LMFDB - Group of Dirichlet characters of modulus 51714

Show commands: PariGP / SageMath

sage: H = DirichletGroup(51714)

pari: g = idealstar(,51714,2)

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	=	$\chi_{51714}(40223,\cdot)$, $\chi_{51714}(40393,\cdot)$, $\chi_{51714}(45631,\cdot)$

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	$-1$	$1$	$5$	$7$	$11$	$19$	$23$	$25$	$29$	$31$	$35$	$37$
$\chi_{51714}(1,\cdot)$	51714.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{51714}(5,\cdot)$	51714.nv	624	no	$-1$	$1$	$e\left(\frac{155}{624}\right)$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{431}{624}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{208}\right)$
$\chi_{51714}(7,\cdot)$	51714.ni	624	no	$1$	$1$	$e\left(\frac{589}{624}\right)$	$e\left(\frac{129}{208}\right)$	$e\left(\frac{79}{624}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{25}{624}\right)$	$e\left(\frac{577}{624}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{161}{624}\right)$
$\chi_{51714}(11,\cdot)$	51714.ne	624	no	$-1$	$1$	$e\left(\frac{601}{624}\right)$	$e\left(\frac{79}{624}\right)$	$e\left(\frac{49}{208}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{289}{312}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{85}{624}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{85}{624}\right)$
$\chi_{51714}(19,\cdot)$	51714.eq	24	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{24}\right)$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{51714}(23,\cdot)$	51714.hc	48	no	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{51714}(25,\cdot)$	51714.lt	312	no	$1$	$1$	$e\left(\frac{155}{312}\right)$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{289}{312}\right)$	$i$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{119}{312}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{104}\right)$
$\chi_{51714}(29,\cdot)$	51714.my	624	no	$1$	$1$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{25}{624}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{127}{312}\right)$	$e\left(\frac{205}{208}\right)$	$e\left(\frac{19}{624}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{331}{624}\right)$
$\chi_{51714}(31,\cdot)$	51714.mq	624	no	$1$	$1$	$e\left(\frac{431}{624}\right)$	$e\left(\frac{577}{624}\right)$	$e\left(\frac{85}{624}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{119}{312}\right)$	$e\left(\frac{19}{624}\right)$	$e\left(\frac{347}{624}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{185}{208}\right)$
$\chi_{51714}(35,\cdot)$	51714.iw	78	no	$-1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{51714}(37,\cdot)$	51714.ng	624	no	$1$	$1$	$e\left(\frac{5}{208}\right)$	$e\left(\frac{161}{624}\right)$	$e\left(\frac{85}{624}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{104}\right)$	$e\left(\frac{331}{624}\right)$	$e\left(\frac{185}{208}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{139}{624}\right)$
$\chi_{51714}(41,\cdot)$	51714.mv	624	no	$-1$	$1$	$e\left(\frac{317}{624}\right)$	$e\left(\frac{41}{208}\right)$	$e\left(\frac{479}{624}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{312}\right)$	$e\left(\frac{353}{624}\right)$	$e\left(\frac{185}{624}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{601}{624}\right)$
$\chi_{51714}(43,\cdot)$	51714.me	312	no	$1$	$1$	$e\left(\frac{311}{312}\right)$	$e\left(\frac{75}{104}\right)$	$e\left(\frac{29}{312}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{179}{312}\right)$	$e\left(\frac{275}{312}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{67}{312}\right)$
$\chi_{51714}(47,\cdot)$	51714.kw	156	no	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{20}{39}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{51714}(49,\cdot)$	51714.me	312	no	$1$	$1$	$e\left(\frac{277}{312}\right)$	$e\left(\frac{25}{104}\right)$	$e\left(\frac{79}{312}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{25}{312}\right)$	$e\left(\frac{265}{312}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{161}{312}\right)$
$\chi_{51714}(53,\cdot)$	51714.jc	104	no	$-1$	$1$	$e\left(\frac{83}{104}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{89}{104}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{67}{104}\right)$	$e\left(\frac{3}{104}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{3}{104}\right)$
