Properties

Modulus 59
Structure \(C_{58}\)
Order 58

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(59)
pari: g = idealstar(,59,2)

Character group

sage: G.order()
pari: g.no
Order = 58
sage: H.invariants()
pari: g.cyc
Structure = \(C_{58}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{59}(2,\cdot)$

First 32 of 58 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
\(\chi_{59}(1,\cdot)\) 59.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{59}(2,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{25}{58}\right)\)
\(\chi_{59}(3,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{16}{29}\right)\)
\(\chi_{59}(4,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{25}{29}\right)\)
\(\chi_{59}(5,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{17}{29}\right)\)
\(\chi_{59}(6,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{57}{58}\right)\)
\(\chi_{59}(7,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{22}{29}\right)\)
\(\chi_{59}(8,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{17}{58}\right)\)
\(\chi_{59}(9,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{3}{29}\right)\)
\(\chi_{59}(10,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{1}{58}\right)\)
\(\chi_{59}(11,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{45}{58}\right)\)
\(\chi_{59}(12,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{12}{29}\right)\)
\(\chi_{59}(13,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{23}{58}\right)\)
\(\chi_{59}(14,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{11}{58}\right)\)
\(\chi_{59}(15,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{4}{29}\right)\)
\(\chi_{59}(16,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{21}{29}\right)\)
\(\chi_{59}(17,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{7}{29}\right)\)
\(\chi_{59}(18,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{31}{58}\right)\)
\(\chi_{59}(19,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{11}{29}\right)\)
\(\chi_{59}(20,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{13}{29}\right)\)
\(\chi_{59}(21,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{9}{29}\right)\)
\(\chi_{59}(22,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{6}{29}\right)\)
\(\chi_{59}(23,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{27}{58}\right)\)
\(\chi_{59}(24,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{49}{58}\right)\)
\(\chi_{59}(25,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{5}{29}\right)\)
\(\chi_{59}(26,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{24}{29}\right)\)
\(\chi_{59}(27,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{19}{29}\right)\)
\(\chi_{59}(28,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{18}{29}\right)\)
\(\chi_{59}(29,\cdot)\) 59.c 29 Yes \(1\) \(1\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{2}{29}\right)\)
\(\chi_{59}(30,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{33}{58}\right)\)
\(\chi_{59}(31,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{7}{58}\right)\)
\(\chi_{59}(32,\cdot)\) 59.d 58 Yes \(-1\) \(1\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{9}{58}\right)\)