Dirichlet character χ43904(1721,⋅)\chi_{43904}(1721,\cdot)

• Label: 43904.1721
• Modulus: $43904$
• Conductor: $21952$
• Order: $784$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$43904$
Conductor:	$21952$
Order:	$784$
Real:	no
Primitive:	no, induced from $\chi_{21952}(3093,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 43904.eu

$\chi_{43904}(41,\cdot)$ $\chi_{43904}(153,\cdot)$ $\chi_{43904}(265,\cdot)$ $\chi_{43904}(377,\cdot)$ $\chi_{43904}(601,\cdot)$ $\chi_{43904}(713,\cdot)$ $\chi_{43904}(825,\cdot)$ $\chi_{43904}(937,\cdot)$ $\chi_{43904}(1049,\cdot)$ $\chi_{43904}(1161,\cdot)$ $\chi_{43904}(1385,\cdot)$ $\chi_{43904}(1497,\cdot)$ $\chi_{43904}(1609,\cdot)$ $\chi_{43904}(1721,\cdot)$ $\chi_{43904}(1833,\cdot)$ $\chi_{43904}(1945,\cdot)$ $\chi_{43904}(2169,\cdot)$ $\chi_{43904}(2281,\cdot)$ $\chi_{43904}(2393,\cdot)$ $\chi_{43904}(2505,\cdot)$ $\chi_{43904}(2617,\cdot)$ $\chi_{43904}(2729,\cdot)$ $\chi_{43904}(2953,\cdot)$ $\chi_{43904}(3065,\cdot)$ $\chi_{43904}(3177,\cdot)$ $\chi_{43904}(3289,\cdot)$ $\chi_{43904}(3401,\cdot)$ $\chi_{43904}(3513,\cdot)$ $\chi_{43904}(3737,\cdot)$ $\chi_{43904}(3849,\cdot)$ ...

Related number fields

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

Values on generators

$(17151,9605,17153)$ → $(1,e\left(\frac{13}{16}\right),e\left(\frac{65}{98}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 43904 }(1721, a)$	$-1$	$1$	$e\left(\frac{79}{784}\right)$	$e\left(\frac{37}{784}\right)$	$e\left(\frac{79}{392}\right)$	$e\left(\frac{17}{784}\right)$	$e\left(\frac{171}{784}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{59}{392}\right)$	$e\left(\frac{37}{392}\right)$