Dirichlet character χ1225(501,⋅)\chi_{1225}(501,\cdot)

• Label: 1225.501
• Modulus: $1225$
• Conductor: $49$
• Order: $21$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1225$
Conductor:	$49$
Order:	$21$
Real:	no
Primitive:	no, induced from $\chi_{49}(11,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1225.x

$\chi_{1225}(51,\cdot)$ $\chi_{1225}(151,\cdot)$ $\chi_{1225}(326,\cdot)$ $\chi_{1225}(401,\cdot)$ $\chi_{1225}(501,\cdot)$ $\chi_{1225}(576,\cdot)$ $\chi_{1225}(676,\cdot)$ $\chi_{1225}(751,\cdot)$ $\chi_{1225}(926,\cdot)$ $\chi_{1225}(1026,\cdot)$ $\chi_{1225}(1101,\cdot)$ $\chi_{1225}(1201,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 21 polynomial

Values on generators

$(1177,101)$ → $(1,e\left(\frac{20}{21}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{ 1225 }(501, a)$	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$