Dirichlet character \(\chi_{1984}(331,\cdot)\)

• Label: 1984.331
• Modulus: $1984$
• Conductor: $1984$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1984\)
Conductor:	\(1984\)
Order:	\(240\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1984.cy

\(\chi_{1984}(3,\cdot)\) \(\chi_{1984}(11,\cdot)\) \(\chi_{1984}(43,\cdot)\) \(\chi_{1984}(75,\cdot)\) \(\chi_{1984}(83,\cdot)\) \(\chi_{1984}(115,\cdot)\) \(\chi_{1984}(179,\cdot)\) \(\chi_{1984}(203,\cdot)\) \(\chi_{1984}(251,\cdot)\) \(\chi_{1984}(259,\cdot)\) \(\chi_{1984}(291,\cdot)\) \(\chi_{1984}(323,\cdot)\) \(\chi_{1984}(331,\cdot)\) \(\chi_{1984}(363,\cdot)\) \(\chi_{1984}(427,\cdot)\) \(\chi_{1984}(451,\cdot)\) \(\chi_{1984}(499,\cdot)\) \(\chi_{1984}(507,\cdot)\) \(\chi_{1984}(539,\cdot)\) \(\chi_{1984}(571,\cdot)\) \(\chi_{1984}(579,\cdot)\) \(\chi_{1984}(611,\cdot)\) \(\chi_{1984}(675,\cdot)\) \(\chi_{1984}(699,\cdot)\) \(\chi_{1984}(747,\cdot)\) \(\chi_{1984}(755,\cdot)\) \(\chi_{1984}(787,\cdot)\) \(\chi_{1984}(819,\cdot)\) \(\chi_{1984}(827,\cdot)\) \(\chi_{1984}(859,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

Values on generators

\((63,1861,65)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{29}{30}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1984 }(331, a) \)	\(1\)	\(1\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{23}{240}\right)\)