Properties

Modulus $869$
Structure \(C_{390}\times C_{2}\)
Order $780$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(869)
 
pari: g = idealstar(,869,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 780
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{390}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{869}(475,\cdot)$, $\chi_{869}(793,\cdot)$

First 32 of 780 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{869}(1,\cdot)\) 869.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{869}(2,\cdot)\) 869.be 390 yes \(-1\) \(1\) \(e\left(\frac{119}{390}\right)\) \(e\left(\frac{166}{195}\right)\) \(e\left(\frac{119}{195}\right)\) \(e\left(\frac{113}{195}\right)\) \(e\left(\frac{61}{390}\right)\) \(e\left(\frac{163}{390}\right)\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{137}{195}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{869}(3,\cdot)\) 869.bd 390 yes \(-1\) \(1\) \(e\left(\frac{166}{195}\right)\) \(e\left(\frac{161}{390}\right)\) \(e\left(\frac{137}{195}\right)\) \(e\left(\frac{194}{195}\right)\) \(e\left(\frac{103}{390}\right)\) \(e\left(\frac{109}{390}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{161}{195}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{869}(4,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{119}{195}\right)\) \(e\left(\frac{137}{195}\right)\) \(e\left(\frac{43}{195}\right)\) \(e\left(\frac{31}{195}\right)\) \(e\left(\frac{61}{195}\right)\) \(e\left(\frac{163}{195}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{79}{195}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{869}(5,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{113}{195}\right)\) \(e\left(\frac{194}{195}\right)\) \(e\left(\frac{31}{195}\right)\) \(e\left(\frac{172}{195}\right)\) \(e\left(\frac{112}{195}\right)\) \(e\left(\frac{181}{195}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{193}{195}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{869}(6,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{61}{390}\right)\) \(e\left(\frac{103}{390}\right)\) \(e\left(\frac{61}{195}\right)\) \(e\left(\frac{112}{195}\right)\) \(e\left(\frac{82}{195}\right)\) \(e\left(\frac{136}{195}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{103}{195}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{869}(7,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{163}{390}\right)\) \(e\left(\frac{109}{390}\right)\) \(e\left(\frac{163}{195}\right)\) \(e\left(\frac{181}{195}\right)\) \(e\left(\frac{136}{195}\right)\) \(e\left(\frac{178}{195}\right)\) \(e\left(\frac{33}{130}\right)\) \(e\left(\frac{109}{195}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{869}(8,\cdot)\) 869.ba 130 yes \(-1\) \(1\) \(e\left(\frac{119}{130}\right)\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{54}{65}\right)\) \(e\left(\frac{48}{65}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{33}{130}\right)\) \(e\left(\frac{97}{130}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{869}(9,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{137}{195}\right)\) \(e\left(\frac{161}{195}\right)\) \(e\left(\frac{79}{195}\right)\) \(e\left(\frac{193}{195}\right)\) \(e\left(\frac{103}{195}\right)\) \(e\left(\frac{109}{195}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{127}{195}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{869}(10,\cdot)\) 869.p 26 yes \(-1\) \(1\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{869}(12,\cdot)\) 869.o 26 no \(-1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{869}(13,\cdot)\) 869.be 390 yes \(-1\) \(1\) \(e\left(\frac{329}{390}\right)\) \(e\left(\frac{46}{195}\right)\) \(e\left(\frac{134}{195}\right)\) \(e\left(\frac{83}{195}\right)\) \(e\left(\frac{31}{390}\right)\) \(e\left(\frac{313}{390}\right)\) \(e\left(\frac{69}{130}\right)\) \(e\left(\frac{92}{195}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{869}(14,\cdot)\) 869.bb 130 yes \(-1\) \(1\) \(e\left(\frac{47}{65}\right)\) \(e\left(\frac{17}{130}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{33}{65}\right)\) \(e\left(\frac{111}{130}\right)\) \(e\left(\frac{43}{130}\right)\) \(e\left(\frac{11}{65}\right)\) \(e\left(\frac{17}{65}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{869}(15,\cdot)\) 869.bb 130 yes \(-1\) \(1\) \(e\left(\frac{28}{65}\right)\) \(e\left(\frac{53}{130}\right)\) \(e\left(\frac{56}{65}\right)\) \(e\left(\frac{57}{65}\right)\) \(e\left(\frac{109}{130}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{53}{65}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{869}(16,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{43}{195}\right)\) \(e\left(\frac{79}{195}\right)\) \(e\left(\frac{86}{195}\right)\) \(e\left(\frac{62}{195}\right)\) \(e\left(\frac{122}{195}\right)\) \(e\left(\frac{131}{195}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{158}{195}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{869}(17,\cdot)\) 869.z 130 yes \(1\) \(1\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{61}{130}\right)\) \(e\left(\frac{62}{65}\right)\) \(e\left(\frac{19}{65}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{121}{130}\right)\) \(e\left(\frac{61}{65}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{11}{26}\right)\)
