Properties

Modulus $4725$
Structure \(C_{2}\times C_{6}\times C_{180}\)
Order $2160$

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4725)
 
pari: g = idealstar(,4725,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2160
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{6}\times C_{180}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4725}(4376,\cdot)$, $\chi_{4725}(1702,\cdot)$, $\chi_{4725}(2026,\cdot)$

First 32 of 2160 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 \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(23\)
\(\chi_{4725}(1,\cdot)\) 4725.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4725}(2,\cdot)\) 4725.hc 180 yes \(1\) \(1\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{149}{180}\right)\)
\(\chi_{4725}(4,\cdot)\) 4725.gg 90 yes \(1\) \(1\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{59}{90}\right)\)
\(\chi_{4725}(8,\cdot)\) 4725.fs 60 no \(1\) \(1\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{60}\right)\)
\(\chi_{4725}(11,\cdot)\) 4725.go 90 yes \(-1\) \(1\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{7}{90}\right)\)
\(\chi_{4725}(13,\cdot)\) 4725.he 180 yes \(1\) \(1\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{61}{180}\right)\)
\(\chi_{4725}(16,\cdot)\) 4725.fl 45 yes \(1\) \(1\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{14}{45}\right)\)
\(\chi_{4725}(17,\cdot)\) 4725.fy 60 no \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{4725}(19,\cdot)\) 4725.ea 30 no \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{4725}(22,\cdot)\) 4725.hd 180 no \(-1\) \(1\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{67}{180}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{163}{180}\right)\)
\(\chi_{4725}(23,\cdot)\) 4725.hj 180 yes \(1\) \(1\) \(e\left(\frac{149}{180}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{7}{90}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{79}{180}\right)\)
\(\chi_{4725}(26,\cdot)\) 4725.bk 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4725}(29,\cdot)\) 4725.gu 90 no \(-1\) \(1\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{32}{45}\right)\)
\(\chi_{4725}(31,\cdot)\) 4725.gs 90 yes \(-1\) \(1\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{43}{45}\right)\)
\(\chi_{4725}(32,\cdot)\) 4725.fg 36 no \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{4725}(34,\cdot)\) 4725.gj 90 yes \(-1\) \(1\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{41}{45}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{31}{90}\right)\) \(e\left(\frac{43}{90}\right)\)
\(\chi_{4725}(37,\cdot)\) 4725.gb 60 no \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{60}\right)\)
\(\chi_{4725}(38,\cdot)\) 4725.gy 180 yes \(-1\) \(1\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{59}{180}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{47}{180}\right)\) \(e\left(\frac{131}{180}\right)\)
\(\chi_{4725}(41,\cdot)\) 4725.gm 90 yes \(1\) \(1\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{53}{90}\right)\)
\(\chi_{4725}(43,\cdot)\) 4725.fh 36 no \(-1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{4725}(44,\cdot)\) 4725.dw 30 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{4725}(46,\cdot)\) 4725.ct 15 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{4725}(47,\cdot)\) 4725.hf 180 yes \(-1\) \(1\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{89}{90}\right)\) \(e\left(\frac{137}{180}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{53}{180}\right)\)
\(\chi_{4725}(52,\cdot)\) 4725.gz 180 yes \(1\) \(1\) \(e\left(\frac{169}{180}\right)\) \(e\left(\frac{79}{90}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{179}{180}\right)\)
\(\chi_{4725}(53,\cdot)\) 4725.fq 60 no \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{41}{60}\right)\)
\(\chi_{4725}(58,\cdot)\) 4725.hi 180 yes \(-1\) \(1\) \(e\left(\frac{167}{180}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{97}{180}\right)\)
\(\chi_{4725}(59,\cdot)\) 4725.gr 90 yes \(1\) \(1\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{4}{45}\right)\)
\(\chi_{4725}(61,\cdot)\) 4725.gs 90 yes \(-1\) \(1\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{11}{45}\right)\)
\(\chi_{4725}(62,\cdot)\) 4725.fp 60 no \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{47}{60}\right)\)
\(\chi_{4725}(64,\cdot)\) 4725.eg 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{4725}(67,\cdot)\) 4725.hb 180 yes \(-1\) \(1\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{67}{180}\right)\)
\(\chi_{4725}(68,\cdot)\) 4725.fi 36 no \(-1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(-i\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{36}\right)\)
Click here to search among the remaining 2128 characters.