Dirichlet character \(\chi_{8041}(978,\cdot)\)

• Label: 8041.978
• Modulus: $8041$
• Conductor: $8041$
• Order: $56$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8041\)
Conductor:	\(8041\)
Order:	\(56\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8041.dh

\(\chi_{8041}(32,\cdot)\) \(\chi_{8041}(604,\cdot)\) \(\chi_{8041}(978,\cdot)\) \(\chi_{8041}(1011,\cdot)\) \(\chi_{8041}(1341,\cdot)\) \(\chi_{8041}(1759,\cdot)\) \(\chi_{8041}(1957,\cdot)\) \(\chi_{8041}(2287,\cdot)\) \(\chi_{8041}(2650,\cdot)\) \(\chi_{8041}(2705,\cdot)\) \(\chi_{8041}(3442,\cdot)\) \(\chi_{8041}(3596,\cdot)\) \(\chi_{8041}(3816,\cdot)\) \(\chi_{8041}(4388,\cdot)\) \(\chi_{8041}(4762,\cdot)\) \(\chi_{8041}(5125,\cdot)\) \(\chi_{8041}(5268,\cdot)\) \(\chi_{8041}(6016,\cdot)\) \(\chi_{8041}(6071,\cdot)\) \(\chi_{8041}(6214,\cdot)\) \(\chi_{8041}(6434,\cdot)\) \(\chi_{8041}(6962,\cdot)\) \(\chi_{8041}(7380,\cdot)\) \(\chi_{8041}(7699,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Values on generators

\((6580,2366,562)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{3}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(978, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)