Properties

Modulus $1216$
Structure \(C_{144}\times C_{2}\times C_{2}\)
Order $576$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1216)
 
pari: g = idealstar(,1216,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 576
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{144}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1216}(191,\cdot)$, $\chi_{1216}(837,\cdot)$, $\chi_{1216}(705,\cdot)$

First 32 of 576 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(21\) \(23\)
\(\chi_{1216}(1,\cdot)\) 1216.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1216}(3,\cdot)\) 1216.ch 144 yes \(1\) \(1\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{107}{144}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{61}{144}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{23}{144}\right)\) \(e\left(\frac{41}{72}\right)\)
\(\chi_{1216}(5,\cdot)\) 1216.cg 144 yes \(1\) \(1\) \(e\left(\frac{107}{144}\right)\) \(e\left(\frac{41}{144}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{55}{144}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{101}{144}\right)\) \(e\left(\frac{47}{72}\right)\)
\(\chi_{1216}(7,\cdot)\) 1216.bo 24 no \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1216}(9,\cdot)\) 1216.ca 72 no \(1\) \(1\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{72}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{1216}(11,\cdot)\) 1216.bz 48 yes \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{1216}(13,\cdot)\) 1216.cf 144 yes \(-1\) \(1\) \(e\left(\frac{61}{144}\right)\) \(e\left(\frac{55}{144}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{67}{144}\right)\) \(e\left(\frac{49}{72}\right)\)
\(\chi_{1216}(15,\cdot)\) 1216.bs 36 no \(1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{1216}(17,\cdot)\) 1216.bu 36 no \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{1216}(21,\cdot)\) 1216.cf 144 yes \(-1\) \(1\) \(e\left(\frac{23}{144}\right)\) \(e\left(\frac{101}{144}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{23}{72}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{67}{144}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{89}{144}\right)\) \(e\left(\frac{35}{72}\right)\)
\(\chi_{1216}(23,\cdot)\) 1216.cc 72 no \(-1\) \(1\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{47}{72}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{1216}(25,\cdot)\) 1216.ca 72 no \(1\) \(1\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{1216}(27,\cdot)\) 1216.bw 48 yes \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{1216}(29,\cdot)\) 1216.cf 144 yes \(-1\) \(1\) \(e\left(\frac{49}{144}\right)\) \(e\left(\frac{115}{144}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{144}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{37}{72}\right)\)
\(\chi_{1216}(31,\cdot)\) 1216.s 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1216}(33,\cdot)\) 1216.bi 18 no \(-1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{1216}(35,\cdot)\) 1216.ce 144 yes \(-1\) \(1\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{35}{144}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{61}{144}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{23}{144}\right)\) \(e\left(\frac{41}{72}\right)\)
\(\chi_{1216}(37,\cdot)\) 1216.bg 16 yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{1216}(39,\cdot)\) 1216.x 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{1216}(41,\cdot)\) 1216.cd 72 no \(-1\) \(1\) \(e\left(\frac{1}{72}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{53}{72}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{1216}(43,\cdot)\) 1216.ce 144 yes \(-1\) \(1\) \(e\left(\frac{71}{144}\right)\) \(e\left(\frac{5}{144}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{71}{72}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{91}{144}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{47}{72}\right)\)
\(\chi_{1216}(45,\cdot)\) 1216.bx 48 yes \(1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{1216}(47,\cdot)\) 1216.bt 36 no \(-1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{1216}(49,\cdot)\) 1216.z 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1216}(51,\cdot)\) 1216.ch 144 yes \(1\) \(1\) \(e\left(\frac{133}{144}\right)\) \(e\left(\frac{55}{144}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{67}{144}\right)\) \(e\left(\frac{13}{72}\right)\)
\(\chi_{1216}(53,\cdot)\) 1216.cf 144 yes \(-1\) \(1\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{13}{144}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{107}{144}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{97}{144}\right)\) \(e\left(\frac{43}{72}\right)\)
\(\chi_{1216}(55,\cdot)\) 1216.cc 72 no \(-1\) \(1\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{19}{72}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{31}{36}\right)\)
\(\chi_{1216}(59,\cdot)\) 1216.ch 144 yes \(1\) \(1\) \(e\left(\frac{59}{144}\right)\) \(e\left(\frac{137}{144}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{31}{144}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{125}{144}\right)\) \(e\left(\frac{35}{72}\right)\)
\(\chi_{1216}(61,\cdot)\) 1216.cg 144 yes \(1\) \(1\) \(e\left(\frac{1}{144}\right)\) \(e\left(\frac{139}{144}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{72}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{53}{144}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{79}{144}\right)\) \(e\left(\frac{61}{72}\right)\)
\(\chi_{1216}(63,\cdot)\) 1216.bn 18 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{1216}(65,\cdot)\) 1216.r 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1216}(67,\cdot)\) 1216.ch 144 yes \(1\) \(1\) \(e\left(\frac{49}{144}\right)\) \(e\left(\frac{43}{144}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{77}{144}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{55}{144}\right)\) \(e\left(\frac{1}{72}\right)\)