Dirichlet character χ1470(41,⋅)\chi_{1470}(41,\cdot)

• Label: 1470.41
• Modulus: $1470$
• Conductor: $147$
• Order: $14$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1470$
Conductor:	$147$
Order:	$14$
Real:	no
Primitive:	no, induced from $\chi_{147}(41,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1470.be

$\chi_{1470}(41,\cdot)$ $\chi_{1470}(251,\cdot)$ $\chi_{1470}(461,\cdot)$ $\chi_{1470}(671,\cdot)$ $\chi_{1470}(1091,\cdot)$ $\chi_{1470}(1301,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	14.14.2932917071205091238064909.1

Values on generators

$(491,1177,1081)$ → $(-1,1,e\left(\frac{5}{14}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 1470 }(41, a)$	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$-1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$-1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$