Properties

Modulus 367
Structure \(C_{366}\)
Order 366

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(367)
pari: g = idealstar(,367,2)

Character group

sage: G.order()
pari: g.no
Order = 366
sage: H.invariants()
pari: g.cyc
Structure = \(C_{366}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{367}(6,\cdot)$

First 32 of 366 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
\(\chi_{367}(1,\cdot)\) 367.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{367}(2,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{176}{183}\right)\) \(e\left(\frac{51}{61}\right)\) \(e\left(\frac{169}{183}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{146}{183}\right)\) \(e\left(\frac{35}{61}\right)\) \(e\left(\frac{54}{61}\right)\) \(e\left(\frac{41}{61}\right)\) \(e\left(\frac{179}{183}\right)\) \(e\left(\frac{8}{183}\right)\)
\(\chi_{367}(3,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{51}{61}\right)\) \(e\left(\frac{45}{122}\right)\) \(e\left(\frac{41}{61}\right)\) \(e\left(\frac{87}{122}\right)\) \(e\left(\frac{25}{122}\right)\) \(e\left(\frac{28}{61}\right)\) \(e\left(\frac{31}{61}\right)\) \(e\left(\frac{45}{61}\right)\) \(e\left(\frac{67}{122}\right)\) \(e\left(\frac{49}{122}\right)\)
\(\chi_{367}(4,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{169}{183}\right)\) \(e\left(\frac{41}{61}\right)\) \(e\left(\frac{155}{183}\right)\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{109}{183}\right)\) \(e\left(\frac{9}{61}\right)\) \(e\left(\frac{47}{61}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{175}{183}\right)\) \(e\left(\frac{16}{183}\right)\)
\(\chi_{367}(5,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{87}{122}\right)\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{95}{122}\right)\) \(e\left(\frac{89}{122}\right)\) \(e\left(\frac{46}{61}\right)\) \(e\left(\frac{3}{61}\right)\) \(e\left(\frac{26}{61}\right)\) \(e\left(\frac{97}{122}\right)\) \(e\left(\frac{111}{122}\right)\)
\(\chi_{367}(6,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{146}{183}\right)\) \(e\left(\frac{25}{122}\right)\) \(e\left(\frac{109}{183}\right)\) \(e\left(\frac{89}{122}\right)\) \(e\left(\frac{1}{366}\right)\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{24}{61}\right)\) \(e\left(\frac{25}{61}\right)\) \(e\left(\frac{193}{366}\right)\) \(e\left(\frac{163}{366}\right)\)
\(\chi_{367}(7,\cdot)\) 367.e 61 Yes \(1\) \(1\) \(e\left(\frac{35}{61}\right)\) \(e\left(\frac{28}{61}\right)\) \(e\left(\frac{9}{61}\right)\) \(e\left(\frac{46}{61}\right)\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{24}{61}\right)\) \(e\left(\frac{44}{61}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{20}{61}\right)\) \(e\left(\frac{21}{61}\right)\)
\(\chi_{367}(8,\cdot)\) 367.e 61 Yes \(1\) \(1\) \(e\left(\frac{54}{61}\right)\) \(e\left(\frac{31}{61}\right)\) \(e\left(\frac{47}{61}\right)\) \(e\left(\frac{3}{61}\right)\) \(e\left(\frac{24}{61}\right)\) \(e\left(\frac{44}{61}\right)\) \(e\left(\frac{40}{61}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{57}{61}\right)\) \(e\left(\frac{8}{61}\right)\)
\(\chi_{367}(9,\cdot)\) 367.e 61 Yes \(1\) \(1\) \(e\left(\frac{41}{61}\right)\) \(e\left(\frac{45}{61}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{26}{61}\right)\) \(e\left(\frac{25}{61}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{29}{61}\right)\) \(e\left(\frac{6}{61}\right)\) \(e\left(\frac{49}{61}\right)\)
\(\chi_{367}(10,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{179}{183}\right)\) \(e\left(\frac{67}{122}\right)\) \(e\left(\frac{175}{183}\right)\) \(e\left(\frac{97}{122}\right)\) \(e\left(\frac{193}{366}\right)\) \(e\left(\frac{20}{61}\right)\) \(e\left(\frac{57}{61}\right)\) \(e\left(\frac{6}{61}\right)\) \(e\left(\frac{283}{366}\right)\) \(e\left(\frac{349}{366}\right)\)
\(\chi_{367}(11,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{8}{183}\right)\) \(e\left(\frac{49}{122}\right)\) \(e\left(\frac{16}{183}\right)\) \(e\left(\frac{111}{122}\right)\) \(e\left(\frac{163}{366}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{8}{61}\right)\) \(e\left(\frac{49}{61}\right)\) \(e\left(\frac{349}{366}\right)\) \(e\left(\frac{217}{366}\right)\)
