Dirichlet character χ3332(407,⋅)\chi_{3332}(407,\cdot)

• Label: 3332.407
• Modulus: $3332$
• Conductor: $3332$
• Order: $14$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3332$
Conductor:	$3332$
Order:	$14$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3332.be

$\chi_{3332}(407,\cdot)$ $\chi_{3332}(1359,\cdot)$ $\chi_{3332}(1835,\cdot)$ $\chi_{3332}(2311,\cdot)$ $\chi_{3332}(2787,\cdot)$ $\chi_{3332}(3263,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	Number field defined by a degree 14 polynomial

Values on generators

$(1667,885,785)$ → $(-1,e\left(\frac{5}{7}\right),-1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{ 3332 }(407, a)$	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$