information:filtering
Examples m = 2, 4, 8, 16

The only character mod 2 is the principal character χ 2, 1 {\displaystyle \chi _{2,1}}.

−1 is a primitive root mod 4 (ϕ (4) = 2 {\displaystyle \phi (4)=2})

The nonzero values of the characters mod 4 are

−1 is and 5 generate the units mod 8 (ϕ (8) = 4 {\displaystyle \phi (8)=4})

The nonzero values of the characters mod 8 are

−1 and 5 generate the units mod 16 (ϕ (16) = 8 {\displaystyle \phi (16)=8})

The nonzero values of the characters mod 16 are