Dirichlet character \(\chi_{508288}(1251,\cdot)\)

• Label: 508288.1251
• 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.wd

\(\chi_{508288}(35,\cdot)\) \(\chi_{508288}(123,\cdot)\) \(\chi_{508288}(139,\cdot)\) \(\chi_{508288}(195,\cdot)\) \(\chi_{508288}(283,\cdot)\) \(\chi_{508288}(347,\cdot)\) \(\chi_{508288}(403,\cdot)\) \(\chi_{508288}(435,\cdot)\) \(\chi_{508288}(491,\cdot)\) \(\chi_{508288}(579,\cdot)\) \(\chi_{508288}(651,\cdot)\) \(\chi_{508288}(739,\cdot)\) \(\chi_{508288}(899,\cdot)\) \(\chi_{508288}(1051,\cdot)\) \(\chi_{508288}(1107,\cdot)\) \(\chi_{508288}(1163,\cdot)\) \(\chi_{508288}(1195,\cdot)\) \(\chi_{508288}(1251,\cdot)\) \(\chi_{508288}(1315,\cdot)\) \(\chi_{508288}(1339,\cdot)\) \(\chi_{508288}(1355,\cdot)\) \(\chi_{508288}(1403,\cdot)\) \(\chi_{508288}(1491,\cdot)\)

Related number fields

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

Values on generators

\((166783,174725,323457,14081)\) → \((-1,e\left(\frac{27}{32}\right),e\left(\frac{3}{10}\right),e\left(\frac{146}{171}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 508288 }(1251, a) \)	\(1\)	\(1\)	\(e\left(\frac{2999}{27360}\right)\)	\(e\left(\frac{3437}{27360}\right)\)	\(e\left(\frac{491}{4560}\right)\)	\(e\left(\frac{2999}{13680}\right)\)	\(e\left(\frac{23443}{27360}\right)\)	\(e\left(\frac{1609}{6840}\right)\)	\(e\left(\frac{1943}{6840}\right)\)	\(e\left(\frac{1189}{5472}\right)\)	\(e\left(\frac{2647}{2736}\right)\)	\(e\left(\frac{3437}{13680}\right)\)