Dirichlet character \(\chi_{1156}(999,\cdot)\)

• Label: 1156.999
• Modulus: $1156$
• Conductor: $1156$
• Order: $68$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1156\)
Conductor:	\(1156\)
Order:	\(68\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1156.o

\(\chi_{1156}(47,\cdot)\) \(\chi_{1156}(55,\cdot)\) \(\chi_{1156}(115,\cdot)\) \(\chi_{1156}(123,\cdot)\) \(\chi_{1156}(183,\cdot)\) \(\chi_{1156}(191,\cdot)\) \(\chi_{1156}(259,\cdot)\) \(\chi_{1156}(319,\cdot)\) \(\chi_{1156}(387,\cdot)\) \(\chi_{1156}(395,\cdot)\) \(\chi_{1156}(455,\cdot)\) \(\chi_{1156}(463,\cdot)\) \(\chi_{1156}(523,\cdot)\) \(\chi_{1156}(531,\cdot)\) \(\chi_{1156}(591,\cdot)\) \(\chi_{1156}(599,\cdot)\) \(\chi_{1156}(659,\cdot)\) \(\chi_{1156}(667,\cdot)\) \(\chi_{1156}(727,\cdot)\) \(\chi_{1156}(735,\cdot)\) \(\chi_{1156}(795,\cdot)\) \(\chi_{1156}(803,\cdot)\) \(\chi_{1156}(863,\cdot)\) \(\chi_{1156}(871,\cdot)\) \(\chi_{1156}(931,\cdot)\) \(\chi_{1156}(939,\cdot)\) \(\chi_{1156}(999,\cdot)\) \(\chi_{1156}(1007,\cdot)\) \(\chi_{1156}(1067,\cdot)\) \(\chi_{1156}(1075,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{68})$
Fixed field:	Number field defined by a degree 68 polynomial

Values on generators

\((579,581)\) → \((-1,e\left(\frac{33}{68}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 1156 }(999, a) \)	\(-1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)