Dirichlet character χ680(677,⋅)\chi_{680}(677,\cdot)

• Label: 680.677
• 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.cf

$\chi_{680}(37,\cdot)$ $\chi_{680}(277,\cdot)$ $\chi_{680}(333,\cdot)$ $\chi_{680}(437,\cdot)$ $\chi_{680}(453,\cdot)$ $\chi_{680}(533,\cdot)$ $\chi_{680}(653,\cdot)$ $\chi_{680}(677,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.11724484818984205488128000000000000.1

Values on generators

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

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 680 }(677, a)$	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$

Gauss sum

Jacobi sum

Kloosterman sum