Properties

Modulus 101
Structure \(C_{100}\)
Order 100

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(101)
pari: g = idealstar(,101,2)

Character group

sage: G.order()
pari: g.no
Order = 100
sage: H.invariants()
pari: g.cyc
Structure = \(C_{100}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{101}(2,\cdot)$

First 32 of 100 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 11
\(\chi_{101}(1,\cdot)\) 101.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{101}(2,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(i\) \(e\left(\frac{13}{100}\right)\)
\(\chi_{101}(3,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(i\) \(e\left(\frac{97}{100}\right)\)
\(\chi_{101}(4,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(-1\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{101}(5,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(1\) \(e\left(\frac{3}{25}\right)\)
\(\chi_{101}(6,\cdot)\) 101.e 10 Yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{101}(7,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(i\) \(e\left(\frac{17}{100}\right)\)
\(\chi_{101}(8,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(-i\) \(e\left(\frac{39}{100}\right)\)
\(\chi_{101}(9,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(-1\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{101}(10,\cdot)\) 101.c 4 Yes \(-1\) \(1\) \(i\) \(i\) \(-1\) \(1\) \(-1\) \(i\) \(-i\) \(-1\) \(i\) \(i\)
\(\chi_{101}(11,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(i\) \(e\left(\frac{69}{100}\right)\)
\(\chi_{101}(12,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(-i\) \(e\left(\frac{23}{100}\right)\)
\(\chi_{101}(13,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(-1\) \(e\left(\frac{29}{50}\right)\)
\(\chi_{101}(14,\cdot)\) 101.e 10 Yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{101}(15,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(i\) \(e\left(\frac{9}{100}\right)\)
\(\chi_{101}(16,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(1\) \(e\left(\frac{13}{25}\right)\)
\(\chi_{101}(17,\cdot)\) 101.e 10 Yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{101}(18,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(-i\) \(e\left(\frac{7}{100}\right)\)
\(\chi_{101}(19,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{12}{25}\right)\) \(1\) \(e\left(\frac{12}{25}\right)\)
\(\chi_{101}(20,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(-1\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{101}(21,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(-1\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{101}(22,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(-1\) \(e\left(\frac{41}{50}\right)\)
\(\chi_{101}(23,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(-1\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{101}(24,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{9}{25}\right)\) \(1\) \(e\left(\frac{9}{25}\right)\)
\(\chi_{101}(25,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{6}{25}\right)\) \(1\) \(e\left(\frac{6}{25}\right)\)
\(\chi_{101}(26,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(-i\) \(e\left(\frac{71}{100}\right)\)
\(\chi_{101}(27,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(-i\) \(e\left(\frac{91}{100}\right)\)
\(\chi_{101}(28,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(-i\) \(e\left(\frac{43}{100}\right)\)
\(\chi_{101}(29,\cdot)\) 101.i 100 Yes \(-1\) \(1\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(-i\) \(e\left(\frac{83}{100}\right)\)
\(\chi_{101}(30,\cdot)\) 101.h 50 Yes \(1\) \(1\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(-1\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{101}(31,\cdot)\) 101.g 25 Yes \(1\) \(1\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{23}{25}\right)\) \(1\) \(e\left(\frac{23}{25}\right)\)
\(\chi_{101}(32,\cdot)\) 101.f 20 Yes \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\)