$\chi_{51714}(55,\cdot)$	51714.kr	156	no	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{25}{156}\right)$
$\chi_{51714}(59,\cdot)$	51714.lo	312	no	$1$	$1$	$e\left(\frac{97}{312}\right)$	$e\left(\frac{67}{312}\right)$	$e\left(\frac{33}{104}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{97}{104}\right)$	$e\left(\frac{1}{312}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{157}{312}\right)$
$\chi_{51714}(61,\cdot)$	51714.no	624	no	$-1$	$1$	$e\left(\frac{217}{624}\right)$	$e\left(\frac{157}{208}\right)$	$e\left(\frac{259}{624}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{217}{312}\right)$	$e\left(\frac{1}{624}\right)$	$e\left(\frac{541}{624}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{437}{624}\right)$
$\chi_{51714}(67,\cdot)$	51714.kl	156	no	$-1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{49}{156}\right)$
$\chi_{51714}(71,\cdot)$	51714.mu	624	no	$-1$	$1$	$e\left(\frac{149}{208}\right)$	$e\left(\frac{409}{624}\right)$	$e\left(\frac{245}{624}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{45}{104}\right)$	$e\left(\frac{275}{624}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{419}{624}\right)$
$\chi_{51714}(73,\cdot)$	51714.lc	208	no	$1$	$1$	$e\left(\frac{105}{208}\right)$	$e\left(\frac{87}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{104}\right)$	$e\left(\frac{29}{208}\right)$	$e\left(\frac{141}{208}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{141}{208}\right)$
$\chi_{51714}(77,\cdot)$	51714.mg	312	no	$-1$	$1$	$e\left(\frac{283}{312}\right)$	$e\left(\frac{233}{312}\right)$	$e\left(\frac{113}{312}\right)$	$i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{95}{312}\right)$	$e\left(\frac{19}{312}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{104}\right)$
$\chi_{51714}(79,\cdot)$	51714.mr	624	no	$-1$	$1$	$e\left(\frac{565}{624}\right)$	$e\left(\frac{587}{624}\right)$	$e\left(\frac{359}{624}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{253}{312}\right)$	$e\left(\frac{317}{624}\right)$	$e\left(\frac{313}{624}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{139}{208}\right)$
$\chi_{51714}(83,\cdot)$	51714.mp	312	no	$1$	$1$	$e\left(\frac{95}{312}\right)$	$e\left(\frac{205}{312}\right)$	$e\left(\frac{157}{312}\right)$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{181}{312}\right)$	$e\left(\frac{239}{312}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{97}{104}\right)$
$\chi_{51714}(89,\cdot)$	51714.ci	12	no	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{51714}(95,\cdot)$	51714.na	624	no	$1$	$1$	$e\left(\frac{233}{624}\right)$	$e\left(\frac{95}{624}\right)$	$e\left(\frac{1}{208}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{233}{312}\right)$	$e\left(\frac{51}{208}\right)$	$e\left(\frac{197}{624}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{509}{624}\right)$
$\chi_{51714}(97,\cdot)$	51714.ni	624	no	$1$	$1$	$e\left(\frac{235}{624}\right)$	$e\left(\frac{55}{208}\right)$	$e\left(\frac{361}{624}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{235}{312}\right)$	$e\left(\frac{367}{624}\right)$	$e\left(\frac{583}{624}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{167}{624}\right)$
$\chi_{51714}(101,\cdot)$	51714.ii	78	no	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{51714}(103,\cdot)$	51714.ib	78	no	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{29}{78}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{51714}(107,\cdot)$	51714.mz	624	no	$1$	$1$	$e\left(\frac{173}{208}\right)$	$e\left(\frac{17}{624}\right)$	$e\left(\frac{445}{624}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{69}{104}\right)$	$e\left(\frac{127}{624}\right)$	$e\left(\frac{57}{208}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{67}{624}\right)$
$\chi_{51714}(109,\cdot)$	51714.lc	208	no	$1$	$1$	$e\left(\frac{151}{208}\right)$	$e\left(\frac{137}{208}\right)$	$e\left(\frac{93}{208}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{47}{104}\right)$	$e\left(\frac{115}{208}\right)$	$e\left(\frac{179}{208}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{179}{208}\right)$

