Dirichlet Characters of Orders 1-20

• Imprimitive

• Primitive

The table below displays Dirichlet characters of a given order.

Order	Characters
1	\( \chi_{ 1 }( 1, ·) \)	\( \chi_{ 2 }( 1, ·) \)	\( \chi_{ 3 }( 1, ·) \)	\( \chi_{ 4 }( 1, ·) \)	\( \chi_{ 5 }( 1, ·) \)	\( \chi_{ 6 }( 1, ·) \)	\( \chi_{ 7 }( 1, ·) \)
2	\(\displaystyle\left(\frac{-3}{\bullet}\right)\) (mod 3)	\(\displaystyle\left(\frac{-4}{\bullet}\right)\) (mod 4)	\(\displaystyle\left(\frac{5}{\bullet}\right)\) (mod 5)	\(\displaystyle\left(\frac{-3}{\bullet}\right)\) (mod 6)	\(\displaystyle\left(\frac{-7}{\bullet}\right)\) (mod 7)	\(\displaystyle\left(\frac{-8}{\bullet}\right)\) (mod 8)	\(\displaystyle\left(\frac{8}{\bullet}\right)\) (mod 8)
3	\( \chi_{ 7 }( 2, ·) \)	\( \chi_{ 7 }( 4, ·) \)	\( \chi_{ 9 }( 4, ·) \)	\( \chi_{ 9 }( 7, ·) \)	\( \chi_{ 13 }( 3, ·) \)	\( \chi_{ 13 }( 9, ·) \)	\( \chi_{ 14 }( 9, ·) \)
4	\( \chi_{ 5 }( 2, ·) \)	\( \chi_{ 5 }( 3, ·) \)	\( \chi_{ 10 }( 3, ·) \)	\( \chi_{ 10 }( 7, ·) \)	\( \chi_{ 13 }( 5, ·) \)	\( \chi_{ 13 }( 8, ·) \)	\( \chi_{ 15 }( 2, ·) \)
5	\( \chi_{ 11 }( 3, ·) \)	\( \chi_{ 11 }( 4, ·) \)	\( \chi_{ 11 }( 5, ·) \)	\( \chi_{ 11 }( 9, ·) \)	\( \chi_{ 22 }( 3, ·) \)	\( \chi_{ 22 }( 5, ·) \)	\( \chi_{ 22 }( 9, ·) \)
6	\( \chi_{ 7 }( 3, ·) \)	\( \chi_{ 7 }( 5, ·) \)	\( \chi_{ 9 }( 2, ·) \)	\( \chi_{ 9 }( 5, ·) \)	\( \chi_{ 13 }( 4, ·) \)	\( \chi_{ 13 }( 10, ·) \)	\( \chi_{ 14 }( 3, ·) \)
7	\( \chi_{ 29 }( 7, ·) \)	\( \chi_{ 29 }( 16, ·) \)	\( \chi_{ 29 }( 20, ·) \)	\( \chi_{ 29 }( 23, ·) \)	\( \chi_{ 29 }( 24, ·) \)	\( \chi_{ 29 }( 25, ·) \)	\( \chi_{ 43 }( 4, ·) \)
8	\( \chi_{ 17 }( 2, ·) \)	\( \chi_{ 17 }( 8, ·) \)	\( \chi_{ 17 }( 9, ·) \)	\( \chi_{ 17 }( 15, ·) \)	\( \chi_{ 32 }( 3, ·) \)	\( \chi_{ 32 }( 5, ·) \)	\( \chi_{ 32 }( 11, ·) \)
9	\( \chi_{ 19 }( 4, ·) \)	\( \chi_{ 19 }( 5, ·) \)	\( \chi_{ 19 }( 6, ·) \)	\( \chi_{ 19 }( 9, ·) \)	\( \chi_{ 19 }( 16, ·) \)	\( \chi_{ 19 }( 17, ·) \)	\( \chi_{ 27 }( 4, ·) \)
