Dirichlet character χ1440(19,⋅)\chi_{1440}(19,\cdot)

• Label: 1440.19
• Modulus: $1440$
• Conductor: $160$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1440$
Conductor:	$160$
Order:	$8$
Real:	no
Primitive:	no, induced from $\chi_{160}(19,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1440.cm

$\chi_{1440}(19,\cdot)$ $\chi_{1440}(379,\cdot)$ $\chi_{1440}(739,\cdot)$ $\chi_{1440}(1099,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	8.0.1342177280000.1

Values on generators

$(991,901,641,577)$ → $(-1,e\left(\frac{7}{8}\right),1,-1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1440 }(19, a)$	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$