Dirichlet character \(\chi_{5041}(522,\cdot)\)

• Label: 5041.522
• Modulus: $5041$
• Conductor: $5041$
• Order: $355$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5041\)
Conductor:	\(5041\)
Order:	\(355\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 5041.k

\(\chi_{5041}(5,\cdot)\) \(\chi_{5041}(25,\cdot)\) \(\chi_{5041}(54,\cdot)\) \(\chi_{5041}(57,\cdot)\) \(\chi_{5041}(76,\cdot)\) \(\chi_{5041}(96,\cdot)\) \(\chi_{5041}(125,\cdot)\) \(\chi_{5041}(128,\cdot)\) \(\chi_{5041}(147,\cdot)\) \(\chi_{5041}(167,\cdot)\) \(\chi_{5041}(196,\cdot)\) \(\chi_{5041}(199,\cdot)\) \(\chi_{5041}(218,\cdot)\) \(\chi_{5041}(238,\cdot)\) \(\chi_{5041}(267,\cdot)\) \(\chi_{5041}(270,\cdot)\) \(\chi_{5041}(289,\cdot)\) \(\chi_{5041}(309,\cdot)\) \(\chi_{5041}(338,\cdot)\) \(\chi_{5041}(341,\cdot)\) \(\chi_{5041}(360,\cdot)\) \(\chi_{5041}(380,\cdot)\) \(\chi_{5041}(409,\cdot)\) \(\chi_{5041}(412,\cdot)\) \(\chi_{5041}(431,\cdot)\) \(\chi_{5041}(451,\cdot)\) \(\chi_{5041}(480,\cdot)\) \(\chi_{5041}(483,\cdot)\) \(\chi_{5041}(502,\cdot)\) \(\chi_{5041}(522,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{355})$
Fixed field:	Number field defined by a degree 355 polynomial (not computed)

Values on generators

\(7\) → \(e\left(\frac{219}{355}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 5041 }(522, a) \)	\(1\)	\(1\)	\(e\left(\frac{149}{355}\right)\)	\(e\left(\frac{254}{355}\right)\)	\(e\left(\frac{298}{355}\right)\)	\(e\left(\frac{97}{355}\right)\)	\(e\left(\frac{48}{355}\right)\)	\(e\left(\frac{219}{355}\right)\)	\(e\left(\frac{92}{355}\right)\)	\(e\left(\frac{153}{355}\right)\)	\(e\left(\frac{246}{355}\right)\)	\(e\left(\frac{4}{5}\right)\)