Dirichlet character orbit 8325.ie

• Label: 8325.ie
• Modulus: $8325$
• Conductor: $8325$
• Order: $45$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8325$
Conductor:	$8325$
Order:	$45$
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 45 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{8325}(16,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{8325}(256,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{8325}(1291,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{8325}(1561,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{8325}(1681,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{8325}(1921,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{8325}(2266,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{8325}(2491,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{8325}(2956,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{8325}(3346,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{8325}(3586,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{8325}(3931,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{8325}(4156,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{8325}(4621,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{8325}(4891,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{8325}(5011,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{8325}(5596,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{8325}(5821,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{8325}(6286,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{8325}(6556,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{8325}(6916,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{8325}(7261,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{8325}(7486,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{8325}(8221,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{41}{45}\right)$