Dirichlet character χ3528(43,⋅)\chi_{3528}(43,\cdot)

• Label: 3528.43
• Modulus: $3528$
• Conductor: $3528$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3528$
Conductor:	$3528$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3528.er

$\chi_{3528}(43,\cdot)$ $\chi_{3528}(211,\cdot)$ $\chi_{3528}(547,\cdot)$ $\chi_{3528}(715,\cdot)$ $\chi_{3528}(1051,\cdot)$ $\chi_{3528}(1219,\cdot)$ $\chi_{3528}(1555,\cdot)$ $\chi_{3528}(1723,\cdot)$ $\chi_{3528}(2227,\cdot)$ $\chi_{3528}(2563,\cdot)$ $\chi_{3528}(2731,\cdot)$ $\chi_{3528}(3067,\cdot)$

Related number fields

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

Values on generators

$(2647,1765,785,1081)$ → $(-1,-1,e\left(\frac{2}{3}\right),e\left(\frac{1}{7}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 3528 }(43, a)$	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{14}\right)$