LMFDB - Group of Dirichlet characters of modulus 310464

Show commands: PariGP / SageMath

sage: H = DirichletGroup(310464)

pari: g = idealstar(,310464,2)

Character group

sage: G.order() pari: g.no
Order	=	80640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{1680}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{310464}(48511,\cdot)$, $\chi_{310464}(213445,\cdot)$, $\chi_{310464}(275969,\cdot)$, $\chi_{310464}(145729,\cdot)$, $\chi_{310464}(141121,\cdot)$

First 32 of 80640 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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{310464}(1,\cdot)$	310464.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{310464}(5,\cdot)$	310464.chj	1680	yes	$1$	$1$	$e\left(\frac{1433}{1680}\right)$	$e\left(\frac{1327}{1680}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{593}{840}\right)$	$e\left(\frac{1259}{1680}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{769}{1680}\right)$	$e\left(\frac{503}{840}\right)$
$\chi_{310464}(13,\cdot)$	310464.cil	1680	yes	$1$	$1$	$e\left(\frac{1327}{1680}\right)$	$e\left(\frac{1273}{1680}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{487}{840}\right)$	$e\left(\frac{821}{1680}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{437}{560}\right)$	$e\left(\frac{737}{840}\right)$
$\chi_{310464}(17,\cdot)$	310464.cdi	420	no	$-1$	$1$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{310464}(19,\cdot)$	310464.bwu	240	no	$-1$	$1$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{310464}(23,\cdot)$	310464.bqd	168	no	$1$	$1$	$e\left(\frac{47}{168}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{125}{168}\right)$	$-1$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{310464}(25,\cdot)$	310464.cfw	840	no	$1$	$1$	$e\left(\frac{593}{840}\right)$	$e\left(\frac{487}{840}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{419}{840}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{83}{420}\right)$
$\chi_{310464}(29,\cdot)$	310464.cid	1680	yes	$1$	$1$	$e\left(\frac{1259}{1680}\right)$	$e\left(\frac{821}{1680}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{419}{840}\right)$	$e\left(\frac{577}{1680}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{560}\right)$	$e\left(\frac{829}{840}\right)$
$\chi_{310464}(31,\cdot)$	310464.rg	30	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{310464}(37,\cdot)$	310464.cih	1680	no	$1$	$1$	$e\left(\frac{769}{1680}\right)$	$e\left(\frac{437}{560}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{769}{840}\right)$	$e\left(\frac{169}{560}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1417}{1680}\right)$	$e\left(\frac{253}{280}\right)$
$\chi_{310464}(41,\cdot)$	310464.cgx	840	no	$-1$	$1$	$e\left(\frac{503}{840}\right)$	$e\left(\frac{737}{840}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{83}{420}\right)$	$e\left(\frac{829}{840}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{253}{280}\right)$	$e\left(\frac{283}{420}\right)$
$\chi_{310464}(43,\cdot)$	310464.bzn	336	yes	$1$	$1$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{59}{168}\right)$
$\chi_{310464}(47,\cdot)$	310464.cct	420	no	$-1$	$1$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{109}{210}\right)$
$\chi_{310464}(53,\cdot)$	310464.chp	1680	no	$-1$	$1$	$e\left(\frac{197}{1680}\right)$	$e\left(\frac{81}{560}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{197}{840}\right)$	$e\left(\frac{237}{560}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1061}{1680}\right)$	$e\left(\frac{69}{280}\right)$
$\chi_{310464}(59,\cdot)$	310464.cht	1680	yes	$-1$	$1$	$e\left(\frac{3}{560}\right)$	$e\left(\frac{31}{1680}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{3}{280}\right)$	$e\left(\frac{827}{1680}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1457}{1680}\right)$	$e\left(\frac{239}{840}\right)$
$\chi_{310464}(61,\cdot)$	310464.cik	1680	yes	$1$	$1$	$e\left(\frac{401}{560}\right)$	$e\left(\frac{1157}{1680}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{121}{280}\right)$	$e\left(\frac{1249}{1680}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1459}{1680}\right)$	$e\left(\frac{493}{840}\right)$
$\chi_{310464}(65,\cdot)$	310464.bau	42	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{310464}(67,\cdot)$	310464.bbo	48	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{310464}(71,\cdot)$	310464.byz	280	no	$1$	$1$	$e\left(\frac{83}{280}\right)$	$e\left(\frac{177}{280}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{129}{280}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{199}{280}\right)$	$e\left(\frac{3}{140}\right)$
$\chi_{310464}(73,\cdot)$	310464.cgb	840	no	$1$	$1$	$e\left(\frac{607}{840}\right)$	$e\left(\frac{111}{280}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{247}{280}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{811}{840}\right)$	$e\left(\frac{79}{140}\right)$
$\chi_{310464}(79,\cdot)$	310464.bfh	60	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{60}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{310464}(83,\cdot)$	310464.cia	1680	yes	$1$	$1$	$e\left(\frac{143}{1680}\right)$	$e\left(\frac{1457}{1680}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{143}{840}\right)$	$e\left(\frac{229}{1680}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{333}{560}\right)$	$e\left(\frac{733}{840}\right)$
$\chi_{310464}(85,\cdot)$	310464.chk	1680	yes	$-1$	$1$	$e\left(\frac{1621}{1680}\right)$	$e\left(\frac{979}{1680}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{151}{168}\right)$	$e\left(\frac{781}{840}\right)$	$e\left(\frac{863}{1680}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{560}\right)$	$e\left(\frac{191}{840}\right)$
$\chi_{310464}(89,\cdot)$	310464.bpo	168	no	$1$	$1$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{310464}(95,\cdot)$	310464.bvl	210	no	$-1$	$1$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{310464}(97,\cdot)$	310464.uq	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{310464}(101,\cdot)$	310464.chc	1680	yes	$-1$	$1$	$e\left(\frac{817}{1680}\right)$	$e\left(\frac{1103}{1680}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{817}{840}\right)$	$e\left(\frac{811}{1680}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{1680}\right)$	$e\left(\frac{307}{840}\right)$
$\chi_{310464}(103,\cdot)$	310464.cey	840	no	$1$	$1$	$e\left(\frac{517}{840}\right)$	$e\left(\frac{443}{840}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{451}{840}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{521}{840}\right)$	$e\left(\frac{157}{420}\right)$
$\chi_{310464}(107,\cdot)$	310464.ciz	1680	no	$-1$	$1$	$e\left(\frac{1501}{1680}\right)$	$e\left(\frac{33}{560}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{661}{840}\right)$	$e\left(\frac{221}{560}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{733}{1680}\right)$	$e\left(\frac{137}{280}\right)$
$\chi_{310464}(109,\cdot)$	310464.cap	336	no	$-1$	$1$	$e\left(\frac{19}{336}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{51}{56}\right)$
$\chi_{310464}(113,\cdot)$	310464.cbv	420	no	$-1$	$1$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{82}{105}\right)$
$\chi_{310464}(115,\cdot)$	310464.cji	1680	yes	$1$	$1$	$e\left(\frac{223}{1680}\right)$	$e\left(\frac{737}{1680}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{223}{840}\right)$	$e\left(\frac{829}{1680}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{479}{1680}\right)$	$e\left(\frac{493}{840}\right)$

