# Properties

 Modulus 187 Structure $$C_{80}\times C_{2}$$ Order 160

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(187)

pari: g = idealstar(,187,2)

## Character group

 sage: G.order()  pari: g.no Order = 160 sage: H.invariants()  pari: g.cyc Structure = $$C_{80}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{187}(105,\cdot)$, $\chi_{187}(120,\cdot)$

## First 32 of 160 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 12
$$\chi_{187}(1,\cdot)$$ 187.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{187}(2,\cdot)$$ 187.q 40 yes $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{187}(3,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{187}(4,\cdot)$$ 187.p 20 yes $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$-i$$
$$\chi_{187}(5,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{187}(6,\cdot)$$ 187.t 80 yes $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{187}(7,\cdot)$$ 187.t 80 yes $$1$$ $$1$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{187}(8,\cdot)$$ 187.q 40 yes $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{187}(9,\cdot)$$ 187.r 40 yes $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{187}(10,\cdot)$$ 187.m 16 yes $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{187}(12,\cdot)$$ 187.n 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{187}(13,\cdot)$$ 187.o 20 yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$i$$
$$\chi_{187}(14,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{187}(15,\cdot)$$ 187.r 40 yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{187}(16,\cdot)$$ 187.j 10 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$-1$$
$$\chi_{187}(18,\cdot)$$ 187.k 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$1$$
$$\chi_{187}(19,\cdot)$$ 187.q 40 yes $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{187}(20,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{187}(21,\cdot)$$ 187.f 4 yes $$-1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$-i$$ $$-i$$
$$\chi_{187}(23,\cdot)$$ 187.n 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{187}(24,\cdot)$$ 187.t 80 yes $$1$$ $$1$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{187}(25,\cdot)$$ 187.r 40 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{187}(26,\cdot)$$ 187.r 40 yes $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{187}(27,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{187}(28,\cdot)$$ 187.t 80 yes $$1$$ $$1$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{187}(29,\cdot)$$ 187.t 80 yes $$1$$ $$1$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{187}(30,\cdot)$$ 187.o 20 yes $$-1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$i$$ $$i$$
$$\chi_{187}(31,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{187}(32,\cdot)$$ 187.i 8 yes $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{187}(35,\cdot)$$ 187.k 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$1$$
$$\chi_{187}(36,\cdot)$$ 187.r 40 yes $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{187}(37,\cdot)$$ 187.s 80 yes $$-1$$ $$1$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$