Dirichlet character \(\chi_{980}(443,\cdot)\)

• Label: 980.443
• Modulus: $980$
• Conductor: $980$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(980\)
Conductor:	\(980\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 980.bs

\(\chi_{980}(23,\cdot)\) \(\chi_{980}(107,\cdot)\) \(\chi_{980}(123,\cdot)\) \(\chi_{980}(163,\cdot)\) \(\chi_{980}(207,\cdot)\) \(\chi_{980}(247,\cdot)\) \(\chi_{980}(303,\cdot)\) \(\chi_{980}(347,\cdot)\) \(\chi_{980}(387,\cdot)\) \(\chi_{980}(403,\cdot)\) \(\chi_{980}(443,\cdot)\) \(\chi_{980}(487,\cdot)\) \(\chi_{980}(527,\cdot)\) \(\chi_{980}(543,\cdot)\) \(\chi_{980}(583,\cdot)\) \(\chi_{980}(627,\cdot)\) \(\chi_{980}(683,\cdot)\) \(\chi_{980}(723,\cdot)\) \(\chi_{980}(767,\cdot)\) \(\chi_{980}(807,\cdot)\) \(\chi_{980}(823,\cdot)\) \(\chi_{980}(907,\cdot)\) \(\chi_{980}(947,\cdot)\) \(\chi_{980}(963,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((491,197,101)\) → \((-1,-i,e\left(\frac{13}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\( \chi_{ 980 }(443, a) \)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum