Dirichlet character \(\chi_{6304}(13,\cdot)\)

• Label: 6304.13
• 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.de

\(\chi_{6304}(13,\cdot)\) \(\chi_{6304}(21,\cdot)\) \(\chi_{6304}(117,\cdot)\) \(\chi_{6304}(149,\cdot)\) \(\chi_{6304}(165,\cdot)\) \(\chi_{6304}(189,\cdot)\) \(\chi_{6304}(253,\cdot)\) \(\chi_{6304}(269,\cdot)\) \(\chi_{6304}(349,\cdot)\) \(\chi_{6304}(389,\cdot)\) \(\chi_{6304}(397,\cdot)\) \(\chi_{6304}(421,\cdot)\) \(\chi_{6304}(461,\cdot)\) \(\chi_{6304}(469,\cdot)\) \(\chi_{6304}(485,\cdot)\) \(\chi_{6304}(509,\cdot)\) \(\chi_{6304}(517,\cdot)\) \(\chi_{6304}(525,\cdot)\) \(\chi_{6304}(533,\cdot)\) \(\chi_{6304}(541,\cdot)\) \(\chi_{6304}(573,\cdot)\) \(\chi_{6304}(629,\cdot)\) \(\chi_{6304}(637,\cdot)\) \(\chi_{6304}(677,\cdot)\) \(\chi_{6304}(717,\cdot)\) \(\chi_{6304}(757,\cdot)\) \(\chi_{6304}(805,\cdot)\) \(\chi_{6304}(861,\cdot)\) \(\chi_{6304}(941,\cdot)\) \(\chi_{6304}(973,\cdot)\) ...

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{25}{196}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(13, a) \)	\(-1\)	\(1\)	\(e\left(\frac{279}{392}\right)\)	\(e\left(\frac{89}{392}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{29}{392}\right)\)	\(e\left(\frac{123}{392}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{33}{392}\right)\)