Properties

Modulus $273$
Structure \(C_{12}\times C_{6}\times C_{2}\)
Order $144$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(273)
 
pari: g = idealstar(,273,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 144
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{273}(92,\cdot)$, $\chi_{273}(157,\cdot)$, $\chi_{273}(106,\cdot)$

First 32 of 144 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{273}(1,\cdot)\) 273.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{273}(2,\cdot)\) 273.bv 12 yes \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{273}(4,\cdot)\) 273.t 6 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{273}(5,\cdot)\) 273.cb 12 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\)
\(\chi_{273}(8,\cdot)\) 273.n 4 no \(1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(i\)
\(\chi_{273}(10,\cdot)\) 273.bg 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{273}(11,\cdot)\) 273.bw 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(-1\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{273}(16,\cdot)\) 273.l 3 no \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{273}(17,\cdot)\) 273.br 6 yes \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{273}(19,\cdot)\) 273.cg 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{273}(20,\cdot)\) 273.ca 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{273}(22,\cdot)\) 273.k 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{273}(23,\cdot)\) 273.bp 6 yes \(-1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{273}(25,\cdot)\) 273.bj 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)
\(\chi_{273}(29,\cdot)\) 273.be 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{273}(31,\cdot)\) 273.bz 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\)
\(\chi_{273}(32,\cdot)\) 273.bv 12 yes \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{273}(34,\cdot)\) 273.p 4 no \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(1\) \(-i\) \(1\) \(1\) \(-i\) \(i\)
\(\chi_{273}(37,\cdot)\) 273.bu 12 no \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{273}(38,\cdot)\) 273.ba 6 yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{273}(40,\cdot)\) 273.bb 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)
\(\chi_{273}(41,\cdot)\) 273.ca 12 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{273}(43,\cdot)\) 273.bd 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{273}(44,\cdot)\) 273.cd 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\)
\(\chi_{273}(46,\cdot)\) 273.bu 12 no \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{273}(47,\cdot)\) 273.cb 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\)
\(\chi_{273}(50,\cdot)\) 273.cc 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{273}(53,\cdot)\) 273.bk 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{273}(55,\cdot)\) 273.v 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{273}(58,\cdot)\) 273.bx 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(-1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{273}(59,\cdot)\) 273.bs 12 yes \(-1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{273}(61,\cdot)\) 273.z 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)