Properties

Modulus $5184$
Structure \(C_{2}\times C_{2}\times C_{432}\)
Order $1728$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5184)
 
pari: g = idealstar(,5184,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1728
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{432}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{5184}(2431,\cdot)$, $\chi_{5184}(325,\cdot)$, $\chi_{5184}(1217,\cdot)$

First 32 of 1728 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{5184}(1,\cdot)\) 5184.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5184}(5,\cdot)\) 5184.da 432 yes \(-1\) \(1\) \(e\left(\frac{371}{432}\right)\) \(e\left(\frac{95}{216}\right)\) \(e\left(\frac{367}{432}\right)\) \(e\left(\frac{149}{432}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{121}{216}\right)\) \(e\left(\frac{155}{216}\right)\) \(e\left(\frac{193}{432}\right)\) \(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(7,\cdot)\) 5184.cw 216 no \(-1\) \(1\) \(e\left(\frac{95}{216}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{103}{216}\right)\) \(e\left(\frac{161}{216}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{181}{216}\right)\) \(e\left(\frac{23}{54}\right)\)
\(\chi_{5184}(11,\cdot)\) 5184.db 432 yes \(1\) \(1\) \(e\left(\frac{367}{432}\right)\) \(e\left(\frac{103}{216}\right)\) \(e\left(\frac{83}{432}\right)\) \(e\left(\frac{265}{432}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{35}{144}\right)\) \(e\left(\frac{113}{216}\right)\) \(e\left(\frac{151}{216}\right)\) \(e\left(\frac{149}{432}\right)\) \(e\left(\frac{22}{27}\right)\)
\(\chi_{5184}(13,\cdot)\) 5184.cy 432 yes \(1\) \(1\) \(e\left(\frac{149}{432}\right)\) \(e\left(\frac{161}{216}\right)\) \(e\left(\frac{265}{432}\right)\) \(e\left(\frac{107}{432}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{97}{144}\right)\) \(e\left(\frac{163}{216}\right)\) \(e\left(\frac{149}{216}\right)\) \(e\left(\frac{343}{432}\right)\) \(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(17,\cdot)\) 5184.bv 36 no \(-1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{5184}(19,\cdot)\) 5184.cs 144 no \(-1\) \(1\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{35}{144}\right)\) \(e\left(\frac{97}{144}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{101}{144}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{5184}(23,\cdot)\) 5184.cu 216 no \(1\) \(1\) \(e\left(\frac{121}{216}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{113}{216}\right)\) \(e\left(\frac{163}{216}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{107}{108}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{35}{216}\right)\) \(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(25,\cdot)\) 5184.cx 216 no \(1\) \(1\) \(e\left(\frac{155}{216}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{151}{216}\right)\) \(e\left(\frac{149}{216}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{193}{216}\right)\) \(e\left(\frac{1}{27}\right)\)
\(\chi_{5184}(29,\cdot)\) 5184.da 432 yes \(-1\) \(1\) \(e\left(\frac{193}{432}\right)\) \(e\left(\frac{181}{216}\right)\) \(e\left(\frac{149}{432}\right)\) \(e\left(\frac{343}{432}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{101}{144}\right)\) \(e\left(\frac{35}{216}\right)\) \(e\left(\frac{193}{216}\right)\) \(e\left(\frac{395}{432}\right)\) \(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(31,\cdot)\) 5184.ch 54 no \(-1\) \(1\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(35,\cdot)\) 5184.ct 144 no \(1\) \(1\) \(e\left(\frac{43}{144}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{47}{144}\right)\) \(e\left(\frac{13}{144}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{41}{144}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{5184}(37,\cdot)\) 5184.cq 144 no \(1\) \(1\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{133}{144}\right)\) \(e\left(\frac{95}{144}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{139}{144}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{5184}(41,\cdot)\) 5184.cv 216 no \(-1\) \(1\) \(e\left(\frac{97}{216}\right)\) \(e\left(\frac{49}{108}\right)\) \(e\left(\frac{29}{216}\right)\) \(e\left(\frac{211}{216}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{203}{216}\right)\) \(e\left(\frac{17}{27}\right)\)
