Properties

Modulus $4608$
Structure \(C_{2}\times C_{2}\times C_{384}\)
Order $1536$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4608)
 
pari: g = idealstar(,4608,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1536
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{384}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4608}(3583,\cdot)$, $\chi_{4608}(2053,\cdot)$, $\chi_{4608}(4097,\cdot)$

First 32 of 1536 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{4608}(1,\cdot)\) 4608.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4608}(5,\cdot)\) 4608.ci 384 yes \(-1\) \(1\) \(e\left(\frac{67}{384}\right)\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{191}{384}\right)\) \(e\left(\frac{205}{384}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{23}{128}\right)\) \(e\left(\frac{53}{192}\right)\) \(e\left(\frac{67}{192}\right)\) \(e\left(\frac{305}{384}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{4608}(7,\cdot)\) 4608.cg 192 no \(-1\) \(1\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{59}{192}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{149}{192}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{4608}(11,\cdot)\) 4608.cj 384 yes \(1\) \(1\) \(e\left(\frac{191}{384}\right)\) \(e\left(\frac{59}{192}\right)\) \(e\left(\frac{43}{384}\right)\) \(e\left(\frac{17}{384}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{99}{128}\right)\) \(e\left(\frac{121}{192}\right)\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{325}{384}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{4608}(13,\cdot)\) 4608.ck 384 yes \(1\) \(1\) \(e\left(\frac{205}{384}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{17}{384}\right)\) \(e\left(\frac{355}{384}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{121}{128}\right)\) \(e\left(\frac{155}{192}\right)\) \(e\left(\frac{13}{192}\right)\) \(e\left(\frac{383}{384}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{4608}(17,\cdot)\) 4608.bn 32 no \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(-i\)
\(\chi_{4608}(19,\cdot)\) 4608.ca 128 no \(-1\) \(1\) \(e\left(\frac{23}{128}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{99}{128}\right)\) \(e\left(\frac{121}{128}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{81}{128}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{13}{128}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{4608}(23,\cdot)\) 4608.ch 192 no \(1\) \(1\) \(e\left(\frac{53}{192}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{121}{192}\right)\) \(e\left(\frac{155}{192}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{55}{192}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{4608}(25,\cdot)\) 4608.ce 192 no \(1\) \(1\) \(e\left(\frac{67}{192}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{191}{192}\right)\) \(e\left(\frac{13}{192}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{113}{192}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{4608}(29,\cdot)\) 4608.ci 384 yes \(-1\) \(1\) \(e\left(\frac{305}{384}\right)\) \(e\left(\frac{149}{192}\right)\) \(e\left(\frac{325}{384}\right)\) \(e\left(\frac{383}{384}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{128}\right)\) \(e\left(\frac{55}{192}\right)\) \(e\left(\frac{113}{192}\right)\) \(e\left(\frac{139}{384}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{4608}(31,\cdot)\) 4608.bo 48 no \(-1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4608}(35,\cdot)\) 4608.cc 128 no \(1\) \(1\) \(e\left(\frac{11}{128}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{103}{128}\right)\) \(e\left(\frac{5}{128}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{125}{128}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{73}{128}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{4608}(37,\cdot)\) 4608.cb 128 no \(1\) \(1\) \(e\left(\frac{25}{128}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{77}{128}\right)\) \(e\left(\frac{87}{128}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{63}{128}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{3}{128}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{4608}(41,\cdot)\) 4608.cf 192 no \(-1\) \(1\) \(e\left(\frac{29}{192}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{179}{192}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{4608}(43,\cdot)\) 4608.cl 384 yes \(-1\) \(1\) \(e\left(\frac{311}{384}\right)\) \(e\left(\frac{83}{192}\right)\) \(e\left(\frac{259}{384}\right)\) \(e\left(\frac{89}{384}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{59}{128}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{119}{192}\right)\) \(e\left(\frac{109}{384}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{4608}(47,\cdot)\) 4608.bw 96 no \(1\) \(1\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(49,\cdot)\) 4608.bz 96 no \(1\) \(1\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(53,\cdot)\) 4608.cd 128 no \(-1\) \(1\) \(e\left(\frac{69}{128}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{105}{128}\right)\) \(e\left(\frac{43}{128}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{115}{128}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{39}{128}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{4608}(55,\cdot)\) 4608.bv 64 no \(-1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(59,\cdot)\) 4608.cj 384 yes \(1\) \(1\) \(e\left(\frac{307}{384}\right)\) \(e\left(\frac{127}{192}\right)\) \(e\left(\frac{47}{384}\right)\) \(e\left(\frac{349}{384}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{7}{128}\right)\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{115}{192}\right)\) \(e\left(\frac{257}{384}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{4608}(61,\cdot)\) 4608.ck 384 yes \(1\) \(1\) \(e\left(\frac{377}{384}\right)\) \(e\left(\frac{125}{192}\right)\) \(e\left(\frac{301}{384}\right)\) \(e\left(\frac{119}{384}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{117}{128}\right)\) \(e\left(\frac{79}{192}\right)\) \(e\left(\frac{185}{192}\right)\) \(e\left(\frac{163}{384}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{4608}(65,\cdot)\) 4608.bi 24 no \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4608}(67,\cdot)\) 4608.cl 384 yes \(-1\) \(1\) \(e\left(\frac{217}{384}\right)\) \(e\left(\frac{61}{192}\right)\) \(e\left(\frac{77}{384}\right)\) \(e\left(\frac{151}{384}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{21}{128}\right)\) \(e\left(\frac{143}{192}\right)\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{323}{384}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{4608}(71,\cdot)\) 4608.bu 64 no \(1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(73,\cdot)\) 4608.bt 64 no \(1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(77,\cdot)\) 4608.ci 384 yes \(-1\) \(1\) \(e\left(\frac{157}{384}\right)\) \(e\left(\frac{49}{192}\right)\) \(e\left(\frac{161}{384}\right)\) \(e\left(\frac{211}{384}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{73}{128}\right)\) \(e\left(\frac{107}{192}\right)\) \(e\left(\frac{157}{192}\right)\) \(e\left(\frac{239}{384}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{4608}(79,\cdot)\) 4608.by 96 no \(-1\) \(1\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(83,\cdot)\) 4608.cj 384 yes \(1\) \(1\) \(e\left(\frac{245}{384}\right)\) \(e\left(\frac{137}{192}\right)\) \(e\left(\frac{25}{384}\right)\) \(e\left(\frac{251}{384}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{1}{128}\right)\) \(e\left(\frac{115}{192}\right)\) \(e\left(\frac{53}{192}\right)\) \(e\left(\frac{55}{384}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{4608}(85,\cdot)\) 4608.ck 384 yes \(1\) \(1\) \(e\left(\frac{343}{384}\right)\) \(e\left(\frac{19}{192}\right)\) \(e\left(\frac{227}{384}\right)\) \(e\left(\frac{313}{384}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{27}{128}\right)\) \(e\left(\frac{161}{192}\right)\) \(e\left(\frac{151}{192}\right)\) \(e\left(\frac{77}{384}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{4608}(89,\cdot)\) 4608.bs 64 no \(-1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(91,\cdot)\) 4608.ca 128 no \(-1\) \(1\) \(e\left(\frac{57}{128}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{45}{128}\right)\) \(e\left(\frac{55}{128}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{95}{128}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{99}{128}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{4608}(95,\cdot)\) 4608.bp 48 no \(1\) \(1\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{2}{3}\right)\)
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