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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	$310464$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{1680}\)
Order	$80640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{310464}(1,\cdot)\)	310464.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{310464}(5,\cdot)\)	310464.chj	1680	yes	\(1\)	\(1\)	\(e\left(\frac{1433}{1680}\right)\)	\(e\left(\frac{1327}{1680}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{593}{840}\right)\)	\(e\left(\frac{1259}{1680}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{769}{1680}\right)\)	\(e\left(\frac{503}{840}\right)\)
\(\chi_{310464}(13,\cdot)\)	310464.cil	1680	yes	\(1\)	\(1\)	\(e\left(\frac{1327}{1680}\right)\)	\(e\left(\frac{1273}{1680}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{487}{840}\right)\)	\(e\left(\frac{821}{1680}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{437}{560}\right)\)	\(e\left(\frac{737}{840}\right)\)
\(\chi_{310464}(17,\cdot)\)	310464.cdi	420	no	\(-1\)	\(1\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{310464}(19,\cdot)\)	310464.bwu	240	no	\(-1\)	\(1\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{310464}(23,\cdot)\)	310464.bqd	168	no	\(1\)	\(1\)	\(e\left(\frac{47}{168}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(-1\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{310464}(25,\cdot)\)	310464.cfw	840	no	\(1\)	\(1\)	\(e\left(\frac{593}{840}\right)\)	\(e\left(\frac{487}{840}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{419}{840}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{83}{420}\right)\)
\(\chi_{310464}(29,\cdot)\)	310464.cid	1680	yes	\(1\)	\(1\)	\(e\left(\frac{1259}{1680}\right)\)	\(e\left(\frac{821}{1680}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{419}{840}\right)\)	\(e\left(\frac{577}{1680}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{560}\right)\)	\(e\left(\frac{829}{840}\right)\)
\(\chi_{310464}(31,\cdot)\)	310464.rg	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{310464}(37,\cdot)\)	310464.cih	1680	no	\(1\)	\(1\)	\(e\left(\frac{769}{1680}\right)\)	\(e\left(\frac{437}{560}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{769}{840}\right)\)	\(e\left(\frac{169}{560}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1417}{1680}\right)\)	\(e\left(\frac{253}{280}\right)\)
\(\chi_{310464}(41,\cdot)\)	310464.cgx	840	no	\(-1\)	\(1\)	\(e\left(\frac{503}{840}\right)\)	\(e\left(\frac{737}{840}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{83}{420}\right)\)	\(e\left(\frac{829}{840}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{253}{280}\right)\)	\(e\left(\frac{283}{420}\right)\)
\(\chi_{310464}(43,\cdot)\)	310464.bzn	336	yes	\(1\)	\(1\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{59}{168}\right)\)
\(\chi_{310464}(47,\cdot)\)	310464.cct	420	no	\(-1\)	\(1\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)
\(\chi_{310464}(53,\cdot)\)	310464.chp	1680	no	\(-1\)	\(1\)	\(e\left(\frac{197}{1680}\right)\)	\(e\left(\frac{81}{560}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{197}{840}\right)\)	\(e\left(\frac{237}{560}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1061}{1680}\right)\)	\(e\left(\frac{69}{280}\right)\)
\(\chi_{310464}(59,\cdot)\)	310464.cht	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{560}\right)\)	\(e\left(\frac{31}{1680}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{3}{280}\right)\)	\(e\left(\frac{827}{1680}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1457}{1680}\right)\)	\(e\left(\frac{239}{840}\right)\)
