Properties

Modulus $1148$
Structure \(C_{120}\times C_{2}\times C_{2}\)
Order $480$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1148)
 
pari: g = idealstar(,1148,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{120}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1148}(575,\cdot)$, $\chi_{1148}(493,\cdot)$, $\chi_{1148}(785,\cdot)$

First 32 of 480 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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1148}(1,\cdot)\) 1148.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1148}(3,\cdot)\) 1148.bq 24 yes \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1148}(5,\cdot)\) 1148.ch 60 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1148}(9,\cdot)\) 1148.bi 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1148}(11,\cdot)\) 1148.cl 120 yes \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(13,\cdot)\) 1148.cc 40 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(15,\cdot)\) 1148.ca 40 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1148}(17,\cdot)\) 1148.cj 120 no \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{1148}(19,\cdot)\) 1148.ck 120 yes \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1148}(23,\cdot)\) 1148.bv 30 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1148}(25,\cdot)\) 1148.bz 30 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1148}(27,\cdot)\) 1148.x 8 yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\)
\(\chi_{1148}(29,\cdot)\) 1148.cd 40 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1148}(31,\cdot)\) 1148.bw 30 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{1148}(33,\cdot)\) 1148.ch 60 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1148}(37,\cdot)\) 1148.bk 15 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1148}(39,\cdot)\) 1148.ce 60 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1148}(43,\cdot)\) 1148.bo 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1148}(45,\cdot)\) 1148.bt 30 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1148}(47,\cdot)\) 1148.ck 120 yes \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{109}{120}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1148}(51,\cdot)\) 1148.by 30 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1148}(53,\cdot)\) 1148.ci 120 no \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1148}(55,\cdot)\) 1148.x 8 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(-1\)
\(\chi_{1148}(57,\cdot)\) 1148.n 5 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1148}(59,\cdot)\) 1148.bu 30 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1148}(61,\cdot)\) 1148.ch 60 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{1148}(65,\cdot)\) 1148.ci 120 no \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{71}{120}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1148}(67,\cdot)\) 1148.cl 120 yes \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1148}(69,\cdot)\) 1148.cc 40 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1148}(71,\cdot)\) 1148.ca 40 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1148}(73,\cdot)\) 1148.bg 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1148}(75,\cdot)\) 1148.ck 120 yes \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{61}{120}\right)\) \(e\left(\frac{113}{120}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{30}\right)\)