Dirichlet character \(\chi_{6223}(4493,\cdot)\)

• Label: 6223.4493
• 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.jf

\(\chi_{6223}(83,\cdot)\) \(\chi_{6223}(363,\cdot)\) \(\chi_{6223}(384,\cdot)\) \(\chi_{6223}(566,\cdot)\) \(\chi_{6223}(601,\cdot)\) \(\chi_{6223}(678,\cdot)\) \(\chi_{6223}(818,\cdot)\) \(\chi_{6223}(986,\cdot)\) \(\chi_{6223}(1896,\cdot)\) \(\chi_{6223}(2078,\cdot)\) \(\chi_{6223}(2099,\cdot)\) \(\chi_{6223}(2442,\cdot)\) \(\chi_{6223}(2505,\cdot)\) \(\chi_{6223}(2519,\cdot)\) \(\chi_{6223}(2673,\cdot)\) \(\chi_{6223}(2806,\cdot)\) \(\chi_{6223}(2960,\cdot)\) \(\chi_{6223}(2974,\cdot)\) \(\chi_{6223}(3149,\cdot)\) \(\chi_{6223}(3240,\cdot)\) \(\chi_{6223}(3261,\cdot)\) \(\chi_{6223}(3387,\cdot)\) \(\chi_{6223}(3443,\cdot)\) \(\chi_{6223}(3982,\cdot)\) \(\chi_{6223}(4269,\cdot)\) \(\chi_{6223}(4430,\cdot)\) \(\chi_{6223}(4493,\cdot)\) \(\chi_{6223}(4500,\cdot)\) \(\chi_{6223}(4682,\cdot)\) \(\chi_{6223}(4815,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{3}{14}\right),e\left(\frac{37}{126}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(4493, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)