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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.
ModulusOrder $1$Order $2$Order $3$Order $4$Order $5$Order $6$Order $7$Order $8$
$21$
$1$
$8$
$13$
$20$
$4$
$16$
$2$
$11$
$5$
$17$
$10$
$19$
$22$
$1$
$21$
$3$
$15$
$5$
$9$
$23$
$1$
$22$
$24$
$1$
$5$
$7$
$11$
$13$
$17$
$19$
$23$
$25$
$1$
$24$
$7$
$18$
$6$
$21$
$11$
$16$
$26$
$1$
$25$
$3$
$9$
$5$
$21$
$17$
$23$
$27$
$1$
$26$
$10$
$19$
$8$
$17$
$28$
$1$
$13$
$15$
$27$
$9$
$25$
$3$
$19$
$5$
$17$
$11$
$23$
$29$
$1$
$28$
$12$
$17$
$7$
$25$
$16$
$20$
$23$
$24$
$30$
$1$
$11$
$19$
$29$
$7$
$13$
$17$
$23$
$31$
$1$
$30$
$5$
$25$
$2$
$16$
$4$
$8$
$6$
$26$
$32$
$1$
$15$
$17$
$31$
$7$
$23$
$9$
$25$
$3$
$11$
$5$
$13$
$19$
$27$
$21$
$29$
$33$
$1$
$10$
$23$
$32$
$4$
$25$
$16$
$31$
$34$
$1$
$33$
$13$
$21$
$9$
$19$
$15$
$25$
$35$
$1$
$6$
$29$
$34$
$11$
$16$
$8$
$22$
$13$
$27$
$4$
$9$
$19$
$24$
$26$
$31$
$36$
$1$
$17$
$19$
$35$
$13$
$25$
$5$
$29$
$7$
$31$
$11$
$23$
$37$
$1$
$36$
$10$
$26$
$6$
$31$
$11$
$27$
$38$
$1$
$37$
$7$
$11$
$27$
$31$
$39$
$1$
$14$
$25$
$38$
$16$
$22$
$5$
$8$
$31$
$34$
$4$
$10$
$17$
$23$
$29$
$35$
$40$
$1$
$9$
$11$
$19$
$21$
$29$
$31$
$39$
$3$
$27$
$7$
$23$
$13$
$37$
$17$
$33$