# Properties

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

Show commands: PariGP / 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 $$1$$ $$1$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{43}{54}\right)$$