Dirichlet character orbit 325.bi

• Label: 325.bi
• Modulus: $325$
• Conductor: $325$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$325$
Conductor:	$325$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{325}(28,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{325}(37,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{325}(58,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{325}(72,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{325}(102,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{325}(123,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{325}(137,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{325}(158,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{325}(167,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{325}(188,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{325}(202,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{325}(223,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{325}(253,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{325}(267,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{325}(288,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{325}(297,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$