\(\chi_{310464}(61,\cdot)\)	310464.cik	1680	yes	\(1\)	\(1\)	\(e\left(\frac{401}{560}\right)\)	\(e\left(\frac{1157}{1680}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{121}{280}\right)\)	\(e\left(\frac{1249}{1680}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1459}{1680}\right)\)	\(e\left(\frac{493}{840}\right)\)
\(\chi_{310464}(65,\cdot)\)	310464.bau	42	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{310464}(67,\cdot)\)	310464.bbo	48	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{310464}(71,\cdot)\)	310464.byz	280	no	\(1\)	\(1\)	\(e\left(\frac{83}{280}\right)\)	\(e\left(\frac{177}{280}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{129}{280}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{199}{280}\right)\)	\(e\left(\frac{3}{140}\right)\)
\(\chi_{310464}(73,\cdot)\)	310464.cgb	840	no	\(1\)	\(1\)	\(e\left(\frac{607}{840}\right)\)	\(e\left(\frac{111}{280}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{247}{280}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{811}{840}\right)\)	\(e\left(\frac{79}{140}\right)\)
\(\chi_{310464}(79,\cdot)\)	310464.bfh	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{310464}(83,\cdot)\)	310464.cia	1680	yes	\(1\)	\(1\)	\(e\left(\frac{143}{1680}\right)\)	\(e\left(\frac{1457}{1680}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{143}{840}\right)\)	\(e\left(\frac{229}{1680}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{333}{560}\right)\)	\(e\left(\frac{733}{840}\right)\)
\(\chi_{310464}(85,\cdot)\)	310464.chk	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{1621}{1680}\right)\)	\(e\left(\frac{979}{1680}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{151}{168}\right)\)	\(e\left(\frac{781}{840}\right)\)	\(e\left(\frac{863}{1680}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{560}\right)\)	\(e\left(\frac{191}{840}\right)\)
\(\chi_{310464}(89,\cdot)\)	310464.bpo	168	no	\(1\)	\(1\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{310464}(95,\cdot)\)	310464.bvl	210	no	\(-1\)	\(1\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{310464}(97,\cdot)\)	310464.uq	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{310464}(101,\cdot)\)	310464.chc	1680	yes	\(-1\)	\(1\)	\(e\left(\frac{817}{1680}\right)\)	\(e\left(\frac{1103}{1680}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{817}{840}\right)\)	\(e\left(\frac{811}{1680}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{1680}\right)\)	\(e\left(\frac{307}{840}\right)\)
\(\chi_{310464}(103,\cdot)\)	310464.cey	840	no	\(1\)	\(1\)	\(e\left(\frac{517}{840}\right)\)	\(e\left(\frac{443}{840}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{451}{840}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{521}{840}\right)\)	\(e\left(\frac{157}{420}\right)\)
\(\chi_{310464}(107,\cdot)\)	310464.ciz	1680	no	\(-1\)	\(1\)	\(e\left(\frac{1501}{1680}\right)\)	\(e\left(\frac{33}{560}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{661}{840}\right)\)	\(e\left(\frac{221}{560}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{733}{1680}\right)\)	\(e\left(\frac{137}{280}\right)\)
\(\chi_{310464}(109,\cdot)\)	310464.cap	336	no	\(-1\)	\(1\)	\(e\left(\frac{19}{336}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{51}{56}\right)\)
\(\chi_{310464}(113,\cdot)\)	310464.cbv	420	no	\(-1\)	\(1\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{82}{105}\right)\)
\(\chi_{310464}(115,\cdot)\)	310464.cji	1680	yes	\(1\)	\(1\)	\(e\left(\frac{223}{1680}\right)\)	\(e\left(\frac{737}{1680}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{223}{840}\right)\)	\(e\left(\frac{829}{1680}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{479}{1680}\right)\)	\(e\left(\frac{493}{840}\right)\)

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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.