Dirichlet character χ240(77,⋅)\chi_{240}(77,\cdot)

• Label: 240.77
• Modulus: $240$
• Conductor: $240$
• Order: $4$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$240$
Conductor:	$240$
Order:	$4$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 240.bf

$\chi_{240}(53,\cdot)$ $\chi_{240}(77,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(i)$
Fixed field:	4.4.2304000.2

Values on generators

$(31,181,161,97)$ → $(1,-i,-1,i)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 240 }(77, a)$	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$	$-i$	$i$	$1$	$1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum