Properties

Modulus 283
Structure \(C_{282}\)
Order 282

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(283)
pari: g = idealstar(,283,2)

Character group

sage: G.order()
pari: g.no
Order = 282
sage: H.invariants()
pari: g.cyc
Structure = \(C_{282}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{283}(3,\cdot)$

First 32 of 282 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
\(\chi_{283}(1,\cdot)\) 283.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{283}(2,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{61}{94}\right)\) \(e\left(\frac{53}{94}\right)\) \(e\left(\frac{14}{47}\right)\) \(e\left(\frac{35}{94}\right)\) \(e\left(\frac{10}{47}\right)\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{89}{94}\right)\) \(e\left(\frac{6}{47}\right)\) \(e\left(\frac{1}{47}\right)\) \(e\left(\frac{33}{47}\right)\)
\(\chi_{283}(3,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{53}{94}\right)\) \(e\left(\frac{1}{282}\right)\) \(e\left(\frac{6}{47}\right)\) \(e\left(\frac{233}{282}\right)\) \(e\left(\frac{80}{141}\right)\) \(e\left(\frac{139}{141}\right)\) \(e\left(\frac{65}{94}\right)\) \(e\left(\frac{1}{141}\right)\) \(e\left(\frac{55}{141}\right)\) \(e\left(\frac{76}{141}\right)\)
\(\chi_{283}(4,\cdot)\) 283.e 47 Yes \(1\) \(1\) \(e\left(\frac{14}{47}\right)\) \(e\left(\frac{6}{47}\right)\) \(e\left(\frac{28}{47}\right)\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{20}{47}\right)\) \(e\left(\frac{23}{47}\right)\) \(e\left(\frac{42}{47}\right)\) \(e\left(\frac{12}{47}\right)\) \(e\left(\frac{2}{47}\right)\) \(e\left(\frac{19}{47}\right)\)
\(\chi_{283}(5,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{35}{94}\right)\) \(e\left(\frac{233}{282}\right)\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{145}{282}\right)\) \(e\left(\frac{28}{141}\right)\) \(e\left(\frac{98}{141}\right)\) \(e\left(\frac{11}{94}\right)\) \(e\left(\frac{92}{141}\right)\) \(e\left(\frac{125}{141}\right)\) \(e\left(\frac{83}{141}\right)\)
\(\chi_{283}(6,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{10}{47}\right)\) \(e\left(\frac{80}{141}\right)\) \(e\left(\frac{20}{47}\right)\) \(e\left(\frac{28}{141}\right)\) \(e\left(\frac{110}{141}\right)\) \(e\left(\frac{103}{141}\right)\) \(e\left(\frac{30}{47}\right)\) \(e\left(\frac{19}{141}\right)\) \(e\left(\frac{58}{141}\right)\) \(e\left(\frac{34}{141}\right)\)
\(\chi_{283}(7,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{139}{141}\right)\) \(e\left(\frac{23}{47}\right)\) \(e\left(\frac{98}{141}\right)\) \(e\left(\frac{103}{141}\right)\) \(e\left(\frac{8}{141}\right)\) \(e\left(\frac{11}{47}\right)\) \(e\left(\frac{137}{141}\right)\) \(e\left(\frac{62}{141}\right)\) \(e\left(\frac{119}{141}\right)\)
\(\chi_{283}(8,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{89}{94}\right)\) \(e\left(\frac{65}{94}\right)\) \(e\left(\frac{42}{47}\right)\) \(e\left(\frac{11}{94}\right)\) \(e\left(\frac{30}{47}\right)\) \(e\left(\frac{11}{47}\right)\) \(e\left(\frac{79}{94}\right)\) \(e\left(\frac{18}{47}\right)\) \(e\left(\frac{3}{47}\right)\) \(e\left(\frac{5}{47}\right)\)
