Dirichlet character \(\chi_{28665}(229,\cdot)\)

• Label: 28665.229
• Modulus: $28665$
• Conductor: $28665$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(28665\)
Conductor:	\(28665\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 28665.bno

\(\chi_{28665}(229,\cdot)\) \(\chi_{28665}(304,\cdot)\) \(\chi_{28665}(4009,\cdot)\) \(\chi_{28665}(4324,\cdot)\) \(\chi_{28665}(4399,\cdot)\) \(\chi_{28665}(4714,\cdot)\) \(\chi_{28665}(8419,\cdot)\) \(\chi_{28665}(8494,\cdot)\) \(\chi_{28665}(8809,\cdot)\) \(\chi_{28665}(12199,\cdot)\) \(\chi_{28665}(12589,\cdot)\) \(\chi_{28665}(12904,\cdot)\) \(\chi_{28665}(16294,\cdot)\) \(\chi_{28665}(16609,\cdot)\) \(\chi_{28665}(16684,\cdot)\) \(\chi_{28665}(16999,\cdot)\) \(\chi_{28665}(20389,\cdot)\) \(\chi_{28665}(20704,\cdot)\) \(\chi_{28665}(20779,\cdot)\) \(\chi_{28665}(21094,\cdot)\) \(\chi_{28665}(24484,\cdot)\) \(\chi_{28665}(24799,\cdot)\) \(\chi_{28665}(25189,\cdot)\) \(\chi_{28665}(28579,\cdot)\)

Related number fields

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

Values on generators

\((25481,11467,18721,11026)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{41}{42}\right),i)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)	\(29\)
\( \chi_{ 28665 }(229, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)