Properties

Modulus $4017$
Structure \(C_{204}\times C_{6}\times C_{2}\)
Order $2448$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(4017)
 
pari: g = idealstar(,4017,2)
 

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 = $\chi_{4017}(1340,\cdot)$, $\chi_{4017}(1237,\cdot)$, $\chi_{4017}(1756,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{4017}(1,\cdot)\) 4017.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4017}(2,\cdot)\) 4017.ee 204 yes \(1\) \(1\) \(e\left(\frac{115}{204}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{139}{204}\right)\) \(e\left(\frac{131}{204}\right)\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{27}{68}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{44}{51}\right)\)
\(\chi_{4017}(4,\cdot)\) 4017.de 102 no \(1\) \(1\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{37}{51}\right)\)
\(\chi_{4017}(5,\cdot)\) 4017.eb 204 yes \(-1\) \(1\) \(e\left(\frac{139}{204}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{53}{204}\right)\) \(e\left(\frac{59}{204}\right)\) \(e\left(\frac{3}{68}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{71}{204}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{35}{51}\right)\)
\(\chi_{4017}(7,\cdot)\) 4017.ec 204 no \(-1\) \(1\) \(e\left(\frac{131}{204}\right)\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{59}{204}\right)\) \(e\left(\frac{49}{204}\right)\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{59}{102}\right)\)
\(\chi_{4017}(8,\cdot)\) 4017.cx 68 yes \(1\) \(1\) \(e\left(\frac{47}{68}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{3}{68}\right)\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{5}{68}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{4017}(10,\cdot)\) 4017.db 102 no \(-1\) \(1\) \(e\left(\frac{25}{102}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{28}{51}\right)\)
\(\chi_{4017}(11,\cdot)\) 4017.ep 204 yes \(-1\) \(1\) \(e\left(\frac{27}{68}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{71}{204}\right)\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{13}{68}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{13}{204}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{4017}(14,\cdot)\) 4017.co 34 no \(-1\) \(1\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\)
\(\chi_{4017}(16,\cdot)\) 4017.ct 51 no \(1\) \(1\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{23}{51}\right)\)
\(\chi_{4017}(17,\cdot)\) 4017.dt 102 yes \(-1\) \(1\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{89}{102}\right)\)
\(\chi_{4017}(19,\cdot)\) 4017.em 204 no \(-1\) \(1\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{109}{204}\right)\) \(e\left(\frac{49}{68}\right)\) \(e\left(\frac{53}{68}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{155}{204}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{4017}(20,\cdot)\) 4017.ep 204 yes \(-1\) \(1\) \(e\left(\frac{55}{68}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{127}{204}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{29}{68}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{29}{204}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{4017}(22,\cdot)\) 4017.dv 102 no \(-1\) \(1\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{101}{102}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{20}{51}\right)\)
\(\chi_{4017}(23,\cdot)\) 4017.dn 102 yes \(-1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{11}{102}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{65}{102}\right)\)
\(\chi_{4017}(25,\cdot)\) 4017.dd 102 no \(1\) \(1\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{53}{102}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{19}{51}\right)\)
\(\chi_{4017}(28,\cdot)\) 4017.ec 204 no \(-1\) \(1\) \(e\left(\frac{157}{204}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{133}{204}\right)\) \(e\left(\frac{107}{204}\right)\) \(e\left(\frac{21}{68}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{41}{68}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{31}{102}\right)\)
\(\chi_{4017}(29,\cdot)\) 4017.dg 102 yes \(-1\) \(1\) \(e\left(\frac{95}{102}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{35}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{37}{51}\right)\) \(e\left(\frac{19}{102}\right)\)
\(\chi_{4017}(31,\cdot)\) 4017.cu 68 no \(1\) \(1\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{21}{68}\right)\) \(e\left(\frac{33}{68}\right)\) \(e\left(\frac{1}{68}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{23}{68}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{4017}(32,\cdot)\) 4017.ee 204 yes \(1\) \(1\) \(e\left(\frac{167}{204}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{83}{204}\right)\) \(e\left(\frac{43}{204}\right)\) \(e\left(\frac{31}{68}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{16}{51}\right)\)
\(\chi_{4017}(34,\cdot)\) 4017.cw 68 no \(-1\) \(1\) \(e\left(\frac{29}{68}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{25}{68}\right)\) \(e\left(\frac{15}{68}\right)\) \(e\left(\frac{19}{68}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{4017}(35,\cdot)\) 4017.dy 102 yes \(1\) \(1\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{4017}(37,\cdot)\) 4017.eh 204 no \(1\) \(1\) \(e\left(\frac{143}{204}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{11}{68}\right)\) \(e\left(\frac{13}{204}\right)\) \(e\left(\frac{7}{68}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{143}{204}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{101}{102}\right)\)
\(\chi_{4017}(38,\cdot)\) 4017.ds 102 yes \(-1\) \(1\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{61}{102}\right)\)
\(\chi_{4017}(40,\cdot)\) 4017.dr 102 no \(-1\) \(1\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{14}{51}\right)\)
\(\chi_{4017}(41,\cdot)\) 4017.ee 204 yes \(1\) \(1\) \(e\left(\frac{31}{204}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{151}{204}\right)\) \(e\left(\frac{179}{204}\right)\) \(e\left(\frac{31}{68}\right)\) \(e\left(\frac{91}{102}\right)\) \(e\left(\frac{67}{68}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{50}{51}\right)\)
\(\chi_{4017}(43,\cdot)\) 4017.dz 102 no \(-1\) \(1\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{4017}(44,\cdot)\) 4017.eb 204 yes \(-1\) \(1\) \(e\left(\frac{107}{204}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{145}{204}\right)\) \(e\left(\frac{19}{204}\right)\) \(e\left(\frac{39}{68}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{175}{204}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{5}{51}\right)\) \(e\left(\frac{13}{51}\right)\)
\(\chi_{4017}(46,\cdot)\) 4017.bv 12 no \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(1\) \(-1\)
\(\chi_{4017}(47,\cdot)\) 4017.cg 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4017}(49,\cdot)\) 4017.de 102 no \(1\) \(1\) \(e\left(\frac{29}{102}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{59}{102}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{4017}(50,\cdot)\) 4017.en 204 yes \(1\) \(1\) \(e\left(\frac{63}{68}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{41}{204}\right)\) \(e\left(\frac{15}{68}\right)\) \(e\left(\frac{53}{68}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{19}{204}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{4}{17}\right)\)