Dirichlet character \(\chi_{1183}(16,\cdot)\)

• Label: 1183.16
• Modulus: $1183$
• Conductor: $1183$
• Order: $39$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1183\)
Conductor:	\(1183\)
Order:	\(39\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1183.bi

\(\chi_{1183}(16,\cdot)\) \(\chi_{1183}(74,\cdot)\) \(\chi_{1183}(107,\cdot)\) \(\chi_{1183}(165,\cdot)\) \(\chi_{1183}(198,\cdot)\) \(\chi_{1183}(256,\cdot)\) \(\chi_{1183}(289,\cdot)\) \(\chi_{1183}(347,\cdot)\) \(\chi_{1183}(380,\cdot)\) \(\chi_{1183}(438,\cdot)\) \(\chi_{1183}(471,\cdot)\) \(\chi_{1183}(562,\cdot)\) \(\chi_{1183}(620,\cdot)\) \(\chi_{1183}(711,\cdot)\) \(\chi_{1183}(744,\cdot)\) \(\chi_{1183}(802,\cdot)\) \(\chi_{1183}(835,\cdot)\) \(\chi_{1183}(893,\cdot)\) \(\chi_{1183}(926,\cdot)\) \(\chi_{1183}(984,\cdot)\) \(\chi_{1183}(1017,\cdot)\) \(\chi_{1183}(1075,\cdot)\) \(\chi_{1183}(1108,\cdot)\) \(\chi_{1183}(1166,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2

Values on generators

\((339,1016)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{39}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(16, a) \)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)