Dirichlet character \(\chi_{1183}(1123,\cdot)\)

• Label: 1183.1123
• Modulus: $1183$
• Conductor: $1183$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1183\)
Conductor:	\(1183\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1183.cc

\(\chi_{1183}(5,\cdot)\) \(\chi_{1183}(31,\cdot)\) \(\chi_{1183}(47,\cdot)\) \(\chi_{1183}(73,\cdot)\) \(\chi_{1183}(96,\cdot)\) \(\chi_{1183}(122,\cdot)\) \(\chi_{1183}(138,\cdot)\) \(\chi_{1183}(164,\cdot)\) \(\chi_{1183}(187,\cdot)\) \(\chi_{1183}(213,\cdot)\) \(\chi_{1183}(229,\cdot)\) \(\chi_{1183}(255,\cdot)\) \(\chi_{1183}(278,\cdot)\) \(\chi_{1183}(304,\cdot)\) \(\chi_{1183}(320,\cdot)\) \(\chi_{1183}(346,\cdot)\) \(\chi_{1183}(369,\cdot)\) \(\chi_{1183}(395,\cdot)\) \(\chi_{1183}(411,\cdot)\) \(\chi_{1183}(460,\cdot)\) \(\chi_{1183}(486,\cdot)\) \(\chi_{1183}(502,\cdot)\) \(\chi_{1183}(528,\cdot)\) \(\chi_{1183}(551,\cdot)\) \(\chi_{1183}(593,\cdot)\) \(\chi_{1183}(619,\cdot)\) \(\chi_{1183}(642,\cdot)\) \(\chi_{1183}(668,\cdot)\) \(\chi_{1183}(684,\cdot)\) \(\chi_{1183}(710,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{19}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(1123, a) \)	\(1\)	\(1\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)