Properties

Modulus 121
Structure \(C_{110}\)
Order 110

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(121)
 
pari: g = idealstar(,121,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 110
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{110}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{121}(2,\cdot)$

First 32 of 110 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
\(\chi_{121}(1,\cdot)\) 121.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{121}(2,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{121}(3,\cdot)\) 121.c 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)
\(\chi_{121}(4,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{121}(5,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{37}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{121}(6,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{89}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{48}{55}\right)\) \(e\left(\frac{1}{110}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{121}(7,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{7}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{39}{55}\right)\) \(e\left(\frac{73}{110}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{121}(8,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{3}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{1}{55}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{21}{110}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{121}(9,\cdot)\) 121.c 5 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)
\(\chi_{121}(10,\cdot)\) 121.f 22 yes \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{121}(12,\cdot)\) 121.e 11 yes \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{121}(13,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{101}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{79}{110}\right)\) \(e\left(\frac{47}{110}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{121}(14,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{55}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{121}(15,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{52}{55}\right)\) \(e\left(\frac{54}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{121}(16,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{13}{55}\right)\) \(e\left(\frac{14}{55}\right)\) \(e\left(\frac{6}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{121}(17,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{49}{55}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{71}{110}\right)\) \(e\left(\frac{13}{110}\right)\) \(e\left(\frac{37}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{121}(18,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{67}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{121}(19,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{28}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{29}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{121}(20,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{21}{55}\right)\) \(e\left(\frac{7}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{46}{55}\right)\) \(e\left(\frac{4}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{121}(21,\cdot)\) 121.f 22 yes \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{121}(23,\cdot)\) 121.e 11 yes \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{121}(24,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{91}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{12}{55}\right)\) \(e\left(\frac{69}{110}\right)\) \(e\left(\frac{87}{110}\right)\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{121}(25,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{38}{55}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{41}{55}\right)\) \(e\left(\frac{23}{55}\right)\) \(e\left(\frac{2}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{121}(26,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{51}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{34}{55}\right)\) \(e\left(\frac{29}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{121}(27,\cdot)\) 121.c 5 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)
\(\chi_{121}(28,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{55}\right)\) \(e\left(\frac{3}{55}\right)\) \(e\left(\frac{31}{110}\right)\) \(e\left(\frac{63}{110}\right)\) \(e\left(\frac{27}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{121}(29,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{55}\right)\) \(e\left(\frac{24}{55}\right)\) \(e\left(\frac{83}{110}\right)\) \(e\left(\frac{9}{110}\right)\) \(e\left(\frac{51}{110}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{121}(30,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{53}{110}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{53}{55}\right)\) \(e\left(\frac{36}{55}\right)\) \(e\left(\frac{97}{110}\right)\) \(e\left(\frac{41}{110}\right)\) \(e\left(\frac{49}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{121}(31,\cdot)\) 121.g 55 yes \(1\) \(1\) \(e\left(\frac{43}{55}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{55}\right)\) \(e\left(\frac{47}{55}\right)\) \(e\left(\frac{32}{55}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{19}{55}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{121}(32,\cdot)\) 121.f 22 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{121}(34,\cdot)\) 121.e 11 yes \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{121}(35,\cdot)\) 121.h 110 yes \(-1\) \(1\) \(e\left(\frac{81}{110}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{26}{55}\right)\) \(e\left(\frac{27}{55}\right)\) \(e\left(\frac{59}{110}\right)\) \(e\left(\frac{17}{110}\right)\) \(e\left(\frac{23}{110}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\)