Dirichlet character \(\chi_{6304}(45,\cdot)\)

• Label: 6304.45
• 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.dc

\(\chi_{6304}(5,\cdot)\) \(\chi_{6304}(45,\cdot)\) \(\chi_{6304}(125,\cdot)\) \(\chi_{6304}(141,\cdot)\) \(\chi_{6304}(205,\cdot)\) \(\chi_{6304}(229,\cdot)\) \(\chi_{6304}(245,\cdot)\) \(\chi_{6304}(277,\cdot)\) \(\chi_{6304}(373,\cdot)\) \(\chi_{6304}(381,\cdot)\) \(\chi_{6304}(405,\cdot)\) \(\chi_{6304}(429,\cdot)\) \(\chi_{6304}(493,\cdot)\) \(\chi_{6304}(589,\cdot)\) \(\chi_{6304}(621,\cdot)\) \(\chi_{6304}(669,\cdot)\) \(\chi_{6304}(685,\cdot)\) \(\chi_{6304}(693,\cdot)\) \(\chi_{6304}(709,\cdot)\) \(\chi_{6304}(845,\cdot)\) \(\chi_{6304}(877,\cdot)\) \(\chi_{6304}(933,\cdot)\) \(\chi_{6304}(1037,\cdot)\) \(\chi_{6304}(1093,\cdot)\) \(\chi_{6304}(1125,\cdot)\) \(\chi_{6304}(1261,\cdot)\) \(\chi_{6304}(1277,\cdot)\) \(\chi_{6304}(1285,\cdot)\) \(\chi_{6304}(1301,\cdot)\) \(\chi_{6304}(1349,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{59}{196}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(45, a) \)	\(-1\)	\(1\)	\(e\left(\frac{43}{392}\right)\)	\(e\left(\frac{261}{392}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{41}{392}\right)\)	\(e\left(\frac{255}{392}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{317}{392}\right)\)