Dirichlet character χ132300(38413,⋅)\chi_{132300}(38413,\cdot)

• Label: 132300.38413
• Modulus: $132300$
• Conductor: $11025$
• Order: $420$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$132300$
Conductor:	$11025$
Order:	$420$
Real:	no
Primitive:	no, induced from $\chi_{11025}(1663,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 132300.zz

$\chi_{132300}(37,\cdot)$ $\chi_{132300}(613,\cdot)$ $\chi_{132300}(3637,\cdot)$ $\chi_{132300}(3817,\cdot)$ $\chi_{132300}(4573,\cdot)$ $\chi_{132300}(7597,\cdot)$ $\chi_{132300}(8173,\cdot)$ $\chi_{132300}(8353,\cdot)$ $\chi_{132300}(11197,\cdot)$ $\chi_{132300}(11377,\cdot)$ $\chi_{132300}(11953,\cdot)$ $\chi_{132300}(14977,\cdot)$ $\chi_{132300}(15733,\cdot)$ $\chi_{132300}(15913,\cdot)$ $\chi_{132300}(18937,\cdot)$ $\chi_{132300}(19513,\cdot)$ $\chi_{132300}(22537,\cdot)$ $\chi_{132300}(23473,\cdot)$ $\chi_{132300}(26317,\cdot)$ $\chi_{132300}(26497,\cdot)$ $\chi_{132300}(27073,\cdot)$ $\chi_{132300}(27253,\cdot)$ $\chi_{132300}(30097,\cdot)$ $\chi_{132300}(30277,\cdot)$ $\chi_{132300}(30853,\cdot)$ $\chi_{132300}(31033,\cdot)$ $\chi_{132300}(34633,\cdot)$ $\chi_{132300}(34813,\cdot)$ $\chi_{132300}(37837,\cdot)$ $\chi_{132300}(38413,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

$(66151,122501,15877,54001)$ → $(1,e\left(\frac{2}{3}\right),e\left(\frac{19}{20}\right),e\left(\frac{11}{21}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(38413, a)$	$-1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{5}{84}\right)$