Dirichlet character orbit 3150.em

• Label: 3150.em
• Modulus: $3150$
• Conductor: $175$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3150$
Conductor:	$175$
Order:	$60$
Real:	no
Primitive:	no, induced from 175.x
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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{3150}(73,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{3150}(397,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{3150}(523,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{3150}(577,\cdot)$	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{3150}(703,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{3150}(1027,\cdot)$	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{3150}(1153,\cdot)$	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{3150}(1333,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{10}\right)$	$i$
$\chi_{3150}(1783,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{10}\right)$	$i$
$\chi_{3150}(1837,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{3150}(1963,\cdot)$	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{3150}(2287,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{3150}(2413,\cdot)$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{3150}(2467,\cdot)$	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{3150}(2917,\cdot)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{3150}(3097,\cdot)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{9}{10}\right)$	$-i$