Properties

Modulus $8034$
Structure \(C_{204}\times C_{6}\times C_{2}\)
Order $2448$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(8034)
 
pari: g = idealstar(,8034,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2448
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{204}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{8034}(5357,\cdot)$, $\chi_{8034}(1237,\cdot)$, $\chi_{8034}(5773,\cdot)$

First 32 of 2448 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{8034}(1,\cdot)\) 8034.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8034}(5,\cdot)\) 8034.ej 204 no \(-1\) \(1\) \(e\left(\frac{53}{204}\right)\) \(e\left(\frac{59}{204}\right)\) \(e\left(\frac{71}{204}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{109}{204}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{21}{68}\right)\) \(e\left(\frac{28}{51}\right)\)
\(\chi_{8034}(7,\cdot)\) 8034.ec 204 no \(-1\) \(1\) \(e\left(\frac{59}{204}\right)\) \(e\left(\frac{49}{204}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{8034}(11,\cdot)\) 8034.eb 204 no \(-1\) \(1\) \(e\left(\frac{71}{204}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{13}{204}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{155}{204}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{8034}(17,\cdot)\) 8034.do 102 no \(-1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{8034}(19,\cdot)\) 8034.ep 204 no \(-1\) \(1\) \(e\left(\frac{109}{204}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{155}{204}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{169}{204}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{31}{68}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{8034}(23,\cdot)\) 8034.cy 102 no \(-1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{35}{102}\right)\)
\(\chi_{8034}(25,\cdot)\) 8034.de 102 no \(1\) \(1\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{8034}(29,\cdot)\) 8034.dj 102 no \(-1\) \(1\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{8034}(31,\cdot)\) 8034.cx 68 no \(1\) \(1\) \(e\left(\frac{21}{68}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{31}{68}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{41}{68}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{8034}(35,\cdot)\) 8034.dn 102 no \(1\) \(1\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{4}{51}\right)\)
\(\chi_{8034}(37,\cdot)\) 8034.ee 204 no \(1\) \(1\) \(e\left(\frac{11}{68}\right)\) \(e\left(\frac{13}{204}\right)\) \(e\left(\frac{143}{204}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{175}{204}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{15}{68}\right)\) \(e\left(\frac{23}{102}\right)\)
\(\chi_{8034}(41,\cdot)\) 8034.el 204 no \(1\) \(1\) \(e\left(\frac{151}{204}\right)\) \(e\left(\frac{179}{204}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{43}{68}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{8034}(43,\cdot)\) 8034.du 102 no \(-1\) \(1\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{102}\right)\)
\(\chi_{8034}(47,\cdot)\) 8034.by 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{8034}(49,\cdot)\) 8034.dg 102 no \(1\) \(1\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{8034}(53,\cdot)\) 8034.dt 102 no \(1\) \(1\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{7}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{8034}(55,\cdot)\) 8034.cs 51 no \(1\) \(1\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{8034}(59,\cdot)\) 8034.ea 204 no \(1\) \(1\) \(e\left(\frac{145}{204}\right)\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{107}{204}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{91}{204}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{65}{102}\right)\)
\(\chi_{8034}(61,\cdot)\) 8034.cq 51 no \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{8034}(67,\cdot)\) 8034.eo 204 no \(1\) \(1\) \(e\left(\frac{179}{204}\right)\) \(e\left(\frac{29}{68}\right)\) \(e\left(\frac{73}{204}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{125}{204}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{31}{102}\right)\)
\(\chi_{8034}(71,\cdot)\) 8034.ek 204 no \(-1\) \(1\) \(e\left(\frac{185}{204}\right)\) \(e\left(\frac{43}{204}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{43}{68}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{83}{102}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{8034}(73,\cdot)\) 8034.cx 68 no \(1\) \(1\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{3}{68}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{9}{68}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{8034}(77,\cdot)\) 8034.dd 102 no \(1\) \(1\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{35}{51}\right)\)
\(\chi_{8034}(79,\cdot)\) 8034.ci 17 no \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{15}{17}\right)\)
\(\chi_{8034}(83,\cdot)\) 8034.ei 204 no \(1\) \(1\) \(e\left(\frac{127}{204}\right)\) \(e\left(\frac{151}{204}\right)\) \(e\left(\frac{97}{204}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{113}{204}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{37}{102}\right)\)
\(\chi_{8034}(85,\cdot)\) 8034.eo 204 no \(1\) \(1\) \(e\left(\frac{193}{204}\right)\) \(e\left(\frac{59}{68}\right)\) \(e\left(\frac{179}{204}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{55}{204}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{83}{102}\right)\)
\(\chi_{8034}(89,\cdot)\) 8034.en 204 no \(-1\) \(1\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{61}{204}\right)\) \(e\left(\frac{161}{204}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{115}{204}\right)\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{1}{51}\right)\)
\(\chi_{8034}(95,\cdot)\) 8034.dw 102 no \(1\) \(1\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{1}{102}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{41}{51}\right)\)
\(\chi_{8034}(97,\cdot)\) 8034.ep 204 no \(-1\) \(1\) \(e\left(\frac{13}{204}\right)\) \(e\left(\frac{57}{68}\right)\) \(e\left(\frac{11}{204}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{37}{204}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{43}{68}\right)\) \(e\left(\frac{46}{51}\right)\)
\(\chi_{8034}(101,\cdot)\) 8034.df 102 no \(1\) \(1\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{8034}(107,\cdot)\) 8034.dc 102 no \(-1\) \(1\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{49}{102}\right)\)