Dirichlet character \(\chi_{2349}(322,\cdot)\)

• Label: 2349.322
• 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

\((407,1945)\) → \((e\left(\frac{14}{27}\right),e\left(\frac{5}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2349 }(322, a) \)	\(-1\)	\(1\)	\(e\left(\frac{527}{756}\right)\)	\(e\left(\frac{149}{378}\right)\)	\(e\left(\frac{323}{378}\right)\)	\(e\left(\frac{83}{189}\right)\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{155}{756}\right)\)	\(e\left(\frac{137}{378}\right)\)	\(e\left(\frac{103}{756}\right)\)	\(e\left(\frac{149}{189}\right)\)