Properties

Modulus $265$
Structure \(C_{52}\times C_{4}\)
Order $208$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(265)
 
pari: g = idealstar(,265,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 208
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{52}\times C_{4}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{265}(107,\cdot)$, $\chi_{265}(161,\cdot)$

First 32 of 208 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{265}(1,\cdot)\) 265.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{265}(2,\cdot)\) 265.t 52 yes \(1\) \(1\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{11}{52}\right)\)
\(\chi_{265}(3,\cdot)\) 265.o 52 yes \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{5}{52}\right)\)
\(\chi_{265}(4,\cdot)\) 265.l 26 yes \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\)
\(\chi_{265}(6,\cdot)\) 265.m 26 no \(1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{265}(7,\cdot)\) 265.p 52 yes \(-1\) \(1\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{11}{52}\right)\)
\(\chi_{265}(8,\cdot)\) 265.t 52 yes \(1\) \(1\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{33}{52}\right)\)
\(\chi_{265}(9,\cdot)\) 265.l 26 yes \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\)
\(\chi_{265}(11,\cdot)\) 265.m 26 no \(1\) \(1\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{265}(12,\cdot)\) 265.o 52 yes \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{27}{52}\right)\)
\(\chi_{265}(13,\cdot)\) 265.q 52 yes \(-1\) \(1\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{17}{52}\right)\)
\(\chi_{265}(14,\cdot)\) 265.r 52 yes \(-1\) \(1\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{19}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{11}{26}\right)\)
\(\chi_{265}(16,\cdot)\) 265.k 13 no \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{265}(17,\cdot)\) 265.p 52 yes \(-1\) \(1\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{19}{52}\right)\)
\(\chi_{265}(18,\cdot)\) 265.t 52 yes \(1\) \(1\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{52}\right)\)
\(\chi_{265}(19,\cdot)\) 265.r 52 yes \(-1\) \(1\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{1}{52}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{265}(21,\cdot)\) 265.s 52 no \(-1\) \(1\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{265}(22,\cdot)\) 265.o 52 yes \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{51}{52}\right)\)
\(\chi_{265}(23,\cdot)\) 265.e 4 yes \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(i\) \(-1\) \(1\) \(-1\) \(1\) \(i\)
\(\chi_{265}(24,\cdot)\) 265.n 26 yes \(1\) \(1\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{265}(26,\cdot)\) 265.s 52 no \(-1\) \(1\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{265}(27,\cdot)\) 265.o 52 yes \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{15}{52}\right)\)
\(\chi_{265}(28,\cdot)\) 265.q 52 yes \(-1\) \(1\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{33}{52}\right)\)
\(\chi_{265}(29,\cdot)\) 265.l 26 yes \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{265}(31,\cdot)\) 265.s 52 no \(-1\) \(1\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{265}(32,\cdot)\) 265.t 52 yes \(1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{3}{52}\right)\)
\(\chi_{265}(33,\cdot)\) 265.t 52 yes \(1\) \(1\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{45}{52}\right)\)
\(\chi_{265}(34,\cdot)\) 265.r 52 yes \(-1\) \(1\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{5}{52}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{265}(36,\cdot)\) 265.k 13 no \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{265}(37,\cdot)\) 265.p 52 yes \(-1\) \(1\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{17}{52}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{52}\right)\) \(e\left(\frac{31}{52}\right)\)
\(\chi_{265}(38,\cdot)\) 265.p 52 yes \(-1\) \(1\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{23}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{41}{52}\right)\)
\(\chi_{265}(39,\cdot)\) 265.r 52 yes \(-1\) \(1\) \(e\left(\frac{15}{52}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{11}{26}\right)\)