Dirichlet character χ392(229,⋅)\chi_{392}(229,\cdot)

• Label: 392.229
• Modulus: $392$
• Conductor: $392$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$392$
Conductor:	$392$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 392.bf

$\chi_{392}(5,\cdot)$ $\chi_{392}(45,\cdot)$ $\chi_{392}(61,\cdot)$ $\chi_{392}(101,\cdot)$ $\chi_{392}(157,\cdot)$ $\chi_{392}(173,\cdot)$ $\chi_{392}(213,\cdot)$ $\chi_{392}(229,\cdot)$ $\chi_{392}(269,\cdot)$ $\chi_{392}(285,\cdot)$ $\chi_{392}(341,\cdot)$ $\chi_{392}(381,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	42.0.1090030896264192289800449659845679818091197961133776603876122561317234873686091104256.1

Values on generators

$(295,197,297)$ → $(1,-1,e\left(\frac{41}{42}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 392 }(229, a)$	$-1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum