Dirichlet character \(\chi_{2349}(1096,\cdot)\)

• Label: 2349.1096
• Modulus: $2349$
• Conductor: $2349$
• Order: $189$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2349\)
Conductor:	\(2349\)
Order:	\(189\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2349.bo

\(\chi_{2349}(7,\cdot)\) \(\chi_{2349}(16,\cdot)\) \(\chi_{2349}(25,\cdot)\) \(\chi_{2349}(49,\cdot)\) \(\chi_{2349}(52,\cdot)\) \(\chi_{2349}(94,\cdot)\) \(\chi_{2349}(103,\cdot)\) \(\chi_{2349}(112,\cdot)\) \(\chi_{2349}(139,\cdot)\) \(\chi_{2349}(169,\cdot)\) \(\chi_{2349}(223,\cdot)\) \(\chi_{2349}(256,\cdot)\) \(\chi_{2349}(268,\cdot)\) \(\chi_{2349}(277,\cdot)\) \(\chi_{2349}(286,\cdot)\) \(\chi_{2349}(310,\cdot)\) \(\chi_{2349}(313,\cdot)\) \(\chi_{2349}(355,\cdot)\) \(\chi_{2349}(364,\cdot)\) \(\chi_{2349}(373,\cdot)\) \(\chi_{2349}(400,\cdot)\) \(\chi_{2349}(430,\cdot)\) \(\chi_{2349}(484,\cdot)\) \(\chi_{2349}(517,\cdot)\) \(\chi_{2349}(529,\cdot)\) \(\chi_{2349}(538,\cdot)\) \(\chi_{2349}(547,\cdot)\) \(\chi_{2349}(571,\cdot)\) \(\chi_{2349}(574,\cdot)\) \(\chi_{2349}(616,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{189})$
Fixed field:	Number field defined by a degree 189 polynomial (not computed)

Values on generators

\((407,1945)\) → \((e\left(\frac{11}{27}\right),e\left(\frac{5}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 2349 }(1096, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{189}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{16}{189}\right)\)	\(e\left(\frac{17}{189}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{29}{189}\right)\)	\(e\left(\frac{22}{189}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{92}{189}\right)\)