Dirichlet character \(\chi_{2349}(1055,\cdot)\)

• Label: 2349.1055
• Modulus: $2349$
• Conductor: $2349$
• Order: $756$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 2349.bu

\(\chi_{2349}(2,\cdot)\) \(\chi_{2349}(11,\cdot)\) \(\chi_{2349}(14,\cdot)\) \(\chi_{2349}(32,\cdot)\) \(\chi_{2349}(47,\cdot)\) \(\chi_{2349}(50,\cdot)\) \(\chi_{2349}(56,\cdot)\) \(\chi_{2349}(68,\cdot)\) \(\chi_{2349}(77,\cdot)\) \(\chi_{2349}(95,\cdot)\) \(\chi_{2349}(101,\cdot)\) \(\chi_{2349}(113,\cdot)\) \(\chi_{2349}(119,\cdot)\) \(\chi_{2349}(131,\cdot)\) \(\chi_{2349}(137,\cdot)\) \(\chi_{2349}(155,\cdot)\) \(\chi_{2349}(164,\cdot)\) \(\chi_{2349}(176,\cdot)\) \(\chi_{2349}(182,\cdot)\) \(\chi_{2349}(185,\cdot)\) \(\chi_{2349}(200,\cdot)\) \(\chi_{2349}(218,\cdot)\) \(\chi_{2349}(221,\cdot)\) \(\chi_{2349}(230,\cdot)\) \(\chi_{2349}(263,\cdot)\) \(\chi_{2349}(272,\cdot)\) \(\chi_{2349}(275,\cdot)\) \(\chi_{2349}(293,\cdot)\) \(\chi_{2349}(308,\cdot)\) \(\chi_{2349}(311,\cdot)\) ...

Related number fields

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

Values on generators

\((407,1945)\) → \((e\left(\frac{1}{54}\right),e\left(\frac{25}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2349 }(1055, a) \)	\(1\)	\(1\)	\(e\left(\frac{689}{756}\right)\)	\(e\left(\frac{311}{378}\right)\)	\(e\left(\frac{13}{189}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{185}{252}\right)\)	\(e\left(\frac{247}{252}\right)\)	\(e\left(\frac{425}{756}\right)\)	\(e\left(\frac{83}{378}\right)\)	\(e\left(\frac{697}{756}\right)\)	\(e\left(\frac{122}{189}\right)\)