Dirichlet character χ43904(31,⋅)\chi_{43904}(31,\cdot)

• Label: 43904.31
• Modulus: $43904$
• Conductor: $784$
• Order: $84$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$43904$
Conductor:	$784$
Order:	$84$
Real:	no
Primitive:	no, induced from $\chi_{784}(283,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 43904.ct

$\chi_{43904}(31,\cdot)$ $\chi_{43904}(607,\cdot)$ $\chi_{43904}(3167,\cdot)$ $\chi_{43904}(3743,\cdot)$ $\chi_{43904}(6303,\cdot)$ $\chi_{43904}(9439,\cdot)$ $\chi_{43904}(10015,\cdot)$ $\chi_{43904}(12575,\cdot)$ $\chi_{43904}(13151,\cdot)$ $\chi_{43904}(15711,\cdot)$ $\chi_{43904}(16287,\cdot)$ $\chi_{43904}(19423,\cdot)$ $\chi_{43904}(21983,\cdot)$ $\chi_{43904}(22559,\cdot)$ $\chi_{43904}(25119,\cdot)$ $\chi_{43904}(25695,\cdot)$ $\chi_{43904}(28255,\cdot)$ $\chi_{43904}(31391,\cdot)$ $\chi_{43904}(31967,\cdot)$ $\chi_{43904}(34527,\cdot)$ $\chi_{43904}(35103,\cdot)$ $\chi_{43904}(37663,\cdot)$ $\chi_{43904}(38239,\cdot)$ $\chi_{43904}(41375,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(17151,9605,17153)$ → $(-1,i,e\left(\frac{19}{42}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 43904 }(31, a)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$