Dirichlet character χ5850(1127,⋅)\chi_{5850}(1127,\cdot)

• Label: 5850.1127
• Modulus: $5850$
• Conductor: $2925$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5850$
Conductor:	$2925$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{2925}(1127,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 5850.gi

$\chi_{5850}(653,\cdot)$ $\chi_{5850}(887,\cdot)$ $\chi_{5850}(1127,\cdot)$ $\chi_{5850}(1823,\cdot)$ $\chi_{5850}(2063,\cdot)$ $\chi_{5850}(2297,\cdot)$ $\chi_{5850}(3227,\cdot)$ $\chi_{5850}(3233,\cdot)$ $\chi_{5850}(3467,\cdot)$ $\chi_{5850}(4163,\cdot)$ $\chi_{5850}(4397,\cdot)$ $\chi_{5850}(4403,\cdot)$ $\chi_{5850}(4637,\cdot)$ $\chi_{5850}(5333,\cdot)$ $\chi_{5850}(5567,\cdot)$ $\chi_{5850}(5573,\cdot)$

Related number fields

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

Values on generators

$(3251,3277,2251)$ → $(e\left(\frac{1}{6}\right),e\left(\frac{1}{20}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 5850 }(1127, a)$	$1$	$1$	$i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$