[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that for the cyclic group [math]\mathbb Z_N\subset O_N[/math] we have

[[math]] law(\chi)=\left(1-\frac{1}{N}\right)\delta_0+\frac{1}{N}\delta_N [[/math]]

and look as well at truncated characters.