Dirichlet character χ3528(1405,⋅)\chi_{3528}(1405,\cdot)

• Label: 3528.1405
• Modulus: $3528$
• Conductor: $392$
• Order: $42$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3528$
Conductor:	$392$
Order:	$42$
Real:	no
Primitive:	no, induced from $\chi_{392}(229,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3528.fb

$\chi_{3528}(397,\cdot)$ $\chi_{3528}(829,\cdot)$ $\chi_{3528}(1333,\cdot)$ $\chi_{3528}(1405,\cdot)$ $\chi_{3528}(1837,\cdot)$ $\chi_{3528}(1909,\cdot)$ $\chi_{3528}(2341,\cdot)$ $\chi_{3528}(2413,\cdot)$ $\chi_{3528}(2845,\cdot)$ $\chi_{3528}(2917,\cdot)$ $\chi_{3528}(3349,\cdot)$ $\chi_{3528}(3421,\cdot)$

Related number fields

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

Values on generators

$(2647,1765,785,1081)$ → $(1,-1,1,e\left(\frac{41}{42}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{ 3528 }(1405, a)$	$-1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$