Dirichlet character \(\chi_{1323}(34,\cdot)\)

• Label: 1323.34
• Modulus: $1323$
• Conductor: $1323$
• Order: $126$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1323\)
Conductor:	\(1323\)
Order:	\(126\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1323.ck

\(\chi_{1323}(13,\cdot)\) \(\chi_{1323}(34,\cdot)\) \(\chi_{1323}(76,\cdot)\) \(\chi_{1323}(139,\cdot)\) \(\chi_{1323}(160,\cdot)\) \(\chi_{1323}(202,\cdot)\) \(\chi_{1323}(223,\cdot)\) \(\chi_{1323}(265,\cdot)\) \(\chi_{1323}(286,\cdot)\) \(\chi_{1323}(328,\cdot)\) \(\chi_{1323}(349,\cdot)\) \(\chi_{1323}(412,\cdot)\) \(\chi_{1323}(454,\cdot)\) \(\chi_{1323}(475,\cdot)\) \(\chi_{1323}(517,\cdot)\) \(\chi_{1323}(580,\cdot)\) \(\chi_{1323}(601,\cdot)\) \(\chi_{1323}(643,\cdot)\) \(\chi_{1323}(664,\cdot)\) \(\chi_{1323}(706,\cdot)\) \(\chi_{1323}(727,\cdot)\) \(\chi_{1323}(769,\cdot)\) \(\chi_{1323}(790,\cdot)\) \(\chi_{1323}(853,\cdot)\) \(\chi_{1323}(895,\cdot)\) \(\chi_{1323}(916,\cdot)\) \(\chi_{1323}(958,\cdot)\) \(\chi_{1323}(1021,\cdot)\) \(\chi_{1323}(1042,\cdot)\) \(\chi_{1323}(1084,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

Values on generators

\((785,1081)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{3}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(34, a) \)	\(-1\)	\(1\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)