\(\chi_{283}(9,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{6}{47}\right)\) \(e\left(\frac{1}{141}\right)\) \(e\left(\frac{12}{47}\right)\) \(e\left(\frac{92}{141}\right)\) \(e\left(\frac{19}{141}\right)\) \(e\left(\frac{137}{141}\right)\) \(e\left(\frac{18}{47}\right)\) \(e\left(\frac{2}{141}\right)\) \(e\left(\frac{110}{141}\right)\) \(e\left(\frac{11}{141}\right)\)
\(\chi_{283}(10,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{1}{47}\right)\) \(e\left(\frac{55}{141}\right)\) \(e\left(\frac{2}{47}\right)\) \(e\left(\frac{125}{141}\right)\) \(e\left(\frac{58}{141}\right)\) \(e\left(\frac{62}{141}\right)\) \(e\left(\frac{3}{47}\right)\) \(e\left(\frac{110}{141}\right)\) \(e\left(\frac{128}{141}\right)\) \(e\left(\frac{41}{141}\right)\)
\(\chi_{283}(11,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{33}{47}\right)\) \(e\left(\frac{76}{141}\right)\) \(e\left(\frac{19}{47}\right)\) \(e\left(\frac{83}{141}\right)\) \(e\left(\frac{34}{141}\right)\) \(e\left(\frac{119}{141}\right)\) \(e\left(\frac{5}{47}\right)\) \(e\left(\frac{11}{141}\right)\) \(e\left(\frac{41}{141}\right)\) \(e\left(\frac{131}{141}\right)\)
\(\chi_{283}(12,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{81}{94}\right)\) \(e\left(\frac{37}{282}\right)\) \(e\left(\frac{34}{47}\right)\) \(e\left(\frac{161}{282}\right)\) \(e\left(\frac{140}{141}\right)\) \(e\left(\frac{67}{141}\right)\) \(e\left(\frac{55}{94}\right)\) \(e\left(\frac{37}{141}\right)\) \(e\left(\frac{61}{141}\right)\) \(e\left(\frac{133}{141}\right)\)
\(\chi_{283}(13,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{10}{47}\right)\) \(e\left(\frac{127}{141}\right)\) \(e\left(\frac{20}{47}\right)\) \(e\left(\frac{122}{141}\right)\) \(e\left(\frac{16}{141}\right)\) \(e\left(\frac{56}{141}\right)\) \(e\left(\frac{30}{47}\right)\) \(e\left(\frac{113}{141}\right)\) \(e\left(\frac{11}{141}\right)\) \(e\left(\frac{128}{141}\right)\)
\(\chi_{283}(14,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{37}{94}\right)\) \(e\left(\frac{155}{282}\right)\) \(e\left(\frac{37}{47}\right)\) \(e\left(\frac{19}{282}\right)\) \(e\left(\frac{133}{141}\right)\) \(e\left(\frac{113}{141}\right)\) \(e\left(\frac{17}{94}\right)\) \(e\left(\frac{14}{141}\right)\) \(e\left(\frac{65}{141}\right)\) \(e\left(\frac{77}{141}\right)\)
\(\chi_{283}(15,\cdot)\) 283.e 47 Yes \(1\) \(1\) \(e\left(\frac{44}{47}\right)\) \(e\left(\frac{39}{47}\right)\) \(e\left(\frac{41}{47}\right)\) \(e\left(\frac{16}{47}\right)\) \(e\left(\frac{36}{47}\right)\) \(e\left(\frac{32}{47}\right)\) \(e\left(\frac{38}{47}\right)\) \(e\left(\frac{31}{47}\right)\) \(e\left(\frac{13}{47}\right)\) \(e\left(\frac{6}{47}\right)\)
\(\chi_{283}(16,\cdot)\) 283.e 47 Yes \(1\) \(1\) \(e\left(\frac{28}{47}\right)\) \(e\left(\frac{12}{47}\right)\) \(e\left(\frac{9}{47}\right)\) \(e\left(\frac{23}{47}\right)\) \(e\left(\frac{40}{47}\right)\) \(e\left(\frac{46}{47}\right)\) \(e\left(\frac{37}{47}\right)\) \(e\left(\frac{24}{47}\right)\) \(e\left(\frac{4}{47}\right)\) \(e\left(\frac{38}{47}\right)\)
