Dirichlet character χ357(23,⋅)\chi_{357}(23,\cdot)

• Label: 357.23
• Modulus: $357$
• Conductor: $357$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$357$
Conductor:	$357$
Order:	$48$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 357.bm

$\chi_{357}(11,\cdot)$ $\chi_{357}(23,\cdot)$ $\chi_{357}(44,\cdot)$ $\chi_{357}(65,\cdot)$ $\chi_{357}(74,\cdot)$ $\chi_{357}(95,\cdot)$ $\chi_{357}(107,\cdot)$ $\chi_{357}(116,\cdot)$ $\chi_{357}(158,\cdot)$ $\chi_{357}(233,\cdot)$ $\chi_{357}(275,\cdot)$ $\chi_{357}(284,\cdot)$ $\chi_{357}(296,\cdot)$ $\chi_{357}(317,\cdot)$ $\chi_{357}(326,\cdot)$ $\chi_{357}(347,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(239,52,190)$ → $(-1,e\left(\frac{1}{3}\right),e\left(\frac{15}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{ 357 }(23, a)$	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{19}{48}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{16}\right)$

Gauss sum

Jacobi sum

Kloosterman sum