\(\chi_{367}(12,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{139}{183}\right)\) \(e\left(\frac{5}{122}\right)\) \(e\left(\frac{95}{183}\right)\) \(e\left(\frac{91}{122}\right)\) \(e\left(\frac{293}{366}\right)\) \(e\left(\frac{37}{61}\right)\) \(e\left(\frac{17}{61}\right)\) \(e\left(\frac{5}{61}\right)\) \(e\left(\frac{185}{366}\right)\) \(e\left(\frac{179}{366}\right)\)
\(\chi_{367}(13,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{62}{183}\right)\) \(e\left(\frac{45}{61}\right)\) \(e\left(\frac{124}{183}\right)\) \(e\left(\frac{26}{61}\right)\) \(e\left(\frac{14}{183}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{29}{61}\right)\) \(e\left(\frac{140}{183}\right)\) \(e\left(\frac{86}{183}\right)\)
\(\chi_{367}(14,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{98}{183}\right)\) \(e\left(\frac{18}{61}\right)\) \(e\left(\frac{13}{183}\right)\) \(e\left(\frac{47}{61}\right)\) \(e\left(\frac{152}{183}\right)\) \(e\left(\frac{59}{61}\right)\) \(e\left(\frac{37}{61}\right)\) \(e\left(\frac{36}{61}\right)\) \(e\left(\frac{56}{183}\right)\) \(e\left(\frac{71}{183}\right)\)
\(\chi_{367}(15,\cdot)\) 367.e 61 Yes \(1\) \(1\) \(e\left(\frac{52}{61}\right)\) \(e\left(\frac{5}{61}\right)\) \(e\left(\frac{43}{61}\right)\) \(e\left(\frac{30}{61}\right)\) \(e\left(\frac{57}{61}\right)\) \(e\left(\frac{13}{61}\right)\) \(e\left(\frac{34}{61}\right)\) \(e\left(\frac{10}{61}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{19}{61}\right)\)
\(\chi_{367}(16,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{155}{183}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{127}{183}\right)\) \(e\left(\frac{4}{61}\right)\) \(e\left(\frac{35}{183}\right)\) \(e\left(\frac{18}{61}\right)\) \(e\left(\frac{33}{61}\right)\) \(e\left(\frac{42}{61}\right)\) \(e\left(\frac{167}{183}\right)\) \(e\left(\frac{32}{183}\right)\)
\(\chi_{367}(17,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{104}{183}\right)\) \(e\left(\frac{27}{122}\right)\) \(e\left(\frac{25}{183}\right)\) \(e\left(\frac{101}{122}\right)\) \(e\left(\frac{289}{366}\right)\) \(e\left(\frac{29}{61}\right)\) \(e\left(\frac{43}{61}\right)\) \(e\left(\frac{27}{61}\right)\) \(e\left(\frac{145}{366}\right)\) \(e\left(\frac{259}{366}\right)\)
\(\chi_{367}(18,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{116}{183}\right)\) \(e\left(\frac{35}{61}\right)\) \(e\left(\frac{49}{183}\right)\) \(e\left(\frac{27}{61}\right)\) \(e\left(\frac{38}{183}\right)\) \(e\left(\frac{30}{61}\right)\) \(e\left(\frac{55}{61}\right)\) \(e\left(\frac{9}{61}\right)\) \(e\left(\frac{14}{183}\right)\) \(e\left(\frac{155}{183}\right)\)
\(\chi_{367}(19,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{73}{183}\right)\) \(e\left(\frac{43}{122}\right)\) \(e\left(\frac{146}{183}\right)\) \(e\left(\frac{75}{122}\right)\) \(e\left(\frac{275}{366}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{12}{61}\right)\) \(e\left(\frac{43}{61}\right)\) \(e\left(\frac{5}{366}\right)\) \(e\left(\frac{173}{366}\right)\)
\(\chi_{367}(20,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{172}{183}\right)\) \(e\left(\frac{47}{122}\right)\) \(e\left(\frac{161}{183}\right)\) \(e\left(\frac{99}{122}\right)\) \(e\left(\frac{119}{366}\right)\) \(e\left(\frac{55}{61}\right)\) \(e\left(\frac{50}{61}\right)\) \(e\left(\frac{47}{61}\right)\) \(e\left(\frac{275}{366}\right)\) \(e\left(\frac{365}{366}\right)\)
\(\chi_{367}(21,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{25}{61}\right)\) \(e\left(\frac{101}{122}\right)\) \(e\left(\frac{50}{61}\right)\) \(e\left(\frac{57}{122}\right)\) \(e\left(\frac{29}{122}\right)\) \(e\left(\frac{52}{61}\right)\) \(e\left(\frac{14}{61}\right)\) \(e\left(\frac{40}{61}\right)\) \(e\left(\frac{107}{122}\right)\) \(e\left(\frac{91}{122}\right)\)
