Properties

Modulus $361$
Structure \(C_{342}\)
Order $342$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(361)
 
pari: g = idealstar(,361,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 342
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{342}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{361}(2,\cdot)$

First 32 of 342 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{361}(1,\cdot)\) 361.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{361}(2,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{1}{342}\right)\) \(e\left(\frac{139}{342}\right)\) \(e\left(\frac{1}{171}\right)\) \(e\left(\frac{116}{171}\right)\) \(e\left(\frac{70}{171}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{139}{171}\right)\) \(e\left(\frac{233}{342}\right)\) \(e\left(\frac{17}{57}\right)\)
\(\chi_{361}(3,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{139}{342}\right)\) \(e\left(\frac{169}{342}\right)\) \(e\left(\frac{139}{171}\right)\) \(e\left(\frac{50}{171}\right)\) \(e\left(\frac{154}{171}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{169}{171}\right)\) \(e\left(\frac{239}{342}\right)\) \(e\left(\frac{26}{57}\right)\)
\(\chi_{361}(4,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{1}{171}\right)\) \(e\left(\frac{139}{171}\right)\) \(e\left(\frac{2}{171}\right)\) \(e\left(\frac{61}{171}\right)\) \(e\left(\frac{140}{171}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{107}{171}\right)\) \(e\left(\frac{62}{171}\right)\) \(e\left(\frac{34}{57}\right)\)
\(\chi_{361}(5,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{116}{171}\right)\) \(e\left(\frac{50}{171}\right)\) \(e\left(\frac{61}{171}\right)\) \(e\left(\frac{65}{171}\right)\) \(e\left(\frac{166}{171}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{100}{171}\right)\) \(e\left(\frac{10}{171}\right)\) \(e\left(\frac{11}{57}\right)\)
\(\chi_{361}(6,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{70}{171}\right)\) \(e\left(\frac{154}{171}\right)\) \(e\left(\frac{140}{171}\right)\) \(e\left(\frac{166}{171}\right)\) \(e\left(\frac{53}{171}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{137}{171}\right)\) \(e\left(\frac{65}{171}\right)\) \(e\left(\frac{43}{57}\right)\)
\(\chi_{361}(7,\cdot)\) 361.i 57 yes \(1\) \(1\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{23}{57}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{14}{19}\right)\)
\(\chi_{361}(8,\cdot)\) 361.j 114 yes \(-1\) \(1\) \(e\left(\frac{1}{114}\right)\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{1}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{6}{19}\right)\) \(e\left(\frac{1}{38}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{17}{19}\right)\)
\(\chi_{361}(9,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{139}{171}\right)\) \(e\left(\frac{169}{171}\right)\) \(e\left(\frac{107}{171}\right)\) \(e\left(\frac{100}{171}\right)\) \(e\left(\frac{137}{171}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{167}{171}\right)\) \(e\left(\frac{68}{171}\right)\) \(e\left(\frac{52}{57}\right)\)
\(\chi_{361}(10,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{233}{342}\right)\) \(e\left(\frac{239}{342}\right)\) \(e\left(\frac{62}{171}\right)\) \(e\left(\frac{10}{171}\right)\) \(e\left(\frac{65}{171}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{68}{171}\right)\) \(e\left(\frac{253}{342}\right)\) \(e\left(\frac{28}{57}\right)\)
