Dirichlet character \(\chi_{8820}(1663,\cdot)\)

• Label: 8820.1663
• Modulus: $8820$
• Conductor: $8820$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8820\)
Conductor:	\(8820\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8820.ih

\(\chi_{8820}(247,\cdot)\) \(\chi_{8820}(403,\cdot)\) \(\chi_{8820}(907,\cdot)\) \(\chi_{8820}(1003,\cdot)\) \(\chi_{8820}(1507,\cdot)\) \(\chi_{8820}(1663,\cdot)\) \(\chi_{8820}(2167,\cdot)\) \(\chi_{8820}(2263,\cdot)\) \(\chi_{8820}(2767,\cdot)\) \(\chi_{8820}(2923,\cdot)\) \(\chi_{8820}(3427,\cdot)\) \(\chi_{8820}(3523,\cdot)\) \(\chi_{8820}(4027,\cdot)\) \(\chi_{8820}(4687,\cdot)\) \(\chi_{8820}(5287,\cdot)\) \(\chi_{8820}(5443,\cdot)\) \(\chi_{8820}(6043,\cdot)\) \(\chi_{8820}(6703,\cdot)\) \(\chi_{8820}(7207,\cdot)\) \(\chi_{8820}(7303,\cdot)\) \(\chi_{8820}(7807,\cdot)\) \(\chi_{8820}(7963,\cdot)\) \(\chi_{8820}(8467,\cdot)\) \(\chi_{8820}(8563,\cdot)\)

Related number fields

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

Values on generators

\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{2}{3}\right),-i,e\left(\frac{11}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 8820 }(1663, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)