Dirichlet character χ1328(363,⋅)\chi_{1328}(363,\cdot)

• Label: 1328.363
• Modulus: $1328$
• Conductor: $1328$
• Order: $164$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1328$
Conductor:	$1328$
Order:	$164$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1328.v

$\chi_{1328}(3,\cdot)$ $\chi_{1328}(11,\cdot)$ $\chi_{1328}(27,\cdot)$ $\chi_{1328}(51,\cdot)$ $\chi_{1328}(59,\cdot)$ $\chi_{1328}(75,\cdot)$ $\chi_{1328}(99,\cdot)$ $\chi_{1328}(123,\cdot)$ $\chi_{1328}(131,\cdot)$ $\chi_{1328}(147,\cdot)$ $\chi_{1328}(187,\cdot)$ $\chi_{1328}(195,\cdot)$ $\chi_{1328}(203,\cdot)$ $\chi_{1328}(227,\cdot)$ $\chi_{1328}(235,\cdot)$ $\chi_{1328}(243,\cdot)$ $\chi_{1328}(259,\cdot)$ $\chi_{1328}(275,\cdot)$ $\chi_{1328}(339,\cdot)$ $\chi_{1328}(355,\cdot)$ $\chi_{1328}(363,\cdot)$ $\chi_{1328}(395,\cdot)$ $\chi_{1328}(419,\cdot)$ $\chi_{1328}(427,\cdot)$ $\chi_{1328}(443,\cdot)$ $\chi_{1328}(451,\cdot)$ $\chi_{1328}(459,\cdot)$ $\chi_{1328}(483,\cdot)$ $\chi_{1328}(507,\cdot)$ $\chi_{1328}(515,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{164})$
Fixed field:	Number field defined by a degree 164 polynomial (not computed)

Values on generators

$(831,997,417)$ → $(-1,i,e\left(\frac{19}{41}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 1328 }(363, a)$	$-1$	$1$	$e\left(\frac{101}{164}\right)$	$e\left(\frac{125}{164}\right)$	$e\left(\frac{29}{41}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{143}{164}\right)$	$e\left(\frac{71}{164}\right)$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{5}{164}\right)$	$e\left(\frac{53}{164}\right)$