LMFDB - Group of Dirichlet characters of modulus 62400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(62400)

pari: g = idealstar(,62400,2)

Character group

sage: G.order() pari: g.no
Order	=	15360
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{62400}(33151,\cdot)$, $\chi_{62400}(58501,\cdot)$, $\chi_{62400}(20801,\cdot)$, $\chi_{62400}(14977,\cdot)$, $\chi_{62400}(43201,\cdot)$

First 32 of 15360 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{62400}(1,\cdot)$	62400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{62400}(7,\cdot)$	62400.wx	24	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{62400}(11,\cdot)$	62400.bow	240	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{62400}(17,\cdot)$	62400.bgj	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{62400}(19,\cdot)$	62400.bor	240	no	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{62400}(23,\cdot)$	62400.bmy	120	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{62400}(29,\cdot)$	62400.bpd	240	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{62400}(31,\cdot)$	62400.tw	20	no	$1$	$1$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$-1$
$\chi_{62400}(37,\cdot)$	62400.bnu	240	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{62400}(41,\cdot)$	62400.bky	120	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{62400}(43,\cdot)$	62400.bdq	48	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{48}\right)$	$-1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{62400}(47,\cdot)$	62400.vn	20	no	$1$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$-1$
$\chi_{62400}(49,\cdot)$	62400.om	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{62400}(53,\cdot)$	62400.biz	80	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{62400}(59,\cdot)$	62400.bok	240	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{62400}(61,\cdot)$	62400.bpa	240	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{62400}(67,\cdot)$	62400.bpk	240	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{62400}(71,\cdot)$	62400.blb	120	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{62400}(73,\cdot)$	62400.bai	40	no	$1$	$1$	$i$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{62400}(77,\cdot)$	62400.bip	80	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{62400}(79,\cdot)$	62400.sa	20	no	$-1$	$1$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{62400}(83,\cdot)$	62400.biq	80	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{62400}(89,\cdot)$	62400.bnh	120	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{62400}(97,\cdot)$	62400.bid	60	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{62400}(101,\cdot)$	62400.bdg	48	no	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{48}\right)$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{62400}(103,\cdot)$	62400.bbl	40	no	$1$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{62400}(107,\cdot)$	62400.bed	48	no	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{48}\right)$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{62400}(109,\cdot)$	62400.bjk	80	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{62400}(113,\cdot)$	62400.bgg	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{62400}(119,\cdot)$	62400.blk	120	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{62400}(121,\cdot)$	62400.blu	120	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{62400}(127,\cdot)$	62400.bhc	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 $\F_{q}$

Modulus	$62400$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{4}\times C_{240}\)
Order	$15360$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{62400}(1,\cdot)\)	62400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{62400}(7,\cdot)\)	62400.wx	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{62400}(11,\cdot)\)	62400.bow	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{62400}(17,\cdot)\)	62400.bgj	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{62400}(19,\cdot)\)	62400.bor	240	no	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{62400}(23,\cdot)\)	62400.bmy	120	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{62400}(29,\cdot)\)	62400.bpd	240	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{62400}(31,\cdot)\)	62400.tw	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)
\(\chi_{62400}(37,\cdot)\)	62400.bnu	240	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{62400}(41,\cdot)\)	62400.bky	120	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{62400}(43,\cdot)\)	62400.bdq	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(-1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{62400}(47,\cdot)\)	62400.vn	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)
\(\chi_{62400}(49,\cdot)\)	62400.om	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{62400}(53,\cdot)\)	62400.biz	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{62400}(59,\cdot)\)	62400.bok	240	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{62400}(61,\cdot)\)	62400.bpa	240	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{62400}(67,\cdot)\)	62400.bpk	240	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{62400}(71,\cdot)\)	62400.blb	120	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{62400}(73,\cdot)\)	62400.bai	40	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{62400}(77,\cdot)\)	62400.bip	80	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{62400}(79,\cdot)\)	62400.sa	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{62400}(83,\cdot)\)	62400.biq	80	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{62400}(89,\cdot)\)	62400.bnh	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{62400}(97,\cdot)\)	62400.bid	60	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{62400}(101,\cdot)\)	62400.bdg	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{62400}(103,\cdot)\)	62400.bbl	40	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{62400}(107,\cdot)\)	62400.bed	48	no	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{62400}(109,\cdot)\)	62400.bjk	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{62400}(113,\cdot)\)	62400.bgg	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{62400}(119,\cdot)\)	62400.blk	120	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{62400}(121,\cdot)\)	62400.blu	120	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{62400}(127,\cdot)\)	62400.bhc	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.