Dirichlet character χ248400(4813,⋅)\chi_{248400}(4813,\cdot)

• Label: 248400.4813
• Modulus: $248400$
• Conductor: $248400$
• Order: $1980$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$248400$
Conductor:	$248400$
Order:	$1980$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 248400.bkg

$\chi_{248400}(13,\cdot)$ $\chi_{248400}(997,\cdot)$ $\chi_{248400}(1237,\cdot)$ $\chi_{248400}(1453,\cdot)$ $\chi_{248400}(2653,\cdot)$ $\chi_{248400}(2677,\cdot)$ $\chi_{248400}(3397,\cdot)$ $\chi_{248400}(3613,\cdot)$ $\chi_{248400}(3877,\cdot)$ $\chi_{248400}(4333,\cdot)$ $\chi_{248400}(4813,\cdot)$ $\chi_{248400}(5053,\cdot)$ $\chi_{248400}(5317,\cdot)$ $\chi_{248400}(5533,\cdot)$ $\chi_{248400}(6973,\cdot)$ $\chi_{248400}(7477,\cdot)$ $\chi_{248400}(7717,\cdot)$ $\chi_{248400}(8197,\cdot)$ $\chi_{248400}(8413,\cdot)$ $\chi_{248400}(8917,\cdot)$ $\chi_{248400}(9133,\cdot)$ $\chi_{248400}(9373,\cdot)$ $\chi_{248400}(9853,\cdot)$ $\chi_{248400}(10573,\cdot)$ $\chi_{248400}(10813,\cdot)$ $\chi_{248400}(12037,\cdot)$ $\chi_{248400}(13237,\cdot)$ $\chi_{248400}(14197,\cdot)$ $\chi_{248400}(14677,\cdot)$ $\chi_{248400}(14917,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{1980})$
Fixed field:	Number field defined by a degree 1980 polynomial (not computed)

Values on generators

$(93151,62101,211601,158977,194401)$ → $(1,-i,e\left(\frac{8}{9}\right),e\left(\frac{19}{20}\right),e\left(\frac{9}{11}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 248400 }(4813, a)$	$-1$	$1$	$e\left(\frac{7}{396}\right)$	$e\left(\frac{1721}{1980}\right)$	$e\left(\frac{857}{990}\right)$	$e\left(\frac{271}{660}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{1517}{1980}\right)$	$e\left(\frac{142}{495}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{227}{990}\right)$	$e\left(\frac{64}{99}\right)$