Properties

Modulus 55
Structure \(C_{20}\times C_{2}\)
Order 40

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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(55)
pari: g = idealstar(,55,2)

Character group

sage: G.order()
pari: g.no
Order = 40
sage: H.invariants()
pari: g.cyc
Structure = \(C_{20}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{55}(13,\cdot)$, $\chi_{55}(21,\cdot)$

First 32 of 40 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 3 4 6 7 8 9 12 13 14
\(\chi_{55}(1,\cdot)\) 55.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{55}(2,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{55}(3,\cdot)\) 55.k 20 Yes \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{55}(4,\cdot)\) 55.j 10 Yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{55}(6,\cdot)\) 55.i 10 No \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{55}(7,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{55}(8,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{55}(9,\cdot)\) 55.j 10 Yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{55}(12,\cdot)\) 55.f 4 No \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\)
\(\chi_{55}(13,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{55}(14,\cdot)\) 55.j 10 Yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{55}(16,\cdot)\) 55.g 5 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{55}(17,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{55}(18,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{55}(19,\cdot)\) 55.h 10 Yes \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{55}(21,\cdot)\) 55.c 2 No \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{55}(23,\cdot)\) 55.f 4 No \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(i\) \(-1\)
\(\chi_{55}(24,\cdot)\) 55.h 10 Yes \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{55}(26,\cdot)\) 55.g 5 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{55}(27,\cdot)\) 55.k 20 Yes \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{55}(28,\cdot)\) 55.l 20 Yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{55}(29,\cdot)\) 55.h 10 Yes \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{55}(31,\cdot)\) 55.g 5 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{55}(32,\cdot)\) 55.e 4 Yes \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(-1\) \(i\) \(i\) \(-1\)
\(\chi_{55}(34,\cdot)\) 55.b 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{55}(36,\cdot)\) 55.g 5 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{55}(37,\cdot)\) 55.k 20 Yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{55}(38,\cdot)\) 55.k 20 Yes \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{55}(39,\cdot)\) 55.h 10 Yes \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{55}(41,\cdot)\) 55.i 10 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{55}(42,\cdot)\) 55.k 20 Yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{55}(43,\cdot)\) 55.e 4 Yes \(1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(-1\) \(-i\) \(-i\) \(-1\)