Dirichlet character χ132300(59,⋅)\chi_{132300}(59,\cdot)

• Label: 132300.59
• Modulus: $132300$
• Conductor: $132300$
• Order: $630$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$132300$
Conductor:	$132300$
Order:	$630$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 132300.bcb

$\chi_{132300}(59,\cdot)$ $\chi_{132300}(1319,\cdot)$ $\chi_{132300}(1559,\cdot)$ $\chi_{132300}(2819,\cdot)$ $\chi_{132300}(3839,\cdot)$ $\chi_{132300}(4079,\cdot)$ $\chi_{132300}(5339,\cdot)$ $\chi_{132300}(6359,\cdot)$ $\chi_{132300}(7619,\cdot)$ $\chi_{132300}(8879,\cdot)$ $\chi_{132300}(9119,\cdot)$ $\chi_{132300}(10139,\cdot)$ $\chi_{132300}(10379,\cdot)$ $\chi_{132300}(11639,\cdot)$ $\chi_{132300}(12659,\cdot)$ $\chi_{132300}(13919,\cdot)$ $\chi_{132300}(14159,\cdot)$ $\chi_{132300}(15179,\cdot)$ $\chi_{132300}(15419,\cdot)$ $\chi_{132300}(16439,\cdot)$ $\chi_{132300}(17939,\cdot)$ $\chi_{132300}(18959,\cdot)$ $\chi_{132300}(20459,\cdot)$ $\chi_{132300}(21479,\cdot)$ $\chi_{132300}(21719,\cdot)$ $\chi_{132300}(22739,\cdot)$ $\chi_{132300}(22979,\cdot)$ $\chi_{132300}(24239,\cdot)$ $\chi_{132300}(25259,\cdot)$ $\chi_{132300}(26519,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{315})$
Fixed field:	Number field defined by a degree 630 polynomial (not computed)

Values on generators

$(66151,122501,15877,54001)$ → $(-1,e\left(\frac{5}{18}\right),e\left(\frac{7}{10}\right),e\left(\frac{13}{42}\right))$

First values

$a$	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 132300 }(59, a)$	$-1$	$1$	$e\left(\frac{218}{315}\right)$	$e\left(\frac{232}{315}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{630}\right)$	$e\left(\frac{157}{630}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{52}{315}\right)$	$e\left(\frac{61}{63}\right)$