Dirichlet character χ680(99,⋅)\chi_{680}(99,\cdot)

• Label: 680.99
• Modulus: $680$
• Conductor: $680$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$680$
Conductor:	$680$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 680.co

$\chi_{680}(99,\cdot)$ $\chi_{680}(139,\cdot)$ $\chi_{680}(299,\cdot)$ $\chi_{680}(379,\cdot)$ $\chi_{680}(419,\cdot)$ $\chi_{680}(499,\cdot)$ $\chi_{680}(539,\cdot)$ $\chi_{680}(619,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.18759175710374728781004800000000.1

Values on generators

$(511,341,137,241)$ → $(-1,-1,-1,e\left(\frac{9}{16}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 680 }(99, a)$	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$

Gauss sum

Jacobi sum

Kloosterman sum