sage: H = DirichletGroup(14520)
pari: g = idealstar(,14520,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 3520 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{220}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{14520}(3631,\cdot)$, $\chi_{14520}(7261,\cdot)$, $\chi_{14520}(4841,\cdot)$, $\chi_{14520}(11617,\cdot)$, $\chi_{14520}(14401,\cdot)$ |
First 32 of 3520 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 | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{14520}(1,\cdot)\) | 14520.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{14520}(7,\cdot)\) | 14520.gy | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{14520}(13,\cdot)\) | 14520.gw | 220 | no | \(1\) | \(1\) | \(e\left(\frac{39}{220}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{31}{44}\right)\) |
\(\chi_{14520}(17,\cdot)\) | 14520.hf | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{39}{44}\right)\) |
\(\chi_{14520}(19,\cdot)\) | 14520.ft | 110 | no | \(1\) | \(1\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{14520}(23,\cdot)\) | 14520.fb | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{14520}(29,\cdot)\) | 14520.gh | 110 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{14520}(31,\cdot)\) | 14520.gc | 110 | no | \(-1\) | \(1\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{1}{22}\right)\) |
\(\chi_{14520}(37,\cdot)\) | 14520.hj | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{173}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{14520}(41,\cdot)\) | 14520.fu | 110 | no | \(1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{14520}(43,\cdot)\) | 14520.ff | 44 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{14520}(47,\cdot)\) | 14520.hg | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{217}{220}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{89}{220}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{14520}(49,\cdot)\) | 14520.fs | 110 | no | \(1\) | \(1\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{14520}(53,\cdot)\) | 14520.he | 220 | yes | \(1\) | \(1\) | \(e\left(\frac{109}{220}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{159}{220}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{14520}(59,\cdot)\) | 14520.gt | 110 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{17}{22}\right)\) |
\(\chi_{14520}(61,\cdot)\) | 14520.fz | 110 | no | \(-1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{14520}(67,\cdot)\) | 14520.fi | 44 | no | \(1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{14520}(71,\cdot)\) | 14520.fx | 110 | no | \(1\) | \(1\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{14520}(73,\cdot)\) | 14520.hi | 220 | no | \(1\) | \(1\) | \(e\left(\frac{23}{220}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{29}{44}\right)\) |
\(\chi_{14520}(79,\cdot)\) | 14520.gd | 110 | no | \(1\) | \(1\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{14520}(83,\cdot)\) | 14520.hh | 220 | yes | \(1\) | \(1\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{37}{220}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{19}{110}\right)\) | \(e\left(\frac{71}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{37}{44}\right)\) |
\(\chi_{14520}(89,\cdot)\) | 14520.eq | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
\(\chi_{14520}(91,\cdot)\) | 14520.fw | 110 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{14520}(97,\cdot)\) | 14520.gx | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{119}{220}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{219}{220}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{14520}(101,\cdot)\) | 14520.ge | 110 | no | \(1\) | \(1\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{14520}(103,\cdot)\) | 14520.hd | 220 | no | \(1\) | \(1\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{59}{220}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{73}{220}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{14520}(107,\cdot)\) | 14520.hh | 220 | yes | \(1\) | \(1\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{13}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{14520}(109,\cdot)\) | 14520.eb | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{14520}(113,\cdot)\) | 14520.ha | 220 | no | \(1\) | \(1\) | \(e\left(\frac{97}{220}\right)\) | \(e\left(\frac{111}{220}\right)\) | \(e\left(\frac{19}{220}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{197}{220}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{19}{44}\right)\) |
\(\chi_{14520}(119,\cdot)\) | 14520.gk | 110 | no | \(1\) | \(1\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{8}{11}\right)\) |
\(\chi_{14520}(127,\cdot)\) | 14520.gy | 220 | no | \(-1\) | \(1\) | \(e\left(\frac{91}{220}\right)\) | \(e\left(\frac{103}{220}\right)\) | \(e\left(\frac{197}{220}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{14520}(131,\cdot)\) | 14520.du | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) |