# Properties

 Modulus $7098$ Structure $$C_{156}\times C_{6}\times C_{2}$$ Order $1872$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(7098)

pari: g = idealstar(,7098,2)

## Character group

 sage: G.order()  pari: g.no Order = 1872 sage: H.invariants()  pari: g.cyc Structure = $$C_{156}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7098}(4733,\cdot)$, $\chi_{7098}(5071,\cdot)$, $\chi_{7098}(6931,\cdot)$

## First 32 of 1872 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7098}(1,\cdot)$$ 7098.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7098}(5,\cdot)$$ 7098.ed 156 no $$-1$$ $$1$$ $$e\left(\frac{29}{156}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{47}{52}\right)$$
$$\chi_{7098}(11,\cdot)$$ 7098.ei 156 no $$1$$ $$1$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{97}{156}\right)$$
$$\chi_{7098}(17,\cdot)$$ 7098.dh 78 no $$1$$ $$1$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{43}{78}\right)$$
$$\chi_{7098}(19,\cdot)$$ 7098.by 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{7098}(23,\cdot)$$ 7098.w 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7098}(25,\cdot)$$ 7098.df 78 no $$1$$ $$1$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{21}{26}\right)$$
$$\chi_{7098}(29,\cdot)$$ 7098.dw 78 no $$-1$$ $$1$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{23}{78}\right)$$
$$\chi_{7098}(31,\cdot)$$ 7098.el 156 no $$1$$ $$1$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{49}{52}\right)$$
$$\chi_{7098}(37,\cdot)$$ 7098.eo 156 no $$-1$$ $$1$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{43}{156}\right)$$
$$\chi_{7098}(41,\cdot)$$ 7098.ee 156 no $$-1$$ $$1$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{49}{156}\right)$$
$$\chi_{7098}(43,\cdot)$$ 7098.dx 78 no $$1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{37}{78}\right)$$
$$\chi_{7098}(47,\cdot)$$ 7098.ed 156 no $$-1$$ $$1$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{17}{52}\right)$$
$$\chi_{7098}(53,\cdot)$$ 7098.de 78 no $$-1$$ $$1$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{23}{26}\right)$$
$$\chi_{7098}(55,\cdot)$$ 7098.dy 78 no $$-1$$ $$1$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{41}{78}\right)$$
$$\chi_{7098}(59,\cdot)$$ 7098.ep 156 no $$-1$$ $$1$$ $$e\left(\frac{55}{156}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{11}{156}\right)$$
$$\chi_{7098}(61,\cdot)$$ 7098.db 78 no $$-1$$ $$1$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{61}{78}\right)$$
$$\chi_{7098}(67,\cdot)$$ 7098.eg 156 no $$-1$$ $$1$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{25}{156}\right)$$
$$\chi_{7098}(71,\cdot)$$ 7098.ek 156 no $$1$$ $$1$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{149}{156}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{23}{156}\right)$$
$$\chi_{7098}(73,\cdot)$$ 7098.el 156 no $$1$$ $$1$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{15}{52}\right)$$
$$\chi_{7098}(79,\cdot)$$ 7098.ct 39 no $$1$$ $$1$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$
$$\chi_{7098}(83,\cdot)$$ 7098.cx 52 no $$-1$$ $$1$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$i$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{27}{52}\right)$$
$$\chi_{7098}(85,\cdot)$$ 7098.eh 156 no $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{71}{156}\right)$$
$$\chi_{7098}(89,\cdot)$$ 7098.bt 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{7098}(95,\cdot)$$ 7098.dt 78 no $$-1$$ $$1$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{32}{39}\right)$$
$$\chi_{7098}(97,\cdot)$$ 7098.en 156 no $$1$$ $$1$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{35}{156}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{71}{156}\right)$$ $$e\left(\frac{119}{156}\right)$$
$$\chi_{7098}(101,\cdot)$$ 7098.dc 78 no $$1$$ $$1$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{11}{78}\right)$$
$$\chi_{7098}(103,\cdot)$$ 7098.dp 78 no $$-1$$ $$1$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{7098}(107,\cdot)$$ 7098.dg 78 no $$-1$$ $$1$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{77}{78}\right)$$
$$\chi_{7098}(109,\cdot)$$ 7098.ef 156 no $$-1$$ $$1$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{3}{52}\right)$$
$$\chi_{7098}(113,\cdot)$$ 7098.dw 78 no $$-1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$
$$\chi_{7098}(115,\cdot)$$ 7098.em 156 no $$1$$ $$1$$ $$e\left(\frac{133}{156}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{37}{156}\right)$$