\(\chi_{361}(11,\cdot)\) 361.i 57 yes \(1\) \(1\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{34}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{52}{57}\right)\) \(e\left(\frac{28}{57}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{361}(12,\cdot)\) 361.j 114 yes \(-1\) \(1\) \(e\left(\frac{47}{114}\right)\) \(e\left(\frac{35}{114}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{37}{57}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{16}{19}\right)\) \(e\left(\frac{9}{38}\right)\) \(e\left(\frac{35}{57}\right)\) \(e\left(\frac{7}{114}\right)\) \(e\left(\frac{1}{19}\right)\)
\(\chi_{361}(13,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{329}{342}\right)\) \(e\left(\frac{245}{342}\right)\) \(e\left(\frac{158}{171}\right)\) \(e\left(\frac{31}{171}\right)\) \(e\left(\frac{116}{171}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{74}{171}\right)\) \(e\left(\frac{49}{342}\right)\) \(e\left(\frac{7}{57}\right)\)
\(\chi_{361}(14,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{151}{342}\right)\) \(e\left(\frac{127}{342}\right)\) \(e\left(\frac{151}{171}\right)\) \(e\left(\frac{74}{171}\right)\) \(e\left(\frac{139}{171}\right)\) \(e\left(\frac{13}{57}\right)\) \(e\left(\frac{37}{114}\right)\) \(e\left(\frac{127}{171}\right)\) \(e\left(\frac{299}{342}\right)\) \(e\left(\frac{2}{57}\right)\)
\(\chi_{361}(15,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{29}{342}\right)\) \(e\left(\frac{269}{342}\right)\) \(e\left(\frac{29}{171}\right)\) \(e\left(\frac{115}{171}\right)\) \(e\left(\frac{149}{171}\right)\) \(e\left(\frac{41}{57}\right)\) \(e\left(\frac{29}{114}\right)\) \(e\left(\frac{98}{171}\right)\) \(e\left(\frac{259}{342}\right)\) \(e\left(\frac{37}{57}\right)\)
\(\chi_{361}(16,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{2}{171}\right)\) \(e\left(\frac{107}{171}\right)\) \(e\left(\frac{4}{171}\right)\) \(e\left(\frac{122}{171}\right)\) \(e\left(\frac{109}{171}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{43}{171}\right)\) \(e\left(\frac{124}{171}\right)\) \(e\left(\frac{11}{57}\right)\)
\(\chi_{361}(17,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{113}{171}\right)\) \(e\left(\frac{146}{171}\right)\) \(e\left(\frac{55}{171}\right)\) \(e\left(\frac{53}{171}\right)\) \(e\left(\frac{88}{171}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{56}{57}\right)\) \(e\left(\frac{121}{171}\right)\) \(e\left(\frac{166}{171}\right)\) \(e\left(\frac{23}{57}\right)\)
\(\chi_{361}(18,\cdot)\) 361.h 38 yes \(-1\) \(1\) \(e\left(\frac{31}{38}\right)\) \(e\left(\frac{15}{38}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{17}{38}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{3}{38}\right)\) \(e\left(\frac{4}{19}\right)\)
\(\chi_{361}(20,\cdot)\) 361.g 19 yes \(1\) \(1\) \(e\left(\frac{13}{19}\right)\) \(e\left(\frac{2}{19}\right)\) \(e\left(\frac{7}{19}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{15}{19}\right)\) \(e\left(\frac{12}{19}\right)\) \(e\left(\frac{1}{19}\right)\) \(e\left(\frac{4}{19}\right)\) \(e\left(\frac{8}{19}\right)\) \(e\left(\frac{15}{19}\right)\)
\(\chi_{361}(21,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{289}{342}\right)\) \(e\left(\frac{157}{342}\right)\) \(e\left(\frac{118}{171}\right)\) \(e\left(\frac{8}{171}\right)\) \(e\left(\frac{52}{171}\right)\) \(e\left(\frac{43}{57}\right)\) \(e\left(\frac{61}{114}\right)\) \(e\left(\frac{157}{171}\right)\) \(e\left(\frac{305}{342}\right)\) \(e\left(\frac{11}{57}\right)\)
\(\chi_{361}(22,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{103}{342}\right)\) \(e\left(\frac{295}{342}\right)\) \(e\left(\frac{103}{171}\right)\) \(e\left(\frac{149}{171}\right)\) \(e\left(\frac{28}{171}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{103}{114}\right)\) \(e\left(\frac{124}{171}\right)\) \(e\left(\frac{59}{342}\right)\) \(e\left(\frac{41}{57}\right)\)
