Dirichlet character χ664(643,⋅)\chi_{664}(643,\cdot)

• Label: 664.643
• Modulus: $664$
• Conductor: $664$
• Order: $82$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$664$
Conductor:	$664$
Order:	$82$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 664.j

$\chi_{664}(19,\cdot)$ $\chi_{664}(35,\cdot)$ $\chi_{664}(43,\cdot)$ $\chi_{664}(67,\cdot)$ $\chi_{664}(91,\cdot)$ $\chi_{664}(107,\cdot)$ $\chi_{664}(115,\cdot)$ $\chi_{664}(139,\cdot)$ $\chi_{664}(155,\cdot)$ $\chi_{664}(163,\cdot)$ $\chi_{664}(171,\cdot)$ $\chi_{664}(179,\cdot)$ $\chi_{664}(211,\cdot)$ $\chi_{664}(219,\cdot)$ $\chi_{664}(251,\cdot)$ $\chi_{664}(267,\cdot)$ $\chi_{664}(283,\cdot)$ $\chi_{664}(291,\cdot)$ $\chi_{664}(299,\cdot)$ $\chi_{664}(307,\cdot)$ $\chi_{664}(315,\cdot)$ $\chi_{664}(323,\cdot)$ $\chi_{664}(347,\cdot)$ $\chi_{664}(371,\cdot)$ $\chi_{664}(379,\cdot)$ $\chi_{664}(387,\cdot)$ $\chi_{664}(403,\cdot)$ $\chi_{664}(411,\cdot)$ $\chi_{664}(435,\cdot)$ $\chi_{664}(467,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{41})$
Fixed field:	Number field defined by a degree 82 polynomial

Values on generators

$(167,333,417)$ → $(-1,-1,e\left(\frac{39}{82}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 664 }(643, a)$	$1$	$1$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{25}{82}\right)$	$e\left(\frac{20}{41}\right)$	$e\left(\frac{17}{41}\right)$	$e\left(\frac{5}{41}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{26}{41}\right)$	$e\left(\frac{29}{82}\right)$	$e\left(\frac{45}{82}\right)$

Gauss sum

Jacobi sum

Kloosterman sum