\(\chi_{367}(22,\cdot)\) 367.h 366 Yes \(-1\) \(1\) \(e\left(\frac{1}{183}\right)\) \(e\left(\frac{29}{122}\right)\) \(e\left(\frac{2}{183}\right)\) \(e\left(\frac{113}{122}\right)\) \(e\left(\frac{89}{366}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{29}{61}\right)\) \(e\left(\frac{341}{366}\right)\) \(e\left(\frac{233}{366}\right)\)
\(\chi_{367}(23,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{28}{183}\right)\) \(e\left(\frac{40}{61}\right)\) \(e\left(\frac{56}{183}\right)\) \(e\left(\frac{57}{61}\right)\) \(e\left(\frac{148}{183}\right)\) \(e\left(\frac{43}{61}\right)\) \(e\left(\frac{28}{61}\right)\) \(e\left(\frac{19}{61}\right)\) \(e\left(\frac{16}{183}\right)\) \(e\left(\frac{151}{183}\right)\)
\(\chi_{367}(24,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{44}{61}\right)\) \(e\left(\frac{107}{122}\right)\) \(e\left(\frac{27}{61}\right)\) \(e\left(\frac{93}{122}\right)\) \(e\left(\frac{73}{122}\right)\) \(e\left(\frac{11}{61}\right)\) \(e\left(\frac{10}{61}\right)\) \(e\left(\frac{46}{61}\right)\) \(e\left(\frac{59}{122}\right)\) \(e\left(\frac{65}{122}\right)\)
\(\chi_{367}(25,\cdot)\) 367.e 61 Yes \(1\) \(1\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{26}{61}\right)\) \(e\left(\frac{4}{61}\right)\) \(e\left(\frac{34}{61}\right)\) \(e\left(\frac{28}{61}\right)\) \(e\left(\frac{31}{61}\right)\) \(e\left(\frac{6}{61}\right)\) \(e\left(\frac{52}{61}\right)\) \(e\left(\frac{36}{61}\right)\) \(e\left(\frac{50}{61}\right)\)
\(\chi_{367}(26,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{55}{183}\right)\) \(e\left(\frac{35}{61}\right)\) \(e\left(\frac{110}{183}\right)\) \(e\left(\frac{27}{61}\right)\) \(e\left(\frac{160}{183}\right)\) \(e\left(\frac{30}{61}\right)\) \(e\left(\frac{55}{61}\right)\) \(e\left(\frac{9}{61}\right)\) \(e\left(\frac{136}{183}\right)\) \(e\left(\frac{94}{183}\right)\)
\(\chi_{367}(27,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{31}{61}\right)\) \(e\left(\frac{13}{122}\right)\) \(e\left(\frac{1}{61}\right)\) \(e\left(\frac{17}{122}\right)\) \(e\left(\frac{75}{122}\right)\) \(e\left(\frac{23}{61}\right)\) \(e\left(\frac{32}{61}\right)\) \(e\left(\frac{13}{61}\right)\) \(e\left(\frac{79}{122}\right)\) \(e\left(\frac{25}{122}\right)\)
\(\chi_{367}(28,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{91}{183}\right)\) \(e\left(\frac{8}{61}\right)\) \(e\left(\frac{182}{183}\right)\) \(e\left(\frac{48}{61}\right)\) \(e\left(\frac{115}{183}\right)\) \(e\left(\frac{33}{61}\right)\) \(e\left(\frac{30}{61}\right)\) \(e\left(\frac{16}{61}\right)\) \(e\left(\frac{52}{183}\right)\) \(e\left(\frac{79}{183}\right)\)
\(\chi_{367}(29,\cdot)\) 367.f 122 Yes \(-1\) \(1\) \(e\left(\frac{39}{61}\right)\) \(e\left(\frac{99}{122}\right)\) \(e\left(\frac{17}{61}\right)\) \(e\left(\frac{45}{122}\right)\) \(e\left(\frac{55}{122}\right)\) \(e\left(\frac{25}{61}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{38}{61}\right)\) \(e\left(\frac{1}{122}\right)\) \(e\left(\frac{59}{122}\right)\)
\(\chi_{367}(30,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{149}{183}\right)\) \(e\left(\frac{56}{61}\right)\) \(e\left(\frac{115}{183}\right)\) \(e\left(\frac{31}{61}\right)\) \(e\left(\frac{134}{183}\right)\) \(e\left(\frac{48}{61}\right)\) \(e\left(\frac{27}{61}\right)\) \(e\left(\frac{51}{61}\right)\) \(e\left(\frac{59}{183}\right)\) \(e\left(\frac{65}{183}\right)\)
\(\chi_{367}(31,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{47}{183}\right)\) \(e\left(\frac{41}{61}\right)\) \(e\left(\frac{94}{183}\right)\) \(e\left(\frac{2}{61}\right)\) \(e\left(\frac{170}{183}\right)\) \(e\left(\frac{9}{61}\right)\) \(e\left(\frac{47}{61}\right)\) \(e\left(\frac{21}{61}\right)\) \(e\left(\frac{53}{183}\right)\) \(e\left(\frac{77}{183}\right)\)
\(\chi_{367}(32,\cdot)\) 367.g 183 Yes \(1\) \(1\) \(e\left(\frac{148}{183}\right)\) \(e\left(\frac{11}{61}\right)\) \(e\left(\frac{113}{183}\right)\) \(e\left(\frac{5}{61}\right)\) \(e\left(\frac{181}{183}\right)\) \(e\left(\frac{53}{61}\right)\) \(e\left(\frac{26}{61}\right)\) \(e\left(\frac{22}{61}\right)\) \(e\left(\frac{163}{183}\right)\) \(e\left(\frac{40}{183}\right)\)