LMFDB - Group of Dirichlet characters of modulus 31360

sage:H = DirichletGroup(31360)

pari:g = idealstar(,31360,2)

Character group

sage:G.order() pari:g.no
Order	=	10752
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{672}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{31360}(17151,\cdot)$, $\chi_{31360}(28421,\cdot)$, $\chi_{31360}(18817,\cdot)$, $\chi_{31360}(10881,\cdot)$

First 32 of 10752 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{31360}(1,\cdot)$	31360.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{31360}(3,\cdot)$	31360.nl	672	yes	$-1$	$1$	$e\left(\frac{37}{672}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{283}{672}\right)$	$e\left(\frac{99}{224}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{37}{224}\right)$	$e\left(\frac{103}{224}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{31360}(9,\cdot)$	31360.ms	336	no	$1$	$1$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{31360}(11,\cdot)$	31360.nh	672	no	$-1$	$1$	$e\left(\frac{283}{672}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{253}{672}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{31360}(13,\cdot)$	31360.lv	224	yes	$1$	$1$	$e\left(\frac{99}{224}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{61}{224}\right)$	$e\left(\frac{47}{224}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{73}{224}\right)$	$e\left(\frac{67}{224}\right)$	$i$
$\chi_{31360}(17,\cdot)$	31360.lm	168	no	$1$	$1$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{31360}(19,\cdot)$	31360.kg	96	no	$1$	$1$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{31360}(23,\cdot)$	31360.mu	336	no	$1$	$1$	$e\left(\frac{325}{336}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{295}{336}\right)$	$e\left(\frac{75}{112}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{31360}(27,\cdot)$	31360.lu	224	yes	$-1$	$1$	$e\left(\frac{37}{224}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{73}{224}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{111}{224}\right)$	$e\left(\frac{85}{224}\right)$	$i$
$\chi_{31360}(29,\cdot)$	31360.md	224	yes	$1$	$1$	$e\left(\frac{103}{224}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{67}{112}\right)$	$e\left(\frac{85}{224}\right)$	$e\left(\frac{111}{224}\right)$	$-i$
$\chi_{31360}(31,\cdot)$	31360.dh	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-i$	$e\left(\frac{2}{3}\right)$
$\chi_{31360}(33,\cdot)$	31360.jt	84	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{31360}(37,\cdot)$	31360.na	672	yes	$-1$	$1$	$e\left(\frac{575}{672}\right)$	$e\left(\frac{239}{336}\right)$	$e\left(\frac{593}{672}\right)$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{215}{336}\right)$	$e\left(\frac{127}{224}\right)$	$e\left(\frac{69}{224}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31360}(39,\cdot)$	31360.mo	336	no	$-1$	$1$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{31360}(41,\cdot)$	31360.ku	112	no	$-1$	$1$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{95}{112}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{83}{112}\right)$	$1$
$\chi_{31360}(43,\cdot)$	31360.ls	224	yes	$1$	$1$	$e\left(\frac{137}{224}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{55}{224}\right)$	$e\left(\frac{125}{224}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{97}{112}\right)$	$e\left(\frac{187}{224}\right)$	$e\left(\frac{121}{224}\right)$	$-i$
$\chi_{31360}(47,\cdot)$	31360.lg	168	no	$-1$	$1$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{31360}(51,\cdot)$	31360.nh	672	no	$-1$	$1$	$e\left(\frac{17}{672}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{407}{672}\right)$	$e\left(\frac{215}{224}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{17}{224}\right)$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31360}(53,\cdot)$	31360.nm	672	yes	$-1$	$1$	$e\left(\frac{643}{672}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{541}{672}\right)$	$e\left(\frac{101}{224}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{163}{336}\right)$	$e\left(\frac{195}{224}\right)$	$e\left(\frac{1}{224}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31360}(57,\cdot)$	31360.km	112	no	$-1$	$1$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{97}{112}\right)$	$-1$
