LMFDB - Group of Dirichlet characters of modulus 23400

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(23400)

gp:g = idealstar(,23400,2)

magma:G = FullDirichletGroup(23400);

Character group

Order	=	5760	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{60}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{23400}(17551,\cdot)$, $\chi_{23400}(11701,\cdot)$, $\chi_{23400}(20801,\cdot)$, $\chi_{23400}(14977,\cdot)$, $\chi_{23400}(19801,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 5760 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{23400}(1,\cdot)$	23400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{23400}(7,\cdot)$	23400.jl	12	no	$-1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-i$
$\chi_{23400}(11,\cdot)$	23400.bbg	60	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{23400}(17,\cdot)$	23400.bdb	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{23400}(19,\cdot)$	23400.bbi	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{23400}(23,\cdot)$	23400.zi	60	no	$-1$	$1$	$-i$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{5}\right)$	$-i$
$\chi_{23400}(29,\cdot)$	23400.ve	30	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{23400}(31,\cdot)$	23400.bcg	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{23400}(37,\cdot)$	23400.yg	60	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{23400}(41,\cdot)$	23400.bbd	60	no	$1$	$1$	$i$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{20}\right)$	$-1$
$\chi_{23400}(43,\cdot)$	23400.oi	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$
$\chi_{23400}(47,\cdot)$	23400.beb	60	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{23400}(49,\cdot)$	23400.hz	6	no	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$
$\chi_{23400}(53,\cdot)$	23400.rf	20	no	$1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{23400}(59,\cdot)$	23400.bar	60	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{23400}(61,\cdot)$	23400.wz	30	yes	$1$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{23400}(67,\cdot)$	23400.bet	60	yes	$-1$	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{20}\right)$	$i$
$\chi_{23400}(71,\cdot)$	23400.bbj	60	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{23400}(73,\cdot)$	23400.rb	20	no	$1$	$1$	$-1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$-i$
$\chi_{23400}(77,\cdot)$	23400.zt	60	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{23400}(79,\cdot)$	23400.uc	30	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{23400}(83,\cdot)$	23400.bdz	60	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{23400}(89,\cdot)$	23400.bak	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{23400}(97,\cdot)$	23400.xk	60	no	$1$	$1$	$-1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{20}\right)$	$i$
$\chi_{23400}(101,\cdot)$	23400.fv	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{23400}(103,\cdot)$	23400.bdc	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{23400}(107,\cdot)$	23400.ov	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{23400}(109,\cdot)$	23400.rm	20	no	$-1$	$1$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{20}\right)$	$-1$
$\chi_{23400}(113,\cdot)$	23400.bdg	60	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{23400}(119,\cdot)$	23400.baw	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{23400}(121,\cdot)$	23400.ws	30	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{23400}(127,\cdot)$	23400.bcm	60	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$23400$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{60}\)
Order	$5760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{23400}(1,\cdot)\)	23400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{23400}(7,\cdot)\)	23400.jl	12	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-i\)
\(\chi_{23400}(11,\cdot)\)	23400.bbg	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{23400}(17,\cdot)\)	23400.bdb	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{23400}(19,\cdot)\)	23400.bbi	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{23400}(23,\cdot)\)	23400.zi	60	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)
\(\chi_{23400}(29,\cdot)\)	23400.ve	30	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{23400}(31,\cdot)\)	23400.bcg	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{23400}(37,\cdot)\)	23400.yg	60	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{23400}(41,\cdot)\)	23400.bbd	60	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)
\(\chi_{23400}(43,\cdot)\)	23400.oi	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{23400}(47,\cdot)\)	23400.beb	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{23400}(49,\cdot)\)	23400.hz	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{23400}(53,\cdot)\)	23400.rf	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{23400}(59,\cdot)\)	23400.bar	60	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{23400}(61,\cdot)\)	23400.wz	30	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{23400}(67,\cdot)\)	23400.bet	60	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(i\)
\(\chi_{23400}(71,\cdot)\)	23400.bbj	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{23400}(73,\cdot)\)	23400.rb	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)
\(\chi_{23400}(77,\cdot)\)	23400.zt	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{23400}(79,\cdot)\)	23400.uc	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{23400}(83,\cdot)\)	23400.bdz	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{23400}(89,\cdot)\)	23400.bak	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{23400}(97,\cdot)\)	23400.xk	60	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)
\(\chi_{23400}(101,\cdot)\)	23400.fv	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{23400}(103,\cdot)\)	23400.bdc	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{23400}(107,\cdot)\)	23400.ov	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{23400}(109,\cdot)\)	23400.rm	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)
\(\chi_{23400}(113,\cdot)\)	23400.bdg	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{23400}(119,\cdot)\)	23400.baw	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{23400}(121,\cdot)\)	23400.ws	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{23400}(127,\cdot)\)	23400.bcm	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)

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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.