Properties

Modulus 67
Structure \(C_{66}\)
Order 66

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(67)
pari: g = idealstar(,67,2)

Character group

sage: G.order()
pari: g.no
Order = 66
sage: H.invariants()
pari: g.cyc
Structure = \(C_{66}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{67}(2,\cdot)$

First 32 of 66 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
\(\chi_{67}(1,\cdot)\) 67.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{67}(2,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{67}(3,\cdot)\) 67.f 22 Yes \(-1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{67}(4,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{67}(5,\cdot)\) 67.f 22 Yes \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{67}(6,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{25}{33}\right)\)
\(\chi_{67}(7,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{37}{66}\right)\)
\(\chi_{67}(8,\cdot)\) 67.f 22 Yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{67}(9,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{67}(10,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{67}(11,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{67}(12,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{67}(13,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{67}(14,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{67}(15,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{67}(16,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{67}(17,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{7}{33}\right)\)
\(\chi_{67}(18,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{67}(19,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{67}(20,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{13}{66}\right)\)
\(\chi_{67}(21,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{67}(22,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{67}(23,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{67}(24,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{67}(25,\cdot)\) 67.e 11 Yes \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{67}(26,\cdot)\) 67.g 33 Yes \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{67}(27,\cdot)\) 67.f 22 Yes \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{67}(28,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{67}(29,\cdot)\) 67.c 3 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{67}(30,\cdot)\) 67.d 6 Yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{67}(31,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{66}\right)\)
\(\chi_{67}(32,\cdot)\) 67.h 66 Yes \(-1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{31}{66}\right)\)