Dirichlet character χ1815(56,⋅)\chi_{1815}(56,\cdot)

• Label: 1815.56
• Modulus: $1815$
• Conductor: $363$
• Order: $22$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1815$
Conductor:	$363$
Order:	$22$
Real:	no
Primitive:	no, induced from $\chi_{363}(56,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1815.bc

$\chi_{1815}(56,\cdot)$ $\chi_{1815}(221,\cdot)$ $\chi_{1815}(386,\cdot)$ $\chi_{1815}(551,\cdot)$ $\chi_{1815}(716,\cdot)$ $\chi_{1815}(881,\cdot)$ $\chi_{1815}(1046,\cdot)$ $\chi_{1815}(1376,\cdot)$ $\chi_{1815}(1541,\cdot)$ $\chi_{1815}(1706,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{11})$
Fixed field:	Number field defined by a degree 22 polynomial

Values on generators

$(1211,727,1696)$ → $(-1,1,e\left(\frac{1}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{ 1815 }(56, a)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$