Dirichlet character χ165(61,⋅)\chi_{165}(61,\cdot)

• Label: 165.61
• Modulus: $165$
• Conductor: $11$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$165$
Conductor:	$11$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{11}(6,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 165.t

$\chi_{165}(46,\cdot)$ $\chi_{165}(61,\cdot)$ $\chi_{165}(106,\cdot)$ $\chi_{165}(151,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	$\Q(\zeta_{11})$

Values on generators

$(56,67,46)$ → $(1,1,e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{ 165 }(61, a)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum