Properties

Modulus $690$
Structure \(C_{44}\times C_{2}\times C_{2}\)
Order $176$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(690)
 
pari: g = idealstar(,690,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 176
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{44}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{690}(461,\cdot)$, $\chi_{690}(277,\cdot)$, $\chi_{690}(511,\cdot)$

First 32 of 176 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{690}(1,\cdot)\) 690.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{690}(7,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{690}(11,\cdot)\) 690.q 22 no \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{690}(13,\cdot)\) 690.v 44 no \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{690}(17,\cdot)\) 690.u 44 no \(-1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{690}(19,\cdot)\) 690.p 22 no \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{690}(29,\cdot)\) 690.t 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{690}(31,\cdot)\) 690.m 11 no \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{690}(37,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{690}(41,\cdot)\) 690.o 22 no \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{690}(43,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{690}(47,\cdot)\) 690.i 4 no \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(1\) \(1\) \(i\) \(-1\) \(-i\)
\(\chi_{690}(49,\cdot)\) 690.r 22 no \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{690}(53,\cdot)\) 690.u 44 no \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{690}(59,\cdot)\) 690.t 22 no \(-1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{690}(61,\cdot)\) 690.s 22 no \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{690}(67,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{690}(71,\cdot)\) 690.o 22 no \(-1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{690}(73,\cdot)\) 690.v 44 no \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{690}(77,\cdot)\) 690.x 44 no \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{690}(79,\cdot)\) 690.p 22 no \(-1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{690}(83,\cdot)\) 690.u 44 no \(-1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{690}(89,\cdot)\) 690.n 22 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{690}(91,\cdot)\) 690.c 2 no \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{690}(97,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{690}(101,\cdot)\) 690.o 22 no \(-1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{690}(103,\cdot)\) 690.w 44 no \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{690}(107,\cdot)\) 690.u 44 no \(-1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{690}(109,\cdot)\) 690.p 22 no \(-1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{690}(113,\cdot)\) 690.u 44 no \(-1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{690}(119,\cdot)\) 690.t 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{690}(121,\cdot)\) 690.m 11 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\)