Dirichlet character \(\chi_{6304}(19,\cdot)\)

• Label: 6304.19
• Modulus: $6304$
• Conductor: $6304$
• Order: $56$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 6304.bx

\(\chi_{6304}(19,\cdot)\) \(\chi_{6304}(83,\cdot)\) \(\chi_{6304}(203,\cdot)\) \(\chi_{6304}(427,\cdot)\) \(\chi_{6304}(555,\cdot)\) \(\chi_{6304}(1275,\cdot)\) \(\chi_{6304}(1595,\cdot)\) \(\chi_{6304}(1659,\cdot)\) \(\chi_{6304}(1779,\cdot)\) \(\chi_{6304}(2003,\cdot)\) \(\chi_{6304}(2131,\cdot)\) \(\chi_{6304}(2851,\cdot)\) \(\chi_{6304}(3171,\cdot)\) \(\chi_{6304}(3235,\cdot)\) \(\chi_{6304}(3355,\cdot)\) \(\chi_{6304}(3579,\cdot)\) \(\chi_{6304}(3707,\cdot)\) \(\chi_{6304}(4427,\cdot)\) \(\chi_{6304}(4747,\cdot)\) \(\chi_{6304}(4811,\cdot)\) \(\chi_{6304}(4931,\cdot)\) \(\chi_{6304}(5155,\cdot)\) \(\chi_{6304}(5283,\cdot)\) \(\chi_{6304}(6003,\cdot)\)

Related number fields

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

Values on generators

\((1183,3941,3745)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{11}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 6304 }(19, a) \)	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{56}\right)\)