# Properties

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

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 $$1$$ $$1$$ $$e\left(\frac{63}{68}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{41}{204}\right)$$ $$e\left(\frac{15}{68}\right)$$ $$e\left(\frac{53}{68}\right)$$ $$e\left(\frac{13}{102}\right)$$ $$e\left(\frac{19}{204}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$