Properties

Modulus 224
Structure \(C_{24}\times C_{2}\times C_{2}\)
Order 96

Learn more about

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(224)
 
pari: g = idealstar(,224,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{24}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{224}(5,\cdot)$, $\chi_{224}(209,\cdot)$, $\chi_{224}(127,\cdot)$

First 32 of 96 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 3 5 9 11 13 15 17 19 23 25
\(\chi_{224}(1,\cdot)\) 224.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{224}(3,\cdot)\) 224.be 24 yes \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{224}(5,\cdot)\) 224.bc 24 yes \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{224}(9,\cdot)\) 224.ba 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{224}(11,\cdot)\) 224.bf 24 yes \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{224}(13,\cdot)\) 224.v 8 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\)
\(\chi_{224}(15,\cdot)\) 224.g 2 no \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{224}(17,\cdot)\) 224.n 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{224}(19,\cdot)\) 224.be 24 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{224}(23,\cdot)\) 224.y 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{224}(25,\cdot)\) 224.ba 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{224}(27,\cdot)\) 224.x 8 yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\)
\(\chi_{224}(29,\cdot)\) 224.u 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\)
\(\chi_{224}(31,\cdot)\) 224.p 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{224}(33,\cdot)\) 224.s 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{224}(37,\cdot)\) 224.bd 24 yes \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{224}(39,\cdot)\) 224.y 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{224}(41,\cdot)\) 224.l 4 no \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(-i\) \(1\) \(-1\) \(-i\) \(-1\) \(-1\)
\(\chi_{224}(43,\cdot)\) 224.w 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\)
\(\chi_{224}(45,\cdot)\) 224.bc 24 yes \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{224}(47,\cdot)\) 224.q 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{224}(51,\cdot)\) 224.bf 24 yes \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{224}(53,\cdot)\) 224.bd 24 yes \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{224}(55,\cdot)\) 224.j 4 no \(1\) \(1\) \(i\) \(i\) \(-1\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(-1\)
\(\chi_{224}(57,\cdot)\) 224.m 4 no \(1\) \(1\) \(-i\) \(i\) \(-1\) \(i\) \(-i\) \(1\) \(1\) \(-i\) \(-1\) \(-1\)
\(\chi_{224}(59,\cdot)\) 224.be 24 yes \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{224}(61,\cdot)\) 224.bc 24 yes \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{224}(65,\cdot)\) 224.i 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{224}(67,\cdot)\) 224.bf 24 yes \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{224}(69,\cdot)\) 224.v 8 yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(i\)
\(\chi_{224}(71,\cdot)\) 224.k 4 no \(-1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(1\) \(i\) \(1\) \(-1\)
\(\chi_{224}(73,\cdot)\) 224.bb 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)