Dirichlet character \(\chi_{8041}(180,\cdot)\)

• Label: 8041.180
• 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.ft

\(\chi_{8041}(27,\cdot)\) \(\chi_{8041}(75,\cdot)\) \(\chi_{8041}(82,\cdot)\) \(\chi_{8041}(108,\cdot)\) \(\chi_{8041}(113,\cdot)\) \(\chi_{8041}(125,\cdot)\) \(\chi_{8041}(180,\cdot)\) \(\chi_{8041}(328,\cdot)\) \(\chi_{8041}(333,\cdot)\) \(\chi_{8041}(346,\cdot)\) \(\chi_{8041}(432,\cdot)\) \(\chi_{8041}(500,\cdot)\) \(\chi_{8041}(555,\cdot)\) \(\chi_{8041}(581,\cdot)\) \(\chi_{8041}(598,\cdot)\) \(\chi_{8041}(641,\cdot)\) \(\chi_{8041}(653,\cdot)\) \(\chi_{8041}(720,\cdot)\) \(\chi_{8041}(753,\cdot)\) \(\chi_{8041}(796,\cdot)\) \(\chi_{8041}(806,\cdot)\) \(\chi_{8041}(819,\cdot)\) \(\chi_{8041}(839,\cdot)\) \(\chi_{8041}(856,\cdot)\) \(\chi_{8041}(862,\cdot)\) \(\chi_{8041}(911,\cdot)\) \(\chi_{8041}(1059,\cdot)\) \(\chi_{8041}(1083,\cdot)\) \(\chi_{8041}(1193,\cdot)\) \(\chi_{8041}(1236,\cdot)\) ...

Related number fields

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

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{3}{16}\right),e\left(\frac{13}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(180, a) \)	\(1\)	\(1\)	\(e\left(\frac{251}{280}\right)\)	\(e\left(\frac{401}{560}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{533}{560}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{193}{280}\right)\)	\(e\left(\frac{121}{280}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{57}{112}\right)\)