Dirichlet character χ676(511,⋅)\chi_{676}(511,\cdot)

• Label: 676.511
• Modulus: $676$
• Conductor: $676$
• Order: $78$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$676$
Conductor:	$676$
Order:	$78$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 676.u

$\chi_{676}(43,\cdot)$ $\chi_{676}(75,\cdot)$ $\chi_{676}(95,\cdot)$ $\chi_{676}(127,\cdot)$ $\chi_{676}(179,\cdot)$ $\chi_{676}(199,\cdot)$ $\chi_{676}(231,\cdot)$ $\chi_{676}(251,\cdot)$ $\chi_{676}(283,\cdot)$ $\chi_{676}(303,\cdot)$ $\chi_{676}(335,\cdot)$ $\chi_{676}(355,\cdot)$ $\chi_{676}(387,\cdot)$ $\chi_{676}(407,\cdot)$ $\chi_{676}(439,\cdot)$ $\chi_{676}(459,\cdot)$ $\chi_{676}(491,\cdot)$ $\chi_{676}(511,\cdot)$ $\chi_{676}(543,\cdot)$ $\chi_{676}(563,\cdot)$ $\chi_{676}(595,\cdot)$ $\chi_{676}(615,\cdot)$ $\chi_{676}(647,\cdot)$ $\chi_{676}(667,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Values on generators

$(339,509)$ → $(-1,e\left(\frac{1}{78}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 676 }(511, a)$	$-1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{1}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum