Dirichlet character χ538(21,⋅)\chi_{538}(21,\cdot)

• Label: 538.21
• Modulus: $538$
• Conductor: $269$
• Order: $67$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$538$
Conductor:	$269$
Order:	$67$
Real:	no
Primitive:	no, induced from $\chi_{269}(21,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 538.d

$\chi_{538}(5,\cdot)$ $\chi_{538}(21,\cdot)$ $\chi_{538}(23,\cdot)$ $\chi_{538}(25,\cdot)$ $\chi_{538}(37,\cdot)$ $\chi_{538}(41,\cdot)$ $\chi_{538}(47,\cdot)$ $\chi_{538}(53,\cdot)$ $\chi_{538}(57,\cdot)$ $\chi_{538}(61,\cdot)$ $\chi_{538}(67,\cdot)$ $\chi_{538}(81,\cdot)$ $\chi_{538}(87,\cdot)$ $\chi_{538}(93,\cdot)$ $\chi_{538}(99,\cdot)$ $\chi_{538}(105,\cdot)$ $\chi_{538}(115,\cdot)$ $\chi_{538}(117,\cdot)$ $\chi_{538}(119,\cdot)$ $\chi_{538}(121,\cdot)$ $\chi_{538}(125,\cdot)$ $\chi_{538}(131,\cdot)$ $\chi_{538}(143,\cdot)$ $\chi_{538}(169,\cdot)$ $\chi_{538}(173,\cdot)$ $\chi_{538}(177,\cdot)$ $\chi_{538}(185,\cdot)$ $\chi_{538}(205,\cdot)$ $\chi_{538}(213,\cdot)$ $\chi_{538}(235,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{67})$
Fixed field:	Number field defined by a degree 67 polynomial

Values on generators

$271$ → $e\left(\frac{32}{67}\right)$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 538 }(21, a)$	$1$	$1$	$e\left(\frac{4}{67}\right)$	$e\left(\frac{23}{67}\right)$	$e\left(\frac{5}{67}\right)$	$e\left(\frac{8}{67}\right)$	$e\left(\frac{57}{67}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{27}{67}\right)$	$e\left(\frac{10}{67}\right)$	$e\left(\frac{34}{67}\right)$	$e\left(\frac{9}{67}\right)$

Gauss sum

Jacobi sum

Kloosterman sum