Dirichlet character χ345(14,⋅)\chi_{345}(14,\cdot)

• Label: 345.14
• Modulus: $345$
• Conductor: $345$
• Order: $22$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$345$
Conductor:	$345$
Order:	$22$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 345.n

$\chi_{345}(14,\cdot)$ $\chi_{345}(44,\cdot)$ $\chi_{345}(74,\cdot)$ $\chi_{345}(89,\cdot)$ $\chi_{345}(134,\cdot)$ $\chi_{345}(149,\cdot)$ $\chi_{345}(194,\cdot)$ $\chi_{345}(224,\cdot)$ $\chi_{345}(314,\cdot)$ $\chi_{345}(329,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	Number field defined by a degree 22 polynomial

Values on generators

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

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 345 }(14, a)$	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$

Gauss sum

Jacobi sum

Kloosterman sum