Dirichlet character \(\chi_{11319}(389,\cdot)\)

• Label: 11319.389
• Modulus: $11319$
• Conductor: $11319$
• Order: $1470$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(11319\)
Conductor:	\(11319\)
Order:	\(1470\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 11319.dp

\(\chi_{11319}(53,\cdot)\) \(\chi_{11319}(86,\cdot)\) \(\chi_{11319}(137,\cdot)\) \(\chi_{11319}(158,\cdot)\) \(\chi_{11319}(170,\cdot)\) \(\chi_{11319}(179,\cdot)\) \(\chi_{11319}(191,\cdot)\) \(\chi_{11319}(212,\cdot)\) \(\chi_{11319}(284,\cdot)\) \(\chi_{11319}(317,\cdot)\) \(\chi_{11319}(368,\cdot)\) \(\chi_{11319}(389,\cdot)\) \(\chi_{11319}(401,\cdot)\) \(\chi_{11319}(443,\cdot)\) \(\chi_{11319}(515,\cdot)\) \(\chi_{11319}(548,\cdot)\) \(\chi_{11319}(599,\cdot)\) \(\chi_{11319}(620,\cdot)\) \(\chi_{11319}(632,\cdot)\) \(\chi_{11319}(641,\cdot)\) \(\chi_{11319}(653,\cdot)\) \(\chi_{11319}(674,\cdot)\) \(\chi_{11319}(746,\cdot)\) \(\chi_{11319}(779,\cdot)\) \(\chi_{11319}(830,\cdot)\) \(\chi_{11319}(872,\cdot)\) \(\chi_{11319}(884,\cdot)\) \(\chi_{11319}(905,\cdot)\) \(\chi_{11319}(977,\cdot)\) \(\chi_{11319}(1061,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{735})$
Fixed field:	Number field defined by a degree 1470 polynomial (not computed)

Values on generators

\((7547,3433,2059)\) → \((-1,e\left(\frac{32}{147}\right),e\left(\frac{1}{5}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 11319 }(389, a) \)	\(-1\)	\(1\)	\(e\left(\frac{1369}{1470}\right)\)	\(e\left(\frac{634}{735}\right)\)	\(e\left(\frac{901}{1470}\right)\)	\(e\left(\frac{389}{490}\right)\)	\(e\left(\frac{80}{147}\right)\)	\(e\left(\frac{59}{245}\right)\)	\(e\left(\frac{533}{735}\right)\)	\(e\left(\frac{1091}{1470}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{233}{490}\right)\)