Properties

Modulus $177$
Structure \(C_{58}\times C_{2}\)
Order $116$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(177)
 
pari: g = idealstar(,177,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 116
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{58}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{177}(119,\cdot)$, $\chi_{177}(61,\cdot)$

First 32 of 116 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{177}(1,\cdot)\) 177.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{177}(2,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{2}{29}\right)\)
\(\chi_{177}(4,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{4}{29}\right)\)
\(\chi_{177}(5,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{27}{58}\right)\) \(e\left(\frac{12}{29}\right)\)
\(\chi_{177}(7,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{7}{29}\right)\)
\(\chi_{177}(8,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{6}{29}\right)\)
\(\chi_{177}(10,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{14}{29}\right)\)
\(\chi_{177}(11,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{21}{29}\right)\)
\(\chi_{177}(13,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{3}{29}\right)\)
\(\chi_{177}(14,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{27}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{9}{29}\right)\)
\(\chi_{177}(16,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{8}{29}\right)\)
\(\chi_{177}(17,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{11}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{22}{29}\right)\)
\(\chi_{177}(19,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{18}{29}\right)\)
\(\chi_{177}(20,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{16}{29}\right)\)
\(\chi_{177}(22,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{23}{29}\right)\)
\(\chi_{177}(23,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{1}{29}\right)\)
\(\chi_{177}(25,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{24}{29}\right)\)
\(\chi_{177}(26,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{5}{29}\right)\)
\(\chi_{177}(28,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{11}{29}\right)\)
\(\chi_{177}(29,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{23}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{27}{29}\right)\)
\(\chi_{177}(31,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{6}{29}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{3}{58}\right)\) \(e\left(\frac{11}{29}\right)\)
\(\chi_{177}(32,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{17}{29}\right)\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{22}{29}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{10}{29}\right)\)
\(\chi_{177}(34,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{21}{29}\right)\) \(e\left(\frac{7}{58}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{25}{58}\right)\) \(e\left(\frac{24}{29}\right)\)
\(\chi_{177}(35,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{53}{58}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{13}{29}\right)\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{18}{29}\right)\) \(e\left(\frac{21}{58}\right)\) \(e\left(\frac{19}{29}\right)\)
\(\chi_{177}(37,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{2}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{37}{58}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{39}{58}\right)\) \(e\left(\frac{1}{58}\right)\) \(e\left(\frac{23}{29}\right)\)
\(\chi_{177}(38,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{5}{29}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{3}{29}\right)\) \(e\left(\frac{15}{29}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{20}{29}\right)\)
\(\chi_{177}(40,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{9}{58}\right)\) \(e\left(\frac{9}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{27}{58}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{18}{29}\right)\)
\(\chi_{177}(41,\cdot)\) 177.h 58 yes \(-1\) \(1\) \(e\left(\frac{43}{58}\right)\) \(e\left(\frac{14}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{31}{58}\right)\) \(e\left(\frac{25}{29}\right)\) \(e\left(\frac{5}{58}\right)\) \(e\left(\frac{28}{29}\right)\)
\(\chi_{177}(43,\cdot)\) 177.g 58 no \(-1\) \(1\) \(e\left(\frac{33}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{41}{58}\right)\) \(e\left(\frac{57}{58}\right)\) \(e\left(\frac{13}{58}\right)\) \(e\left(\frac{35}{58}\right)\) \(e\left(\frac{47}{58}\right)\) \(e\left(\frac{8}{29}\right)\)
\(\chi_{177}(44,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{17}{58}\right)\) \(e\left(\frac{11}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{15}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{55}{58}\right)\) \(e\left(\frac{10}{29}\right)\) \(e\left(\frac{25}{29}\right)\)
\(\chi_{177}(46,\cdot)\) 177.e 29 no \(1\) \(1\) \(e\left(\frac{8}{29}\right)\) \(e\left(\frac{16}{29}\right)\) \(e\left(\frac{19}{29}\right)\) \(e\left(\frac{28}{29}\right)\) \(e\left(\frac{24}{29}\right)\) \(e\left(\frac{27}{29}\right)\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{7}{29}\right)\) \(e\left(\frac{3}{29}\right)\)
\(\chi_{177}(47,\cdot)\) 177.f 58 yes \(1\) \(1\) \(e\left(\frac{26}{29}\right)\) \(e\left(\frac{23}{29}\right)\) \(e\left(\frac{51}{58}\right)\) \(e\left(\frac{4}{29}\right)\) \(e\left(\frac{20}{29}\right)\) \(e\left(\frac{45}{58}\right)\) \(e\left(\frac{12}{29}\right)\) \(e\left(\frac{49}{58}\right)\) \(e\left(\frac{1}{29}\right)\) \(e\left(\frac{17}{29}\right)\)