LMFDB - Group of Dirichlet characters of modulus 33600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(33600)

pari: g = idealstar(,33600,2)

Character group

sage: G.order() pari: g.no
Order	=	7680
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{33600}(28351,\cdot)$, $\chi_{33600}(10501,\cdot)$, $\chi_{33600}(11201,\cdot)$, $\chi_{33600}(5377,\cdot)$, $\chi_{33600}(28801,\cdot)$

First 32 of 7680 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{33600}(1,\cdot)$	33600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{33600}(11,\cdot)$	33600.vu	240	yes	$1$	$1$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{33600}(13,\cdot)$	33600.tm	80	no	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{33600}(17,\cdot)$	33600.rz	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$-1$
$\chi_{33600}(19,\cdot)$	33600.vl	240	no	$1$	$1$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{33600}(23,\cdot)$	33600.ua	120	no	$-1$	$1$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{33600}(29,\cdot)$	33600.te	80	no	$-1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{33600}(31,\cdot)$	33600.np	30	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{33600}(37,\cdot)$	33600.vz	240	no	$-1$	$1$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{33600}(41,\cdot)$	33600.pj	40	no	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{33600}(43,\cdot)$	33600.ix	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{33600}(47,\cdot)$	33600.sd	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$1$
$\chi_{33600}(53,\cdot)$	33600.vy	240	yes	$1$	$1$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{33600}(59,\cdot)$	33600.vn	240	yes	$-1$	$1$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{33600}(61,\cdot)$	33600.vq	240	no	$-1$	$1$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{33600}(67,\cdot)$	33600.ve	240	no	$1$	$1$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{33600}(71,\cdot)$	33600.ok	40	no	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{33600}(73,\cdot)$	33600.ud	120	no	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{33600}(79,\cdot)$	33600.rj	60	no	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{33600}(83,\cdot)$	33600.ss	80	yes	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{33600}(89,\cdot)$	33600.us	120	no	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{33600}(97,\cdot)$	33600.lq	20	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{33600}(101,\cdot)$	33600.py	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{33600}(103,\cdot)$	33600.ue	120	no	$-1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{33600}(107,\cdot)$	33600.qi	48	no	$-1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{33600}(109,\cdot)$	33600.vj	240	no	$1$	$1$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{33600}(113,\cdot)$	33600.kf	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{33600}(121,\cdot)$	33600.tw	120	no	$1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{33600}(127,\cdot)$	33600.lo	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{33600}(131,\cdot)$	33600.vi	240	yes	$-1$	$1$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{33600}(137,\cdot)$	33600.uh	120	no	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{33600}(139,\cdot)$	33600.ti	80	no	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{16}\right)$

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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	$33600$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{240}\)
Order	$7680$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{33600}(1,\cdot)\)	33600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{33600}(11,\cdot)\)	33600.vu	240	yes	\(1\)	\(1\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{33600}(13,\cdot)\)	33600.tm	80	no	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{33600}(17,\cdot)\)	33600.rz	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)
\(\chi_{33600}(19,\cdot)\)	33600.vl	240	no	\(1\)	\(1\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{33600}(23,\cdot)\)	33600.ua	120	no	\(-1\)	\(1\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{33600}(29,\cdot)\)	33600.te	80	no	\(-1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{33600}(31,\cdot)\)	33600.np	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{33600}(37,\cdot)\)	33600.vz	240	no	\(-1\)	\(1\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{33600}(41,\cdot)\)	33600.pj	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{33600}(43,\cdot)\)	33600.ix	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{33600}(47,\cdot)\)	33600.sd	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)
\(\chi_{33600}(53,\cdot)\)	33600.vy	240	yes	\(1\)	\(1\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{33600}(59,\cdot)\)	33600.vn	240	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{33600}(61,\cdot)\)	33600.vq	240	no	\(-1\)	\(1\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{33600}(67,\cdot)\)	33600.ve	240	no	\(1\)	\(1\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{33600}(71,\cdot)\)	33600.ok	40	no	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{33600}(73,\cdot)\)	33600.ud	120	no	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{33600}(79,\cdot)\)	33600.rj	60	no	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{33600}(83,\cdot)\)	33600.ss	80	yes	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{33600}(89,\cdot)\)	33600.us	120	no	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{33600}(97,\cdot)\)	33600.lq	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{33600}(101,\cdot)\)	33600.py	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{33600}(103,\cdot)\)	33600.ue	120	no	\(-1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{33600}(107,\cdot)\)	33600.qi	48	no	\(-1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{33600}(109,\cdot)\)	33600.vj	240	no	\(1\)	\(1\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{33600}(113,\cdot)\)	33600.kf	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{33600}(121,\cdot)\)	33600.tw	120	no	\(1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{33600}(127,\cdot)\)	33600.lo	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{33600}(131,\cdot)\)	33600.vi	240	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{33600}(137,\cdot)\)	33600.uh	120	no	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{33600}(139,\cdot)\)	33600.ti	80	no	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)

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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.