Dirichlet character χ4140(11,⋅)\chi_{4140}(11,\cdot)

• Label: 4140.11
• Modulus: $4140$
• Conductor: $828$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$4140$
Conductor:	$828$
Order:	$66$
Real:	no
Primitive:	no, induced from $\chi_{828}(11,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 4140.df

$\chi_{4140}(11,\cdot)$ $\chi_{4140}(191,\cdot)$ $\chi_{4140}(911,\cdot)$ $\chi_{4140}(1031,\cdot)$ $\chi_{4140}(1091,\cdot)$ $\chi_{4140}(1211,\cdot)$ $\chi_{4140}(1391,\cdot)$ $\chi_{4140}(1571,\cdot)$ $\chi_{4140}(1631,\cdot)$ $\chi_{4140}(1811,\cdot)$ $\chi_{4140}(2291,\cdot)$ $\chi_{4140}(2351,\cdot)$ $\chi_{4140}(2471,\cdot)$ $\chi_{4140}(2711,\cdot)$ $\chi_{4140}(3011,\cdot)$ $\chi_{4140}(3191,\cdot)$ $\chi_{4140}(3731,\cdot)$ $\chi_{4140}(3791,\cdot)$ $\chi_{4140}(3971,\cdot)$ $\chi_{4140}(4091,\cdot)$

Related number fields

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

Values on generators

$(2071,461,1657,3961)$ → $(-1,e\left(\frac{1}{6}\right),1,e\left(\frac{9}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(11, a)$	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{7}{33}\right)$