Dirichlet character \(\chi_{6223}(1037,\cdot)\)

• Label: 6223.1037
• Modulus: $6223$
• Conductor: $6223$
• Order: $63$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6223\)
Conductor:	\(6223\)
Order:	\(63\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6223.hp

\(\chi_{6223}(36,\cdot)\) \(\chi_{6223}(211,\cdot)\) \(\chi_{6223}(463,\cdot)\) \(\chi_{6223}(505,\cdot)\) \(\chi_{6223}(596,\cdot)\) \(\chi_{6223}(960,\cdot)\) \(\chi_{6223}(1002,\cdot)\) \(\chi_{6223}(1037,\cdot)\) \(\chi_{6223}(1065,\cdot)\) \(\chi_{6223}(1296,\cdot)\) \(\chi_{6223}(1478,\cdot)\) \(\chi_{6223}(1639,\cdot)\) \(\chi_{6223}(1695,\cdot)\) \(\chi_{6223}(1947,\cdot)\) \(\chi_{6223}(1975,\cdot)\) \(\chi_{6223}(2094,\cdot)\) \(\chi_{6223}(2101,\cdot)\) \(\chi_{6223}(2136,\cdot)\) \(\chi_{6223}(2612,\cdot)\) \(\chi_{6223}(2787,\cdot)\) \(\chi_{6223}(2829,\cdot)\) \(\chi_{6223}(2934,\cdot)\) \(\chi_{6223}(3193,\cdot)\) \(\chi_{6223}(3508,\cdot)\) \(\chi_{6223}(3844,\cdot)\) \(\chi_{6223}(4208,\cdot)\) \(\chi_{6223}(4222,\cdot)\) \(\chi_{6223}(4348,\cdot)\) \(\chi_{6223}(4670,\cdot)\) \(\chi_{6223}(5013,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 63 polynomial

Values on generators

\((5589,638)\) → \((e\left(\frac{6}{7}\right),e\left(\frac{58}{63}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\( \chi_{ 6223 }(1037, a) \)	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{58}{63}\right)\)