Properties

Modulus $5185$
Structure \(C_{240}\times C_{4}\times C_{4}\)
Order $3840$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(5185)
 
pari: g = idealstar(,5185,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 3840
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{240}\times C_{4}\times C_{4}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{5185}(3112,\cdot)$, $\chi_{5185}(4576,\cdot)$, $\chi_{5185}(2381,\cdot)$

First 32 of 3840 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{5185}(1,\cdot)\) 5185.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5185}(2,\cdot)\) 5185.jm 120 yes \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5185}(3,\cdot)\) 5185.is 80 yes \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{29}{80}\right)\) \(-1\)
\(\chi_{5185}(4,\cdot)\) 5185.hr 60 yes \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(6,\cdot)\) 5185.kc 240 no \(1\) \(1\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{211}{240}\right)\) \(e\left(\frac{7}{240}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{240}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{5185}(7,\cdot)\) 5185.ki 240 yes \(-1\) \(1\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{240}\right)\) \(e\left(\frac{199}{240}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{173}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5185}(8,\cdot)\) 5185.gr 40 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{40}\right)\) \(-i\)
\(\chi_{5185}(9,\cdot)\) 5185.gt 40 yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{29}{40}\right)\) \(1\)
\(\chi_{5185}(11,\cdot)\) 5185.ec 16 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\)
\(\chi_{5185}(12,\cdot)\) 5185.jy 240 yes \(1\) \(1\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{29}{240}\right)\) \(e\left(\frac{173}{240}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{211}{240}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{5185}(13,\cdot)\) 5185.cz 12 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5185}(14,\cdot)\) 5185.hc 48 yes \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{5185}(16,\cdot)\) 5185.gg 30 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5185}(18,\cdot)\) 5185.hp 60 no \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{5185}(19,\cdot)\) 5185.jl 120 yes \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{43}{120}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{5185}(21,\cdot)\) 5185.dd 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5185}(22,\cdot)\) 5185.jy 240 yes \(1\) \(1\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{133}{240}\right)\) \(e\left(\frac{181}{240}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{107}{240}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{5185}(23,\cdot)\) 5185.jc 80 yes \(-1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{43}{80}\right)\) \(1\)
\(\chi_{5185}(24,\cdot)\) 5185.iw 80 yes \(1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{51}{80}\right)\) \(i\)
\(\chi_{5185}(26,\cdot)\) 5185.jj 120 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(27,\cdot)\) 5185.is 80 yes \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{80}\right)\) \(-1\)
\(\chi_{5185}(28,\cdot)\) 5185.jf 80 yes \(-1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{19}{80}\right)\) \(1\)
\(\chi_{5185}(29,\cdot)\) 5185.hh 48 yes \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{5185}(31,\cdot)\) 5185.kf 240 no \(1\) \(1\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{77}{240}\right)\) \(e\left(\frac{89}{240}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{43}{240}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{5185}(32,\cdot)\) 5185.fu 24 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{5185}(33,\cdot)\) 5185.fg 20 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(i\)
\(\chi_{5185}(36,\cdot)\) 5185.jq 120 no \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{120}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5185}(37,\cdot)\) 5185.jc 80 yes \(-1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{80}\right)\) \(1\)
\(\chi_{5185}(38,\cdot)\) 5185.fk 20 yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{1}{10}\right)\) \(i\)
\(\chi_{5185}(39,\cdot)\) 5185.kh 240 yes \(-1\) \(1\) \(e\left(\frac{77}{120}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{13}{240}\right)\) \(e\left(\frac{121}{240}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{167}{240}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{5185}(41,\cdot)\) 5185.ja 80 no \(-1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{80}\right)\) \(-i\)
\(\chi_{5185}(42,\cdot)\) 5185.ju 120 yes \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{103}{120}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{7}{12}\right)\)