Dirichlet character χ1815(47,⋅)\chi_{1815}(47,\cdot)

• Label: 1815.47
• Modulus: $1815$
• Conductor: $1815$
• Order: $220$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1815$
Conductor:	$1815$
Order:	$220$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1815.bu

$\chi_{1815}(38,\cdot)$ $\chi_{1815}(47,\cdot)$ $\chi_{1815}(53,\cdot)$ $\chi_{1815}(92,\cdot)$ $\chi_{1815}(113,\cdot)$ $\chi_{1815}(137,\cdot)$ $\chi_{1815}(152,\cdot)$ $\chi_{1815}(158,\cdot)$ $\chi_{1815}(203,\cdot)$ $\chi_{1815}(212,\cdot)$ $\chi_{1815}(218,\cdot)$ $\chi_{1815}(257,\cdot)$ $\chi_{1815}(278,\cdot)$ $\chi_{1815}(302,\cdot)$ $\chi_{1815}(317,\cdot)$ $\chi_{1815}(368,\cdot)$ $\chi_{1815}(377,\cdot)$ $\chi_{1815}(383,\cdot)$ $\chi_{1815}(422,\cdot)$ $\chi_{1815}(443,\cdot)$ $\chi_{1815}(467,\cdot)$ $\chi_{1815}(482,\cdot)$ $\chi_{1815}(488,\cdot)$ $\chi_{1815}(533,\cdot)$ $\chi_{1815}(542,\cdot)$ $\chi_{1815}(548,\cdot)$ $\chi_{1815}(587,\cdot)$ $\chi_{1815}(647,\cdot)$ $\chi_{1815}(653,\cdot)$ $\chi_{1815}(698,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{220})$
Fixed field:	Number field defined by a degree 220 polynomial (not computed)

Values on generators

$(1211,727,1696)$ → $(-1,i,e\left(\frac{49}{55}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{ 1815 }(47, a)$	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{27}{44}\right)$