Dirichlet character χ273(257,⋅)\chi_{273}(257,\cdot)

• Label: 273.257
• Modulus: $273$
• Conductor: $273$
• Order: $6$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$273$
Conductor:	$273$
Order:	$6$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 273.br

$\chi_{273}(17,\cdot)$ $\chi_{273}(257,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	6.6.168488679177.2

Values on generators

$(92,157,106)$ → $(-1,e\left(\frac{5}{6}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 273 }(257, a)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum