Dirichlet character orbit 12825.pe

• Label: 12825.pe
• Modulus: $12825$
• Conductor: $12825$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$12825$
Conductor:	$12825$
Order:	$180$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{12825}(23,\cdot)$	$1$	$1$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{12825}(92,\cdot)$	$1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{12825}(758,\cdot)$	$1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{12825}(803,\cdot)$	$1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{12825}(842,\cdot)$	$1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{12825}(1472,\cdot)$	$1$	$1$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{12825}(1562,\cdot)$	$1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{12825}(2297,\cdot)$	$1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{12825}(2342,\cdot)$	$1$	$1$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{12825}(2498,\cdot)$	$1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{12825}(2588,\cdot)$	$1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{12825}(3323,\cdot)$	$1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{12825}(3683,\cdot)$	$1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{12825}(4037,\cdot)$	$1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{12825}(4127,\cdot)$	$1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{12825}(4433,\cdot)$	$1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{12825}(4862,\cdot)$	$1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{12825}(5063,\cdot)$	$1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{12825}(5153,\cdot)$	$1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{12825}(5222,\cdot)$	$1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{12825}(5888,\cdot)$	$1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{12825}(5933,\cdot)$	$1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{12825}(5972,\cdot)$	$1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{12825}(6248,\cdot)$	$1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{12825}(6602,\cdot)$	$1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{12825}(6692,\cdot)$	$1$	$1$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{12825}(6998,\cdot)$	$1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{12825}(7427,\cdot)$	$1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{12825}(7472,\cdot)$	$1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{12825}(7628,\cdot)$	$1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{12825}(7787,\cdot)$	$1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{13}{20}\right)$