Group of Dirichlet characters of modulus 107

• Modulus: $107$
• Structure: $C_{106}$
• Order: $106$

Character group

Order	=	106
Structure	=	$C_{106}$
Generators	=	$\chi_{107}(2,\cdot)$

First 32 of 106 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{107}(1,\cdot)$	107.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{107}(2,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{11}{53}\right)$
$\chi_{107}(3,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{28}{53}\right)$
$\chi_{107}(4,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{22}{53}\right)$
$\chi_{107}(5,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{40}{53}\right)$
$\chi_{107}(6,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{71}{106}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{51}{106}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{39}{53}\right)$
$\chi_{107}(7,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{85}{106}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{49}{53}\right)$
$\chi_{107}(8,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{1}{106}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{33}{53}\right)$
$\chi_{107}(9,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{3}{53}\right)$
$\chi_{107}(10,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{24}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{51}{53}\right)$
$\chi_{107}(11,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{30}{53}\right)$
$\chi_{107}(12,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{50}{53}\right)$
$\chi_{107}(13,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{21}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{48}{53}\right)$
$\chi_{107}(14,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{7}{53}\right)$
$\chi_{107}(15,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{15}{53}\right)$
$\chi_{107}(16,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{44}{53}\right)$
$\chi_{107}(17,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{29}{53}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{1}{53}\right)$
$\chi_{107}(18,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{47}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{14}{53}\right)$
$\chi_{107}(19,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{39}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{25}{53}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{34}{53}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{1}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{10}{53}\right)$
$\chi_{107}(20,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{87}{106}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{9}{53}\right)$
$\chi_{107}(21,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{24}{53}\right)$
$\chi_{107}(22,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{21}{106}\right)$	$e\left(\frac{43}{106}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{41}{53}\right)$
$\chi_{107}(23,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{9}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{28}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{40}{53}\right)$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{46}{53}\right)$
$\chi_{107}(24,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{73}{106}\right)$	$e\left(\frac{11}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{39}{106}\right)$	$e\left(\frac{95}{106}\right)$	$e\left(\frac{65}{106}\right)$	$e\left(\frac{7}{106}\right)$	$e\left(\frac{22}{53}\right)$	$e\left(\frac{3}{53}\right)$	$e\left(\frac{8}{53}\right)$
$\chi_{107}(25,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{47}{53}\right)$	$e\left(\frac{4}{53}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{8}{53}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{27}{53}\right)$
$\chi_{107}(26,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{43}{53}\right)$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{6}{53}\right)$
$\chi_{107}(27,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{51}{53}\right)$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{50}{53}\right)$	$e\left(\frac{19}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{31}{53}\right)$
$\chi_{107}(28,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{45}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{29}{106}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{18}{53}\right)$
$\chi_{107}(29,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{52}{53}\right)$	$e\left(\frac{48}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{26}{53}\right)$	$e\left(\frac{34}{53}\right)$
$\chi_{107}(30,\cdot)$	107.c	53	yes	$1$	$1$	$e\left(\frac{6}{53}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{2}{53}\right)$	$e\left(\frac{46}{53}\right)$	$e\left(\frac{18}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{26}{53}\right)$
$\chi_{107}(31,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{27}{106}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{27}{53}\right)$	$e\left(\frac{103}{106}\right)$	$e\left(\frac{9}{106}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{81}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{12}{53}\right)$	$e\left(\frac{32}{53}\right)$
$\chi_{107}(32,\cdot)$	107.d	106	yes	$-1$	$1$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{16}{53}\right)$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{23}{106}\right)$	$e\left(\frac{37}{106}\right)$	$e\left(\frac{3}{106}\right)$	$e\left(\frac{15}{106}\right)$	$e\left(\frac{32}{53}\right)$	$e\left(\frac{14}{53}\right)$	$e\left(\frac{2}{53}\right)$

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