Dirichlet character \(\chi_{1183}(600,\cdot)\)

• Label: 1183.600
• 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.cd

\(\chi_{1183}(45,\cdot)\) \(\chi_{1183}(54,\cdot)\) \(\chi_{1183}(59,\cdot)\) \(\chi_{1183}(136,\cdot)\) \(\chi_{1183}(145,\cdot)\) \(\chi_{1183}(180,\cdot)\) \(\chi_{1183}(227,\cdot)\) \(\chi_{1183}(236,\cdot)\) \(\chi_{1183}(241,\cdot)\) \(\chi_{1183}(271,\cdot)\) \(\chi_{1183}(318,\cdot)\) \(\chi_{1183}(327,\cdot)\) \(\chi_{1183}(332,\cdot)\) \(\chi_{1183}(362,\cdot)\) \(\chi_{1183}(409,\cdot)\) \(\chi_{1183}(423,\cdot)\) \(\chi_{1183}(453,\cdot)\) \(\chi_{1183}(500,\cdot)\) \(\chi_{1183}(509,\cdot)\) \(\chi_{1183}(514,\cdot)\) \(\chi_{1183}(544,\cdot)\) \(\chi_{1183}(591,\cdot)\) \(\chi_{1183}(600,\cdot)\) \(\chi_{1183}(605,\cdot)\) \(\chi_{1183}(635,\cdot)\) \(\chi_{1183}(682,\cdot)\) \(\chi_{1183}(691,\cdot)\) \(\chi_{1183}(696,\cdot)\) \(\chi_{1183}(726,\cdot)\) \(\chi_{1183}(773,\cdot)\) ...

Related number fields

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

Values on generators

\((339,1016)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{145}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(600, a) \)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)