Dirichlet character χ132300(44179,⋅)\chi_{132300}(44179,\cdot)

• Label: 132300.44179
• Modulus: $132300$
• Conductor: $18900$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$132300$
Conductor:	$18900$
Order:	$90$
Real:	no
Primitive:	no, induced from $\chi_{18900}(6379,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 132300.rz

$\chi_{132300}(79,\cdot)$ $\chi_{132300}(5359,\cdot)$ $\chi_{132300}(14179,\cdot)$ $\chi_{132300}(17719,\cdot)$ $\chi_{132300}(26539,\cdot)$ $\chi_{132300}(31819,\cdot)$ $\chi_{132300}(35359,\cdot)$ $\chi_{132300}(40639,\cdot)$ $\chi_{132300}(44179,\cdot)$ $\chi_{132300}(49459,\cdot)$ $\chi_{132300}(58279,\cdot)$ $\chi_{132300}(61819,\cdot)$ $\chi_{132300}(70639,\cdot)$ $\chi_{132300}(75919,\cdot)$ $\chi_{132300}(79459,\cdot)$ $\chi_{132300}(84739,\cdot)$ $\chi_{132300}(88279,\cdot)$ $\chi_{132300}(93559,\cdot)$ $\chi_{132300}(102379,\cdot)$ $\chi_{132300}(105919,\cdot)$ $\chi_{132300}(114739,\cdot)$ $\chi_{132300}(120019,\cdot)$ $\chi_{132300}(123559,\cdot)$ $\chi_{132300}(128839,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

$(66151,122501,15877,54001)$ → $(-1,e\left(\frac{8}{9}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(44179, a)$	$-1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{9}\right)$