  Plutonium (Pu), in which the 5$f$ valence electrons always wander the
boundary between localized and itinerant states, exhibits quite complex crystal
structures and unprecedentedly anomalous properties with respect to temperature
and alloying. Understanding its chemical and physical properties, especially
its 5$f$ electronic structure is one of the central and unsolved topics in
condensed matter theory. In the present work, the electronic structures of the
six allotropes of Pu (including its $\alpha$, $\beta$, $\gamma$, $\delta$,
$\delta'$, and $\epsilon$ phases) at ambient pressure are studied
comprehensively by means of the density functional theory in combination with
the single-site dynamical mean-field theory. The band structures, total and
partial density of states, valence state histograms, 5$f$ orbital occupancies,
X-ray branching ratios, and self-energy functions are carefully studied. It is
suggested that the $\alpha$, $\beta$, and $\gamma$ phases of Pu are typical
Racah metals in which the atomic multiple effect dominates near the Fermi
level. The calculated results reveal that not only the $\delta$ phase, but also
all the six allotropes are archetypal mixed-valence metals with remarkable
atomic eigenstate fluctuation. In consequence of that, the 5$f$ occupancy
$n_{5f}$ is around 5.1 $\sim$ 5.4, which varies with respect to the atomic
volume and electronic correlation strength of Pu. The 5$f$ electronic
correlation in Pu is moderately orbital-dependent. Moreover, the 5$f$ electrons
in the $\delta'$ phase are the most correlated and localized.
