Dirichlet character \(\chi_{6304}(403,\cdot)\)

• Label: 6304.403
• 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.cz

\(\chi_{6304}(43,\cdot)\) \(\chi_{6304}(107,\cdot)\) \(\chi_{6304}(155,\cdot)\) \(\chi_{6304}(163,\cdot)\) \(\chi_{6304}(219,\cdot)\) \(\chi_{6304}(259,\cdot)\) \(\chi_{6304}(331,\cdot)\) \(\chi_{6304}(371,\cdot)\) \(\chi_{6304}(403,\cdot)\) \(\chi_{6304}(419,\cdot)\) \(\chi_{6304}(435,\cdot)\) \(\chi_{6304}(459,\cdot)\) \(\chi_{6304}(491,\cdot)\) \(\chi_{6304}(515,\cdot)\) \(\chi_{6304}(531,\cdot)\) \(\chi_{6304}(563,\cdot)\) \(\chi_{6304}(595,\cdot)\) \(\chi_{6304}(683,\cdot)\) \(\chi_{6304}(707,\cdot)\) \(\chi_{6304}(739,\cdot)\) \(\chi_{6304}(795,\cdot)\) \(\chi_{6304}(803,\cdot)\) \(\chi_{6304}(827,\cdot)\) \(\chi_{6304}(835,\cdot)\) \(\chi_{6304}(843,\cdot)\) \(\chi_{6304}(915,\cdot)\) \(\chi_{6304}(931,\cdot)\) \(\chi_{6304}(995,\cdot)\) \(\chi_{6304}(1011,\cdot)\) \(\chi_{6304}(1123,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{83}{98}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(403, a) \)	\(-1\)	\(1\)	\(e\left(\frac{165}{392}\right)\)	\(e\left(\frac{99}{392}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{171}{392}\right)\)	\(e\left(\frac{117}{392}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{127}{392}\right)\)