Dirichlet character χ132300(82001,⋅)\chi_{132300}(82001,\cdot)

• Label: 132300.82001
• Modulus: $132300$
• Conductor: $1323$
• Order: $126$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$132300$
Conductor:	$1323$
Order:	$126$
Real:	no
Primitive:	no, induced from $\chi_{1323}(1298,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 132300.tl

$\chi_{132300}(101,\cdot)$ $\chi_{132300}(12101,\cdot)$ $\chi_{132300}(12701,\cdot)$ $\chi_{132300}(18401,\cdot)$ $\chi_{132300}(19001,\cdot)$ $\chi_{132300}(24701,\cdot)$ $\chi_{132300}(25301,\cdot)$ $\chi_{132300}(31001,\cdot)$ $\chi_{132300}(31601,\cdot)$ $\chi_{132300}(37301,\cdot)$ $\chi_{132300}(37901,\cdot)$ $\chi_{132300}(43601,\cdot)$ $\chi_{132300}(44201,\cdot)$ $\chi_{132300}(56201,\cdot)$ $\chi_{132300}(56801,\cdot)$ $\chi_{132300}(62501,\cdot)$ $\chi_{132300}(63101,\cdot)$ $\chi_{132300}(68801,\cdot)$ $\chi_{132300}(69401,\cdot)$ $\chi_{132300}(75101,\cdot)$ $\chi_{132300}(75701,\cdot)$ $\chi_{132300}(81401,\cdot)$ $\chi_{132300}(82001,\cdot)$ $\chi_{132300}(87701,\cdot)$ $\chi_{132300}(88301,\cdot)$ $\chi_{132300}(100301,\cdot)$ $\chi_{132300}(100901,\cdot)$ $\chi_{132300}(106601,\cdot)$ $\chi_{132300}(107201,\cdot)$ $\chi_{132300}(112901,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

Values on generators

$(66151,122501,15877,54001)$ → $(1,e\left(\frac{1}{18}\right),1,e\left(\frac{37}{42}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(82001, a)$	$1$	$1$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{32}{63}\right)$