Dirichlet character \(\chi_{6223}(12,\cdot)\)

• Label: 6223.12
• 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.ii

\(\chi_{6223}(12,\cdot)\) \(\chi_{6223}(194,\cdot)\) \(\chi_{6223}(283,\cdot)\) \(\chi_{6223}(355,\cdot)\) \(\chi_{6223}(495,\cdot)\) \(\chi_{6223}(642,\cdot)\) \(\chi_{6223}(649,\cdot)\) \(\chi_{6223}(810,\cdot)\) \(\chi_{6223}(1062,\cdot)\) \(\chi_{6223}(1515,\cdot)\) \(\chi_{6223}(1963,\cdot)\) \(\chi_{6223}(2182,\cdot)\) \(\chi_{6223}(2341,\cdot)\) \(\chi_{6223}(2593,\cdot)\) \(\chi_{6223}(2637,\cdot)\) \(\chi_{6223}(2712,\cdot)\) \(\chi_{6223}(3232,\cdot)\) \(\chi_{6223}(3358,\cdot)\) \(\chi_{6223}(3414,\cdot)\) \(\chi_{6223}(3435,\cdot)\) \(\chi_{6223}(3538,\cdot)\) \(\chi_{6223}(3545,\cdot)\) \(\chi_{6223}(3895,\cdot)\) \(\chi_{6223}(4156,\cdot)\) \(\chi_{6223}(4541,\cdot)\) \(\chi_{6223}(4658,\cdot)\) \(\chi_{6223}(4702,\cdot)\) \(\chi_{6223}(4742,\cdot)\) \(\chi_{6223}(4777,\cdot)\) \(\chi_{6223}(4891,\cdot)\) ...

Related number fields

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

Values on generators

\((5589,638)\) → \((e\left(\frac{11}{42}\right),e\left(\frac{19}{126}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(12, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)