Dirichlet character χ250(49,⋅)\chi_{250}(49,\cdot)

• Label: 250.49
• Modulus: $250$
• Conductor: $25$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$250$
Conductor:	$25$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{25}(9,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 250.e

$\chi_{250}(49,\cdot)$ $\chi_{250}(99,\cdot)$ $\chi_{250}(149,\cdot)$ $\chi_{250}(199,\cdot)$

Related number fields

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

Values on generators

$127$ → $e\left(\frac{7}{10}\right)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 250 }(49, a)$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$

Gauss sum

Jacobi sum

Kloosterman sum