Dirichlet character χ21952(1203,⋅)\chi_{21952}(1203,\cdot)

• Label: 21952.1203
• Modulus: $21952$
• Conductor: $21952$
• Order: $784$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$21952$
Conductor:	$21952$
Order:	$784$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 21952.eg

$\chi_{21952}(27,\cdot)$ $\chi_{21952}(83,\cdot)$ $\chi_{21952}(139,\cdot)$ $\chi_{21952}(251,\cdot)$ $\chi_{21952}(307,\cdot)$ $\chi_{21952}(363,\cdot)$ $\chi_{21952}(419,\cdot)$ $\chi_{21952}(475,\cdot)$ $\chi_{21952}(531,\cdot)$ $\chi_{21952}(643,\cdot)$ $\chi_{21952}(699,\cdot)$ $\chi_{21952}(755,\cdot)$ $\chi_{21952}(811,\cdot)$ $\chi_{21952}(867,\cdot)$ $\chi_{21952}(923,\cdot)$ $\chi_{21952}(1035,\cdot)$ $\chi_{21952}(1091,\cdot)$ $\chi_{21952}(1147,\cdot)$ $\chi_{21952}(1203,\cdot)$ $\chi_{21952}(1259,\cdot)$ $\chi_{21952}(1315,\cdot)$ $\chi_{21952}(1427,\cdot)$ $\chi_{21952}(1483,\cdot)$ $\chi_{21952}(1539,\cdot)$ $\chi_{21952}(1595,\cdot)$ $\chi_{21952}(1651,\cdot)$ $\chi_{21952}(1707,\cdot)$ $\chi_{21952}(1819,\cdot)$ $\chi_{21952}(1875,\cdot)$ $\chi_{21952}(1931,\cdot)$ ...

Related number fields

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

Values on generators

$(17151,9605,17153)$ → $(-1,e\left(\frac{15}{16}\right),e\left(\frac{43}{98}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 21952 }(1203, a)$	$1$	$1$	$e\left(\frac{589}{784}\right)$	$e\left(\frac{519}{784}\right)$	$e\left(\frac{197}{392}\right)$	$e\left(\frac{355}{784}\right)$	$e\left(\frac{89}{784}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{229}{392}\right)$	$e\left(\frac{127}{392}\right)$