Dirichlet character χ8800(6357,⋅)\chi_{8800}(6357,\cdot)

• Label: 8800.6357
• Modulus: $8800$
• Conductor: $1760$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8800$
Conductor:	$1760$
Order:	$8$
Real:	no
Primitive:	no, induced from $\chi_{1760}(1077,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8800.ch

$\chi_{8800}(1693,\cdot)$ $\chi_{8800}(1957,\cdot)$ $\chi_{8800}(6093,\cdot)$ $\chi_{8800}(6357,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.491270438912000000.1

Values on generators

$(2751,3301,4577,5601)$ → $(1,e\left(\frac{5}{8}\right),i,-1)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 8800 }(6357, a)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$