Dirichlet characters of modulus 1-25

Imprimitive

Primitive

The table below displays Dirichlet characters of a given modulus \(q\) and index \(n\) of order up to 8. The characters are grouped with respect to order and stacked integers indicate (complex) conjugate characters.

Modulus

Order $1$

Order $2$

Order $3$

Order $4$

Order $5$

Order $6$

Order $8$

$1$

$1$

$2$

$1$

$3$

$1$

$2$

$4$

$1$

$3$

$5$

$1$

$4$

$2$
$3$

$6$

$1$

$5$

$7$

$1$

$6$

$2$
$4$

$3$
$5$

$8$

$1$

$3$

$5$

$7$

$9$

$1$

$8$

$4$
$7$

$2$
$5$

$10$

$1$

$9$

$3$
$7$

$11$

$1$

$10$

$3$ $4$

$5$ $9$

$12$

$1$

$5$

$7$

$11$

$13$

$1$

$12$

$3$
$9$

$5$
$8$

$4$
$10$

$14$

$1$

$13$

$9$
$11$

$3$
$5$

$15$

$1$

$4$

$11$

$14$

$2$ $8$

$7$ $13$

$16$

$1$

$7$

$9$

$15$

$3$ $11$

$5$ $13$

$17$

$1$

$16$

$4$
$13$

$2$ $9$

$8$ $15$

$18$

$1$

$17$

$7$
$13$

$5$
$11$

$19$

$1$

$18$

$7$
$11$

$8$
$12$

$20$

$1$

$9$

$11$

$19$

$3$ $7$

$13$ $17$

$21$

$1$

$8$

$13$

$20$

$4$
$16$

$2$ $11$

$5$ $17$

$10$ $19$

$22$

$1$

$21$

$3$ $15$

$5$ $9$

$23$

$1$

$22$

$24$

$1$

$5$

$7$

$11$

$13$

$17$

$19$

$23$

$25$

$1$

$24$

$7$
$18$

$6$ $21$

$11$ $16$