Dirichlet character χ676(395,⋅)\chi_{676}(395,\cdot)

• Label: 676.395
• Modulus: $676$
• Conductor: $676$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$676$
Conductor:	$676$
Order:	$52$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 676.s

$\chi_{676}(31,\cdot)$ $\chi_{676}(47,\cdot)$ $\chi_{676}(83,\cdot)$ $\chi_{676}(135,\cdot)$ $\chi_{676}(151,\cdot)$ $\chi_{676}(187,\cdot)$ $\chi_{676}(203,\cdot)$ $\chi_{676}(255,\cdot)$ $\chi_{676}(291,\cdot)$ $\chi_{676}(307,\cdot)$ $\chi_{676}(343,\cdot)$ $\chi_{676}(359,\cdot)$ $\chi_{676}(395,\cdot)$ $\chi_{676}(411,\cdot)$ $\chi_{676}(447,\cdot)$ $\chi_{676}(463,\cdot)$ $\chi_{676}(499,\cdot)$ $\chi_{676}(515,\cdot)$ $\chi_{676}(551,\cdot)$ $\chi_{676}(567,\cdot)$ $\chi_{676}(603,\cdot)$ $\chi_{676}(619,\cdot)$ $\chi_{676}(655,\cdot)$ $\chi_{676}(671,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

$(339,509)$ → $(-1,e\left(\frac{11}{52}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 676 }(395, a)$	$1$	$1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{23}{26}\right)$	$i$	$e\left(\frac{45}{52}\right)$	$1$

Gauss sum

Jacobi sum

Kloosterman sum