\(\chi_{283}(17,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{57}{94}\right)\) \(e\left(\frac{221}{282}\right)\) \(e\left(\frac{10}{47}\right)\) \(e\left(\frac{169}{282}\right)\) \(e\left(\frac{55}{141}\right)\) \(e\left(\frac{122}{141}\right)\) \(e\left(\frac{77}{94}\right)\) \(e\left(\frac{80}{141}\right)\) \(e\left(\frac{29}{141}\right)\) \(e\left(\frac{17}{141}\right)\)
\(\chi_{283}(18,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{73}{94}\right)\) \(e\left(\frac{161}{282}\right)\) \(e\left(\frac{26}{47}\right)\) \(e\left(\frac{7}{282}\right)\) \(e\left(\frac{49}{141}\right)\) \(e\left(\frac{101}{141}\right)\) \(e\left(\frac{31}{94}\right)\) \(e\left(\frac{20}{141}\right)\) \(e\left(\frac{113}{141}\right)\) \(e\left(\frac{110}{141}\right)\)
\(\chi_{283}(19,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{67}{94}\right)\) \(e\left(\frac{69}{94}\right)\) \(e\left(\frac{20}{47}\right)\) \(e\left(\frac{3}{94}\right)\) \(e\left(\frac{21}{47}\right)\) \(e\left(\frac{3}{47}\right)\) \(e\left(\frac{13}{94}\right)\) \(e\left(\frac{22}{47}\right)\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{27}{47}\right)\)
\(\chi_{283}(20,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{63}{94}\right)\) \(e\left(\frac{269}{282}\right)\) \(e\left(\frac{16}{47}\right)\) \(e\left(\frac{73}{282}\right)\) \(e\left(\frac{88}{141}\right)\) \(e\left(\frac{26}{141}\right)\) \(e\left(\frac{1}{94}\right)\) \(e\left(\frac{128}{141}\right)\) \(e\left(\frac{131}{141}\right)\) \(e\left(\frac{140}{141}\right)\)
\(\chi_{283}(21,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{29}{94}\right)\) \(e\left(\frac{93}{94}\right)\) \(e\left(\frac{29}{47}\right)\) \(e\left(\frac{49}{94}\right)\) \(e\left(\frac{14}{47}\right)\) \(e\left(\frac{2}{47}\right)\) \(e\left(\frac{87}{94}\right)\) \(e\left(\frac{46}{47}\right)\) \(e\left(\frac{39}{47}\right)\) \(e\left(\frac{18}{47}\right)\)
\(\chi_{283}(22,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{33}{94}\right)\) \(e\left(\frac{29}{282}\right)\) \(e\left(\frac{33}{47}\right)\) \(e\left(\frac{271}{282}\right)\) \(e\left(\frac{64}{141}\right)\) \(e\left(\frac{83}{141}\right)\) \(e\left(\frac{5}{94}\right)\) \(e\left(\frac{29}{141}\right)\) \(e\left(\frac{44}{141}\right)\) \(e\left(\frac{89}{141}\right)\)
\(\chi_{283}(23,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{18}{47}\right)\) \(e\left(\frac{50}{141}\right)\) \(e\left(\frac{36}{47}\right)\) \(e\left(\frac{88}{141}\right)\) \(e\left(\frac{104}{141}\right)\) \(e\left(\frac{82}{141}\right)\) \(e\left(\frac{7}{47}\right)\) \(e\left(\frac{100}{141}\right)\) \(e\left(\frac{1}{141}\right)\) \(e\left(\frac{127}{141}\right)\)
\(\chi_{283}(24,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{24}{47}\right)\) \(e\left(\frac{98}{141}\right)\) \(e\left(\frac{1}{47}\right)\) \(e\left(\frac{133}{141}\right)\) \(e\left(\frac{29}{141}\right)\) \(e\left(\frac{31}{141}\right)\) \(e\left(\frac{25}{47}\right)\) \(e\left(\frac{55}{141}\right)\) \(e\left(\frac{64}{141}\right)\) \(e\left(\frac{91}{141}\right)\)
