Dirichlet character \(\chi_{2299}(97,\cdot)\)

• Label: 2299.97
• 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

\((970,1332)\) → \((e\left(\frac{18}{55}\right),e\left(\frac{1}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 2299 }(97, a) \)	\(-1\)	\(1\)	\(e\left(\frac{379}{990}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{379}{495}\right)\)	\(e\left(\frac{53}{495}\right)\)	\(e\left(\frac{448}{495}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{19}{66}\right)\)