# Properties

 Modulus $4056$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{156}$$ Order $1248$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4056)

pari: g = idealstar(,4056,2)

## Character group

 sage: G.order()  pari: g.no Order = 1248 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{156}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4056}(1015,\cdot)$, $\chi_{4056}(2029,\cdot)$, $\chi_{4056}(2705,\cdot)$, $\chi_{4056}(3889,\cdot)$

## First 32 of 1248 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{4056}(1,\cdot)$$ 4056.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4056}(5,\cdot)$$ 4056.cp 52 yes $$1$$ $$1$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{9}{13}\right)$$
$$\chi_{4056}(7,\cdot)$$ 4056.dl 156 no $$1$$ $$1$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{5}{78}\right)$$
$$\chi_{4056}(11,\cdot)$$ 4056.dr 156 yes $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{7}{78}\right)$$
$$\chi_{4056}(17,\cdot)$$ 4056.cx 78 no $$-1$$ $$1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{78}\right)$$
$$\chi_{4056}(19,\cdot)$$ 4056.bt 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4056}(23,\cdot)$$ 4056.bj 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4056}(25,\cdot)$$ 4056.ck 26 no $$1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{4056}(29,\cdot)$$ 4056.db 78 yes $$-1$$ $$1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{29}{39}\right)$$
$$\chi_{4056}(31,\cdot)$$ 4056.ct 52 no $$1$$ $$1$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$i$$ $$1$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{3}{26}\right)$$
$$\chi_{4056}(35,\cdot)$$ 4056.cv 78 yes $$1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{7}{78}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{59}{78}\right)$$
$$\chi_{4056}(37,\cdot)$$ 4056.dm 156 no $$-1$$ $$1$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{31}{156}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{61}{78}\right)$$
$$\chi_{4056}(41,\cdot)$$ 4056.do 156 no $$1$$ $$1$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{55}{78}\right)$$
$$\chi_{4056}(43,\cdot)$$ 4056.da 78 no $$-1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$
$$\chi_{4056}(47,\cdot)$$ 4056.co 52 no $$-1$$ $$1$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{11}{13}\right)$$
$$\chi_{4056}(49,\cdot)$$ 4056.dd 78 no $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{5}{39}\right)$$
$$\chi_{4056}(53,\cdot)$$ 4056.bx 26 yes $$-1$$ $$1$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{4056}(55,\cdot)$$ 4056.cw 78 no $$-1$$ $$1$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{61}{78}\right)$$
$$\chi_{4056}(59,\cdot)$$ 4056.dr 156 yes $$-1$$ $$1$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{41}{78}\right)$$
$$\chi_{4056}(61,\cdot)$$ 4056.dh 78 no $$1$$ $$1$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{47}{78}\right)$$
$$\chi_{4056}(67,\cdot)$$ 4056.dk 156 no $$1$$ $$1$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{4056}(71,\cdot)$$ 4056.dq 156 no $$-1$$ $$1$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{71}{156}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{34}{39}\right)$$
$$\chi_{4056}(73,\cdot)$$ 4056.cr 52 no $$-1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{4056}(77,\cdot)$$ 4056.cl 26 yes $$-1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$
$$\chi_{4056}(79,\cdot)$$ 4056.cc 26 no $$-1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$
$$\chi_{4056}(83,\cdot)$$ 4056.cn 52 yes $$-1$$ $$1$$ $$e\left(\frac{31}{52}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{4056}(85,\cdot)$$ 4056.dm 156 no $$-1$$ $$1$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{131}{156}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{59}{78}\right)$$
$$\chi_{4056}(89,\cdot)$$ 4056.bp 12 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4056}(95,\cdot)$$ 4056.cz 78 no $$1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{1}{39}\right)$$
$$\chi_{4056}(97,\cdot)$$ 4056.dn 156 no $$-1$$ $$1$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{35}{156}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{25}{39}\right)$$
$$\chi_{4056}(101,\cdot)$$ 4056.dc 78 yes $$-1$$ $$1$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{2}{39}\right)$$
$$\chi_{4056}(103,\cdot)$$ 4056.ce 26 no $$-1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$