Dirichlet character \(\chi_{1323}(38,\cdot)\)

• Label: 1323.38
• 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.ci

\(\chi_{1323}(5,\cdot)\) \(\chi_{1323}(38,\cdot)\) \(\chi_{1323}(101,\cdot)\) \(\chi_{1323}(131,\cdot)\) \(\chi_{1323}(164,\cdot)\) \(\chi_{1323}(194,\cdot)\) \(\chi_{1323}(257,\cdot)\) \(\chi_{1323}(290,\cdot)\) \(\chi_{1323}(320,\cdot)\) \(\chi_{1323}(353,\cdot)\) \(\chi_{1323}(383,\cdot)\) \(\chi_{1323}(416,\cdot)\) \(\chi_{1323}(446,\cdot)\) \(\chi_{1323}(479,\cdot)\) \(\chi_{1323}(542,\cdot)\) \(\chi_{1323}(572,\cdot)\) \(\chi_{1323}(605,\cdot)\) \(\chi_{1323}(635,\cdot)\) \(\chi_{1323}(698,\cdot)\) \(\chi_{1323}(731,\cdot)\) \(\chi_{1323}(761,\cdot)\) \(\chi_{1323}(794,\cdot)\) \(\chi_{1323}(824,\cdot)\) \(\chi_{1323}(857,\cdot)\) \(\chi_{1323}(887,\cdot)\) \(\chi_{1323}(920,\cdot)\) \(\chi_{1323}(983,\cdot)\) \(\chi_{1323}(1013,\cdot)\) \(\chi_{1323}(1046,\cdot)\) \(\chi_{1323}(1076,\cdot)\) ...

Related number fields

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

Values on generators

\((785,1081)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{19}{42}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\( \chi_{ 1323 }(38, a) \)	\(1\)	\(1\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)