Properties

Modulus $750$
Structure \(C_{100}\times C_{2}\)
Order $200$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(750)
 
pari: g = idealstar(,750,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 200
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{100}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{750}(251,\cdot)$, $\chi_{750}(127,\cdot)$

First 32 of 200 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{750}(1,\cdot)\) 750.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{750}(7,\cdot)\) 750.k 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{750}(11,\cdot)\) 750.n 50 no \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{750}(13,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{4}{25}\right)\)
\(\chi_{750}(17,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{31}{50}\right)\)
\(\chi_{750}(19,\cdot)\) 750.o 50 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{750}(23,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{750}(29,\cdot)\) 750.p 50 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{750}(31,\cdot)\) 750.m 25 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{750}(37,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{750}(41,\cdot)\) 750.n 50 no \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{43}{50}\right)\)
\(\chi_{750}(43,\cdot)\) 750.k 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{750}(47,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{750}(49,\cdot)\) 750.h 10 no \(1\) \(1\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{750}(53,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{750}(59,\cdot)\) 750.p 50 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{750}(61,\cdot)\) 750.m 25 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{16}{25}\right)\)
\(\chi_{750}(67,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{18}{25}\right)\)
\(\chi_{750}(71,\cdot)\) 750.n 50 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{750}(73,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{1}{25}\right)\)
\(\chi_{750}(77,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{17}{50}\right)\)
\(\chi_{750}(79,\cdot)\) 750.o 50 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{2}{25}\right)\)
\(\chi_{750}(83,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{750}(89,\cdot)\) 750.p 50 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{750}(91,\cdot)\) 750.m 25 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{14}{25}\right)\)
\(\chi_{750}(97,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{7}{25}\right)\)
\(\chi_{750}(101,\cdot)\) 750.j 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{750}(103,\cdot)\) 750.q 100 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{22}{25}\right)\)
\(\chi_{750}(107,\cdot)\) 750.l 20 no \(1\) \(1\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{750}(109,\cdot)\) 750.o 50 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{19}{25}\right)\)
\(\chi_{750}(113,\cdot)\) 750.r 100 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{750}(119,\cdot)\) 750.p 50 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{1}{50}\right)\)