Dirichlet character χ25(9,⋅)\chi_{25}(9,\cdot)

• Label: 25.9
• Modulus: $25$
• Conductor: $25$
• Order: $10$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$25$
Conductor:	$25$
Order:	$10$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 25.e

$\chi_{25}(4,\cdot)$ $\chi_{25}(9,\cdot)$ $\chi_{25}(14,\cdot)$ $\chi_{25}(19,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	$\Q(\zeta_{25})^+$

Values on generators

$2$ → $e\left(\frac{7}{10}\right)$

Values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 25 }(9, a)$	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$

Gauss sum

Jacobi sum

Kloosterman sum