Dirichlet character \(\chi_{19355}(17078,\cdot)\)

• Label: 19355.17078
• Modulus: $19355$
• Conductor: $19355$
• Order: $1092$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(19355\)
Conductor:	\(19355\)
Order:	\(1092\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 19355.jf

\(\chi_{19355}(12,\cdot)\) \(\chi_{19355}(17,\cdot)\) \(\chi_{19355}(33,\cdot)\) \(\chi_{19355}(173,\cdot)\) \(\chi_{19355}(278,\cdot)\) \(\chi_{19355}(453,\cdot)\) \(\chi_{19355}(488,\cdot)\) \(\chi_{19355}(507,\cdot)\) \(\chi_{19355}(647,\cdot)\) \(\chi_{19355}(703,\cdot)\) \(\chi_{19355}(738,\cdot)\) \(\chi_{19355}(752,\cdot)\) \(\chi_{19355}(768,\cdot)\) \(\chi_{19355}(782,\cdot)\) \(\chi_{19355}(817,\cdot)\) \(\chi_{19355}(927,\cdot)\) \(\chi_{19355}(1088,\cdot)\) \(\chi_{19355}(1118,\cdot)\) \(\chi_{19355}(1123,\cdot)\) \(\chi_{19355}(1167,\cdot)\) \(\chi_{19355}(1202,\cdot)\) \(\chi_{19355}(1242,\cdot)\) \(\chi_{19355}(1333,\cdot)\) \(\chi_{19355}(1412,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{1092})$
Fixed field:	Number field defined by a degree 1092 polynomial (not computed)

Values on generators

\((3872,6716,4901)\) → \((-i,e\left(\frac{17}{42}\right),e\left(\frac{19}{26}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\( \chi_{ 19355 }(17078, a) \)	\(-1\)	\(1\)	\(e\left(\frac{215}{1092}\right)\)	\(e\left(\frac{421}{1092}\right)\)	\(e\left(\frac{215}{546}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{215}{364}\right)\)	\(e\left(\frac{421}{546}\right)\)	\(e\left(\frac{241}{273}\right)\)	\(e\left(\frac{851}{1092}\right)\)	\(e\left(\frac{165}{364}\right)\)	\(e\left(\frac{215}{273}\right)\)