Dirichlet character \(\chi_{5041}(174,\cdot)\)

• Label: 5041.174
• Modulus: $5041$
• Conductor: $5041$
• Order: $497$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5041\)
Conductor:	\(5041\)
Order:	\(497\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5041.l

\(\chi_{5041}(20,\cdot)\) \(\chi_{5041}(30,\cdot)\) \(\chi_{5041}(32,\cdot)\) \(\chi_{5041}(37,\cdot)\) \(\chi_{5041}(45,\cdot)\) \(\chi_{5041}(48,\cdot)\) \(\chi_{5041}(91,\cdot)\) \(\chi_{5041}(101,\cdot)\) \(\chi_{5041}(103,\cdot)\) \(\chi_{5041}(108,\cdot)\) \(\chi_{5041}(116,\cdot)\) \(\chi_{5041}(119,\cdot)\) \(\chi_{5041}(162,\cdot)\) \(\chi_{5041}(172,\cdot)\) \(\chi_{5041}(174,\cdot)\) \(\chi_{5041}(179,\cdot)\) \(\chi_{5041}(187,\cdot)\) \(\chi_{5041}(190,\cdot)\) \(\chi_{5041}(233,\cdot)\) \(\chi_{5041}(243,\cdot)\) \(\chi_{5041}(245,\cdot)\) \(\chi_{5041}(250,\cdot)\) \(\chi_{5041}(258,\cdot)\) \(\chi_{5041}(304,\cdot)\) \(\chi_{5041}(314,\cdot)\) \(\chi_{5041}(316,\cdot)\) \(\chi_{5041}(321,\cdot)\) \(\chi_{5041}(329,\cdot)\) \(\chi_{5041}(332,\cdot)\) \(\chi_{5041}(375,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{497})$
Fixed field:	Number field defined by a degree 497 polynomial (not computed)

Values on generators

\(7\) → \(e\left(\frac{87}{497}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 5041 }(174, a) \)	\(1\)	\(1\)	\(e\left(\frac{137}{497}\right)\)	\(e\left(\frac{204}{497}\right)\)	\(e\left(\frac{274}{497}\right)\)	\(e\left(\frac{64}{71}\right)\)	\(e\left(\frac{341}{497}\right)\)	\(e\left(\frac{87}{497}\right)\)	\(e\left(\frac{411}{497}\right)\)	\(e\left(\frac{408}{497}\right)\)	\(e\left(\frac{88}{497}\right)\)	\(e\left(\frac{2}{7}\right)\)