Properties

 Modulus $210$ Structure $$C_{12}\times C_{2}\times C_{2}$$ Order $48$

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(210)

pari: g = idealstar(,210,2)

Character group

 sage: G.order()  pari: g.no Order = 48 sage: H.invariants()  pari: g.cyc Structure = $$C_{12}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{210}(73,\cdot)$, $\chi_{210}(139,\cdot)$, $\chi_{210}(71,\cdot)$

First 32 of 48 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{210}(1,\cdot)$$ 210.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{210}(11,\cdot)$$ 210.s 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$
$$\chi_{210}(13,\cdot)$$ 210.m 4 no $$1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{210}(17,\cdot)$$ 210.w 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$-i$$
$$\chi_{210}(19,\cdot)$$ 210.p 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$
$$\chi_{210}(23,\cdot)$$ 210.x 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{210}(29,\cdot)$$ 210.c 2 no $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{210}(31,\cdot)$$ 210.o 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$
$$\chi_{210}(37,\cdot)$$ 210.v 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-i$$
$$\chi_{210}(41,\cdot)$$ 210.b 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$
$$\chi_{210}(43,\cdot)$$ 210.l 4 no $$-1$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$
$$\chi_{210}(47,\cdot)$$ 210.w 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-i$$
$$\chi_{210}(53,\cdot)$$ 210.x 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{210}(59,\cdot)$$ 210.t 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$
$$\chi_{210}(61,\cdot)$$ 210.o 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$
$$\chi_{210}(67,\cdot)$$ 210.v 12 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$-i$$
$$\chi_{210}(71,\cdot)$$ 210.e 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{210}(73,\cdot)$$ 210.u 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{210}(79,\cdot)$$ 210.n 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$
$$\chi_{210}(83,\cdot)$$ 210.k 4 no $$-1$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$i$$
$$\chi_{210}(89,\cdot)$$ 210.t 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$
$$\chi_{210}(97,\cdot)$$ 210.m 4 no $$1$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{210}(101,\cdot)$$ 210.r 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$
$$\chi_{210}(103,\cdot)$$ 210.u 12 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{210}(107,\cdot)$$ 210.x 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-i$$
$$\chi_{210}(109,\cdot)$$ 210.n 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$
$$\chi_{210}(113,\cdot)$$ 210.j 4 no $$1$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{210}(121,\cdot)$$ 210.i 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$
$$\chi_{210}(127,\cdot)$$ 210.l 4 no $$-1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$1$$ $$-i$$
$$\chi_{210}(131,\cdot)$$ 210.r 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$
$$\chi_{210}(137,\cdot)$$ 210.x 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$-i$$
$$\chi_{210}(139,\cdot)$$ 210.h 2 no $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$