Properties

Modulus 98
Structure \(C_{42}\)
Order 42

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(98)
pari: g = idealstar(,98,2)

Character group

sage: G.order()
pari: g.no
Order = 42
sage: H.invariants()
pari: g.cyc
Structure = \(C_{42}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{98}(3,\cdot)$

First 32 of 42 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 9 11 13 15 17 19 23 25
\(\chi_{98}(1,\cdot)\) 98.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{98}(3,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{98}(5,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{98}(9,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{98}(11,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{98}(13,\cdot)\) 98.f 14 No \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{98}(15,\cdot)\) 98.e 7 No \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{98}(17,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{98}(19,\cdot)\) 98.d 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{98}(23,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{98}(25,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{98}(27,\cdot)\) 98.f 14 No \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{98}(29,\cdot)\) 98.e 7 No \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{98}(31,\cdot)\) 98.d 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{98}(33,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{98}(37,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{98}(39,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{98}(41,\cdot)\) 98.f 14 No \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{98}(43,\cdot)\) 98.e 7 No \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{98}(45,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{98}(47,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{98}(51,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{98}(53,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{98}(55,\cdot)\) 98.f 14 No \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{98}(57,\cdot)\) 98.e 7 No \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{98}(59,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{98}(61,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{98}(65,\cdot)\) 98.g 21 No \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{98}(67,\cdot)\) 98.c 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{98}(69,\cdot)\) 98.f 14 No \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{98}(71,\cdot)\) 98.e 7 No \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{98}(73,\cdot)\) 98.h 42 No \(-1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\)