Template:Character table facts to check against

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FACTS TO CHECK AGAINST FOR CHARACTERS OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD:
Orthogonality relations: Character orthogonality theorem | Column orthogonality theorem | Splitting implies characters span class functions
Separation results (basically says any two rows distinct, any two columns distinct): splitting implies character-separating
Numerical facts: Characters are cyclotomic integers | Size-degree-weighted characters are algebraic integers | Irreducible character of degree greater than one takes value zero on some conjugacy class | Zero-or-scalar lemma