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 \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{48}\right)\)