Properties

Modulus $245$
Structure \(C_{84}\times C_{2}\)
Order $168$

Learn more

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(245)
 
pari: g = idealstar(,245,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 168
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{245}(197,\cdot)$, $\chi_{245}(101,\cdot)$

First 32 of 168 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(11\) \(12\) \(13\) \(16\)
\(\chi_{245}(1,\cdot)\) 245.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{245}(2,\cdot)\) 245.w 84 yes \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{245}(3,\cdot)\) 245.x 84 yes \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{245}(4,\cdot)\) 245.t 42 yes \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{245}(6,\cdot)\) 245.n 14 no \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{245}(8,\cdot)\) 245.r 28 yes \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{245}(9,\cdot)\) 245.t 42 yes \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{245}(11,\cdot)\) 245.q 21 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{245}(12,\cdot)\) 245.x 84 yes \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{245}(13,\cdot)\) 245.s 28 yes \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{245}(16,\cdot)\) 245.q 21 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{245}(17,\cdot)\) 245.x 84 yes \(1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{245}(18,\cdot)\) 245.m 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{245}(19,\cdot)\) 245.i 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{245}(22,\cdot)\) 245.r 28 yes \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{245}(23,\cdot)\) 245.w 84 yes \(-1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{245}(24,\cdot)\) 245.u 42 yes \(-1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{245}(26,\cdot)\) 245.v 42 no \(-1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{245}(27,\cdot)\) 245.s 28 yes \(1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{245}(29,\cdot)\) 245.p 14 yes \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{245}(31,\cdot)\) 245.h 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{245}(32,\cdot)\) 245.w 84 yes \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{245}(33,\cdot)\) 245.x 84 yes \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{21}\right)\)
\(\chi_{245}(34,\cdot)\) 245.o 14 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{245}(36,\cdot)\) 245.k 7 no \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{245}(37,\cdot)\) 245.w 84 yes \(-1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{245}(38,\cdot)\) 245.x 84 yes \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{245}(39,\cdot)\) 245.t 42 yes \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{245}(41,\cdot)\) 245.n 14 no \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{245}(43,\cdot)\) 245.r 28 yes \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{245}(44,\cdot)\) 245.t 42 yes \(1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{245}(46,\cdot)\) 245.q 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{10}{21}\right)\)