Properties

Modulus $280$
Structure \(C_{12}\times C_{2}\times C_{2}\times C_{2}\)
Order $96$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(280)
 
pari: g = idealstar(,280,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{280}(71,\cdot)$, $\chi_{280}(141,\cdot)$, $\chi_{280}(57,\cdot)$, $\chi_{280}(241,\cdot)$

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.

Character Orbit Order Primitive \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{280}(1,\cdot)\) 280.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{280}(3,\cdot)\) 280.bp 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(9,\cdot)\) 280.bg 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{280}(11,\cdot)\) 280.z 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{280}(13,\cdot)\) 280.s 4 yes \(1\) \(1\) \(i\) \(-1\) \(-1\) \(i\) \(i\) \(-1\) \(i\) \(-i\) \(1\) \(-1\)
\(\chi_{280}(17,\cdot)\) 280.bo 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{280}(19,\cdot)\) 280.ba 6 yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{280}(23,\cdot)\) 280.bs 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(27,\cdot)\) 280.y 4 yes \(-1\) \(1\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(1\) \(i\) \(-i\) \(1\) \(1\)
\(\chi_{280}(29,\cdot)\) 280.l 2 no \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{280}(31,\cdot)\) 280.bc 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(33,\cdot)\) 280.bo 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(37,\cdot)\) 280.bt 12 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{280}(39,\cdot)\) 280.bd 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{280}(41,\cdot)\) 280.f 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{280}(43,\cdot)\) 280.w 4 no \(1\) \(1\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-i\) \(-i\) \(1\) \(-1\)
\(\chi_{280}(47,\cdot)\) 280.bu 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{280}(51,\cdot)\) 280.z 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(53,\cdot)\) 280.bt 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(57,\cdot)\) 280.v 4 no \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(i\) \(-1\) \(1\)
\(\chi_{280}(59,\cdot)\) 280.ba 6 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(61,\cdot)\) 280.be 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(67,\cdot)\) 280.br 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{280}(69,\cdot)\) 280.c 2 yes \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\)
\(\chi_{280}(71,\cdot)\) 280.d 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\)
\(\chi_{280}(73,\cdot)\) 280.bo 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{280}(79,\cdot)\) 280.bd 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(81,\cdot)\) 280.q 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(83,\cdot)\) 280.y 4 yes \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(i\) \(i\) \(1\) \(-i\) \(i\) \(1\) \(1\)
\(\chi_{280}(87,\cdot)\) 280.bu 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{280}(89,\cdot)\) 280.bb 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{280}(93,\cdot)\) 280.bt 12 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{3}\right)\)