Dirichlet character χ784(523,⋅)\chi_{784}(523,\cdot)

• Label: 784.523
• Modulus: $784$
• Conductor: $784$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$784$
Conductor:	$784$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 784.bu

$\chi_{784}(3,\cdot)$ $\chi_{784}(59,\cdot)$ $\chi_{784}(75,\cdot)$ $\chi_{784}(115,\cdot)$ $\chi_{784}(131,\cdot)$ $\chi_{784}(171,\cdot)$ $\chi_{784}(187,\cdot)$ $\chi_{784}(243,\cdot)$ $\chi_{784}(283,\cdot)$ $\chi_{784}(299,\cdot)$ $\chi_{784}(339,\cdot)$ $\chi_{784}(355,\cdot)$ $\chi_{784}(395,\cdot)$ $\chi_{784}(451,\cdot)$ $\chi_{784}(467,\cdot)$ $\chi_{784}(507,\cdot)$ $\chi_{784}(523,\cdot)$ $\chi_{784}(563,\cdot)$ $\chi_{784}(579,\cdot)$ $\chi_{784}(635,\cdot)$ $\chi_{784}(675,\cdot)$ $\chi_{784}(691,\cdot)$ $\chi_{784}(731,\cdot)$ $\chi_{784}(747,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(687,197,689)$ → $(-1,i,e\left(\frac{41}{42}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 784 }(523, a)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$

Gauss sum

Jacobi sum

Kloosterman sum