Dirichlet character χ156(145,⋅)\chi_{156}(145,\cdot)

• Label: 156.145
• Modulus: $156$
• Conductor: $13$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$156$
Conductor:	$13$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{13}(2,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 156.x

$\chi_{156}(37,\cdot)$ $\chi_{156}(85,\cdot)$ $\chi_{156}(97,\cdot)$ $\chi_{156}(145,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	$\Q(\zeta_{13})$

Values on generators

$(79,53,145)$ → $(1,1,e\left(\frac{1}{12}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 156 }(145, a)$	$-1$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum