Dirichlet character \(\chi_{4719}(530,\cdot)\)

• Label: 4719.530
• Modulus: $4719$
• Conductor: $4719$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4719\)
Conductor:	\(4719\)
Order:	\(330\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4719.dm

\(\chi_{4719}(17,\cdot)\) \(\chi_{4719}(62,\cdot)\) \(\chi_{4719}(95,\cdot)\) \(\chi_{4719}(101,\cdot)\) \(\chi_{4719}(134,\cdot)\) \(\chi_{4719}(140,\cdot)\) \(\chi_{4719}(173,\cdot)\) \(\chi_{4719}(413,\cdot)\) \(\chi_{4719}(446,\cdot)\) \(\chi_{4719}(491,\cdot)\) \(\chi_{4719}(530,\cdot)\) \(\chi_{4719}(563,\cdot)\) \(\chi_{4719}(569,\cdot)\) \(\chi_{4719}(842,\cdot)\) \(\chi_{4719}(875,\cdot)\) \(\chi_{4719}(920,\cdot)\) \(\chi_{4719}(953,\cdot)\) \(\chi_{4719}(992,\cdot)\) \(\chi_{4719}(998,\cdot)\) \(\chi_{4719}(1031,\cdot)\) \(\chi_{4719}(1271,\cdot)\) \(\chi_{4719}(1349,\cdot)\) \(\chi_{4719}(1382,\cdot)\) \(\chi_{4719}(1388,\cdot)\) \(\chi_{4719}(1421,\cdot)\) \(\chi_{4719}(1427,\cdot)\) \(\chi_{4719}(1460,\cdot)\) \(\chi_{4719}(1700,\cdot)\) \(\chi_{4719}(1733,\cdot)\) \(\chi_{4719}(1778,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

\((1574,3511,4357)\) → \((-1,e\left(\frac{71}{110}\right),e\left(\frac{5}{6}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 4719 }(530, a) \)	\(1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)