Dirichlet character χ2299(53,⋅)\chi_{2299}(53,\cdot)

• Label: 2299.53
• Modulus: $2299$
• Conductor: $2299$
• Order: $990$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2299$
Conductor:	$2299$
Order:	$990$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2299.bt

$\chi_{2299}(14,\cdot)$ $\chi_{2299}(15,\cdot)$ $\chi_{2299}(48,\cdot)$ $\chi_{2299}(53,\cdot)$ $\chi_{2299}(59,\cdot)$ $\chi_{2299}(60,\cdot)$ $\chi_{2299}(70,\cdot)$ $\chi_{2299}(71,\cdot)$ $\chi_{2299}(86,\cdot)$ $\chi_{2299}(91,\cdot)$ $\chi_{2299}(97,\cdot)$ $\chi_{2299}(108,\cdot)$ $\chi_{2299}(135,\cdot)$ $\chi_{2299}(136,\cdot)$ $\chi_{2299}(146,\cdot)$ $\chi_{2299}(147,\cdot)$ $\chi_{2299}(174,\cdot)$ $\chi_{2299}(181,\cdot)$ $\chi_{2299}(185,\cdot)$ $\chi_{2299}(192,\cdot)$ $\chi_{2299}(203,\cdot)$ $\chi_{2299}(212,\cdot)$ $\chi_{2299}(223,\cdot)$ $\chi_{2299}(224,\cdot)$ $\chi_{2299}(257,\cdot)$ $\chi_{2299}(262,\cdot)$ $\chi_{2299}(268,\cdot)$ $\chi_{2299}(279,\cdot)$ $\chi_{2299}(280,\cdot)$ $\chi_{2299}(295,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{495})$
Fixed field:	Number field defined by a degree 990 polynomial (not computed)

Values on generators

$(970,1332)$ → $(e\left(\frac{53}{55}\right),e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 2299 }(53, a)$	$-1$	$1$	$e\left(\frac{569}{990}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{74}{495}\right)$	$e\left(\frac{43}{495}\right)$	$e\left(\frac{158}{495}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{59}{66}\right)$