Dirichlet character \(\chi_{1089}(412,\cdot)\)

• Label: 1089.412
• Modulus: $1089$
• Conductor: $1089$
• Order: $165$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1089\)
Conductor:	\(1089\)
Order:	\(165\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1089.bc

\(\chi_{1089}(4,\cdot)\) \(\chi_{1089}(16,\cdot)\) \(\chi_{1089}(25,\cdot)\) \(\chi_{1089}(31,\cdot)\) \(\chi_{1089}(49,\cdot)\) \(\chi_{1089}(58,\cdot)\) \(\chi_{1089}(70,\cdot)\) \(\chi_{1089}(97,\cdot)\) \(\chi_{1089}(103,\cdot)\) \(\chi_{1089}(115,\cdot)\) \(\chi_{1089}(157,\cdot)\) \(\chi_{1089}(169,\cdot)\) \(\chi_{1089}(196,\cdot)\) \(\chi_{1089}(214,\cdot)\) \(\chi_{1089}(223,\cdot)\) \(\chi_{1089}(229,\cdot)\) \(\chi_{1089}(247,\cdot)\) \(\chi_{1089}(256,\cdot)\) \(\chi_{1089}(268,\cdot)\) \(\chi_{1089}(295,\cdot)\) \(\chi_{1089}(301,\cdot)\) \(\chi_{1089}(313,\cdot)\) \(\chi_{1089}(322,\cdot)\) \(\chi_{1089}(328,\cdot)\) \(\chi_{1089}(346,\cdot)\) \(\chi_{1089}(355,\cdot)\) \(\chi_{1089}(367,\cdot)\) \(\chi_{1089}(394,\cdot)\) \(\chi_{1089}(400,\cdot)\) \(\chi_{1089}(412,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 165 polynomial (not computed)

Values on generators

\((848,244)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{55}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\( \chi_{ 1089 }(412, a) \)	\(1\)	\(1\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)