Dirichlet character χ259200(10297,⋅)\chi_{259200}(10297,\cdot)

• Label: 259200.10297
• Modulus: $259200$
• Conductor: $43200$
• Order: $720$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$259200$
Conductor:	$43200$
Order:	$720$
Real:	no
Primitive:	no, induced from $\chi_{43200}(21397,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 259200.xx

$\chi_{259200}(73,\cdot)$ $\chi_{259200}(2953,\cdot)$ $\chi_{259200}(3097,\cdot)$ $\chi_{259200}(5977,\cdot)$ $\chi_{259200}(7273,\cdot)$ $\chi_{259200}(7417,\cdot)$ $\chi_{259200}(8713,\cdot)$ $\chi_{259200}(10297,\cdot)$ $\chi_{259200}(11737,\cdot)$ $\chi_{259200}(13033,\cdot)$ $\chi_{259200}(14617,\cdot)$ $\chi_{259200}(15913,\cdot)$ $\chi_{259200}(17353,\cdot)$ $\chi_{259200}(18937,\cdot)$ $\chi_{259200}(20233,\cdot)$ $\chi_{259200}(20377,\cdot)$ $\chi_{259200}(21673,\cdot)$ $\chi_{259200}(24553,\cdot)$ $\chi_{259200}(24697,\cdot)$ $\chi_{259200}(27577,\cdot)$ $\chi_{259200}(28873,\cdot)$ $\chi_{259200}(29017,\cdot)$ $\chi_{259200}(30313,\cdot)$ $\chi_{259200}(31897,\cdot)$ $\chi_{259200}(33337,\cdot)$ $\chi_{259200}(34633,\cdot)$ $\chi_{259200}(36217,\cdot)$ $\chi_{259200}(37513,\cdot)$ $\chi_{259200}(38953,\cdot)$ $\chi_{259200}(40537,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{720})$
Fixed field:	Number field defined by a degree 720 polynomial (not computed)

Values on generators

$(157951,202501,6401,72577)$ → $(1,e\left(\frac{13}{16}\right),e\left(\frac{4}{9}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 259200 }(10297, a)$	$-1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{317}{720}\right)$	$e\left(\frac{643}{720}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{221}{360}\right)$	$e\left(\frac{59}{720}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{119}{360}\right)$