Dirichlet character χ46208(613,⋅)\chi_{46208}(613,\cdot)

• Label: 46208.613
• Modulus: $46208$
• Conductor: $46208$
• Order: $5472$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$46208$
Conductor:	$46208$
Order:	$5472$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 46208.fl

$\chi_{46208}(5,\cdot)$ $\chi_{46208}(61,\cdot)$ $\chi_{46208}(85,\cdot)$ $\chi_{46208}(93,\cdot)$ $\chi_{46208}(101,\cdot)$ $\chi_{46208}(149,\cdot)$ $\chi_{46208}(157,\cdot)$ $\chi_{46208}(213,\cdot)$ $\chi_{46208}(237,\cdot)$ $\chi_{46208}(253,\cdot)$ $\chi_{46208}(301,\cdot)$ $\chi_{46208}(309,\cdot)$ $\chi_{46208}(365,\cdot)$ $\chi_{46208}(397,\cdot)$ $\chi_{46208}(405,\cdot)$ $\chi_{46208}(453,\cdot)$ $\chi_{46208}(461,\cdot)$ $\chi_{46208}(517,\cdot)$ $\chi_{46208}(541,\cdot)$ $\chi_{46208}(549,\cdot)$ $\chi_{46208}(557,\cdot)$ $\chi_{46208}(605,\cdot)$ $\chi_{46208}(613,\cdot)$ $\chi_{46208}(669,\cdot)$ $\chi_{46208}(693,\cdot)$ $\chi_{46208}(701,\cdot)$ $\chi_{46208}(709,\cdot)$ $\chi_{46208}(757,\cdot)$ $\chi_{46208}(765,\cdot)$ $\chi_{46208}(845,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{5472})$
Fixed field:	Number field defined by a degree 5472 polynomial (not computed)

Values on generators

$(28159,36101,14081)$ → $(1,e\left(\frac{9}{32}\right),e\left(\frac{44}{171}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{ 46208 }(613, a)$	$1$	$1$	$e\left(\frac{3337}{5472}\right)$	$e\left(\frac{5347}{5472}\right)$	$e\left(\frac{373}{912}\right)$	$e\left(\frac{601}{2736}\right)$	$e\left(\frac{277}{1824}\right)$	$e\left(\frac{4781}{5472}\right)$	$e\left(\frac{803}{1368}\right)$	$e\left(\frac{37}{1368}\right)$	$e\left(\frac{103}{5472}\right)$	$e\left(\frac{1381}{2736}\right)$