Dirichlet character orbit 4655.gc

• Label: 4655.gc
• Modulus: $4655$
• Conductor: $4655$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4655$
Conductor:	$4655$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{4655}(107,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{4655}(578,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4655}(772,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4655}(977,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4655}(1038,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{4655}(1437,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4655}(1642,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{4655}(1703,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4655}(1908,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4655}(2102,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4655}(2307,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4655}(2368,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4655}(2573,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{4655}(2767,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4655}(2972,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4655}(3033,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{4655}(3238,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4655}(3432,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4655}(3637,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4655}(3698,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{4655}(3903,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{4655}(4302,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{4655}(4363,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4655}(4568,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{7}\right)$