Dirichlet character χ475(71,⋅)\chi_{475}(71,\cdot)

• Label: 475.71
• Modulus: $475$
• Conductor: $475$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$475$
Conductor:	$475$
Order:	$90$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 475.bf

$\chi_{475}(21,\cdot)$ $\chi_{475}(41,\cdot)$ $\chi_{475}(71,\cdot)$ $\chi_{475}(86,\cdot)$ $\chi_{475}(91,\cdot)$ $\chi_{475}(116,\cdot)$ $\chi_{475}(136,\cdot)$ $\chi_{475}(146,\cdot)$ $\chi_{475}(166,\cdot)$ $\chi_{475}(181,\cdot)$ $\chi_{475}(186,\cdot)$ $\chi_{475}(211,\cdot)$ $\chi_{475}(231,\cdot)$ $\chi_{475}(241,\cdot)$ $\chi_{475}(261,\cdot)$ $\chi_{475}(281,\cdot)$ $\chi_{475}(306,\cdot)$ $\chi_{475}(336,\cdot)$ $\chi_{475}(356,\cdot)$ $\chi_{475}(371,\cdot)$ $\chi_{475}(421,\cdot)$ $\chi_{475}(431,\cdot)$ $\chi_{475}(466,\cdot)$ $\chi_{475}(471,\cdot)$

Related number fields

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

Values on generators

$(77,401)$ → $(e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 475 }(71, a)$	$-1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{90}\right)$

Gauss sum

Jacobi sum

Kloosterman sum