Properties

Modulus $683$
Structure \(C_{682}\)
Order $682$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(683)
 
pari: g = idealstar(,683,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 682
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{682}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{683}(5,\cdot)$

First 32 of 682 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.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{683}(1,\cdot)\) 683.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{683}(2,\cdot)\) 683.d 22 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{683}(3,\cdot)\) 683.e 31 yes \(1\) \(1\) \(1\) \(e\left(\frac{21}{31}\right)\) \(1\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{7}{31}\right)\) \(1\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{28}{31}\right)\)
\(\chi_{683}(4,\cdot)\) 683.c 11 yes \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{683}(5,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{682}\right)\) \(e\left(\frac{547}{682}\right)\) \(e\left(\frac{265}{682}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{109}{341}\right)\) \(e\left(\frac{657}{682}\right)\)
\(\chi_{683}(6,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{547}{682}\right)\) \(e\left(\frac{493}{682}\right)\) \(e\left(\frac{371}{682}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{289}{341}\right)\) \(e\left(\frac{647}{682}\right)\)
\(\chi_{683}(7,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{265}{682}\right)\) \(e\left(\frac{371}{682}\right)\) \(e\left(\frac{661}{682}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{241}{341}\right)\) \(e\left(\frac{195}{682}\right)\)
\(\chi_{683}(8,\cdot)\) 683.d 22 yes \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{683}(9,\cdot)\) 683.e 31 yes \(1\) \(1\) \(1\) \(e\left(\frac{11}{31}\right)\) \(1\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{14}{31}\right)\) \(1\) \(e\left(\frac{22}{31}\right)\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{25}{31}\right)\)
\(\chi_{683}(10,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{109}{341}\right)\) \(e\left(\frac{289}{341}\right)\) \(e\left(\frac{241}{341}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{233}{341}\right)\) \(e\left(\frac{3}{341}\right)\)
\(\chi_{683}(11,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{657}{682}\right)\) \(e\left(\frac{647}{682}\right)\) \(e\left(\frac{195}{682}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{25}{31}\right)\) \(e\left(\frac{3}{341}\right)\) \(e\left(\frac{625}{682}\right)\)
\(\chi_{683}(12,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{41}{341}\right)\) \(e\left(\frac{262}{341}\right)\) \(e\left(\frac{294}{341}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{72}{341}\right)\) \(e\left(\frac{339}{341}\right)\)
\(\chi_{683}(13,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{19}{31}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{427}{682}\right)\) \(e\left(\frac{325}{682}\right)\) \(e\left(\frac{625}{682}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{167}{341}\right)\) \(e\left(\frac{237}{682}\right)\)
\(\chi_{683}(14,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{241}{341}\right)\) \(e\left(\frac{201}{341}\right)\) \(e\left(\frac{98}{341}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{24}{341}\right)\) \(e\left(\frac{113}{341}\right)\)
\(\chi_{683}(15,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{31}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{331}{682}\right)\) \(e\left(\frac{327}{682}\right)\) \(e\left(\frac{419}{682}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{10}{31}\right)\) \(e\left(\frac{274}{341}\right)\) \(e\left(\frac{591}{682}\right)\)
\(\chi_{683}(16,\cdot)\) 683.c 11 yes \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{683}(17,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{6}{31}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{682}\right)\) \(e\left(\frac{163}{682}\right)\) \(e\left(\frac{261}{682}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{12}{31}\right)\) \(e\left(\frac{25}{341}\right)\) \(e\left(\frac{207}{682}\right)\)
\(\chi_{683}(18,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{195}{682}\right)\) \(e\left(\frac{273}{682}\right)\) \(e\left(\frac{525}{682}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{22}{31}\right)\) \(e\left(\frac{113}{341}\right)\) \(e\left(\frac{581}{682}\right)\)
\(\chi_{683}(19,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{20}{31}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{135}{341}\right)\) \(e\left(\frac{189}{341}\right)\) \(e\left(\frac{311}{341}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{31}\right)\) \(e\left(\frac{104}{341}\right)\) \(e\left(\frac{35}{341}\right)\)
\(\chi_{683}(20,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{31}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{435}{682}\right)\) \(e\left(\frac{609}{682}\right)\) \(e\left(\frac{17}{682}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{16}{341}\right)\) \(e\left(\frac{37}{682}\right)\)
\(\chi_{683}(21,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{595}{682}\right)\) \(e\left(\frac{151}{682}\right)\) \(e\left(\frac{133}{682}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{25}{31}\right)\) \(e\left(\frac{65}{341}\right)\) \(e\left(\frac{129}{682}\right)\)
\(\chi_{683}(22,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{28}{31}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{96}{341}\right)\) \(e\left(\frac{339}{341}\right)\) \(e\left(\frac{206}{341}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{25}{31}\right)\) \(e\left(\frac{127}{341}\right)\) \(e\left(\frac{328}{341}\right)\)
\(\chi_{683}(23,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{399}{682}\right)\) \(e\left(\frac{13}{682}\right)\) \(e\left(\frac{25}{682}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{4}{31}\right)\) \(e\left(\frac{184}{341}\right)\) \(e\left(\frac{255}{682}\right)\)
\(\chi_{683}(24,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{21}{31}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{299}{682}\right)\) \(e\left(\frac{555}{682}\right)\) \(e\left(\frac{123}{682}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{11}{31}\right)\) \(e\left(\frac{196}{341}\right)\) \(e\left(\frac{27}{682}\right)\)
\(\chi_{683}(25,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{30}{31}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{341}\right)\) \(e\left(\frac{206}{341}\right)\) \(e\left(\frac{265}{341}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{29}{31}\right)\) \(e\left(\frac{218}{341}\right)\) \(e\left(\frac{316}{341}\right)\)
\(\chi_{683}(26,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{31}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{322}{341}\right)\) \(e\left(\frac{178}{341}\right)\) \(e\left(\frac{80}{341}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{291}{341}\right)\) \(e\left(\frac{134}{341}\right)\)
\(\chi_{683}(27,\cdot)\) 683.e 31 yes \(1\) \(1\) \(1\) \(e\left(\frac{1}{31}\right)\) \(1\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{1}{31}\right)\) \(e\left(\frac{21}{31}\right)\) \(1\) \(e\left(\frac{2}{31}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{22}{31}\right)\)
\(\chi_{683}(28,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{31}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{682}\right)\) \(e\left(\frac{433}{682}\right)\) \(e\left(\frac{413}{682}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{14}{31}\right)\) \(e\left(\frac{148}{341}\right)\) \(e\left(\frac{257}{682}\right)\)
\(\chi_{683}(29,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{31}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{64}{341}\right)\) \(e\left(\frac{226}{341}\right)\) \(e\left(\frac{251}{341}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{27}{31}\right)\) \(e\left(\frac{312}{341}\right)\) \(e\left(\frac{105}{341}\right)\)
\(\chi_{683}(30,\cdot)\) 683.g 341 yes \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{31}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{274}{341}\right)\) \(e\left(\frac{179}{341}\right)\) \(e\left(\frac{318}{341}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{31}\right)\) \(e\left(\frac{57}{341}\right)\) \(e\left(\frac{311}{341}\right)\)
\(\chi_{683}(31,\cdot)\) 683.h 682 yes \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{31}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{149}{682}\right)\) \(e\left(\frac{345}{682}\right)\) \(e\left(\frac{611}{682}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{6}{31}\right)\) \(e\left(\frac{214}{341}\right)\) \(e\left(\frac{367}{682}\right)\)
\(\chi_{683}(32,\cdot)\) 683.d 22 yes \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{22}\right)\)