LMFDB - Group of Dirichlet characters of modulus 291312

Show commands: PariGP / SageMath

sage: H = DirichletGroup(291312)

pari: g = idealstar(,291312,2)

Character group

sage: G.order() pari: g.no
Order	=	78336
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{816}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{291312}(36415,\cdot)$, $\chi_{291312}(218485,\cdot)$, $\chi_{291312}(226577,\cdot)$, $\chi_{291312}(83233,\cdot)$, $\chi_{291312}(82657,\cdot)$

First 32 of 78336 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	$-1$	$1$	$5$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{291312}(1,\cdot)$	291312.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{291312}(5,\cdot)$	291312.bzi	816	yes	$-1$	$1$	$e\left(\frac{311}{816}\right)$	$e\left(\frac{637}{816}\right)$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{65}{816}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{671}{816}\right)$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{427}{816}\right)$	$e\left(\frac{109}{816}\right)$
$\chi_{291312}(11,\cdot)$	291312.bzm	816	yes	$-1$	$1$	$e\left(\frac{637}{816}\right)$	$e\left(\frac{431}{816}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{19}{816}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{397}{816}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{401}{816}\right)$	$e\left(\frac{647}{816}\right)$
$\chi_{291312}(13,\cdot)$	291312.bli	204	yes	$-1$	$1$	$e\left(\frac{95}{102}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{181}{204}\right)$
$\chi_{291312}(19,\cdot)$	291312.bvc	408	no	$1$	$1$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{109}{136}\right)$
$\chi_{291312}(23,\cdot)$	291312.cbx	816	no	$-1$	$1$	$e\left(\frac{65}{816}\right)$	$e\left(\frac{19}{816}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{131}{816}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{757}{816}\right)$	$e\left(\frac{295}{816}\right)$
$\chi_{291312}(25,\cdot)$	291312.byc	408	no	$1$	$1$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{44}{51}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{65}{408}\right)$	$e\left(\frac{107}{204}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{19}{408}\right)$	$e\left(\frac{109}{408}\right)$
$\chi_{291312}(29,\cdot)$	291312.bzb	816	no	$1$	$1$	$e\left(\frac{671}{816}\right)$	$e\left(\frac{397}{816}\right)$	$e\left(\frac{67}{102}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{665}{816}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{703}{816}\right)$	$e\left(\frac{383}{816}\right)$	$e\left(\frac{9}{272}\right)$	$e\left(\frac{749}{816}\right)$
$\chi_{291312}(31,\cdot)$	291312.caz	816	no	$-1$	$1$	$e\left(\frac{21}{272}\right)$	$e\left(\frac{71}{272}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{239}{272}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{383}{816}\right)$	$e\left(\frac{515}{816}\right)$	$e\left(\frac{491}{816}\right)$	$e\left(\frac{673}{816}\right)$
$\chi_{291312}(37,\cdot)$	291312.byo	816	no	$-1$	$1$	$e\left(\frac{427}{816}\right)$	$e\left(\frac{401}{816}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{23}{408}\right)$	$e\left(\frac{757}{816}\right)$	$e\left(\frac{19}{408}\right)$	$e\left(\frac{9}{272}\right)$	$e\left(\frac{491}{816}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{163}{272}\right)$
$\chi_{291312}(41,\cdot)$	291312.cbk	816	no	$-1$	$1$	$e\left(\frac{109}{816}\right)$	$e\left(\frac{647}{816}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{109}{136}\right)$	$e\left(\frac{295}{816}\right)$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{749}{816}\right)$	$e\left(\frac{673}{816}\right)$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{139}{816}\right)$
$\chi_{291312}(43,\cdot)$	291312.bvb	408	no	$-1$	$1$	$e\left(\frac{349}{408}\right)$	$e\left(\frac{215}{408}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{253}{408}\right)$	$e\left(\frac{145}{204}\right)$	$e\left(\frac{113}{408}\right)$	$e\left(\frac{127}{408}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{373}{408}\right)$
