8 and small Hr >= 8 Neptune Trojans appear to have markedly different
eccentricities and inclinations. We propose that like the classical Kuiper
belt, the stable intrinsic Neptunian Trojan population have dynamically `hot'
and dynamically `cold' components to its eccentricity/inclination distribution,
with $\sigma_{e-cold}$ ~ 0.02 / $\sigma_{i-cold}$ ~ 6$^\circ$ and
$\sigma_{e-hot}$~ 0.05 / $\sigma_{i-hot}$ ~ 18$^\circ$. In this scenario, the
`cold' L4 Neptunian Trojan population lacks the Hr >= 8 members and has 13
+11/-6 `cold' Trojans with Hr < 8. On the other hand, the `hot' L4 Neptunian
Trojan population has 136 +57/-48 Trojans with Hr < 10 -- a population 2.4
times greater than that of the L4 Jovian Trojans in the same luminosity range.
