Dirichlet character χ132300(131,⋅)\chi_{132300}(131,\cdot)

• Label: 132300.131
• Modulus: $132300$
• Conductor: $132300$
• Order: $630$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$132300$
Conductor:	$132300$
Order:	$630$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 132300.bcj

$\chi_{132300}(131,\cdot)$ $\chi_{132300}(731,\cdot)$ $\chi_{132300}(3911,\cdot)$ $\chi_{132300}(4511,\cdot)$ $\chi_{132300}(5171,\cdot)$ $\chi_{132300}(5771,\cdot)$ $\chi_{132300}(6431,\cdot)$ $\chi_{132300}(7031,\cdot)$ $\chi_{132300}(7691,\cdot)$ $\chi_{132300}(8291,\cdot)$ $\chi_{132300}(11471,\cdot)$ $\chi_{132300}(12071,\cdot)$ $\chi_{132300}(12731,\cdot)$ $\chi_{132300}(13331,\cdot)$ $\chi_{132300}(13991,\cdot)$ $\chi_{132300}(14591,\cdot)$ $\chi_{132300}(16511,\cdot)$ $\chi_{132300}(17111,\cdot)$ $\chi_{132300}(17771,\cdot)$ $\chi_{132300}(18371,\cdot)$ $\chi_{132300}(20291,\cdot)$ $\chi_{132300}(20891,\cdot)$ $\chi_{132300}(22811,\cdot)$ $\chi_{132300}(23411,\cdot)$ $\chi_{132300}(24071,\cdot)$ $\chi_{132300}(24671,\cdot)$ $\chi_{132300}(25331,\cdot)$ $\chi_{132300}(25931,\cdot)$ $\chi_{132300}(26591,\cdot)$ $\chi_{132300}(27191,\cdot)$ ...

Related number fields

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

Values on generators

$(66151,122501,15877,54001)$ → $(-1,e\left(\frac{11}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{41}{42}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(131, a)$	$-1$	$1$	$e\left(\frac{281}{315}\right)$	$e\left(\frac{443}{630}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{226}{315}\right)$	$e\left(\frac{619}{630}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{199}{315}\right)$	$e\left(\frac{101}{126}\right)$