Dirichlet character χ4140(97,⋅)\chi_{4140}(97,\cdot)

• Label: 4140.97
• Modulus: $4140$
• Conductor: $1035$
• Order: $132$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4140$
Conductor:	$1035$
Order:	$132$
Real:	no
Primitive:	no, induced from $\chi_{1035}(97,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 4140.dl

$\chi_{4140}(97,\cdot)$ $\chi_{4140}(157,\cdot)$ $\chi_{4140}(313,\cdot)$ $\chi_{4140}(337,\cdot)$ $\chi_{4140}(373,\cdot)$ $\chi_{4140}(457,\cdot)$ $\chi_{4140}(493,\cdot)$ $\chi_{4140}(517,\cdot)$ $\chi_{4140}(697,\cdot)$ $\chi_{4140}(733,\cdot)$ $\chi_{4140}(1033,\cdot)$ $\chi_{4140}(1213,\cdot)$ $\chi_{4140}(1417,\cdot)$ $\chi_{4140}(1537,\cdot)$ $\chi_{4140}(1597,\cdot)$ $\chi_{4140}(1717,\cdot)$ $\chi_{4140}(1753,\cdot)$ $\chi_{4140}(1813,\cdot)$ $\chi_{4140}(1897,\cdot)$ $\chi_{4140}(1993,\cdot)$ $\chi_{4140}(2077,\cdot)$ $\chi_{4140}(2113,\cdot)$ $\chi_{4140}(2137,\cdot)$ $\chi_{4140}(2173,\cdot)$ $\chi_{4140}(2317,\cdot)$ $\chi_{4140}(2353,\cdot)$ $\chi_{4140}(2797,\cdot)$ $\chi_{4140}(2857,\cdot)$ $\chi_{4140}(2977,\cdot)$ $\chi_{4140}(3073,\cdot)$ ...

Related number fields

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

Values on generators

$(2071,461,1657,3961)$ → $(1,e\left(\frac{2}{3}\right),i,e\left(\frac{1}{22}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 4140 }(97, a)$	$1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{85}{132}\right)$