Dirichlet character χ132300(12997,⋅)\chi_{132300}(12997,\cdot)

• Label: 132300.12997
• Modulus: $132300$
• Conductor: $11025$
• Order: $420$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$132300$
Conductor:	$11025$
Order:	$420$
Real:	no
Primitive:	no, induced from $\chi_{11025}(5647,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 132300.bad

$\chi_{132300}(73,\cdot)$ $\chi_{132300}(2413,\cdot)$ $\chi_{132300}(3097,\cdot)$ $\chi_{132300}(5437,\cdot)$ $\chi_{132300}(6877,\cdot)$ $\chi_{132300}(7633,\cdot)$ $\chi_{132300}(9217,\cdot)$ $\chi_{132300}(9973,\cdot)$ $\chi_{132300}(11413,\cdot)$ $\chi_{132300}(12997,\cdot)$ $\chi_{132300}(13753,\cdot)$ $\chi_{132300}(17533,\cdot)$ $\chi_{132300}(18217,\cdot)$ $\chi_{132300}(18973,\cdot)$ $\chi_{132300}(21313,\cdot)$ $\chi_{132300}(21997,\cdot)$ $\chi_{132300}(22753,\cdot)$ $\chi_{132300}(24337,\cdot)$ $\chi_{132300}(25777,\cdot)$ $\chi_{132300}(26533,\cdot)$ $\chi_{132300}(28117,\cdot)$ $\chi_{132300}(28873,\cdot)$ $\chi_{132300}(31897,\cdot)$ $\chi_{132300}(33337,\cdot)$ $\chi_{132300}(35677,\cdot)$ $\chi_{132300}(36433,\cdot)$ $\chi_{132300}(37117,\cdot)$ $\chi_{132300}(37873,\cdot)$ $\chi_{132300}(40213,\cdot)$ $\chi_{132300}(41653,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

Values on generators

$(66151,122501,15877,54001)$ → $(1,e\left(\frac{1}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{11}{42}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(12997, a)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{55}{84}\right)$