  The R\'enyi (Shannon) entropy, i.e. $Re_{\alpha}(Sh)$, of the ground state of
quantum systems in local bases normally show a volume-law behavior. For a
subsystem of quantum chains at critical point there is an extra logarithmic
subleading term with a coefficient which is universal. In this paper we study
this coefficient for generic time-reversal translational invariant quadratic
critical free fermions. These models can be parameterized by a complex function
which has zeros on the unit circle. When the zeros on the unit circle do not
have degeneracy and there is no zero outside of the unit circle we are able to
classify the coefficient of the logarithm. In particular, we numerically
calculate the R\'enyi (Shannon) entropy in configuration basis for wide variety
of these models and show that there are two distinct classes. For systems with
$U(1)$ symmetry the coefficient is proportional to the central charge, i.e. one
half of the number of points that one can linearize the dispersion relation of
the system; for all the values of $\alpha$ with transition point at $\alpha=4$.
For systems without this symmetry, when $\alpha>1$ this coefficient is again
proportional to the central charge. However, the coefficient for $\alpha\leq 1$
is a new universal number. Finally, by using the discrete version of
Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these
coefficients are universal and dependent on the underlying CFT.
