Dirichlet character \(\chi_{8041}(589,\cdot)\)

• Label: 8041.589
• Modulus: $8041$
• Conductor: $8041$
• Order: $1680$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(8041\)
Conductor:	\(8041\)
Order:	\(1680\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 8041.ga

\(\chi_{8041}(28,\cdot)\) \(\chi_{8041}(29,\cdot)\) \(\chi_{8041}(46,\cdot)\) \(\chi_{8041}(61,\cdot)\) \(\chi_{8041}(62,\cdot)\) \(\chi_{8041}(63,\cdot)\) \(\chi_{8041}(73,\cdot)\) \(\chi_{8041}(105,\cdot)\) \(\chi_{8041}(112,\cdot)\) \(\chi_{8041}(116,\cdot)\) \(\chi_{8041}(184,\cdot)\) \(\chi_{8041}(227,\cdot)\) \(\chi_{8041}(233,\cdot)\) \(\chi_{8041}(244,\cdot)\) \(\chi_{8041}(248,\cdot)\) \(\chi_{8041}(249,\cdot)\) \(\chi_{8041}(261,\cdot)\) \(\chi_{8041}(277,\cdot)\) \(\chi_{8041}(292,\cdot)\) \(\chi_{8041}(347,\cdot)\) \(\chi_{8041}(413,\cdot)\) \(\chi_{8041}(415,\cdot)\) \(\chi_{8041}(420,\cdot)\) \(\chi_{8041}(435,\cdot)\) \(\chi_{8041}(448,\cdot)\) \(\chi_{8041}(464,\cdot)\) \(\chi_{8041}(503,\cdot)\) \(\chi_{8041}(534,\cdot)\) \(\chi_{8041}(585,\cdot)\) \(\chi_{8041}(589,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{1680})$
Fixed field:	Number field defined by a degree 1680 polynomial (not computed)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{7}{16}\right),e\left(\frac{11}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(589, a) \)	\(-1\)	\(1\)	\(e\left(\frac{27}{280}\right)\)	\(e\left(\frac{1511}{1680}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{563}{1680}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{81}{280}\right)\)	\(e\left(\frac{671}{840}\right)\)	\(e\left(\frac{145}{336}\right)\)	\(e\left(\frac{31}{336}\right)\)