Properties

Modulus 62
Structure \(C_{30}\)
Order 30

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(62)
pari: g = idealstar(,62,2)

Character group

sage: G.order()
pari: g.no
Order = 30
sage: H.invariants()
pari: g.cyc
Structure = \(C_{30}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{62}(3,\cdot)$

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 3 5 7 9 11 13 15 17 19 21
\(\chi_{62}(1,\cdot)\) 62.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{62}(3,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{62}(5,\cdot)\) 62.c 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{62}(7,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{62}(9,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{62}(11,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{62}(13,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{62}(15,\cdot)\) 62.f 10 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{62}(17,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{62}(19,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{62}(21,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{62}(23,\cdot)\) 62.f 10 No \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{62}(25,\cdot)\) 62.c 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{62}(27,\cdot)\) 62.f 10 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{62}(29,\cdot)\) 62.f 10 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{62}(33,\cdot)\) 62.d 5 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{62}(35,\cdot)\) 62.d 5 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{62}(37,\cdot)\) 62.e 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{62}(39,\cdot)\) 62.d 5 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{62}(41,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{62}(43,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{62}(45,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{62}(47,\cdot)\) 62.d 5 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{62}(49,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{62}(51,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{62}(53,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{62}(55,\cdot)\) 62.h 30 No \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{62}(57,\cdot)\) 62.e 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{62}(59,\cdot)\) 62.g 15 No \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{62}(61,\cdot)\) 62.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\)