Dirichlet character χ36864(8191,⋅)\chi_{36864}(8191,\cdot)

• Label: 36864.8191
• Modulus: $36864$
• Conductor: $4$
• Order: $2$
• Real: yes
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$36864$
Conductor:	$4$
Order:	$2$
Real:	yes
Primitive:	no, induced from $\chi_{4}(3,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 36864.g

$\chi_{36864}(8191,\cdot)$

Related number fields

Field of values:	$\Q$
Fixed field:	$\Q(\sqrt{-1})$

Values on generators

$(8191,20485,4097)$ → $(-1,1,1)$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 36864 }(8191, a)$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$