Properties

Modulus 43
Structure \(C_{42}\)
Order 42

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(43)
 
pari: g = idealstar(,43,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 42
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{42}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{43}(3,\cdot)$

First 32 of 42 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 5 6 7 8 9 10 11
\(\chi_{43}(1,\cdot)\) 43.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{43}(2,\cdot)\) 43.f 14 yes \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{43}(3,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{43}(4,\cdot)\) 43.e 7 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{43}(5,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{43}(6,\cdot)\) 43.c 3 yes \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{43}(7,\cdot)\) 43.d 6 yes \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{43}(8,\cdot)\) 43.f 14 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{43}(9,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{43}(10,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{43}(11,\cdot)\) 43.e 7 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{43}(12,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{43}(13,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{43}(14,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{43}(15,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{43}(16,\cdot)\) 43.e 7 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{43}(17,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{43}(18,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{43}(19,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{43}(20,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{43}(21,\cdot)\) 43.e 7 yes \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{43}(22,\cdot)\) 43.f 14 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{43}(23,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{43}(24,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{43}(25,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{43}(26,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{43}(27,\cdot)\) 43.f 14 yes \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(-1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{43}(28,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{43}(29,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{43}(30,\cdot)\) 43.h 42 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{43}(31,\cdot)\) 43.g 21 yes \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{43}(32,\cdot)\) 43.f 14 yes \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\)