Dirichlet character \(\chi_{6223}(1007,\cdot)\)

• Label: 6223.1007
• 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.lb

\(\chi_{6223}(237,\cdot)\) \(\chi_{6223}(300,\cdot)\) \(\chi_{6223}(573,\cdot)\) \(\chi_{6223}(720,\cdot)\) \(\chi_{6223}(741,\cdot)\) \(\chi_{6223}(944,\cdot)\) \(\chi_{6223}(1007,\cdot)\) \(\chi_{6223}(1182,\cdot)\) \(\chi_{6223}(1490,\cdot)\) \(\chi_{6223}(1511,\cdot)\) \(\chi_{6223}(1581,\cdot)\) \(\chi_{6223}(1602,\cdot)\) \(\chi_{6223}(1658,\cdot)\) \(\chi_{6223}(2085,\cdot)\) \(\chi_{6223}(2344,\cdot)\) \(\chi_{6223}(2631,\cdot)\) \(\chi_{6223}(2652,\cdot)\) \(\chi_{6223}(3051,\cdot)\) \(\chi_{6223}(3345,\cdot)\) \(\chi_{6223}(3604,\cdot)\) \(\chi_{6223}(3695,\cdot)\) \(\chi_{6223}(3779,\cdot)\) \(\chi_{6223}(4038,\cdot)\) \(\chi_{6223}(4332,\cdot)\) \(\chi_{6223}(4451,\cdot)\) \(\chi_{6223}(4542,\cdot)\) \(\chi_{6223}(4766,\cdot)\) \(\chi_{6223}(4808,\cdot)\) \(\chi_{6223}(4871,\cdot)\) \(\chi_{6223}(4976,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{65}{126}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(1007, a) \)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{37}{63}\right)\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)