Dirichlet character χ345(244,⋅)\chi_{345}(244,\cdot)

• Label: 345.244
• Modulus: $345$
• Conductor: $115$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$345$
Conductor:	$115$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{115}(14,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 345.r

$\chi_{345}(19,\cdot)$ $\chi_{345}(34,\cdot)$ $\chi_{345}(79,\cdot)$ $\chi_{345}(109,\cdot)$ $\chi_{345}(199,\cdot)$ $\chi_{345}(214,\cdot)$ $\chi_{345}(244,\cdot)$ $\chi_{345}(274,\cdot)$ $\chi_{345}(304,\cdot)$ $\chi_{345}(319,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	22.0.1927323443393334271838358868310546875.1

Values on generators

$(116,277,166)$ → $(1,-1,e\left(\frac{21}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 345 }(244, a)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$

Gauss sum

Jacobi sum

Kloosterman sum