$\chi_{31360}(59,\cdot)$	31360.nf	672	yes	$1$	$1$	$e\left(\frac{607}{672}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{25}{672}\right)$	$e\left(\frac{153}{224}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{67}{336}\right)$	$e\left(\frac{159}{224}\right)$	$e\left(\frac{205}{224}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31360}(61,\cdot)$	31360.ne	672	no	$-1$	$1$	$e\left(\frac{29}{672}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{635}{672}\right)$	$e\left(\frac{123}{224}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{89}{336}\right)$	$e\left(\frac{29}{224}\right)$	$e\left(\frac{167}{224}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{31360}(67,\cdot)$	31360.jy	96	no	$1$	$1$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{31360}(69,\cdot)$	31360.mb	224	yes	$-1$	$1$	$e\left(\frac{5}{224}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{67}{224}\right)$	$e\left(\frac{25}{224}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{25}{112}\right)$	$e\left(\frac{15}{224}\right)$	$e\left(\frac{13}{224}\right)$	$-i$
$\chi_{31360}(71,\cdot)$	31360.kx	112	no	$-1$	$1$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{25}{112}\right)$	$1$
$\chi_{31360}(73,\cdot)$	31360.mi	336	no	$1$	$1$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{227}{336}\right)$	$e\left(\frac{71}{112}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{31360}(79,\cdot)$	31360.fc	24	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{31360}(81,\cdot)$	31360.lc	168	no	$1$	$1$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{31360}(83,\cdot)$	31360.lu	224	yes	$-1$	$1$	$e\left(\frac{139}{224}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{149}{224}\right)$	$e\left(\frac{135}{224}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{193}{224}\right)$	$e\left(\frac{59}{224}\right)$	$-i$
$\chi_{31360}(87,\cdot)$	31360.mw	336	no	$-1$	$1$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{5}{168}\right)$	$e\left(\frac{95}{336}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{95}{168}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{31360}(89,\cdot)$	31360.mn	336	no	$-1$	$1$	$e\left(\frac{247}{336}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{241}{336}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{23}{112}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{31360}(93,\cdot)$	31360.na	672	yes	$-1$	$1$	$e\left(\frac{317}{672}\right)$	$e\left(\frac{317}{336}\right)$	$e\left(\frac{563}{672}\right)$	$e\left(\frac{155}{224}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{93}{224}\right)$	$e\left(\frac{47}{224}\right)$	$e\left(\frac{1}{12}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$31360$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{672}\)
Order	$10752$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{31360}(1,\cdot)\)	31360.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{31360}(3,\cdot)\)	31360.nl	672	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{672}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{283}{672}\right)\)	\(e\left(\frac{99}{224}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{37}{224}\right)\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{31360}(9,\cdot)\)	31360.ms	336	no	\(1\)	\(1\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{31360}(11,\cdot)\)	31360.nh	672	no	\(-1\)	\(1\)	\(e\left(\frac{283}{672}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{253}{672}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{31360}(13,\cdot)\)	31360.lv	224	yes	\(1\)	\(1\)	\(e\left(\frac{99}{224}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{61}{224}\right)\)	\(e\left(\frac{47}{224}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{73}{224}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(i\)
\(\chi_{31360}(17,\cdot)\)	31360.lm	168	no	\(1\)	\(1\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{31360}(19,\cdot)\)	31360.kg	96	no	\(1\)	\(1\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{31360}(23,\cdot)\)	31360.mu	336	no	\(1\)	\(1\)	\(e\left(\frac{325}{336}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{295}{336}\right)\)	\(e\left(\frac{75}{112}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{31360}(27,\cdot)\)	31360.lu	224	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{224}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{73}{224}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(e\left(\frac{85}{224}\right)\)	\(i\)
\(\chi_{31360}(29,\cdot)\)	31360.md	224	yes	\(1\)	\(1\)	\(e\left(\frac{103}{224}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{67}{112}\right)\)	\(e\left(\frac{85}{224}\right)\)	\(e\left(\frac{111}{224}\right)\)	\(-i\)
