Properties

Modulus $2280$
Structure \(C_{36}\times C_{2}\times C_{2}\times C_{2}\times C_{2}\)
Order $576$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2280)
 
pari: g = idealstar(,2280,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 576
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{2}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2280}(1711,\cdot)$, $\chi_{2280}(1141,\cdot)$, $\chi_{2280}(761,\cdot)$, $\chi_{2280}(457,\cdot)$, $\chi_{2280}(1921,\cdot)$

First 32 of 576 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{2280}(1,\cdot)\) 2280.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2280}(7,\cdot)\) 2280.dh 12 no \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2280}(11,\cdot)\) 2280.cd 6 no \(1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2280}(13,\cdot)\) 2280.fn 36 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{36}\right)\)
\(\chi_{2280}(17,\cdot)\) 2280.fg 36 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{2280}(23,\cdot)\) 2280.ff 36 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2280}(29,\cdot)\) 2280.en 18 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{2280}(31,\cdot)\) 2280.cc 6 no \(1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2280}(37,\cdot)\) 2280.bh 4 no \(1\) \(1\) \(i\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(-1\) \(i\)
\(\chi_{2280}(41,\cdot)\) 2280.ef 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2280}(43,\cdot)\) 2280.fe 36 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{2280}(47,\cdot)\) 2280.ff 36 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{2280}(49,\cdot)\) 2280.cm 6 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2280}(53,\cdot)\) 2280.fc 36 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2280}(59,\cdot)\) 2280.ea 18 yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{2280}(61,\cdot)\) 2280.eb 18 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{2280}(67,\cdot)\) 2280.ey 36 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{36}\right)\)
\(\chi_{2280}(71,\cdot)\) 2280.ei 18 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{2280}(73,\cdot)\) 2280.fb 36 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{2280}(77,\cdot)\) 2280.bp 4 no \(1\) \(1\) \(i\) \(1\) \(i\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(-1\) \(i\)
\(\chi_{2280}(79,\cdot)\) 2280.ec 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{2280}(83,\cdot)\) 2280.dj 12 yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2280}(89,\cdot)\) 2280.ew 18 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{2280}(91,\cdot)\) 2280.ek 18 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2280}(97,\cdot)\) 2280.fd 36 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{2280}(101,\cdot)\) 2280.dt 18 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{2280}(103,\cdot)\) 2280.dg 12 no \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2280}(107,\cdot)\) 2280.de 12 yes \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2280}(109,\cdot)\) 2280.eu 18 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2280}(113,\cdot)\) 2280.bj 4 no \(-1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(i\)
\(\chi_{2280}(119,\cdot)\) 2280.dx 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2280}(121,\cdot)\) 2280.bg 3 no \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)