Dirichlet character \(\chi_{1083}(287,\cdot)\)

• Label: 1083.287
• Modulus: $1083$
• Conductor: $1083$
• Order: $342$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1083\)
Conductor:	\(1083\)
Order:	\(342\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1083.x

\(\chi_{1083}(2,\cdot)\) \(\chi_{1083}(14,\cdot)\) \(\chi_{1083}(29,\cdot)\) \(\chi_{1083}(32,\cdot)\) \(\chi_{1083}(41,\cdot)\) \(\chi_{1083}(53,\cdot)\) \(\chi_{1083}(59,\cdot)\) \(\chi_{1083}(71,\cdot)\) \(\chi_{1083}(86,\cdot)\) \(\chi_{1083}(89,\cdot)\) \(\chi_{1083}(98,\cdot)\) \(\chi_{1083}(110,\cdot)\) \(\chi_{1083}(128,\cdot)\) \(\chi_{1083}(143,\cdot)\) \(\chi_{1083}(146,\cdot)\) \(\chi_{1083}(155,\cdot)\) \(\chi_{1083}(167,\cdot)\) \(\chi_{1083}(173,\cdot)\) \(\chi_{1083}(185,\cdot)\) \(\chi_{1083}(200,\cdot)\) \(\chi_{1083}(203,\cdot)\) \(\chi_{1083}(212,\cdot)\) \(\chi_{1083}(224,\cdot)\) \(\chi_{1083}(230,\cdot)\) \(\chi_{1083}(242,\cdot)\) \(\chi_{1083}(257,\cdot)\) \(\chi_{1083}(260,\cdot)\) \(\chi_{1083}(269,\cdot)\) \(\chi_{1083}(281,\cdot)\) \(\chi_{1083}(287,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

Values on generators

\((362,724)\) → \((-1,e\left(\frac{217}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 1083 }(287, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{257}{342}\right)\)	\(e\left(\frac{53}{171}\right)\)	\(e\left(\frac{92}{171}\right)\)