# Properties

 Modulus $1014$ Structure $$C_{2}\times C_{156}$$ Order $312$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1014)

pari: g = idealstar(,1014,2)

## Character group

 sage: G.order()  pari: g.no Order = 312 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{156}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1014}(677,\cdot)$, $\chi_{1014}(847,\cdot)$

## First 32 of 312 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{1014}(1,\cdot)$$ 1014.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1014}(5,\cdot)$$ 1014.r 52 no $$1$$ $$1$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$
$$\chi_{1014}(7,\cdot)$$ 1014.w 156 no $$-1$$ $$1$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{61}{156}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{22}{39}\right)$$
$$\chi_{1014}(11,\cdot)$$ 1014.x 156 no $$1$$ $$1$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{7}{78}\right)$$
$$\chi_{1014}(17,\cdot)$$ 1014.t 78 no $$-1$$ $$1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{78}\right)$$
$$\chi_{1014}(19,\cdot)$$ 1014.l 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1014}(23,\cdot)$$ 1014.j 6 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1014}(25,\cdot)$$ 1014.p 26 no $$1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{1014}(29,\cdot)$$ 1014.v 78 no $$-1$$ $$1$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{19}{78}\right)$$
$$\chi_{1014}(31,\cdot)$$ 1014.s 52 no $$-1$$ $$1$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{8}{13}\right)$$
$$\chi_{1014}(35,\cdot)$$ 1014.v 78 no $$-1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{59}{78}\right)$$
$$\chi_{1014}(37,\cdot)$$ 1014.w 156 no $$-1$$ $$1$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{11}{39}\right)$$
$$\chi_{1014}(41,\cdot)$$ 1014.x 156 no $$1$$ $$1$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{55}{78}\right)$$
$$\chi_{1014}(43,\cdot)$$ 1014.u 78 no $$1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{28}{39}\right)$$
$$\chi_{1014}(47,\cdot)$$ 1014.r 52 no $$1$$ $$1$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$i$$ $$1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{9}{26}\right)$$
$$\chi_{1014}(49,\cdot)$$ 1014.u 78 no $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{5}{39}\right)$$
$$\chi_{1014}(53,\cdot)$$ 1014.o 26 no $$-1$$ $$1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$
$$\chi_{1014}(55,\cdot)$$ 1014.q 39 no $$1$$ $$1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{11}{39}\right)$$
$$\chi_{1014}(59,\cdot)$$ 1014.x 156 no $$1$$ $$1$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{41}{78}\right)$$
$$\chi_{1014}(61,\cdot)$$ 1014.q 39 no $$1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{4}{39}\right)$$
$$\chi_{1014}(67,\cdot)$$ 1014.w 156 no $$-1$$ $$1$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{1014}(71,\cdot)$$ 1014.x 156 no $$1$$ $$1$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{149}{156}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{29}{78}\right)$$
$$\chi_{1014}(73,\cdot)$$ 1014.s 52 no $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{1014}(77,\cdot)$$ 1014.n 26 no $$-1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$
$$\chi_{1014}(79,\cdot)$$ 1014.m 13 no $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{1014}(83,\cdot)$$ 1014.r 52 no $$1$$ $$1$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{1014}(85,\cdot)$$ 1014.w 156 no $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{10}{39}\right)$$
$$\chi_{1014}(89,\cdot)$$ 1014.k 12 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1014}(95,\cdot)$$ 1014.t 78 no $$-1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{41}{78}\right)$$
$$\chi_{1014}(97,\cdot)$$ 1014.w 156 no $$-1$$ $$1$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{35}{156}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{25}{39}\right)$$
$$\chi_{1014}(101,\cdot)$$ 1014.t 78 no $$-1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{43}{78}\right)$$
$$\chi_{1014}(103,\cdot)$$ 1014.p 26 no $$1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$