sage: H = DirichletGroup(6001)
pari: g = idealstar(,6001,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 5632 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{352}\times C_{16}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{6001}(2825,\cdot)$, $\chi_{6001}(3180,\cdot)$ |
First 32 of 5632 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{6001}(1,\cdot)\) | 6001.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{6001}(2,\cdot)\) | 6001.dc | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(1\) | \(e\left(\frac{7}{88}\right)\) |
\(\chi_{6001}(3,\cdot)\) | 6001.er | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{23}{352}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{67}{352}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{23}{176}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{107}{176}\right)\) |
\(\chi_{6001}(4,\cdot)\) | 6001.ct | 44 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(1\) | \(-1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(1\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{6001}(5,\cdot)\) | 6001.er | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{67}{352}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{287}{352}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{67}{176}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{151}{176}\right)\) |
\(\chi_{6001}(6,\cdot)\) | 6001.cm | 32 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{13}{32}\right)\) | \(1\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{6001}(7,\cdot)\) | 6001.cd | 32 | yes | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{31}{32}\right)\) | \(-1\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(i\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{11}{16}\right)\) |
\(\chi_{6001}(8,\cdot)\) | 6001.dc | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(1\) | \(i\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(1\) | \(e\left(\frac{21}{88}\right)\) |
\(\chi_{6001}(9,\cdot)\) | 6001.ec | 176 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{23}{176}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{67}{176}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{19}{88}\right)\) |
\(\chi_{6001}(10,\cdot)\) | 6001.cn | 32 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{17}{32}\right)\) | \(1\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{6001}(11,\cdot)\) | 6001.do | 176 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{107}{176}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{151}{176}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{51}{176}\right)\) |
\(\chi_{6001}(12,\cdot)\) | 6001.ep | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{263}{352}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{307}{352}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{87}{176}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{135}{176}\right)\) |
\(\chi_{6001}(13,\cdot)\) | 6001.ej | 352 | yes | \(-1\) | \(1\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{73}{352}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{29}{352}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{73}{176}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{17}{88}\right)\) |
\(\chi_{6001}(14,\cdot)\) | 6001.es | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{109}{352}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{241}{352}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{109}{176}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{135}{176}\right)\) |
\(\chi_{6001}(15,\cdot)\) | 6001.ec | 176 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{45}{176}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{41}{88}\right)\) |
\(\chi_{6001}(16,\cdot)\) | 6001.bv | 22 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(1\) | \(1\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(1\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{6001}(18,\cdot)\) | 6001.dy | 176 | no | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{83}{176}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{127}{176}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{13}{44}\right)\) |
\(\chi_{6001}(19,\cdot)\) | 6001.ed | 176 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{13}{176}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{145}{176}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{88}\right)\) |
\(\chi_{6001}(20,\cdot)\) | 6001.ep | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{307}{352}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{175}{352}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{131}{176}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{3}{176}\right)\) |
\(\chi_{6001}(21,\cdot)\) | 6001.cv | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{13}{44}\right)\) |
\(\chi_{6001}(22,\cdot)\) | 6001.dn | 176 | yes | \(-1\) | \(1\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{167}{176}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{35}{176}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{65}{176}\right)\) |
\(\chi_{6001}(23,\cdot)\) | 6001.eb | 176 | yes | \(-1\) | \(1\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{103}{176}\right)\) |
\(\chi_{6001}(24,\cdot)\) | 6001.et | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{31}{352}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{75}{352}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{31}{176}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{149}{176}\right)\) |
\(\chi_{6001}(25,\cdot)\) | 6001.ec | 176 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{67}{176}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{111}{176}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{67}{88}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{63}{88}\right)\) |
\(\chi_{6001}(26,\cdot)\) | 6001.eg | 352 | yes | \(-1\) | \(1\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{193}{352}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{149}{352}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{17}{176}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{6001}(27,\cdot)\) | 6001.er | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{69}{352}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{201}{352}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{69}{176}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{145}{176}\right)\) |
\(\chi_{6001}(28,\cdot)\) | 6001.ep | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{229}{352}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{352}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{53}{176}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{149}{176}\right)\) |
\(\chi_{6001}(29,\cdot)\) | 6001.dq | 176 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{45}{176}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{1}{176}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{176}\right)\) |
\(\chi_{6001}(30,\cdot)\) | 6001.dx | 176 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{105}{176}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{61}{176}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{6001}(31,\cdot)\) | 6001.eq | 352 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{291}{352}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{159}{352}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{115}{176}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{139}{176}\right)\) |
\(\chi_{6001}(32,\cdot)\) | 6001.dc | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(1\) | \(-i\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(1\) | \(e\left(\frac{35}{88}\right)\) |
\(\chi_{6001}(33,\cdot)\) | 6001.em | 352 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{237}{352}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{17}{352}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{61}{176}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{79}{88}\right)\) |