Properties

Modulus 34
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(34)
 
pari: g = idealstar(,34,2)
 

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 = $\chi_{34}(3,\cdot)$

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 3 5 7 9 11 13 15 19 21 23
\(\chi_{34}(1,\cdot)\) 34.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{34}(3,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{34}(5,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{34}(7,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{34}(9,\cdot)\) 34.d 8 No \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\) \(-i\) \(-1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{34}(11,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{34}(13,\cdot)\) 34.c 4 No \(1\) \(1\) \(i\) \(i\) \(-i\) \(-1\) \(-i\) \(1\) \(-1\) \(-1\) \(1\) \(-i\)
\(\chi_{34}(15,\cdot)\) 34.d 8 No \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(i\) \(-1\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{34}(19,\cdot)\) 34.d 8 No \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(i\) \(i\) \(-1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{34}(21,\cdot)\) 34.c 4 No \(1\) \(1\) \(-i\) \(-i\) \(i\) \(-1\) \(i\) \(1\) \(-1\) \(-1\) \(1\) \(i\)
\(\chi_{34}(23,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{34}(25,\cdot)\) 34.d 8 No \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(-i\) \(-1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{34}(27,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{34}(29,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{34}(31,\cdot)\) 34.e 16 No \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{34}(33,\cdot)\) 34.b 2 No \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\)