Dirichlet character \(\chi_{124509}(332,\cdot)\)

• Label: 124509.332
• 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.hd

\(\chi_{124509}(17,\cdot)\) \(\chi_{124509}(101,\cdot)\) \(\chi_{124509}(173,\cdot)\) \(\chi_{124509}(194,\cdot)\) \(\chi_{124509}(206,\cdot)\) \(\chi_{124509}(248,\cdot)\) \(\chi_{124509}(299,\cdot)\) \(\chi_{124509}(332,\cdot)\) \(\chi_{124509}(404,\cdot)\) \(\chi_{124509}(425,\cdot)\) \(\chi_{124509}(437,\cdot)\) \(\chi_{124509}(446,\cdot)\) \(\chi_{124509}(458,\cdot)\) \(\chi_{124509}(479,\cdot)\) \(\chi_{124509}(530,\cdot)\) \(\chi_{124509}(563,\cdot)\) \(\chi_{124509}(635,\cdot)\) \(\chi_{124509}(677,\cdot)\) \(\chi_{124509}(689,\cdot)\) \(\chi_{124509}(710,\cdot)\) \(\chi_{124509}(761,\cdot)\) \(\chi_{124509}(794,\cdot)\) \(\chi_{124509}(866,\cdot)\) \(\chi_{124509}(899,\cdot)\) \(\chi_{124509}(908,\cdot)\) \(\chi_{124509}(920,\cdot)\) \(\chi_{124509}(992,\cdot)\) \(\chi_{124509}(1025,\cdot)\) \(\chi_{124509}(1118,\cdot)\) \(\chi_{124509}(1130,\cdot)\) ...

Related number fields

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

Values on generators

\((41504,37390,2059)\) → \((-1,e\left(\frac{61}{294}\right),e\left(\frac{31}{110}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\( \chi_{ 124509 }(332, a) \)	\(-1\)	\(1\)	\(e\left(\frac{271}{8085}\right)\)	\(e\left(\frac{542}{8085}\right)\)	\(e\left(\frac{3004}{8085}\right)\)	\(e\left(\frac{271}{2695}\right)\)	\(e\left(\frac{655}{1617}\right)\)	\(e\left(\frac{1607}{2695}\right)\)	\(e\left(\frac{1084}{8085}\right)\)	\(e\left(\frac{8023}{16170}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{1182}{2695}\right)\)