LMFDB - Group of Dirichlet characters of modulus 2592

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2592)

pari: g = idealstar(,2592,2)

Character group

sage: G.order() pari: g.no
Order	=	864
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{216}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2592}(2431,\cdot)$, $\chi_{2592}(325,\cdot)$, $\chi_{2592}(1217,\cdot)$

First 32 of 864 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2592}(1,\cdot)$	2592.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2592}(5,\cdot)$	2592.cj	216	yes	$-1$	$1$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{2592}(7,\cdot)$	2592.cf	108	no	$-1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{2592}(11,\cdot)$	2592.ci	216	yes	$1$	$1$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{2592}(13,\cdot)$	2592.cl	216	yes	$1$	$1$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{67}{216}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{2592}(17,\cdot)$	2592.bj	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2592}(19,\cdot)$	2592.cd	72	no	$-1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2592}(23,\cdot)$	2592.ce	108	no	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{2592}(25,\cdot)$	2592.ch	108	no	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{2592}(29,\cdot)$	2592.cj	216	yes	$-1$	$1$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2592}(31,\cdot)$	2592.bu	54	no	$-1$	$1$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{2592}(35,\cdot)$	2592.cb	72	no	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{2592}(37,\cdot)$	2592.cc	72	no	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{2592}(41,\cdot)$	2592.cg	108	no	$-1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{2592}(43,\cdot)$	2592.ck	216	yes	$-1$	$1$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{2592}(47,\cdot)$	2592.bv	54	no	$1$	$1$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{2592}(49,\cdot)$	2592.bx	54	no	$1$	$1$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{2592}(53,\cdot)$	2592.bm	24	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2592}(55,\cdot)$	2592.ba	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2592}(59,\cdot)$	2592.ci	216	yes	$1$	$1$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{2592}(61,\cdot)$	2592.cl	216	yes	$1$	$1$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{2592}(65,\cdot)$	2592.bw	54	no	$-1$	$1$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{2592}(67,\cdot)$	2592.ck	216	yes	$-1$	$1$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{209}{216}\right)$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{2592}(71,\cdot)$	2592.bs	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2592}(73,\cdot)$	2592.bp	36	no	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2592}(77,\cdot)$	2592.cj	216	yes	$-1$	$1$	$e\left(\frac{49}{216}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{2592}(79,\cdot)$	2592.bz	54	no	$-1$	$1$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{2592}(83,\cdot)$	2592.ci	216	yes	$1$	$1$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{67}{216}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{2592}(85,\cdot)$	2592.cl	216	yes	$1$	$1$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{2592}(89,\cdot)$	2592.br	36	no	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2592}(91,\cdot)$	2592.cd	72	no	$-1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2592}(95,\cdot)$	2592.by	54	no	$1$	$1$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{43}{54}\right)$

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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	$2592$
Structure	\(C_{2}\times C_{2}\times C_{216}\)
Order	$864$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2592}(1,\cdot)\)	2592.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2592}(5,\cdot)\)	2592.cj	216	yes	\(-1\)	\(1\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{2592}(7,\cdot)\)	2592.cf	108	no	\(-1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{2592}(11,\cdot)\)	2592.ci	216	yes	\(1\)	\(1\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{2592}(13,\cdot)\)	2592.cl	216	yes	\(1\)	\(1\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{67}{216}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{2592}(17,\cdot)\)	2592.bj	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2592}(19,\cdot)\)	2592.cd	72	no	\(-1\)	\(1\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2592}(23,\cdot)\)	2592.ce	108	no	\(1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{2592}(25,\cdot)\)	2592.ch	108	no	\(1\)	\(1\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{2592}(29,\cdot)\)	2592.cj	216	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2592}(31,\cdot)\)	2592.bu	54	no	\(-1\)	\(1\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{2592}(35,\cdot)\)	2592.cb	72	no	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{2592}(37,\cdot)\)	2592.cc	72	no	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{2592}(41,\cdot)\)	2592.cg	108	no	\(-1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{2592}(43,\cdot)\)	2592.ck	216	yes	\(-1\)	\(1\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{2592}(47,\cdot)\)	2592.bv	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{2592}(49,\cdot)\)	2592.bx	54	no	\(1\)	\(1\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{2592}(53,\cdot)\)	2592.bm	24	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2592}(55,\cdot)\)	2592.ba	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2592}(59,\cdot)\)	2592.ci	216	yes	\(1\)	\(1\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{2592}(61,\cdot)\)	2592.cl	216	yes	\(1\)	\(1\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{2592}(65,\cdot)\)	2592.bw	54	no	\(-1\)	\(1\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{2592}(67,\cdot)\)	2592.ck	216	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{209}{216}\right)\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{2592}(71,\cdot)\)	2592.bs	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2592}(73,\cdot)\)	2592.bp	36	no	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2592}(77,\cdot)\)	2592.cj	216	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{216}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{2592}(79,\cdot)\)	2592.bz	54	no	\(-1\)	\(1\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{2592}(83,\cdot)\)	2592.ci	216	yes	\(1\)	\(1\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{67}{216}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{2592}(85,\cdot)\)	2592.cl	216	yes	\(1\)	\(1\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{2592}(89,\cdot)\)	2592.br	36	no	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2592}(91,\cdot)\)	2592.cd	72	no	\(-1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2592}(95,\cdot)\)	2592.by	54	no	\(1\)	\(1\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{43}{54}\right)\)

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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.