Dirichlet character χ5850(4969,⋅)\chi_{5850}(4969,\cdot)

• Label: 5850.4969
• Modulus: $5850$
• Conductor: $325$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5850$
Conductor:	$325$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{325}(94,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5850.fo

$\chi_{5850}(289,\cdot)$ $\chi_{5850}(919,\cdot)$ $\chi_{5850}(1459,\cdot)$ $\chi_{5850}(2089,\cdot)$ $\chi_{5850}(2629,\cdot)$ $\chi_{5850}(3259,\cdot)$ $\chi_{5850}(4429,\cdot)$ $\chi_{5850}(4969,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(3251,3277,2251)$ → $(1,e\left(\frac{9}{10}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 5850 }(4969, a)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$