Dirichlet character χ475(446,⋅)\chi_{475}(446,\cdot)

• Label: 475.446
• Modulus: $475$
• Conductor: $475$
• Order: $45$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$475$
Conductor:	$475$
Order:	$45$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 475.bc

$\chi_{475}(6,\cdot)$ $\chi_{475}(16,\cdot)$ $\chi_{475}(36,\cdot)$ $\chi_{475}(61,\cdot)$ $\chi_{475}(66,\cdot)$ $\chi_{475}(81,\cdot)$ $\chi_{475}(111,\cdot)$ $\chi_{475}(131,\cdot)$ $\chi_{475}(156,\cdot)$ $\chi_{475}(161,\cdot)$ $\chi_{475}(196,\cdot)$ $\chi_{475}(206,\cdot)$ $\chi_{475}(256,\cdot)$ $\chi_{475}(271,\cdot)$ $\chi_{475}(291,\cdot)$ $\chi_{475}(321,\cdot)$ $\chi_{475}(346,\cdot)$ $\chi_{475}(366,\cdot)$ $\chi_{475}(386,\cdot)$ $\chi_{475}(396,\cdot)$ $\chi_{475}(416,\cdot)$ $\chi_{475}(441,\cdot)$ $\chi_{475}(446,\cdot)$ $\chi_{475}(461,\cdot)$

Related number fields

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

Values on generators

$(77,401)$ → $(e\left(\frac{3}{5}\right),e\left(\frac{4}{9}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 475 }(446, a)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{28}{45}\right)$

Gauss sum

Jacobi sum

Kloosterman sum