Properties

Modulus 3232
Structure C2×C8C_{2}\times C_{8}
Order 1616

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(32)
 
pari: g = idealstar(,32,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 16
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C8C_{2}\times C_{8}
sage: H.gens()
 
pari: g.gen
 
Generators = χ32(31,)\chi_{32}(31,\cdot), χ32(5,)\chi_{32}(5,\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 11 33 55 77 99 1111 1313 1515 1717 1919 2121
χ32(1,)\chi_{32}(1,\cdot) 32.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ32(3,)\chi_{32}(3,\cdot) 32.h 8 yes 1-1 11 e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) ii ii e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) 11 1-1 e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right)
χ32(5,)\chi_{32}(5,\cdot) 32.g 8 yes 11 11 e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) ii i-i e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) 1-1 1-1 e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right)
χ32(7,)\chi_{32}(7,\cdot) 32.f 4 no 1-1 11 ii ii 11 1-1 i-i i-i 1-1 11 ii ii
χ32(9,)\chi_{32}(9,\cdot) 32.e 4 no 11 11 ii i-i 1-1 1-1 i-i ii 11 11 ii i-i
χ32(11,)\chi_{32}(11,\cdot) 32.h 8 yes 1-1 11 e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right) i-i i-i e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right) 11 1-1 e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right)
χ32(13,)\chi_{32}(13,\cdot) 32.g 8 yes 11 11 e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right) i-i ii e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right) 1-1 1-1 e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right)
χ32(15,)\chi_{32}(15,\cdot) 32.d 2 no 1-1 11 11 1-1 1-1 11 11 1-1 1-1 11 11 1-1
χ32(17,)\chi_{32}(17,\cdot) 32.b 2 no 11 11 1-1 1-1 11 11 1-1 1-1 11 11 1-1 1-1
χ32(19,)\chi_{32}(19,\cdot) 32.h 8 yes 1-1 11 e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) ii ii e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) 11 1-1 e(58)e\left(\frac{5}{8}\right) e(38)e\left(\frac{3}{8}\right)
χ32(21,)\chi_{32}(21,\cdot) 32.g 8 yes 11 11 e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) ii i-i e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) 1-1 1-1 e(38)e\left(\frac{3}{8}\right) e(18)e\left(\frac{1}{8}\right)
χ32(23,)\chi_{32}(23,\cdot) 32.f 4 no 1-1 11 i-i i-i 11 1-1 ii ii 1-1 11 i-i i-i
χ32(25,)\chi_{32}(25,\cdot) 32.e 4 no 11 11 i-i ii 1-1 1-1 ii i-i 11 11 i-i ii
χ32(27,)\chi_{32}(27,\cdot) 32.h 8 yes 1-1 11 e(78)e\left(\frac{7}{8}\right) e(18)e\left(\frac{1}{8}\right) i-i i-i e(18)e\left(\frac{1}{8}\right) e(78)e\left(\frac{7}{8}\right) 11 1-1 e(38)e\left(\frac{3}{8}\right) e(58)e\left(\frac{5}{8}\right)
χ32(29,)\chi_{32}(29,\cdot) 32.g 8 yes 11 11 e(18)e\left(\frac{1}{8}\right) e(38)e\left(\frac{3}{8}\right) i-i ii e(78)e\left(\frac{7}{8}\right) e(58)e\left(\frac{5}{8}\right) 1-1 1-1 e(58)e\left(\frac{5}{8}\right) e(78)e\left(\frac{7}{8}\right)
χ32(31,)\chi_{32}(31,\cdot) 32.c 2 no 1-1 11 1-1 11 1-1 11 1-1 11 1-1 11 1-1 11