Dirichlet character \(\chi_{1323}(1159,\cdot)\)

• Label: 1323.1159
• 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.ca

\(\chi_{1323}(25,\cdot)\) \(\chi_{1323}(58,\cdot)\) \(\chi_{1323}(88,\cdot)\) \(\chi_{1323}(121,\cdot)\) \(\chi_{1323}(151,\cdot)\) \(\chi_{1323}(184,\cdot)\) \(\chi_{1323}(247,\cdot)\) \(\chi_{1323}(277,\cdot)\) \(\chi_{1323}(310,\cdot)\) \(\chi_{1323}(340,\cdot)\) \(\chi_{1323}(403,\cdot)\) \(\chi_{1323}(436,\cdot)\) \(\chi_{1323}(466,\cdot)\) \(\chi_{1323}(499,\cdot)\) \(\chi_{1323}(529,\cdot)\) \(\chi_{1323}(562,\cdot)\) \(\chi_{1323}(592,\cdot)\) \(\chi_{1323}(625,\cdot)\) \(\chi_{1323}(688,\cdot)\) \(\chi_{1323}(718,\cdot)\) \(\chi_{1323}(751,\cdot)\) \(\chi_{1323}(781,\cdot)\) \(\chi_{1323}(844,\cdot)\) \(\chi_{1323}(877,\cdot)\) \(\chi_{1323}(907,\cdot)\) \(\chi_{1323}(940,\cdot)\) \(\chi_{1323}(970,\cdot)\) \(\chi_{1323}(1003,\cdot)\) \(\chi_{1323}(1033,\cdot)\) \(\chi_{1323}(1066,\cdot)\) ...

Related number fields

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

Values on generators

\((785,1081)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{21}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(1159, a) \)	\(1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)