Properties

Modulus $102$
Structure \(C_{2}\times C_{16}\)
Order $32$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(102)
 
pari: g = idealstar(,102,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 32
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{16}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{102}(35,\cdot)$, $\chi_{102}(37,\cdot)$

First 32 of 32 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{102}(1,\cdot)\) 102.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{102}(5,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{102}(7,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\)
\(\chi_{102}(11,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{102}(13,\cdot)\) 102.f 4 no \(1\) \(1\) \(i\) \(-i\) \(-i\) \(1\) \(-1\) \(-i\) \(-1\) \(i\) \(i\) \(1\)
\(\chi_{102}(19,\cdot)\) 102.h 8 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{102}(23,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{102}(25,\cdot)\) 102.h 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\)
\(\chi_{102}(29,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{102}(31,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(1\)
\(\chi_{102}(35,\cdot)\) 102.c 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{102}(37,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\)
\(\chi_{102}(41,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{102}(43,\cdot)\) 102.h 8 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{102}(47,\cdot)\) 102.e 4 no \(-1\) \(1\) \(-i\) \(-i\) \(i\) \(1\) \(-1\) \(i\) \(-1\) \(-i\) \(i\) \(-1\)
\(\chi_{102}(49,\cdot)\) 102.h 8 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{102}(53,\cdot)\) 102.g 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\)
\(\chi_{102}(55,\cdot)\) 102.f 4 no \(1\) \(1\) \(-i\) \(i\) \(i\) \(1\) \(-1\) \(i\) \(-1\) \(-i\) \(-i\) \(1\)
\(\chi_{102}(59,\cdot)\) 102.g 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\)
\(\chi_{102}(61,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(1\)
\(\chi_{102}(65,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{102}(67,\cdot)\) 102.b 2 no \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{102}(71,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{102}(73,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\)
\(\chi_{102}(77,\cdot)\) 102.g 8 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\)
\(\chi_{102}(79,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\)
\(\chi_{102}(83,\cdot)\) 102.g 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\)
\(\chi_{102}(89,\cdot)\) 102.e 4 no \(-1\) \(1\) \(i\) \(i\) \(-i\) \(1\) \(-1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\)
\(\chi_{102}(91,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{102}(95,\cdot)\) 102.i 16 no \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{102}(97,\cdot)\) 102.j 16 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(1\)
\(\chi_{102}(101,\cdot)\) 102.d 2 no \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\)
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