Dirichlet character χ403(214,⋅)\chi_{403}(214,\cdot)

• Label: 403.214
• Modulus: $403$
• Conductor: $403$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$403$
Conductor:	$403$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 403.ca

$\chi_{403}(7,\cdot)$ $\chi_{403}(19,\cdot)$ $\chi_{403}(41,\cdot)$ $\chi_{403}(45,\cdot)$ $\chi_{403}(59,\cdot)$ $\chi_{403}(80,\cdot)$ $\chi_{403}(102,\cdot)$ $\chi_{403}(162,\cdot)$ $\chi_{403}(206,\cdot)$ $\chi_{403}(214,\cdot)$ $\chi_{403}(258,\cdot)$ $\chi_{403}(267,\cdot)$ $\chi_{403}(288,\cdot)$ $\chi_{403}(293,\cdot)$ $\chi_{403}(297,\cdot)$ $\chi_{403}(392,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(249,313)$ → $(e\left(\frac{5}{12}\right),e\left(\frac{8}{15}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 403 }(214, a)$	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{60}\right)$

Gauss sum

Jacobi sum

Kloosterman sum