Dirichlet character χ185(168,⋅)\chi_{185}(168,\cdot)

• Label: 185.168
• Modulus: $185$
• Conductor: $185$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$185$
Conductor:	$185$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 185.z

$\chi_{185}(17,\cdot)$ $\chi_{185}(18,\cdot)$ $\chi_{185}(22,\cdot)$ $\chi_{185}(42,\cdot)$ $\chi_{185}(72,\cdot)$ $\chi_{185}(87,\cdot)$ $\chi_{185}(98,\cdot)$ $\chi_{185}(113,\cdot)$ $\chi_{185}(143,\cdot)$ $\chi_{185}(163,\cdot)$ $\chi_{185}(167,\cdot)$ $\chi_{185}(168,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.36.57444765302724909954814307473256133361395843470561362005770206451416015625.2

Values on generators

$(112,76)$ → $(-i,e\left(\frac{25}{36}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 185 }(168, a)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{8}{9}\right)$	$-i$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum