Dirichlet character χ507(203,⋅)\chi_{507}(203,\cdot)

• Label: 507.203
• Modulus: $507$
• Conductor: $507$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$507$
Conductor:	$507$
Order:	$52$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 507.s

$\chi_{507}(5,\cdot)$ $\chi_{507}(8,\cdot)$ $\chi_{507}(44,\cdot)$ $\chi_{507}(47,\cdot)$ $\chi_{507}(83,\cdot)$ $\chi_{507}(86,\cdot)$ $\chi_{507}(122,\cdot)$ $\chi_{507}(125,\cdot)$ $\chi_{507}(161,\cdot)$ $\chi_{507}(164,\cdot)$ $\chi_{507}(200,\cdot)$ $\chi_{507}(203,\cdot)$ $\chi_{507}(242,\cdot)$ $\chi_{507}(278,\cdot)$ $\chi_{507}(281,\cdot)$ $\chi_{507}(317,\cdot)$ $\chi_{507}(320,\cdot)$ $\chi_{507}(356,\cdot)$ $\chi_{507}(359,\cdot)$ $\chi_{507}(395,\cdot)$ $\chi_{507}(398,\cdot)$ $\chi_{507}(434,\cdot)$ $\chi_{507}(473,\cdot)$ $\chi_{507}(476,\cdot)$

Related number fields

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

Values on generators

$(170,340)$ → $(-1,e\left(\frac{49}{52}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 507 }(203, a)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{13}\right)$

Gauss sum

Jacobi sum

Kloosterman sum