Dirichlet character \(\chi_{6304}(443,\cdot)\)

• Label: 6304.443
• Modulus: $6304$
• Conductor: $6304$
• Order: $392$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(6304\)
Conductor:	\(6304\)
Order:	\(392\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 6304.db

\(\chi_{6304}(51,\cdot)\) \(\chi_{6304}(59,\cdot)\) \(\chi_{6304}(171,\cdot)\) \(\chi_{6304}(187,\cdot)\) \(\chi_{6304}(251,\cdot)\) \(\chi_{6304}(267,\cdot)\) \(\chi_{6304}(339,\cdot)\) \(\chi_{6304}(347,\cdot)\) \(\chi_{6304}(355,\cdot)\) \(\chi_{6304}(379,\cdot)\) \(\chi_{6304}(387,\cdot)\) \(\chi_{6304}(443,\cdot)\) \(\chi_{6304}(475,\cdot)\) \(\chi_{6304}(499,\cdot)\) \(\chi_{6304}(587,\cdot)\) \(\chi_{6304}(619,\cdot)\) \(\chi_{6304}(651,\cdot)\) \(\chi_{6304}(667,\cdot)\) \(\chi_{6304}(691,\cdot)\) \(\chi_{6304}(723,\cdot)\) \(\chi_{6304}(747,\cdot)\) \(\chi_{6304}(763,\cdot)\) \(\chi_{6304}(779,\cdot)\) \(\chi_{6304}(811,\cdot)\) \(\chi_{6304}(851,\cdot)\) \(\chi_{6304}(923,\cdot)\) \(\chi_{6304}(963,\cdot)\) \(\chi_{6304}(1019,\cdot)\) \(\chi_{6304}(1027,\cdot)\) \(\chi_{6304}(1075,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{392})$
Fixed field:	Number field defined by a degree 392 polynomial (not computed)

Values on generators

\((1183,3941,3745)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{24}{49}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(443, a) \)	\(-1\)	\(1\)	\(e\left(\frac{207}{392}\right)\)	\(e\left(\frac{281}{392}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{129}{392}\right)\)	\(e\left(\frac{47}{392}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{309}{392}\right)\)