Dirichlet character \(\chi_{6223}(24,\cdot)\)

• Label: 6223.24
• Modulus: $6223$
• Conductor: $6223$
• Order: $126$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 6223.kg

\(\chi_{6223}(24,\cdot)\) \(\chi_{6223}(409,\cdot)\) \(\chi_{6223}(710,\cdot)\) \(\chi_{6223}(740,\cdot)\) \(\chi_{6223}(1202,\cdot)\) \(\chi_{6223}(1298,\cdot)\) \(\chi_{6223}(1629,\cdot)\) \(\chi_{6223}(1741,\cdot)\) \(\chi_{6223}(1802,\cdot)\) \(\chi_{6223}(2091,\cdot)\) \(\chi_{6223}(2488,\cdot)\) \(\chi_{6223}(2630,\cdot)\) \(\chi_{6223}(2691,\cdot)\) \(\chi_{6223}(2980,\cdot)\) \(\chi_{6223}(3076,\cdot)\) \(\chi_{6223}(3377,\cdot)\) \(\chi_{6223}(3407,\cdot)\) \(\chi_{6223}(3519,\cdot)\) \(\chi_{6223}(3580,\cdot)\) \(\chi_{6223}(3869,\cdot)\) \(\chi_{6223}(3965,\cdot)\) \(\chi_{6223}(4266,\cdot)\) \(\chi_{6223}(4296,\cdot)\) \(\chi_{6223}(4408,\cdot)\) \(\chi_{6223}(4469,\cdot)\) \(\chi_{6223}(4758,\cdot)\) \(\chi_{6223}(4854,\cdot)\) \(\chi_{6223}(5155,\cdot)\) \(\chi_{6223}(5185,\cdot)\) \(\chi_{6223}(5297,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{37}{42}\right),e\left(\frac{13}{18}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(24, a) \)	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)