Dirichlet characters of modulus 41-60

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 $7$

Order $8$

$41$

$1$

$40$

$9$
$32$

$10$ $37$

$16$ $18$

$3$ $14$

$27$ $38$

$42$

$1$

$13$

$29$

$41$

$25$
$37$

$5$ $17$

$11$ $23$

$19$ $31$

$43$

$1$

$42$

$6$
$36$

$7$
$37$

$4$ $11$

$16$ $35$

$21$ $41$

$44$

$1$

$21$

$23$

$43$

$5$ $9$

$25$ $37$

$45$

$1$

$19$

$26$

$44$

$16$
$31$

$8$ $17$

$28$ $37$

$4$ $34$

$11$ $41$

$14$ $29$

$46$

$1$

$45$

$47$

$1$

$46$

$48$

$1$

$7$

$17$

$23$

$25$

$31$

$41$

$47$

$5$ $29$

$11$ $35$

$13$ $37$

$19$ $43$

$49$

$1$

$48$

$18$
$30$

$19$
$31$

$8$ $43$

$15$ $36$

$22$ $29$

$50$

$1$

$49$

$7$
$43$

$11$ $41$

$21$ $31$

$51$

$1$

$16$

$35$

$50$

$4$ $13$

$38$ $47$

$2$ $26$

$8$ $32$

$19$ $43$

$25$ $49$

$52$

$1$

$25$

$27$

$51$

$9$
$29$

$5$ $21$

$31$ $47$

$3$ $35$

$17$ $49$

$23$ $43$

$53$

$1$

$52$

$23$
$30$

$54$

$1$

$53$

$19$
$37$

$17$
$35$

$55$

$1$

$21$

$34$

$54$

$12$ $23$

$32$ $43$

$16$ $31$

$26$ $36$

$56$

$1$

$13$

$15$

$27$

$29$

$41$

$43$

$55$

$9$
$25$

$3$ $19$

$5$ $45$

$11$ $51$

$17$ $33$

$23$ $39$

$31$ $47$

$37$ $53$

$57$

$1$

$20$

$37$

$56$

$7$
$49$

$8$ $50$

$11$ $26$

$31$ $46$

$58$

$1$

$57$

$17$
$41$

$7$ $25$

$23$ $53$

$45$ $49$

$59$

$1$

$58$

$60$

$1$

$11$

$19$

$29$

$31$

$41$

$49$

$59$

$7$ $43$

$13$ $37$

$17$ $53$

$23$ $47$