$\chi_{291312}(47,\cdot)$	291312.bmw	204	no	$-1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{199}{204}\right)$	$e\left(\frac{19}{204}\right)$	$e\left(\frac{41}{204}\right)$
$\chi_{291312}(53,\cdot)$	291312.bwc	408	no	$-1$	$1$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{341}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{91}{408}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{197}{408}\right)$	$e\left(\frac{115}{408}\right)$	$e\left(\frac{69}{136}\right)$
$\chi_{291312}(55,\cdot)$	291312.bdm	68	no	$1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{63}{68}\right)$
$\chi_{291312}(59,\cdot)$	291312.bvs	408	yes	$-1$	$1$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{5}{136}\right)$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{13}{102}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{49}{408}\right)$	$e\left(\frac{31}{408}\right)$	$e\left(\frac{229}{408}\right)$	$e\left(\frac{113}{408}\right)$
$\chi_{291312}(61,\cdot)$	291312.byx	816	yes	$1$	$1$	$e\left(\frac{83}{272}\right)$	$e\left(\frac{177}{272}\right)$	$e\left(\frac{73}{102}\right)$	$e\left(\frac{305}{408}\right)$	$e\left(\frac{229}{272}\right)$	$e\left(\frac{83}{136}\right)$	$e\left(\frac{769}{816}\right)$	$e\left(\frac{601}{816}\right)$	$e\left(\frac{205}{816}\right)$	$e\left(\frac{131}{816}\right)$
$\chi_{291312}(65,\cdot)$	291312.bbi	48	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{291312}(67,\cdot)$	291312.bpu	204	yes	$-1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{103}{204}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{29}{204}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{43}{51}\right)$
$\chi_{291312}(71,\cdot)$	291312.btf	272	no	$-1$	$1$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{63}{272}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{191}{272}\right)$	$e\left(\frac{101}{136}\right)$	$e\left(\frac{29}{272}\right)$	$e\left(\frac{1}{272}\right)$	$e\left(\frac{105}{272}\right)$	$e\left(\frac{19}{272}\right)$
$\chi_{291312}(73,\cdot)$	291312.cbe	816	no	$1$	$1$	$e\left(\frac{203}{816}\right)$	$e\left(\frac{97}{816}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{497}{816}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{511}{816}\right)$	$e\left(\frac{71}{816}\right)$	$e\left(\frac{63}{272}\right)$
$\chi_{291312}(79,\cdot)$	291312.cbv	816	no	$1$	$1$	$e\left(\frac{163}{272}\right)$	$e\left(\frac{169}{272}\right)$	$e\left(\frac{137}{204}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{113}{272}\right)$	$e\left(\frac{27}{136}\right)$	$e\left(\frac{337}{816}\right)$	$e\left(\frac{565}{816}\right)$	$e\left(\frac{709}{816}\right)$	$e\left(\frac{263}{816}\right)$
$\chi_{291312}(83,\cdot)$	291312.bxe	408	yes	$-1$	$1$	$e\left(\frac{175}{408}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{23}{204}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{235}{408}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{97}{408}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{7}{408}\right)$
$\chi_{291312}(89,\cdot)$	291312.bmf	204	no	$1$	$1$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{155}{204}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{97}{204}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{43}{204}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{291312}(95,\cdot)$	291312.cbb	816	no	$-1$	$1$	$e\left(\frac{23}{272}\right)$	$e\left(\frac{149}{272}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{61}{272}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{413}{816}\right)$	$e\left(\frac{713}{816}\right)$	$e\left(\frac{473}{816}\right)$	$e\left(\frac{763}{816}\right)$
