Dirichlet character χ580(499,⋅)\chi_{580}(499,\cdot)

• Label: 580.499
• Modulus: $580$
• Conductor: $580$
• Order: $14$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$580$
Conductor:	$580$
Order:	$14$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 580.y

$\chi_{580}(179,\cdot)$ $\chi_{580}(299,\cdot)$ $\chi_{580}(399,\cdot)$ $\chi_{580}(419,\cdot)$ $\chi_{580}(439,\cdot)$ $\chi_{580}(499,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	14.0.13133604752587010801920000000.1

Values on generators

$(291,117,321)$ → $(-1,-1,e\left(\frac{3}{14}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 580 }(499, a)$	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$

Gauss sum

Jacobi sum

Kloosterman sum