Dirichlet character \(\chi_{124509}(47,\cdot)\)

• Label: 124509.47
• Modulus: $124509$
• Conductor: $124509$
• Order: $16170$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 124509.hh

\(\chi_{124509}(5,\cdot)\) \(\chi_{124509}(26,\cdot)\) \(\chi_{124509}(38,\cdot)\) \(\chi_{124509}(47,\cdot)\) \(\chi_{124509}(59,\cdot)\) \(\chi_{124509}(152,\cdot)\) \(\chi_{124509}(185,\cdot)\) \(\chi_{124509}(236,\cdot)\) \(\chi_{124509}(257,\cdot)\) \(\chi_{124509}(278,\cdot)\) \(\chi_{124509}(290,\cdot)\) \(\chi_{124509}(311,\cdot)\) \(\chi_{124509}(383,\cdot)\) \(\chi_{124509}(416,\cdot)\) \(\chi_{124509}(467,\cdot)\) \(\chi_{124509}(488,\cdot)\) \(\chi_{124509}(500,\cdot)\) \(\chi_{124509}(542,\cdot)\) \(\chi_{124509}(647,\cdot)\) \(\chi_{124509}(698,\cdot)\) \(\chi_{124509}(719,\cdot)\) \(\chi_{124509}(731,\cdot)\) \(\chi_{124509}(740,\cdot)\) \(\chi_{124509}(752,\cdot)\) \(\chi_{124509}(773,\cdot)\) \(\chi_{124509}(845,\cdot)\) \(\chi_{124509}(878,\cdot)\) \(\chi_{124509}(929,\cdot)\) \(\chi_{124509}(983,\cdot)\) \(\chi_{124509}(1004,\cdot)\) ...

Related number fields

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

Values on generators

\((41504,37390,2059)\) → \((-1,e\left(\frac{215}{294}\right),e\left(\frac{49}{55}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 124509 }(47, a) \)	\(1\)	\(1\)	\(e\left(\frac{4231}{16170}\right)\)	\(e\left(\frac{4231}{8085}\right)\)	\(e\left(\frac{5132}{8085}\right)\)	\(e\left(\frac{4231}{5390}\right)\)	\(e\left(\frac{2899}{3234}\right)\)	\(e\left(\frac{2157}{5390}\right)\)	\(e\left(\frac{377}{8085}\right)\)	\(e\left(\frac{3532}{8085}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{426}{2695}\right)\)