Dirichlet character χ259200(839,⋅)\chi_{259200}(839,\cdot)

• Label: 259200.839
• Modulus: $259200$
• Conductor: $129600$
• Order: $2160$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$259200$
Conductor:	$129600$
Order:	$2160$
Real:	no
Primitive:	no, induced from $\chi_{129600}(8939,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 259200.bab

$\chi_{259200}(119,\cdot)$ $\chi_{259200}(839,\cdot)$ $\chi_{259200}(1319,\cdot)$ $\chi_{259200}(1559,\cdot)$ $\chi_{259200}(2039,\cdot)$ $\chi_{259200}(2279,\cdot)$ $\chi_{259200}(2759,\cdot)$ $\chi_{259200}(3479,\cdot)$ $\chi_{259200}(3719,\cdot)$ $\chi_{259200}(4439,\cdot)$ $\chi_{259200}(4919,\cdot)$ $\chi_{259200}(5159,\cdot)$ $\chi_{259200}(5639,\cdot)$ $\chi_{259200}(5879,\cdot)$ $\chi_{259200}(6359,\cdot)$ $\chi_{259200}(7079,\cdot)$ $\chi_{259200}(7319,\cdot)$ $\chi_{259200}(8039,\cdot)$ $\chi_{259200}(8519,\cdot)$ $\chi_{259200}(8759,\cdot)$ $\chi_{259200}(9239,\cdot)$ $\chi_{259200}(9479,\cdot)$ $\chi_{259200}(9959,\cdot)$ $\chi_{259200}(10679,\cdot)$ $\chi_{259200}(10919,\cdot)$ $\chi_{259200}(11639,\cdot)$ $\chi_{259200}(12119,\cdot)$ $\chi_{259200}(12359,\cdot)$ $\chi_{259200}(12839,\cdot)$ $\chi_{259200}(13079,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{2160})$
Fixed field:	Number field defined by a degree 2160 polynomial (not computed)

Values on generators

$(157951,202501,6401,72577)$ → $(-1,e\left(\frac{13}{16}\right),e\left(\frac{37}{54}\right),e\left(\frac{3}{10}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 259200 }(839, a)$	$1$	$1$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{583}{2160}\right)$	$e\left(\frac{797}{2160}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{343}{720}\right)$	$e\left(\frac{769}{1080}\right)$	$e\left(\frac{1921}{2160}\right)$	$e\left(\frac{14}{135}\right)$	$e\left(\frac{569}{720}\right)$	$e\left(\frac{961}{1080}\right)$