Dirichlet character \(\chi_{6304}(1205,\cdot)\)

• Label: 6304.1205
• Modulus: $6304$
• Conductor: $6304$
• Order: $392$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 6304.da

\(\chi_{6304}(29,\cdot)\) \(\chi_{6304}(37,\cdot)\) \(\chi_{6304}(53,\cdot)\) \(\chi_{6304}(61,\cdot)\) \(\chi_{6304}(85,\cdot)\) \(\chi_{6304}(101,\cdot)\) \(\chi_{6304}(133,\cdot)\) \(\chi_{6304}(213,\cdot)\) \(\chi_{6304}(221,\cdot)\) \(\chi_{6304}(237,\cdot)\) \(\chi_{6304}(285,\cdot)\) \(\chi_{6304}(445,\cdot)\) \(\chi_{6304}(453,\cdot)\) \(\chi_{6304}(565,\cdot)\) \(\chi_{6304}(581,\cdot)\) \(\chi_{6304}(645,\cdot)\) \(\chi_{6304}(661,\cdot)\) \(\chi_{6304}(733,\cdot)\) \(\chi_{6304}(741,\cdot)\) \(\chi_{6304}(749,\cdot)\) \(\chi_{6304}(773,\cdot)\) \(\chi_{6304}(781,\cdot)\) \(\chi_{6304}(837,\cdot)\) \(\chi_{6304}(869,\cdot)\) \(\chi_{6304}(893,\cdot)\) \(\chi_{6304}(981,\cdot)\) \(\chi_{6304}(1013,\cdot)\) \(\chi_{6304}(1045,\cdot)\) \(\chi_{6304}(1061,\cdot)\) \(\chi_{6304}(1085,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{30}{49}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(1205, a) \)	\(1\)	\(1\)	\(e\left(\frac{271}{392}\right)\)	\(e\left(\frac{45}{392}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{345}{392}\right)\)	\(e\left(\frac{267}{392}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{129}{392}\right)\)