Dirichlet character χ8325(3368,⋅)\chi_{8325}(3368,\cdot)

• Label: 8325.3368
• Modulus: $8325$
• Conductor: $45$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8325$
Conductor:	$45$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{45}(38,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8325.dn

$\chi_{8325}(482,\cdot)$ $\chi_{8325}(3368,\cdot)$ $\chi_{8325}(6032,\cdot)$ $\chi_{8325}(6143,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	$\Q(\zeta_{45})^+$

Values on generators

$(3701,7327,5626)$ → $(e\left(\frac{1}{6}\right),-i,1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 8325 }(3368, a)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$