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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 $8$
$41$
$1$
$40$
$9$
$32$
$10$
$37$
$16$
$18$
$3$
$14$
$27$
$38$
$42$
$1$
$13$
$29$
$41$
$25$
$37$
$5$
$17$
$11$
$23$
$19$
$31$
$43$
$1$
$42$
$6$
$36$
$7$
$37$
$4$
$11$
$16$
$35$
$21$
$41$
$44$
$1$
$21$
$23$
$43$
$5$
$9$
$25$
$37$
$45$
$1$
$19$
$26$
$44$
$16$
$31$
$8$
$17$
$28$
$37$
$4$
$34$
$11$
$41$
$14$
$29$
$46$
$1$
$45$
$47$
$1$
$46$
$48$
$1$
$7$
$17$
$23$
$25$
$31$
$41$
$47$
$5$
$29$
$11$
$35$
$13$
$37$
$19$
$43$
$49$
$1$
$48$
$18$
$30$
$19$
$31$
$8$
$43$
$15$
$36$
$22$
$29$
$50$
$1$
$49$
$7$
$43$
$11$
$41$
$21$
$31$
$51$
$1$
$16$
$35$
$50$
$4$
$13$
$38$
$47$
$2$
$26$
$8$
$32$
$19$
$43$
$25$
$49$
$52$
$1$
$25$
$27$
$51$
$9$
$29$
$5$
$21$
$31$
$47$
$3$
$35$
$17$
$49$
$23$
$43$
$53$
$1$
$52$
$23$
$30$
$54$
$1$
$53$
$19$
$37$
$17$
$35$
$55$
$1$
$21$
$34$
$54$
$12$
$23$
$32$
$43$
$16$
$31$
$26$
$36$
$56$
$1$
$13$
$15$
$27$
$29$
$41$
$43$
$55$
$9$
$25$
$3$
$19$
$5$
$45$
$11$
$51$
$17$
$33$
$23$
$39$
$31$
$47$
$37$
$53$
$57$
$1$
$20$
$37$
$56$
$7$
$49$
$8$
$50$
$11$
$26$
$31$
$46$
$58$
$1$
$57$
$17$
$41$
$7$
$25$
$23$
$53$
$45$
$49$
$59$
$1$
$58$
$60$
$1$
$11$
$19$
$29$
$31$
$41$
$49$
$59$
$7$
$43$
$13$
$37$
$17$
$53$
$23$
$47$