Properties

Modulus $712$
Structure \(C_{88}\times C_{2}\times C_{2}\)
Order $352$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(712)
 
pari: g = idealstar(,712,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 352
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{88}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{712}(535,\cdot)$, $\chi_{712}(357,\cdot)$, $\chi_{712}(537,\cdot)$

First 32 of 352 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{712}(1,\cdot)\) 712.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{712}(3,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{1}{88}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{37}{88}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{67}{88}\right)\) \(e\left(\frac{27}{88}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{35}{88}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{712}(5,\cdot)\) 712.z 44 yes \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{712}(7,\cdot)\) 712.bd 88 no \(1\) \(1\) \(e\left(\frac{37}{88}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{88}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{75}{88}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{63}{88}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{712}(9,\cdot)\) 712.ba 44 no \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{712}(11,\cdot)\) 712.w 22 yes \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{712}(13,\cdot)\) 712.bc 88 yes \(-1\) \(1\) \(e\left(\frac{67}{88}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{45}{88}\right)\) \(e\left(\frac{49}{88}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{57}{88}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{712}(15,\cdot)\) 712.bd 88 no \(1\) \(1\) \(e\left(\frac{27}{88}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{75}{88}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{49}{88}\right)\) \(e\left(\frac{69}{88}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{65}{88}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{712}(17,\cdot)\) 712.ba 44 no \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{712}(19,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{35}{88}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{63}{88}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{57}{88}\right)\) \(e\left(\frac{65}{88}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{81}{88}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{712}(21,\cdot)\) 712.z 44 yes \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{712}(23,\cdot)\) 712.bd 88 no \(1\) \(1\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{79}{88}\right)\) \(e\left(\frac{43}{88}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{712}(25,\cdot)\) 712.u 22 no \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{712}(27,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{23}{88}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{25}{88}\right)\) \(e\left(\frac{81}{88}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{17}{88}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{712}(29,\cdot)\) 712.bc 88 yes \(-1\) \(1\) \(e\left(\frac{15}{88}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{27}{88}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{81}{88}\right)\) \(e\left(\frac{53}{88}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{712}(31,\cdot)\) 712.bd 88 no \(1\) \(1\) \(e\left(\frac{75}{88}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{88}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{88}\right)\) \(e\left(\frac{45}{88}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{73}{88}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{712}(33,\cdot)\) 712.be 88 no \(-1\) \(1\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{21}{88}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{88}\right)\) \(e\left(\frac{51}{88}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{71}{88}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{712}(35,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{63}{88}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{43}{88}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{85}{88}\right)\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{88}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{712}(37,\cdot)\) 712.p 8 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(i\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{712}(39,\cdot)\) 712.v 22 no \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{712}(41,\cdot)\) 712.be 88 no \(-1\) \(1\) \(e\left(\frac{21}{88}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{43}{88}\right)\) \(e\left(\frac{83}{88}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{31}{88}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{712}(43,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{88}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{79}{88}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{47}{88}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{712}(45,\cdot)\) 712.x 22 yes \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{712}(47,\cdot)\) 712.bb 44 no \(-1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{712}(49,\cdot)\) 712.ba 44 no \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{712}(51,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{83}{88}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{29}{88}\right)\) \(e\left(\frac{13}{88}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{69}{88}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{712}(53,\cdot)\) 712.z 44 yes \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{712}(55,\cdot)\) 712.i 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(-1\) \(-i\) \(-1\)
\(\chi_{712}(57,\cdot)\) 712.u 22 no \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{712}(59,\cdot)\) 712.bf 88 yes \(1\) \(1\) \(e\left(\frac{43}{88}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{7}{88}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{65}{88}\right)\) \(e\left(\frac{17}{88}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{88}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{712}(61,\cdot)\) 712.bc 88 yes \(-1\) \(1\) \(e\left(\frac{25}{88}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{45}{88}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{47}{88}\right)\) \(e\left(\frac{59}{88}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{83}{88}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{712}(63,\cdot)\) 712.bd 88 no \(1\) \(1\) \(e\left(\frac{39}{88}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{79}{88}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{61}{88}\right)\) \(e\left(\frac{41}{88}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{45}{88}\right)\) \(e\left(\frac{15}{44}\right)\)