Dirichlet character χ43904(653,⋅)\chi_{43904}(653,\cdot)

• Label: 43904.653
• Modulus: $43904$
• Conductor: $43904$
• Order: $4704$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$43904$
Conductor:	$43904$
Order:	$4704$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 43904.fn

$\chi_{43904}(37,\cdot)$ $\chi_{43904}(53,\cdot)$ $\chi_{43904}(93,\cdot)$ $\chi_{43904}(109,\cdot)$ $\chi_{43904}(149,\cdot)$ $\chi_{43904}(205,\cdot)$ $\chi_{43904}(221,\cdot)$ $\chi_{43904}(261,\cdot)$ $\chi_{43904}(277,\cdot)$ $\chi_{43904}(317,\cdot)$ $\chi_{43904}(333,\cdot)$ $\chi_{43904}(389,\cdot)$ $\chi_{43904}(429,\cdot)$ $\chi_{43904}(445,\cdot)$ $\chi_{43904}(485,\cdot)$ $\chi_{43904}(501,\cdot)$ $\chi_{43904}(541,\cdot)$ $\chi_{43904}(597,\cdot)$ $\chi_{43904}(613,\cdot)$ $\chi_{43904}(653,\cdot)$ $\chi_{43904}(669,\cdot)$ $\chi_{43904}(709,\cdot)$ $\chi_{43904}(725,\cdot)$ $\chi_{43904}(781,\cdot)$ $\chi_{43904}(821,\cdot)$ $\chi_{43904}(837,\cdot)$ $\chi_{43904}(877,\cdot)$ $\chi_{43904}(893,\cdot)$ $\chi_{43904}(933,\cdot)$ $\chi_{43904}(989,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{4704})$
Fixed field:	Number field defined by a degree 4704 polynomial (not computed)

Values on generators

$(17151,9605,17153)$ → $(1,e\left(\frac{15}{32}\right),e\left(\frac{31}{147}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 43904 }(653, a)$	$1$	$1$	$e\left(\frac{2903}{4704}\right)$	$e\left(\frac{2749}{4704}\right)$	$e\left(\frac{551}{2352}\right)$	$e\left(\frac{3329}{4704}\right)$	$e\left(\frac{209}{1568}\right)$	$e\left(\frac{79}{392}\right)$	$e\left(\frac{467}{1176}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{347}{2352}\right)$	$e\left(\frac{397}{2352}\right)$