\(\chi_{283}(25,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{35}{47}\right)\) \(e\left(\frac{92}{141}\right)\) \(e\left(\frac{23}{47}\right)\) \(e\left(\frac{4}{141}\right)\) \(e\left(\frac{56}{141}\right)\) \(e\left(\frac{55}{141}\right)\) \(e\left(\frac{11}{47}\right)\) \(e\left(\frac{43}{141}\right)\) \(e\left(\frac{109}{141}\right)\) \(e\left(\frac{25}{141}\right)\)
\(\chi_{283}(26,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{81}{94}\right)\) \(e\left(\frac{131}{282}\right)\) \(e\left(\frac{34}{47}\right)\) \(e\left(\frac{67}{282}\right)\) \(e\left(\frac{46}{141}\right)\) \(e\left(\frac{20}{141}\right)\) \(e\left(\frac{55}{94}\right)\) \(e\left(\frac{131}{141}\right)\) \(e\left(\frac{14}{141}\right)\) \(e\left(\frac{86}{141}\right)\)
\(\chi_{283}(27,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{65}{94}\right)\) \(e\left(\frac{1}{94}\right)\) \(e\left(\frac{18}{47}\right)\) \(e\left(\frac{45}{94}\right)\) \(e\left(\frac{33}{47}\right)\) \(e\left(\frac{45}{47}\right)\) \(e\left(\frac{7}{94}\right)\) \(e\left(\frac{1}{47}\right)\) \(e\left(\frac{8}{47}\right)\) \(e\left(\frac{29}{47}\right)\)
\(\chi_{283}(28,\cdot)\) 283.g 141 Yes \(1\) \(1\) \(e\left(\frac{2}{47}\right)\) \(e\left(\frac{16}{141}\right)\) \(e\left(\frac{4}{47}\right)\) \(e\left(\frac{62}{141}\right)\) \(e\left(\frac{22}{141}\right)\) \(e\left(\frac{77}{141}\right)\) \(e\left(\frac{6}{47}\right)\) \(e\left(\frac{32}{141}\right)\) \(e\left(\frac{68}{141}\right)\) \(e\left(\frac{35}{141}\right)\)
\(\chi_{283}(29,\cdot)\) 283.e 47 Yes \(1\) \(1\) \(e\left(\frac{34}{47}\right)\) \(e\left(\frac{28}{47}\right)\) \(e\left(\frac{21}{47}\right)\) \(e\left(\frac{38}{47}\right)\) \(e\left(\frac{15}{47}\right)\) \(e\left(\frac{29}{47}\right)\) \(e\left(\frac{8}{47}\right)\) \(e\left(\frac{9}{47}\right)\) \(e\left(\frac{25}{47}\right)\) \(e\left(\frac{26}{47}\right)\)
\(\chi_{283}(30,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{55}{94}\right)\) \(e\left(\frac{37}{94}\right)\) \(e\left(\frac{8}{47}\right)\) \(e\left(\frac{67}{94}\right)\) \(e\left(\frac{46}{47}\right)\) \(e\left(\frac{20}{47}\right)\) \(e\left(\frac{71}{94}\right)\) \(e\left(\frac{37}{47}\right)\) \(e\left(\frac{14}{47}\right)\) \(e\left(\frac{39}{47}\right)\)
\(\chi_{283}(31,\cdot)\) 283.h 282 Yes \(-1\) \(1\) \(e\left(\frac{63}{94}\right)\) \(e\left(\frac{175}{282}\right)\) \(e\left(\frac{16}{47}\right)\) \(e\left(\frac{167}{282}\right)\) \(e\left(\frac{41}{141}\right)\) \(e\left(\frac{73}{141}\right)\) \(e\left(\frac{1}{94}\right)\) \(e\left(\frac{34}{141}\right)\) \(e\left(\frac{37}{141}\right)\) \(e\left(\frac{46}{141}\right)\)
\(\chi_{283}(32,\cdot)\) 283.f 94 Yes \(-1\) \(1\) \(e\left(\frac{23}{94}\right)\) \(e\left(\frac{77}{94}\right)\) \(e\left(\frac{23}{47}\right)\) \(e\left(\frac{81}{94}\right)\) \(e\left(\frac{3}{47}\right)\) \(e\left(\frac{34}{47}\right)\) \(e\left(\frac{69}{94}\right)\) \(e\left(\frac{30}{47}\right)\) \(e\left(\frac{5}{47}\right)\) \(e\left(\frac{24}{47}\right)\)