Dirichlet character \(\chi_{1183}(1116,\cdot)\)

• Label: 1183.1116
• 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.ch

\(\chi_{1183}(24,\cdot)\) \(\chi_{1183}(33,\cdot)\) \(\chi_{1183}(110,\cdot)\) \(\chi_{1183}(115,\cdot)\) \(\chi_{1183}(124,\cdot)\) \(\chi_{1183}(171,\cdot)\) \(\chi_{1183}(201,\cdot)\) \(\chi_{1183}(206,\cdot)\) \(\chi_{1183}(215,\cdot)\) \(\chi_{1183}(262,\cdot)\) \(\chi_{1183}(292,\cdot)\) \(\chi_{1183}(297,\cdot)\) \(\chi_{1183}(306,\cdot)\) \(\chi_{1183}(353,\cdot)\) \(\chi_{1183}(383,\cdot)\) \(\chi_{1183}(388,\cdot)\) \(\chi_{1183}(397,\cdot)\) \(\chi_{1183}(444,\cdot)\) \(\chi_{1183}(474,\cdot)\) \(\chi_{1183}(479,\cdot)\) \(\chi_{1183}(535,\cdot)\) \(\chi_{1183}(565,\cdot)\) \(\chi_{1183}(570,\cdot)\) \(\chi_{1183}(579,\cdot)\) \(\chi_{1183}(626,\cdot)\) \(\chi_{1183}(656,\cdot)\) \(\chi_{1183}(661,\cdot)\) \(\chi_{1183}(670,\cdot)\) \(\chi_{1183}(717,\cdot)\) \(\chi_{1183}(747,\cdot)\) ...

Related number fields

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

Values on generators

\((339,1016)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{115}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(1116, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)