# Properties

 Modulus 29 Structure $$C_{28}$$ Order 28

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(29)

pari: g = idealstar(,29,2)

## Character group

 sage: G.order()  pari: g.no Order = 28 sage: H.invariants()  pari: g.cyc Structure = $$C_{28}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{29}(2,\cdot)$

## 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 2 3 4 5 6 7 8 9 10 11
$$\chi_{29}(1,\cdot)$$ 29.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{29}(2,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$
$$\chi_{29}(3,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{29}(4,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{29}(5,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{29}(6,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$
$$\chi_{29}(7,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{29}(8,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{29}(9,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{29}(10,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{29}(11,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{29}(12,\cdot)$$ 29.c 4 yes $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$
$$\chi_{29}(13,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{29}(14,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{29}(15,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{29}(16,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{29}(17,\cdot)$$ 29.c 4 yes $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$
$$\chi_{29}(18,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{29}(19,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$
$$\chi_{29}(20,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{29}(21,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$
$$\chi_{29}(22,\cdot)$$ 29.e 14 yes $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{29}(23,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{29}(24,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{29}(25,\cdot)$$ 29.d 7 yes $$1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{29}(26,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{29}(27,\cdot)$$ 29.f 28 yes $$-1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{29}(28,\cdot)$$ 29.b 2 yes $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$