Dirichlet character χ2070(569,⋅)\chi_{2070}(569,\cdot)

• Label: 2070.569
• Modulus: $2070$
• Conductor: $1035$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2070$
Conductor:	$1035$
Order:	$66$
Real:	no
Primitive:	no, induced from $\chi_{1035}(569,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2070.br

$\chi_{2070}(149,\cdot)$ $\chi_{2070}(329,\cdot)$ $\chi_{2070}(389,\cdot)$ $\chi_{2070}(419,\cdot)$ $\chi_{2070}(479,\cdot)$ $\chi_{2070}(569,\cdot)$ $\chi_{2070}(659,\cdot)$ $\chi_{2070}(779,\cdot)$ $\chi_{2070}(839,\cdot)$ $\chi_{2070}(1019,\cdot)$ $\chi_{2070}(1049,\cdot)$ $\chi_{2070}(1109,\cdot)$ $\chi_{2070}(1229,\cdot)$ $\chi_{2070}(1469,\cdot)$ $\chi_{2070}(1739,\cdot)$ $\chi_{2070}(1769,\cdot)$ $\chi_{2070}(1859,\cdot)$ $\chi_{2070}(1919,\cdot)$ $\chi_{2070}(1949,\cdot)$ $\chi_{2070}(2039,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(461,1657,1891)$ → $(e\left(\frac{1}{6}\right),-1,e\left(\frac{7}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 2070 }(569, a)$	$1$	$1$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{25}{33}\right)$