Properties

Modulus $764$
Structure \(C_{190}\times C_{2}\)
Order $380$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(764)
 
pari: g = idealstar(,764,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 380
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{190}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{764}(383,\cdot)$, $\chi_{764}(401,\cdot)$

First 32 of 380 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{764}(1,\cdot)\) 764.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{764}(3,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{61}{190}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{161}{190}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{21}{190}\right)\) \(e\left(\frac{21}{95}\right)\)
\(\chi_{764}(5,\cdot)\) 764.i 19 no \(1\) \(1\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{10}{19}\right)\)
\(\chi_{764}(7,\cdot)\) 764.g 10 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{764}(9,\cdot)\) 764.m 95 no \(1\) \(1\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{42}{95}\right)\)
\(\chi_{764}(11,\cdot)\) 764.l 38 yes \(1\) \(1\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{7}{19}\right)\) \(1\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{15}{38}\right)\)
\(\chi_{764}(13,\cdot)\) 764.m 95 no \(1\) \(1\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{72}{95}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{17}{95}\right)\)
\(\chi_{764}(15,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{161}{190}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{66}{95}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{101}{190}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{71}{95}\right)\)
\(\chi_{764}(17,\cdot)\) 764.m 95 no \(1\) \(1\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{52}{95}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{3}{95}\right)\)
\(\chi_{764}(19,\cdot)\) 764.n 190 yes \(1\) \(1\) \(e\left(\frac{21}{190}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{56}{95}\right)\) \(e\left(\frac{71}{190}\right)\) \(e\left(\frac{49}{95}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{97}{190}\right)\)
\(\chi_{764}(21,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{17}{95}\right)\) \(e\left(\frac{71}{95}\right)\) \(e\left(\frac{3}{95}\right)\) \(e\left(\frac{97}{190}\right)\) \(e\left(\frac{99}{190}\right)\)
\(\chi_{764}(23,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{59}{190}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{109}{190}\right)\) \(e\left(\frac{11}{95}\right)\) \(e\left(\frac{39}{190}\right)\) \(e\left(\frac{39}{95}\right)\)
\(\chi_{764}(25,\cdot)\) 764.i 19 no \(1\) \(1\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(1\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{764}(27,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{183}{190}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{88}{95}\right)\) \(e\left(\frac{7}{38}\right)\) \(e\left(\frac{13}{95}\right)\) \(e\left(\frac{103}{190}\right)\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{63}{190}\right)\) \(e\left(\frac{63}{95}\right)\)
\(\chi_{764}(29,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{28}{95}\right)\) \(e\left(\frac{29}{38}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{79}{95}\right)\) \(e\left(\frac{2}{95}\right)\) \(e\left(\frac{33}{190}\right)\) \(e\left(\frac{161}{190}\right)\)
\(\chi_{764}(31,\cdot)\) 764.l 38 yes \(1\) \(1\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{1}{19}\right)\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{13}{38}\right)\)
\(\chi_{764}(33,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{58}{95}\right)\) \(e\left(\frac{64}{95}\right)\) \(e\left(\frac{11}{190}\right)\) \(e\left(\frac{117}{190}\right)\)
\(\chi_{764}(35,\cdot)\) 764.n 190 yes \(1\) \(1\) \(e\left(\frac{81}{190}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{81}{95}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{26}{95}\right)\) \(e\left(\frac{111}{190}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{63}{95}\right)\) \(e\left(\frac{157}{190}\right)\)
\(\chi_{764}(37,\cdot)\) 764.j 38 no \(-1\) \(1\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{18}{19}\right)\) \(-1\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{27}{38}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{25}{38}\right)\)
\(\chi_{764}(39,\cdot)\) 764.h 10 yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{764}(41,\cdot)\) 764.j 38 no \(-1\) \(1\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(-1\) \(e\left(\frac{9}{19}\right)\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{33}{38}\right)\) \(e\left(\frac{9}{38}\right)\)
\(\chi_{764}(43,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{73}{190}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{68}{95}\right)\) \(e\left(\frac{93}{190}\right)\) \(e\left(\frac{12}{95}\right)\) \(e\left(\frac{103}{190}\right)\) \(e\left(\frac{8}{95}\right)\)
\(\chi_{764}(45,\cdot)\) 764.m 95 no \(1\) \(1\) \(e\left(\frac{16}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{32}{95}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{22}{95}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{43}{95}\right)\) \(e\left(\frac{46}{95}\right)\) \(e\left(\frac{92}{95}\right)\)
\(\chi_{764}(47,\cdot)\) 764.n 190 yes \(1\) \(1\) \(e\left(\frac{113}{190}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{18}{95}\right)\) \(e\left(\frac{10}{19}\right)\) \(e\left(\frac{48}{95}\right)\) \(e\left(\frac{183}{190}\right)\) \(e\left(\frac{42}{95}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{151}{190}\right)\)
\(\chi_{764}(49,\cdot)\) 764.e 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{764}(51,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{29}{190}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{14}{95}\right)\) \(e\left(\frac{89}{190}\right)\) \(e\left(\frac{36}{95}\right)\) \(e\left(\frac{119}{190}\right)\) \(e\left(\frac{24}{95}\right)\)
\(\chi_{764}(53,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{47}{95}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{94}{95}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{29}{95}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{61}{95}\right)\) \(e\left(\frac{9}{190}\right)\) \(e\left(\frac{113}{190}\right)\)
\(\chi_{764}(55,\cdot)\) 764.l 38 yes \(1\) \(1\) \(e\left(\frac{35}{38}\right)\) \(e\left(\frac{10}{19}\right)\) \(1\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{11}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{35}{38}\right)\)
\(\chi_{764}(57,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{13}{38}\right)\) \(e\left(\frac{92}{95}\right)\) \(e\left(\frac{21}{95}\right)\) \(e\left(\frac{33}{95}\right)\) \(e\left(\frac{117}{190}\right)\) \(e\left(\frac{139}{190}\right)\)
\(\chi_{764}(59,\cdot)\) 764.o 190 yes \(-1\) \(1\) \(e\left(\frac{179}{190}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{84}{95}\right)\) \(e\left(\frac{11}{38}\right)\) \(e\left(\frac{34}{95}\right)\) \(e\left(\frac{189}{190}\right)\) \(e\left(\frac{6}{95}\right)\) \(e\left(\frac{99}{190}\right)\) \(e\left(\frac{4}{95}\right)\)
\(\chi_{764}(61,\cdot)\) 764.p 190 no \(-1\) \(1\) \(e\left(\frac{73}{95}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{51}{95}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{41}{95}\right)\) \(e\left(\frac{93}{95}\right)\) \(e\left(\frac{24}{95}\right)\) \(e\left(\frac{111}{190}\right)\) \(e\left(\frac{127}{190}\right)\)
\(\chi_{764}(63,\cdot)\) 764.n 190 yes \(1\) \(1\) \(e\left(\frac{103}{190}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{8}{95}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{53}{95}\right)\) \(e\left(\frac{113}{190}\right)\) \(e\left(\frac{82}{95}\right)\) \(e\left(\frac{59}{95}\right)\) \(e\left(\frac{141}{190}\right)\)