Dirichlet character \(\chi_{1323}(1004,\cdot)\)

• Label: 1323.1004
• Modulus: $1323$
• Conductor: $1323$
• Order: $126$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1323.cf

\(\chi_{1323}(47,\cdot)\) \(\chi_{1323}(59,\cdot)\) \(\chi_{1323}(110,\cdot)\) \(\chi_{1323}(122,\cdot)\) \(\chi_{1323}(173,\cdot)\) \(\chi_{1323}(185,\cdot)\) \(\chi_{1323}(236,\cdot)\) \(\chi_{1323}(248,\cdot)\) \(\chi_{1323}(299,\cdot)\) \(\chi_{1323}(311,\cdot)\) \(\chi_{1323}(425,\cdot)\) \(\chi_{1323}(437,\cdot)\) \(\chi_{1323}(488,\cdot)\) \(\chi_{1323}(500,\cdot)\) \(\chi_{1323}(551,\cdot)\) \(\chi_{1323}(563,\cdot)\) \(\chi_{1323}(614,\cdot)\) \(\chi_{1323}(626,\cdot)\) \(\chi_{1323}(677,\cdot)\) \(\chi_{1323}(689,\cdot)\) \(\chi_{1323}(740,\cdot)\) \(\chi_{1323}(752,\cdot)\) \(\chi_{1323}(866,\cdot)\) \(\chi_{1323}(878,\cdot)\) \(\chi_{1323}(929,\cdot)\) \(\chi_{1323}(941,\cdot)\) \(\chi_{1323}(992,\cdot)\) \(\chi_{1323}(1004,\cdot)\) \(\chi_{1323}(1055,\cdot)\) \(\chi_{1323}(1067,\cdot)\) ...

Related number fields

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

Values on generators

\((785,1081)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{37}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(1004, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)