# Properties

 Modulus $1280$ Structure $$C_{2}\times C_{4}\times C_{64}$$ Order $512$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1280)

pari: g = idealstar(,1280,2)

## Character group

 sage: G.order()  pari: g.no Order = 512 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}\times C_{64}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1280}(511,\cdot)$, $\chi_{1280}(261,\cdot)$, $\chi_{1280}(257,\cdot)$

## First 32 of 512 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{1280}(1,\cdot)$$ 1280.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1280}(3,\cdot)$$ 1280.bt 64 yes $$1$$ $$1$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{43}{64}\right)$$
$$\chi_{1280}(7,\cdot)$$ 1280.bl 32 no $$1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$
$$\chi_{1280}(9,\cdot)$$ 1280.bo 32 no $$1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{1280}(11,\cdot)$$ 1280.bx 64 no $$-1$$ $$1$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$
$$\chi_{1280}(13,\cdot)$$ 1280.bz 64 yes $$-1$$ $$1$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{55}{64}\right)$$
$$\chi_{1280}(17,\cdot)$$ 1280.bc 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{1280}(19,\cdot)$$ 1280.bu 64 yes $$-1$$ $$1$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{47}{64}\right)$$
$$\chi_{1280}(21,\cdot)$$ 1280.bv 64 no $$1$$ $$1$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{53}{64}\right)$$
$$\chi_{1280}(23,\cdot)$$ 1280.bl 32 no $$1$$ $$1$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{32}\right)$$
$$\chi_{1280}(27,\cdot)$$ 1280.bt 64 yes $$1$$ $$1$$ $$e\left(\frac{43}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{47}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{1}{64}\right)$$
$$\chi_{1280}(29,\cdot)$$ 1280.bw 64 yes $$1$$ $$1$$ $$e\left(\frac{49}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{19}{64}\right)$$
$$\chi_{1280}(31,\cdot)$$ 1280.w 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1280}(33,\cdot)$$ 1280.v 8 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1280}(37,\cdot)$$ 1280.bz 64 yes $$-1$$ $$1$$ $$e\left(\frac{27}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{37}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{17}{64}\right)$$
$$\chi_{1280}(39,\cdot)$$ 1280.bn 32 no $$-1$$ $$1$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{17}{32}\right)$$
$$\chi_{1280}(41,\cdot)$$ 1280.bm 32 no $$1$$ $$1$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$
$$\chi_{1280}(43,\cdot)$$ 1280.by 64 yes $$1$$ $$1$$ $$e\left(\frac{7}{64}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{3}{64}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{57}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{21}{64}\right)$$
$$\chi_{1280}(47,\cdot)$$ 1280.bd 16 no $$1$$ $$1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1280}(49,\cdot)$$ 1280.bf 16 no $$1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{1280}(51,\cdot)$$ 1280.bx 64 no $$-1$$ $$1$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{17}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{55}{64}\right)$$
$$\chi_{1280}(53,\cdot)$$ 1280.bs 64 yes $$-1$$ $$1$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{59}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{61}{64}\right)$$
$$\chi_{1280}(57,\cdot)$$ 1280.bk 32 no $$-1$$ $$1$$ $$e\left(\frac{15}{32}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{32}\right)$$
$$\chi_{1280}(59,\cdot)$$ 1280.bu 64 yes $$-1$$ $$1$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{21}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{63}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$
$$\chi_{1280}(61,\cdot)$$ 1280.bv 64 no $$1$$ $$1$$ $$e\left(\frac{25}{64}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{61}{64}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{53}{64}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$
$$\chi_{1280}(63,\cdot)$$ 1280.j 4 no $$1$$ $$1$$ $$-1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$i$$ $$-1$$
$$\chi_{1280}(67,\cdot)$$ 1280.by 64 yes $$1$$ $$1$$ $$e\left(\frac{9}{64}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{15}{64}\right)$$ $$e\left(\frac{13}{64}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{21}{64}\right)$$ $$e\left(\frac{55}{64}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{27}{64}\right)$$
$$\chi_{1280}(69,\cdot)$$ 1280.bw 64 yes $$1$$ $$1$$ $$e\left(\frac{19}{64}\right)$$ $$e\left(\frac{5}{32}\right)$$ $$e\left(\frac{19}{32}\right)$$ $$e\left(\frac{5}{64}\right)$$ $$e\left(\frac{31}{64}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{39}{64}\right)$$ $$e\left(\frac{29}{64}\right)$$ $$e\left(\frac{7}{32}\right)$$ $$e\left(\frac{57}{64}\right)$$
$$\chi_{1280}(71,\cdot)$$ 1280.bp 32 no $$-1$$ $$1$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{32}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{27}{32}\right)$$ $$e\left(\frac{9}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{32}\right)$$
$$\chi_{1280}(73,\cdot)$$ 1280.bk 32 no $$-1$$ $$1$$ $$e\left(\frac{25}{32}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{29}{32}\right)$$ $$e\left(\frac{31}{32}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{32}\right)$$
$$\chi_{1280}(77,\cdot)$$ 1280.bs 64 yes $$-1$$ $$1$$ $$e\left(\frac{45}{64}\right)$$ $$e\left(\frac{3}{32}\right)$$ $$e\left(\frac{13}{32}\right)$$ $$e\left(\frac{11}{64}\right)$$ $$e\left(\frac{33}{64}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{41}{64}\right)$$ $$e\left(\frac{51}{64}\right)$$ $$e\left(\frac{17}{32}\right)$$ $$e\left(\frac{7}{64}\right)$$
$$\chi_{1280}(79,\cdot)$$ 1280.bh 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$