\(\chi_{361}(23,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{73}{171}\right)\) \(e\left(\frac{58}{171}\right)\) \(e\left(\frac{146}{171}\right)\) \(e\left(\frac{7}{171}\right)\) \(e\left(\frac{131}{171}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{116}{171}\right)\) \(e\left(\frac{80}{171}\right)\) \(e\left(\frac{31}{57}\right)\)
\(\chi_{361}(24,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{71}{171}\right)\) \(e\left(\frac{122}{171}\right)\) \(e\left(\frac{142}{171}\right)\) \(e\left(\frac{56}{171}\right)\) \(e\left(\frac{22}{171}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{73}{171}\right)\) \(e\left(\frac{127}{171}\right)\) \(e\left(\frac{20}{57}\right)\)
\(\chi_{361}(25,\cdot)\) 361.k 171 yes \(1\) \(1\) \(e\left(\frac{61}{171}\right)\) \(e\left(\frac{100}{171}\right)\) \(e\left(\frac{122}{171}\right)\) \(e\left(\frac{130}{171}\right)\) \(e\left(\frac{161}{171}\right)\) \(e\left(\frac{29}{57}\right)\) \(e\left(\frac{4}{57}\right)\) \(e\left(\frac{29}{171}\right)\) \(e\left(\frac{20}{171}\right)\) \(e\left(\frac{22}{57}\right)\)
\(\chi_{361}(26,\cdot)\) 361.i 57 yes \(1\) \(1\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{7}{57}\right)\) \(e\left(\frac{53}{57}\right)\) \(e\left(\frac{49}{57}\right)\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{14}{19}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{14}{57}\right)\) \(e\left(\frac{47}{57}\right)\) \(e\left(\frac{8}{19}\right)\)
\(\chi_{361}(27,\cdot)\) 361.j 114 yes \(-1\) \(1\) \(e\left(\frac{25}{114}\right)\) \(e\left(\frac{55}{114}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{50}{57}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{55}{57}\right)\) \(e\left(\frac{11}{114}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{361}(28,\cdot)\) 361.e 9 no \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{361}(29,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{17}{342}\right)\) \(e\left(\frac{311}{342}\right)\) \(e\left(\frac{17}{171}\right)\) \(e\left(\frac{91}{171}\right)\) \(e\left(\frac{164}{171}\right)\) \(e\left(\frac{26}{57}\right)\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{140}{171}\right)\) \(e\left(\frac{199}{342}\right)\) \(e\left(\frac{4}{57}\right)\)
\(\chi_{361}(30,\cdot)\) 361.i 57 yes \(1\) \(1\) \(e\left(\frac{5}{57}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{10}{57}\right)\) \(e\left(\frac{20}{57}\right)\) \(e\left(\frac{16}{57}\right)\) \(e\left(\frac{3}{19}\right)\) \(e\left(\frac{5}{19}\right)\) \(e\left(\frac{22}{57}\right)\) \(e\left(\frac{25}{57}\right)\) \(e\left(\frac{18}{19}\right)\)
\(\chi_{361}(31,\cdot)\) 361.j 114 yes \(-1\) \(1\) \(e\left(\frac{101}{114}\right)\) \(e\left(\frac{17}{114}\right)\) \(e\left(\frac{44}{57}\right)\) \(e\left(\frac{31}{57}\right)\) \(e\left(\frac{2}{57}\right)\) \(e\left(\frac{17}{19}\right)\) \(e\left(\frac{25}{38}\right)\) \(e\left(\frac{17}{57}\right)\) \(e\left(\frac{49}{114}\right)\) \(e\left(\frac{7}{19}\right)\)
\(\chi_{361}(32,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{5}{342}\right)\) \(e\left(\frac{11}{342}\right)\) \(e\left(\frac{5}{171}\right)\) \(e\left(\frac{67}{171}\right)\) \(e\left(\frac{8}{171}\right)\) \(e\left(\frac{11}{57}\right)\) \(e\left(\frac{5}{114}\right)\) \(e\left(\frac{11}{171}\right)\) \(e\left(\frac{139}{342}\right)\) \(e\left(\frac{28}{57}\right)\)
\(\chi_{361}(33,\cdot)\) 361.l 342 yes \(-1\) \(1\) \(e\left(\frac{241}{342}\right)\) \(e\left(\frac{325}{342}\right)\) \(e\left(\frac{70}{171}\right)\) \(e\left(\frac{83}{171}\right)\) \(e\left(\frac{112}{171}\right)\) \(e\left(\frac{40}{57}\right)\) \(e\left(\frac{13}{114}\right)\) \(e\left(\frac{154}{171}\right)\) \(e\left(\frac{65}{342}\right)\) \(e\left(\frac{50}{57}\right)\)
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