Dirichlet character \(\chi_{2349}(292,\cdot)\)

• Label: 2349.292
• Modulus: $2349$
• Conductor: $2349$
• Order: $756$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2349\)
Conductor:	\(2349\)
Order:	\(756\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2349.bv

\(\chi_{2349}(31,\cdot)\) \(\chi_{2349}(40,\cdot)\) \(\chi_{2349}(43,\cdot)\) \(\chi_{2349}(61,\cdot)\) \(\chi_{2349}(76,\cdot)\) \(\chi_{2349}(79,\cdot)\) \(\chi_{2349}(85,\cdot)\) \(\chi_{2349}(97,\cdot)\) \(\chi_{2349}(106,\cdot)\) \(\chi_{2349}(124,\cdot)\) \(\chi_{2349}(130,\cdot)\) \(\chi_{2349}(142,\cdot)\) \(\chi_{2349}(148,\cdot)\) \(\chi_{2349}(160,\cdot)\) \(\chi_{2349}(166,\cdot)\) \(\chi_{2349}(184,\cdot)\) \(\chi_{2349}(193,\cdot)\) \(\chi_{2349}(205,\cdot)\) \(\chi_{2349}(211,\cdot)\) \(\chi_{2349}(214,\cdot)\) \(\chi_{2349}(229,\cdot)\) \(\chi_{2349}(247,\cdot)\) \(\chi_{2349}(250,\cdot)\) \(\chi_{2349}(259,\cdot)\) \(\chi_{2349}(292,\cdot)\) \(\chi_{2349}(301,\cdot)\) \(\chi_{2349}(304,\cdot)\) \(\chi_{2349}(322,\cdot)\) \(\chi_{2349}(337,\cdot)\) \(\chi_{2349}(340,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{756})$
Fixed field:	Number field defined by a degree 756 polynomial (not computed)

Values on generators

\((407,1945)\) → \((e\left(\frac{16}{27}\right),e\left(\frac{1}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2349 }(292, a) \)	\(-1\)	\(1\)	\(e\left(\frac{475}{756}\right)\)	\(e\left(\frac{97}{378}\right)\)	\(e\left(\frac{157}{378}\right)\)	\(e\left(\frac{172}{189}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{11}{252}\right)\)	\(e\left(\frac{451}{756}\right)\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{407}{756}\right)\)	\(e\left(\frac{97}{189}\right)\)