Dirichlet character χ693(403,⋅)\chi_{693}(403,\cdot)

• Label: 693.403
• Modulus: $693$
• Conductor: $693$
• Order: $30$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$693$
Conductor:	$693$
Order:	$30$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 693.da

$\chi_{693}(151,\cdot)$ $\chi_{693}(184,\cdot)$ $\chi_{693}(277,\cdot)$ $\chi_{693}(310,\cdot)$ $\chi_{693}(403,\cdot)$ $\chi_{693}(436,\cdot)$ $\chi_{693}(655,\cdot)$ $\chi_{693}(688,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(155,199,442)$ → $(e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{7}{10}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{ 693 }(403, a)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$

Gauss sum

Jacobi sum

Kloosterman sum