Dirichlet character \(\chi_{1984}(789,\cdot)\)

• Label: 1984.789
• 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.db

\(\chi_{1984}(45,\cdot)\) \(\chi_{1984}(69,\cdot)\) \(\chi_{1984}(133,\cdot)\) \(\chi_{1984}(165,\cdot)\) \(\chi_{1984}(173,\cdot)\) \(\chi_{1984}(205,\cdot)\) \(\chi_{1984}(237,\cdot)\) \(\chi_{1984}(245,\cdot)\) \(\chi_{1984}(293,\cdot)\) \(\chi_{1984}(317,\cdot)\) \(\chi_{1984}(381,\cdot)\) \(\chi_{1984}(413,\cdot)\) \(\chi_{1984}(421,\cdot)\) \(\chi_{1984}(453,\cdot)\) \(\chi_{1984}(485,\cdot)\) \(\chi_{1984}(493,\cdot)\) \(\chi_{1984}(541,\cdot)\) \(\chi_{1984}(565,\cdot)\) \(\chi_{1984}(629,\cdot)\) \(\chi_{1984}(661,\cdot)\) \(\chi_{1984}(669,\cdot)\) \(\chi_{1984}(701,\cdot)\) \(\chi_{1984}(733,\cdot)\) \(\chi_{1984}(741,\cdot)\) \(\chi_{1984}(789,\cdot)\) \(\chi_{1984}(813,\cdot)\) \(\chi_{1984}(877,\cdot)\) \(\chi_{1984}(909,\cdot)\) \(\chi_{1984}(917,\cdot)\) \(\chi_{1984}(949,\cdot)\) ...

Related number fields

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

Values on generators

\((63,1861,65)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{11}{15}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\( \chi_{ 1984 }(789, a) \)	\(1\)	\(1\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{199}{240}\right)\)