# Properties

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

Show commands: PariGP / SageMath

sage: H = DirichletGroup(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.

Character Orbit 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 $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$