Dirichlet character χ234(149,⋅)\chi_{234}(149,\cdot)

• Label: 234.149
• Modulus: $234$
• Conductor: $117$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$234$
Conductor:	$117$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{117}(32,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 234.y

$\chi_{234}(11,\cdot)$ $\chi_{234}(59,\cdot)$ $\chi_{234}(119,\cdot)$ $\chi_{234}(149,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.694319656224247224093.2

Values on generators

$(209,145)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{5}{12}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 234 }(149, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum