Dirichlet character χ132300(2981,⋅)\chi_{132300}(2981,\cdot)

• Label: 132300.2981
• Modulus: $132300$
• Conductor: $33075$
• Order: $630$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$132300$
Conductor:	$33075$
Order:	$630$
Real:	no
Primitive:	no, induced from $\chi_{33075}(2981,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 132300.bbh

$\chi_{132300}(41,\cdot)$ $\chi_{132300}(461,\cdot)$ $\chi_{132300}(1721,\cdot)$ $\chi_{132300}(2561,\cdot)$ $\chi_{132300}(2981,\cdot)$ $\chi_{132300}(4241,\cdot)$ $\chi_{132300}(5081,\cdot)$ $\chi_{132300}(6341,\cdot)$ $\chi_{132300}(8021,\cdot)$ $\chi_{132300}(8861,\cdot)$ $\chi_{132300}(9281,\cdot)$ $\chi_{132300}(10121,\cdot)$ $\chi_{132300}(10541,\cdot)$ $\chi_{132300}(11381,\cdot)$ $\chi_{132300}(13061,\cdot)$ $\chi_{132300}(14321,\cdot)$ $\chi_{132300}(15161,\cdot)$ $\chi_{132300}(16421,\cdot)$ $\chi_{132300}(16841,\cdot)$ $\chi_{132300}(17681,\cdot)$ $\chi_{132300}(18941,\cdot)$ $\chi_{132300}(19361,\cdot)$ $\chi_{132300}(20621,\cdot)$ $\chi_{132300}(21881,\cdot)$ $\chi_{132300}(22721,\cdot)$ $\chi_{132300}(23141,\cdot)$ $\chi_{132300}(23981,\cdot)$ $\chi_{132300}(25241,\cdot)$ $\chi_{132300}(25661,\cdot)$ $\chi_{132300}(26921,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{315})$
Fixed field:	Number field defined by a degree 630 polynomial (not computed)

Values on generators

$(66151,122501,15877,54001)$ → $(1,e\left(\frac{13}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{5}{14}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(2981, a)$	$1$	$1$	$e\left(\frac{47}{630}\right)$	$e\left(\frac{103}{630}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{577}{630}\right)$	$e\left(\frac{599}{630}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{74}{315}\right)$	$e\left(\frac{2}{63}\right)$