sage: H = DirichletGroup(151)
pari: g = idealstar(,151,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 150 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{150}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{151}(6,\cdot)$ |
First 32 of 150 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{151}(1,\cdot)\) | 151.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{151}(2,\cdot)\) | 151.g | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{151}(3,\cdot)\) | 151.j | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) |
\(\chi_{151}(4,\cdot)\) | 151.g | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{151}(5,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) |
\(\chi_{151}(6,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{1}{150}\right)\) | \(e\left(\frac{67}{150}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{47}{75}\right)\) |
\(\chi_{151}(7,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{67}{150}\right)\) | \(e\left(\frac{139}{150}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{74}{75}\right)\) |
\(\chi_{151}(8,\cdot)\) | 151.d | 5 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{151}(9,\cdot)\) | 151.h | 25 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) |
\(\chi_{151}(10,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{4}{75}\right)\) |
\(\chi_{151}(11,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{4}{75}\right)\) | \(e\left(\frac{68}{75}\right)\) |
\(\chi_{151}(12,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{71}{150}\right)\) | \(e\left(\frac{107}{150}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{11}{75}\right)\) | \(e\left(\frac{37}{75}\right)\) |
\(\chi_{151}(13,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{46}{75}\right)\) | \(e\left(\frac{41}{150}\right)\) | \(e\left(\frac{47}{150}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{52}{75}\right)\) |
\(\chi_{151}(14,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{22}{75}\right)\) | \(e\left(\frac{137}{150}\right)\) | \(e\left(\frac{29}{150}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{17}{75}\right)\) | \(e\left(\frac{64}{75}\right)\) |
\(\chi_{151}(15,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{43}{150}\right)\) | \(e\left(\frac{31}{150}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{71}{75}\right)\) |
\(\chi_{151}(16,\cdot)\) | 151.g | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{151}(17,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{75}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{68}{75}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{26}{75}\right)\) |
\(\chi_{151}(18,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{75}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{37}{75}\right)\) | \(e\left(\frac{29}{75}\right)\) |
\(\chi_{151}(19,\cdot)\) | 151.d | 5 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{151}(20,\cdot)\) | 151.h | 25 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) |
\(\chi_{151}(21,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{38}{75}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{56}{75}\right)\) |
\(\chi_{151}(22,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{19}{75}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{58}{75}\right)\) |
\(\chi_{151}(23,\cdot)\) | 151.i | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{151}(24,\cdot)\) | 151.j | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) |
\(\chi_{151}(25,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{75}\right)\) | \(e\left(\frac{37}{75}\right)\) | \(e\left(\frac{4}{75}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{59}{75}\right)\) | \(e\left(\frac{28}{75}\right)\) |
\(\chi_{151}(26,\cdot)\) | 151.j | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) |
\(\chi_{151}(27,\cdot)\) | 151.j | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) |
\(\chi_{151}(28,\cdot)\) | 151.j | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) |
\(\chi_{151}(29,\cdot)\) | 151.h | 25 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) |
\(\chi_{151}(30,\cdot)\) | 151.l | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{113}{150}\right)\) | \(e\left(\frac{71}{150}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{61}{75}\right)\) |
\(\chi_{151}(31,\cdot)\) | 151.k | 75 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{68}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) | \(e\left(\frac{38}{75}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{41}{75}\right)\) |
\(\chi_{151}(32,\cdot)\) | 151.c | 3 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |