LMFDB - Group of Dirichlet characters of modulus 92400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(92400)

pari: g = idealstar(,92400,2)

Character group

sage: G.order() pari: g.no
Order	=	19200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{92400}(11551,\cdot)$, $\chi_{92400}(69301,\cdot)$, $\chi_{92400}(61601,\cdot)$, $\chi_{92400}(22177,\cdot)$, $\chi_{92400}(79201,\cdot)$, $\chi_{92400}(67201,\cdot)$

First 32 of 19200 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	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{92400}(1,\cdot)$	92400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{92400}(13,\cdot)$	92400.bvk	20	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{9}{20}\right)$
$\chi_{92400}(17,\cdot)$	92400.cwb	60	no	$1$	$1$	$-i$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{7}{12}\right)$
$\chi_{92400}(19,\cdot)$	92400.cqq	60	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{60}\right)$	$-1$	$i$	$e\left(\frac{11}{30}\right)$
$\chi_{92400}(23,\cdot)$	92400.cwf	60	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{1}{60}\right)$
$\chi_{92400}(29,\cdot)$	92400.bss	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$1$	$e\left(\frac{1}{20}\right)$	$-1$	$-i$	$e\left(\frac{4}{5}\right)$
$\chi_{92400}(31,\cdot)$	92400.cfk	30	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{30}\right)$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{14}{15}\right)$
$\chi_{92400}(37,\cdot)$	92400.cml	60	no	$-1$	$1$	$-1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{11}{12}\right)$
$\chi_{92400}(41,\cdot)$	92400.ti	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$
$\chi_{92400}(43,\cdot)$	92400.cu	4	no	$-1$	$1$	$-1$	$i$	$i$	$i$	$-i$	$-1$	$1$	$1$	$-1$	$i$
$\chi_{92400}(47,\cdot)$	92400.cuu	60	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{1}{60}\right)$
$\chi_{92400}(53,\cdot)$	92400.dia	60	yes	$1$	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{7}{12}\right)$
$\chi_{92400}(59,\cdot)$	92400.css	60	yes	$-1$	$1$	$-i$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{92400}(61,\cdot)$	92400.cpu	60	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{29}{30}\right)$
$\chi_{92400}(67,\cdot)$	92400.cny	60	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{53}{60}\right)$
$\chi_{92400}(71,\cdot)$	92400.vk	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$
$\chi_{92400}(73,\cdot)$	92400.ctk	60	no	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{60}\right)$	$-1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{47}{60}\right)$
$\chi_{92400}(79,\cdot)$	92400.cly	30	no	$1$	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{92400}(83,\cdot)$	92400.bbn	20	yes	$-1$	$1$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$i$
$\chi_{92400}(89,\cdot)$	92400.cha	30	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{23}{30}\right)$
$\chi_{92400}(97,\cdot)$	92400.blz	20	no	$1$	$1$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$-i$
$\chi_{92400}(101,\cdot)$	92400.cqj	60	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{2}{15}\right)$
$\chi_{92400}(103,\cdot)$	92400.cxd	60	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{60}\right)$	$-1$	$i$	$e\left(\frac{13}{60}\right)$
$\chi_{92400}(107,\cdot)$	92400.cnn	60	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{19}{60}\right)$
$\chi_{92400}(109,\cdot)$	92400.dda	60	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{7}{30}\right)$
$\chi_{92400}(113,\cdot)$	92400.bjc	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{1}{20}\right)$
$\chi_{92400}(127,\cdot)$	92400.bnt	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{11}{20}\right)$
$\chi_{92400}(131,\cdot)$	92400.crh	60	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{29}{30}\right)$
$\chi_{92400}(137,\cdot)$	92400.cyq	60	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{60}\right)$	$-1$	$i$	$e\left(\frac{41}{60}\right)$
$\chi_{92400}(139,\cdot)$	92400.bse	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{7}{10}\right)$
$\chi_{92400}(149,\cdot)$	92400.ctj	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{13}{15}\right)$
$\chi_{92400}(151,\cdot)$	92400.caj	30	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{7}{30}\right)$

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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	$92400$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{20}\times C_{60}\)
Order	$19200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{92400}(1,\cdot)\)	92400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{92400}(13,\cdot)\)	92400.bvk	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{92400}(17,\cdot)\)	92400.cwb	60	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{92400}(19,\cdot)\)	92400.cqq	60	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{92400}(23,\cdot)\)	92400.cwf	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{92400}(29,\cdot)\)	92400.bss	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{92400}(31,\cdot)\)	92400.cfk	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{92400}(37,\cdot)\)	92400.cml	60	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{92400}(41,\cdot)\)	92400.ti	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{92400}(43,\cdot)\)	92400.cu	4	no	\(-1\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(i\)
\(\chi_{92400}(47,\cdot)\)	92400.cuu	60	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{92400}(53,\cdot)\)	92400.dia	60	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{92400}(59,\cdot)\)	92400.css	60	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{92400}(61,\cdot)\)	92400.cpu	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{92400}(67,\cdot)\)	92400.cny	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{92400}(71,\cdot)\)	92400.vk	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{92400}(73,\cdot)\)	92400.ctk	60	no	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(-1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{92400}(79,\cdot)\)	92400.cly	30	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{92400}(83,\cdot)\)	92400.bbn	20	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(i\)
\(\chi_{92400}(89,\cdot)\)	92400.cha	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{92400}(97,\cdot)\)	92400.blz	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(-i\)
\(\chi_{92400}(101,\cdot)\)	92400.cqj	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{92400}(103,\cdot)\)	92400.cxd	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{92400}(107,\cdot)\)	92400.cnn	60	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{92400}(109,\cdot)\)	92400.dda	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{92400}(113,\cdot)\)	92400.bjc	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{92400}(127,\cdot)\)	92400.bnt	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{92400}(131,\cdot)\)	92400.crh	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{92400}(137,\cdot)\)	92400.cyq	60	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{92400}(139,\cdot)\)	92400.bse	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{92400}(149,\cdot)\)	92400.ctj	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{92400}(151,\cdot)\)	92400.caj	30	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{30}\right)\)

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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.