Dirichlet character χ1575(694,⋅)\chi_{1575}(694,\cdot)

• Label: 1575.694
• Modulus: $1575$
• Conductor: $25$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1575$
Conductor:	$25$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{25}(19,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1575.bx

$\chi_{1575}(64,\cdot)$ $\chi_{1575}(379,\cdot)$ $\chi_{1575}(694,\cdot)$ $\chi_{1575}(1009,\cdot)$

Related number fields

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

Values on generators

$(1226,127,451)$ → $(1,e\left(\frac{9}{10}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 1575 }(694, a)$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$