$\chi_{291312}(97,\cdot)$	291312.can	816	no	$1$	$1$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{529}{816}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{233}{816}\right)$	$e\left(\frac{371}{408}\right)$	$e\left(\frac{427}{816}\right)$	$e\left(\frac{71}{816}\right)$	$e\left(\frac{173}{272}\right)$	$e\left(\frac{533}{816}\right)$
$\chi_{291312}(101,\cdot)$	291312.bnu	204	yes	$1$	$1$	$e\left(\frac{109}{204}\right)$	$e\left(\frac{35}{204}\right)$	$e\left(\frac{95}{204}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{1}{204}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{5}{51}\right)$
$\chi_{291312}(103,\cdot)$	291312.bit	102	no	$1$	$1$	$e\left(\frac{11}{51}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{41}{102}\right)$
$\chi_{291312}(107,\cdot)$	291312.byr	816	no	$-1$	$1$	$e\left(\frac{319}{816}\right)$	$e\left(\frac{677}{816}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{169}{816}\right)$	$e\left(\frac{319}{408}\right)$	$e\left(\frac{101}{272}\right)$	$e\left(\frac{191}{816}\right)$	$e\left(\frac{811}{816}\right)$	$e\left(\frac{167}{272}\right)$
$\chi_{291312}(109,\cdot)$	291312.byo	816	no	$-1$	$1$	$e\left(\frac{809}{816}\right)$	$e\left(\frac{475}{816}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{13}{408}\right)$	$e\left(\frac{215}{816}\right)$	$e\left(\frac{401}{408}\right)$	$e\left(\frac{147}{272}\right)$	$e\left(\frac{313}{816}\right)$	$e\left(\frac{293}{816}\right)$	$e\left(\frac{33}{272}\right)$
$\chi_{291312}(113,\cdot)$	291312.car	816	no	$1$	$1$	$e\left(\frac{721}{816}\right)$	$e\left(\frac{443}{816}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{313}{408}\right)$	$e\left(\frac{137}{816}\right)$	$e\left(\frac{61}{816}\right)$	$e\left(\frac{231}{272}\right)$	$e\left(\frac{751}{816}\right)$
$\chi_{291312}(115,\cdot)$	291312.blw	204	yes	$1$	$1$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{161}{204}\right)$	$e\left(\frac{173}{204}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{23}{51}\right)$	$e\left(\frac{101}{204}\right)$

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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	$291312$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{816}\)
Order	$78336$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{291312}(1,\cdot)\)	291312.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{291312}(5,\cdot)\)	291312.bzi	816	yes	\(-1\)	\(1\)	\(e\left(\frac{311}{816}\right)\)	\(e\left(\frac{637}{816}\right)\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{65}{816}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{671}{816}\right)\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{427}{816}\right)\)	\(e\left(\frac{109}{816}\right)\)
\(\chi_{291312}(11,\cdot)\)	291312.bzm	816	yes	\(-1\)	\(1\)	\(e\left(\frac{637}{816}\right)\)	\(e\left(\frac{431}{816}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{19}{816}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{397}{816}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{401}{816}\right)\)	\(e\left(\frac{647}{816}\right)\)
\(\chi_{291312}(13,\cdot)\)	291312.bli	204	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{102}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{181}{204}\right)\)
\(\chi_{291312}(19,\cdot)\)	291312.bvc	408	no	\(1\)	\(1\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{109}{136}\right)\)
\(\chi_{291312}(23,\cdot)\)	291312.cbx	816	no	\(-1\)	\(1\)	\(e\left(\frac{65}{816}\right)\)	\(e\left(\frac{19}{816}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{131}{816}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{757}{816}\right)\)	\(e\left(\frac{295}{816}\right)\)
\(\chi_{291312}(25,\cdot)\)	291312.byc	408	no	\(1\)	\(1\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{44}{51}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{65}{408}\right)\)	\(e\left(\frac{107}{204}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{19}{408}\right)\)	\(e\left(\frac{109}{408}\right)\)
