Dirichlet character χ644(493,⋅)\chi_{644}(493,\cdot)

• Label: 644.493
• Modulus: $644$
• Conductor: $161$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$644$
Conductor:	$161$
Order:	$66$
Real:	no
Primitive:	no, induced from $\chi_{161}(10,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 644.bc

$\chi_{644}(5,\cdot)$ $\chi_{644}(17,\cdot)$ $\chi_{644}(33,\cdot)$ $\chi_{644}(61,\cdot)$ $\chi_{644}(89,\cdot)$ $\chi_{644}(129,\cdot)$ $\chi_{644}(145,\cdot)$ $\chi_{644}(157,\cdot)$ $\chi_{644}(201,\cdot)$ $\chi_{644}(241,\cdot)$ $\chi_{644}(297,\cdot)$ $\chi_{644}(313,\cdot)$ $\chi_{644}(341,\cdot)$ $\chi_{644}(425,\cdot)$ $\chi_{644}(465,\cdot)$ $\chi_{644}(481,\cdot)$ $\chi_{644}(493,\cdot)$ $\chi_{644}(521,\cdot)$ $\chi_{644}(549,\cdot)$ $\chi_{644}(605,\cdot)$

Related number fields

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

Values on generators

$(323,185,281)$ → $(1,e\left(\frac{1}{6}\right),e\left(\frac{3}{22}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{ 644 }(493, a)$	$1$	$1$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{1}{22}\right)$

Gauss sum

Jacobi sum

Kloosterman sum