# Properties

 Modulus 64 Structure $$C_{16}\times C_{2}$$ Order 32

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(64)

pari: g = idealstar(,64,2)

## Character group

 sage: G.order()  pari: g.no Order = 32 sage: H.invariants()  pari: g.cyc Structure = $$C_{16}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{64}(5,\cdot)$, $\chi_{64}(63,\cdot)$

## First 32 of 32 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 17 19 21
$$\chi_{64}(1,\cdot)$$ 64.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{64}(3,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{64}(5,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{64}(7,\cdot)$$ 64.h 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{64}(9,\cdot)$$ 64.g 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{64}(11,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{64}(13,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{64}(15,\cdot)$$ 64.f 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$i$$
$$\chi_{64}(17,\cdot)$$ 64.e 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$i$$ $$-i$$
$$\chi_{64}(19,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{64}(21,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{64}(23,\cdot)$$ 64.h 8 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{64}(25,\cdot)$$ 64.g 8 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{64}(27,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{64}(29,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{64}(31,\cdot)$$ 64.d 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{64}(33,\cdot)$$ 64.b 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{64}(35,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{64}(37,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{64}(39,\cdot)$$ 64.h 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{64}(41,\cdot)$$ 64.g 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{64}(43,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{64}(45,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{64}(47,\cdot)$$ 64.f 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$-i$$
$$\chi_{64}(49,\cdot)$$ 64.e 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$1$$ $$-i$$ $$i$$
$$\chi_{64}(51,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{64}(53,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{64}(55,\cdot)$$ 64.h 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{64}(57,\cdot)$$ 64.g 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{64}(59,\cdot)$$ 64.j 16 yes $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{64}(61,\cdot)$$ 64.i 16 yes $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{64}(63,\cdot)$$ 64.c 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$