Dirichlet character χ680(83,⋅)\chi_{680}(83,\cdot)

• Label: 680.83
• Modulus: $680$
• Conductor: $680$
• Order: $8$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$680$
Conductor:	$680$
Order:	$8$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 680.bz

$\chi_{680}(83,\cdot)$ $\chi_{680}(467,\cdot)$ $\chi_{680}(563,\cdot)$ $\chi_{680}(587,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.26261675072000000.2

Values on generators

$(511,341,137,241)$ → $(-1,-1,-i,e\left(\frac{3}{8}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 680 }(83, a)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$

Gauss sum

Jacobi sum

Kloosterman sum