Dirichlet character χ1575(541,⋅)\chi_{1575}(541,\cdot)

• Label: 1575.541
• Modulus: $1575$
• Conductor: $175$
• Order: $15$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1575$
Conductor:	$175$
Order:	$15$
Real:	no
Primitive:	no, induced from $\chi_{175}(16,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1575.cs

$\chi_{1575}(46,\cdot)$ $\chi_{1575}(361,\cdot)$ $\chi_{1575}(541,\cdot)$ $\chi_{1575}(856,\cdot)$ $\chi_{1575}(991,\cdot)$ $\chi_{1575}(1171,\cdot)$ $\chi_{1575}(1306,\cdot)$ $\chi_{1575}(1486,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 15 polynomial

Values on generators

$(1226,127,451)$ → $(1,e\left(\frac{1}{5}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 1575 }(541, a)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$