Dirichlet character χ3174(31,⋅)\chi_{3174}(31,\cdot)

• Label: 3174.31
• Modulus: $3174$
• Conductor: $529$
• Order: $253$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3174$
Conductor:	$529$
Order:	$253$
Real:	no
Primitive:	no, induced from $\chi_{529}(31,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 3174.m

$\chi_{3174}(13,\cdot)$ $\chi_{3174}(25,\cdot)$ $\chi_{3174}(31,\cdot)$ $\chi_{3174}(49,\cdot)$ $\chi_{3174}(55,\cdot)$ $\chi_{3174}(73,\cdot)$ $\chi_{3174}(85,\cdot)$ $\chi_{3174}(121,\cdot)$ $\chi_{3174}(127,\cdot)$ $\chi_{3174}(133,\cdot)$ $\chi_{3174}(151,\cdot)$ $\chi_{3174}(163,\cdot)$ $\chi_{3174}(169,\cdot)$ $\chi_{3174}(187,\cdot)$ $\chi_{3174}(193,\cdot)$ $\chi_{3174}(211,\cdot)$ $\chi_{3174}(223,\cdot)$ $\chi_{3174}(259,\cdot)$ $\chi_{3174}(265,\cdot)$ $\chi_{3174}(271,\cdot)$ $\chi_{3174}(289,\cdot)$ $\chi_{3174}(301,\cdot)$ $\chi_{3174}(307,\cdot)$ $\chi_{3174}(325,\cdot)$ $\chi_{3174}(331,\cdot)$ $\chi_{3174}(349,\cdot)$ $\chi_{3174}(361,\cdot)$ $\chi_{3174}(397,\cdot)$ $\chi_{3174}(403,\cdot)$ $\chi_{3174}(409,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{253})$
Fixed field:	Number field defined by a degree 253 polynomial (not computed)

Values on generators

$(2117,1063)$ → $(1,e\left(\frac{212}{253}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$35$
$\chi_{ 3174 }(31, a)$	$1$	$1$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{236}{253}\right)$