# Properties

 Modulus $3744$ Structure $$C_{24}\times C_{12}\times C_{2}\times C_{2}$$ Order $1152$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3744)

pari: g = idealstar(,3744,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{24}\times C_{12}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3744}(703,\cdot)$, $\chi_{3744}(2341,\cdot)$, $\chi_{3744}(2081,\cdot)$, $\chi_{3744}(2017,\cdot)$

## 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{3744}(1,\cdot)$$ 3744.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3744}(5,\cdot)$$ 3744.ke 24 yes $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{3744}(7,\cdot)$$ 3744.ia 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{3744}(11,\cdot)$$ 3744.km 24 yes $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{3744}(17,\cdot)$$ 3744.bz 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3744}(19,\cdot)$$ 3744.kh 24 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{7}{24}\right)$$ $$i$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{3744}(23,\cdot)$$ 3744.fi 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3744}(25,\cdot)$$ 3744.fv 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$
$$\chi_{3744}(29,\cdot)$$ 3744.jh 24 yes $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{3744}(31,\cdot)$$ 3744.fw 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$
$$\chi_{3744}(35,\cdot)$$ 3744.jd 24 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{24}\right)$$ $$-1$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{3744}(37,\cdot)$$ 3744.io 24 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{17}{24}\right)$$ $$i$$ $$e\left(\frac{1}{24}\right)$$
$$\chi_{3744}(41,\cdot)$$ 3744.fb 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{3744}(43,\cdot)$$ 3744.jq 24 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$i$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{3744}(47,\cdot)$$ 3744.ha 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$
$$\chi_{3744}(49,\cdot)$$ 3744.ca 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3744}(53,\cdot)$$ 3744.ek 8 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{3744}(55,\cdot)$$ 3744.fm 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{3744}(59,\cdot)$$ 3744.km 24 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{3744}(61,\cdot)$$ 3744.jr 24 yes $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$-i$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{3744}(67,\cdot)$$ 3744.ij 24 yes $$1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$-1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{3744}(71,\cdot)$$ 3744.es 12 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{3744}(73,\cdot)$$ 3744.bo 4 no $$-1$$ $$1$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$i$$ $$i$$ $$i$$
$$\chi_{3744}(77,\cdot)$$ 3744.kd 24 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{3744}(79,\cdot)$$ 3744.dk 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{3744}(83,\cdot)$$ 3744.kf 24 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{3744}(85,\cdot)$$ 3744.ip 24 yes $$-1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{3744}(89,\cdot)$$ 3744.ig 12 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3744}(95,\cdot)$$ 3744.cf 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3744}(97,\cdot)$$ 3744.gm 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3744}(101,\cdot)$$ 3744.jl 24 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{3744}(103,\cdot)$$ 3744.hm 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$