Properties

Modulus $276$
Structure \(C_{22}\times C_{2}\times C_{2}\)
Order $88$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(276)
 
pari: g = idealstar(,276,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 88
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{22}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{276}(139,\cdot)$, $\chi_{276}(185,\cdot)$, $\chi_{276}(97,\cdot)$

First 32 of 88 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{276}(1,\cdot)\) 276.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{276}(5,\cdot)\) 276.k 22 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{276}(7,\cdot)\) 276.m 22 no \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{276}(11,\cdot)\) 276.j 22 yes \(-1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{276}(13,\cdot)\) 276.i 11 no \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{276}(17,\cdot)\) 276.k 22 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{276}(19,\cdot)\) 276.m 22 no \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{276}(25,\cdot)\) 276.i 11 no \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{276}(29,\cdot)\) 276.n 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{276}(31,\cdot)\) 276.l 22 no \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{276}(35,\cdot)\) 276.o 22 yes \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{276}(37,\cdot)\) 276.p 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{276}(41,\cdot)\) 276.n 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{276}(43,\cdot)\) 276.m 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{276}(47,\cdot)\) 276.c 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{276}(49,\cdot)\) 276.i 11 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{276}(53,\cdot)\) 276.k 22 no \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{276}(55,\cdot)\) 276.l 22 no \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{276}(59,\cdot)\) 276.o 22 yes \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{276}(61,\cdot)\) 276.p 22 no \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{276}(65,\cdot)\) 276.k 22 no \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{276}(67,\cdot)\) 276.m 22 no \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{276}(71,\cdot)\) 276.o 22 yes \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{276}(73,\cdot)\) 276.i 11 no \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{276}(77,\cdot)\) 276.n 22 no \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{276}(79,\cdot)\) 276.m 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{276}(83,\cdot)\) 276.j 22 yes \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{276}(85,\cdot)\) 276.i 11 no \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{276}(89,\cdot)\) 276.k 22 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{276}(91,\cdot)\) 276.e 2 no \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{276}(95,\cdot)\) 276.o 22 yes \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{276}(97,\cdot)\) 276.p 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{11}\right)\)