Dirichlet character \(\chi_{6304}(4709,\cdot)\)

• Label: 6304.4709
• Modulus: $6304$
• Conductor: $6304$
• Order: $56$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6304\)
Conductor:	\(6304\)
Order:	\(56\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6304.ce

\(\chi_{6304}(301,\cdot)\) \(\chi_{6304}(1021,\cdot)\) \(\chi_{6304}(1149,\cdot)\) \(\chi_{6304}(1373,\cdot)\) \(\chi_{6304}(1493,\cdot)\) \(\chi_{6304}(1557,\cdot)\) \(\chi_{6304}(1877,\cdot)\) \(\chi_{6304}(2597,\cdot)\) \(\chi_{6304}(2725,\cdot)\) \(\chi_{6304}(2949,\cdot)\) \(\chi_{6304}(3069,\cdot)\) \(\chi_{6304}(3133,\cdot)\) \(\chi_{6304}(3453,\cdot)\) \(\chi_{6304}(4173,\cdot)\) \(\chi_{6304}(4301,\cdot)\) \(\chi_{6304}(4525,\cdot)\) \(\chi_{6304}(4645,\cdot)\) \(\chi_{6304}(4709,\cdot)\) \(\chi_{6304}(5029,\cdot)\) \(\chi_{6304}(5749,\cdot)\) \(\chi_{6304}(5877,\cdot)\) \(\chi_{6304}(6101,\cdot)\) \(\chi_{6304}(6221,\cdot)\) \(\chi_{6304}(6285,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Values on generators

\((1183,3941,3745)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{2}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(4709, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{56}\right)\)