Dirichlet character χ967(23,⋅)\chi_{967}(23,\cdot)

• Label: 967.23
• Modulus: $967$
• Conductor: $967$
• Order: $322$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$967$
Conductor:	$967$
Order:	$322$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 967.n

$\chi_{967}(3,\cdot)$ $\chi_{967}(10,\cdot)$ $\chi_{967}(23,\cdot)$ $\chi_{967}(24,\cdot)$ $\chi_{967}(26,\cdot)$ $\chi_{967}(27,\cdot)$ $\chi_{967}(29,\cdot)$ $\chi_{967}(33,\cdot)$ $\chi_{967}(67,\cdot)$ $\chi_{967}(76,\cdot)$ $\chi_{967}(80,\cdot)$ $\chi_{967}(90,\cdot)$ $\chi_{967}(109,\cdot)$ $\chi_{967}(110,\cdot)$ $\chi_{967}(112,\cdot)$ $\chi_{967}(125,\cdot)$ $\chi_{967}(126,\cdot)$ $\chi_{967}(154,\cdot)$ $\chi_{967}(158,\cdot)$ $\chi_{967}(167,\cdot)$ $\chi_{967}(170,\cdot)$ $\chi_{967}(178,\cdot)$ $\chi_{967}(184,\cdot)$ $\chi_{967}(186,\cdot)$ $\chi_{967}(191,\cdot)$ $\chi_{967}(192,\cdot)$ $\chi_{967}(207,\cdot)$ $\chi_{967}(208,\cdot)$ $\chi_{967}(213,\cdot)$ $\chi_{967}(214,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{161})$
Fixed field:	Number field defined by a degree 322 polynomial (not computed)

Values on generators

$5$ → $e\left(\frac{257}{322}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 967 }(23, a)$	$-1$	$1$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{51}{322}\right)$	$e\left(\frac{1}{161}\right)$	$e\left(\frac{257}{322}\right)$	$e\left(\frac{213}{322}\right)$	$e\left(\frac{153}{322}\right)$	$e\left(\frac{82}{161}\right)$	$e\left(\frac{51}{161}\right)$	$e\left(\frac{97}{322}\right)$	$e\left(\frac{120}{161}\right)$

Gauss sum

Jacobi sum

Kloosterman sum