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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	$51714$
Structure	\(C_{2}\times C_{12}\times C_{624}\)
Order	$14976$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)	\(37\)
\(\chi_{51714}(1,\cdot)\)	51714.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{51714}(5,\cdot)\)	51714.nv	624	no	\(-1\)	\(1\)	\(e\left(\frac{155}{624}\right)\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{431}{624}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{208}\right)\)
\(\chi_{51714}(7,\cdot)\)	51714.ni	624	no	\(1\)	\(1\)	\(e\left(\frac{589}{624}\right)\)	\(e\left(\frac{129}{208}\right)\)	\(e\left(\frac{79}{624}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{25}{624}\right)\)	\(e\left(\frac{577}{624}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{161}{624}\right)\)
\(\chi_{51714}(11,\cdot)\)	51714.ne	624	no	\(-1\)	\(1\)	\(e\left(\frac{601}{624}\right)\)	\(e\left(\frac{79}{624}\right)\)	\(e\left(\frac{49}{208}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{289}{312}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{85}{624}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{85}{624}\right)\)
\(\chi_{51714}(19,\cdot)\)	51714.eq	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{51714}(23,\cdot)\)	51714.hc	48	no	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{51714}(25,\cdot)\)	51714.lt	312	no	\(1\)	\(1\)	\(e\left(\frac{155}{312}\right)\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{289}{312}\right)\)	\(i\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{119}{312}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{104}\right)\)
\(\chi_{51714}(29,\cdot)\)	51714.my	624	no	\(1\)	\(1\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{25}{624}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{127}{312}\right)\)	\(e\left(\frac{205}{208}\right)\)	\(e\left(\frac{19}{624}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{331}{624}\right)\)
\(\chi_{51714}(31,\cdot)\)	51714.mq	624	no	\(1\)	\(1\)	\(e\left(\frac{431}{624}\right)\)	\(e\left(\frac{577}{624}\right)\)	\(e\left(\frac{85}{624}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{119}{312}\right)\)	\(e\left(\frac{19}{624}\right)\)	\(e\left(\frac{347}{624}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{185}{208}\right)\)
\(\chi_{51714}(35,\cdot)\)	51714.iw	78	no	\(-1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{51714}(37,\cdot)\)	51714.ng	624	no	\(1\)	\(1\)	\(e\left(\frac{5}{208}\right)\)	\(e\left(\frac{161}{624}\right)\)	\(e\left(\frac{85}{624}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{104}\right)\)	\(e\left(\frac{331}{624}\right)\)	\(e\left(\frac{185}{208}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{139}{624}\right)\)
\(\chi_{51714}(41,\cdot)\)	51714.mv	624	no	\(-1\)	\(1\)	\(e\left(\frac{317}{624}\right)\)	\(e\left(\frac{41}{208}\right)\)	\(e\left(\frac{479}{624}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{312}\right)\)	\(e\left(\frac{353}{624}\right)\)	\(e\left(\frac{185}{624}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{601}{624}\right)\)
\(\chi_{51714}(43,\cdot)\)	51714.me	312	no	\(1\)	\(1\)	\(e\left(\frac{311}{312}\right)\)	\(e\left(\frac{75}{104}\right)\)	\(e\left(\frac{29}{312}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{179}{312}\right)\)	\(e\left(\frac{275}{312}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{67}{312}\right)\)
\(\chi_{51714}(47,\cdot)\)	51714.kw	156	no	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{51714}(49,\cdot)\)	51714.me	312	no	\(1\)	\(1\)	\(e\left(\frac{277}{312}\right)\)	\(e\left(\frac{25}{104}\right)\)	\(e\left(\frac{79}{312}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{25}{312}\right)\)	\(e\left(\frac{265}{312}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{161}{312}\right)\)
\(\chi_{51714}(53,\cdot)\)	51714.jc	104	no	\(-1\)	\(1\)	\(e\left(\frac{83}{104}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{89}{104}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{67}{104}\right)\)	\(e\left(\frac{3}{104}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{3}{104}\right)\)
\(\chi_{51714}(55,\cdot)\)	51714.kr	156	no	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{25}{156}\right)\)
