LMFDB - Group of Dirichlet characters of modulus 4650

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(4650)

gp:g = idealstar(,4650,2)

magma:G := FullDirichletGroup(4650);

Character group

Order	=	1200	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{10}\times C_{60}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(AbelianGroup(G));
Generators	=	$\chi_{4650}(3101,\cdot)$, $\chi_{4650}(2977,\cdot)$, $\chi_{4650}(1801,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1200 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$37$	$41$	$43$
$\chi_{4650}(1,\cdot)$	4650.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4650}(7,\cdot)$	4650.gg	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{4650}(11,\cdot)$	4650.fg	30	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4650}(13,\cdot)$	4650.fv	60	no	$1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{4650}(17,\cdot)$	4650.gd	60	no	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{4650}(19,\cdot)$	4650.em	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{15}\right)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4650}(23,\cdot)$	4650.dx	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{4650}(29,\cdot)$	4650.cl	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{4650}(37,\cdot)$	4650.fw	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{4650}(41,\cdot)$	4650.fc	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{4650}(43,\cdot)$	4650.fu	60	no	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{4650}(47,\cdot)$	4650.dv	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{4650}(49,\cdot)$	4650.eo	30	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4650}(53,\cdot)$	4650.gj	60	no	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{4650}(59,\cdot)$	4650.ek	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4650}(61,\cdot)$	4650.cp	10	no	$-1$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{4650}(67,\cdot)$	4650.gi	60	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{4650}(71,\cdot)$	4650.fc	30	no	$-1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{4650}(73,\cdot)$	4650.fz	60	no	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{30}\right)$	$-i$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{49}{60}\right)$
$\chi_{4650}(77,\cdot)$	4650.de	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{1}{20}\right)$
$\chi_{4650}(79,\cdot)$	4650.ei	30	no	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{4650}(83,\cdot)$	4650.ga	60	no	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{17}{30}\right)$	$i$	$-1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{4650}(89,\cdot)$	4650.bw	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{4650}(91,\cdot)$	4650.bq	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$
$\chi_{4650}(97,\cdot)$	4650.dg	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{4650}(101,\cdot)$	4650.bn	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{4650}(103,\cdot)$	4650.fp	60	no	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{4650}(107,\cdot)$	4650.fs	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{4650}(109,\cdot)$	4650.bv	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{4650}(113,\cdot)$	4650.gk	60	no	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{4650}(119,\cdot)$	4650.fn	30	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4650}(121,\cdot)$	4650.cz	15	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$4650$
Structure	\(C_{2}\times C_{10}\times C_{60}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(37\)	\(41\)	\(43\)
\(\chi_{4650}(1,\cdot)\)	4650.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4650}(7,\cdot)\)	4650.gg	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{4650}(11,\cdot)\)	4650.fg	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4650}(13,\cdot)\)	4650.fv	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{4650}(17,\cdot)\)	4650.gd	60	no	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{4650}(19,\cdot)\)	4650.em	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4650}(23,\cdot)\)	4650.dx	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{4650}(29,\cdot)\)	4650.cl	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{4650}(37,\cdot)\)	4650.fw	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{4650}(41,\cdot)\)	4650.fc	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{4650}(43,\cdot)\)	4650.fu	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{4650}(47,\cdot)\)	4650.dv	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{4650}(49,\cdot)\)	4650.eo	30	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4650}(53,\cdot)\)	4650.gj	60	no	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{4650}(59,\cdot)\)	4650.ek	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4650}(61,\cdot)\)	4650.cp	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{4650}(67,\cdot)\)	4650.gi	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{4650}(71,\cdot)\)	4650.fc	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{4650}(73,\cdot)\)	4650.fz	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{4650}(77,\cdot)\)	4650.de	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{4650}(79,\cdot)\)	4650.ei	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{4650}(83,\cdot)\)	4650.ga	60	no	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{4650}(89,\cdot)\)	4650.bw	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{4650}(91,\cdot)\)	4650.bq	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{4650}(97,\cdot)\)	4650.dg	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{4650}(101,\cdot)\)	4650.bn	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{4650}(103,\cdot)\)	4650.fp	60	no	\(-1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{4650}(107,\cdot)\)	4650.fs	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{4650}(109,\cdot)\)	4650.bv	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{4650}(113,\cdot)\)	4650.gk	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{4650}(119,\cdot)\)	4650.fn	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4650}(121,\cdot)\)	4650.cz	15	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)

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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.