Dirichlet character χ2243(2,⋅)\chi_{2243}(2,\cdot)

• Label: 2243.2
• Modulus: $2243$
• Conductor: $2243$
• Order: $2242$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2243$
Conductor:	$2243$
Order:	$2242$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2243.h

$\chi_{2243}(2,\cdot)$ $\chi_{2243}(5,\cdot)$ $\chi_{2243}(6,\cdot)$ $\chi_{2243}(8,\cdot)$ $\chi_{2243}(13,\cdot)$ $\chi_{2243}(14,\cdot)$ $\chi_{2243}(15,\cdot)$ $\chi_{2243}(18,\cdot)$ $\chi_{2243}(19,\cdot)$ $\chi_{2243}(20,\cdot)$ $\chi_{2243}(22,\cdot)$ $\chi_{2243}(23,\cdot)$ $\chi_{2243}(24,\cdot)$ $\chi_{2243}(29,\cdot)$ $\chi_{2243}(32,\cdot)$ $\chi_{2243}(34,\cdot)$ $\chi_{2243}(35,\cdot)$ $\chi_{2243}(37,\cdot)$ $\chi_{2243}(39,\cdot)$ $\chi_{2243}(41,\cdot)$ $\chi_{2243}(42,\cdot)$ $\chi_{2243}(45,\cdot)$ $\chi_{2243}(47,\cdot)$ $\chi_{2243}(50,\cdot)$ $\chi_{2243}(52,\cdot)$ $\chi_{2243}(54,\cdot)$ $\chi_{2243}(55,\cdot)$ $\chi_{2243}(56,\cdot)$ $\chi_{2243}(59,\cdot)$ $\chi_{2243}(60,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1121})$
Fixed field:	Number field defined by a degree 2242 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{1}{2242}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 2243 }(2, a)$	$-1$	$1$	$e\left(\frac{1}{2242}\right)$	$e\left(\frac{73}{1121}\right)$	$e\left(\frac{1}{1121}\right)$	$e\left(\frac{1363}{2242}\right)$	$e\left(\frac{147}{2242}\right)$	$e\left(\frac{1070}{1121}\right)$	$e\left(\frac{3}{2242}\right)$	$e\left(\frac{146}{1121}\right)$	$e\left(\frac{682}{1121}\right)$	$e\left(\frac{1014}{1121}\right)$