# Properties

 Modulus $3648$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{144}$$ Order $1152$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3648)

pari: g = idealstar(,3648,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{144}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3648}(2623,\cdot)$, $\chi_{3648}(2053,\cdot)$, $\chi_{3648}(1217,\cdot)$, $\chi_{3648}(1921,\cdot)$

## First 32 of 1152 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{3648}(1,\cdot)$$ 3648.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3648}(5,\cdot)$$ 3648.eo 144 yes $$-1$$ $$1$$ $$e\left(\frac{113}{144}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{11}{72}\right)$$ $$e\left(\frac{41}{72}\right)$$ $$e\left(\frac{43}{144}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{107}{144}\right)$$
$$\chi_{3648}(7,\cdot)$$ 3648.dg 24 no $$-1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$-1$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{3648}(11,\cdot)$$ 3648.dx 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$1$$ $$e\left(\frac{5}{48}\right)$$
$$\chi_{3648}(13,\cdot)$$ 3648.el 144 no $$-1$$ $$1$$ $$e\left(\frac{55}{144}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{55}{72}\right)$$ $$e\left(\frac{5}{144}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{61}{144}\right)$$
$$\chi_{3648}(17,\cdot)$$ 3648.dp 36 no $$-1$$ $$1$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{35}{36}\right)$$
$$\chi_{3648}(23,\cdot)$$ 3648.eh 72 no $$1$$ $$1$$ $$e\left(\frac{11}{72}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{72}\right)$$
$$\chi_{3648}(25,\cdot)$$ 3648.eb 72 no $$1$$ $$1$$ $$e\left(\frac{41}{72}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{55}{72}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{43}{72}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{35}{72}\right)$$
$$\chi_{3648}(29,\cdot)$$ 3648.ei 144 yes $$1$$ $$1$$ $$e\left(\frac{43}{144}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{144}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{43}{72}\right)$$ $$e\left(\frac{17}{144}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{121}{144}\right)$$
$$\chi_{3648}(31,\cdot)$$ 3648.bg 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3648}(35,\cdot)$$ 3648.ek 144 yes $$1$$ $$1$$ $$e\left(\frac{107}{144}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{61}{144}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{72}\right)$$ $$e\left(\frac{35}{72}\right)$$ $$e\left(\frac{121}{144}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{65}{144}\right)$$
$$\chi_{3648}(37,\cdot)$$ 3648.ck 16 no $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$1$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{3648}(41,\cdot)$$ 3648.ee 72 no $$1$$ $$1$$ $$e\left(\frac{67}{72}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{53}{72}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{29}{72}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{72}\right)$$
$$\chi_{3648}(43,\cdot)$$ 3648.ej 144 no $$-1$$ $$1$$ $$e\left(\frac{5}{144}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{91}{144}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{47}{72}\right)$$ $$e\left(\frac{5}{72}\right)$$ $$e\left(\frac{7}{144}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{143}{144}\right)$$
$$\chi_{3648}(47,\cdot)$$ 3648.dn 36 no $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{3648}(49,\cdot)$$ 3648.by 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{3648}(53,\cdot)$$ 3648.ei 144 yes $$1$$ $$1$$ $$e\left(\frac{85}{144}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{107}{144}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{72}\right)$$ $$e\left(\frac{13}{72}\right)$$ $$e\left(\frac{47}{144}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{55}{144}\right)$$
$$\chi_{3648}(55,\cdot)$$ 3648.ef 72 no $$-1$$ $$1$$ $$e\left(\frac{19}{72}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{29}{72}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{41}{72}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{61}{72}\right)$$
$$\chi_{3648}(59,\cdot)$$ 3648.em 144 yes $$-1$$ $$1$$ $$e\left(\frac{65}{144}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{31}{144}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{71}{72}\right)$$ $$e\left(\frac{65}{72}\right)$$ $$e\left(\frac{19}{144}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{131}{144}\right)$$
$$\chi_{3648}(61,\cdot)$$ 3648.en 144 no $$1$$ $$1$$ $$e\left(\frac{139}{144}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{53}{144}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{67}{72}\right)$$ $$e\left(\frac{137}{144}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{73}{144}\right)$$
$$\chi_{3648}(65,\cdot)$$ 3648.bn 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3648}(67,\cdot)$$ 3648.ep 144 no $$1$$ $$1$$ $$e\left(\frac{43}{144}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{77}{144}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{43}{72}\right)$$ $$e\left(\frac{17}{144}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{49}{144}\right)$$
$$\chi_{3648}(71,\cdot)$$ 3648.ea 72 no $$-1$$ $$1$$ $$e\left(\frac{25}{72}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{23}{72}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{71}{72}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{72}\right)$$
$$\chi_{3648}(73,\cdot)$$ 3648.eb 72 no $$1$$ $$1$$ $$e\left(\frac{67}{72}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{53}{72}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{65}{72}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{72}\right)$$
$$\chi_{3648}(77,\cdot)$$ 3648.cf 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{13}{16}\right)$$
$$\chi_{3648}(79,\cdot)$$ 3648.dl 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{3648}(83,\cdot)$$ 3648.dx 48 yes $$1$$ $$1$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$1$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{3648}(85,\cdot)$$ 3648.en 144 no $$1$$ $$1$$ $$e\left(\frac{133}{144}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{59}{144}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{19}{72}\right)$$ $$e\left(\frac{61}{72}\right)$$ $$e\left(\frac{71}{144}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{103}{144}\right)$$
$$\chi_{3648}(89,\cdot)$$ 3648.ee 72 no $$1$$ $$1$$ $$e\left(\frac{5}{72}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{72}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{43}{72}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{71}{72}\right)$$
$$\chi_{3648}(91,\cdot)$$ 3648.ep 144 no $$1$$ $$1$$ $$e\left(\frac{49}{144}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{71}{144}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{43}{72}\right)$$ $$e\left(\frac{49}{72}\right)$$ $$e\left(\frac{83}{144}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{144}\right)$$
$$\chi_{3648}(97,\cdot)$$ 3648.ct 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{3648}(101,\cdot)$$ 3648.eo 144 yes $$-1$$ $$1$$ $$e\left(\frac{73}{144}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{47}{144}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{67}{72}\right)$$ $$e\left(\frac{1}{72}\right)$$ $$e\left(\frac{131}{144}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{115}{144}\right)$$