Dirichlet character χ59(10,⋅)\chi_{59}(10,\cdot)

• Label: 59.10
• Modulus: $59$
• Conductor: $59$
• Order: $58$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$59$
Conductor:	$59$
Order:	$58$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 59.d

$\chi_{59}(2,\cdot)$ $\chi_{59}(6,\cdot)$ $\chi_{59}(8,\cdot)$ $\chi_{59}(10,\cdot)$ $\chi_{59}(11,\cdot)$ $\chi_{59}(13,\cdot)$ $\chi_{59}(14,\cdot)$ $\chi_{59}(18,\cdot)$ $\chi_{59}(23,\cdot)$ $\chi_{59}(24,\cdot)$ $\chi_{59}(30,\cdot)$ $\chi_{59}(31,\cdot)$ $\chi_{59}(32,\cdot)$ $\chi_{59}(33,\cdot)$ $\chi_{59}(34,\cdot)$ $\chi_{59}(37,\cdot)$ $\chi_{59}(38,\cdot)$ $\chi_{59}(39,\cdot)$ $\chi_{59}(40,\cdot)$ $\chi_{59}(42,\cdot)$ $\chi_{59}(43,\cdot)$ $\chi_{59}(44,\cdot)$ $\chi_{59}(47,\cdot)$ $\chi_{59}(50,\cdot)$ $\chi_{59}(52,\cdot)$ $\chi_{59}(54,\cdot)$ $\chi_{59}(55,\cdot)$ $\chi_{59}(56,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{29})$
Fixed field:	Number field defined by a degree 58 polynomial

Values on generators

$2$ → $e\left(\frac{7}{58}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 59 }(10, a)$	$-1$	$1$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{1}{58}\right)$

Gauss sum

Jacobi sum

Kloosterman sum