\(\chi_{291312}(29,\cdot)\)	291312.bzb	816	no	\(1\)	\(1\)	\(e\left(\frac{671}{816}\right)\)	\(e\left(\frac{397}{816}\right)\)	\(e\left(\frac{67}{102}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{665}{816}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{703}{816}\right)\)	\(e\left(\frac{383}{816}\right)\)	\(e\left(\frac{9}{272}\right)\)	\(e\left(\frac{749}{816}\right)\)
\(\chi_{291312}(31,\cdot)\)	291312.caz	816	no	\(-1\)	\(1\)	\(e\left(\frac{21}{272}\right)\)	\(e\left(\frac{71}{272}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{239}{272}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{383}{816}\right)\)	\(e\left(\frac{515}{816}\right)\)	\(e\left(\frac{491}{816}\right)\)	\(e\left(\frac{673}{816}\right)\)
\(\chi_{291312}(37,\cdot)\)	291312.byo	816	no	\(-1\)	\(1\)	\(e\left(\frac{427}{816}\right)\)	\(e\left(\frac{401}{816}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{23}{408}\right)\)	\(e\left(\frac{757}{816}\right)\)	\(e\left(\frac{19}{408}\right)\)	\(e\left(\frac{9}{272}\right)\)	\(e\left(\frac{491}{816}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{163}{272}\right)\)
\(\chi_{291312}(41,\cdot)\)	291312.cbk	816	no	\(-1\)	\(1\)	\(e\left(\frac{109}{816}\right)\)	\(e\left(\frac{647}{816}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{109}{136}\right)\)	\(e\left(\frac{295}{816}\right)\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{749}{816}\right)\)	\(e\left(\frac{673}{816}\right)\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{139}{816}\right)\)
\(\chi_{291312}(43,\cdot)\)	291312.bvb	408	no	\(-1\)	\(1\)	\(e\left(\frac{349}{408}\right)\)	\(e\left(\frac{215}{408}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{253}{408}\right)\)	\(e\left(\frac{145}{204}\right)\)	\(e\left(\frac{113}{408}\right)\)	\(e\left(\frac{127}{408}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{373}{408}\right)\)
\(\chi_{291312}(47,\cdot)\)	291312.bmw	204	no	\(-1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{199}{204}\right)\)	\(e\left(\frac{19}{204}\right)\)	\(e\left(\frac{41}{204}\right)\)
\(\chi_{291312}(53,\cdot)\)	291312.bwc	408	no	\(-1\)	\(1\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{341}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{91}{408}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{197}{408}\right)\)	\(e\left(\frac{115}{408}\right)\)	\(e\left(\frac{69}{136}\right)\)
\(\chi_{291312}(55,\cdot)\)	291312.bdm	68	no	\(1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)
\(\chi_{291312}(59,\cdot)\)	291312.bvs	408	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{5}{136}\right)\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{13}{102}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{49}{408}\right)\)	\(e\left(\frac{31}{408}\right)\)	\(e\left(\frac{229}{408}\right)\)	\(e\left(\frac{113}{408}\right)\)
\(\chi_{291312}(61,\cdot)\)	291312.byx	816	yes	\(1\)	\(1\)	\(e\left(\frac{83}{272}\right)\)	\(e\left(\frac{177}{272}\right)\)	\(e\left(\frac{73}{102}\right)\)	\(e\left(\frac{305}{408}\right)\)	\(e\left(\frac{229}{272}\right)\)	\(e\left(\frac{83}{136}\right)\)	\(e\left(\frac{769}{816}\right)\)	\(e\left(\frac{601}{816}\right)\)	\(e\left(\frac{205}{816}\right)\)	\(e\left(\frac{131}{816}\right)\)
\(\chi_{291312}(65,\cdot)\)	291312.bbi	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{291312}(67,\cdot)\)	291312.bpu	204	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{103}{204}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{29}{204}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{43}{51}\right)\)
\(\chi_{291312}(71,\cdot)\)	291312.btf	272	no	\(-1\)	\(1\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{63}{272}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{191}{272}\right)\)	\(e\left(\frac{101}{136}\right)\)	\(e\left(\frac{29}{272}\right)\)	\(e\left(\frac{1}{272}\right)\)	\(e\left(\frac{105}{272}\right)\)	\(e\left(\frac{19}{272}\right)\)
