Dirichlet character orbit 5850.gi

• Label: 5850.gi
• Modulus: $5850$
• Conductor: $2925$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5850$
Conductor:	$2925$
Order:	$60$
Real:	no
Primitive:	no, induced from 2925.gh
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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{5850}(653,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{5850}(887,\cdot)$	$1$	$1$	$i$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{5850}(1127,\cdot)$	$1$	$1$	$i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{5850}(1823,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{5850}(2063,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{5850}(2297,\cdot)$	$1$	$1$	$i$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{5850}(3227,\cdot)$	$1$	$1$	$i$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{5850}(3233,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{10}\right)$	$i$
$\chi_{5850}(3467,\cdot)$	$1$	$1$	$i$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{5850}(4163,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{5850}(4397,\cdot)$	$1$	$1$	$i$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{5850}(4403,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{5850}(4637,\cdot)$	$1$	$1$	$i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{5850}(5333,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{10}\right)$	$i$
$\chi_{5850}(5567,\cdot)$	$1$	$1$	$i$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{5850}(5573,\cdot)$	$1$	$1$	$-i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$