Dirichlet character χ43904(61,⋅)\chi_{43904}(61,\cdot)

• Label: 43904.61
• Modulus: $43904$
• Conductor: $43904$
• Order: $4704$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 43904.fl

$\chi_{43904}(5,\cdot)$ $\chi_{43904}(45,\cdot)$ $\chi_{43904}(61,\cdot)$ $\chi_{43904}(101,\cdot)$ $\chi_{43904}(157,\cdot)$ $\chi_{43904}(173,\cdot)$ $\chi_{43904}(213,\cdot)$ $\chi_{43904}(229,\cdot)$ $\chi_{43904}(269,\cdot)$ $\chi_{43904}(285,\cdot)$ $\chi_{43904}(341,\cdot)$ $\chi_{43904}(381,\cdot)$ $\chi_{43904}(397,\cdot)$ $\chi_{43904}(437,\cdot)$ $\chi_{43904}(453,\cdot)$ $\chi_{43904}(493,\cdot)$ $\chi_{43904}(549,\cdot)$ $\chi_{43904}(565,\cdot)$ $\chi_{43904}(605,\cdot)$ $\chi_{43904}(621,\cdot)$ $\chi_{43904}(661,\cdot)$ $\chi_{43904}(677,\cdot)$ $\chi_{43904}(733,\cdot)$ $\chi_{43904}(773,\cdot)$ $\chi_{43904}(789,\cdot)$ $\chi_{43904}(829,\cdot)$ $\chi_{43904}(845,\cdot)$ $\chi_{43904}(885,\cdot)$ $\chi_{43904}(941,\cdot)$ $\chi_{43904}(957,\cdot)$ ...

Related number fields

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

Values on generators

$(17151,9605,17153)$ → $(1,e\left(\frac{19}{32}\right),e\left(\frac{263}{294}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 43904 }(61, a)$	$-1$	$1$	$e\left(\frac{3179}{4704}\right)$	$e\left(\frac{2521}{4704}\right)$	$e\left(\frac{827}{2352}\right)$	$e\left(\frac{2525}{4704}\right)$	$e\left(\frac{1341}{1568}\right)$	$e\left(\frac{83}{392}\right)$	$e\left(\frac{1163}{1176}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{47}{2352}\right)$	$e\left(\frac{169}{2352}\right)$