Properties

Modulus 235
Structure \(C_{92}\times C_{2}\)
Order 184

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(235)
pari: g = idealstar(,235,2)

Character group

sage: G.order()
pari: g.no
Order = 184
sage: H.invariants()
pari: g.cyc
Structure = \(C_{92}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{235}(193,\cdot)$, $\chi_{235}(234,\cdot)$

First 32 of 184 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.

orbit label order primitive -1 1 2 3 4 6 7 8 9 11 12 13
\(\chi_{235}(1,\cdot)\) 235.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{235}(2,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{5}{92}\right)\)
\(\chi_{235}(3,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{3}{92}\right)\)
\(\chi_{235}(4,\cdot)\) 235.i 46 Yes \(1\) \(1\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{5}{46}\right)\)
\(\chi_{235}(6,\cdot)\) 235.g 23 No \(1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{235}(7,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{71}{92}\right)\) \(e\left(\frac{61}{92}\right)\) \(e\left(\frac{25}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{37}{92}\right)\)
\(\chi_{235}(8,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{15}{92}\right)\)
\(\chi_{235}(9,\cdot)\) 235.i 46 Yes \(1\) \(1\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{3}{46}\right)\)
\(\chi_{235}(11,\cdot)\) 235.h 46 No \(-1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{31}{46}\right)\)
\(\chi_{235}(12,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{45}{92}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{13}{92}\right)\)
\(\chi_{235}(13,\cdot)\) 235.l 92 Yes \(1\) \(1\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{15}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{13}{92}\right)\) \(e\left(\frac{81}{92}\right)\)
\(\chi_{235}(14,\cdot)\) 235.i 46 Yes \(1\) \(1\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{21}{46}\right)\)
\(\chi_{235}(16,\cdot)\) 235.g 23 No \(1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{235}(17,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{47}{92}\right)\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{53}{92}\right)\)
\(\chi_{235}(18,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{31}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{11}{92}\right)\)
\(\chi_{235}(19,\cdot)\) 235.j 46 Yes \(-1\) \(1\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{235}(21,\cdot)\) 235.g 23 No \(1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{235}(22,\cdot)\) 235.l 92 Yes \(1\) \(1\) \(e\left(\frac{3}{92}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{9}{92}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{67}{92}\right)\)
\(\chi_{235}(23,\cdot)\) 235.l 92 Yes \(1\) \(1\) \(e\left(\frac{65}{92}\right)\) \(e\left(\frac{39}{92}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{21}{92}\right)\) \(e\left(\frac{11}{92}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{41}{92}\right)\)
\(\chi_{235}(24,\cdot)\) 235.i 46 Yes \(1\) \(1\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{9}{46}\right)\)
\(\chi_{235}(26,\cdot)\) 235.h 46 No \(-1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{43}{46}\right)\)
\(\chi_{235}(27,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{67}{92}\right)\) \(e\left(\frac{77}{92}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{17}{92}\right)\) \(e\left(\frac{31}{46}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{27}{92}\right)\) \(e\left(\frac{9}{92}\right)\)
\(\chi_{235}(28,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{33}{92}\right)\) \(e\left(\frac{75}{92}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{7}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{47}{92}\right)\)
\(\chi_{235}(29,\cdot)\) 235.j 46 Yes \(-1\) \(1\) \(e\left(\frac{9}{46}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{39}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{15}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{235}(31,\cdot)\) 235.h 46 No \(-1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{21}{46}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{33}{46}\right)\)
\(\chi_{235}(32,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{81}{92}\right)\) \(e\left(\frac{43}{46}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{79}{92}\right)\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{35}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{75}{92}\right)\) \(e\left(\frac{25}{92}\right)\)
\(\chi_{235}(33,\cdot)\) 235.l 92 Yes \(1\) \(1\) \(e\left(\frac{29}{92}\right)\) \(e\left(\frac{91}{92}\right)\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{49}{92}\right)\) \(e\left(\frac{87}{92}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{5}{46}\right)\) \(e\left(\frac{57}{92}\right)\) \(e\left(\frac{65}{92}\right)\)
\(\chi_{235}(34,\cdot)\) 235.i 46 Yes \(1\) \(1\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{7}{46}\right)\) \(e\left(\frac{19}{46}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{29}{46}\right)\)
\(\chi_{235}(36,\cdot)\) 235.g 23 No \(1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{235}(37,\cdot)\) 235.k 92 Yes \(-1\) \(1\) \(e\left(\frac{63}{92}\right)\) \(e\left(\frac{1}{92}\right)\) \(e\left(\frac{17}{46}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{43}{92}\right)\) \(e\left(\frac{5}{92}\right)\) \(e\left(\frac{1}{46}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{35}{92}\right)\) \(e\left(\frac{73}{92}\right)\)
\(\chi_{235}(38,\cdot)\) 235.l 92 Yes \(1\) \(1\) \(e\left(\frac{37}{92}\right)\) \(e\left(\frac{59}{92}\right)\) \(e\left(\frac{37}{46}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{53}{92}\right)\) \(e\left(\frac{19}{92}\right)\) \(e\left(\frac{13}{46}\right)\) \(e\left(\frac{27}{46}\right)\) \(e\left(\frac{41}{92}\right)\) \(e\left(\frac{29}{92}\right)\)
\(\chi_{235}(39,\cdot)\) 235.j 46 Yes \(-1\) \(1\) \(e\left(\frac{29}{46}\right)\) \(e\left(\frac{45}{46}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{3}{46}\right)\) \(e\left(\frac{41}{46}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{33}{46}\right)\) \(e\left(\frac{11}{46}\right)\) \(e\left(\frac{21}{23}\right)\)