\(\chi_{51714}(59,\cdot)\)	51714.lo	312	no	\(1\)	\(1\)	\(e\left(\frac{97}{312}\right)\)	\(e\left(\frac{67}{312}\right)\)	\(e\left(\frac{33}{104}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{97}{104}\right)\)	\(e\left(\frac{1}{312}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{157}{312}\right)\)
\(\chi_{51714}(61,\cdot)\)	51714.no	624	no	\(-1\)	\(1\)	\(e\left(\frac{217}{624}\right)\)	\(e\left(\frac{157}{208}\right)\)	\(e\left(\frac{259}{624}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{217}{312}\right)\)	\(e\left(\frac{1}{624}\right)\)	\(e\left(\frac{541}{624}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{437}{624}\right)\)
\(\chi_{51714}(67,\cdot)\)	51714.kl	156	no	\(-1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{49}{156}\right)\)
\(\chi_{51714}(71,\cdot)\)	51714.mu	624	no	\(-1\)	\(1\)	\(e\left(\frac{149}{208}\right)\)	\(e\left(\frac{409}{624}\right)\)	\(e\left(\frac{245}{624}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{45}{104}\right)\)	\(e\left(\frac{275}{624}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{419}{624}\right)\)
\(\chi_{51714}(73,\cdot)\)	51714.lc	208	no	\(1\)	\(1\)	\(e\left(\frac{105}{208}\right)\)	\(e\left(\frac{87}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{104}\right)\)	\(e\left(\frac{29}{208}\right)\)	\(e\left(\frac{141}{208}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{141}{208}\right)\)
\(\chi_{51714}(77,\cdot)\)	51714.mg	312	no	\(-1\)	\(1\)	\(e\left(\frac{283}{312}\right)\)	\(e\left(\frac{233}{312}\right)\)	\(e\left(\frac{113}{312}\right)\)	\(i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{95}{312}\right)\)	\(e\left(\frac{19}{312}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{104}\right)\)
\(\chi_{51714}(79,\cdot)\)	51714.mr	624	no	\(-1\)	\(1\)	\(e\left(\frac{565}{624}\right)\)	\(e\left(\frac{587}{624}\right)\)	\(e\left(\frac{359}{624}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{253}{312}\right)\)	\(e\left(\frac{317}{624}\right)\)	\(e\left(\frac{313}{624}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{139}{208}\right)\)
\(\chi_{51714}(83,\cdot)\)	51714.mp	312	no	\(1\)	\(1\)	\(e\left(\frac{95}{312}\right)\)	\(e\left(\frac{205}{312}\right)\)	\(e\left(\frac{157}{312}\right)\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{181}{312}\right)\)	\(e\left(\frac{239}{312}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{97}{104}\right)\)
\(\chi_{51714}(89,\cdot)\)	51714.ci	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{51714}(95,\cdot)\)	51714.na	624	no	\(1\)	\(1\)	\(e\left(\frac{233}{624}\right)\)	\(e\left(\frac{95}{624}\right)\)	\(e\left(\frac{1}{208}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{233}{312}\right)\)	\(e\left(\frac{51}{208}\right)\)	\(e\left(\frac{197}{624}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{509}{624}\right)\)
\(\chi_{51714}(97,\cdot)\)	51714.ni	624	no	\(1\)	\(1\)	\(e\left(\frac{235}{624}\right)\)	\(e\left(\frac{55}{208}\right)\)	\(e\left(\frac{361}{624}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{235}{312}\right)\)	\(e\left(\frac{367}{624}\right)\)	\(e\left(\frac{583}{624}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{167}{624}\right)\)
\(\chi_{51714}(101,\cdot)\)	51714.ii	78	no	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{51714}(103,\cdot)\)	51714.ib	78	no	\(1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{51714}(107,\cdot)\)	51714.mz	624	no	\(1\)	\(1\)	\(e\left(\frac{173}{208}\right)\)	\(e\left(\frac{17}{624}\right)\)	\(e\left(\frac{445}{624}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{69}{104}\right)\)	\(e\left(\frac{127}{624}\right)\)	\(e\left(\frac{57}{208}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{67}{624}\right)\)
\(\chi_{51714}(109,\cdot)\)	51714.lc	208	no	\(1\)	\(1\)	\(e\left(\frac{151}{208}\right)\)	\(e\left(\frac{137}{208}\right)\)	\(e\left(\frac{93}{208}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{47}{104}\right)\)	\(e\left(\frac{115}{208}\right)\)	\(e\left(\frac{179}{208}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{179}{208}\right)\)

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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.