LMFDB - Group of Dirichlet characters of modulus 723

Show commands: PariGP / SageMath

sage: H = DirichletGroup(723)

pari: g = idealstar(,723,2)

Character group

sage: G.order() pari: g.no
Order	=	480
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{723}(242,\cdot)$, $\chi_{723}(7,\cdot)$

First 32 of 480 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{723}(1,\cdot)$	723.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{723}(2,\cdot)$	723.x	24	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{19}{24}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{723}(4,\cdot)$	723.r	12	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{723}(5,\cdot)$	723.bc	40	yes	$-1$	$1$	$-i$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{23}{40}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{40}\right)$	$1$
$\chi_{723}(7,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(8,\cdot)$	723.m	8	yes	$-1$	$1$	$-i$	$-1$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{723}(10,\cdot)$	723.z	30	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{723}(11,\cdot)$	723.be	48	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(13,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{723}(14,\cdot)$	723.bn	240	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{723}(16,\cdot)$	723.i	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{723}(17,\cdot)$	723.bj	80	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{67}{80}\right)$	$-1$
$\chi_{723}(19,\cdot)$	723.bf	48	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(20,\cdot)$	723.bl	120	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{120}\right)$	$-i$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{723}(22,\cdot)$	723.bf	48	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{723}(23,\cdot)$	723.bj	80	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{69}{80}\right)$	$-1$
$\chi_{723}(25,\cdot)$	723.v	20	no	$1$	$1$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$1$
$\chi_{723}(26,\cdot)$	723.bj	80	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{9}{80}\right)$	$-1$
$\chi_{723}(28,\cdot)$	723.bi	80	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{17}{80}\right)$	$-1$
$\chi_{723}(29,\cdot)$	723.bl	120	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{77}{120}\right)$	$i$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{723}(31,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(32,\cdot)$	723.x	24	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{23}{24}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{723}(34,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(35,\cdot)$	723.bn	240	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(37,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(38,\cdot)$	723.be	48	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{723}(40,\cdot)$	723.v	20	no	$1$	$1$	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$1$
$\chi_{723}(41,\cdot)$	723.bc	40	yes	$-1$	$1$	$i$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{40}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{40}\right)$	$1$
$\chi_{723}(43,\cdot)$	723.bi	80	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{23}{80}\right)$	$-1$
$\chi_{723}(44,\cdot)$	723.t	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$
$\chi_{723}(46,\cdot)$	723.bm	240	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{723}(47,\cdot)$	723.bc	40	yes	$-1$	$1$	$-i$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{40}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{40}\right)$	$1$

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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	$723$
Structure	\(C_{2}\times C_{240}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{723}(1,\cdot)\)	723.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{723}(2,\cdot)\)	723.x	24	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{19}{24}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(4,\cdot)\)	723.r	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(5,\cdot)\)	723.bc	40	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(1\)
\(\chi_{723}(7,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(8,\cdot)\)	723.m	8	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{723}(10,\cdot)\)	723.z	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(11,\cdot)\)	723.be	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(13,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(14,\cdot)\)	723.bn	240	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(16,\cdot)\)	723.i	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(17,\cdot)\)	723.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(-1\)
\(\chi_{723}(19,\cdot)\)	723.bf	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(20,\cdot)\)	723.bl	120	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(-i\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(22,\cdot)\)	723.bf	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(23,\cdot)\)	723.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(-1\)
\(\chi_{723}(25,\cdot)\)	723.v	20	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)
\(\chi_{723}(26,\cdot)\)	723.bj	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(-1\)
\(\chi_{723}(28,\cdot)\)	723.bi	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(-1\)
\(\chi_{723}(29,\cdot)\)	723.bl	120	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(i\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(31,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(32,\cdot)\)	723.x	24	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{23}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(34,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(35,\cdot)\)	723.bn	240	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(37,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(38,\cdot)\)	723.be	48	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(40,\cdot)\)	723.v	20	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)
\(\chi_{723}(41,\cdot)\)	723.bc	40	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(1\)
\(\chi_{723}(43,\cdot)\)	723.bi	80	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(-1\)
\(\chi_{723}(44,\cdot)\)	723.t	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)
\(\chi_{723}(46,\cdot)\)	723.bm	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(47,\cdot)\)	723.bc	40	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(1\)

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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.