# Properties

 Modulus 94 Structure $$C_{46}$$ Order 46

# Learn more about

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(94)

pari: g = idealstar(,94,2)

## Character group

 sage: G.order()  pari: g.no Order = 46 sage: H.invariants()  pari: g.cyc Structure = $$C_{46}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{94}(5,\cdot)$

## First 32 of 46 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
$$\chi_{94}(1,\cdot)$$ 94.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{94}(3,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$
$$\chi_{94}(5,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{3}{23}\right)$$
$$\chi_{94}(7,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$
$$\chi_{94}(9,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$
$$\chi_{94}(11,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{21}{23}\right)$$
$$\chi_{94}(13,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{29}{46}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$
$$\chi_{94}(15,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$
$$\chi_{94}(17,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$
$$\chi_{94}(19,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{20}{23}\right)$$
$$\chi_{94}(21,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$
$$\chi_{94}(23,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{9}{46}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{15}{23}\right)$$
$$\chi_{94}(25,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$
$$\chi_{94}(27,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{3}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$
$$\chi_{94}(29,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{35}{46}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{17}{46}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$
$$\chi_{94}(31,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{17}{46}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{94}(33,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{21}{46}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{94}(35,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{1}{46}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{3}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{7}{23}\right)$$
$$\chi_{94}(37,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$
$$\chi_{94}(39,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{7}{46}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{1}{23}\right)$$
$$\chi_{94}(41,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{15}{46}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{39}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{22}{23}\right)$$
$$\chi_{94}(43,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{13}{46}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{45}{46}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{43}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{16}{23}\right)$$
$$\chi_{94}(45,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{11}{46}\right)$$ $$e\left(\frac{37}{46}\right)$$ $$e\left(\frac{33}{46}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{5}{46}\right)$$ $$e\left(\frac{8}{23}\right)$$
$$\chi_{94}(49,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$
$$\chi_{94}(51,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$
$$\chi_{94}(53,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$
$$\chi_{94}(55,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{15}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$
$$\chi_{94}(57,\cdot)$$ 94.d 46 no $$-1$$ $$1$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{19}{46}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{41}{46}\right)$$ $$e\left(\frac{25}{46}\right)$$ $$e\left(\frac{31}{46}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{27}{46}\right)$$ $$e\left(\frac{11}{23}\right)$$
$$\chi_{94}(59,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{16}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{7}{23}\right)$$
$$\chi_{94}(61,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{18}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$ $$e\left(\frac{21}{23}\right)$$ $$e\left(\frac{12}{23}\right)$$
$$\chi_{94}(63,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{7}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$ $$e\left(\frac{2}{23}\right)$$ $$e\left(\frac{14}{23}\right)$$ $$e\left(\frac{22}{23}\right)$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{1}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{9}{23}\right)$$
$$\chi_{94}(65,\cdot)$$ 94.c 23 no $$1$$ $$1$$ $$e\left(\frac{5}{23}\right)$$ $$e\left(\frac{6}{23}\right)$$ $$e\left(\frac{8}{23}\right)$$ $$e\left(\frac{10}{23}\right)$$ $$e\left(\frac{19}{23}\right)$$ $$e\left(\frac{20}{23}\right)$$ $$e\left(\frac{11}{23}\right)$$ $$e\left(\frac{4}{23}\right)$$ $$e\left(\frac{17}{23}\right)$$ $$e\left(\frac{13}{23}\right)$$