Dirichlet character χ1785(31,⋅)\chi_{1785}(31,\cdot)

• Label: 1785.31
• Modulus: $1785$
• Conductor: $119$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1785$
Conductor:	$119$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{119}(31,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1785.fi

$\chi_{1785}(31,\cdot)$ $\chi_{1785}(61,\cdot)$ $\chi_{1785}(241,\cdot)$ $\chi_{1785}(346,\cdot)$ $\chi_{1785}(481,\cdot)$ $\chi_{1785}(556,\cdot)$ $\chi_{1785}(691,\cdot)$ $\chi_{1785}(796,\cdot)$ $\chi_{1785}(976,\cdot)$ $\chi_{1785}(1006,\cdot)$ $\chi_{1785}(1081,\cdot)$ $\chi_{1785}(1111,\cdot)$ $\chi_{1785}(1321,\cdot)$ $\chi_{1785}(1501,\cdot)$ $\chi_{1785}(1711,\cdot)$ $\chi_{1785}(1741,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(596,1072,766,1261)$ → $(1,1,e\left(\frac{1}{6}\right),e\left(\frac{9}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{ 1785 }(31, a)$	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{23}{24}\right)$