Dirichlet character \(\chi_{8041}(20,\cdot)\)

• Label: 8041.20
• Modulus: $8041$
• Conductor: $8041$
• Order: $1680$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 8041.gd

\(\chi_{8041}(3,\cdot)\) \(\chi_{8041}(5,\cdot)\) \(\chi_{8041}(20,\cdot)\) \(\chi_{8041}(48,\cdot)\) \(\chi_{8041}(71,\cdot)\) \(\chi_{8041}(91,\cdot)\) \(\chi_{8041}(114,\cdot)\) \(\chi_{8041}(141,\cdot)\) \(\chi_{8041}(147,\cdot)\) \(\chi_{8041}(148,\cdot)\) \(\chi_{8041}(158,\cdot)\) \(\chi_{8041}(159,\cdot)\) \(\chi_{8041}(163,\cdot)\) \(\chi_{8041}(190,\cdot)\) \(\chi_{8041}(192,\cdot)\) \(\chi_{8041}(201,\cdot)\) \(\chi_{8041}(218,\cdot)\) \(\chi_{8041}(235,\cdot)\) \(\chi_{8041}(245,\cdot)\) \(\chi_{8041}(278,\cdot)\) \(\chi_{8041}(284,\cdot)\) \(\chi_{8041}(313,\cdot)\) \(\chi_{8041}(334,\cdot)\) \(\chi_{8041}(335,\cdot)\) \(\chi_{8041}(377,\cdot)\) \(\chi_{8041}(405,\cdot)\) \(\chi_{8041}(449,\cdot)\) \(\chi_{8041}(456,\cdot)\) \(\chi_{8041}(499,\cdot)\) \(\chi_{8041}(521,\cdot)\) ...

Related number fields

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

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{16}\right),e\left(\frac{37}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(20, a) \)	\(1\)	\(1\)	\(e\left(\frac{73}{280}\right)\)	\(e\left(\frac{1249}{1680}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{1237}{1680}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{219}{280}\right)\)	\(e\left(\frac{409}{840}\right)\)	\(e\left(\frac{335}{336}\right)\)	\(e\left(\frac{89}{336}\right)\)