Dirichlet character orbit 1125.bc

• Label: 1125.bc
• Modulus: $1125$
• Conductor: $1125$
• Order: $75$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1125$
Conductor:	$1125$
Order:	$75$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{75})$
Fixed field:	Number field defined by a degree 75 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1125}(16,\cdot)$	$1$	$1$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{1125}(31,\cdot)$	$1$	$1$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{1125}(61,\cdot)$	$1$	$1$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$
$\chi_{1125}(106,\cdot)$	$1$	$1$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{1125}(121,\cdot)$	$1$	$1$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{9}{25}\right)$
$\chi_{1125}(166,\cdot)$	$1$	$1$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{23}{25}\right)$
$\chi_{1125}(196,\cdot)$	$1$	$1$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{24}{25}\right)$
$\chi_{1125}(211,\cdot)$	$1$	$1$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{1125}(241,\cdot)$	$1$	$1$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{25}\right)$
$\chi_{1125}(256,\cdot)$	$1$	$1$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{25}\right)$
$\chi_{1125}(286,\cdot)$	$1$	$1$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{1125}(331,\cdot)$	$1$	$1$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{1125}(346,\cdot)$	$1$	$1$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{1125}(391,\cdot)$	$1$	$1$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$
$\chi_{1125}(421,\cdot)$	$1$	$1$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{1125}(436,\cdot)$	$1$	$1$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$
$\chi_{1125}(466,\cdot)$	$1$	$1$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{25}\right)$
$\chi_{1125}(481,\cdot)$	$1$	$1$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{1125}(511,\cdot)$	$1$	$1$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{17}{25}\right)$
$\chi_{1125}(556,\cdot)$	$1$	$1$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{21}{25}\right)$
$\chi_{1125}(571,\cdot)$	$1$	$1$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{24}{25}\right)$
$\chi_{1125}(616,\cdot)$	$1$	$1$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{25}\right)$
$\chi_{1125}(646,\cdot)$	$1$	$1$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{14}{25}\right)$
$\chi_{1125}(661,\cdot)$	$1$	$1$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$
$\chi_{1125}(691,\cdot)$	$1$	$1$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$
$\chi_{1125}(706,\cdot)$	$1$	$1$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{1125}(736,\cdot)$	$1$	$1$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{1125}(781,\cdot)$	$1$	$1$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{1125}(796,\cdot)$	$1$	$1$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{25}\right)$
$\chi_{1125}(841,\cdot)$	$1$	$1$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{25}\right)$
$\chi_{1125}(871,\cdot)$	$1$	$1$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{9}{25}\right)$