Properties

Modulus 93
Structure \(C_{30}\times C_{2}\)
Order 60

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(93)
pari: g = idealstar(,93,2)

Character group

sage: G.order()
pari: g.no
Order = 60
sage: H.invariants()
pari: g.cyc
Structure = \(C_{30}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{93}(34,\cdot)$, $\chi_{93}(32,\cdot)$

First 32 of 60 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 4 5 7 8 10 11 13 14 16
\(\chi_{93}(1,\cdot)\) 93.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{93}(2,\cdot)\) 93.l 10 Yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(4,\cdot)\) 93.f 5 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(5,\cdot)\) 93.h 6 Yes \(-1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{93}(7,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(8,\cdot)\) 93.l 10 Yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(10,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(11,\cdot)\) 93.p 30 Yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(13,\cdot)\) 93.n 30 No \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(14,\cdot)\) 93.o 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(16,\cdot)\) 93.f 5 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(17,\cdot)\) 93.p 30 Yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(19,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(20,\cdot)\) 93.o 30 Yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(22,\cdot)\) 93.n 30 No \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(23,\cdot)\) 93.k 10 Yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(25,\cdot)\) 93.e 3 No \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{93}(26,\cdot)\) 93.g 6 Yes \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{93}(28,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(29,\cdot)\) 93.k 10 Yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(32,\cdot)\) 93.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{93}(34,\cdot)\) 93.n 30 No \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(35,\cdot)\) 93.l 10 Yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(37,\cdot)\) 93.i 6 No \(-1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{93}(38,\cdot)\) 93.o 30 Yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{93}(40,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{93}(41,\cdot)\) 93.o 30 Yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(43,\cdot)\) 93.n 30 No \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{93}(44,\cdot)\) 93.p 30 Yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(46,\cdot)\) 93.j 10 No \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(47,\cdot)\) 93.l 10 Yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{93}(49,\cdot)\) 93.m 15 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\)