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 \(1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{13}{23}\right)\)