Dirichlet character χ400(101,⋅)\chi_{400}(101,\cdot)

• Label: 400.101
• Modulus: $400$
• Conductor: $16$
• Order: $4$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$400$
Conductor:	$16$
Order:	$4$
Real:	no
Primitive:	no, induced from $\chi_{16}(5,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 400.l

$\chi_{400}(101,\cdot)$ $\chi_{400}(301,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(i)$
Fixed field:	$\Q(\zeta_{16})^+$

Values on generators

$(351,101,177)$ → $(1,i,1)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(101, a)$	$1$	$1$	$-i$	$-1$	$-1$	$i$	$-i$	$1$	$-i$	$i$	$-1$	$i$

Gauss sum

Jacobi sum

Kloosterman sum