Dirichlet character \(\chi_{6223}(39,\cdot)\)

• Label: 6223.39
• 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.im

\(\chi_{6223}(23,\cdot)\) \(\chi_{6223}(39,\cdot)\) \(\chi_{6223}(53,\cdot)\) \(\chi_{6223}(340,\cdot)\) \(\chi_{6223}(387,\cdot)\) \(\chi_{6223}(466,\cdot)\) \(\chi_{6223}(604,\cdot)\) \(\chi_{6223}(1061,\cdot)\) \(\chi_{6223}(1199,\cdot)\) \(\chi_{6223}(1348,\cdot)\) \(\chi_{6223}(1409,\cdot)\) \(\chi_{6223}(1579,\cdot)\) \(\chi_{6223}(1752,\cdot)\) \(\chi_{6223}(1761,\cdot)\) \(\chi_{6223}(1894,\cdot)\) \(\chi_{6223}(1962,\cdot)\) \(\chi_{6223}(2046,\cdot)\) \(\chi_{6223}(2377,\cdot)\) \(\chi_{6223}(3145,\cdot)\) \(\chi_{6223}(3348,\cdot)\) \(\chi_{6223}(3385,\cdot)\) \(\chi_{6223}(3432,\cdot)\) \(\chi_{6223}(3665,\cdot)\) \(\chi_{6223}(3670,\cdot)\) \(\chi_{6223}(3817,\cdot)\) \(\chi_{6223}(3868,\cdot)\) \(\chi_{6223}(3903,\cdot)\) \(\chi_{6223}(3980,\cdot)\) \(\chi_{6223}(4664,\cdot)\) \(\chi_{6223}(4874,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{17}{21}\right),e\left(\frac{95}{126}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(39, a) \)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(1\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)