Dirichlet character χ58(11,⋅)\chi_{58}(11,\cdot)

• Label: 58.11
• Modulus: $58$
• Conductor: $29$
• Order: $28$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$58$
Conductor:	$29$
Order:	$28$
Real:	no
Primitive:	no, induced from $\chi_{29}(11,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 58.f

$\chi_{58}(3,\cdot)$ $\chi_{58}(11,\cdot)$ $\chi_{58}(15,\cdot)$ $\chi_{58}(19,\cdot)$ $\chi_{58}(21,\cdot)$ $\chi_{58}(27,\cdot)$ $\chi_{58}(31,\cdot)$ $\chi_{58}(37,\cdot)$ $\chi_{58}(39,\cdot)$ $\chi_{58}(43,\cdot)$ $\chi_{58}(47,\cdot)$ $\chi_{58}(55,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{28})$
Fixed field:	Number field defined by a degree 28 polynomial

Values on generators

$31$ → $e\left(\frac{25}{28}\right)$

Values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 58 }(11, a)$	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{28}\right)$	$-i$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$

Gauss sum

Jacobi sum

Kloosterman sum