Dirichlet character χ475(148,⋅)\chi_{475}(148,\cdot)

• Label: 475.148
• Modulus: $475$
• Conductor: $475$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$475$
Conductor:	$475$
Order:	$180$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 475.bi

$\chi_{475}(2,\cdot)$ $\chi_{475}(3,\cdot)$ $\chi_{475}(13,\cdot)$ $\chi_{475}(22,\cdot)$ $\chi_{475}(33,\cdot)$ $\chi_{475}(48,\cdot)$ $\chi_{475}(52,\cdot)$ $\chi_{475}(53,\cdot)$ $\chi_{475}(67,\cdot)$ $\chi_{475}(72,\cdot)$ $\chi_{475}(78,\cdot)$ $\chi_{475}(97,\cdot)$ $\chi_{475}(98,\cdot)$ $\chi_{475}(108,\cdot)$ $\chi_{475}(117,\cdot)$ $\chi_{475}(127,\cdot)$ $\chi_{475}(128,\cdot)$ $\chi_{475}(147,\cdot)$ $\chi_{475}(148,\cdot)$ $\chi_{475}(162,\cdot)$ $\chi_{475}(167,\cdot)$ $\chi_{475}(173,\cdot)$ $\chi_{475}(192,\cdot)$ $\chi_{475}(203,\cdot)$ $\chi_{475}(212,\cdot)$ $\chi_{475}(222,\cdot)$ $\chi_{475}(223,\cdot)$ $\chi_{475}(238,\cdot)$ $\chi_{475}(242,\cdot)$ $\chi_{475}(262,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

$(77,401)$ → $(e\left(\frac{11}{20}\right),e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 475 }(148, a)$	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{91}{180}\right)$

Gauss sum

Jacobi sum

Kloosterman sum