Properties

Modulus $2240$
Structure \(C_{48}\times C_{4}\times C_{2}\times C_{2}\)
Order $768$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2240)
 
pari: g = idealstar(,2240,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 768
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{48}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2240}(1471,\cdot)$, $\chi_{2240}(1541,\cdot)$, $\chi_{2240}(897,\cdot)$, $\chi_{2240}(1921,\cdot)$

First 32 of 768 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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{2240}(1,\cdot)\) 2240.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2240}(3,\cdot)\) 2240.fm 48 yes \(-1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(9,\cdot)\) 2240.ei 24 no \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(11,\cdot)\) 2240.fe 48 no \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(13,\cdot)\) 2240.du 16 yes \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\)
\(\chi_{2240}(17,\cdot)\) 2240.dp 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(19,\cdot)\) 2240.fj 48 yes \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(23,\cdot)\) 2240.eo 24 no \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(27,\cdot)\) 2240.dt 16 yes \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{2240}(29,\cdot)\) 2240.dz 16 no \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{2240}(31,\cdot)\) 2240.bz 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(33,\cdot)\) 2240.dn 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(37,\cdot)\) 2240.fa 48 yes \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(39,\cdot)\) 2240.el 24 no \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(41,\cdot)\) 2240.cr 8 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\)
\(\chi_{2240}(43,\cdot)\) 2240.dv 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{2240}(47,\cdot)\) 2240.cu 12 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(51,\cdot)\) 2240.fe 48 no \(-1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(53,\cdot)\) 2240.fn 48 yes \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(57,\cdot)\) 2240.ck 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\)
\(\chi_{2240}(59,\cdot)\) 2240.fj 48 yes \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(61,\cdot)\) 2240.fd 48 no \(-1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2240}(67,\cdot)\) 2240.fk 48 yes \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(69,\cdot)\) 2240.ea 16 yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(1\)
\(\chi_{2240}(71,\cdot)\) 2240.cf 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\)
\(\chi_{2240}(73,\cdot)\) 2240.es 24 no \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2240}(79,\cdot)\) 2240.di 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(81,\cdot)\) 2240.df 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(83,\cdot)\) 2240.dt 16 yes \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{2240}(87,\cdot)\) 2240.er 24 no \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2240}(89,\cdot)\) 2240.ex 24 no \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2240}(93,\cdot)\) 2240.fa 48 yes \(-1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{6}\right)\)