Dirichlet character \(\chi_{6223}(993,\cdot)\)

• Label: 6223.993
• 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.ji

\(\chi_{6223}(34,\cdot)\) \(\chi_{6223}(69,\cdot)\) \(\chi_{6223}(251,\cdot)\) \(\chi_{6223}(272,\cdot)\) \(\chi_{6223}(552,\cdot)\) \(\chi_{6223}(755,\cdot)\) \(\chi_{6223}(902,\cdot)\) \(\chi_{6223}(993,\cdot)\) \(\chi_{6223}(1301,\cdot)\) \(\chi_{6223}(1560,\cdot)\) \(\chi_{6223}(1721,\cdot)\) \(\chi_{6223}(2043,\cdot)\) \(\chi_{6223}(2176,\cdot)\) \(\chi_{6223}(2358,\cdot)\) \(\chi_{6223}(2365,\cdot)\) \(\chi_{6223}(2428,\cdot)\) \(\chi_{6223}(2589,\cdot)\) \(\chi_{6223}(2876,\cdot)\) \(\chi_{6223}(3415,\cdot)\) \(\chi_{6223}(3471,\cdot)\) \(\chi_{6223}(3597,\cdot)\) \(\chi_{6223}(3618,\cdot)\) \(\chi_{6223}(3709,\cdot)\) \(\chi_{6223}(3884,\cdot)\) \(\chi_{6223}(3898,\cdot)\) \(\chi_{6223}(4052,\cdot)\) \(\chi_{6223}(4185,\cdot)\) \(\chi_{6223}(4339,\cdot)\) \(\chi_{6223}(4353,\cdot)\) \(\chi_{6223}(4416,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{29}{63}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(993, a) \)	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{7}{18}\right)\)