Dirichlet character χ43904(3639,⋅)\chi_{43904}(3639,\cdot)

• Label: 43904.3639
• Modulus: $43904$
• Conductor: $21952$
• Order: $784$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$43904$
Conductor:	$21952$
Order:	$784$
Real:	no
Primitive:	no, induced from $\chi_{21952}(21475,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 43904.ew

$\chi_{43904}(55,\cdot)$ $\chi_{43904}(167,\cdot)$ $\chi_{43904}(279,\cdot)$ $\chi_{43904}(503,\cdot)$ $\chi_{43904}(615,\cdot)$ $\chi_{43904}(727,\cdot)$ $\chi_{43904}(839,\cdot)$ $\chi_{43904}(951,\cdot)$ $\chi_{43904}(1063,\cdot)$ $\chi_{43904}(1287,\cdot)$ $\chi_{43904}(1399,\cdot)$ $\chi_{43904}(1511,\cdot)$ $\chi_{43904}(1623,\cdot)$ $\chi_{43904}(1735,\cdot)$ $\chi_{43904}(1847,\cdot)$ $\chi_{43904}(2071,\cdot)$ $\chi_{43904}(2183,\cdot)$ $\chi_{43904}(2295,\cdot)$ $\chi_{43904}(2407,\cdot)$ $\chi_{43904}(2519,\cdot)$ $\chi_{43904}(2631,\cdot)$ $\chi_{43904}(2855,\cdot)$ $\chi_{43904}(2967,\cdot)$ $\chi_{43904}(3079,\cdot)$ $\chi_{43904}(3191,\cdot)$ $\chi_{43904}(3303,\cdot)$ $\chi_{43904}(3415,\cdot)$ $\chi_{43904}(3639,\cdot)$ $\chi_{43904}(3751,\cdot)$ $\chi_{43904}(3863,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{784})$
Fixed field:	Number field defined by a degree 784 polynomial (not computed)

Values on generators

$(17151,9605,17153)$ → $(-1,e\left(\frac{11}{16}\right),e\left(\frac{53}{98}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 43904 }(3639, a)$	$1$	$1$	$e\left(\frac{81}{784}\right)$	$e\left(\frac{291}{784}\right)$	$e\left(\frac{81}{392}\right)$	$e\left(\frac{335}{784}\right)$	$e\left(\frac{349}{784}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{321}{392}\right)$	$e\left(\frac{291}{392}\right)$