\(\chi_{31360}(31,\cdot)\)	31360.dh	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{31360}(33,\cdot)\)	31360.jt	84	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{31360}(37,\cdot)\)	31360.na	672	yes	\(-1\)	\(1\)	\(e\left(\frac{575}{672}\right)\)	\(e\left(\frac{239}{336}\right)\)	\(e\left(\frac{593}{672}\right)\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{215}{336}\right)\)	\(e\left(\frac{127}{224}\right)\)	\(e\left(\frac{69}{224}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31360}(39,\cdot)\)	31360.mo	336	no	\(-1\)	\(1\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{31360}(41,\cdot)\)	31360.ku	112	no	\(-1\)	\(1\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{95}{112}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(1\)
\(\chi_{31360}(43,\cdot)\)	31360.ls	224	yes	\(1\)	\(1\)	\(e\left(\frac{137}{224}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{55}{224}\right)\)	\(e\left(\frac{125}{224}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(e\left(\frac{187}{224}\right)\)	\(e\left(\frac{121}{224}\right)\)	\(-i\)
\(\chi_{31360}(47,\cdot)\)	31360.lg	168	no	\(-1\)	\(1\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{31360}(51,\cdot)\)	31360.nh	672	no	\(-1\)	\(1\)	\(e\left(\frac{17}{672}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{407}{672}\right)\)	\(e\left(\frac{215}{224}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{17}{224}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31360}(53,\cdot)\)	31360.nm	672	yes	\(-1\)	\(1\)	\(e\left(\frac{643}{672}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{541}{672}\right)\)	\(e\left(\frac{101}{224}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{163}{336}\right)\)	\(e\left(\frac{195}{224}\right)\)	\(e\left(\frac{1}{224}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31360}(57,\cdot)\)	31360.km	112	no	\(-1\)	\(1\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{97}{112}\right)\)	\(-1\)
\(\chi_{31360}(59,\cdot)\)	31360.nf	672	yes	\(1\)	\(1\)	\(e\left(\frac{607}{672}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{25}{672}\right)\)	\(e\left(\frac{153}{224}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{67}{336}\right)\)	\(e\left(\frac{159}{224}\right)\)	\(e\left(\frac{205}{224}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31360}(61,\cdot)\)	31360.ne	672	no	\(-1\)	\(1\)	\(e\left(\frac{29}{672}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{635}{672}\right)\)	\(e\left(\frac{123}{224}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{89}{336}\right)\)	\(e\left(\frac{29}{224}\right)\)	\(e\left(\frac{167}{224}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{31360}(67,\cdot)\)	31360.jy	96	no	\(1\)	\(1\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{31360}(69,\cdot)\)	31360.mb	224	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{224}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{67}{224}\right)\)	\(e\left(\frac{25}{224}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(e\left(\frac{15}{224}\right)\)	\(e\left(\frac{13}{224}\right)\)	\(-i\)
\(\chi_{31360}(71,\cdot)\)	31360.kx	112	no	\(-1\)	\(1\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)	\(1\)
\(\chi_{31360}(73,\cdot)\)	31360.mi	336	no	\(1\)	\(1\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{227}{336}\right)\)	\(e\left(\frac{71}{112}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{31360}(79,\cdot)\)	31360.fc	24	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{31360}(81,\cdot)\)	31360.lc	168	no	\(1\)	\(1\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{31360}(83,\cdot)\)	31360.lu	224	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{224}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{149}{224}\right)\)	\(e\left(\frac{135}{224}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{193}{224}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(-i\)
\(\chi_{31360}(87,\cdot)\)	31360.mw	336	no	\(-1\)	\(1\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{5}{168}\right)\)	\(e\left(\frac{95}{336}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{95}{168}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{31360}(89,\cdot)\)	31360.mn	336	no	\(-1\)	\(1\)	\(e\left(\frac{247}{336}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{241}{336}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{23}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{31360}(93,\cdot)\)	31360.na	672	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{672}\right)\)	\(e\left(\frac{317}{336}\right)\)	\(e\left(\frac{563}{672}\right)\)	\(e\left(\frac{155}{224}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{93}{224}\right)\)	\(e\left(\frac{47}{224}\right)\)	\(e\left(\frac{1}{12}\right)\)

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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.