Properties

Modulus $1476$
Structure \(C_{2}\times C_{2}\times C_{120}\)
Order $480$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1476)
 
pari: g = idealstar(,1476,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{120}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1476}(739,\cdot)$, $\chi_{1476}(821,\cdot)$, $\chi_{1476}(1441,\cdot)$

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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{1476}(1,\cdot)\) 1476.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1476}(5,\cdot)\) 1476.cg 60 no \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(7,\cdot)\) 1476.cl 120 yes \(1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{23}{120}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(11,\cdot)\) 1476.cj 120 yes \(-1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{11}{120}\right)\) \(e\left(\frac{107}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1476}(13,\cdot)\) 1476.ci 120 no \(-1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{67}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1476}(17,\cdot)\) 1476.cb 40 no \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1476}(19,\cdot)\) 1476.ca 40 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1476}(23,\cdot)\) 1476.bv 30 yes \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1476}(25,\cdot)\) 1476.bx 30 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(29,\cdot)\) 1476.ck 120 no \(1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{59}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{91}{120}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{47}{120}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1476}(31,\cdot)\) 1476.bz 30 yes \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{1476}(35,\cdot)\) 1476.cc 40 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1476}(37,\cdot)\) 1476.n 5 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1476}(43,\cdot)\) 1476.ce 60 yes \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1476}(47,\cdot)\) 1476.cj 120 yes \(-1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1476}(49,\cdot)\) 1476.cf 60 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1476}(53,\cdot)\) 1476.cb 40 no \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1476}(55,\cdot)\) 1476.y 8 no \(1\) \(1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{1476}(59,\cdot)\) 1476.bu 30 yes \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1476}(61,\cdot)\) 1476.cf 60 no \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1476}(65,\cdot)\) 1476.ck 120 no \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{41}{120}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{1476}(67,\cdot)\) 1476.cl 120 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{49}{120}\right)\) \(e\left(\frac{13}{120}\right)\) \(e\left(\frac{101}{120}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{37}{120}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(71,\cdot)\) 1476.cc 40 no \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1476}(73,\cdot)\) 1476.k 4 no \(1\) \(1\) \(-1\) \(-i\) \(-i\) \(-i\) \(i\) \(i\) \(1\) \(1\) \(-i\) \(1\)
\(\chi_{1476}(77,\cdot)\) 1476.cg 60 no \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{1476}(79,\cdot)\) 1476.bp 24 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1476}(83,\cdot)\) 1476.t 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1476}(85,\cdot)\) 1476.bs 24 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1476}(89,\cdot)\) 1476.cb 40 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1476}(91,\cdot)\) 1476.j 4 no \(-1\) \(1\) \(-1\) \(-i\) \(-i\) \(i\) \(-i\) \(i\) \(-1\) \(1\) \(i\) \(-1\)
\(\chi_{1476}(95,\cdot)\) 1476.cj 120 yes \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{79}{120}\right)\) \(e\left(\frac{83}{120}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{31}{120}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1476}(97,\cdot)\) 1476.ci 120 no \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{1}{120}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{120}\right)\) \(e\left(\frac{7}{30}\right)\)
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