Dirichlet character \(\chi_{6897}(83,\cdot)\)

• Label: 6897.83
• Modulus: $6897$
• Conductor: $6897$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(6897\)
Conductor:	\(6897\)
Order:	\(330\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6897.de

\(\chi_{6897}(68,\cdot)\) \(\chi_{6897}(83,\cdot)\) \(\chi_{6897}(140,\cdot)\) \(\chi_{6897}(182,\cdot)\) \(\chi_{6897}(425,\cdot)\) \(\chi_{6897}(695,\cdot)\) \(\chi_{6897}(710,\cdot)\) \(\chi_{6897}(767,\cdot)\) \(\chi_{6897}(809,\cdot)\) \(\chi_{6897}(866,\cdot)\) \(\chi_{6897}(1052,\cdot)\) \(\chi_{6897}(1151,\cdot)\) \(\chi_{6897}(1223,\cdot)\) \(\chi_{6897}(1337,\cdot)\) \(\chi_{6897}(1394,\cdot)\) \(\chi_{6897}(1436,\cdot)\) \(\chi_{6897}(1493,\cdot)\) \(\chi_{6897}(1679,\cdot)\) \(\chi_{6897}(1778,\cdot)\) \(\chi_{6897}(1850,\cdot)\) \(\chi_{6897}(1949,\cdot)\) \(\chi_{6897}(1964,\cdot)\) \(\chi_{6897}(2021,\cdot)\) \(\chi_{6897}(2063,\cdot)\) \(\chi_{6897}(2120,\cdot)\) \(\chi_{6897}(2306,\cdot)\) \(\chi_{6897}(2405,\cdot)\) \(\chi_{6897}(2477,\cdot)\) \(\chi_{6897}(2576,\cdot)\) \(\chi_{6897}(2591,\cdot)\) ...

Related number fields

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

Values on generators

\((2300,970,3631)\) → \((-1,e\left(\frac{29}{110}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 6897 }(83, a) \)	\(1\)	\(1\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)