10	\( \chi_{ 11 }( 2, ·) \)	\( \chi_{ 11 }( 6, ·) \)	\( \chi_{ 11 }( 7, ·) \)	\( \chi_{ 11 }( 8, ·) \)	\( \chi_{ 22 }( 7, ·) \)	\( \chi_{ 22 }( 13, ·) \)	\( \chi_{ 22 }( 17, ·) \)
11	\( \chi_{ 23 }( 2, ·) \)	\( \chi_{ 23 }( 3, ·) \)	\( \chi_{ 23 }( 4, ·) \)	\( \chi_{ 23 }( 6, ·) \)	\( \chi_{ 23 }( 8, ·) \)	\( \chi_{ 23 }( 9, ·) \)	\( \chi_{ 23 }( 12, ·) \)
12	\( \chi_{ 13 }( 2, ·) \)	\( \chi_{ 13 }( 6, ·) \)	\( \chi_{ 13 }( 7, ·) \)	\( \chi_{ 13 }( 11, ·) \)	\( \chi_{ 26 }( 7, ·) \)	\( \chi_{ 26 }( 11, ·) \)	\( \chi_{ 26 }( 15, ·) \)
13	\( \chi_{ 53 }( 10, ·) \)	\( \chi_{ 53 }( 13, ·) \)	\( \chi_{ 53 }( 15, ·) \)	\( \chi_{ 53 }( 16, ·) \)	\( \chi_{ 53 }( 24, ·) \)	\( \chi_{ 53 }( 28, ·) \)	\( \chi_{ 53 }( 36, ·) \)
14	\( \chi_{ 29 }( 4, ·) \)	\( \chi_{ 29 }( 5, ·) \)	\( \chi_{ 29 }( 6, ·) \)	\( \chi_{ 29 }( 9, ·) \)	\( \chi_{ 29 }( 13, ·) \)	\( \chi_{ 29 }( 22, ·) \)	\( \chi_{ 43 }( 2, ·) \)
15	\( \chi_{ 31 }( 7, ·) \)	\( \chi_{ 31 }( 9, ·) \)	\( \chi_{ 31 }( 10, ·) \)	\( \chi_{ 31 }( 14, ·) \)	\( \chi_{ 31 }( 18, ·) \)	\( \chi_{ 31 }( 19, ·) \)	\( \chi_{ 31 }( 20, ·) \)
16	\( \chi_{ 17 }( 3, ·) \)	\( \chi_{ 17 }( 5, ·) \)	\( \chi_{ 17 }( 6, ·) \)	\( \chi_{ 17 }( 7, ·) \)	\( \chi_{ 17 }( 10, ·) \)	\( \chi_{ 17 }( 11, ·) \)	\( \chi_{ 17 }( 12, ·) \)
17	\( \chi_{ 103 }( 8, ·) \)	\( \chi_{ 103 }( 9, ·) \)	\( \chi_{ 103 }( 13, ·) \)	\( \chi_{ 103 }( 14, ·) \)	\( \chi_{ 103 }( 23, ·) \)	\( \chi_{ 103 }( 30, ·) \)	\( \chi_{ 103 }( 34, ·) \)
18	\( \chi_{ 19 }( 2, ·) \)	\( \chi_{ 19 }( 3, ·) \)	\( \chi_{ 19 }( 10, ·) \)	\( \chi_{ 19 }( 13, ·) \)	\( \chi_{ 19 }( 14, ·) \)	\( \chi_{ 19 }( 15, ·) \)	\( \chi_{ 27 }( 2, ·) \)
19	\( \chi_{ 191 }( 5, ·) \)	\( \chi_{ 191 }( 6, ·) \)	\( \chi_{ 191 }( 25, ·) \)	\( \chi_{ 191 }( 30, ·) \)	\( \chi_{ 191 }( 32, ·) \)	\( \chi_{ 191 }( 36, ·) \)	\( \chi_{ 191 }( 52, ·) \)
20	\( \chi_{ 25 }( 2, ·) \)	\( \chi_{ 25 }( 3, ·) \)	\( \chi_{ 25 }( 8, ·) \)	\( \chi_{ 25 }( 12, ·) \)	\( \chi_{ 25 }( 13, ·) \)	\( \chi_{ 25 }( 17, ·) \)	\( \chi_{ 25 }( 22, ·) \)