Dirichlet character χ259200(7,⋅)\chi_{259200}(7,\cdot)

• Label: 259200.7
• Modulus: $259200$
• Conductor: $25920$
• Order: $432$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$259200$
Conductor:	$25920$
Order:	$432$
Real:	no
Primitive:	no, induced from $\chi_{25920}(21067,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 259200.vg

$\chi_{259200}(7,\cdot)$ $\chi_{259200}(2407,\cdot)$ $\chi_{259200}(2743,\cdot)$ $\chi_{259200}(5143,\cdot)$ $\chi_{259200}(7207,\cdot)$ $\chi_{259200}(9607,\cdot)$ $\chi_{259200}(9943,\cdot)$ $\chi_{259200}(12343,\cdot)$ $\chi_{259200}(14407,\cdot)$ $\chi_{259200}(16807,\cdot)$ $\chi_{259200}(17143,\cdot)$ $\chi_{259200}(19543,\cdot)$ $\chi_{259200}(21607,\cdot)$ $\chi_{259200}(24007,\cdot)$ $\chi_{259200}(24343,\cdot)$ $\chi_{259200}(26743,\cdot)$ $\chi_{259200}(28807,\cdot)$ $\chi_{259200}(31207,\cdot)$ $\chi_{259200}(31543,\cdot)$ $\chi_{259200}(33943,\cdot)$ $\chi_{259200}(36007,\cdot)$ $\chi_{259200}(38407,\cdot)$ $\chi_{259200}(38743,\cdot)$ $\chi_{259200}(41143,\cdot)$ $\chi_{259200}(43207,\cdot)$ $\chi_{259200}(45607,\cdot)$ $\chi_{259200}(45943,\cdot)$ $\chi_{259200}(48343,\cdot)$ $\chi_{259200}(50407,\cdot)$ $\chi_{259200}(52807,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{432})$
Fixed field:	Number field defined by a degree 432 polynomial (not computed)

Values on generators

$(157951,202501,6401,72577)$ → $(-1,e\left(\frac{5}{16}\right),e\left(\frac{8}{27}\right),i)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 259200 }(7, a)$	$1$	$1$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{395}{432}\right)$	$e\left(\frac{349}{432}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{389}{432}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{17}{216}\right)$