Dirichlet character \(\chi_{1323}(457,\cdot)\)

• Label: 1323.457
• Modulus: $1323$
• Conductor: $1323$
• Order: $63$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1323\)
Conductor:	\(1323\)
Order:	\(63\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1323.cc

\(\chi_{1323}(4,\cdot)\) \(\chi_{1323}(16,\cdot)\) \(\chi_{1323}(130,\cdot)\) \(\chi_{1323}(142,\cdot)\) \(\chi_{1323}(193,\cdot)\) \(\chi_{1323}(205,\cdot)\) \(\chi_{1323}(256,\cdot)\) \(\chi_{1323}(268,\cdot)\) \(\chi_{1323}(319,\cdot)\) \(\chi_{1323}(331,\cdot)\) \(\chi_{1323}(382,\cdot)\) \(\chi_{1323}(394,\cdot)\) \(\chi_{1323}(445,\cdot)\) \(\chi_{1323}(457,\cdot)\) \(\chi_{1323}(571,\cdot)\) \(\chi_{1323}(583,\cdot)\) \(\chi_{1323}(634,\cdot)\) \(\chi_{1323}(646,\cdot)\) \(\chi_{1323}(697,\cdot)\) \(\chi_{1323}(709,\cdot)\) \(\chi_{1323}(760,\cdot)\) \(\chi_{1323}(772,\cdot)\) \(\chi_{1323}(823,\cdot)\) \(\chi_{1323}(835,\cdot)\) \(\chi_{1323}(886,\cdot)\) \(\chi_{1323}(898,\cdot)\) \(\chi_{1323}(1012,\cdot)\) \(\chi_{1323}(1024,\cdot)\) \(\chi_{1323}(1075,\cdot)\) \(\chi_{1323}(1087,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 63 polynomial

Values on generators

\((785,1081)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{10}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(457, a) \)	\(1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)