# Properties

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

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 $$-1$$ $$1$$ $$e\left(\frac{37}{102}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{47}{102}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{35}{51}\right)$$ $$e\left(\frac{55}{102}\right)$$ $$e\left(\frac{37}{51}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{49}{102}\right)$$