# Properties

 Modulus 34 Structure $$C_{16}$$ Order 16

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(34)

pari: g = idealstar(,34,2)

## Character group

 sage: G.order()  pari: g.no Order = 16 sage: H.invariants()  pari: g.cyc Structure = $$C_{16}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{34}(3,\cdot)$

## 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.

orbit label order primitive -1 1 3 5 7 9 11 13 15 19 21 23
$$\chi_{34}(1,\cdot)$$ 34.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{34}(3,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{34}(5,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{34}(7,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{34}(9,\cdot)$$ 34.d 8 No $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{34}(11,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{34}(13,\cdot)$$ 34.c 4 No $$1$$ $$1$$ $$i$$ $$i$$ $$-i$$ $$-1$$ $$-i$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-i$$
$$\chi_{34}(15,\cdot)$$ 34.d 8 No $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{34}(19,\cdot)$$ 34.d 8 No $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{34}(21,\cdot)$$ 34.c 4 No $$1$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$i$$
$$\chi_{34}(23,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{34}(25,\cdot)$$ 34.d 8 No $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{34}(27,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{34}(29,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{34}(31,\cdot)$$ 34.e 16 No $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{34}(33,\cdot)$$ 34.b 2 No $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$