Properties

Modulus $1400$
Structure \(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
Order $480$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1400)
 
pari: g = idealstar(,1400,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1400}(351,\cdot)$, $\chi_{1400}(701,\cdot)$, $\chi_{1400}(1177,\cdot)$, $\chi_{1400}(801,\cdot)$

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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{1400}(1,\cdot)\) 1400.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1400}(3,\cdot)\) 1400.dq 60 yes \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{1400}(9,\cdot)\) 1400.dc 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1400}(11,\cdot)\) 1400.dj 30 yes \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(13,\cdot)\) 1400.ct 20 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1400}(17,\cdot)\) 1400.dr 60 no \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1400}(19,\cdot)\) 1400.di 30 yes \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{1400}(23,\cdot)\) 1400.dn 60 no \(1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(27,\cdot)\) 1400.cn 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1400}(29,\cdot)\) 1400.bt 10 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1400}(31,\cdot)\) 1400.dg 30 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1400}(33,\cdot)\) 1400.dr 60 no \(1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{1400}(37,\cdot)\) 1400.dm 60 yes \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{1400}(39,\cdot)\) 1400.df 30 no \(-1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(41,\cdot)\) 1400.bz 10 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1400}(43,\cdot)\) 1400.w 4 no \(1\) \(1\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\) \(-1\)
\(\chi_{1400}(47,\cdot)\) 1400.dl 60 no \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{1400}(51,\cdot)\) 1400.ba 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1400}(53,\cdot)\) 1400.dm 60 yes \(-1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{1400}(57,\cdot)\) 1400.v 4 no \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(i\) \(-1\) \(1\)
\(\chi_{1400}(59,\cdot)\) 1400.di 30 yes \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1400}(61,\cdot)\) 1400.de 30 yes \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(67,\cdot)\) 1400.do 60 yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{1400}(69,\cdot)\) 1400.cc 10 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1400}(71,\cdot)\) 1400.cb 10 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1400}(73,\cdot)\) 1400.dr 60 no \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{1400}(79,\cdot)\) 1400.df 30 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{1400}(81,\cdot)\) 1400.cm 15 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{1400}(83,\cdot)\) 1400.cn 20 yes \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1400}(87,\cdot)\) 1400.dl 60 no \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{1400}(89,\cdot)\) 1400.dh 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{1400}(93,\cdot)\) 1400.cj 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{3}\right)\)