Dirichlet character \(\chi_{1305}(967,\cdot)\)

• Label: 1305.967
• Modulus: $1305$
• Conductor: $1305$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1305\)
Conductor:	\(1305\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1305.cq

\(\chi_{1305}(43,\cdot)\) \(\chi_{1305}(97,\cdot)\) \(\chi_{1305}(142,\cdot)\) \(\chi_{1305}(148,\cdot)\) \(\chi_{1305}(193,\cdot)\) \(\chi_{1305}(247,\cdot)\) \(\chi_{1305}(337,\cdot)\) \(\chi_{1305}(472,\cdot)\) \(\chi_{1305}(553,\cdot)\) \(\chi_{1305}(583,\cdot)\) \(\chi_{1305}(607,\cdot)\) \(\chi_{1305}(628,\cdot)\) \(\chi_{1305}(682,\cdot)\) \(\chi_{1305}(688,\cdot)\) \(\chi_{1305}(772,\cdot)\) \(\chi_{1305}(823,\cdot)\) \(\chi_{1305}(907,\cdot)\) \(\chi_{1305}(913,\cdot)\) \(\chi_{1305}(967,\cdot)\) \(\chi_{1305}(988,\cdot)\) \(\chi_{1305}(1012,\cdot)\) \(\chi_{1305}(1042,\cdot)\) \(\chi_{1305}(1123,\cdot)\) \(\chi_{1305}(1258,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((146,262,901)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{23}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1305 }(967, a) \)	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(-1\)	\(e\left(\frac{25}{28}\right)\)