Dirichlet character χ1911(1868,⋅)\chi_{1911}(1868,\cdot)

• Label: 1911.1868
• Modulus: $1911$
• Conductor: $1911$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1911$
Conductor:	$1911$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1911.dc

$\chi_{1911}(230,\cdot)$ $\chi_{1911}(419,\cdot)$ $\chi_{1911}(503,\cdot)$ $\chi_{1911}(692,\cdot)$ $\chi_{1911}(776,\cdot)$ $\chi_{1911}(965,\cdot)$ $\chi_{1911}(1049,\cdot)$ $\chi_{1911}(1238,\cdot)$ $\chi_{1911}(1511,\cdot)$ $\chi_{1911}(1595,\cdot)$ $\chi_{1911}(1784,\cdot)$ $\chi_{1911}(1868,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(638,1522,1471)$ → $(-1,e\left(\frac{9}{14}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{ 1911 }(1868, a)$	$1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{21}\right)$