Properties

Modulus 99
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(99)
pari: g = idealstar(,99,2)

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 = $\chi_{99}(68,\cdot)$, $\chi_{99}(10,\cdot)$

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 13 14 16 17
\(\chi_{99}(1,\cdot)\) 99.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{99}(2,\cdot)\) 99.p 30 Yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{99}(4,\cdot)\) 99.m 15 Yes \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{99}(5,\cdot)\) 99.n 30 Yes \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{99}(7,\cdot)\) 99.o 30 Yes \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{99}(8,\cdot)\) 99.j 10 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{99}(10,\cdot)\) 99.c 2 No \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{99}(13,\cdot)\) 99.o 30 Yes \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{99}(14,\cdot)\) 99.n 30 Yes \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{99}(16,\cdot)\) 99.m 15 Yes \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{99}(17,\cdot)\) 99.j 10 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{99}(19,\cdot)\) 99.k 10 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{99}(20,\cdot)\) 99.n 30 Yes \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{99}(23,\cdot)\) 99.i 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{99}(25,\cdot)\) 99.m 15 Yes \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{99}(26,\cdot)\) 99.l 10 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{99}(28,\cdot)\) 99.k 10 No \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{99}(29,\cdot)\) 99.p 30 Yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{99}(31,\cdot)\) 99.m 15 Yes \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{99}(32,\cdot)\) 99.g 6 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{99}(34,\cdot)\) 99.e 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{99}(35,\cdot)\) 99.j 10 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{99}(37,\cdot)\) 99.f 5 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{99}(38,\cdot)\) 99.n 30 Yes \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{99}(40,\cdot)\) 99.o 30 Yes \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{99}(41,\cdot)\) 99.p 30 Yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{99}(43,\cdot)\) 99.h 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{99}(46,\cdot)\) 99.k 10 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{99}(47,\cdot)\) 99.n 30 Yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{99}(49,\cdot)\) 99.m 15 Yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{99}(50,\cdot)\) 99.p 30 Yes \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{99}(52,\cdot)\) 99.o 30 Yes \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\)