Properties

Modulus $1375$
Structure \(C_{100}\times C_{10}\)
Order $1000$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1375)
 
pari: g = idealstar(,1375,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1000
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{100}\times C_{10}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1375}(1002,\cdot)$, $\chi_{1375}(376,\cdot)$

First 32 of 1000 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1375}(1,\cdot)\) 1375.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1375}(2,\cdot)\) 1375.cm 100 yes \(1\) \(1\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{1375}(3,\cdot)\) 1375.ck 100 yes \(-1\) \(1\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{1375}(4,\cdot)\) 1375.cf 50 yes \(1\) \(1\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{8}{25}\right)\)
\(\chi_{1375}(6,\cdot)\) 1375.cc 50 yes \(-1\) \(1\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{1375}(7,\cdot)\) 1375.bn 20 no \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1375}(8,\cdot)\) 1375.cm 100 yes \(1\) \(1\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{1375}(9,\cdot)\) 1375.ci 50 yes \(1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{21}{25}\right)\)
\(\chi_{1375}(12,\cdot)\) 1375.cq 100 no \(-1\) \(1\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{37}{50}\right)\)
\(\chi_{1375}(13,\cdot)\) 1375.ct 100 yes \(1\) \(1\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{17}{50}\right)\)
\(\chi_{1375}(14,\cdot)\) 1375.cb 50 yes \(1\) \(1\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{1375}(16,\cdot)\) 1375.br 25 yes \(1\) \(1\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{1375}(17,\cdot)\) 1375.co 100 yes \(1\) \(1\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{1375}(18,\cdot)\) 1375.bg 20 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(-1\)
\(\chi_{1375}(19,\cdot)\) 1375.by 50 yes \(-1\) \(1\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{1375}(21,\cdot)\) 1375.ch 50 yes \(-1\) \(1\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{1375}(23,\cdot)\) 1375.cq 100 no \(-1\) \(1\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{1375}(24,\cdot)\) 1375.o 10 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1375}(26,\cdot)\) 1375.j 5 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{1375}(27,\cdot)\) 1375.ck 100 yes \(-1\) \(1\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{1375}(28,\cdot)\) 1375.cl 100 yes \(1\) \(1\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(i\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{1}{50}\right)\)
\(\chi_{1375}(29,\cdot)\) 1375.by 50 yes \(-1\) \(1\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{1375}(31,\cdot)\) 1375.bu 25 yes \(1\) \(1\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(1\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{1375}(32,\cdot)\) 1375.bo 20 no \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1375}(34,\cdot)\) 1375.ce 50 no \(1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{1375}(36,\cdot)\) 1375.bt 25 yes \(1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{1375}(37,\cdot)\) 1375.cs 100 yes \(-1\) \(1\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{1375}(38,\cdot)\) 1375.cr 100 yes \(-1\) \(1\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{1375}(39,\cdot)\) 1375.bx 50 yes \(-1\) \(1\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{1375}(41,\cdot)\) 1375.bw 50 yes \(-1\) \(1\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(-1\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{1375}(42,\cdot)\) 1375.cp 100 yes \(-1\) \(1\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(i\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{1375}(43,\cdot)\) 1375.bo 20 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\)