Dirichlet character orbit 4140.dk

• Label: 4140.dk
• Modulus: $4140$
• Conductor: $4140$
• Order: $132$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$4140$
Conductor:	$4140$
Order:	$132$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{4140}(187,\cdot)$	$1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{73}{132}\right)$
$\chi_{4140}(223,\cdot)$	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{132}\right)$
$\chi_{4140}(403,\cdot)$	$1$	$1$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{127}{132}\right)$
$\chi_{4140}(427,\cdot)$	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{101}{132}\right)$
$\chi_{4140}(463,\cdot)$	$1$	$1$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{95}{132}\right)$
$\chi_{4140}(547,\cdot)$	$1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{4140}(583,\cdot)$	$1$	$1$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{103}{132}\right)$
$\chi_{4140}(607,\cdot)$	$1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{113}{132}\right)$
$\chi_{4140}(763,\cdot)$	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{43}{132}\right)$
$\chi_{4140}(823,\cdot)$	$1$	$1$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{4140}(1087,\cdot)$	$1$	$1$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{4140}(1267,\cdot)$	$1$	$1$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{49}{132}\right)$
$\chi_{4140}(1327,\cdot)$	$1$	$1$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{53}{132}\right)$
$\chi_{4140}(1363,\cdot)$	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{132}\right)$
$\chi_{4140}(1507,\cdot)$	$1$	$1$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{17}{132}\right)$
$\chi_{4140}(1543,\cdot)$	$1$	$1$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{71}{132}\right)$
$\chi_{4140}(1687,\cdot)$	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{125}{132}\right)$
$\chi_{4140}(1807,\cdot)$	$1$	$1$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{13}{132}\right)$
$\chi_{4140}(1843,\cdot)$	$1$	$1$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{7}{132}\right)$
$\chi_{4140}(1867,\cdot)$	$1$	$1$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{65}{132}\right)$
$\chi_{4140}(1987,\cdot)$	$1$	$1$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{25}{132}\right)$
$\chi_{4140}(2083,\cdot)$	$1$	$1$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{4140}(2203,\cdot)$	$1$	$1$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{19}{132}\right)$
$\chi_{4140}(2263,\cdot)$	$1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{47}{132}\right)$
$\chi_{4140}(2707,\cdot)$	$1$	$1$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{97}{132}\right)$
$\chi_{4140}(2743,\cdot)$	$1$	$1$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{4140}(2887,\cdot)$	$1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{61}{132}\right)$
$\chi_{4140}(2923,\cdot)$	$1$	$1$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{115}{132}\right)$
$\chi_{4140}(2947,\cdot)$	$1$	$1$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{29}{132}\right)$
$\chi_{4140}(2983,\cdot)$	$1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{119}{132}\right)$
$\chi_{4140}(3067,\cdot)$	$1$	$1$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{37}{132}\right)$