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Properties

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

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Show commands: Pari/GP / SageMath

Copy content sage:H = DirichletGroup(17)
 
Copy content pari:g = idealstar(,17,2)
 

Character group

Copy content sage:G.order()
 
Copy content pari:g.no
 
Order = 16
Copy content sage:H.invariants()
 
Copy content pari:g.cyc
 
Structure = \(C_{16}\)
Copy content sage:H.gens()
 
Copy content 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.

Character Orbit 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 \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)