When the character in a point group table is listed as 1 or -1, I understand how an object/orbital etc. transforms to give either itself or the negative of itself.
When the character in a point group table is 2 or -2, what does this mean in terms of transformation? To understand this would be very helpful in terms of assigning the correct irreducible representations to atomic orbitals/LGOs to then determine which pairs mix.
Similarly, I do not understand how to interpret a character of sin or cos of an angle, nor a character of 0.
I am hoping there is a conceptual/visual way of explaining this as I am not up to speed on the matrix math, and the class that this is relevant too does not include that math either.