Properties

Modulus 17
Structure \(C_{16}\)
Order 16

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(17)
pari: g = idealstar(,17,2)

Character group

sage: G.order()
pari: g.no
Order = 16
sage: H.invariants()
pari: g.cyc
Structure = \(C_{16}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{17}(3,\cdot)$

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
\(\chi_{17}(1,\cdot)\) 17.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{17}(2,\cdot)\) 17.d 8 Yes \(1\) \(1\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{17}(3,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{17}(4,\cdot)\) 17.c 4 Yes \(1\) \(1\) \(-1\) \(-i\) \(1\) \(-i\) \(i\) \(i\) \(-1\) \(-1\) \(i\) \(i\)
\(\chi_{17}(5,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{17}(6,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{17}(7,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{17}(8,\cdot)\) 17.d 8 Yes \(1\) \(1\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{17}(9,\cdot)\) 17.d 8 Yes \(1\) \(1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{17}(10,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{17}(11,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{17}(12,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{17}(13,\cdot)\) 17.c 4 Yes \(1\) \(1\) \(-1\) \(i\) \(1\) \(i\) \(-i\) \(-i\) \(-1\) \(-1\) \(-i\) \(-i\)
\(\chi_{17}(14,\cdot)\) 17.e 16 Yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{17}(15,\cdot)\) 17.d 8 Yes \(1\) \(1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{17}(16,\cdot)\) 17.b 2 Yes \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)