\(\chi_{869}(18,\cdot)\) 869.ba 130 yes \(-1\) \(1\) \(e\left(\frac{1}{130}\right)\) \(e\left(\frac{44}{65}\right)\) \(e\left(\frac{1}{65}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{89}{130}\right)\) \(e\left(\frac{127}{130}\right)\) \(e\left(\frac{3}{130}\right)\) \(e\left(\frac{23}{65}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{869}(19,\cdot)\) 869.be 390 yes \(-1\) \(1\) \(e\left(\frac{367}{390}\right)\) \(e\left(\frac{158}{195}\right)\) \(e\left(\frac{172}{195}\right)\) \(e\left(\frac{124}{195}\right)\) \(e\left(\frac{293}{390}\right)\) \(e\left(\frac{329}{390}\right)\) \(e\left(\frac{107}{130}\right)\) \(e\left(\frac{121}{195}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{869}(20,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{37}{195}\right)\) \(e\left(\frac{136}{195}\right)\) \(e\left(\frac{74}{195}\right)\) \(e\left(\frac{8}{195}\right)\) \(e\left(\frac{173}{195}\right)\) \(e\left(\frac{149}{195}\right)\) \(e\left(\frac{37}{65}\right)\) \(e\left(\frac{77}{195}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{869}(21,\cdot)\) 869.p 26 yes \(-1\) \(1\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{869}(23,\cdot)\) 869.e 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)
\(\chi_{869}(24,\cdot)\) 869.r 30 yes \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(-1\) \(-1\)
\(\chi_{869}(25,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{31}{195}\right)\) \(e\left(\frac{193}{195}\right)\) \(e\left(\frac{62}{195}\right)\) \(e\left(\frac{149}{195}\right)\) \(e\left(\frac{29}{195}\right)\) \(e\left(\frac{167}{195}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{191}{195}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{869}(26,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{29}{195}\right)\) \(e\left(\frac{17}{195}\right)\) \(e\left(\frac{58}{195}\right)\) \(e\left(\frac{1}{195}\right)\) \(e\left(\frac{46}{195}\right)\) \(e\left(\frac{43}{195}\right)\) \(e\left(\frac{29}{65}\right)\) \(e\left(\frac{34}{195}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\)
\(\chi_{869}(27,\cdot)\) 869.bb 130 yes \(-1\) \(1\) \(e\left(\frac{36}{65}\right)\) \(e\left(\frac{31}{130}\right)\) \(e\left(\frac{7}{65}\right)\) \(e\left(\frac{64}{65}\right)\) \(e\left(\frac{103}{130}\right)\) \(e\left(\frac{109}{130}\right)\) \(e\left(\frac{43}{65}\right)\) \(e\left(\frac{31}{65}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\)
\(\chi_{869}(28,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{11}{390}\right)\) \(e\left(\frac{383}{390}\right)\) \(e\left(\frac{11}{195}\right)\) \(e\left(\frac{17}{195}\right)\) \(e\left(\frac{2}{195}\right)\) \(e\left(\frac{146}{195}\right)\) \(e\left(\frac{11}{130}\right)\) \(e\left(\frac{188}{195}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{869}(29,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{103}{390}\right)\) \(e\left(\frac{289}{390}\right)\) \(e\left(\frac{103}{195}\right)\) \(e\left(\frac{106}{195}\right)\) \(e\left(\frac{1}{195}\right)\) \(e\left(\frac{73}{195}\right)\) \(e\left(\frac{103}{130}\right)\) \(e\left(\frac{94}{195}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{869}(30,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{287}{390}\right)\) \(e\left(\frac{101}{390}\right)\) \(e\left(\frac{92}{195}\right)\) \(e\left(\frac{89}{195}\right)\) \(e\left(\frac{194}{195}\right)\) \(e\left(\frac{122}{195}\right)\) \(e\left(\frac{27}{130}\right)\) \(e\left(\frac{101}{195}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{869}(31,\cdot)\) 869.bc 195 yes \(1\) \(1\) \(e\left(\frac{92}{195}\right)\) \(e\left(\frac{101}{195}\right)\) \(e\left(\frac{184}{195}\right)\) \(e\left(\frac{178}{195}\right)\) \(e\left(\frac{193}{195}\right)\) \(e\left(\frac{49}{195}\right)\) \(e\left(\frac{27}{65}\right)\) \(e\left(\frac{7}{195}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{869}(32,\cdot)\) 869.x 78 yes \(-1\) \(1\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{869}(34,\cdot)\) 869.y 78 no \(-1\) \(1\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\)
\(\chi_{869}(35,\cdot)\) 869.bf 390 yes \(1\) \(1\) \(e\left(\frac{389}{390}\right)\) \(e\left(\frac{107}{390}\right)\) \(e\left(\frac{194}{195}\right)\) \(e\left(\frac{158}{195}\right)\) \(e\left(\frac{53}{195}\right)\) \(e\left(\frac{164}{195}\right)\) \(e\left(\frac{129}{130}\right)\) \(e\left(\frac{107}{195}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{26}\right)\)