sage: H = DirichletGroup(294)
pari: g = idealstar(,294,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 84 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{42}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{294}(197,\cdot)$, $\chi_{294}(199,\cdot)$ |
First 32 of 84 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 | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{294}(1,\cdot)\) | 294.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{294}(5,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{294}(11,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{294}(13,\cdot)\) | 294.k | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(-1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(-1\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{294}(17,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{294}(19,\cdot)\) | 294.g | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{294}(23,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{294}(25,\cdot)\) | 294.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{294}(29,\cdot)\) | 294.l | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{294}(31,\cdot)\) | 294.g | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{294}(37,\cdot)\) | 294.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{294}(41,\cdot)\) | 294.j | 14 | no | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(-1\) | \(e\left(\frac{3}{7}\right)\) |
\(\chi_{294}(43,\cdot)\) | 294.i | 7 | no | \(1\) | \(1\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{294}(47,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{294}(53,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{294}(55,\cdot)\) | 294.k | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(-1\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{294}(59,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{294}(61,\cdot)\) | 294.o | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{294}(65,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{294}(67,\cdot)\) | 294.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{294}(71,\cdot)\) | 294.l | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(1\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(1\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{294}(73,\cdot)\) | 294.o | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{294}(79,\cdot)\) | 294.e | 3 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{294}(83,\cdot)\) | 294.j | 14 | no | \(1\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(-1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(-1\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{294}(85,\cdot)\) | 294.i | 7 | no | \(1\) | \(1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(1\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{294}(89,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{294}(95,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{294}(97,\cdot)\) | 294.c | 2 | no | \(-1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
\(\chi_{294}(101,\cdot)\) | 294.p | 42 | no | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{294}(103,\cdot)\) | 294.o | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{294}(107,\cdot)\) | 294.n | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{294}(109,\cdot)\) | 294.m | 21 | no | \(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{10}{21}\right)\) |