Dirichlet character \(\chi_{1183}(1024,\cdot)\)

• Label: 1183.1024
• 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.bz

\(\chi_{1183}(4,\cdot)\) \(\chi_{1183}(95,\cdot)\) \(\chi_{1183}(114,\cdot)\) \(\chi_{1183}(186,\cdot)\) \(\chi_{1183}(205,\cdot)\) \(\chi_{1183}(277,\cdot)\) \(\chi_{1183}(296,\cdot)\) \(\chi_{1183}(368,\cdot)\) \(\chi_{1183}(387,\cdot)\) \(\chi_{1183}(459,\cdot)\) \(\chi_{1183}(478,\cdot)\) \(\chi_{1183}(550,\cdot)\) \(\chi_{1183}(569,\cdot)\) \(\chi_{1183}(641,\cdot)\) \(\chi_{1183}(660,\cdot)\) \(\chi_{1183}(732,\cdot)\) \(\chi_{1183}(751,\cdot)\) \(\chi_{1183}(842,\cdot)\) \(\chi_{1183}(914,\cdot)\) \(\chi_{1183}(933,\cdot)\) \(\chi_{1183}(1005,\cdot)\) \(\chi_{1183}(1024,\cdot)\) \(\chi_{1183}(1096,\cdot)\) \(\chi_{1183}(1115,\cdot)\)

Related number fields

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

Values on generators

\((339,1016)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{5}{78}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(1024, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)