# Properties

 Modulus $7056$ Structure $$C_{2}\times C_{2}\times C_{6}\times C_{84}$$ Order $2016$

# Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7056)

pari: g = idealstar(,7056,2)

## Character group

 sage: G.order()  pari: g.no Order = 2016 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{6}\times C_{84}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7056}(6175,\cdot)$, $\chi_{7056}(1765,\cdot)$, $\chi_{7056}(785,\cdot)$, $\chi_{7056}(4609,\cdot)$

## First 32 of 2016 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$
$$\chi_{7056}(1,\cdot)$$ 7056.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7056}(5,\cdot)$$ 7056.iw 84 yes $$1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$-1$$ $$e\left(\frac{29}{84}\right)$$
$$\chi_{7056}(11,\cdot)$$ 7056.ig 84 yes $$1$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$-1$$ $$e\left(\frac{61}{84}\right)$$
$$\chi_{7056}(13,\cdot)$$ 7056.jc 84 yes $$-1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-i$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{28}\right)$$
$$\chi_{7056}(17,\cdot)$$ 7056.hi 42 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{7056}(19,\cdot)$$ 7056.ed 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{7056}(23,\cdot)$$ 7056.ha 42 no $$1$$ $$1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$-1$$ $$e\left(\frac{19}{42}\right)$$
$$\chi_{7056}(25,\cdot)$$ 7056.gd 42 no $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$1$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{7056}(29,\cdot)$$ 7056.je 84 yes $$-1$$ $$1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$i$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{7056}(31,\cdot)$$ 7056.bf 6 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7056}(37,\cdot)$$ 7056.it 84 no $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{53}{84}\right)$$
$$\chi_{7056}(41,\cdot)$$ 7056.gr 42 no $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{7056}(43,\cdot)$$ 7056.ic 84 yes $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$i$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{7056}(47,\cdot)$$ 7056.ft 42 no $$-1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{7056}(53,\cdot)$$ 7056.ik 84 no $$-1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{73}{84}\right)$$
$$\chi_{7056}(55,\cdot)$$ 7056.er 14 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{7056}(59,\cdot)$$ 7056.ja 84 yes $$-1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{84}\right)$$
$$\chi_{7056}(61,\cdot)$$ 7056.io 84 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{84}\right)$$
$$\chi_{7056}(65,\cdot)$$ 7056.hy 42 no $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{7056}(67,\cdot)$$ 7056.ea 12 no $$-1$$ $$1$$ $$-i$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{7056}(71,\cdot)$$ 7056.ex 14 no $$1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{7056}(73,\cdot)$$ 7056.gx 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{7056}(79,\cdot)$$ 7056.dd 6 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7056}(83,\cdot)$$ 7056.ia 84 yes $$-1$$ $$1$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$i$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{7056}(85,\cdot)$$ 7056.ib 84 yes $$1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-i$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{7056}(89,\cdot)$$ 7056.gm 42 no $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$
$$\chi_{7056}(95,\cdot)$$ 7056.hu 42 no $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{7056}(97,\cdot)$$ 7056.cl 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{7056}(101,\cdot)$$ 7056.iw 84 yes $$1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$-1$$ $$e\left(\frac{1}{84}\right)$$
$$\chi_{7056}(103,\cdot)$$ 7056.ho 42 no $$1$$ $$1$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$1$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{7056}(107,\cdot)$$ 7056.ij 84 no $$1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$
$$\chi_{7056}(109,\cdot)$$ 7056.it 84 no $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{84}\right)$$
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