Dirichlet character \(\chi_{1183}(1117,\cdot)\)

• Label: 1183.1117
• Modulus: $1183$
• Conductor: $1183$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1183\)
Conductor:	\(1183\)
Order:	\(78\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1183.bs

\(\chi_{1183}(25,\cdot)\) \(\chi_{1183}(51,\cdot)\) \(\chi_{1183}(116,\cdot)\) \(\chi_{1183}(142,\cdot)\) \(\chi_{1183}(207,\cdot)\) \(\chi_{1183}(233,\cdot)\) \(\chi_{1183}(298,\cdot)\) \(\chi_{1183}(324,\cdot)\) \(\chi_{1183}(389,\cdot)\) \(\chi_{1183}(415,\cdot)\) \(\chi_{1183}(480,\cdot)\) \(\chi_{1183}(571,\cdot)\) \(\chi_{1183}(597,\cdot)\) \(\chi_{1183}(662,\cdot)\) \(\chi_{1183}(688,\cdot)\) \(\chi_{1183}(753,\cdot)\) \(\chi_{1183}(779,\cdot)\) \(\chi_{1183}(870,\cdot)\) \(\chi_{1183}(935,\cdot)\) \(\chi_{1183}(961,\cdot)\) \(\chi_{1183}(1026,\cdot)\) \(\chi_{1183}(1052,\cdot)\) \(\chi_{1183}(1117,\cdot)\) \(\chi_{1183}(1143,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

\((339,1016)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(1117, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)