Dirichlet character χ3528(2993,⋅)\chi_{3528}(2993,\cdot)

• Label: 3528.2993
• Modulus: $3528$
• Conductor: $441$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3528$
Conductor:	$441$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{441}(347,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3528.gc

$\chi_{3528}(65,\cdot)$ $\chi_{3528}(473,\cdot)$ $\chi_{3528}(977,\cdot)$ $\chi_{3528}(1073,\cdot)$ $\chi_{3528}(1481,\cdot)$ $\chi_{3528}(1577,\cdot)$ $\chi_{3528}(1985,\cdot)$ $\chi_{3528}(2081,\cdot)$ $\chi_{3528}(2489,\cdot)$ $\chi_{3528}(2585,\cdot)$ $\chi_{3528}(2993,\cdot)$ $\chi_{3528}(3089,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(2647,1765,785,1081)$ → $(1,1,e\left(\frac{5}{6}\right),e\left(\frac{5}{21}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 3528 }(2993, a)$	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{21}\right)$