Dirichlet character χ12825(10037,⋅)\chi_{12825}(10037,\cdot)

• Label: 12825.10037
• Modulus: $12825$
• Conductor: $12825$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$12825$
Conductor:	$12825$
Order:	$180$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 12825.pe

$\chi_{12825}(23,\cdot)$ $\chi_{12825}(92,\cdot)$ $\chi_{12825}(758,\cdot)$ $\chi_{12825}(803,\cdot)$ $\chi_{12825}(842,\cdot)$ $\chi_{12825}(1472,\cdot)$ $\chi_{12825}(1562,\cdot)$ $\chi_{12825}(2297,\cdot)$ $\chi_{12825}(2342,\cdot)$ $\chi_{12825}(2498,\cdot)$ $\chi_{12825}(2588,\cdot)$ $\chi_{12825}(3323,\cdot)$ $\chi_{12825}(3683,\cdot)$ $\chi_{12825}(4037,\cdot)$ $\chi_{12825}(4127,\cdot)$ $\chi_{12825}(4433,\cdot)$ $\chi_{12825}(4862,\cdot)$ $\chi_{12825}(5063,\cdot)$ $\chi_{12825}(5153,\cdot)$ $\chi_{12825}(5222,\cdot)$ $\chi_{12825}(5888,\cdot)$ $\chi_{12825}(5933,\cdot)$ $\chi_{12825}(5972,\cdot)$ $\chi_{12825}(6248,\cdot)$ $\chi_{12825}(6602,\cdot)$ $\chi_{12825}(6692,\cdot)$ $\chi_{12825}(6998,\cdot)$ $\chi_{12825}(7427,\cdot)$ $\chi_{12825}(7472,\cdot)$ $\chi_{12825}(7628,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

$(10451,1027,1351)$ → $(e\left(\frac{7}{18}\right),e\left(\frac{9}{20}\right),e\left(\frac{8}{9}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{ 12825 }(10037, a)$	$1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{13}{20}\right)$