  For a projective hyperplane arrangement, we study sufficient conditions in
terms of combinatorial data for ESV-calculability of the monodromy eigenspaces
of the first Milnor fiber cohomology for eigenvalues of order $m>1$. This can
be reduced to the line arrangement case by Artin's theorem. These sufficient
conditions are often unsatisfied if efficiency or complexity of the
combinatorics of arrangement is high. In order to measure these, we introduce
the notions of $m$-efficiency and $m$-complexity for $m\ge 3$. The former is
defined to be the number of points with multiplicity divisible by $m$ lying on
one line in average. In many cases, one of the above sufficient conditions is
satisfied if it is at most 2, although there are certain exceptional cases,
especially when $m=3$. The $m$-complexity is defined to be the maximal number
of edges containing one vertex of the associated $m$-graph. We can show that
one of the sufficient condition holds if it is at most $(m+1)/2$.
