Dirichlet character χ8325(1621,⋅)\chi_{8325}(1621,\cdot)

• Label: 8325.1621
• Modulus: $8325$
• Conductor: $925$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8325$
Conductor:	$925$
Order:	$90$
Real:	no
Primitive:	no, induced from $\chi_{925}(696,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 8325.kk

$\chi_{8325}(136,\cdot)$ $\chi_{8325}(361,\cdot)$ $\chi_{8325}(946,\cdot)$ $\chi_{8325}(1261,\cdot)$ $\chi_{8325}(1621,\cdot)$ $\chi_{8325}(1891,\cdot)$ $\chi_{8325}(2611,\cdot)$ $\chi_{8325}(3286,\cdot)$ $\chi_{8325}(3466,\cdot)$ $\chi_{8325}(3556,\cdot)$ $\chi_{8325}(3691,\cdot)$ $\chi_{8325}(4591,\cdot)$ $\chi_{8325}(5131,\cdot)$ $\chi_{8325}(5221,\cdot)$ $\chi_{8325}(5356,\cdot)$ $\chi_{8325}(5941,\cdot)$ $\chi_{8325}(6256,\cdot)$ $\chi_{8325}(6616,\cdot)$ $\chi_{8325}(6796,\cdot)$ $\chi_{8325}(6886,\cdot)$ $\chi_{8325}(7021,\cdot)$ $\chi_{8325}(7606,\cdot)$ $\chi_{8325}(7921,\cdot)$ $\chi_{8325}(8281,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

$(3701,7327,5626)$ → $(1,e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 8325 }(1621, a)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{37}{90}\right)$