Properties

Modulus 103
Structure \(C_{102}\)
Order 102

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(103)
 
pari: g = idealstar(,103,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 102
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{102}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{103}(5,\cdot)$

First 32 of 102 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
\(\chi_{103}(1,\cdot)\) 103.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{103}(2,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{51}\right)\)
\(\chi_{103}(3,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{103}(4,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{103}(5,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{61}{102}\right)\)
\(\chi_{103}(6,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{65}{102}\right)\)
\(\chi_{103}(7,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{20}{51}\right)\)
\(\chi_{103}(8,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{16}{17}\right)\)
\(\chi_{103}(9,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{103}(10,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{103}(11,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{49}{102}\right)\)
\(\chi_{103}(12,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{97}{102}\right)\)
\(\chi_{103}(13,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{103}(14,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{103}(15,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{47}{51}\right)\)
\(\chi_{103}(16,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{103}(17,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{44}{51}\right)\)
\(\chi_{103}(18,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{49}{51}\right)\)
\(\chi_{103}(19,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{43}{51}\right)\)
\(\chi_{103}(20,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{23}{102}\right)\)
\(\chi_{103}(21,\cdot)\) 103.h 102 yes \(-1\) \(1\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{73}{102}\right)\)
\(\chi_{103}(22,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{103}(23,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{103}(24,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{103}(25,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{51}\right)\)
\(\chi_{103}(26,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{51}\right)\)
\(\chi_{103}(27,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{103}(28,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{51}\right)\)
\(\chi_{103}(29,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{22}{51}\right)\)
\(\chi_{103}(30,\cdot)\) 103.e 17 yes \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{103}(31,\cdot)\) 103.f 34 yes \(-1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{103}(32,\cdot)\) 103.g 51 yes \(1\) \(1\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{51}\right)\)