Dirichlet character χ1224(359,⋅)\chi_{1224}(359,\cdot)

• Label: 1224.359
• Modulus: $1224$
• Conductor: $204$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$1224$
Conductor:	$204$
Order:	$8$
Real:	no
Primitive:	no, induced from $\chi_{204}(155,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 1224.br

$\chi_{1224}(287,\cdot)$ $\chi_{1224}(359,\cdot)$ $\chi_{1224}(791,\cdot)$ $\chi_{1224}(1079,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.8.8508782723328.1

Values on generators

$(919,613,137,649)$ → $(-1,1,-1,e\left(\frac{7}{8}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 1224 }(359, a)$	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$