LMFDB - Group of Dirichlet characters of modulus 83200

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(83200)

gp:g = idealstar(,83200,2)

magma:G = FullDirichletGroup(83200);

Character group

Order	=	30720	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{4}\times C_{960}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{83200}(74751,\cdot)$, $\chi_{83200}(16901,\cdot)$, $\chi_{83200}(56577,\cdot)$, $\chi_{83200}(64001,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 30720 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{83200}(1,\cdot)$	83200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{83200}(3,\cdot)$	83200.bdq	960	yes	$1$	$1$	$e\left(\frac{407}{960}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{407}{480}\right)$	$e\left(\frac{881}{960}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{43}{960}\right)$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{87}{320}\right)$	$e\left(\frac{287}{960}\right)$
$\chi_{83200}(7,\cdot)$	83200.wb	96	no	$-1$	$1$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{96}\right)$
$\chi_{83200}(9,\cdot)$	83200.bcy	480	no	$1$	$1$	$e\left(\frac{407}{480}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{43}{480}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{87}{160}\right)$	$e\left(\frac{287}{480}\right)$
$\chi_{83200}(11,\cdot)$	83200.bdo	960	yes	$1$	$1$	$e\left(\frac{881}{960}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{401}{480}\right)$	$e\left(\frac{263}{960}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{349}{960}\right)$	$e\left(\frac{37}{320}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{241}{320}\right)$	$e\left(\frac{281}{960}\right)$
$\chi_{83200}(17,\cdot)$	83200.zx	240	no	$-1$	$1$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{187}{240}\right)$
$\chi_{83200}(19,\cdot)$	83200.bet	960	yes	$1$	$1$	$e\left(\frac{43}{960}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{43}{480}\right)$	$e\left(\frac{349}{960}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{47}{960}\right)$	$e\left(\frac{71}{320}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{43}{320}\right)$	$e\left(\frac{643}{960}\right)$
$\chi_{83200}(21,\cdot)$	83200.bbd	320	yes	$-1$	$1$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{37}{320}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{71}{320}\right)$	$e\left(\frac{189}{320}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{137}{320}\right)$	$e\left(\frac{219}{320}\right)$
$\chi_{83200}(23,\cdot)$	83200.bde	480	no	$1$	$1$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{163}{480}\right)$
$\chi_{83200}(27,\cdot)$	83200.bcf	320	no	$1$	$1$	$e\left(\frac{87}{320}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{87}{160}\right)$	$e\left(\frac{241}{320}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{43}{320}\right)$	$e\left(\frac{137}{320}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{261}{320}\right)$	$e\left(\frac{287}{320}\right)$
$\chi_{83200}(29,\cdot)$	83200.bel	960	yes	$1$	$1$	$e\left(\frac{287}{960}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{287}{480}\right)$	$e\left(\frac{281}{960}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{643}{960}\right)$	$e\left(\frac{219}{320}\right)$	$e\left(\frac{163}{480}\right)$	$e\left(\frac{287}{320}\right)$	$e\left(\frac{887}{960}\right)$
$\chi_{83200}(31,\cdot)$	83200.ov	40	no	$1$	$1$	$e\left(\frac{27}{40}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{83200}(33,\cdot)$	83200.ww	120	no	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{71}{120}\right)$
$\chi_{83200}(37,\cdot)$	83200.beb	960	yes	$1$	$1$	$e\left(\frac{149}{960}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{149}{480}\right)$	$e\left(\frac{467}{960}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{1}{960}\right)$	$e\left(\frac{233}{320}\right)$	$e\left(\frac{121}{480}\right)$	$e\left(\frac{149}{320}\right)$	$e\left(\frac{269}{960}\right)$
