Dirichlet character χ416(365,⋅)\chi_{416}(365,\cdot)

• Label: 416.365
• Modulus: $416$
• Conductor: $32$
• Order: $8$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$416$
Conductor:	$32$
Order:	$8$
Real:	no
Primitive:	no, induced from $\chi_{32}(13,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 416.bf

$\chi_{416}(53,\cdot)$ $\chi_{416}(157,\cdot)$ $\chi_{416}(261,\cdot)$ $\chi_{416}(365,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{8})$
Fixed field:	$\Q(\zeta_{32})^+$

Values on generators

$(287,261,353)$ → $(1,e\left(\frac{7}{8}\right),1)$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 416 }(365, a)$	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$

Gauss sum

Jacobi sum

Kloosterman sum