Dirichlet character \(\chi_{508288}(1459,\cdot)\)

• Label: 508288.1459
• Modulus: $508288$
• Conductor: $508288$
• Order: $27360$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(508288\)
Conductor:	\(508288\)
Order:	\(27360\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 508288.vy

\(\chi_{508288}(51,\cdot)\) \(\chi_{508288}(211,\cdot)\) \(\chi_{508288}(371,\cdot)\) \(\chi_{508288}(459,\cdot)\) \(\chi_{508288}(523,\cdot)\) \(\chi_{508288}(547,\cdot)\) \(\chi_{508288}(611,\cdot)\) \(\chi_{508288}(667,\cdot)\) \(\chi_{508288}(699,\cdot)\) \(\chi_{508288}(755,\cdot)\) \(\chi_{508288}(811,\cdot)\) \(\chi_{508288}(827,\cdot)\) \(\chi_{508288}(915,\cdot)\) \(\chi_{508288}(963,\cdot)\) \(\chi_{508288}(1003,\cdot)\) \(\chi_{508288}(1267,\cdot)\) \(\chi_{508288}(1283,\cdot)\) \(\chi_{508288}(1371,\cdot)\) \(\chi_{508288}(1427,\cdot)\) \(\chi_{508288}(1459,\cdot)\) \(\chi_{508288}(1515,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{27360})$
Fixed field:	Number field defined by a degree 27360 polynomial (not computed)

Values on generators

\((166783,174725,323457,14081)\) → \((-1,e\left(\frac{31}{32}\right),e\left(\frac{7}{10}\right),e\left(\frac{29}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(1459, a) \)	\(-1\)	\(1\)	\(e\left(\frac{21691}{27360}\right)\)	\(e\left(\frac{12073}{27360}\right)\)	\(e\left(\frac{3679}{4560}\right)\)	\(e\left(\frac{8011}{13680}\right)\)	\(e\left(\frac{3527}{27360}\right)\)	\(e\left(\frac{1601}{6840}\right)\)	\(e\left(\frac{4027}{6840}\right)\)	\(e\left(\frac{3281}{5472}\right)\)	\(e\left(\frac{1211}{2736}\right)\)	\(e\left(\frac{12073}{13680}\right)\)