Dirichlet character \(\chi_{508288}(1325,\cdot)\)

• Label: 508288.1325
• 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.wa

\(\chi_{508288}(53,\cdot)\) \(\chi_{508288}(181,\cdot)\) \(\chi_{508288}(269,\cdot)\) \(\chi_{508288}(317,\cdot)\) \(\chi_{508288}(357,\cdot)\) \(\chi_{508288}(421,\cdot)\) \(\chi_{508288}(509,\cdot)\) \(\chi_{508288}(565,\cdot)\) \(\chi_{508288}(621,\cdot)\) \(\chi_{508288}(773,\cdot)\) \(\chi_{508288}(933,\cdot)\) \(\chi_{508288}(1093,\cdot)\) \(\chi_{508288}(1181,\cdot)\) \(\chi_{508288}(1237,\cdot)\) \(\chi_{508288}(1269,\cdot)\) \(\chi_{508288}(1325,\cdot)\) \(\chi_{508288}(1389,\cdot)\) \(\chi_{508288}(1477,\cdot)\) \(\chi_{508288}(1533,\cdot)\) \(\chi_{508288}(1549,\cdot)\)

Related number fields

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

Values on generators

\((166783,174725,323457,14081)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{2}{5}\right),e\left(\frac{205}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(1325, a) \)	\(-1\)	\(1\)	\(e\left(\frac{4787}{27360}\right)\)	\(e\left(\frac{24161}{27360}\right)\)	\(e\left(\frac{4103}{4560}\right)\)	\(e\left(\frac{4787}{13680}\right)\)	\(e\left(\frac{24319}{27360}\right)\)	\(e\left(\frac{397}{6840}\right)\)	\(e\left(\frac{1319}{6840}\right)\)	\(e\left(\frac{409}{5472}\right)\)	\(e\left(\frac{1579}{2736}\right)\)	\(e\left(\frac{10481}{13680}\right)\)