# Properties

 Modulus $1344$ Structure $$C_{48}\times C_{2}\times C_{2}\times C_{2}$$ Order $384$

# Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1344)

pari: g = idealstar(,1344,2)

## Character group

 sage: G.order()  pari: g.no Order = 384 sage: H.invariants()  pari: g.cyc Structure = $$C_{48}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1344}(127,\cdot)$, $\chi_{1344}(1093,\cdot)$, $\chi_{1344}(449,\cdot)$, $\chi_{1344}(577,\cdot)$

## First 32 of 384 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$
$$\chi_{1344}(1,\cdot)$$ 1344.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1344}(5,\cdot)$$ 1344.cw 48 yes $$1$$ $$1$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{48}\right)$$
$$\chi_{1344}(11,\cdot)$$ 1344.cx 48 yes $$1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{1344}(13,\cdot)$$ 1344.ck 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$
$$\chi_{1344}(17,\cdot)$$ 1344.bw 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1344}(19,\cdot)$$ 1344.cy 48 no $$1$$ $$1$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{48}\right)$$
$$\chi_{1344}(23,\cdot)$$ 1344.cp 24 no $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{24}\right)$$
$$\chi_{1344}(25,\cdot)$$ 1344.cr 24 no $$1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{1344}(29,\cdot)$$ 1344.cf 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-1$$ $$e\left(\frac{3}{16}\right)$$
$$\chi_{1344}(31,\cdot)$$ 1344.bb 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1344}(37,\cdot)$$ 1344.cz 48 no $$1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{35}{48}\right)$$
$$\chi_{1344}(41,\cdot)$$ 1344.bo 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{1344}(43,\cdot)$$ 1344.cl 16 no $$-1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{1344}(47,\cdot)$$ 1344.bz 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1344}(53,\cdot)$$ 1344.da 48 yes $$-1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{48}\right)$$
$$\chi_{1344}(55,\cdot)$$ 1344.bu 8 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{1344}(59,\cdot)$$ 1344.db 48 yes $$-1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{43}{48}\right)$$
$$\chi_{1344}(61,\cdot)$$ 1344.cv 48 no $$-1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{48}\right)$$
$$\chi_{1344}(65,\cdot)$$ 1344.bn 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1344}(67,\cdot)$$ 1344.cu 48 no $$-1$$ $$1$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{48}\right)$$
$$\chi_{1344}(71,\cdot)$$ 1344.bs 8 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{1344}(73,\cdot)$$ 1344.co 24 no $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{1344}(79,\cdot)$$ 1344.bx 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1344}(83,\cdot)$$ 1344.ce 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$ $$e\left(\frac{15}{16}\right)$$
$$\chi_{1344}(85,\cdot)$$ 1344.cg 16 no $$1$$ $$1$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$
$$\chi_{1344}(89,\cdot)$$ 1344.ct 24 no $$1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{1344}(95,\cdot)$$ 1344.bd 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1344}(97,\cdot)$$ 1344.l 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{1344}(101,\cdot)$$ 1344.cw 48 yes $$1$$ $$1$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{48}\right)$$
$$\chi_{1344}(103,\cdot)$$ 1344.cn 24 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{1344}(107,\cdot)$$ 1344.cx 48 yes $$1$$ $$1$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{47}{48}\right)$$
$$\chi_{1344}(109,\cdot)$$ 1344.cz 48 no $$1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{48}\right)$$