Dirichlet character \(\chi_{8041}(193,\cdot)\)

• Label: 8041.193
• Modulus: $8041$
• Conductor: $8041$
• Order: $560$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8041\)
Conductor:	\(8041\)
Order:	\(560\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8041.fs

\(\chi_{8041}(41,\cdot)\) \(\chi_{8041}(90,\cdot)\) \(\chi_{8041}(107,\cdot)\) \(\chi_{8041}(150,\cdot)\) \(\chi_{8041}(193,\cdot)\) \(\chi_{8041}(226,\cdot)\) \(\chi_{8041}(250,\cdot)\) \(\chi_{8041}(299,\cdot)\) \(\chi_{8041}(360,\cdot)\) \(\chi_{8041}(398,\cdot)\) \(\chi_{8041}(403,\cdot)\) \(\chi_{8041}(600,\cdot)\) \(\chi_{8041}(618,\cdot)\) \(\chi_{8041}(623,\cdot)\) \(\chi_{8041}(656,\cdot)\) \(\chi_{8041}(666,\cdot)\) \(\chi_{8041}(772,\cdot)\) \(\chi_{8041}(809,\cdot)\) \(\chi_{8041}(821,\cdot)\) \(\chi_{8041}(838,\cdot)\) \(\chi_{8041}(864,\cdot)\) \(\chi_{8041}(981,\cdot)\) \(\chi_{8041}(1030,\cdot)\) \(\chi_{8041}(1091,\cdot)\) \(\chi_{8041}(1129,\cdot)\) \(\chi_{8041}(1196,\cdot)\) \(\chi_{8041}(1251,\cdot)\) \(\chi_{8041}(1282,\cdot)\) \(\chi_{8041}(1306,\cdot)\) \(\chi_{8041}(1337,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{560})$
Fixed field:	Number field defined by a degree 560 polynomial (not computed)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{15}{16}\right),e\left(\frac{6}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(193, a) \)	\(1\)	\(1\)	\(e\left(\frac{47}{280}\right)\)	\(e\left(\frac{557}{560}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{401}{560}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{141}{280}\right)\)	\(e\left(\frac{277}{280}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{37}{112}\right)\)