LMFDB - Group of Dirichlet characters of modulus 25857

Show commands: PariGP / SageMath

sage: H = DirichletGroup(25857)

pari: g = idealstar(,25857,2)

Character group

sage: G.order() pari: g.no
Order	=	14976
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{624}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{25857}(14366,\cdot)$, $\chi_{25857}(14536,\cdot)$, $\chi_{25857}(19774,\cdot)$

First 32 of 14976 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$19$
$\chi_{25857}(1,\cdot)$	25857.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{25857}(2,\cdot)$	25857.mo	312	yes	$1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{83}{312}\right)$	$e\left(\frac{305}{312}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{215}{312}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{125}{312}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{25857}(4,\cdot)$	25857.jg	156	yes	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{25857}(5,\cdot)$	25857.nn	624	yes	$-1$	$1$	$e\left(\frac{83}{312}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{155}{624}\right)$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{131}{624}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{25857}(7,\cdot)$	25857.nd	624	yes	$1$	$1$	$e\left(\frac{305}{312}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{575}{624}\right)$	$e\left(\frac{79}{624}\right)$	$e\left(\frac{373}{624}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{25857}(8,\cdot)$	25857.jf	104	no	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{1}{13}\right)$	$1$
$\chi_{25857}(10,\cdot)$	25857.ng	624	no	$-1$	$1$	$e\left(\frac{215}{312}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{107}{208}\right)$	$e\left(\frac{575}{624}\right)$	$e\left(\frac{7}{104}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{571}{624}\right)$	$e\left(\frac{127}{208}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{25857}(11,\cdot)$	25857.nr	624	yes	$-1$	$1$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{79}{624}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{571}{624}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{49}{624}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{25857}(14,\cdot)$	25857.nm	624	yes	$1$	$1$	$e\left(\frac{125}{312}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{131}{624}\right)$	$e\left(\frac{373}{624}\right)$	$e\left(\frac{21}{104}\right)$	$e\left(\frac{127}{208}\right)$	$e\left(\frac{49}{624}\right)$	$e\left(\frac{623}{624}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{25857}(16,\cdot)$	25857.hw	78	yes	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{25857}(19,\cdot)$	25857.er	24	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{25857}(20,\cdot)$	25857.mv	624	yes	$-1$	$1$	$e\left(\frac{35}{312}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{487}{624}\right)$	$e\left(\frac{187}{208}\right)$	$e\left(\frac{35}{104}\right)$	$e\left(\frac{557}{624}\right)$	$e\left(\frac{541}{624}\right)$	$e\left(\frac{7}{624}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{25857}(22,\cdot)$	25857.gg	48	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{48}\right)$	$-1$	$e\left(\frac{17}{24}\right)$
$\chi_{25857}(23,\cdot)$	25857.ha	48	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{25857}(25,\cdot)$	25857.lt	312	yes	$1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{289}{312}\right)$	$e\left(\frac{131}{312}\right)$	$e\left(\frac{5}{39}\right)$	$i$
