Dirichlet character χ4140(1327,⋅)\chi_{4140}(1327,\cdot)

• Label: 4140.1327
• Modulus: $4140$
• Conductor: $4140$
• Order: $132$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4140$
Conductor:	$4140$
Order:	$132$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4140.dk

$\chi_{4140}(187,\cdot)$ $\chi_{4140}(223,\cdot)$ $\chi_{4140}(403,\cdot)$ $\chi_{4140}(427,\cdot)$ $\chi_{4140}(463,\cdot)$ $\chi_{4140}(547,\cdot)$ $\chi_{4140}(583,\cdot)$ $\chi_{4140}(607,\cdot)$ $\chi_{4140}(763,\cdot)$ $\chi_{4140}(823,\cdot)$ $\chi_{4140}(1087,\cdot)$ $\chi_{4140}(1267,\cdot)$ $\chi_{4140}(1327,\cdot)$ $\chi_{4140}(1363,\cdot)$ $\chi_{4140}(1507,\cdot)$ $\chi_{4140}(1543,\cdot)$ $\chi_{4140}(1687,\cdot)$ $\chi_{4140}(1807,\cdot)$ $\chi_{4140}(1843,\cdot)$ $\chi_{4140}(1867,\cdot)$ $\chi_{4140}(1987,\cdot)$ $\chi_{4140}(2083,\cdot)$ $\chi_{4140}(2203,\cdot)$ $\chi_{4140}(2263,\cdot)$ $\chi_{4140}(2707,\cdot)$ $\chi_{4140}(2743,\cdot)$ $\chi_{4140}(2887,\cdot)$ $\chi_{4140}(2923,\cdot)$ $\chi_{4140}(2947,\cdot)$ $\chi_{4140}(2983,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

Values on generators

$(2071,461,1657,3961)$ → $(-1,e\left(\frac{1}{3}\right),i,e\left(\frac{4}{11}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(1327, a)$	$1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{53}{132}\right)$