Properties

Modulus 107
Structure \(C_{106}\)
Order 106

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(107)
pari: g = idealstar(,107,2)

Character group

sage: G.order()
pari: g.no
Order = 106
sage: H.invariants()
pari: g.cyc
Structure = \(C_{106}\)
sage: H.gens()
pari: g.gen
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.

orbit label 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 \(-1\) \(1\) \(e\left(\frac{5}{106}\right)\) \(e\left(\frac{16}{53}\right)\) \(e\left(\frac{5}{53}\right)\) \(e\left(\frac{23}{106}\right)\) \(e\left(\frac{37}{106}\right)\) \(e\left(\frac{3}{106}\right)\) \(e\left(\frac{15}{106}\right)\) \(e\left(\frac{32}{53}\right)\) \(e\left(\frac{14}{53}\right)\) \(e\left(\frac{2}{53}\right)\)