Dirichlet character χ115(6,⋅)\chi_{115}(6,\cdot)

• Label: 115.6
• Modulus: $115$
• Conductor: $23$
• Order: $11$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$115$
Conductor:	$23$
Order:	$11$
Real:	no
Primitive:	no, induced from $\chi_{23}(6,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 115.g

$\chi_{115}(6,\cdot)$ $\chi_{115}(16,\cdot)$ $\chi_{115}(26,\cdot)$ $\chi_{115}(31,\cdot)$ $\chi_{115}(36,\cdot)$ $\chi_{115}(41,\cdot)$ $\chi_{115}(71,\cdot)$ $\chi_{115}(81,\cdot)$ $\chi_{115}(96,\cdot)$ $\chi_{115}(101,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	$\Q(\zeta_{23})^+$

Values on generators

$(47,51)$ → $(1,e\left(\frac{9}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 115 }(6, a)$	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum