TITLE: Non-real constants
QUESTION [6 upvotes]: Constants are usually real numbers e.g. e, pi, gamma etc. Can you give examples of special constants that are not real? e.g. complex or p-adic constants. 
A real number in base10 can be viewed as the coefficients of a power series evaluated at x=1/10, so I suppose a constant in another context such as a complete ring could just be some value of a function evaluated at some point. Can you give examples of such a value that could be considered as a special mathematical constant.
More generally a whole object such as a set or group could be thought of as a constant if it appeared in many formulae relating such objects.

REPLY [3 votes]: Since all the known non-trivial zeroes of Riemann Zeta function are on the Re(z)=1/2 line we only give their imaginary parts, but in fact their are complex,
$$1/2+ i*14.1347251417346937904572519835624702707842571156992431756855674601499...$$
being the first above the real line.  If Riemann Hypothesis is true we will never have to mention a different real part.

REPLY [3 votes]: Since we do not want to restrict ourselves to values in traditional number systems...

Each remarquable/exceptional finite algebraic structure, graph, can be described/encoded as a specific value in a numbering system.  For instance as a series of generating matrices, multiplication table, representation tables, etc.
We can consider each sporadic group as a remarquable constant. To me the Monster Group is a mathematical attraction point that can be compared to $\pi$ or $e$.  And it is well hidden in the armies of soluble groups around it.