Properties

Modulus 187
Structure \(C_{80}\times C_{2}\)
Order 160

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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(187)
 
pari: g = idealstar(,187,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 160
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{80}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{187}(105,\cdot)$, $\chi_{187}(120,\cdot)$

First 32 of 160 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 5 6 7 8 9 10 12
\(\chi_{187}(1,\cdot)\) 187.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{187}(2,\cdot)\) 187.q 40 Yes \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{187}(3,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{11}{80}\right)\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{187}(4,\cdot)\) 187.p 20 Yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\) \(-i\)
\(\chi_{187}(5,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{187}(6,\cdot)\) 187.t 80 Yes \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{11}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{187}(7,\cdot)\) 187.t 80 Yes \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{187}(8,\cdot)\) 187.q 40 Yes \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{187}(9,\cdot)\) 187.r 40 Yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{187}(10,\cdot)\) 187.m 16 Yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{187}(12,\cdot)\) 187.n 16 No \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{187}(13,\cdot)\) 187.o 20 Yes \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(i\) \(i\)
\(\chi_{187}(14,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{187}(15,\cdot)\) 187.r 40 Yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{187}(16,\cdot)\) 187.j 10 Yes \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{187}(18,\cdot)\) 187.k 10 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(1\)
\(\chi_{187}(19,\cdot)\) 187.q 40 Yes \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{187}(20,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{187}(21,\cdot)\) 187.f 4 Yes \(-1\) \(1\) \(1\) \(-i\) \(1\) \(-i\) \(-i\) \(-i\) \(1\) \(-1\) \(-i\) \(-i\)
\(\chi_{187}(23,\cdot)\) 187.n 16 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{187}(24,\cdot)\) 187.t 80 Yes \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{21}{80}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{187}(25,\cdot)\) 187.r 40 Yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{187}(26,\cdot)\) 187.r 40 Yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{187}(27,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{187}(28,\cdot)\) 187.t 80 Yes \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{187}(29,\cdot)\) 187.t 80 Yes \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{187}(30,\cdot)\) 187.o 20 Yes \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\) \(i\)
\(\chi_{187}(31,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{187}(32,\cdot)\) 187.i 8 Yes \(-1\) \(1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{187}(35,\cdot)\) 187.k 10 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(1\)
\(\chi_{187}(36,\cdot)\) 187.r 40 Yes \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{187}(37,\cdot)\) 187.s 80 Yes \(-1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)