Dirichlet character orbit 8325.ku

• Label: 8325.ku
• Modulus: $8325$
• Conductor: $8325$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8325$
Conductor:	$8325$
Order:	$90$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

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

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{8325}(139,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{8325}(484,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{8325}(844,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{8325}(1114,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{8325}(1579,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{8325}(1804,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{8325}(2389,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{8325}(2509,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{8325}(2779,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{8325}(3244,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{8325}(3469,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{8325}(3814,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{8325}(4054,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{8325}(4444,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{8325}(4909,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{8325}(5134,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{8325}(5479,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{8325}(5719,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{8325}(5839,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{8325}(6109,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{8325}(7144,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{8325}(7384,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{8325}(7504,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{8325}(8239,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{11}{90}\right)$