  The article delivers the only still unknown coefficient in the 4th
post-Newtonian energy expression for binary point masses on circular orbits as
function of orbital angular frequency. Apart from a single coefficient, which
is known solely numerically, all the coefficients are given as exact numbers.
The shown Hamiltonian is presented in the center-of-mass frame and out of its
57 coefficients 51 are given fully explicitly. Those coefficients are six
coefficients more than previously achieved [Jaranowski/Sch\"afer, Phys. Rev. D
86, 061503(R) (2012)]. The local divergences in the point-mass model are
uniquely controlled by the method of dimensional regularization. As
application, the last stable circular orbit is determined as function of the
symmetric-mass-ratio parameter.
