LMFDB - Group of Dirichlet characters of modulus 4672

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4672)

pari: g = idealstar(,4672,2)

Character group

sage: G.order() pari: g.no
Order	=	2304
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{8}\times C_{144}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4672}(1023,\cdot)$, $\chi_{4672}(2629,\cdot)$, $\chi_{4672}(2049,\cdot)$

First 32 of 2304 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4672}(1,\cdot)$	4672.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4672}(3,\cdot)$	4672.fh	48	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{4672}(5,\cdot)$	4672.gr	144	yes	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{4672}(7,\cdot)$	4672.eb	24	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$1$
$\chi_{4672}(9,\cdot)$	4672.dx	24	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{4672}(11,\cdot)$	4672.gx	144	yes	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{4672}(13,\cdot)$	4672.gt	144	yes	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{4672}(15,\cdot)$	4672.gh	72	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{4672}(17,\cdot)$	4672.eh	24	no	$-1$	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{4672}(19,\cdot)$	4672.gl	144	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{4672}(21,\cdot)$	4672.fj	48	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{48}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{4672}(23,\cdot)$	4672.fn	72	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{4672}(25,\cdot)$	4672.ge	72	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{4672}(27,\cdot)$	4672.cq	16	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{4672}(29,\cdot)$	4672.gr	144	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{4672}(31,\cdot)$	4672.gc	72	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{4672}(33,\cdot)$	4672.ga	72	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{4672}(35,\cdot)$	4672.gu	144	yes	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{4672}(37,\cdot)$	4672.go	144	yes	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{4672}(39,\cdot)$	4672.fx	72	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4672}(41,\cdot)$	4672.fo	72	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{4672}(43,\cdot)$	4672.fi	48	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{25}{48}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{4672}(45,\cdot)$	4672.gi	144	yes	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{4672}(47,\cdot)$	4672.fk	72	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{4672}(49,\cdot)$	4672.cj	12	no	$1$	$1$	$i$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$1$
$\chi_{4672}(51,\cdot)$	4672.cu	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{4672}(53,\cdot)$	4672.gr	144	yes	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{4672}(55,\cdot)$	4672.fy	72	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{4672}(57,\cdot)$	4672.fo	72	no	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{4672}(59,\cdot)$	4672.gq	144	yes	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{4672}(61,\cdot)$	4672.gv	144	yes	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{4672}(63,\cdot)$	4672.bk	8	no	$1$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$

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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	$4672$
Structure	\(C_{2}\times C_{8}\times C_{144}\)
Order	$2304$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4672}(1,\cdot)\)	4672.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4672}(3,\cdot)\)	4672.fh	48	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{4672}(5,\cdot)\)	4672.gr	144	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{4672}(7,\cdot)\)	4672.eb	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(1\)
\(\chi_{4672}(9,\cdot)\)	4672.dx	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{4672}(11,\cdot)\)	4672.gx	144	yes	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{4672}(13,\cdot)\)	4672.gt	144	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{4672}(15,\cdot)\)	4672.gh	72	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{4672}(17,\cdot)\)	4672.eh	24	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{4672}(19,\cdot)\)	4672.gl	144	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{4672}(21,\cdot)\)	4672.fj	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{4672}(23,\cdot)\)	4672.fn	72	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{4672}(25,\cdot)\)	4672.ge	72	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{4672}(27,\cdot)\)	4672.cq	16	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{4672}(29,\cdot)\)	4672.gr	144	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{4672}(31,\cdot)\)	4672.gc	72	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{4672}(33,\cdot)\)	4672.ga	72	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{4672}(35,\cdot)\)	4672.gu	144	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{4672}(37,\cdot)\)	4672.go	144	yes	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{4672}(39,\cdot)\)	4672.fx	72	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4672}(41,\cdot)\)	4672.fo	72	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{4672}(43,\cdot)\)	4672.fi	48	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{4672}(45,\cdot)\)	4672.gi	144	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{4672}(47,\cdot)\)	4672.fk	72	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{4672}(49,\cdot)\)	4672.cj	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(1\)
\(\chi_{4672}(51,\cdot)\)	4672.cu	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{4672}(53,\cdot)\)	4672.gr	144	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{4672}(55,\cdot)\)	4672.fy	72	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{4672}(57,\cdot)\)	4672.fo	72	no	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{4672}(59,\cdot)\)	4672.gq	144	yes	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{4672}(61,\cdot)\)	4672.gv	144	yes	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{4672}(63,\cdot)\)	4672.bk	8	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)

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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.