Properties

Modulus 73
Structure \(C_{72}\)
Order 72

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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(73)
 
pari: g = idealstar(,73,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 72
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{72}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{73}(5,\cdot)$

First 32 of 72 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
\(\chi_{73}(1,\cdot)\) 73.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{73}(2,\cdot)\) 73.g 9 Yes \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{73}(3,\cdot)\) 73.h 12 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(1\) \(1\) \(-i\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{73}(4,\cdot)\) 73.g 9 Yes \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{73}(5,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{72}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{55}{72}\right)\)
\(\chi_{73}(6,\cdot)\) 73.k 36 Yes \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{73}(7,\cdot)\) 73.j 24 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{73}(8,\cdot)\) 73.c 3 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{73}(9,\cdot)\) 73.e 6 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{73}(10,\cdot)\) 73.f 8 Yes \(-1\) \(1\) \(1\) \(-i\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{73}(11,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{72}\right)\)
\(\chi_{73}(12,\cdot)\) 73.k 36 Yes \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{73}(13,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{72}\right)\)
\(\chi_{73}(14,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{72}\right)\)
\(\chi_{73}(15,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{25}{72}\right)\)
\(\chi_{73}(16,\cdot)\) 73.g 9 Yes \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{73}(17,\cdot)\) 73.j 24 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{73}(18,\cdot)\) 73.i 18 Yes \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{73}(19,\cdot)\) 73.k 36 Yes \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{73}(20,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{71}{72}\right)\)
\(\chi_{73}(21,\cdot)\) 73.j 24 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{73}(22,\cdot)\) 73.f 8 Yes \(-1\) \(1\) \(1\) \(i\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{73}(23,\cdot)\) 73.k 36 Yes \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{73}(24,\cdot)\) 73.h 12 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(1\) \(1\) \(-i\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{73}(25,\cdot)\) 73.k 36 Yes \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{73}(26,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{72}\right)\)
\(\chi_{73}(27,\cdot)\) 73.d 4 Yes \(1\) \(1\) \(1\) \(-1\) \(1\) \(i\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(-i\)
\(\chi_{73}(28,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{31}{72}\right)\)
\(\chi_{73}(29,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{53}{72}\right)\)
\(\chi_{73}(30,\cdot)\) 73.j 24 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{73}(31,\cdot)\) 73.l 72 Yes \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{72}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{29}{72}\right)\)
\(\chi_{73}(32,\cdot)\) 73.g 9 Yes \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{9}\right)\)