$\chi_{25857}(28,\cdot)$	25857.nc	624	no	$1$	$1$	$e\left(\frac{257}{312}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{99}{208}\right)$	$e\left(\frac{359}{624}\right)$	$e\left(\frac{49}{104}\right)$	$e\left(\frac{187}{624}\right)$	$e\left(\frac{19}{624}\right)$	$e\left(\frac{83}{208}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{25857}(29,\cdot)$	25857.nq	624	yes	$1$	$1$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{25}{624}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{1}{624}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{523}{624}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{25857}(31,\cdot)$	25857.mq	624	yes	$1$	$1$	$e\left(\frac{107}{312}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{431}{624}\right)$	$e\left(\frac{577}{624}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{7}{208}\right)$	$e\left(\frac{85}{624}\right)$	$e\left(\frac{167}{624}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{25857}(32,\cdot)$	25857.mo	312	yes	$1$	$1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{103}{312}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{139}{312}\right)$	$e\left(\frac{79}{104}\right)$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{25857}(35,\cdot)$	25857.ik	78	no	$-1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{25857}(37,\cdot)$	25857.nc	624	no	$1$	$1$	$e\left(\frac{263}{312}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{5}{208}\right)$	$e\left(\frac{161}{624}\right)$	$e\left(\frac{55}{104}\right)$	$e\left(\frac{541}{624}\right)$	$e\left(\frac{85}{624}\right)$	$e\left(\frac{21}{208}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{25857}(38,\cdot)$	25857.jn	156	yes	$-1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{14}{39}\right)$	$1$
$\chi_{25857}(40,\cdot)$	25857.mr	624	yes	$-1$	$1$	$e\left(\frac{167}{312}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{29}{624}\right)$	$e\left(\frac{547}{624}\right)$	$e\left(\frac{63}{104}\right)$	$e\left(\frac{121}{208}\right)$	$e\left(\frac{511}{624}\right)$	$e\left(\frac{257}{624}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{25857}(41,\cdot)$	25857.mv	624	yes	$-1$	$1$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{317}{624}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{319}{624}\right)$	$e\left(\frac{479}{624}\right)$	$e\left(\frac{125}{624}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{25857}(43,\cdot)$	25857.lz	312	yes	$1$	$1$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{311}{312}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{61}{312}\right)$	$e\left(\frac{29}{312}\right)$	$e\left(\frac{287}{312}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{25857}(44,\cdot)$	25857.lj	208	no	$-1$	$1$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{103}{208}\right)$	$e\left(\frac{17}{208}\right)$	$e\left(\frac{41}{104}\right)$	$e\left(\frac{61}{208}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{183}{208}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{25857}(46,\cdot)$	25857.nc	624	no	$1$	$1$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{493}{624}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{521}{624}\right)$	$e\left(\frac{113}{624}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{25857}(47,\cdot)$	25857.kh	156	yes	$1$	$1$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{11}{39}\right)$	$-i$
$\chi_{25857}(49,\cdot)$	25857.lz	312	yes	$1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{263}{312}\right)$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{61}{312}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{25857}(50,\cdot)$	25857.kc	156	yes	$1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{25857}(53,\cdot)$	25857.jc	104	no	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{89}{104}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{1}{13}\right)$	$i$
$\chi_{25857}(55,\cdot)$	25857.jm	156	no	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{6}\right)$

