Dirichlet character \(\chi_{8041}(614,\cdot)\)

• Label: 8041.614
• Modulus: $8041$
• Conductor: $8041$
• Order: $840$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(8041\)
Conductor:	\(8041\)
Order:	\(840\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 8041.fz

\(\chi_{8041}(26,\cdot)\) \(\chi_{8041}(104,\cdot)\) \(\chi_{8041}(202,\cdot)\) \(\chi_{8041}(291,\cdot)\) \(\chi_{8041}(372,\cdot)\) \(\chi_{8041}(399,\cdot)\) \(\chi_{8041}(416,\cdot)\) \(\chi_{8041}(433,\cdot)\) \(\chi_{8041}(478,\cdot)\) \(\chi_{8041}(542,\cdot)\) \(\chi_{8041}(587,\cdot)\) \(\chi_{8041}(614,\cdot)\) \(\chi_{8041}(620,\cdot)\) \(\chi_{8041}(621,\cdot)\) \(\chi_{8041}(631,\cdot)\) \(\chi_{8041}(665,\cdot)\) \(\chi_{8041}(757,\cdot)\) \(\chi_{8041}(807,\cdot)\) \(\chi_{8041}(808,\cdot)\) \(\chi_{8041}(933,\cdot)\) \(\chi_{8041}(994,\cdot)\) \(\chi_{8041}(1103,\cdot)\) \(\chi_{8041}(1137,\cdot)\) \(\chi_{8041}(1147,\cdot)\) \(\chi_{8041}(1148,\cdot)\) \(\chi_{8041}(1164,\cdot)\) \(\chi_{8041}(1181,\cdot)\) \(\chi_{8041}(1318,\cdot)\) \(\chi_{8041}(1324,\cdot)\) \(\chi_{8041}(1345,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{840})$
Fixed field:	Number field defined by a degree 840 polynomial (not computed)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{7}{8}\right),e\left(\frac{13}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\( \chi_{ 8041 }(614, a) \)	\(-1\)	\(1\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{827}{840}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{431}{840}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{67}{168}\right)\)