$\chi_{83200}(41,\cdot)$	83200.bdg	480	no	$-1$	$1$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{61}{480}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{143}{480}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{427}{480}\right)$
$\chi_{83200}(43,\cdot)$	83200.zq	192	no	$1$	$1$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{77}{192}\right)$
$\chi_{83200}(47,\cdot)$	83200.tu	80	no	$-1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{21}{80}\right)$
$\chi_{83200}(49,\cdot)$	83200.py	48	no	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{83200}(51,\cdot)$	83200.ti	64	no	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{5}{64}\right)$
$\chi_{83200}(53,\cdot)$	83200.bcc	320	no	$-1$	$1$	$e\left(\frac{59}{320}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{77}{320}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{229}{320}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{177}{320}\right)$	$e\left(\frac{99}{320}\right)$
$\chi_{83200}(57,\cdot)$	83200.nq	32	no	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{83200}(59,\cdot)$	83200.bet	960	yes	$1$	$1$	$e\left(\frac{349}{960}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{667}{960}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{761}{960}\right)$	$e\left(\frac{33}{320}\right)$	$e\left(\frac{41}{480}\right)$	$e\left(\frac{29}{320}\right)$	$e\left(\frac{709}{960}\right)$
$\chi_{83200}(61,\cdot)$	83200.bdw	960	yes	$1$	$1$	$e\left(\frac{631}{960}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{151}{480}\right)$	$e\left(\frac{673}{960}\right)$	$e\left(\frac{11}{240}\right)$	$e\left(\frac{539}{960}\right)$	$e\left(\frac{307}{320}\right)$	$e\left(\frac{299}{480}\right)$	$e\left(\frac{311}{320}\right)$	$e\left(\frac{751}{960}\right)$
$\chi_{83200}(63,\cdot)$	83200.qs	60	no	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{83200}(67,\cdot)$	83200.bef	960	yes	$-1$	$1$	$e\left(\frac{263}{960}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{209}{960}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{907}{960}\right)$	$e\left(\frac{291}{320}\right)$	$e\left(\frac{307}{480}\right)$	$e\left(\frac{263}{320}\right)$	$e\left(\frac{623}{960}\right)$
$\chi_{83200}(69,\cdot)$	83200.bek	960	yes	$1$	$1$	$e\left(\frac{733}{960}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{253}{480}\right)$	$e\left(\frac{619}{960}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{617}{960}\right)$	$e\left(\frac{241}{320}\right)$	$e\left(\frac{137}{480}\right)$	$e\left(\frac{93}{320}\right)$	$e\left(\frac{613}{960}\right)$
$\chi_{83200}(71,\cdot)$	83200.bdn	480	no	$1$	$1$	$e\left(\frac{281}{480}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{263}{480}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{349}{480}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{401}{480}\right)$
$\chi_{83200}(73,\cdot)$	83200.xp	160	no	$1$	$1$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{141}{160}\right)$
$\chi_{83200}(77,\cdot)$	83200.bbh	320	yes	$-1$	$1$	$e\left(\frac{97}{320}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{151}{320}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{173}{320}\right)$	$e\left(\frac{287}{320}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{291}{320}\right)$	$e\left(\frac{217}{320}\right)$
$\chi_{83200}(79,\cdot)$	83200.ua	80	no	$-1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{11}{80}\right)$
$\chi_{83200}(81,\cdot)$	83200.bar	240	no	$1$	$1$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{47}{240}\right)$
$\chi_{83200}(83,\cdot)$	83200.bbo	320	yes	$-1$	$1$	$e\left(\frac{281}{320}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{303}{320}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{309}{320}\right)$	$e\left(\frac{151}{320}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{203}{320}\right)$	$e\left(\frac{81}{320}\right)$

