Dirichlet character χ400(79,⋅)\chi_{400}(79,\cdot)

• Label: 400.79
• Modulus: $400$
• Conductor: $100$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$400$
Conductor:	$100$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{100}(79,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 400.x

$\chi_{400}(79,\cdot)$ $\chi_{400}(159,\cdot)$ $\chi_{400}(239,\cdot)$ $\chi_{400}(319,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	10.0.781250000000000.1

Values on generators

$(351,101,177)$ → $(-1,1,e\left(\frac{1}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 400 }(79, a)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$

Gauss sum

Jacobi sum

Kloosterman sum