Dirichlet character \(\chi_{6223}(6,\cdot)\)

• Label: 6223.6
• 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.jd

\(\chi_{6223}(6,\cdot)\) \(\chi_{6223}(118,\cdot)\) \(\chi_{6223}(370,\cdot)\) \(\chi_{6223}(594,\cdot)\) \(\chi_{6223}(874,\cdot)\) \(\chi_{6223}(1196,\cdot)\) \(\chi_{6223}(1210,\cdot)\) \(\chi_{6223}(1553,\cdot)\) \(\chi_{6223}(1875,\cdot)\) \(\chi_{6223}(2001,\cdot)\) \(\chi_{6223}(2015,\cdot)\) \(\chi_{6223}(2379,\cdot)\) \(\chi_{6223}(2715,\cdot)\) \(\chi_{6223}(3030,\cdot)\) \(\chi_{6223}(3289,\cdot)\) \(\chi_{6223}(3394,\cdot)\) \(\chi_{6223}(3436,\cdot)\) \(\chi_{6223}(3611,\cdot)\) \(\chi_{6223}(4087,\cdot)\) \(\chi_{6223}(4122,\cdot)\) \(\chi_{6223}(4129,\cdot)\) \(\chi_{6223}(4248,\cdot)\) \(\chi_{6223}(4276,\cdot)\) \(\chi_{6223}(4528,\cdot)\) \(\chi_{6223}(4584,\cdot)\) \(\chi_{6223}(4745,\cdot)\) \(\chi_{6223}(4927,\cdot)\) \(\chi_{6223}(5158,\cdot)\) \(\chi_{6223}(5186,\cdot)\) \(\chi_{6223}(5221,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{73}{126}\right))\)

First values

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