Dirichlet character χ475(464,⋅)\chi_{475}(464,\cdot)

• Label: 475.464
• Modulus: $475$
• Conductor: $475$
• Order: $30$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$475$
Conductor:	$475$
Order:	$30$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 475.z

$\chi_{475}(69,\cdot)$ $\chi_{475}(84,\cdot)$ $\chi_{475}(164,\cdot)$ $\chi_{475}(179,\cdot)$ $\chi_{475}(259,\cdot)$ $\chi_{475}(354,\cdot)$ $\chi_{475}(369,\cdot)$ $\chi_{475}(464,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	30.0.41334267425810406820389890772071250779617912485264241695404052734375.1

Values on generators

$(77,401)$ → $(e\left(\frac{3}{10}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 475 }(464, a)$	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$

Gauss sum

Jacobi sum

Kloosterman sum