These are the outputs of two character tables from Magma. The first is for $A_5$. The second is for $GL_3(2)$. What is the significance of the '$+$' and '$0$' symbols? I can produce more tables if it would be helpful in determining what these symbols mean. $Z1$ in both cases is a polynomial expression evaluated at a root of unity, $\omega$, and $\#k$ means to replace $\omega$ with $\omega^k$ in this expression.
The $+,0$ (and also sometimes $-$) symbols are the same as in the character tables printed in the Atlas of Finite Groups.
It is called the Frobenius-Schur Indicator, and it is defined by
${\rm ind} \chi = \frac{1}{|G|} \sum_{g \in G} \chi(g^2).$
It actually takes the value $0,1$ or $-1$, and these are represented by $0.+,-$
It is equal to $0$ if $\chi$ takes non-real values, $1$ if the representation can be written over ${\mathbb R}$, and $-1$ if $\chi$ is real but the representation is not. For example $Q_8$ has a character with indicator $-1$.