LMFDB - Group of Dirichlet characters of modulus 5184

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

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.