Dirichlet character \(\chi_{1183}(748,\cdot)\)

• Label: 1183.748
• 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.cb

\(\chi_{1183}(6,\cdot)\) \(\chi_{1183}(20,\cdot)\) \(\chi_{1183}(41,\cdot)\) \(\chi_{1183}(76,\cdot)\) \(\chi_{1183}(97,\cdot)\) \(\chi_{1183}(111,\cdot)\) \(\chi_{1183}(132,\cdot)\) \(\chi_{1183}(167,\cdot)\) \(\chi_{1183}(202,\cdot)\) \(\chi_{1183}(223,\cdot)\) \(\chi_{1183}(279,\cdot)\) \(\chi_{1183}(293,\cdot)\) \(\chi_{1183}(314,\cdot)\) \(\chi_{1183}(349,\cdot)\) \(\chi_{1183}(370,\cdot)\) \(\chi_{1183}(384,\cdot)\) \(\chi_{1183}(405,\cdot)\) \(\chi_{1183}(440,\cdot)\) \(\chi_{1183}(461,\cdot)\) \(\chi_{1183}(475,\cdot)\) \(\chi_{1183}(496,\cdot)\) \(\chi_{1183}(531,\cdot)\) \(\chi_{1183}(552,\cdot)\) \(\chi_{1183}(566,\cdot)\) \(\chi_{1183}(622,\cdot)\) \(\chi_{1183}(643,\cdot)\) \(\chi_{1183}(678,\cdot)\) \(\chi_{1183}(713,\cdot)\) \(\chi_{1183}(734,\cdot)\) \(\chi_{1183}(748,\cdot)\) ...

Related number fields

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

Values on generators

\((339,1016)\) → \((-1,e\left(\frac{95}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 1183 }(748, a) \)	\(1\)	\(1\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{3}{13}\right)\)