Dirichlet character \(\chi_{6304}(27,\cdot)\)

• Label: 6304.27
• 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.dd

\(\chi_{6304}(3,\cdot)\) \(\chi_{6304}(27,\cdot)\) \(\chi_{6304}(67,\cdot)\) \(\chi_{6304}(75,\cdot)\) \(\chi_{6304}(91,\cdot)\) \(\chi_{6304}(115,\cdot)\) \(\chi_{6304}(123,\cdot)\) \(\chi_{6304}(131,\cdot)\) \(\chi_{6304}(139,\cdot)\) \(\chi_{6304}(147,\cdot)\) \(\chi_{6304}(179,\cdot)\) \(\chi_{6304}(235,\cdot)\) \(\chi_{6304}(243,\cdot)\) \(\chi_{6304}(283,\cdot)\) \(\chi_{6304}(323,\cdot)\) \(\chi_{6304}(363,\cdot)\) \(\chi_{6304}(411,\cdot)\) \(\chi_{6304}(467,\cdot)\) \(\chi_{6304}(547,\cdot)\) \(\chi_{6304}(579,\cdot)\) \(\chi_{6304}(603,\cdot)\) \(\chi_{6304}(635,\cdot)\) \(\chi_{6304}(715,\cdot)\) \(\chi_{6304}(771,\cdot)\) \(\chi_{6304}(819,\cdot)\) \(\chi_{6304}(859,\cdot)\) \(\chi_{6304}(899,\cdot)\) \(\chi_{6304}(939,\cdot)\) \(\chi_{6304}(947,\cdot)\) \(\chi_{6304}(1003,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{151}{196}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(27, a) \)	\(1\)	\(1\)	\(e\left(\frac{125}{392}\right)\)	\(e\left(\frac{271}{392}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{183}{392}\right)\)	\(e\left(\frac{53}{392}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{215}{392}\right)\)