# Properties

 Modulus $3840$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{64}$$ Order $1024$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3840)

pari: g = idealstar(,3840,2)

## Character group

 sage: G.order()  pari: g.no Order = 1024 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{64}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3840}(511,\cdot)$, $\chi_{3840}(2821,\cdot)$, $\chi_{3840}(2561,\cdot)$, $\chi_{3840}(1537,\cdot)$

## First 32 of 1024 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{3840}(1,\cdot)$$ 3840.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3840}(7,\cdot)$$ 3840.cx 32 no $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$-i$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{3840}(11,\cdot)$$ 3840.dw 64 no $$1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$
$$\chi_{3840}(13,\cdot)$$ 3840.du 64 no $$-1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{3840}(17,\cdot)$$ 3840.cr 16 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{3840}(19,\cdot)$$ 3840.dk 64 no $$-1$$ $$1$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{3840}(23,\cdot)$$ 3840.cv 32 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$i$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$
$$\chi_{3840}(29,\cdot)$$ 3840.dy 64 yes $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{21}{32}\right)$$
$$\chi_{3840}(31,\cdot)$$ 3840.bt 8 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$
$$\chi_{3840}(37,\cdot)$$ 3840.du 64 no $$-1$$ $$1$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{3840}(41,\cdot)$$ 3840.de 32 no $$-1$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$-i$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$
$$\chi_{3840}(43,\cdot)$$ 3840.do 64 no $$1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$
$$\chi_{3840}(47,\cdot)$$ 3840.ct 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{3840}(49,\cdot)$$ 3840.ck 16 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3840}(53,\cdot)$$ 3840.dr 64 yes $$1$$ $$1$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{3840}(59,\cdot)$$ 3840.dn 64 yes $$1$$ $$1$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$
$$\chi_{3840}(61,\cdot)$$ 3840.dm 64 no $$1$$ $$1$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{3840}(67,\cdot)$$ 3840.do 64 no $$1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{3840}(71,\cdot)$$ 3840.cy 32 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$-i$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{3840}(73,\cdot)$$ 3840.cu 32 no $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$-i$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{3840}(77,\cdot)$$ 3840.dr 64 yes $$1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{3840}(79,\cdot)$$ 3840.co 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3840}(83,\cdot)$$ 3840.dt 64 yes $$-1$$ $$1$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{64}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{3840}(89,\cdot)$$ 3840.db 32 no $$-1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$i$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{3840}(91,\cdot)$$ 3840.dz 64 no $$-1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{35}{64}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{3840}(97,\cdot)$$ 3840.bp 8 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$
$$\chi_{3840}(101,\cdot)$$ 3840.dl 64 no $$-1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{3840}(103,\cdot)$$ 3840.di 32 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$-i$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{3840}(107,\cdot)$$ 3840.dt 64 yes $$-1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$
$$\chi_{3840}(109,\cdot)$$ 3840.dx 64 no $$1$$ $$1$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$
$$\chi_{3840}(113,\cdot)$$ 3840.cr 16 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3840}(119,\cdot)$$ 3840.dd 32 no $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$i$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$