Dirichlet character orbit 1700.w

• Label: 1700.w
• Modulus: $1700$
• Conductor: $68$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1700$
Conductor:	$68$
Order:	$8$
Real:	no
Primitive:	no, induced from 68.g
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.0.105046700288.1

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$19$	$21$	$23$	$27$	$29$
$\chi_{1700}(151,\cdot)$	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1700}(451,\cdot)$	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1700}(1351,\cdot)$	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1700}(1651,\cdot)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$