\(\chi_{5184}(43,\cdot)\) 5184.cz 432 yes \(-1\) \(1\) \(e\left(\frac{79}{432}\right)\) \(e\left(\frac{31}{216}\right)\) \(e\left(\frac{371}{432}\right)\) \(e\left(\frac{193}{432}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{107}{144}\right)\) \(e\left(\frac{77}{216}\right)\) \(e\left(\frac{79}{216}\right)\) \(e\left(\frac{5}{432}\right)\) \(e\left(\frac{4}{27}\right)\)
\(\chi_{5184}(47,\cdot)\) 5184.cm 108 no \(1\) \(1\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{101}{108}\right)\) \(e\left(\frac{31}{108}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(49,\cdot)\) 5184.cp 108 no \(1\) \(1\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{103}{108}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{73}{108}\right)\) \(e\left(\frac{23}{27}\right)\)
\(\chi_{5184}(53,\cdot)\) 5184.ca 48 no \(-1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{5184}(55,\cdot)\) 5184.bp 24 no \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{5184}(59,\cdot)\) 5184.db 432 yes \(1\) \(1\) \(e\left(\frac{227}{432}\right)\) \(e\left(\frac{59}{216}\right)\) \(e\left(\frac{295}{432}\right)\) \(e\left(\frac{5}{432}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{55}{144}\right)\) \(e\left(\frac{157}{216}\right)\) \(e\left(\frac{11}{216}\right)\) \(e\left(\frac{337}{432}\right)\) \(e\left(\frac{5}{27}\right)\)
\(\chi_{5184}(61,\cdot)\) 5184.cy 432 yes \(1\) \(1\) \(e\left(\frac{145}{432}\right)\) \(e\left(\frac{61}{216}\right)\) \(e\left(\frac{197}{432}\right)\) \(e\left(\frac{223}{432}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{77}{144}\right)\) \(e\left(\frac{47}{216}\right)\) \(e\left(\frac{145}{216}\right)\) \(e\left(\frac{299}{432}\right)\) \(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(65,\cdot)\) 5184.ce 54 no \(-1\) \(1\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\)
\(\chi_{5184}(67,\cdot)\) 5184.cz 432 yes \(-1\) \(1\) \(e\left(\frac{401}{432}\right)\) \(e\left(\frac{89}{216}\right)\) \(e\left(\frac{13}{432}\right)\) \(e\left(\frac{143}{432}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{133}{144}\right)\) \(e\left(\frac{19}{216}\right)\) \(e\left(\frac{185}{216}\right)\) \(e\left(\frac{91}{432}\right)\) \(e\left(\frac{8}{27}\right)\)
\(\chi_{5184}(71,\cdot)\) 5184.cj 72 no \(1\) \(1\) \(e\left(\frac{25}{72}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{5184}(73,\cdot)\) 5184.ck 72 no \(1\) \(1\) \(e\left(\frac{11}{72}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(77,\cdot)\) 5184.da 432 yes \(-1\) \(1\) \(e\left(\frac{125}{432}\right)\) \(e\left(\frac{209}{216}\right)\) \(e\left(\frac{289}{432}\right)\) \(e\left(\frac{155}{432}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{49}{144}\right)\) \(e\left(\frac{7}{216}\right)\) \(e\left(\frac{125}{216}\right)\) \(e\left(\frac{79}{432}\right)\) \(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(79,\cdot)\) 5184.cn 108 no \(-1\) \(1\) \(e\left(\frac{19}{108}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{101}{108}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{5184}(83,\cdot)\) 5184.db 432 yes \(1\) \(1\) \(e\left(\frac{373}{432}\right)\) \(e\left(\frac{37}{216}\right)\) \(e\left(\frac{401}{432}\right)\) \(e\left(\frac{307}{432}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{179}{216}\right)\) \(e\left(\frac{157}{216}\right)\) \(e\left(\frac{215}{432}\right)\) \(e\left(\frac{10}{27}\right)\)
\(\chi_{5184}(85,\cdot)\) 5184.cy 432 yes \(1\) \(1\) \(e\left(\frac{287}{432}\right)\) \(e\left(\frac{155}{216}\right)\) \(e\left(\frac{235}{432}\right)\) \(e\left(\frac{209}{432}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{67}{144}\right)\) \(e\left(\frac{169}{216}\right)\) \(e\left(\frac{71}{216}\right)\) \(e\left(\frac{133}{432}\right)\) \(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(89,\cdot)\) 5184.ci 72 no \(-1\) \(1\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{72}\right)\) \(e\left(\frac{23}{72}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(91,\cdot)\) 5184.cs 144 no \(-1\) \(1\) \(e\left(\frac{113}{144}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{13}{144}\right)\) \(e\left(\frac{143}{144}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{19}{72}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{91}{144}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{5184}(95,\cdot)\) 5184.cd 54 no \(1\) \(1\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{43}{54}\right)\)
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