Properties

Modulus 51
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(51)
 
pari: g = idealstar(,51,2)
 

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 = $\chi_{51}(37,\cdot)$, $\chi_{51}(35,\cdot)$

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 2 4 5 7 8 10 11 13 14 16
\(\chi_{51}(1,\cdot)\) 51.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{51}(2,\cdot)\) 51.g 8 Yes \(-1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{51}(4,\cdot)\) 51.e 4 No \(1\) \(1\) \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(1\) \(-i\) \(1\)
\(\chi_{51}(5,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{51}(7,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{51}(8,\cdot)\) 51.g 8 Yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{51}(10,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{51}(11,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{51}(13,\cdot)\) 51.e 4 No \(1\) \(1\) \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\) \(i\) \(1\)
\(\chi_{51}(14,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{51}(16,\cdot)\) 51.d 2 No \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{51}(19,\cdot)\) 51.h 8 No \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{51}(20,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{51}(22,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{51}(23,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{51}(25,\cdot)\) 51.h 8 No \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(1\)
\(\chi_{51}(26,\cdot)\) 51.g 8 Yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(1\)
\(\chi_{51}(28,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{51}(29,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{51}(31,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{51}(32,\cdot)\) 51.g 8 Yes \(-1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{51}(35,\cdot)\) 51.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{51}(37,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{51}(38,\cdot)\) 51.f 4 Yes \(-1\) \(1\) \(1\) \(1\) \(i\) \(i\) \(1\) \(i\) \(-i\) \(1\) \(i\) \(1\)
\(\chi_{51}(40,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{51}(41,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{51}(43,\cdot)\) 51.h 8 No \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{51}(44,\cdot)\) 51.i 16 Yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{51}(46,\cdot)\) 51.j 16 No \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{51}(47,\cdot)\) 51.f 4 Yes \(-1\) \(1\) \(1\) \(1\) \(-i\) \(-i\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(1\)
\(\chi_{51}(49,\cdot)\) 51.h 8 No \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{51}(50,\cdot)\) 51.c 2 Yes \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\)