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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	$83200$
Structure	\(C_{2}\times C_{4}\times C_{4}\times C_{960}\)
Order	$30720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{83200}(1,\cdot)\)	83200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{83200}(3,\cdot)\)	83200.bdq	960	yes	\(1\)	\(1\)	\(e\left(\frac{407}{960}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{407}{480}\right)\)	\(e\left(\frac{881}{960}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{43}{960}\right)\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{87}{320}\right)\)	\(e\left(\frac{287}{960}\right)\)
\(\chi_{83200}(7,\cdot)\)	83200.wb	96	no	\(-1\)	\(1\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{83200}(9,\cdot)\)	83200.bcy	480	no	\(1\)	\(1\)	\(e\left(\frac{407}{480}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{43}{480}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{87}{160}\right)\)	\(e\left(\frac{287}{480}\right)\)
\(\chi_{83200}(11,\cdot)\)	83200.bdo	960	yes	\(1\)	\(1\)	\(e\left(\frac{881}{960}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{401}{480}\right)\)	\(e\left(\frac{263}{960}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{349}{960}\right)\)	\(e\left(\frac{37}{320}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{241}{320}\right)\)	\(e\left(\frac{281}{960}\right)\)
\(\chi_{83200}(17,\cdot)\)	83200.zx	240	no	\(-1\)	\(1\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{187}{240}\right)\)
\(\chi_{83200}(19,\cdot)\)	83200.bet	960	yes	\(1\)	\(1\)	\(e\left(\frac{43}{960}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{43}{480}\right)\)	\(e\left(\frac{349}{960}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{47}{960}\right)\)	\(e\left(\frac{71}{320}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{43}{320}\right)\)	\(e\left(\frac{643}{960}\right)\)
\(\chi_{83200}(21,\cdot)\)	83200.bbd	320	yes	\(-1\)	\(1\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{37}{320}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{71}{320}\right)\)	\(e\left(\frac{189}{320}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{137}{320}\right)\)	\(e\left(\frac{219}{320}\right)\)
\(\chi_{83200}(23,\cdot)\)	83200.bde	480	no	\(1\)	\(1\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{163}{480}\right)\)
\(\chi_{83200}(27,\cdot)\)	83200.bcf	320	no	\(1\)	\(1\)	\(e\left(\frac{87}{320}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{87}{160}\right)\)	\(e\left(\frac{241}{320}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{43}{320}\right)\)	\(e\left(\frac{137}{320}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{261}{320}\right)\)	\(e\left(\frac{287}{320}\right)\)
\(\chi_{83200}(29,\cdot)\)	83200.bel	960	yes	\(1\)	\(1\)	\(e\left(\frac{287}{960}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{287}{480}\right)\)	\(e\left(\frac{281}{960}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{643}{960}\right)\)	\(e\left(\frac{219}{320}\right)\)	\(e\left(\frac{163}{480}\right)\)	\(e\left(\frac{287}{320}\right)\)	\(e\left(\frac{887}{960}\right)\)
\(\chi_{83200}(31,\cdot)\)	83200.ov	40	no	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{83200}(33,\cdot)\)	83200.ww	120	no	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{71}{120}\right)\)
\(\chi_{83200}(37,\cdot)\)	83200.beb	960	yes	\(1\)	\(1\)	\(e\left(\frac{149}{960}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{149}{480}\right)\)	\(e\left(\frac{467}{960}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{1}{960}\right)\)	\(e\left(\frac{233}{320}\right)\)	\(e\left(\frac{121}{480}\right)\)	\(e\left(\frac{149}{320}\right)\)	\(e\left(\frac{269}{960}\right)\)
\(\chi_{83200}(41,\cdot)\)	83200.bdg	480	no	\(-1\)	\(1\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{61}{480}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{143}{480}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{427}{480}\right)\)
\(\chi_{83200}(43,\cdot)\)	83200.zq	192	no	\(1\)	\(1\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{77}{192}\right)\)
\(\chi_{83200}(47,\cdot)\)	83200.tu	80	no	\(-1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)
\(\chi_{83200}(49,\cdot)\)	83200.py	48	no	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{83200}(51,\cdot)\)	83200.ti	64	no	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)
\(\chi_{83200}(53,\cdot)\)	83200.bcc	320	no	\(-1\)	\(1\)	\(e\left(\frac{59}{320}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{77}{320}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{229}{320}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{177}{320}\right)\)	\(e\left(\frac{99}{320}\right)\)
\(\chi_{83200}(57,\cdot)\)	83200.nq	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{83200}(59,\cdot)\)	83200.bet	960	yes	\(1\)	\(1\)	\(e\left(\frac{349}{960}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{667}{960}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{761}{960}\right)\)	\(e\left(\frac{33}{320}\right)\)	\(e\left(\frac{41}{480}\right)\)	\(e\left(\frac{29}{320}\right)\)	\(e\left(\frac{709}{960}\right)\)
\(\chi_{83200}(61,\cdot)\)	83200.bdw	960	yes	\(1\)	\(1\)	\(e\left(\frac{631}{960}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{151}{480}\right)\)	\(e\left(\frac{673}{960}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{539}{960}\right)\)	\(e\left(\frac{307}{320}\right)\)	\(e\left(\frac{299}{480}\right)\)	\(e\left(\frac{311}{320}\right)\)	\(e\left(\frac{751}{960}\right)\)
\(\chi_{83200}(63,\cdot)\)	83200.qs	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{83200}(67,\cdot)\)	83200.bef	960	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{960}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{209}{960}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{907}{960}\right)\)	\(e\left(\frac{291}{320}\right)\)	\(e\left(\frac{307}{480}\right)\)	\(e\left(\frac{263}{320}\right)\)	\(e\left(\frac{623}{960}\right)\)
\(\chi_{83200}(69,\cdot)\)	83200.bek	960	yes	\(1\)	\(1\)	\(e\left(\frac{733}{960}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{253}{480}\right)\)	\(e\left(\frac{619}{960}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{617}{960}\right)\)	\(e\left(\frac{241}{320}\right)\)	\(e\left(\frac{137}{480}\right)\)	\(e\left(\frac{93}{320}\right)\)	\(e\left(\frac{613}{960}\right)\)
\(\chi_{83200}(71,\cdot)\)	83200.bdn	480	no	\(1\)	\(1\)	\(e\left(\frac{281}{480}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{263}{480}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{349}{480}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{401}{480}\right)\)
\(\chi_{83200}(73,\cdot)\)	83200.xp	160	no	\(1\)	\(1\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{141}{160}\right)\)
\(\chi_{83200}(77,\cdot)\)	83200.bbh	320	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{320}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{151}{320}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{173}{320}\right)\)	\(e\left(\frac{287}{320}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{291}{320}\right)\)	\(e\left(\frac{217}{320}\right)\)
\(\chi_{83200}(79,\cdot)\)	83200.ua	80	no	\(-1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)
\(\chi_{83200}(81,\cdot)\)	83200.bar	240	no	\(1\)	\(1\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{47}{240}\right)\)
\(\chi_{83200}(83,\cdot)\)	83200.bbo	320	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{320}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{303}{320}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{309}{320}\right)\)	\(e\left(\frac{151}{320}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{203}{320}\right)\)	\(e\left(\frac{81}{320}\right)\)

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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.