Properties

Modulus $6025$
Structure \(C_{240}\times C_{20}\)
Order $4800$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(6025)
 
pari: g = idealstar(,6025,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4800
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{240}\times C_{20}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6025}(2652,\cdot)$, $\chi_{6025}(2176,\cdot)$

First 32 of 4800 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{6025}(1,\cdot)\) 6025.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6025}(2,\cdot)\) 6025.ip 120 yes \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{120}\right)\)
\(\chi_{6025}(3,\cdot)\) 6025.hz 120 yes \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{6025}(4,\cdot)\) 6025.gu 60 yes \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{6025}(6,\cdot)\) 6025.dn 20 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{6025}(7,\cdot)\) 6025.jp 240 no \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{61}{240}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{227}{240}\right)\)
\(\chi_{6025}(8,\cdot)\) 6025.er 40 yes \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{6025}(9,\cdot)\) 6025.gt 60 yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{6025}(11,\cdot)\) 6025.iu 240 yes \(-1\) \(1\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{97}{240}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{23}{240}\right)\)
\(\chi_{6025}(12,\cdot)\) 6025.hx 120 yes \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{73}{120}\right)\)
\(\chi_{6025}(13,\cdot)\) 6025.jb 240 yes \(1\) \(1\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{227}{240}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{240}\right)\) \(e\left(\frac{73}{120}\right)\) \(e\left(\frac{61}{240}\right)\)
\(\chi_{6025}(14,\cdot)\) 6025.jg 240 yes \(-1\) \(1\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{71}{240}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{167}{240}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{6025}(16,\cdot)\) 6025.ei 30 yes \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{6025}(17,\cdot)\) 6025.hn 80 yes \(1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{80}\right)\)
\(\chi_{6025}(18,\cdot)\) 6025.hw 120 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{120}\right)\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{89}{120}\right)\)
\(\chi_{6025}(19,\cdot)\) 6025.iv 240 yes \(-1\) \(1\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{61}{240}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{179}{240}\right)\)
\(\chi_{6025}(21,\cdot)\) 6025.hj 80 yes \(-1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{19}{80}\right)\)
\(\chi_{6025}(22,\cdot)\) 6025.jn 240 yes \(1\) \(1\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{239}{240}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{61}{240}\right)\)
\(\chi_{6025}(23,\cdot)\) 6025.hn 80 yes \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{49}{80}\right)\)
\(\chi_{6025}(24,\cdot)\) 6025.ek 30 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(-1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{6025}(26,\cdot)\) 6025.gz 80 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{40}\right)\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{33}{80}\right)\)
\(\chi_{6025}(27,\cdot)\) 6025.fh 40 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{6025}(28,\cdot)\) 6025.hr 80 yes \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{37}{40}\right)\) \(-i\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{21}{80}\right)\)
\(\chi_{6025}(29,\cdot)\) 6025.ic 120 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(-1\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{120}\right)\)
\(\chi_{6025}(31,\cdot)\) 6025.je 240 yes \(-1\) \(1\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{53}{60}\right)\) \(i\) \(e\left(\frac{151}{240}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{31}{240}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{41}{240}\right)\)
\(\chi_{6025}(32,\cdot)\) 6025.dq 24 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{24}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{6025}(33,\cdot)\) 6025.hs 80 yes \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{31}{80}\right)\)
\(\chi_{6025}(34,\cdot)\) 6025.jk 240 yes \(-1\) \(1\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{181}{240}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{133}{240}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{59}{240}\right)\)
\(\chi_{6025}(36,\cdot)\) 6025.bb 10 yes \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{6025}(37,\cdot)\) 6025.ix 240 yes \(1\) \(1\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{29}{60}\right)\) \(-i\) \(e\left(\frac{133}{240}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{193}{240}\right)\) \(e\left(\frac{119}{120}\right)\) \(e\left(\frac{203}{240}\right)\)
\(\chi_{6025}(38,\cdot)\) 6025.jm 240 yes \(1\) \(1\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{203}{240}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{217}{240}\right)\)
\(\chi_{6025}(39,\cdot)\) 6025.jk 240 yes \(-1\) \(1\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{109}{240}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{157}{240}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{131}{240}\right)\)