Dirichlet character \(\chi_{32805}(43,\cdot)\)

• Label: 32805.43
• Modulus: $32805$
• Conductor: $32805$
• Order: $8748$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(32805\)
Conductor:	\(32805\)
Order:	\(8748\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 32805.bu

\(\chi_{32805}(7,\cdot)\) \(\chi_{32805}(13,\cdot)\) \(\chi_{32805}(22,\cdot)\) \(\chi_{32805}(43,\cdot)\) \(\chi_{32805}(52,\cdot)\) \(\chi_{32805}(58,\cdot)\) \(\chi_{32805}(67,\cdot)\) \(\chi_{32805}(88,\cdot)\) \(\chi_{32805}(97,\cdot)\) \(\chi_{32805}(103,\cdot)\) \(\chi_{32805}(112,\cdot)\) \(\chi_{32805}(133,\cdot)\) \(\chi_{32805}(142,\cdot)\) \(\chi_{32805}(148,\cdot)\) \(\chi_{32805}(157,\cdot)\) \(\chi_{32805}(178,\cdot)\) \(\chi_{32805}(187,\cdot)\) \(\chi_{32805}(193,\cdot)\) \(\chi_{32805}(202,\cdot)\) \(\chi_{32805}(223,\cdot)\) \(\chi_{32805}(232,\cdot)\) \(\chi_{32805}(238,\cdot)\) \(\chi_{32805}(247,\cdot)\) \(\chi_{32805}(268,\cdot)\) \(\chi_{32805}(277,\cdot)\) \(\chi_{32805}(283,\cdot)\) \(\chi_{32805}(292,\cdot)\) \(\chi_{32805}(313,\cdot)\) \(\chi_{32805}(322,\cdot)\) \(\chi_{32805}(328,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{8748})$
Fixed field:	Number field defined by a degree 8748 polynomial (not computed)

Values on generators

\((26246,6562)\) → \((e\left(\frac{1199}{2187}\right),-i)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 32805 }(43, a) \)	\(-1\)	\(1\)	\(e\left(\frac{2609}{8748}\right)\)	\(e\left(\frac{2609}{4374}\right)\)	\(e\left(\frac{785}{8748}\right)\)	\(e\left(\frac{2609}{2916}\right)\)	\(e\left(\frac{575}{2187}\right)\)	\(e\left(\frac{4267}{8748}\right)\)	\(e\left(\frac{1697}{4374}\right)\)	\(e\left(\frac{422}{2187}\right)\)	\(e\left(\frac{1483}{2916}\right)\)	\(e\left(\frac{1225}{1458}\right)\)