Dirichlet character \(\chi_{8820}(2747,\cdot)\)

• Label: 8820.2747
• 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.iy

\(\chi_{8820}(383,\cdot)\) \(\chi_{8820}(887,\cdot)\) \(\chi_{8820}(983,\cdot)\) \(\chi_{8820}(1487,\cdot)\) \(\chi_{8820}(1643,\cdot)\) \(\chi_{8820}(2147,\cdot)\) \(\chi_{8820}(2243,\cdot)\) \(\chi_{8820}(2747,\cdot)\) \(\chi_{8820}(2903,\cdot)\) \(\chi_{8820}(3407,\cdot)\) \(\chi_{8820}(3503,\cdot)\) \(\chi_{8820}(4007,\cdot)\) \(\chi_{8820}(4163,\cdot)\) \(\chi_{8820}(4667,\cdot)\) \(\chi_{8820}(4763,\cdot)\) \(\chi_{8820}(5267,\cdot)\) \(\chi_{8820}(5423,\cdot)\) \(\chi_{8820}(5927,\cdot)\) \(\chi_{8820}(6023,\cdot)\) \(\chi_{8820}(6527,\cdot)\) \(\chi_{8820}(7187,\cdot)\) \(\chi_{8820}(7787,\cdot)\) \(\chi_{8820}(7943,\cdot)\) \(\chi_{8820}(8543,\cdot)\)

Related number fields

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

Values on generators

\((4411,7841,7057,1081)\) → \((-1,e\left(\frac{1}{6}\right),i,e\left(\frac{1}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\( \chi_{ 8820 }(2747, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)