Dirichlet character χ8325(1639,⋅)\chi_{8325}(1639,\cdot)

• Label: 8325.1639
• Modulus: $8325$
• Conductor: $925$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8325$
Conductor:	$925$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{925}(714,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8325.gl

$\chi_{8325}(64,\cdot)$ $\chi_{8325}(1639,\cdot)$ $\chi_{8325}(1729,\cdot)$ $\chi_{8325}(3304,\cdot)$ $\chi_{8325}(3394,\cdot)$ $\chi_{8325}(4969,\cdot)$ $\chi_{8325}(5059,\cdot)$ $\chi_{8325}(6634,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	30.30.712054643298888889330514089285546802246873454578235396184027194976806640625.1

Values on generators

$(3701,7327,5626)$ → $(1,e\left(\frac{3}{10}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 8325 }(1639, a)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$