Properties

Modulus 64
Structure \(C_{16}\times C_{2}\)
Order 32

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(64)
pari: g = idealstar(,64,2)

Character group

sage: G.order()
pari: g.no
Order = 32
sage: H.invariants()
pari: g.cyc
Structure = \(C_{16}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{64}(5,\cdot)$, $\chi_{64}(63,\cdot)$

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.

orbit label order primitive -1 1 3 5 7 9 11 13 15 17 19 21
\(\chi_{64}(1,\cdot)\) 64.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{64}(3,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{64}(5,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{64}(7,\cdot)\) 64.h 8 No \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{64}(9,\cdot)\) 64.g 8 No \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{64}(11,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{64}(13,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{64}(15,\cdot)\) 64.f 4 No \(-1\) \(1\) \(i\) \(i\) \(1\) \(-1\) \(-i\) \(-i\) \(-1\) \(1\) \(i\) \(i\)
\(\chi_{64}(17,\cdot)\) 64.e 4 No \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(1\) \(i\) \(-i\)
\(\chi_{64}(19,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(i\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{64}(21,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{64}(23,\cdot)\) 64.h 8 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{64}(25,\cdot)\) 64.g 8 No \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{64}(27,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{64}(29,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{64}(31,\cdot)\) 64.d 2 No \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{64}(33,\cdot)\) 64.b 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{64}(35,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{64}(37,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{64}(39,\cdot)\) 64.h 8 No \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{64}(41,\cdot)\) 64.g 8 No \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{64}(43,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{64}(45,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{64}(47,\cdot)\) 64.f 4 No \(-1\) \(1\) \(-i\) \(-i\) \(1\) \(-1\) \(i\) \(i\) \(-1\) \(1\) \(-i\) \(-i\)
\(\chi_{64}(49,\cdot)\) 64.e 4 No \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(1\) \(1\) \(-i\) \(i\)
\(\chi_{64}(51,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{64}(53,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{64}(55,\cdot)\) 64.h 8 No \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{64}(57,\cdot)\) 64.g 8 No \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{64}(59,\cdot)\) 64.j 16 Yes \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{64}(61,\cdot)\) 64.i 16 Yes \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{64}(63,\cdot)\) 64.c 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)