\(\chi_{291312}(73,\cdot)\)	291312.cbe	816	no	\(1\)	\(1\)	\(e\left(\frac{203}{816}\right)\)	\(e\left(\frac{97}{816}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{497}{816}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{511}{816}\right)\)	\(e\left(\frac{71}{816}\right)\)	\(e\left(\frac{63}{272}\right)\)
\(\chi_{291312}(79,\cdot)\)	291312.cbv	816	no	\(1\)	\(1\)	\(e\left(\frac{163}{272}\right)\)	\(e\left(\frac{169}{272}\right)\)	\(e\left(\frac{137}{204}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{113}{272}\right)\)	\(e\left(\frac{27}{136}\right)\)	\(e\left(\frac{337}{816}\right)\)	\(e\left(\frac{565}{816}\right)\)	\(e\left(\frac{709}{816}\right)\)	\(e\left(\frac{263}{816}\right)\)
\(\chi_{291312}(83,\cdot)\)	291312.bxe	408	yes	\(-1\)	\(1\)	\(e\left(\frac{175}{408}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{23}{204}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{235}{408}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{97}{408}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{7}{408}\right)\)
\(\chi_{291312}(89,\cdot)\)	291312.bmf	204	no	\(1\)	\(1\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{155}{204}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{97}{204}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{43}{204}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{291312}(95,\cdot)\)	291312.cbb	816	no	\(-1\)	\(1\)	\(e\left(\frac{23}{272}\right)\)	\(e\left(\frac{149}{272}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{61}{272}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{413}{816}\right)\)	\(e\left(\frac{713}{816}\right)\)	\(e\left(\frac{473}{816}\right)\)	\(e\left(\frac{763}{816}\right)\)
\(\chi_{291312}(97,\cdot)\)	291312.can	816	no	\(1\)	\(1\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{529}{816}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{233}{816}\right)\)	\(e\left(\frac{371}{408}\right)\)	\(e\left(\frac{427}{816}\right)\)	\(e\left(\frac{71}{816}\right)\)	\(e\left(\frac{173}{272}\right)\)	\(e\left(\frac{533}{816}\right)\)
\(\chi_{291312}(101,\cdot)\)	291312.bnu	204	yes	\(1\)	\(1\)	\(e\left(\frac{109}{204}\right)\)	\(e\left(\frac{35}{204}\right)\)	\(e\left(\frac{95}{204}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{1}{204}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{5}{51}\right)\)
\(\chi_{291312}(103,\cdot)\)	291312.bit	102	no	\(1\)	\(1\)	\(e\left(\frac{11}{51}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{41}{102}\right)\)
\(\chi_{291312}(107,\cdot)\)	291312.byr	816	no	\(-1\)	\(1\)	\(e\left(\frac{319}{816}\right)\)	\(e\left(\frac{677}{816}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{169}{816}\right)\)	\(e\left(\frac{319}{408}\right)\)	\(e\left(\frac{101}{272}\right)\)	\(e\left(\frac{191}{816}\right)\)	\(e\left(\frac{811}{816}\right)\)	\(e\left(\frac{167}{272}\right)\)
\(\chi_{291312}(109,\cdot)\)	291312.byo	816	no	\(-1\)	\(1\)	\(e\left(\frac{809}{816}\right)\)	\(e\left(\frac{475}{816}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{13}{408}\right)\)	\(e\left(\frac{215}{816}\right)\)	\(e\left(\frac{401}{408}\right)\)	\(e\left(\frac{147}{272}\right)\)	\(e\left(\frac{313}{816}\right)\)	\(e\left(\frac{293}{816}\right)\)	\(e\left(\frac{33}{272}\right)\)
\(\chi_{291312}(113,\cdot)\)	291312.car	816	no	\(1\)	\(1\)	\(e\left(\frac{721}{816}\right)\)	\(e\left(\frac{443}{816}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{313}{408}\right)\)	\(e\left(\frac{137}{816}\right)\)	\(e\left(\frac{61}{816}\right)\)	\(e\left(\frac{231}{272}\right)\)	\(e\left(\frac{751}{816}\right)\)
\(\chi_{291312}(115,\cdot)\)	291312.blw	204	yes	\(1\)	\(1\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{161}{204}\right)\)	\(e\left(\frac{173}{204}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{65}{102}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{23}{51}\right)\)	\(e\left(\frac{101}{204}\right)\)

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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.