I know that the functional equation for the Zeta function has a symmetrical property such that f(s)=f(1-s), but I was curious as to whether or not this applies to the more simplistic version of the equation where it is basically:

sigma[1/(n^(a+bi))], n=1, n=infinity.

Basically, does anyone know if:

sigma[1/(n^(1/2+R+bi))]=sigma[1/(n^(1/2-R+bi))]

Would be true for a zero off the line, should one occur.