Dirichlet character \(\chi_{6223}(314,\cdot)\)

• Label: 6223.314
• 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.ja

\(\chi_{6223}(13,\cdot)\) \(\chi_{6223}(153,\cdot)\) \(\chi_{6223}(314,\cdot)\) \(\chi_{6223}(496,\cdot)\) \(\chi_{6223}(811,\cdot)\) \(\chi_{6223}(1161,\cdot)\) \(\chi_{6223}(1217,\cdot)\) \(\chi_{6223}(1287,\cdot)\) \(\chi_{6223}(1693,\cdot)\) \(\chi_{6223}(1735,\cdot)\) \(\chi_{6223}(1840,\cdot)\) \(\chi_{6223}(2029,\cdot)\) \(\chi_{6223}(2190,\cdot)\) \(\chi_{6223}(2295,\cdot)\) \(\chi_{6223}(2575,\cdot)\) \(\chi_{6223}(2701,\cdot)\) \(\chi_{6223}(2708,\cdot)\) \(\chi_{6223}(3296,\cdot)\) \(\chi_{6223}(3317,\cdot)\) \(\chi_{6223}(3373,\cdot)\) \(\chi_{6223}(3499,\cdot)\) \(\chi_{6223}(4094,\cdot)\) \(\chi_{6223}(4108,\cdot)\) \(\chi_{6223}(4136,\cdot)\) \(\chi_{6223}(4549,\cdot)\) \(\chi_{6223}(4710,\cdot)\) \(\chi_{6223}(4787,\cdot)\) \(\chi_{6223}(5228,\cdot)\) \(\chi_{6223}(5403,\cdot)\) \(\chi_{6223}(5543,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{53}{63}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(314, a) \)	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)