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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	$25857$
Structure	\(C_{2}\times C_{12}\times C_{624}\)
Order	$14976$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(19\)
\(\chi_{25857}(1,\cdot)\)	25857.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{25857}(2,\cdot)\)	25857.mo	312	yes	\(1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{83}{312}\right)\)	\(e\left(\frac{305}{312}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{215}{312}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{125}{312}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{25857}(4,\cdot)\)	25857.jg	156	yes	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{25857}(5,\cdot)\)	25857.nn	624	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{312}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{155}{624}\right)\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{131}{624}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{25857}(7,\cdot)\)	25857.nd	624	yes	\(1\)	\(1\)	\(e\left(\frac{305}{312}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{575}{624}\right)\)	\(e\left(\frac{79}{624}\right)\)	\(e\left(\frac{373}{624}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{25857}(8,\cdot)\)	25857.jf	104	no	\(1\)	\(1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)
\(\chi_{25857}(10,\cdot)\)	25857.ng	624	no	\(-1\)	\(1\)	\(e\left(\frac{215}{312}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{107}{208}\right)\)	\(e\left(\frac{575}{624}\right)\)	\(e\left(\frac{7}{104}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{571}{624}\right)\)	\(e\left(\frac{127}{208}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{25857}(11,\cdot)\)	25857.nr	624	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{79}{624}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{571}{624}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{49}{624}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{25857}(14,\cdot)\)	25857.nm	624	yes	\(1\)	\(1\)	\(e\left(\frac{125}{312}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{131}{624}\right)\)	\(e\left(\frac{373}{624}\right)\)	\(e\left(\frac{21}{104}\right)\)	\(e\left(\frac{127}{208}\right)\)	\(e\left(\frac{49}{624}\right)\)	\(e\left(\frac{623}{624}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{25857}(16,\cdot)\)	25857.hw	78	yes	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{25857}(19,\cdot)\)	25857.er	24	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{25857}(20,\cdot)\)	25857.mv	624	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{312}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{487}{624}\right)\)	\(e\left(\frac{187}{208}\right)\)	\(e\left(\frac{35}{104}\right)\)	\(e\left(\frac{557}{624}\right)\)	\(e\left(\frac{541}{624}\right)\)	\(e\left(\frac{7}{624}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{25857}(22,\cdot)\)	25857.gg	48	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(-1\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{25857}(23,\cdot)\)	25857.ha	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{25857}(25,\cdot)\)	25857.lt	312	yes	\(1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{289}{312}\right)\)	\(e\left(\frac{131}{312}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(i\)
\(\chi_{25857}(28,\cdot)\)	25857.nc	624	no	\(1\)	\(1\)	\(e\left(\frac{257}{312}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{99}{208}\right)\)	\(e\left(\frac{359}{624}\right)\)	\(e\left(\frac{49}{104}\right)\)	\(e\left(\frac{187}{624}\right)\)	\(e\left(\frac{19}{624}\right)\)	\(e\left(\frac{83}{208}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{25857}(29,\cdot)\)	25857.nq	624	yes	\(1\)	\(1\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{25}{624}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{1}{624}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{523}{624}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{25857}(31,\cdot)\)	25857.mq	624	yes	\(1\)	\(1\)	\(e\left(\frac{107}{312}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{431}{624}\right)\)	\(e\left(\frac{577}{624}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{7}{208}\right)\)	\(e\left(\frac{85}{624}\right)\)	\(e\left(\frac{167}{624}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{25857}(32,\cdot)\)	25857.mo	312	yes	\(1\)	\(1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{103}{312}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{139}{312}\right)\)	\(e\left(\frac{79}{104}\right)\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{25857}(35,\cdot)\)	25857.ik	78	no	\(-1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{25857}(37,\cdot)\)	25857.nc	624	no	\(1\)	\(1\)	\(e\left(\frac{263}{312}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{5}{208}\right)\)	\(e\left(\frac{161}{624}\right)\)	\(e\left(\frac{55}{104}\right)\)	\(e\left(\frac{541}{624}\right)\)	\(e\left(\frac{85}{624}\right)\)	\(e\left(\frac{21}{208}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{25857}(38,\cdot)\)	25857.jn	156	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(1\)
\(\chi_{25857}(40,\cdot)\)	25857.mr	624	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{312}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{29}{624}\right)\)	\(e\left(\frac{547}{624}\right)\)	\(e\left(\frac{63}{104}\right)\)	\(e\left(\frac{121}{208}\right)\)	\(e\left(\frac{511}{624}\right)\)	\(e\left(\frac{257}{624}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{25857}(41,\cdot)\)	25857.mv	624	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{317}{624}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{319}{624}\right)\)	\(e\left(\frac{479}{624}\right)\)	\(e\left(\frac{125}{624}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{25857}(43,\cdot)\)	25857.lz	312	yes	\(1\)	\(1\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{311}{312}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{61}{312}\right)\)	\(e\left(\frac{29}{312}\right)\)	\(e\left(\frac{287}{312}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{25857}(44,\cdot)\)	25857.lj	208	no	\(-1\)	\(1\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{103}{208}\right)\)	\(e\left(\frac{17}{208}\right)\)	\(e\left(\frac{41}{104}\right)\)	\(e\left(\frac{61}{208}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{183}{208}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{25857}(46,\cdot)\)	25857.nc	624	no	\(1\)	\(1\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{493}{624}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{521}{624}\right)\)	\(e\left(\frac{113}{624}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{25857}(47,\cdot)\)	25857.kh	156	yes	\(1\)	\(1\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(-i\)
\(\chi_{25857}(49,\cdot)\)	25857.lz	312	yes	\(1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{263}{312}\right)\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{61}{312}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{25857}(50,\cdot)\)	25857.kc	156	yes	\(1\)	\(1\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{25857}(53,\cdot)\)	25857.jc	104	no	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(i\)
\(\chi_{25857}(55,\cdot)\)	25857.jm	156	no	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)

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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.