Dirichlet character χ165(68,⋅)\chi_{165}(68,\cdot)

• Label: 165.68
• Modulus: $165$
• Conductor: $165$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$165$
Conductor:	$165$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 165.u

$\chi_{165}(2,\cdot)$ $\chi_{165}(8,\cdot)$ $\chi_{165}(17,\cdot)$ $\chi_{165}(62,\cdot)$ $\chi_{165}(68,\cdot)$ $\chi_{165}(83,\cdot)$ $\chi_{165}(107,\cdot)$ $\chi_{165}(128,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	Number field defined by a degree 20 polynomial

Values on generators

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

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{ 165 }(68, a)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$

Gauss sum

Jacobi sum

Kloosterman sum