Properties

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

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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 \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\)