Properties

Modulus $155$
Structure \(C_{60}\times C_{2}\)
Order $120$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(155)
 
pari: g = idealstar(,155,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 120
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{155}(32,\cdot)$, $\chi_{155}(96,\cdot)$

First 32 of 120 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.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{155}(1,\cdot)\) 155.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{155}(2,\cdot)\) 155.s 20 yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{155}(3,\cdot)\) 155.x 60 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{37}{60}\right)\)
\(\chi_{155}(4,\cdot)\) 155.n 10 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{155}(6,\cdot)\) 155.k 6 no \(-1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{155}(7,\cdot)\) 155.w 60 yes \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{60}\right)\)
\(\chi_{155}(8,\cdot)\) 155.s 20 yes \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{155}(9,\cdot)\) 155.u 30 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{155}(11,\cdot)\) 155.t 30 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{155}(12,\cdot)\) 155.x 60 yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{43}{60}\right)\)
\(\chi_{155}(13,\cdot)\) 155.x 60 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{155}(14,\cdot)\) 155.u 30 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{155}(16,\cdot)\) 155.h 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{155}(17,\cdot)\) 155.x 60 yes \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{155}(18,\cdot)\) 155.w 60 yes \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{47}{60}\right)\)
\(\chi_{155}(19,\cdot)\) 155.u 30 yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{155}(21,\cdot)\) 155.t 30 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{155}(22,\cdot)\) 155.x 60 yes \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{59}{60}\right)\)
\(\chi_{155}(23,\cdot)\) 155.r 20 yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{155}(24,\cdot)\) 155.v 30 yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{155}(26,\cdot)\) 155.k 6 no \(-1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{155}(27,\cdot)\) 155.r 20 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{155}(28,\cdot)\) 155.w 60 yes \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{155}(29,\cdot)\) 155.m 10 yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{155}(32,\cdot)\) 155.g 4 no \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\)
\(\chi_{155}(33,\cdot)\) 155.s 20 yes \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{155}(34,\cdot)\) 155.v 30 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{155}(36,\cdot)\) 155.e 3 no \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{155}(37,\cdot)\) 155.p 12 yes \(1\) \(1\) \(i\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{155}(38,\cdot)\) 155.w 60 yes \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{155}(39,\cdot)\) 155.n 10 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{155}(41,\cdot)\) 155.q 15 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\)