Dirichlet character χ483(38,⋅)\chi_{483}(38,\cdot)

• Label: 483.38
• Modulus: $483$
• Conductor: $483$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$483$
Conductor:	$483$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 483.ba

$\chi_{483}(5,\cdot)$ $\chi_{483}(17,\cdot)$ $\chi_{483}(38,\cdot)$ $\chi_{483}(80,\cdot)$ $\chi_{483}(89,\cdot)$ $\chi_{483}(122,\cdot)$ $\chi_{483}(143,\cdot)$ $\chi_{483}(152,\cdot)$ $\chi_{483}(194,\cdot)$ $\chi_{483}(227,\cdot)$ $\chi_{483}(290,\cdot)$ $\chi_{483}(320,\cdot)$ $\chi_{483}(332,\cdot)$ $\chi_{483}(341,\cdot)$ $\chi_{483}(362,\cdot)$ $\chi_{483}(383,\cdot)$ $\chi_{483}(425,\cdot)$ $\chi_{483}(458,\cdot)$ $\chi_{483}(467,\cdot)$ $\chi_{483}(479,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(323,346,442)$ → $(-1,e\left(\frac{1}{6}\right),e\left(\frac{17}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{ 483 }(38, a)$	$-1$	$1$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{14}{33}\right)$

Gauss sum

Jacobi sum

Kloosterman sum