Dirichlet character \(\chi_{124509}(884,\cdot)\)

• Label: 124509.884
• Modulus: $124509$
• Conductor: $124509$
• Order: $16170$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(124509\)
Conductor:	\(124509\)
Order:	\(16170\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 124509.hf

\(\chi_{124509}(53,\cdot)\) \(\chi_{124509}(86,\cdot)\) \(\chi_{124509}(137,\cdot)\) \(\chi_{124509}(158,\cdot)\) \(\chi_{124509}(170,\cdot)\) \(\chi_{124509}(179,\cdot)\) \(\chi_{124509}(191,\cdot)\) \(\chi_{124509}(212,\cdot)\) \(\chi_{124509}(284,\cdot)\) \(\chi_{124509}(317,\cdot)\) \(\chi_{124509}(368,\cdot)\) \(\chi_{124509}(389,\cdot)\) \(\chi_{124509}(401,\cdot)\) \(\chi_{124509}(443,\cdot)\) \(\chi_{124509}(515,\cdot)\) \(\chi_{124509}(548,\cdot)\) \(\chi_{124509}(599,\cdot)\) \(\chi_{124509}(620,\cdot)\) \(\chi_{124509}(641,\cdot)\) \(\chi_{124509}(653,\cdot)\) \(\chi_{124509}(674,\cdot)\) \(\chi_{124509}(746,\cdot)\) \(\chi_{124509}(779,\cdot)\) \(\chi_{124509}(830,\cdot)\) \(\chi_{124509}(872,\cdot)\) \(\chi_{124509}(884,\cdot)\) \(\chi_{124509}(905,\cdot)\) \(\chi_{124509}(1061,\cdot)\) \(\chi_{124509}(1082,\cdot)\) \(\chi_{124509}(1094,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{8085})$
Fixed field:	Number field defined by a degree 16170 polynomial (not computed)

Values on generators

\((41504,37390,2059)\) → \((-1,e\left(\frac{55}{147}\right),e\left(\frac{21}{55}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 124509 }(884, a) \)	\(-1\)	\(1\)	\(e\left(\frac{7549}{16170}\right)\)	\(e\left(\frac{7549}{8085}\right)\)	\(e\left(\frac{9781}{16170}\right)\)	\(e\left(\frac{2159}{5390}\right)\)	\(e\left(\frac{116}{1617}\right)\)	\(e\left(\frac{529}{2695}\right)\)	\(e\left(\frac{7013}{8085}\right)\)	\(e\left(\frac{9101}{16170}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{2903}{5390}\right)\)