Dirichlet character χ4140(59,⋅)\chi_{4140}(59,\cdot)

• Label: 4140.59
• Modulus: $4140$
• Conductor: $4140$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4140$
Conductor:	$4140$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4140.dh

$\chi_{4140}(59,\cdot)$ $\chi_{4140}(119,\cdot)$ $\chi_{4140}(239,\cdot)$ $\chi_{4140}(959,\cdot)$ $\chi_{4140}(1139,\cdot)$ $\chi_{4140}(1199,\cdot)$ $\chi_{4140}(1319,\cdot)$ $\chi_{4140}(1499,\cdot)$ $\chi_{4140}(1559,\cdot)$ $\chi_{4140}(2099,\cdot)$ $\chi_{4140}(2279,\cdot)$ $\chi_{4140}(2579,\cdot)$ $\chi_{4140}(2819,\cdot)$ $\chi_{4140}(2939,\cdot)$ $\chi_{4140}(2999,\cdot)$ $\chi_{4140}(3479,\cdot)$ $\chi_{4140}(3659,\cdot)$ $\chi_{4140}(3719,\cdot)$ $\chi_{4140}(3899,\cdot)$ $\chi_{4140}(4079,\cdot)$

Related number fields

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

Values on generators

$(2071,461,1657,3961)$ → $(-1,e\left(\frac{5}{6}\right),-1,e\left(\frac{7}{11}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(59, a)$	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{17}{33}\right)$