Properties

Modulus $309$
Structure \(C_{2}\times C_{102}\)
Order $204$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(309)
 
pari: g = idealstar(,309,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 204
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{102}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{309}(104,\cdot)$, $\chi_{309}(211,\cdot)$

First 32 of 204 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{309}(1,\cdot)\) 309.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{309}(2,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{47}{51}\right)\)
\(\chi_{309}(4,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{43}{51}\right)\)
\(\chi_{309}(5,\cdot)\) 309.o 102 yes \(1\) \(1\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{37}{51}\right)\)
\(\chi_{309}(7,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{46}{51}\right)\)
\(\chi_{309}(8,\cdot)\) 309.l 34 yes \(-1\) \(1\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{309}(10,\cdot)\) 309.j 34 no \(-1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{309}(11,\cdot)\) 309.o 102 yes \(1\) \(1\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{309}(13,\cdot)\) 309.i 17 no \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{309}(14,\cdot)\) 309.l 34 yes \(-1\) \(1\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{309}(16,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{35}{51}\right)\)
\(\chi_{309}(17,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{40}{51}\right)\)
\(\chi_{309}(19,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{51}\right)\)
\(\chi_{309}(20,\cdot)\) 309.o 102 yes \(1\) \(1\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{29}{51}\right)\)
\(\chi_{309}(22,\cdot)\) 309.j 34 no \(-1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{309}(23,\cdot)\) 309.l 34 yes \(-1\) \(1\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{309}(25,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{23}{51}\right)\)
\(\chi_{309}(26,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{309}(28,\cdot)\) 309.m 51 no \(1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{38}{51}\right)\)
\(\chi_{309}(29,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{20}{51}\right)\)
\(\chi_{309}(31,\cdot)\) 309.j 34 no \(-1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{309}(32,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{31}{51}\right)\)
\(\chi_{309}(34,\cdot)\) 309.i 17 no \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{309}(35,\cdot)\) 309.o 102 yes \(1\) \(1\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{309}(37,\cdot)\) 309.j 34 no \(-1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{309}(38,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{49}{51}\right)\)
\(\chi_{309}(40,\cdot)\) 309.p 102 no \(-1\) \(1\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{25}{51}\right)\)
\(\chi_{309}(41,\cdot)\) 309.n 102 yes \(-1\) \(1\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{14}{51}\right)\)
\(\chi_{309}(43,\cdot)\) 309.p 102 no \(-1\) \(1\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{44}{51}\right)\)
\(\chi_{309}(44,\cdot)\) 309.o 102 yes \(1\) \(1\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{309}(46,\cdot)\) 309.e 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{309}(47,\cdot)\) 309.g 6 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)
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