Dirichlet character orbit 103.h

• Label: 103.h
• Modulus: $103$
• Conductor: $103$
• Order: $102$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$103$
Conductor:	$103$
Order:	$102$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{51})$
Fixed field:	Number field defined by a degree 102 polynomial (not computed)

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{103}(5,\cdot)$	$-1$	$1$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{61}{102}\right)$
$\chi_{103}(6,\cdot)$	$-1$	$1$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{65}{102}\right)$
$\chi_{103}(11,\cdot)$	$-1$	$1$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{49}{102}\right)$
$\chi_{103}(12,\cdot)$	$-1$	$1$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{97}{102}\right)$
$\chi_{103}(20,\cdot)$	$-1$	$1$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{23}{102}\right)$
$\chi_{103}(21,\cdot)$	$-1$	$1$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{43}{102}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{73}{102}\right)$
$\chi_{103}(35,\cdot)$	$-1$	$1$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{101}{102}\right)$
$\chi_{103}(40,\cdot)$	$-1$	$1$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{55}{102}\right)$
$\chi_{103}(43,\cdot)$	$-1$	$1$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{5}{102}\right)$
$\chi_{103}(44,\cdot)$	$-1$	$1$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{11}{102}\right)$
$\chi_{103}(45,\cdot)$	$-1$	$1$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{25}{102}\right)$
$\chi_{103}(48,\cdot)$	$-1$	$1$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{59}{102}\right)$
$\chi_{103}(51,\cdot)$	$-1$	$1$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{19}{102}\right)$
$\chi_{103}(53,\cdot)$	$-1$	$1$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{97}{102}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{1}{102}\right)$
$\chi_{103}(54,\cdot)$	$-1$	$1$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{1}{102}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{29}{102}\right)$
$\chi_{103}(62,\cdot)$	$-1$	$1$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{101}{102}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{41}{102}\right)$
$\chi_{103}(65,\cdot)$	$-1$	$1$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{50}{51}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{67}{102}\right)$
$\chi_{103}(67,\cdot)$	$-1$	$1$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{79}{102}\right)$
$\chi_{103}(70,\cdot)$	$-1$	$1$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{14}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{31}{102}\right)$
$\chi_{103}(71,\cdot)$	$-1$	$1$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{7}{102}\right)$
$\chi_{103}(74,\cdot)$	$-1$	$1$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{35}{102}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{95}{102}\right)$
$\chi_{103}(75,\cdot)$	$-1$	$1$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{31}{51}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{53}{102}\right)$
$\chi_{103}(77,\cdot)$	$-1$	$1$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{89}{102}\right)$
$\chi_{103}(78,\cdot)$	$-1$	$1$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{71}{102}\right)$
$\chi_{103}(84,\cdot)$	$-1$	$1$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{29}{102}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{35}{102}\right)$
$\chi_{103}(85,\cdot)$	$-1$	$1$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{47}{102}\right)$
$\chi_{103}(86,\cdot)$	$-1$	$1$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{19}{102}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{37}{102}\right)$
$\chi_{103}(87,\cdot)$	$-1$	$1$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{23}{102}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{46}{51}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{77}{102}\right)$
$\chi_{103}(88,\cdot)$	$-1$	$1$	$e\left(\frac{13}{51}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{26}{51}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{29}{51}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{43}{102}\right)$
$\chi_{103}(96,\cdot)$	$-1$	$1$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{55}{102}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{91}{102}\right)$
$\chi_{103}(99,\cdot)$	$-1$	$1$	$e\left(\frac{49}{51}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{13}{102}\right)$