  We studied complex spectra of a two-level electron system coupled to two
phonon (vibron) modes represented by the E$\otimes$e Jahn-Teller model. For
particular rotation quantum numbers we found a coexistence of up to three
regions of the spectra, (i) the dimerized region of long-range ordered
(extended) pairs of oscillating levels, (ii) the short-range-ordered
(localized) "kink lattice" of avoiding levels, and (iii) the intermediate
region of kink nucleation with variable range of ordering. This structure
appears above a certain critical line as a function of interaction strength.
The level clustering and level avoiding generic patterns reflect themselves in
several intermittent regions between up to three branches of spectral
entropies. Linear scaling behavior of the widths of level curvature probability
distributions provides the conventionally adopted indication for the presence
of quantum chaos. Level spacing probability distributions show peculiarities of
the partial (for fixed quantum angular momentum) as well as of the cumulative
(all angular momenta) case. The clustering of levels with two and three
dominant spacings at fixed angular momenta causes notable deviations of the
cumulative distributions from the Poissonian one.
