Properties

Modulus 58
Structure \(C_{28}\)
Order 28

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(58)
pari: g = idealstar(,58,2)

Character group

sage: G.order()
pari: g.no
Order = 28
sage: H.invariants()
pari: g.cyc
Structure = \(C_{28}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{58}(31,\cdot)$

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
\(\chi_{58}(1,\cdot)\) 58.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{58}(3,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(-i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{28}\right)\)
\(\chi_{58}(5,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{58}(7,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{58}(9,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{58}(11,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(-i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{28}\right)\)
\(\chi_{58}(13,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{58}(15,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(i\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{58}(17,\cdot)\) 58.c 4 No \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(-1\) \(-i\) \(-1\) \(i\) \(-i\) \(-i\) \(-i\)
\(\chi_{58}(19,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(-i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{58}(21,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(-i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{58}(23,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{58}(25,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{58}(27,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{58}(31,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(-i\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{58}(33,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{58}(35,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{58}(37,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(i\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{58}(39,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(i\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{58}(41,\cdot)\) 58.c 4 No \(-1\) \(1\) \(i\) \(-1\) \(1\) \(-1\) \(i\) \(-1\) \(-i\) \(i\) \(i\) \(i\)
\(\chi_{58}(43,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(-i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{58}(45,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{58}(47,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(i\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{58}(49,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{58}(51,\cdot)\) 58.e 14 No \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{58}(53,\cdot)\) 58.d 7 No \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{58}(55,\cdot)\) 58.f 28 No \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{58}(57,\cdot)\) 58.b 2 No \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\)