Dirichlet character χ1785(46,⋅)\chi_{1785}(46,\cdot)

• Label: 1785.46
• Modulus: $1785$
• Conductor: $119$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1785$
Conductor:	$119$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{119}(46,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1785.fe

$\chi_{1785}(46,\cdot)$ $\chi_{1785}(226,\cdot)$ $\chi_{1785}(436,\cdot)$ $\chi_{1785}(466,\cdot)$ $\chi_{1785}(541,\cdot)$ $\chi_{1785}(571,\cdot)$ $\chi_{1785}(751,\cdot)$ $\chi_{1785}(856,\cdot)$ $\chi_{1785}(991,\cdot)$ $\chi_{1785}(1066,\cdot)$ $\chi_{1785}(1201,\cdot)$ $\chi_{1785}(1306,\cdot)$ $\chi_{1785}(1486,\cdot)$ $\chi_{1785}(1516,\cdot)$ $\chi_{1785}(1591,\cdot)$ $\chi_{1785}(1621,\cdot)$

Related number fields

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

Values on generators

$(596,1072,766,1261)$ → $(1,1,e\left(\frac{2}{3}\right),e\left(\frac{13}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{ 1785 }(46, a)$	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{48}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{24}\right)$