Dirichlet character \(\chi_{6223}(780,\cdot)\)

• Label: 6223.780
• Modulus: $6223$
• Conductor: $6223$
• Order: $126$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(6223\)
Conductor:	\(6223\)
Order:	\(126\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 6223.jk

\(\chi_{6223}(17,\cdot)\) \(\chi_{6223}(136,\cdot)\) \(\chi_{6223}(502,\cdot)\) \(\chi_{6223}(780,\cdot)\) \(\chi_{6223}(1013,\cdot)\) \(\chi_{6223}(1088,\cdot)\) \(\chi_{6223}(1179,\cdot)\) \(\chi_{6223}(1438,\cdot)\) \(\chi_{6223}(1468,\cdot)\) \(\chi_{6223}(1510,\cdot)\) \(\chi_{6223}(1804,\cdot)\) \(\chi_{6223}(1949,\cdot)\) \(\chi_{6223}(1986,\cdot)\) \(\chi_{6223}(2147,\cdot)\) \(\chi_{6223}(2208,\cdot)\) \(\chi_{6223}(2483,\cdot)\) \(\chi_{6223}(2602,\cdot)\) \(\chi_{6223}(2644,\cdot)\) \(\chi_{6223}(3090,\cdot)\) \(\chi_{6223}(3146,\cdot)\) \(\chi_{6223}(3209,\cdot)\) \(\chi_{6223}(3295,\cdot)\) \(\chi_{6223}(3337,\cdot)\) \(\chi_{6223}(3442,\cdot)\) \(\chi_{6223}(4016,\cdot)\) \(\chi_{6223}(4133,\cdot)\) \(\chi_{6223}(4406,\cdot)\) \(\chi_{6223}(4730,\cdot)\) \(\chi_{6223}(4847,\cdot)\) \(\chi_{6223}(4856,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

Values on generators

\((5589,638)\) → \((e\left(\frac{31}{42}\right),e\left(\frac{37}{63}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(780, a) \)	\(-1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(-1\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{5}{18}\right)\)