Dirichlet character \(\chi_{508288}(971,\cdot)\)

• Label: 508288.971
• Modulus: $508288$
• Conductor: $508288$
• Order: $27360$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 508288.wc

\(\chi_{508288}(3,\cdot)\) \(\chi_{508288}(59,\cdot)\) \(\chi_{508288}(91,\cdot)\) \(\chi_{508288}(147,\cdot)\) \(\chi_{508288}(203,\cdot)\) \(\chi_{508288}(355,\cdot)\) \(\chi_{508288}(515,\cdot)\) \(\chi_{508288}(603,\cdot)\) \(\chi_{508288}(675,\cdot)\) \(\chi_{508288}(763,\cdot)\) \(\chi_{508288}(819,\cdot)\) \(\chi_{508288}(851,\cdot)\) \(\chi_{508288}(907,\cdot)\) \(\chi_{508288}(971,\cdot)\) \(\chi_{508288}(1059,\cdot)\) \(\chi_{508288}(1115,\cdot)\) \(\chi_{508288}(1131,\cdot)\) \(\chi_{508288}(1219,\cdot)\) \(\chi_{508288}(1307,\cdot)\) \(\chi_{508288}(1435,\cdot)\) \(\chi_{508288}(1523,\cdot)\)

Related number fields

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

Values on generators

\((166783,174725,323457,14081)\) → \((-1,e\left(\frac{5}{32}\right),e\left(\frac{4}{5}\right),e\left(\frac{325}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(971, a) \)	\(1\)	\(1\)	\(e\left(\frac{12569}{27360}\right)\)	\(e\left(\frac{22547}{27360}\right)\)	\(e\left(\frac{941}{4560}\right)\)	\(e\left(\frac{12569}{13680}\right)\)	\(e\left(\frac{21613}{27360}\right)\)	\(e\left(\frac{1939}{6840}\right)\)	\(e\left(\frac{2333}{6840}\right)\)	\(e\left(\frac{3643}{5472}\right)\)	\(e\left(\frac{1177}{2736}\right)\)	\(e\left(\frac{8867}{13680}\right)\)