Dirichlet character χ161(93,⋅)\chi_{161}(93,\cdot)

• Label: 161.93
• Modulus: $161$
• Conductor: $7$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$161$
Conductor:	$7$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{7}(2,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 161.e

$\chi_{161}(93,\cdot)$ $\chi_{161}(116,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{7})^+$

Values on generators

$(24,120)$ → $(e\left(\frac{1}{3}\right),1)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 161 }(93, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum