# Properties

 Modulus $191$ Structure $$C_{190}$$ Order $190$

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(191)

pari: g = idealstar(,191,2)

## Character group

 sage: G.order()  pari: g.no Order = 190 sage: H.invariants()  pari: g.cyc Structure = $$C_{190}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{191}(19,\cdot)$

## First 32 of 190 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$
$$\chi_{191}(1,\cdot)$$ 191.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{191}(2,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{18}{95}\right)$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{54}{95}\right)$$ $$e\left(\frac{69}{95}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$
$$\chi_{191}(3,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{78}{95}\right)$$ $$e\left(\frac{69}{95}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{56}{95}\right)$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{37}{95}\right)$$ $$e\left(\frac{17}{19}\right)$$
$$\chi_{191}(4,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{69}{95}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{191}(5,\cdot)$$ 191.e 19 yes $$1$$ $$1$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$1$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{191}(6,\cdot)$$ 191.e 19 yes $$1$$ $$1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$1$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$
$$\chi_{191}(7,\cdot)$$ 191.d 10 yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$
$$\chi_{191}(8,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{54}{95}\right)$$ $$e\left(\frac{56}{95}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{67}{95}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{191}(9,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{69}{95}\right)$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{27}{95}\right)$$ $$e\left(\frac{74}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{191}(10,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{37}{95}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{95}\right)$$ $$e\left(\frac{74}{95}\right)$$ $$e\left(\frac{48}{95}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{191}(11,\cdot)$$ 191.f 38 yes $$-1$$ $$1$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$-1$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{38}\right)$$
$$\chi_{191}(12,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{23}{95}\right)$$ $$e\left(\frac{52}{95}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{69}{95}\right)$$ $$e\left(\frac{9}{95}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{191}(13,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{89}{95}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{77}{95}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{39}{95}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{191}(14,\cdot)$$ 191.f 38 yes $$-1$$ $$1$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$-1$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{7}{38}\right)$$
$$\chi_{191}(15,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{33}{95}\right)$$ $$e\left(\frac{84}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{31}{95}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{12}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$
$$\chi_{191}(16,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{43}{95}\right)$$ $$e\left(\frac{49}{95}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{26}{95}\right)$$ $$e\left(\frac{86}{95}\right)$$ $$e\left(\frac{7}{95}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{191}(17,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{37}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{95}\right)$$ $$e\left(\frac{63}{95}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{191}(18,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{87}{95}\right)$$ $$e\left(\frac{48}{95}\right)$$ $$e\left(\frac{79}{95}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{1}{95}\right)$$ $$e\left(\frac{52}{95}\right)$$ $$e\left(\frac{9}{19}\right)$$
$$\chi_{191}(19,\cdot)$$ 191.h 190 yes $$-1$$ $$1$$ $$e\left(\frac{22}{95}\right)$$ $$e\left(\frac{58}{95}\right)$$ $$e\left(\frac{44}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{47}{95}\right)$$ $$e\left(\frac{17}{38}\right)$$
$$\chi_{191}(20,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{91}{95}\right)$$ $$e\left(\frac{24}{95}\right)$$ $$e\left(\frac{87}{95}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{48}{95}\right)$$ $$e\left(\frac{26}{95}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{191}(21,\cdot)$$ 191.h 190 yes $$-1$$ $$1$$ $$e\left(\frac{44}{95}\right)$$ $$e\left(\frac{21}{95}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{37}{95}\right)$$ $$e\left(\frac{42}{95}\right)$$ $$e\left(\frac{94}{95}\right)$$ $$e\left(\frac{15}{38}\right)$$
$$\chi_{191}(22,\cdot)$$ 191.h 190 yes $$-1$$ $$1$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{71}{95}\right)$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{49}{95}\right)$$ $$e\left(\frac{78}{95}\right)$$ $$e\left(\frac{27}{38}\right)$$
$$\chi_{191}(23,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{3}{95}\right)$$ $$e\left(\frac{77}{95}\right)$$ $$e\left(\frac{6}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{95}\right)$$ $$e\left(\frac{59}{95}\right)$$ $$e\left(\frac{28}{95}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{191}(24,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{41}{95}\right)$$ $$e\left(\frac{39}{95}\right)$$ $$e\left(\frac{82}{95}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{28}{95}\right)$$ $$e\left(\frac{78}{95}\right)$$ $$e\left(\frac{66}{95}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{191}(25,\cdot)$$ 191.e 19 yes $$1$$ $$1$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$1$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{191}(26,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{12}{95}\right)$$ $$e\left(\frac{23}{95}\right)$$ $$e\left(\frac{24}{95}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{36}{95}\right)$$ $$e\left(\frac{46}{95}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{15}{19}\right)$$
$$\chi_{191}(27,\cdot)$$ 191.g 95 yes $$1$$ $$1$$ $$e\left(\frac{56}{95}\right)$$ $$e\left(\frac{44}{95}\right)$$ $$e\left(\frac{17}{95}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{73}{95}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{16}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$
$$\chi_{191}(28,\cdot)$$ 191.h 190 yes $$-1$$ $$1$$ $$e\left(\frac{93}{95}\right)$$ $$e\left(\frac{12}{95}\right)$$ $$e\left(\frac{91}{95}\right)$$ $$e\left(\frac{3}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{89}{95}\right)$$ $$e\left(\frac{24}{95}\right)$$ $$e\left(\frac{13}{95}\right)$$ $$e\left(\frac{33}{38}\right)$$
$$\chi_{191}(29,\cdot)$$ 191.h 190 yes $$-1$$ $$1$$ $$e\left(\frac{61}{95}\right)$$ $$e\left(\frac{14}{95}\right)$$ $$e\left(\frac{27}{95}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{88}{95}\right)$$ $$e\left(\frac{28}{95}\right)$$ $$e\left(\frac{31}{95}\right)$$ $$e\left(\frac{29}{38}\right)$$
$$\chi_{191}(30,\cdot)$$ 191.e 19 yes $$1$$ $$1$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$1$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{18}{19}\right)$$
$$\chi_{191}(31,\cdot)$$ 191.f 38 yes $$-1$$ $$1$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$-1$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{11}{38}\right)$$
$$\chi_{191}(32,\cdot)$$ 191.e 19 yes $$1$$ $$1$$ $$e\left(\frac{18}{19}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$1$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{16}{19}\right)$$ $$e\left(\frac{8}{19}\right)$$