# Properties

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

# Learn more

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 $$1$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$