Dirichlet character χ350(47,⋅)\chi_{350}(47,\cdot)

• Label: 350.47
• Modulus: $350$
• Conductor: $175$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$350$
Conductor:	$175$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{175}(47,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 350.x

$\chi_{350}(3,\cdot)$ $\chi_{350}(17,\cdot)$ $\chi_{350}(33,\cdot)$ $\chi_{350}(47,\cdot)$ $\chi_{350}(73,\cdot)$ $\chi_{350}(87,\cdot)$ $\chi_{350}(103,\cdot)$ $\chi_{350}(117,\cdot)$ $\chi_{350}(173,\cdot)$ $\chi_{350}(187,\cdot)$ $\chi_{350}(213,\cdot)$ $\chi_{350}(227,\cdot)$ $\chi_{350}(283,\cdot)$ $\chi_{350}(297,\cdot)$ $\chi_{350}(313,\cdot)$ $\chi_{350}(327,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(127,101)$ → $(e\left(\frac{17}{20}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{ 350 }(47, a)$	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$

Gauss sum

Jacobi sum

Kloosterman sum