Dirichlet character \(\chi_{1323}(1123,\cdot)\)

• Label: 1323.1123
• 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.cl

\(\chi_{1323}(40,\cdot)\) \(\chi_{1323}(52,\cdot)\) \(\chi_{1323}(103,\cdot)\) \(\chi_{1323}(115,\cdot)\) \(\chi_{1323}(229,\cdot)\) \(\chi_{1323}(241,\cdot)\) \(\chi_{1323}(292,\cdot)\) \(\chi_{1323}(304,\cdot)\) \(\chi_{1323}(355,\cdot)\) \(\chi_{1323}(367,\cdot)\) \(\chi_{1323}(418,\cdot)\) \(\chi_{1323}(430,\cdot)\) \(\chi_{1323}(481,\cdot)\) \(\chi_{1323}(493,\cdot)\) \(\chi_{1323}(544,\cdot)\) \(\chi_{1323}(556,\cdot)\) \(\chi_{1323}(670,\cdot)\) \(\chi_{1323}(682,\cdot)\) \(\chi_{1323}(733,\cdot)\) \(\chi_{1323}(745,\cdot)\) \(\chi_{1323}(796,\cdot)\) \(\chi_{1323}(808,\cdot)\) \(\chi_{1323}(859,\cdot)\) \(\chi_{1323}(871,\cdot)\) \(\chi_{1323}(922,\cdot)\) \(\chi_{1323}(934,\cdot)\) \(\chi_{1323}(985,\cdot)\) \(\chi_{1323}(997,\cdot)\) \(\chi_{1323}(1111,\cdot)\) \(\chi_{1323}(1123,\cdot)\) ...

Related number fields

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

Values on generators

\((785,1081)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{31}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(1123, a) \)	\(-1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(-1\)